Finite Group Databasebeta

← #2574×D71 #32167685

Subgroups — #2574×D71 #32167685

Order 18176.

2334 conjugacy classes of subgroups.

The subgroup lattice has 1504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22593621C211yesmaximal, characteristic, complemented
2#22593620C211yesmaximal, characteristic, complemented
3#22593619C211yesmaximal, characteristic, complemented
4#22593618C211yesmaximal, characteristic, complemented
5#22593617C211yesmaximal, characteristic, complemented
6#22593616C211yesmaximal, characteristic, complemented
7#22593615C211yesmaximal, characteristic, complemented
8#22593614C211yesmaximal, characteristic, complemented
9#22593613C211yesmaximal, characteristic, complemented
10#22593612C211yesmaximal, characteristic, complemented
11#22593611C211yesmaximal, characteristic, complemented
12#22593610C211yesmaximal, characteristic, complemented
13#22593609C211yesmaximal, characteristic, complemented
14#22593608C211yesmaximal, characteristic, complemented
15#22593607C211yesmaximal, characteristic, complemented
16#398×D71C211yesmaximal, characteristic, complemented
17#396×D71C211yesmaximal, characteristic
18#395×D71C211yesmaximal, characteristic, complemented
19#393×D71C211yesmaximal, characteristic
20#391×D71C211yesmaximal, characteristic, complemented
21#388×D71C211yesmaximal, characteristic
22#388×D71C211yesmaximal, characteristic
23#387×D71C211yesmaximal, characteristic, complemented
24#387×D71C211yesmaximal, characteristic, complemented
25#387×D71C211yesmaximal, characteristic, complemented
26#385×D71C211yesmaximal, characteristic
27#382×D71C211yesmaximal, characteristic, complemented
28#380×D71C211yesmaximal, characteristic
29C4×C4⋊C4×D71C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D71C211yesmaximal, characteristic
31C71×#2574C211yesmaximal, characteristic, complemented
32C22×Q8×D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C2×C4⋊C4×D71C2211yescharacteristic
35C2×C4⋊C4×D71C2211yescharacteristic
36C2×C4⋊C4×D71C2211yescharacteristic
37C2×C4⋊C4×D71C2211yescharacteristic
38C2×C4⋊C4×D71C2211yescharacteristic
39C2×C4⋊C4×D71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43C2×C22⋊C4×D71C2211yescharacteristic
44C2×C22⋊C4×D71C2211yescharacteristic
45C2×C22⋊C4×D71C2211yescharacteristic
46C2×C22⋊C4×D71C2211yescharacteristic
47C2×C22⋊C4×D71C2211yescharacteristic
48C2×C22⋊C4×D71C2211yescharacteristic
49C2×C42×D71C2211yescharacteristic
50C2×C42×D71C2211yescharacteristic
51C2×C42×D71C2211yescharacteristic
52C2×C42×D71C2211yescharacteristic
53#17985933C2211yescharacteristic, complemented
54#17985933C2211yescharacteristic, complemented
55#17985932C2211yescharacteristic, complemented
56#17985932C2211yescharacteristic, complemented
57#17985931C2211yescharacteristic, complemented
58#17985930C2211yescharacteristic, complemented
59#17985929C2211yescharacteristic, complemented
60#17985923C2211yescharacteristic
61#17985922C2211yescharacteristic
62#17985922C2211yescharacteristic
63#17985922C2211yescharacteristic
64#17985921C2211yescharacteristic
