Finite Group Databasebeta

← #2488×D71 #32166378

Subgroups — #2488×D71 #32166378

Order 18176.

3114 conjugacy classes of subgroups.

The subgroup lattice has 1696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D71C211yesmaximal, characteristic
2C2×C22⋊Q8×D71C211yesmaximal, characteristic, complemented
3#22592673C211yesmaximal, characteristic, complemented
4#22592672C211yesmaximal, characteristic, complemented
5#22592671C211yesmaximal, characteristic, complemented
6#22592670C211yesmaximal, characteristic, complemented
7#22592669C211yesmaximal, characteristic, complemented
8#22592668C211yesmaximal, characteristic, complemented
9#22592667C211yesmaximal, characteristic, complemented
10#22592666C211yesmaximal, characteristic, complemented
11#22592665C211yesmaximal, characteristic, complemented
12#22592664C211yesmaximal, characteristic, complemented
13#22592663C211yesmaximal, characteristic, complemented
14#22592662C211yesmaximal, characteristic, complemented
15#22592661C211yesmaximal, characteristic, complemented
16#22592660C211yesmaximal, characteristic, complemented
17#22592659C211yesmaximal, characteristic, complemented
18#400×D71C211yesmaximal, characteristic, complemented
19#400×D71C211yesmaximal, characteristic, complemented
20#397×D71C211yesmaximal, characteristic, complemented
21#393×D71C211yesmaximal, characteristic, complemented
22#391×D71C211yesmaximal, characteristic, complemented
23#388×D71C211yesmaximal, characteristic, complemented
24#388×D71C211yesmaximal, characteristic, complemented
25#386×D71C211yesmaximal, characteristic
26#386×D71C211yesmaximal, characteristic
27#382×D71C211yesmaximal, characteristic, complemented
28#381×D71C211yesmaximal, characteristic, complemented
29C4×C22⋊C4×D71C211yesmaximal, characteristic, complemented
30C2×#95×D71C211yesmaximal, characteristic, complemented
31C71×#2488C211yesmaximal, characteristic, complemented
32C22×Q8×D71C2211yescharacteristic
33C22×D4×D71C2211yescharacteristic
34C23×C4×D71C2211yescharacteristic
35C23×C4×D71C2211yescharacteristic
36C23×C4×D71C2211yescharacteristic
37C2×#14556113C2211yescharacteristic
38C2×#14556113C2211yescharacteristic
39C2×#14556112C2211yescharacteristic
40C2×#14556111C2211yescharacteristic
41C2×#14556110C2211yescharacteristic
42C2×#14556110C2211yescharacteristic
43C2×#14556109C2211yescharacteristic
44#123×D71—28no—
45C2×#14556108C2211yescharacteristic, complemented
46C2×#14556107C2211yescharacteristic, complemented
47C2×#14556106C2211yescharacteristic, complemented
48C2×#14556106C2211yescharacteristic, complemented
49C2×#14556105C2211yescharacteristic, complemented
50C2×#14556105C2211yescharacteristic, complemented
51C2×#14556104C2211yescharacteristic, complemented
52C22⋊Q8×D71—28no—
53C2×C4⋊C4×D71C2211yescharacteristic
54C2×C4⋊C4×D71C2211yescharacteristic
55C2×C4⋊C4×D71C2211yescharacteristic
56C2×C4⋊C4×D71C2211yescharacteristic
57C2×C4⋊C4×D71C2211yescharacteristic
58C2×C22⋊C4×D71C2211yescharacteristic
59C2×C22⋊C4×D71C2211yescharacteristic
60C2×C22⋊C4×D71C2211yescharacteristic
61C2×C22⋊C4×D71C2211yescharacteristic
62C2×C22⋊C4×D71C2211yescharacteristic
63C2×C22⋊C4×D71C2211yescharacteristic
64C2×C22⋊C4×D71C2211yescharacteristic
65C2×C22⋊C4×D71C2211yescharacteristic
66C2×C22⋊C4×D71C2211yescharacteristic
67C2×C42×D71C2211yescharacteristic
68C2×C42×D71C2211yescharacteristic
69#17985941C2211yescharacteristic, complemented
70#17985941C2211yescharacteristic, complemented
71#17985941C2211yescharacteristic, complemented
72#17985941C2211yescharacteristic, complemented
73#17985940C2211yescharacteristic, complemented
74#17985940C2211yescharacteristic, complemented
75#17985940C2211yescharacteristic, complemented
76#17985940C2211yescharacteristic, complemented
77#17985939C2211yescharacteristic, complemented
78#17985939C2211yescharacteristic, complemented
79#17985938C2211yescharacteristic, complemented
80#17985938C2211yescharacteristic, complemented
81#17985937C2211yescharacteristic, complemented
82#17985937C2211yescharacteristic, complemented
83#17985928C2211yescharacteristic, complemented
84#17985928C2211yescharacteristic, complemented
85#17985927C2211yescharacteristic, complemented
86#17985927C2211yescharacteristic, complemented
87#17985926C2211yescharacteristic, complemented
88#17985925C2211yescharacteristic, complemented
89#17985924C2211yescharacteristic, complemented
90#17985912C2211yescharacteristic, complemented
91#17985912C2211yescharacteristic, complemented
92#17985912C2211yescharacteristic, complemented
93#17985911C2211yescharacteristic, complemented
94#17985911C2211yescharacteristic, complemented
95#17985911C2211yescharacteristic, complemented
96#17985910C2211yescharacteristic, complemented
97#17985906C2211yescharacteristic, complemented
98#17985905C2211yescharacteristic, complemented
99#17985904C2211yescharacteristic, complemented
100#17985903C2211yescharacteristic, complemented
101#17985903C2211yescharacteristic, complemented
102#17985903C2211yescharacteristic, complemented
103#17985903C2211yescharacteristic, complemented
104#17985893C2211yescharacteristic, complemented
105#17985893C2211yescharacteristic, complemented
106#17985892C2211yescharacteristic, complemented
107#17985892C2211yescharacteristic, complemented
108#17985891C2211yescharacteristic, complemented
109#17985891C2211yescharacteristic, complemented
110#17985890C2211yescharacteristic, complemented
111#17985890C2211yescharacteristic, complemented
112#17985889C2211yescharacteristic, complemented