65#17985921C2211yescharacteristic
66#17985921C2211yescharacteristic
67#17985920C2211yescharacteristic, complemented
68#17985920C2211yescharacteristic, complemented
69#17985920C2211yescharacteristic, complemented
70#17985919C2211yescharacteristic, complemented
71#17985919C2211yescharacteristic, complemented
72#17985919C2211yescharacteristic, complemented
73#17985918C2211yescharacteristic, complemented
74#17985912C2211yescharacteristic
75#17985912C2211yescharacteristic
76#17985912C2211yescharacteristic
77#17985911C2211yescharacteristic
78#17985911C2211yescharacteristic
79#17985911C2211yescharacteristic
80#17985910C2211yescharacteristic
81#17985906C2211yescharacteristic, complemented
82#17985905C2211yescharacteristic, complemented
83#17985904C2211yescharacteristic, complemented
84#17985903C2211yescharacteristic, complemented
85#17985903C2211yescharacteristic, complemented
86#17985903C2211yescharacteristic, complemented
87#17985903C2211yescharacteristic, complemented
88#17985893C2211yescharacteristic
89#17985893C2211yescharacteristic
90#17985892C2211yescharacteristic
91#17985892C2211yescharacteristic
92#17985891C2211yescharacteristic
93#17985891C2211yescharacteristic
94#17985890C2211yescharacteristic
95#17985890C2211yescharacteristic
96#17985889C2211yescharacteristic
97#17985889C2211yescharacteristic
98#17985888C2211yescharacteristic
99#17985888C2211yescharacteristic
100#17985887C2211yescharacteristic
101#17985887C2211yescharacteristic
102#17985886C2211yescharacteristic, complemented
103#17985886C2211yescharacteristic, complemented
104#17985886C2211yescharacteristic, complemented
105#17985885C2211yescharacteristic, complemented
106#17985885C2211yescharacteristic, complemented
107#17985885C2211yescharacteristic, complemented
108#17985884C2211yescharacteristic, complemented
109#17985884C2211yescharacteristic, complemented
110#17985884C2211yescharacteristic, complemented
111#17985883C2211yescharacteristic, complemented
112#17985883C2211yescharacteristic, complemented
113#17985883C2211yescharacteristic, complemented
114#17985882C2211yescharacteristic, complemented
115#17985882C2211yescharacteristic, complemented
116#17985882C2211yescharacteristic, complemented
117#17985881C2211yescharacteristic, complemented
118#17985881C2211yescharacteristic, complemented
119#17985881C2211yescharacteristic, complemented
120#17985880C2211yescharacteristic, complemented
121#17985880C2211yescharacteristic, complemented
122#17985880C2211yescharacteristic, complemented
123#17985874C2211yescharacteristic
124#17985873C2211yescharacteristic
125#17985873C2211yescharacteristic
126#17985872C2211yescharacteristic
127#17985871C2211yescharacteristic
128#17985870C2211yescharacteristic
129#17985870C2211yescharacteristic
130#17985865C2211yescharacteristic, complemented
131#17985864C2211yescharacteristic, complemented
132#17985864C2211yescharacteristic, complemented
133#17985863C2211yescharacteristic, complemented
134#17985863C2211yescharacteristic, complemented
135#17985863C2211yescharacteristic, complemented
136#17985863C2211yescharacteristic, complemented
137#17985859C2211yescharacteristic
138#17985858C2211yescharacteristic
139#17985858C2211yescharacteristic
140#17985857C2211yescharacteristic
141#17985857C2211yescharacteristic
142#17985856C2211yescharacteristic
143#17985856C2211yescharacteristic
144C4⋊C4×Dic71C2211yescharacteristic, complemented
145C4⋊C4×Dic71C2211yescharacteristic, complemented
146C4×Dic71⋊C4C2211yescharacteristic, complemented
147C4×Dic71⋊C4C2211yescharacteristic, complemented
148C4×C4⋊Dic71C2211yescharacteristic, complemented
149#17985850C2211yescharacteristic, complemented
150#17985850C2211yescharacteristic, complemented
151C22⋊C4×Dic71C2211yescharacteristic
152C22⋊C4×Dic71C2211yescharacteristic
153C4×(C2×D71)⋊C4C2211yescharacteristic
154C4×(C2×D71)⋊C4C2211yescharacteristic
155C4×C22⋊Dic71C2211yescharacteristic
156#17985846C2211yescharacteristic
157#17985846C2211yescharacteristic
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
171#95×D71C2211yescharacteristic
172#398×C71C2211yescharacteristic, complemented
173#396×C71C2211yescharacteristic
174#395×C71C2211yescharacteristic, complemented
175#393×C71C2211yescharacteristic
176#391×C71C2211yescharacteristic, complemented
177#388×C71C2211yescharacteristic
178#388×C71C2211yescharacteristic
179#387×C71C2211yescharacteristic, complemented
180#387×C71C2211yescharacteristic, complemented
181#387×C71C2211yescharacteristic, complemented
182#385×C71C2211yescharacteristic
183#382×C71C2211yescharacteristic, complemented
184#380×C71C2211yescharacteristic
185C4×C4⋊C4×C71C2211yescharacteristic, complemented
186C4×C22⋊C4×C71C2211yescharacteristic
187C24×D71C2311yescharacteristic
188C22×Dic142C2311yescharacteristic
189C22×Dic142C2311yescharacteristic
190C22×Dic142C2311yescharacteristic
191C2×Q8×D71—24no—
192C2×Q8×D71—42no—
193C2×Q8×D71—42no—
194C23×Dic71C2311yescharacteristic
195C22×C4×D71—24no—
196C22×C4×D71—24no—
197C22×C4×D71—42no—
198C22×C4×D71C2311yescharacteristic
199C22×C4×D71C2311yescharacteristic
200C22×C4×D71C2311yescharacteristic
201C22×C4×D71C2311yescharacteristic
202C22×C4×D71C2311yescharacteristic
203C22×C4×D71C2311yescharacteristic
204C22×C4×D71C2311yescharacteristic
205C22×C4×D71C2311yescharacteristic
206C22×C4×D71C2311yescharacteristic
207C22×C4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209C22×C4×D71C2311yescharacteristic
210C22×C4×D71C2311yescharacteristic
211C22×C4×D71C2311yescharacteristic
212C22×C4×D71C2311yescharacteristic
213C22×C4×D71C2311yescharacteristic
214C2×C4⋊Dic71C2311yescharacteristic
215C2×C4⋊Dic71C2311yescharacteristic
216C2×C4⋊Dic71C2311yescharacteristic
217C2×C4⋊Dic71C2311yescharacteristic
218C2×C4⋊Dic71C2311yescharacteristic
219C2×C4⋊Dic71C2311yescharacteristic
220C2×C4⋊Dic71C2311yescharacteristic
221C2×C4⋊Dic71C2311yescharacteristic
222C2×C4⋊Dic71C2311yescharacteristic
223C2×Dic71⋊C4C2311yescharacteristic
224C2×Dic71⋊C4C2311yescharacteristic
225C2×Dic71⋊C4C2311yescharacteristic
226C2×Dic71⋊C4C2311yescharacteristic