113#17985889C2211yescharacteristic, complemented
114#17985888C2211yescharacteristic, complemented
115#17985888C2211yescharacteristic, complemented
116#17985887C2211yescharacteristic, complemented
117#17985887C2211yescharacteristic, complemented
118#17985879C2211yescharacteristic
119#17985879C2211yescharacteristic
120#17985878C2211yescharacteristic
121#17985878C2211yescharacteristic
122#17985877C2211yescharacteristic
123#17985877C2211yescharacteristic
124#17985877C2211yescharacteristic
125#17985877C2211yescharacteristic
126#17985876C2211yescharacteristic
127#17985876C2211yescharacteristic
128#17985875C2211yescharacteristic
129#17985875C2211yescharacteristic
130#17985875C2211yescharacteristic
131#17985875C2211yescharacteristic
132#17985865C2211yescharacteristic, complemented
133#17985864C2211yescharacteristic, complemented
134#17985864C2211yescharacteristic, complemented
135#17985863C2211yescharacteristic, complemented
136#17985863C2211yescharacteristic, complemented
137#17985863C2211yescharacteristic, complemented
138#17985863C2211yescharacteristic, complemented
139#17985862C2211yescharacteristic, complemented
140#17985861C2211yescharacteristic, complemented
141#17985861C2211yescharacteristic, complemented
142#17985861C2211yescharacteristic, complemented
143#17985861C2211yescharacteristic, complemented
144#17985860C2211yescharacteristic, complemented
145#17985860C2211yescharacteristic, complemented
146C22⋊C4×Dic71C2211yescharacteristic, complemented
147C22⋊C4×Dic71C2211yescharacteristic, complemented
148C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
149C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
150C4×C22⋊Dic71C2211yescharacteristic, complemented
151#17985846C2211yescharacteristic, complemented
152#17985846C2211yescharacteristic, complemented
153C2×C71⋊#95C2211yescharacteristic, complemented
154C2×C71⋊#95C2211yescharacteristic, complemented
155C2×C71⋊#95C2211yescharacteristic, complemented
156#95×D71C2211yescharacteristic
157#95×D71C2211yescharacteristic
158#95×D71C2211yescharacteristic
159#95×D71C2211yescharacteristic
160#95×D71C2211yescharacteristic
161#95×D71C2211yescharacteristic
162#95×D71C2211yescharacteristic
163#95×D71C2211yescharacteristic
164#95×D71C2211yescharacteristic
165#95×D71C2211yescharacteristic
166#95×D71C2211yescharacteristic
167#95×D71C2211yescharacteristic
168#95×D71C2211yescharacteristic
169#95×D71C2211yescharacteristic
170#95×D71C2211yescharacteristic, complemented
171#95×D71C2211yescharacteristic, complemented
172#95×D71C2211yescharacteristic, complemented
173#95×D71C2211yescharacteristic, complemented
174C2×#123×C71C2211yescharacteristic
175C2×C22⋊Q8×C71C2211yescharacteristic, complemented
176#400×C71C2211yescharacteristic, complemented
177#400×C71C2211yescharacteristic, complemented
178#397×C71C2211yescharacteristic, complemented
179#393×C71C2211yescharacteristic, complemented
180#391×C71C2211yescharacteristic, complemented
181#388×C71C2211yescharacteristic, complemented
182#388×C71C2211yescharacteristic, complemented
183#386×C71C2211yescharacteristic
184#386×C71C2211yescharacteristic
185#382×C71C2211yescharacteristic, complemented
186#381×C71C2211yescharacteristic, complemented
187C4×C22⋊C4×C71C2211yescharacteristic, complemented
188C2×#95×C71C2211yescharacteristic, complemented
189C24×D71C2311yescharacteristic
190C24×D71C2311yescharacteristic
191C22×Dic142C2311yescharacteristic
192C22×Dic142C2311yescharacteristic
193C22×Dic142C2311yescharacteristic
194C2×Q8×D71—24no—
195C2×Q8×D71—24no—
196C2×Q8×D71—42no—
197C22×D284C2311yescharacteristic
198C22×C22⋊D71C2311yescharacteristic
199C22×C22⋊D71C2311yescharacteristic
200C2×D4×D71—24no—
201C2×D4×D71—24no—
202C2×D4×D71—24no—
203C23×Dic71C2311yescharacteristic
204C23×Dic71C2311yescharacteristic
205C23×Dic71C2311yescharacteristic
206C22×C4×D71—24no—
207C22×C4×D71—24no—
208C22×C4×D71—24no—
209C22×C4×D71—24no—
210C22×C4×D71—24no—
211C22×C4×D71—24no—
212C22×C4×D71—24no—
213C22×C4×D71—42no—
214C22×C4×D71—42no—
215C22×C4×D71C2311yescharacteristic
216C22×C4×D71C2311yescharacteristic
217C22×C4×D71C2311yescharacteristic
218C22×C4×D71C2311yescharacteristic
219C22×C4×D71C2311yescharacteristic
220C22×C4×D71C2311yescharacteristic
221C22×C4×D71C2311yescharacteristic
222C22×C4×D71C2311yescharacteristic
223C22×C4×D71C2311yescharacteristic
224C22×C4×D71C2311yescharacteristic
225C22×C4×D71C2311yescharacteristic
226C22×C4×D71C2311yescharacteristic
227C22×C4×D71C2311yescharacteristic
228C22×C4×D71C2311yescharacteristic
229C22×C4×D71C2311yescharacteristic
230C22×C4×D71C2311yescharacteristic
231C22×C4×D71C2311yescharacteristic
232C22×C4×D71C2311yescharacteristic
233C22×C4×D71C2311yescharacteristic
234#14556113—24no—
235#14556113—24no—
236#14556112—24no—
237#14556111—24no—
238#14556110—24no—
239#14556110—24no—
240#14556109—24no—
241#14556108—24no—
242#14556107—24no—
243#14556106—24no—
244#14556106—24no—
245#14556105—24no—
246#14556105—24no—
247#14556104—24no—
248C2×C4⋊Dic71C2311yescharacteristic
249C2×C4⋊Dic71C2311yescharacteristic
250C2×C4⋊Dic71C2311yescharacteristic
251C2×C4⋊Dic71C2311yescharacteristic
252C2×C4⋊Dic71C2311yescharacteristic
253C2×Dic71⋊C4C2311yescharacteristic
254C2×Dic71⋊C4C2311yescharacteristic
255C2×Dic71⋊C4C2311yescharacteristic
256C2×Dic71⋊C4C2311yescharacteristic
257C2×Dic71⋊C4C2311yescharacteristic
258C2×Dic71⋊C4C2311yescharacteristic
259C2×Dic71⋊C4C2311yescharacteristic
260C2×Dic71⋊C4C2311yescharacteristic
261C2×Dic71⋊C4C2311yescharacteristic
262C2×Dic71⋊C4C2311yescharacteristic