227C2×Dic71⋊C4C2311yescharacteristic
228C2×Dic71⋊C4C2311yescharacteristic
229C2×Dic71⋊C4C2311yescharacteristic
230C2×Dic71⋊C4C2311yescharacteristic
231C2×Dic71⋊C4C2311yescharacteristic
232C2×Dic71⋊C4C2311yescharacteristic
233C2×Dic71⋊C4C2311yescharacteristic
234C2×Dic71⋊C4C2311yescharacteristic
235C2×Dic71⋊C4C2311yescharacteristic
236C2×Dic71⋊C4C2311yescharacteristic
237C2×Dic71⋊C4C2311yescharacteristic
238C2×Dic71⋊C4C2311yescharacteristic
239C2×Dic71⋊C4C2311yescharacteristic
240C2×Dic71⋊C4C2311yescharacteristic
241C4⋊C4×D71—24no—
242C4⋊C4×D71—24no—
243C4⋊C4×D71—24no—
244C4⋊C4×D71—24no—
245C4⋊C4×D71—24no—
246C4⋊C4×D71—42no—
247C4⋊C4×D71—42no—
248C4⋊C4×D71—42no—
249C4⋊C4×D71—42no—
250C2×C22⋊Dic71C2311yescharacteristic
251C2×C22⋊Dic71C2311yescharacteristic
252C2×C22⋊Dic71C2311yescharacteristic
253C2×C22⋊Dic71C2311yescharacteristic
254C2×C22⋊Dic71C2311yescharacteristic
255C2×C22⋊Dic71C2311yescharacteristic
256C2×(C2×D71)⋊C4C2311yescharacteristic
257C2×(C2×D71)⋊C4C2311yescharacteristic
258C2×(C2×D71)⋊C4C2311yescharacteristic
259C2×(C2×D71)⋊C4C2311yescharacteristic
260C2×(C2×D71)⋊C4C2311yescharacteristic
261C2×(C2×D71)⋊C4C2311yescharacteristic
262C2×(C2×D71)⋊C4C2311yescharacteristic
263C2×(C2×D71)⋊C4C2311yescharacteristic
264C2×(C2×D71)⋊C4C2311yescharacteristic
265C2×(C2×D71)⋊C4C2311yescharacteristic
266C2×(C2×D71)⋊C4C2311yescharacteristic
267C2×(C2×D71)⋊C4C2311yescharacteristic
268C22⋊C4×D71—24no—
269C22⋊C4×D71—24no—
270C22⋊C4×D71—42no—
271C22⋊C4×D71—42no—
272C22⋊C4×D71—42no—
273C22⋊C4×D71Q818yescomplemented
274C2×C4×Dic71C2311yescharacteristic
275C2×C4×Dic71C2311yescharacteristic
276C2×C4×Dic71C2311yescharacteristic
277C2×C4×Dic71C2311yescharacteristic
278C2×C4×Dic71C2311yescharacteristic
279C2×C4×Dic71C2311yescharacteristic
280C2×C4×Dic71C2311yescharacteristic
281C2×C4×Dic71C2311yescharacteristic
282C2×C4×Dic71C2311yescharacteristic
283C2×C4×Dic71C2311yescharacteristic
284C2×C4×Dic71C2311yescharacteristic
285C2×C4×Dic71C2311yescharacteristic
286C42×D71—24no—
287C42×D71—24no—
288C42×D71—42no—
289C42×D71—42no—
290C71⋊#95C2311yescharacteristic
291C71⋊#95C2311yescharacteristic
292C71⋊#95C2311yescharacteristic
293C71⋊#95C2311yescharacteristic
294C71⋊#95C2311yescharacteristic
295C71⋊#95C2311yescharacteristic
296C71⋊#95C2311yescharacteristic
297C71⋊#95C2311yescharacteristic
298C71⋊#95C2311yescharacteristic
299C71⋊#95C2311yescharacteristic
300C71⋊#95C2311yescharacteristic
301C71⋊#95C2311yescharacteristic
302C71⋊#95C2311yescharacteristic
303C71⋊#95C2311yescharacteristic
304C71⋊#95C2311yescharacteristic
305C71⋊#95C2311yescharacteristic
306C71⋊#95C2311yescharacteristic
307C71⋊#95C2311yescharacteristic
308C71⋊#95C2311yescharacteristic
309C71⋊#95C2311yescharacteristic
310C71⋊#95C2311yescharacteristic
311C71⋊#95C2311yescharacteristic
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
332C22×Q8×C71C2311yescharacteristic
333C23×C4×C71C2311yescharacteristic
334C2×C4⋊C4×C71C2311yescharacteristic
335C2×C4⋊C4×C71C2311yescharacteristic
336C2×C4⋊C4×C71C2311yescharacteristic
337C2×C4⋊C4×C71C2311yescharacteristic
338C2×C4⋊C4×C71C2311yescharacteristic
339C2×C4⋊C4×C71C2311yescharacteristic
340C2×C4⋊C4×C71C2311yescharacteristic
341C2×C4⋊C4×C71C2311yescharacteristic
342C2×C4⋊C4×C71C2311yescharacteristic
343C2×C22⋊C4×C71C2311yescharacteristic
344C2×C22⋊C4×C71C2311yescharacteristic
345C2×C22⋊C4×C71C2311yescharacteristic
346C2×C22⋊C4×C71C2311yescharacteristic
347C2×C22⋊C4×C71C2311yescharacteristic
348C2×C22⋊C4×C71C2311yescharacteristic
349C2×C42×C71C2311yescharacteristic
350C2×C42×C71C2311yescharacteristic
351C2×C42×C71C2311yescharacteristic
352C2×C42×C71C2311yescharacteristic
353#95×C71C2311yescharacteristic
354#95×C71C2311yescharacteristic
355#95×C71C2311yescharacteristic
356#95×C71C2311yescharacteristic
357#95×C71C2311yescharacteristic
358#95×C71C2311yescharacteristic
359#95×C71C2311yescharacteristic
360#95×C71C2311yescharacteristic
361#95×C71C2311yescharacteristic
362#95×C71C2311yescharacteristic
363#95×C71C2311yescharacteristic
364#95×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367C23×D71—22no—
368C23×D71—22no—
369C23×D71—22no—
370C23×D71—22no—
371C23×D71—22no—
372C23×D71—22no—
373C23×D71C2×Q814yes—
374C23×D71C2411yescharacteristic
375C23×D71C2411yescharacteristic
376C2×Dic142—22no—
377C2×Dic142—22no—
378C2×Dic142—22no—
379C2×Dic142—41no—
380C2×Dic142—41no—
381C2×Dic142—41no—
382C2×Dic142—41no—
383C2×Dic142—41no—
384C2×Dic142—41no—
385Q8×D71—416no—
386C22×Dic71—22no—
387C22×Dic71—22no—
388C22×Dic71—41no—
389C22×Dic71C2411yescharacteristic
390C22×Dic71C2411yescharacteristic
391C22×Dic71C2411yescharacteristic
392C22×Dic71C2411yescharacteristic
393C22×Dic71C2411yescharacteristic
394C22×Dic71C2411yescharacteristic
395C22×Dic71C2411yescharacteristic
396C22×Dic71C2411yescharacteristic
397C22×Dic71C2411yescharacteristic
398C22×Dic71C2411yescharacteristic
399C22×Dic71C2411yescharacteristic
400C22×Dic71C2411yescharacteristic
401C22×Dic71C2411yescharacteristic
402C22×Dic71C2411yescharacteristic
403C2×C4×D71—22no—
404C2×C4×D71—22no—
405C2×C4×D71—22no—
406C2×C4×D71—22no—
407C2×C4×D71—22no—
408C2×C4×D71—22no—
409C2×C4×D71—22no—
410C2×C4×D71—22no—
411C2×C4×D71—22no—
412C2×C4×D71—22no—
413C2×C4×D71—22no—
414C2×C4×D71—22no—
415C2×C4×D71—22no—
416C2×C4×D71—22no—
417C2×C4×D71—22no—
418C2×C4×D71—22no—
419C2×C4×D71—22no—
420C2×C4×D71—22no—
421C2×C4×D71—22no—
422C2×C4×D71—22no—
423C2×C4×D71—22no—
424C2×C4×D71—22no—
425C2×C4×D71—22no—
426C2×C4×D71—22no—
427C2×C4×D71—22no—
428C2×C4×D71—22no—
429C2×C4×D71—22no—
430C2×C4×D71—22no—
431C2×C4×D71—22no—
432C2×C4×D71—22no—
433C2×C4×D71—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—22no—
437C2×C4×D71—22no—
438C2×C4×D71—22no—
439C2×C4×D71—22no—
440C2×C4×D71—22no—
441C2×C4×D71—22no—
442C2×C4×D71—22no—
443C2×C4×D71—416no—
444C2×C4×D71—41no—
445C2×C4×D71—41no—
446C2×C4×D71C2×Q814yes—
447C2×C4×D71C2×Q814yes—
448C2×C4×D71#4114yes—
449C2×C4×D71#4114yes—
450C2×C4×D71#4114yes—
451C2×C4×D71#4114yes—
452C4⋊Dic71—22no—
453C4⋊Dic71—22no—
454C4⋊Dic71—22no—
455C4⋊Dic71—22no—
456C4⋊Dic71—22no—