263C4⋊C4×D71—24no—
264C4⋊C4×D71—24no—
265C4⋊C4×D71—24no—
266C4⋊C4×D71—24no—
267C4⋊C4×D71—24no—
268C2×C22⋊Dic71C2311yescharacteristic
269C2×C22⋊Dic71C2311yescharacteristic
270C2×C22⋊Dic71C2311yescharacteristic
271C2×C22⋊Dic71C2311yescharacteristic
272C2×C22⋊Dic71C2311yescharacteristic
273C2×C22⋊Dic71C2311yescharacteristic
274C2×C22⋊Dic71C2311yescharacteristic
275C2×C22⋊Dic71C2311yescharacteristic
276C2×C22⋊Dic71C2311yescharacteristic
277C2×(C2×D71)⋊C4C2311yescharacteristic
278C2×(C2×D71)⋊C4C2311yescharacteristic
279C2×(C2×D71)⋊C4C2311yescharacteristic
280C2×(C2×D71)⋊C4C2311yescharacteristic
281C2×(C2×D71)⋊C4C2311yescharacteristic
282C2×(C2×D71)⋊C4C2311yescharacteristic
283C2×(C2×D71)⋊C4C2311yescharacteristic
284C2×(C2×D71)⋊C4C2311yescharacteristic
285C2×(C2×D71)⋊C4C2311yescharacteristic
286C2×(C2×D71)⋊C4C2311yescharacteristic
287C2×(C2×D71)⋊C4C2311yescharacteristic
288C2×(C2×D71)⋊C4C2311yescharacteristic
289C2×(C2×D71)⋊C4C2311yescharacteristic
290C2×(C2×D71)⋊C4C2311yescharacteristic
291C2×(C2×D71)⋊C4C2311yescharacteristic
292C2×(C2×D71)⋊C4C2311yescharacteristic
293C2×(C2×D71)⋊C4C2311yescharacteristic
294C2×(C2×D71)⋊C4C2311yescharacteristic
295C22⋊C4×D71—24no—
296C22⋊C4×D71—24no—
297C22⋊C4×D71—24no—
298C22⋊C4×D71—24no—
299C22⋊C4×D71—24no—
300C22⋊C4×D71—24no—
301C22⋊C4×D71—42no—
302C22⋊C4×D71—42no—
303C22⋊C4×D71D418yes—
304C2×C4×Dic71C2311yescharacteristic
305C2×C4×Dic71C2311yescharacteristic
306C2×C4×Dic71C2311yescharacteristic
307C2×C4×Dic71C2311yescharacteristic
308C2×C4×Dic71C2311yescharacteristic
309C2×C4×Dic71C2311yescharacteristic
310C42×D71—24no—
311C42×D71—42no—
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C71⋊#95C2311yescharacteristic
331C71⋊#95C2311yescharacteristic
332C71⋊#95C2311yescharacteristic
333C71⋊#95C2311yescharacteristic
334C71⋊#95C2311yescharacteristic
335C71⋊#95C2311yescharacteristic
336C71⋊#95C2311yescharacteristic
337C71⋊#95C2311yescharacteristic
338C71⋊#95C2311yescharacteristic
339C71⋊#95C2311yescharacteristic
340C71⋊#95C2311yescharacteristic
341C71⋊#95C2311yescharacteristic
342C71⋊#95C2311yescharacteristic
343C71⋊#95C2311yescharacteristic
344C71⋊#95C2311yescharacteristic
345C71⋊#95C2311yescharacteristic
346C71⋊#95C2311yescharacteristic
347C71⋊#95C2311yescharacteristic
348C71⋊#95C2311yescharacteristic
349C71⋊#95C2311yescharacteristic
350C71⋊#95C2311yescharacteristic
351C71⋊#95C2311yescharacteristic
352C71⋊#95C2311yescharacteristic
353C71⋊#95C2311yescharacteristic
354C22×Q8×C71C2311yescharacteristic
355C22×D4×C71C2311yescharacteristic
356C23×C4×C71C2311yescharacteristic
357C23×C4×C71C2311yescharacteristic
358C23×C4×C71C2311yescharacteristic
359#123×C71—24no—
360C22⋊Q8×C71—24no—
361C2×C4⋊C4×C71C2311yescharacteristic
362C2×C4⋊C4×C71C2311yescharacteristic
363C2×C4⋊C4×C71C2311yescharacteristic
364C2×C4⋊C4×C71C2311yescharacteristic
365C2×C4⋊C4×C71C2311yescharacteristic
366C2×C22⋊C4×C71C2311yescharacteristic
367C2×C22⋊C4×C71C2311yescharacteristic
368C2×C22⋊C4×C71C2311yescharacteristic
369C2×C22⋊C4×C71C2311yescharacteristic
370C2×C22⋊C4×C71C2311yescharacteristic
371C2×C22⋊C4×C71C2311yescharacteristic
372C2×C22⋊C4×C71C2311yescharacteristic
373C2×C22⋊C4×C71C2311yescharacteristic
374C2×C22⋊C4×C71C2311yescharacteristic
375C2×C42×C71C2311yescharacteristic
376C2×C42×C71C2311yescharacteristic
377#95×C71C2311yescharacteristic
378#95×C71C2311yescharacteristic
379#95×C71C2311yescharacteristic
380#95×C71C2311yescharacteristic
381#95×C71C2311yescharacteristic
382#95×C71C2311yescharacteristic
383#95×C71C2311yescharacteristic
384#95×C71C2311yescharacteristic
385#95×C71C2311yescharacteristic
386#95×C71C2311yescharacteristic
387#95×C71C2311yescharacteristic
388#95×C71C2311yescharacteristic
389#95×C71C2311yescharacteristic
390#95×C71C2311yescharacteristic
391C23×D71—22no—
392C23×D71—22no—
393C23×D71—22no—
394C23×D71—22no—
395C23×D71—22no—
396C23×D71—22no—
397C23×D71—22no—
398C23×D71—22no—
399C23×D71—22no—
400C23×D71—22no—
401C23×D71—22no—
402C23×D71C2×D414yes—
403C23×D71#4114yes—
404C23×D71#4114yes—
405C23×D71C2411yescharacteristic
406C23×D71C2411yescharacteristic
407C23×D71C2411yescharacteristic
408C2×Dic142—22no—
409C2×Dic142—22no—
410C2×Dic142—22no—
411C2×Dic142—22no—
412C2×Dic142—22no—
413C2×Dic142—22no—
414C2×Dic142—41no—
415C2×Dic142—41no—
416C2×Dic142—41no—
417Q8×D71—416no—
418C2×D284—22no—
419C2×D284—22no—
420C2×D284—22no—
421C2×C22⋊D71—22no—
422C2×C22⋊D71—22no—
423C2×C22⋊D71—22no—
424C2×C22⋊D71—22no—
425C2×C22⋊D71—22no—
426C2×C22⋊D71—22no—
427D4×D71—416no—
428C22×Dic71—22no—
429C22×Dic71—22no—
430C22×Dic71—22no—
431C22×Dic71—22no—
432C22×Dic71—22no—
433C22×Dic71—22no—
434C22×Dic71—22no—
435C22×Dic71—41no—
436C22×Dic71—41no—
437C22×Dic71C2411yescharacteristic
438C22×Dic71C2411yescharacteristic
439C22×Dic71C2411yescharacteristic
440C22×Dic71C2411yescharacteristic
441C22×Dic71C2411yescharacteristic
442C22×Dic71C2411yescharacteristic
443C22×Dic71C2411yescharacteristic
444C22×Dic71C2411yescharacteristic
445C22×Dic71C2411yescharacteristic
446C22×Dic71C2411yescharacteristic
447C22×Dic71C2411yescharacteristic
448C22×Dic71C2411yescharacteristic
449C22×Dic71C2411yescharacteristic
450C2×C4×D71—22no—
451C2×C4×D71—22no—
452C2×C4×D71—22no—
453C2×C4×D71—22no—
454C2×C4×D71—22no—
455C2×C4×D71—22no—
456C2×C4×D71—22no—
457C2×C4×D71—22no—
458C2×C4×D71—22no—
459C2×C4×D71—22no—
460C2×C4×D71—22no—
461C2×C4×D71—22no—
462C2×C4×D71—22no—
463C2×C4×D71—22no—
464C2×C4×D71—22no—
465C2×C4×D71—22no—
466C2×C4×D71—22no—
467C2×C4×D71—22no—
468C2×C4×D71—22no—
469C2×C4×D71—22no—