457C4⋊Dic71—41no—
458C4⋊Dic71—41no—
459C4⋊Dic71—41no—
460C4⋊Dic71—41no—
461Dic71⋊C4—22no—
462Dic71⋊C4—22no—
463Dic71⋊C4—22no—
464Dic71⋊C4—22no—
465Dic71⋊C4—22no—
466Dic71⋊C4—22no—
467Dic71⋊C4—22no—
468Dic71⋊C4—22no—
469Dic71⋊C4—22no—
470Dic71⋊C4—22no—
471Dic71⋊C4—41no—
472Dic71⋊C4—41no—
473Dic71⋊C4—41no—
474Dic71⋊C4—41no—
475Dic71⋊C4—41no—
476Dic71⋊C4—41no—
477Dic71⋊C4—41no—
478Dic71⋊C4—41no—
479C22⋊Dic71—22no—
480C22⋊Dic71—22no—
481C22⋊Dic71—41no—
482C22⋊Dic71—41no—
483C22⋊Dic71—41no—
484C22⋊Dic71C2×Q814yescomplemented
485(C2×D71)⋊C4—22no—
486(C2×D71)⋊C4—22no—
487(C2×D71)⋊C4—22no—
488(C2×D71)⋊C4—22no—
489(C2×D71)⋊C4—41no—
490(C2×D71)⋊C4—41no—
491(C2×D71)⋊C4—41no—
492(C2×D71)⋊C4—41no—
493(C2×D71)⋊C4—41no—
494(C2×D71)⋊C4—41no—
495(C2×D71)⋊C4C2×Q814yescomplemented
496(C2×D71)⋊C4C2×Q814yescomplemented
497C4×Dic71—22no—
498C4×Dic71—22no—
499C4×Dic71—22no—
500C4×Dic71—22no—
501C4×Dic71—22no—
502C4×Dic71—22no—
503C4×Dic71—41no—
504C4×Dic71—41no—
505C4×Dic71—41no—
506C4×Dic71—41no—
507C4×Dic71—41no—
508C4×Dic71—41no—
509C24×C71C2411yescharacteristic
510C2×Q8×C71—22no—
511C2×Q8×C71—41no—
512C2×Q8×C71—41no—
513C22×C4×C71—22no—
514C22×C4×C71—22no—
515C22×C4×C71—41no—
516C22×C4×C71C2411yescharacteristic
517C22×C4×C71C2411yescharacteristic
518C22×C4×C71C2411yescharacteristic
519C22×C4×C71C2411yescharacteristic
520C22×C4×C71C2411yescharacteristic
521C22×C4×C71C2411yescharacteristic
522C22×C4×C71C2411yescharacteristic
523C22×C4×C71C2411yescharacteristic
524C22×C4×C71C2411yescharacteristic
525C22×C4×C71C2411yescharacteristic
526C22×C4×C71C2411yescharacteristic
527C22×C4×C71C2411yescharacteristic
528C22×C4×C71C2411yescharacteristic
529C22×C4×C71C2411yescharacteristic
530C4⋊C4×C71—22no—
531C4⋊C4×C71—22no—
532C4⋊C4×C71—22no—
533C4⋊C4×C71—22no—
534C4⋊C4×C71—22no—
535C4⋊C4×C71—41no—
536C4⋊C4×C71—41no—
537C4⋊C4×C71—41no—
538C4⋊C4×C71—41no—
539C22⋊C4×C71—22no—
540C22⋊C4×C71—22no—
541C22⋊C4×C71—41no—
542C22⋊C4×C71—41no—
543C22⋊C4×C71—41no—
544C22⋊C4×C71C2×Q814yescomplemented
545C42×C71—22no—
546C42×C71—22no—
547C42×C71—41no—
548C42×C71—41no—
549C23×C71—21no—
550C23×C71—21no—
551C23×C71—21no—
552C23×C71—21no—
553C23×C71—21no—
554C23×C71—21no—
555C23×C71C22×Q812yes—
556C23×C71C2511yescharacteristic
557C22×D71—21no—
558C22×D71—21no—
559C22×D71—21no—
560C22×D71—21no—
561C22×D71—21no—
562C22×D71—21no—
563C22×D71—28no—
564C22×D71—28no—
565C22×D71—28no—
566C22×D71—44no—
567C22×D71—44no—
568C22×D71—44no—
569C22×D71—44no—
570C22×D71C22×Q812yes—
571C22×D71C22×Q812yes—
572C22×D71C2×#4112yes—
573C22×D71C2×#4112yes—
574C22×D71C2×#4112yes—
575C22×D71C2×#4112yes—
576C22×D71H(5,𝔽2)12yes—
577C22×D71H(5,𝔽2)12yes—
578Q8×C71—44no—
579C2×C4×C71—21no—
580C2×C4×C71—21no—
581C2×C4×C71—21no—
582C2×C4×C71—21no—
583C2×C4×C71—21no—
584C2×C4×C71—21no—
585C2×C4×C71—21no—
586C2×C4×C71—21no—
587C2×C4×C71—21no—
588C2×C4×C71—21no—
589C2×C4×C71—21no—
590C2×C4×C71—21no—
591C2×C4×C71—21no—
592C2×C4×C71—21no—
593C2×C4×C71—21no—
594C2×C4×C71—21no—
595C2×C4×C71—21no—
596C2×C4×C71—21no—
597C2×C4×C71—21no—
598C2×C4×C71—21no—