470C2×C4×D71—22no—
471C2×C4×D71—22no—
472C2×C4×D71—22no—
473C2×C4×D71—22no—
474C2×C4×D71—22no—
475C2×C4×D71—22no—
476C2×C4×D71—22no—
477C2×C4×D71—22no—
478C2×C4×D71—22no—
479C2×C4×D71—22no—
480C2×C4×D71—22no—
481C2×C4×D71—22no—
482C2×C4×D71—22no—
483C2×C4×D71—22no—
484C2×C4×D71—22no—
485C2×C4×D71—22no—
486C2×C4×D71—22no—
487C2×C4×D71—22no—
488C2×C4×D71—22no—
489C2×C4×D71—22no—
490C2×C4×D71—22no—
491C2×C4×D71—22no—
492C2×C4×D71—22no—
493C2×C4×D71—22no—
494C2×C4×D71—22no—
495C2×C4×D71—22no—
496C2×C4×D71—22no—
497C2×C4×D71—22no—
498C2×C4×D71—22no—
499C2×C4×D71—416no—
500C2×C4×D71—416no—
501C2×C4×D71—41no—
502C2×C4×D71—41no—
503C2×C4×D71—41no—
504C2×C4×D71—41no—
505C2×C4×D71—416no—
506C2×C4×D71C2×D414yes—
507C2×C4×D71C2×D414yes—
508C2×C4×D71#4114yes—
509C2×C4×D71#4114yes—
510C4⋊Dic71—22no—
511C4⋊Dic71—22no—
512C4⋊Dic71—22no—
513C4⋊Dic71—22no—
514C4⋊Dic71—22no—
515Dic71⋊C4—22no—
516Dic71⋊C4—22no—
517Dic71⋊C4—22no—
518Dic71⋊C4—22no—
519Dic71⋊C4—22no—
520Dic71⋊C4—22no—
521Dic71⋊C4—22no—
522Dic71⋊C4—22no—
523Dic71⋊C4—22no—
524Dic71⋊C4—22no—
525C22⋊Dic71—22no—
526C22⋊Dic71—22no—
527C22⋊Dic71—22no—
528C22⋊Dic71—22no—
529C22⋊Dic71—22no—
530C22⋊Dic71—22no—
531C22⋊Dic71—41no—
532C22⋊Dic71—41no—
533C22⋊Dic71C2×D414yes—
534(C2×D71)⋊C4—22no—
535(C2×D71)⋊C4—22no—
536(C2×D71)⋊C4—22no—
537(C2×D71)⋊C4—22no—
538(C2×D71)⋊C4—22no—
539(C2×D71)⋊C4—22no—
540(C2×D71)⋊C4—22no—
541(C2×D71)⋊C4—22no—
542(C2×D71)⋊C4—22no—
543(C2×D71)⋊C4—22no—
544(C2×D71)⋊C4—22no—
545(C2×D71)⋊C4—22no—
546(C2×D71)⋊C4—41no—
547(C2×D71)⋊C4—41no—
548(C2×D71)⋊C4—41no—
549(C2×D71)⋊C4—41no—
550(C2×D71)⋊C4C2×D414yes—
551(C2×D71)⋊C4C2×D414yes—
552C4×Dic71—22no—
553C4×Dic71—22no—
554C4×Dic71—22no—
555C4×Dic71—41no—
556C4×Dic71—41no—
557C4×Dic71—41no—
558C24×C71C2411yescharacteristic
559C24×C71C2411yescharacteristic
560C2×Q8×C71—22no—
561C2×Q8×C71—22no—
562C2×Q8×C71—41no—
563C2×D4×C71—22no—
564C2×D4×C71—22no—
565C2×D4×C71—22no—
566C22×C4×C71—22no—
567C22×C4×C71—22no—
568C22×C4×C71—22no—
569C22×C4×C71—22no—
570C22×C4×C71—22no—
571C22×C4×C71—22no—
572C22×C4×C71—22no—
573C22×C4×C71—41no—
574C22×C4×C71—41no—
575C22×C4×C71C2411yescharacteristic
576C22×C4×C71C2411yescharacteristic
577C22×C4×C71C2411yescharacteristic
578C22×C4×C71C2411yescharacteristic
579C22×C4×C71C2411yescharacteristic
580C22×C4×C71C2411yescharacteristic
581C22×C4×C71C2411yescharacteristic
582C22×C4×C71C2411yescharacteristic
583C22×C4×C71C2411yescharacteristic
584C22×C4×C71C2411yescharacteristic
585C22×C4×C71C2411yescharacteristic
586C22×C4×C71C2411yescharacteristic
587C22×C4×C71C2411yescharacteristic
588C4⋊C4×C71—22no—
589C4⋊C4×C71—22no—
590C4⋊C4×C71—22no—
591C4⋊C4×C71—22no—
592C4⋊C4×C71—22no—
593C22⋊C4×C71—22no—
594C22⋊C4×C71—22no—
595C22⋊C4×C71—22no—
596C22⋊C4×C71—22no—
597C22⋊C4×C71—22no—
598C22⋊C4×C71—22no—
599C22⋊C4×C71—41no—
600C22⋊C4×C71—41no—
601C22⋊C4×C71C2×D414yes—
602C42×C71—22no—
603C42×C71—41no—
604C23×C71—21no—
605C23×C71—21no—
606C23×C71—21no—
607C23×C71—21no—
608C23×C71—21no—
609C23×C71—21no—
610C23×C71—21no—
611C23×C71—21no—
612C23×C71—21no—
613C23×C71—21no—
614C23×C71—21no—
615C23×C71C22×D412yes—
616C23×C71C2×#4112yes—
617C23×C71C2×#4112yes—
618C23×C71C2511yescharacteristic
619C22×D71—21no—
620C22×D71—21no—
621C22×D71—21no—
622C22×D71—21no—
623C22×D71—28no—
624C22×D71—28no—
625C22×D71—28no—
626C22×D71—28no—
627C22×D71—28no—
628C22×D71—28no—
629C22×D71—21no—
630C22×D71—21no—
631C22×D71—21no—
632C22×D71—21no—
633C22×D71—21no—
634C22×D71—21no—
635C22×D71—21no—
636C22×D71—44no—
637C22×D71—44no—
638C22×D71—44no—
639C22×D71—44no—
640C22×D71—44no—
641C22×D71—44no—
642C22×D71—44no—
643C22×D71#124116yes—
644C22×D71C22×D412yes—
645C22×D71C22×D412yes—
646C22×D71C2×#4112yes—
647C22×D71C2×#4112yes—
648C22×D71C2×#4112yes—
649C22×D71C2×#4112yes—
650C22×D71C2×#4112yes—
651C22×D71C2×#4112yes—
652C22×D71H(5,𝔽2)12yes—
653C22×D712−1+412yes—
654Q8×C71—44no—
655D4×C71—44no—
656C2×C4×C71—21no—
657C2×C4×C71—21no—
658C2×C4×C71—21no—
659C2×C4×C71—21no—
660C2×C4×C71—21no—
661C2×C4×C71—21no—
662C2×C4×C71—21no—
663C2×C4×C71—21no—
664C2×C4×C71—21no—
665C2×C4×C71—21no—
666C2×C4×C71—21no—
667C2×C4×C71—21no—
668C2×C4×C71—21no—
669C2×C4×C71—21no—
670C2×C4×C71—21no—
671C2×C4×C71—21no—
672C2×C4×C71—21no—
673C2×C4×C71—21no—
674C2×C4×C71—21no—
675C2×C4×C71—21no—
676C2×C4×C71—21no—
677C2×C4×C71—21no—
678C2×C4×C71—21no—
679C2×C4×C71—21no—
680C2×C4×C71—21no—
681C2×C4×C71—21no—
682C2×C4×C71—21no—
683C2×C4×C71—21no—
684C2×C4×C71—21no—
685C2×C4×C71—21no—
686C2×C4×C71—21no—
687C2×C4×C71—21no—
688C2×C4×C71—21no—
689C2×C4×C71—21no—
690C2×C4×C71—21no—
691C2×C4×C71—44no—
692C2×C4×C71—44no—
693C2×C4×C71—44no—
694C2×C4×C71C22×D412yes—
695C2×C4×C71C22×D412yes—
696C2×C4×C71C2×#4112yes—
697C2×C4×C71C2×#4112yes—
698C22⋊D71—44no—
699C22⋊D71—44no—
700C2×Dic71—21no—
701C2×Dic71—21no—
702C2×Dic71—21no—
703C2×Dic71—21no—
704C2×Dic71—21no—
705C2×Dic71—21no—
706C2×Dic71—21no—
707C2×Dic71—21no—
708C2×Dic71—21no—
709C2×Dic71—21no—
710C2×Dic71—21no—
711C2×Dic71—21no—
712C2×Dic71—21no—
713C2×Dic71—21no—
714C2×Dic71—21no—
715C2×Dic71—21no—
716C2×Dic71—21no—
717C2×Dic71—21no—
718C2×Dic71—21no—
719C2×Dic71—21no—
720C2×Dic71—21no—
721C2×Dic71—21no—
722C2×Dic71—21no—
723C2×Dic71—21no—
724C2×Dic71—21no—
725C2×Dic71—21no—
726C2×Dic71—21no—
727C2×Dic71—21no—
728C2×Dic71—21no—
729C2×Dic71—21no—
730C2×Dic71—21no—
731C2×Dic71—21no—
732C2×Dic71—21no—
733C2×Dic71—21no—
734C2×Dic71—21no—
735C2×Dic71—44no—
736C2×Dic71—44no—
737C2×Dic71—44no—
738C2×Dic71C22×D412yes—
739C2×Dic71C22×D412yes—
740C2×Dic71C2×#4112yes—
741C2×Dic71C2×#4112yes—
742D284—44no—
743C4×D71—28no—
744C4×D71—28no—
745C4×D71—28no—
746C4×D71—28no—
747C4×D71—44no—
748C4×D71—44no—
749C4×D71—44no—
750C4×D71—44no—
751C4×D71—44no—
752C4×D71—44no—
753C4×D71—44no—
754C4×D71—44no—
755C4×D71—44no—
756C4×D71—44no—
757C4×D71—44no—
758C4×D71—44no—
759C4×D71—44no—
760C4×D71—44no—
761C4×D71—44no—
762Dic142—44no—
763Dic142—44no—
764Dic142—44no—
765C22×C71—22no—
766C22×C71—22no—
767C22×C71—22no—
768C22×C71—22no—
769C22×C71—22no—
770C22×C71—22no—
771C22×C71—41no—
772C22×C71—41no—
773C22×C71—41no—
774C22×C71—41no—
775C22×C71—41no—
776C22×C71—41no—
777C22×C71—41no—
778C22×C71C2×#12414yes—
779C22×C71C23×D411yescharacteristic
780C22×C71C22×#4111yescharacteristic
781C22×C71C22×#4111yescharacteristic
782C22×C71C22×#4111yescharacteristic
783C22×C71C22×#4111yescharacteristic
784C22×C71C2×H(5,𝔽2)11yescharacteristic
785C22×C71C2×2−1+411yescharacteristic
786C2×D71—22no—
787C2×D71—22no—
788C2×D71—22no—
789C2×D71—22no—
790C2×D71—22no—
791C2×D71—22no—
792C2×D71—232no—
793C2×D71—41no—
794C2×D71—41no—
795C2×D71—41no—
796C2×D71—41no—
797C2×D71—41no—
798C2×D71—41no—
799C2×D71—41no—
800C2×D71—88no—
801C2×D71C2×#12414yes—
802C2×D71C2×#12414yes—
803C2×D71#52914yes—
804C2×D71#53914yes—
805C2×D71#54614yes—
806C2×D71#54714yes—
807C2×D71#55114yes—
808C2×D71#55214yes—
809C4×C71—22no—
810C4×C71—22no—
811C4×C71—22no—
812C4×C71—22no—
813C4×C71—41no—
814C4×C71—41no—
815C4×C71—41no—
816C4×C71—41no—
817C4×C71—41no—
818C4×C71—41no—
819C4×C71—41no—
820C4×C71—41no—
821C4×C71—41no—
822Dic71—22no—
823Dic71—22no—
824Dic71—22no—
825Dic71—22no—
826Dic71—41no—
827Dic71—41no—
828Dic71—41no—
829Dic71—41no—
830Dic71—41no—
831Dic71—41no—
832Dic71—41no—
833Dic71—41no—
834Dic71—41no—
835C2×#2488—711nomaximal, Sylow
836C2×C71—24no—
837C2×C71—81no—
838C2×C71C22×#12411yescharacteristic
839C2×C71C2×#52911yescharacteristic
840C2×C71C2×#53911yescharacteristic
841C2×C71C2×#54611yescharacteristic
842C2×C71C2×#54711yescharacteristic
843C2×C71C2×#55111yescharacteristic
844C2×C71C2×#55211yescharacteristic
845D71—24no—
846D71—81no—
847D71#248818yesdirect product factor
848C22×#123—711no—
849C22×C22⋊Q8—711no—
850#2488—711no—
851#2488—711no—
852#2488—711no—
853#2488—711no—
854#2488—711no—
855#2488—711no—
856#2488—711no—
857#2488—711no—
858#2488—711no—
859#2488—711no—
860#2488—711no—
861#2488—711no—
862#2488—711no—
863#2488—711no—
864#2488—711no—
865#2488D7111yescharacteristic, direct product factor
866C2×#400—711no—
867C2×#400—711no—
868C2×#397—711no—
869C2×#393—711no—
870C2×#391—711no—
871C2×#388—711no—
872C2×#388—711no—
873C2×#386—711no—
874C2×#386—711no—
875C2×#382—711no—
876C2×#381—711no—
877C2×C4×C22⋊C4—711no—
878C22×#95—711no—
879C71C2×#248811yescharacteristic, complemented, Sylow
880C23×Q8—711no—
881C23×D4—711no—
882C24×C4—711no—
883C24×C4—711no—
884C24×C4—711no—
885C2×#123—711no—
886C2×#123—711no—
887C2×#123—711no—
888C2×#123—711no—
889C2×#123—711no—
890C2×#123—711no—
891C2×#123—711no—
892C2×#123—1428no—
893C2×#123C2×D7111yescharacteristic
894C2×C22⋊Q8—711no—
895C2×C22⋊Q8—711no—
896C2×C22⋊Q8—711no—
897C2×C22⋊Q8—711no—
898C2×C22⋊Q8—711no—
899C2×C22⋊Q8—711no—
900C2×C22⋊Q8—711no—
901C2×C22⋊Q8—1428no—
902C2×C22⋊Q8C2×D7111yescharacteristic, complemented
903C22×C4⋊C4—711no—
904C22×C4⋊C4—711no—
905C22×C4⋊C4—711no—
906C22×C4⋊C4—711no—
907C22×C4⋊C4—711no—
908C22×C22⋊C4—711no—
909C22×C22⋊C4—711no—
910C22×C22⋊C4—711no—
911C22×C22⋊C4—711no—
912C22×C22⋊C4—711no—
913C22×C22⋊C4—711no—
914C22×C22⋊C4—711no—
915C22×C22⋊C4—711no—
916C22×C22⋊C4—711no—
917C22×C42—711no—
918C22×C42—711no—
919#400—711no—
920#400—711no—
921#400—711no—
922#400—711no—
923#400—711no—
924#400—711no—
925#400—711no—
926#400—711no—
927#400—711no—
928#400—711no—
929#400—711no—
930#400—711no—
931#400—711no—
932#400—711no—
933#400C2×D7111yescharacteristic, complemented
934#400C2×D7111yescharacteristic, complemented
935#397—711no—
936#397—711no—
937#397—711no—
938#397—711no—
939#397—711no—
940#397—711no—
941#397—711no—
942#397C2×D7111yescharacteristic, complemented
943#393—711no—
944#393—711no—
945#393—711no—
946#393—711no—
947#393—711no—
948#393—711no—
949#393—711no—
950#393C2×D7111yescharacteristic, complemented
951#391—711no—
952#391—711no—
953#391—711no—
954#391—711no—
955#391—711no—
956#391—711no—
957#391—711no—
958#391C2×D7111yescharacteristic, complemented
959#388—711no—
960#388—711no—
961#388—711no—
962#388—711no—
963#388—711no—
964#388—711no—
965#388—711no—
966#388—711no—
967#388—711no—
968#388—711no—
969#388—711no—
970#388—711no—
971#388—711no—
972#388—711no—
973#388C2×D7111yescharacteristic, complemented
974#388C2×D7111yescharacteristic, complemented
975#386—711no—
976#386—711no—
977#386—711no—
978#386—711no—
979#386—711no—
980#386—711no—
981#386—711no—
982#386—711no—
983#386—711no—
984#386—711no—
985#386—711no—
986#386—711no—
987#386—711no—
988#386—711no—
989#386C2×D7111yescharacteristic
990#386C2×D7111yescharacteristic
991#382—711no—
992#382—711no—
993#382—711no—
994#382—711no—
995#382—711no—
996#382—711no—
997#382—711no—
998#382C2×D7111yescharacteristic, complemented
999#381—711no—
1000#381—711no—
1001#381—711no—
1002#381—711no—
1003#381—711no—
1004#381—711no—
1005#381—711no—
1006#381C2×D7111yescharacteristic, complemented
1007C4×C22⋊C4—711no—
1008C4×C22⋊C4—711no—
1009C4×C22⋊C4—711no—
1010C4×C22⋊C4—711no—
1011C4×C22⋊C4—711no—
1012C4×C22⋊C4—711no—
1013C4×C22⋊C4—711no—
1014C4×C22⋊C4C2×D7111yescharacteristic, complemented
1015C2×#95—711no—
1016C2×#95—711no—
1017C2×#95—711no—
1018C2×#95—711no—
1019C2×#95—711no—
1020C2×#95—711no—
1021C2×#95—711no—
1022C2×#95—711no—
1023C2×#95—711no—
1024C2×#95—711no—
1025C2×#95—711no—
1026C2×#95—711no—
1027C2×#95—711no—
1028C2×#95—711no—
1029C2×#95—711no—
1030C2×#95—711no—
1031C2×#95—711no—
1032C2×#95—711no—
1033C2×#95—711no—
1034C2×#95—711no—
1035C2×#95—711no—
1036C2×#95C2×D7111yescharacteristic, complemented
1037C25—711no—
1038C25—711no—
1039C22×Q8—2842no—
1040C22×Q8—711no—
1041C22×Q8—711no—
1042C22×Q8—711no—
1043C22×Q8—1424no—
1044C22×Q8—1424no—
1045C22×Q8C22×D7111yescharacteristic
1046C22×D4—711no—
1047C22×D4—711no—
1048C22×D4—711no—
1049C22×D4—1424no—
1050C22×D4—1424no—
1051C22×D4—1424no—
1052C22×D4C22×D7111yescharacteristic
1053C23×C4—2842no—
1054C23×C4—2842no—
1055C23×C4—711no—
1056C23×C4—711no—
1057C23×C4—711no—
1058C23×C4—711no—
1059C23×C4—711no—
1060C23×C4—711no—
1061C23×C4—711no—
1062C23×C4—711no—
1063C23×C4—711no—
1064C23×C4—711no—
1065C23×C4—711no—
1066C23×C4—711no—
1067C23×C4—711no—
1068C23×C4—711no—
1069C23×C4—711no—
1070C23×C4—711no—
1071C23×C4—711no—
1072C23×C4—711no—
1073C23×C4—711no—
1074C23×C4—711no—
1075C23×C4—711no—
1076C23×C4—711no—
1077C23×C4—1424no—
1078C23×C4—1424no—
1079C23×C4—1424no—
1080C23×C4—1424no—
1081C23×C4—1424no—
1082C23×C4—1424no—
1083C23×C4—1424no—
1084C23×C4C22×D7111yescharacteristic
1085C23×C4C22×D7111yescharacteristic
1086C23×C4C22×D7111yescharacteristic
1087#123—24no—
1088#123—1424no—
1089#123—1424no—
1090#123—1424no—
1091#123—1424no—
1092#123—1424no—
1093#123—1424no—
1094#123—1424no—
1095C22⋊Q8—24no—
1096C22⋊Q8—1424no—
1097C22⋊Q8—1424no—
1098C22⋊Q8—1424no—
1099C22⋊Q8—1424no—
1100C22⋊Q8—1424no—
1101C22⋊Q8—1424no—
1102C22⋊Q8—1424no—
1103C2×C4⋊C4—711no—
1104C2×C4⋊C4—711no—
1105C2×C4⋊C4—711no—
1106C2×C4⋊C4—711no—
1107C2×C4⋊C4—711no—
1108C2×C4⋊C4—711no—
1109C2×C4⋊C4—711no—
1110C2×C4⋊C4—711no—
1111C2×C4⋊C4—711no—
1112C2×C4⋊C4—711no—
1113C2×C4⋊C4—711no—
1114C2×C4⋊C4—711no—
1115C2×C4⋊C4—711no—
1116C2×C4⋊C4—711no—
1117C2×C4⋊C4—711no—
1118C2×C4⋊C4—1424no—
1119C2×C4⋊C4—1424no—
1120C2×C4⋊C4—1424no—
1121C2×C4⋊C4—1424no—
1122C2×C4⋊C4—1424no—
1123C2×C4⋊C4C22×D7111yescharacteristic
1124C2×C4⋊C4C22×D7111yescharacteristic
1125C2×C4⋊C4C22×D7111yescharacteristic
1126C2×C4⋊C4C22×D7111yescharacteristic
1127C2×C4⋊C4C22×D7111yescharacteristic
1128C2×C22⋊C4—2842no—
1129C2×C22⋊C4—2842no—
1130C2×C22⋊C4—711no—
1131C2×C22⋊C4—711no—
1132C2×C22⋊C4—711no—
1133C2×C22⋊C4—711no—
1134C2×C22⋊C4—711no—
1135C2×C22⋊C4—711no—
1136C2×C22⋊C4—711no—
1137C2×C22⋊C4—711no—
1138C2×C22⋊C4—711no—
1139C2×C22⋊C4—718no—
1140C2×C22⋊C4—711no—
1141C2×C22⋊C4—711no—
1142C2×C22⋊C4—711no—
1143C2×C22⋊C4—711no—
1144C2×C22⋊C4—711no—
1145C2×C22⋊C4—711no—
1146C2×C22⋊C4—711no—
1147C2×C22⋊C4—711no—
1148C2×C22⋊C4—711no—
1149C2×C22⋊C4—711no—
1150C2×C22⋊C4—711no—
1151C2×C22⋊C4—711no—
1152C2×C22⋊C4—711no—
1153C2×C22⋊C4—711no—
1154C2×C22⋊C4—711no—
1155C2×C22⋊C4—711no—
1156C2×C22⋊C4—711no—
1157C2×C22⋊C4—711no—
1158C2×C22⋊C4—1424no—
1159C2×C22⋊C4—1424no—
1160C2×C22⋊C4—1424no—
1161C2×C22⋊C4—1424no—
1162C2×C22⋊C4—1424no—
1163C2×C22⋊C4—1424no—
1164C2×C22⋊C4C22×D7111yescharacteristic
1165C2×C22⋊C4C22×D7111yescharacteristic
1166C2×C22⋊C4C22×D7111yescharacteristic
1167C2×C22⋊C4C22×D7111yescharacteristic
1168C2×C22⋊C4C22×D7111yescharacteristic
1169C2×C22⋊C4C22×D7111yescharacteristic
1170C2×C22⋊C4C22×D7111yescharacteristic
1171C2×C22⋊C4C22×D7111yescharacteristic
1172C2×C22⋊C4C22×D7111yescharacteristic
1173C2×C42—2842no—
1174C2×C42—711no—
1175C2×C42—711no—
1176C2×C42—711no—
1177C2×C42—711no—
1178C2×C42—711no—
1179C2×C42—711no—
1180C2×C42—1424no—
1181C2×C42C22×D7111yescharacteristic
1182C2×C42C22×D7111yescharacteristic
1183#95—711no—
1184#95—711no—
1185#95—711no—
1186#95—711no—
1187#95—711no—
1188#95—711no—
1189#95—711no—
1190#95—711no—
1191#95—711no—
1192#95—711no—
1193#95—711no—
1194#95—711no—
1195#95—711no—
1196#95—711no—
1197#95—711no—
1198#95—711no—
1199#95—711no—
1200#95—711no—
1201#95—711no—
1202#95—711no—
1203#95—711no—
1204#95—711no—
1205#95—711no—
1206#95—711no—
1207#95—711no—
1208#95—711no—
1209#95—711no—
1210#95—711no—
1211#95—711no—
1212#95—711no—
1213#95—711no—
1214#95—711no—
1215#95—711no—
1216#95—711no—
1217#95—711no—
1218#95—711no—
1219#95—711no—
1220#95—711no—
1221#95—711no—
1222#95—711no—
1223#95—711no—
1224#95—711no—
1225#95C22×D7111yescharacteristic
1226#95C22×D7111yescharacteristic
1227#95C22×D7111yescharacteristic
1228#95C22×D7111yescharacteristic
1229#95C22×D7111yescharacteristic
1230#95C22×D7111yescharacteristic
1231#95C22×D7111yescharacteristic
1232#95C22×D7111yescharacteristic
1233#95C22×D7111yescharacteristic
1234#95C22×D7111yescharacteristic
1235#95C22×D7111yescharacteristic
1236#95C22×D7111yescharacteristic
1237#95C22×D7111yescharacteristic
1238#95C22×D7111yescharacteristic
1239C24—711no—
1240C24—714no—
1241C24—714no—
1242C24—714no—
1243C24—711no—
1244C24—711no—
1245C24—1422no—
1246C24—1422no—
1247C24—1422no—
1248C24—1422no—
1249C24—1422no—
1250C24—1422no—
1251C24—1422no—
1252C24—1422no—
1253C24—1422no—
1254C24—1422no—
1255C24—1422no—
1256C24C23×D7111yescharacteristic
1257C24C23×D7111yescharacteristic
1258C2×Q8—22no—
1259C2×Q8—22no—
1260C2×Q8—41no—
1261C2×Q8—2841no—
1262C2×Q8—2841no—
1263C2×Q8—2841no—
1264C2×Q8—28416no—
1265C2×Q8—1422no—
1266C2×Q8—1422no—
1267C2×Q8—1422no—
1268C2×Q8—1422no—
1269C2×Q8—1422no—
1270C2×Q8—1422no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—28416no—
1275C2×D4—1422no—
1276C2×D4—1422no—
1277C2×D4—1422no—
1278C2×D4—1422no—
1279C2×D4—1422no—
1280C2×D4—1422no—
1281C2×D4—1422no—
1282C2×D4—1422no—
1283C2×D4—1422no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—2841no—
1294C22×C4—2841no—
1295C22×C4—2841no—
1296C22×C4—2841no—
1297C22×C4—28416no—
1298C22×C4—28416no—
1299C22×C4—28416no—
1300C22×C4—2841no—
1301C22×C4—2841no—
1302C22×C4—711no—
1303C22×C4—711no—
1304C22×C4—711no—
1305C22×C4—711no—
1306C22×C4—714no—
1307C22×C4—714no—
1308C22×C4—714no—
1309C22×C4—714no—
1310C22×C4—711no—
1311C22×C4—711no—
1312C22×C4—711no—
1313C22×C4—711no—
1314C22×C4—711no—
1315C22×C4—711no—
1316C22×C4—711no—
1317C22×C4—711no—
1318C22×C4—711no—
1319C22×C4—1422no—
1320C22×C4—1422no—
1321C22×C4—1422no—
1322C22×C4—1422no—
1323C22×C4—1422no—
1324C22×C4—1422no—
1325C22×C4—1422no—
1326C22×C4—1422no—
1327C22×C4—1422no—
1328C22×C4—1422no—
1329C22×C4—1422no—
1330C22×C4—1422no—
1331C22×C4—1422no—
1332C22×C4—1422no—
1333C22×C4—1422no—
1334C22×C4—1422no—
1335C22×C4—1422no—
1336C22×C4—1422no—
1337C22×C4—1422no—
1338C22×C4—1422no—
1339C22×C4—1422no—
1340C22×C4—1422no—
1341C22×C4—1422no—
1342C22×C4—1422no—
1343C22×C4—1422no—
1344C22×C4—1422no—
1345C22×C4—1422no—
1346C22×C4—1422no—
1347C22×C4—1422no—
1348C22×C4—1422no—
1349C22×C4—1422no—
1350C22×C4—1422no—
1351C22×C4—1422no—
1352C22×C4—1422no—
1353C22×C4—1422no—
1354C22×C4—1422no—
1355C22×C4—1422no—
1356C22×C4—1422no—
1357C22×C4—1422no—
1358C22×C4—1422no—
1359C22×C4—1422no—
1360C22×C4—1422no—
1361C22×C4—1422no—
1362C22×C4—1422no—
1363C22×C4—1422no—
1364C22×C4—1422no—
1365C22×C4—1422no—
1366C22×C4—1422no—
1367C22×C4—1422no—
1368C22×C4—1422no—
1369C22×C4—1422no—
1370C22×C4—1422no—
1371C22×C4—1422no—
1372C22×C4—1422no—
1373C22×C4—1422no—
1374C22×C4—1422no—
1375C22×C4C23×D7111yescharacteristic
1376C22×C4C23×D7111yescharacteristic
1377C22×C4C23×D7111yescharacteristic
1378C22×C4C23×D7111yescharacteristic
1379C22×C4C23×D7111yescharacteristic
1380C22×C4C23×D7111yescharacteristic
1381C22×C4C23×D7111yescharacteristic
1382C22×C4C23×D7111yescharacteristic
1383C22×C4C23×D7111yescharacteristic
1384C22×C4C23×D7111yescharacteristic
1385C22×C4C23×D7111yescharacteristic
1386C22×C4C23×D7111yescharacteristic
1387C22×C4C23×D7111yescharacteristic
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—1422no—
1394C4⋊C4—1422no—
1395C4⋊C4—1422no—
1396C4⋊C4—1422no—
1397C4⋊C4—1422no—
1398C4⋊C4—1422no—
1399C4⋊C4—1422no—
1400C4⋊C4—1422no—
1401C4⋊C4—1422no—
1402C4⋊C4—1422no—
1403C4⋊C4—1422no—
1404C4⋊C4—1422no—
1405C4⋊C4—1422no—
1406C4⋊C4—1422no—
1407C4⋊C4—1422no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—41no—
1415C22⋊C4—41no—
1416C22⋊C4—2841no—
1417C22⋊C4—2841no—
1418C22⋊C4—2841no—
1419C22⋊C4—2841no—
1420C22⋊C4—2841no—
1421C22⋊C4—2841no—
1422C22⋊C4—714no—
1423C22⋊C4—714no—
1424C22⋊C4—714no—
1425C22⋊C4—1422no—
1426C22⋊C4—1422no—
1427C22⋊C4—1422no—
1428C22⋊C4—1422no—
1429C22⋊C4—1422no—
1430C22⋊C4—1422no—
1431C22⋊C4—1422no—
1432C22⋊C4—1422no—
1433C22⋊C4—1422no—
1434C22⋊C4—1422no—
1435C22⋊C4—1422no—
1436C22⋊C4—1422no—
1437C22⋊C4—1422no—
1438C22⋊C4—1422no—
1439C22⋊C4—1422no—
1440C22⋊C4—1422no—
1441C22⋊C4—1422no—
1442C22⋊C4—1422no—
1443C22⋊C4D4×D7114yes—
1444C42—22no—
1445C42—41no—
1446C42—2841no—
1447C42—2841no—
1448C42—2841no—
1449C42—1422no—
1450C42—1422no—
1451C42—1422no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—2844no—
1464C23—2844no—
1465C23—2844no—
1466C23—2844no—
1467C23—2844no—
1468C23—2844no—
1469C23—2844no—
1470C23—712no—
1471C23—712no—
1472C23—712no—
1473C23—712no—
1474C23—712no—
1475C23—712no—
1476C23—712no—
1477C23—712no—
1478C23—712no—
1479C23—712no—
1480C23—7116no—
1481C23—1428no—
1482C23—1428no—
1483C23—1428no—
1484C23—1428no—
1485C23—1428no—
1486C23—1428no—
1487C23—1421no—
1488C23—1421no—
1489C23—1421no—
1490C23—1421no—
1491C23—1421no—
1492C23—1421no—
1493C23—1421no—
1494C23—1421no—
1495C23—1421no—
1496C23—1421no—
1497C23—1421no—
1498C23C2×D4×D7112yes—
1499C23#41×D7112yes—
1500C23#41×D7112yes—
1501C23C24×D7111yescharacteristic
1502Q8—44no—
1503Q8—2844no—
1504Q8—2844no—
1505Q8—2844no—
1506D4—44no—
1507D4—2844no—
1508D4—2844no—
1509D4—2844no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—44no—
1546C2×C4—44no—
1547C2×C4—44no—
1548C2×C4—2844no—
1549C2×C4—2844no—
1550C2×C4—2844no—
1551C2×C4—2844no—
1552C2×C4—2844no—
1553C2×C4—2844no—
1554C2×C4—2844no—
1555C2×C4—2844no—
1556C2×C4—2844no—
1557C2×C4—2844no—
1558C2×C4—2844no—
1559C2×C4—2844no—
1560C2×C4—2844no—
1561C2×C4—2844no—
1562C2×C4—2844no—
1563C2×C4—2844no—
1564C2×C4—2844no—
1565C2×C4—2844no—
1566C2×C4—712no—
1567C2×C4—712no—
1568C2×C4—712no—
1569C2×C4—712no—
1570C2×C4—1428no—
1571C2×C4—1428no—
1572C2×C4—1428no—
1573C2×C4—1428no—
1574C2×C4—1421no—
1575C2×C4—1421no—
1576C2×C4—1421no—
1577C2×C4—1421no—
1578C2×C4—1421no—
1579C2×C4—1421no—
1580C2×C4—1421no—
1581C2×C4—1421no—
1582C2×C4—1421no—
1583C2×C4—1421no—
1584C2×C4—1421no—
1585C2×C4—1421no—
1586C2×C4—1421no—
1587C2×C4—1421no—
1588C2×C4—1421no—
1589C2×C4—1421no—
1590C2×C4—1421no—
1591C2×C4—1421no—
1592C2×C4—1421no—
1593C2×C4—1421no—
1594C2×C4—1421no—
1595C2×C4—1421no—
1596C2×C4—1421no—
1597C2×C4—1421no—
1598C2×C4—1421no—
1599C2×C4—1421no—
1600C2×C4—1421no—
1601C2×C4—1421no—
1602C2×C4—1421no—
1603C2×C4—1421no—
1604C2×C4—1421no—
1605C2×C4—1421no—
1606C2×C4—1421no—
1607C2×C4—1421no—
1608C2×C4—1421no—
1609C2×C4C2×D4×D7112yes—
1610C2×C4C2×D4×D7112yes—
1611C2×C4#41×D7112yes—
1612C2×C4#41×D7112yes—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—2841no—
1627C22—2841no—
1628C22—2841no—
1629C22—2841no—
1630C22—2841no—
1631C22—2841no—
1632C22—2841no—
1633C22—5688no—
1634C22—714no—
1635C22—714no—
1636C22—714no—
1637C22—714no—
1638C22—714no—
1639C22—714no—
1640C22—714no—
1641C22—714no—
1642C22—14232no—
1643C22—1422no—
1644C22—1422no—
1645C22—1422no—
1646C22—1422no—
1647C22—1422no—
1648C22—1422no—
1649C22#124×D7114yes—
1650C22C22×D4×D7111yescharacteristic
1651C22C2×#41×D7111yescharacteristic
1652C22C2×#41×D7111yescharacteristic
1653C22C2×#41×D7111yescharacteristic
1654C22C2×#41×D7111yescharacteristic
1655C22H(5,𝔽2)×D7111yescharacteristic
1656C222−1+4×D7111yescharacteristic
1657C4—22no—
1658C4—22no—
1659C4—22no—
1660C4—22no—
1661C4—41no—
1662C4—41no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—41no—
1667C4—41no—
1668C4—41no—
1669C4—41no—
1670C4—2841no—
1671C4—2841no—
1672C4—2841no—
1673C4—2841no—
1674C4—2841no—
1675C4—2841no—
1676C4—2841no—
1677C4—2841no—
1678C4—2841no—
1679C4—1422no—
1680C4—1422no—
1681C4—1422no—
1682C4—1422no—
1683C2—24no—
1684C2—81no—
1685C2—5681no—
1686C2—718no—
1687C2—1424no—
1688C2C2×#124×D7111yescharacteristic
1689C2#529×D7111yescharacteristic
1690C2#539×D7111yescharacteristic
1691C2#546×D7111yescharacteristic
1692C2#547×D7111yescharacteristic
1693C2#551×D7111yescharacteristic
1694C2#552×D7111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2488C2
prime radicalC22×D4×D71C22
hypercenter#2488D71
hypocenterC71C2×#2488
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C22⋊Q8×D71C2semidirect
3. #22592673C2semidirect
4. #22592672C2semidirect
5. #22592671C2semidirect
6. #22592670C2semidirect
7. #22592669C2semidirect
8. #22592668C2semidirect
9. #22592667C2semidirect
10. #22592666C2semidirect
11. #22592665C2semidirect
12. #22592664C2semidirect
13. #22592663C2semidirect
14. #22592662C2semidirect
15. #22592661C2semidirect
16. #22592660C2semidirect
17. #22592659C2semidirect
18. #400×D71C2semidirect
19. #400×D71C2semidirect
20. #397×D71C2semidirect
21. #393×D71C2semidirect
22. #391×D71C2semidirect
23. #388×D71C2semidirect
24. #388×D71C2semidirect
27. #382×D71C2semidirect
28. #381×D71C2semidirect
29. C4×C22⋊C4×D71C2semidirect
30. C2×#95×D71C2semidirect
31. C71×#2488C2semidirect
45. C2×#14556108C22semidirect
46. C2×#14556107C22semidirect
47. C2×#14556106C22semidirect
48. C2×#14556106C22semidirect
49. C2×#14556105C22semidirect
50. C2×#14556105C22semidirect
51. C2×#14556104C22semidirect
69. #17985941C22semidirect
70. #17985941C22semidirect
71. #17985941C22semidirect
72. #17985941C22semidirect
73. #17985940C22semidirect
74. #17985940C22semidirect
75. #17985940C22semidirect
76. #17985940C22semidirect
77. #17985939C22semidirect
78. #17985939C22semidirect
79. #17985938C22semidirect
80. #17985938C22semidirect
81. #17985937C22semidirect
82. #17985937C22semidirect
83. #17985928C22semidirect
84. #17985928C22semidirect
85. #17985927C22semidirect
86. #17985927C22semidirect
87. #17985926C22semidirect
88. #17985925C22semidirect
89. #17985924C22semidirect
90. #17985912C22semidirect
91. #17985912C22semidirect
92. #17985912C22semidirect
93. #17985911C22semidirect
94. #17985911C22semidirect
95. #17985911C22semidirect
96. #17985910C22semidirect
97. #17985906C22semidirect
98. #17985905C22semidirect
99. #17985904C22semidirect
100. #17985903C22semidirect
101. #17985903C22semidirect
102. #17985903C22semidirect
103. #17985903C22semidirect
104. #17985893C22semidirect
105. #17985893C22semidirect
106. #17985892C22semidirect
107. #17985892C22semidirect
108. #17985891C22semidirect
109. #17985891C22semidirect
110. #17985890C22semidirect
111. #17985890C22semidirect
112. #17985889C22semidirect
113. #17985889C22semidirect
114. #17985888C22semidirect
115. #17985888C22semidirect
116. #17985887C22semidirect
117. #17985887C22semidirect
132. #17985865C22semidirect
133. #17985864C22semidirect
134. #17985864C22semidirect
135. #17985863C22semidirect
136. #17985863C22semidirect
137. #17985863C22semidirect
138. #17985863C22semidirect
139. #17985862C22semidirect
140. #17985861C22semidirect
141. #17985861C22semidirect
142. #17985861C22semidirect
143. #17985861C22semidirect
144. #17985860C22semidirect
145. #17985860C22semidirect
146. C22⋊C4×Dic71C22semidirect
147. C22⋊C4×Dic71C22semidirect
148. C4×(C2×D71)⋊C4C22semidirect
149. C4×(C2×D71)⋊C4C22semidirect
150. C4×C22⋊Dic71C22semidirect
151. #17985846C22semidirect
152. #17985846C22semidirect
153. C2×C71⋊#95C22semidirect
154. C2×C71⋊#95C22semidirect
155. C2×C71⋊#95C22semidirect
170. #95×D71C22semidirect
171. #95×D71C22semidirect
172. #95×D71C22semidirect
173. #95×D71C22semidirect
175. C2×C22⋊Q8×C71C22semidirect
176. #400×C71C22semidirect
177. #400×C71C22semidirect
178. #397×C71C22semidirect
179. #393×C71C22semidirect
180. #391×C71C22semidirect
181. #388×C71C22semidirect
182. #388×C71C22semidirect
185. #382×C71C22semidirect
186. #381×C71C22semidirect
187. C4×C22⋊C4×C71C22semidirect
188. C2×#95×C71C22semidirect
847. D71#2488direct (N × H)
865. #2488D71direct (N × H)
879. C71C2×#2488semidirect
902. C2×C22⋊Q8C2×D71semidirect
933. #400C2×D71semidirect
934. #400C2×D71semidirect
942. #397C2×D71semidirect
950. #393C2×D71semidirect
958. #391C2×D71semidirect
973. #388C2×D71semidirect
974. #388C2×D71semidirect
998. #382C2×D71semidirect
1006. #381C2×D71semidirect
1014. C4×C22⋊C4C2×D71semidirect
1036. C2×#95C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#123×D712
C2×C22⋊Q8×D712
#225926732
#225926722
#225926712
#225926702
#225926692
#225926682
#225926672
#225926662
#225926652
#225926642
#225926632
#225926622
#225926612
#225926602
#225926592
#400×D712
#397×D712
#393×D712
#391×D712
#388×D712
#386×D712
#382×D712
#381×D712
C4×C22⋊C4×D712
C2×#95×D712
C71×#24882
C2×#248871