599C2×C4×C71—21no—
600C2×C4×C71—21no—
601C2×C4×C71—21no—
602C2×C4×C71—21no—
603C2×C4×C71—21no—
604C2×C4×C71—21no—
605C2×C4×C71—21no—
606C2×C4×C71—21no—
607C2×C4×C71—21no—
608C2×C4×C71—21no—
609C2×C4×C71—21no—
610C2×C4×C71—21no—
611C2×C4×C71—21no—
612C2×C4×C71—21no—
613C2×C4×C71—21no—
614C2×C4×C71—21no—
615C2×C4×C71—44no—
616C2×C4×C71C22×Q812yes—
617C2×C4×C71C22×Q812yes—
618C2×C4×C71C2×#4112yes—
619C2×C4×C71C2×#4112yes—
620C2×C4×C71C2×#4112yes—
621C2×C4×C71C2×#4112yes—
622C2×Dic71—21no—
623C2×Dic71—21no—
624C2×Dic71—21no—
625C2×Dic71—21no—
626C2×Dic71—21no—
627C2×Dic71—21no—
628C2×Dic71—21no—
629C2×Dic71—21no—
630C2×Dic71—21no—
631C2×Dic71—21no—
632C2×Dic71—21no—
633C2×Dic71—21no—
634C2×Dic71—21no—
635C2×Dic71—21no—
636C2×Dic71—21no—
637C2×Dic71—21no—
638C2×Dic71—21no—
639C2×Dic71—21no—
640C2×Dic71—21no—
641C2×Dic71—21no—
642C2×Dic71—21no—
643C2×Dic71—21no—
644C2×Dic71—21no—
645C2×Dic71—21no—
646C2×Dic71—21no—
647C2×Dic71—21no—
648C2×Dic71—21no—
649C2×Dic71—21no—
650C2×Dic71—21no—
651C2×Dic71—21no—
652C2×Dic71—21no—
653C2×Dic71—21no—
654C2×Dic71—21no—
655C2×Dic71—21no—
656C2×Dic71—21no—
657C2×Dic71—21no—
658C2×Dic71—44no—
659C2×Dic71C22×Q812yes—
660C2×Dic71C22×Q812yes—
661C2×Dic71C2×#4112yes—
662C2×Dic71C2×#4112yes—
663C2×Dic71C2×#4112yes—
664C2×Dic71C2×#4112yes—
665C4×D71—28no—
666C4×D71—28no—
667C4×D71—28no—
668C4×D71—28no—
669C4×D71—28no—
670C4×D71—28no—
671C4×D71—44no—
672C4×D71—44no—
673C4×D71—44no—
674C4×D71—44no—
675C4×D71—44no—
676C4×D71—44no—
677C4×D71—44no—
678C4×D71—44no—
679C4×D71—44no—
680C4×D71—44no—
681Dic142—44no—
682Dic142—44no—
683Dic142—44no—
684C22×C71—22no—
685C22×C71—22no—
686C22×C71—22no—
687C22×C71—41no—
688C22×C71—41no—
689C22×C71—41no—
690C22×C71—41no—
691C22×C71C23×Q811yescharacteristic
692C22×C71C22×#4111yescharacteristic
693C22×C71C22×#4111yescharacteristic
694C22×C71C22×#4111yescharacteristic
695C22×C71C22×#4111yescharacteristic
696C22×C71C2×H(5,𝔽2)11yescharacteristic
697C22×C71C2×H(5,𝔽2)11yescharacteristic
698C2×D71—22no—
699C2×D71—22no—
700C2×D71—22no—
701C2×D71—41no—
702C2×D71—41no—
703C2×D71—41no—
704C2×D71—41no—
705C2×D71—416no—
706C2×D71#52914yes—
707C2×D71#53314yes—
708C2×D71#53814yes—
709C2×D71#55114yes—
710C2×D71#55414yes—
711C2×D71#55414yes—
712C2×D71#55514yes—
713C4×C71—22no—
714C4×C71—22no—
715C4×C71—22no—
716C4×C71—22no—
717C4×C71—22no—
718C4×C71—22no—
719C4×C71—41no—
720C4×C71—41no—
721C4×C71—41no—
722C4×C71—41no—
723C4×C71—41no—
724C4×C71—41no—
725C4×C71—41no—
726C4×C71—41no—
727Dic71—22no—
728Dic71—22no—
729Dic71—22no—
730Dic71—22no—
731Dic71—22no—
732Dic71—22no—
733Dic71—41no—
734Dic71—41no—
735Dic71—41no—
736Dic71—41no—
737Dic71—41no—
738Dic71—41no—
739Dic71—41no—
740Dic71—41no—
741C2×#2574—711nomaximal, Sylow
742C2×C71—42no—
743C2×C71C2×#52911yescharacteristic
744C2×C71C2×#53311yescharacteristic
745C2×C71C2×#53811yescharacteristic
746C2×C71C2×#55111yescharacteristic
747C2×C71C2×#55411yescharacteristic
748C2×C71C2×#55411yescharacteristic
749C2×C71C2×#55511yescharacteristic
750D71—42no—
751D71#257418yesdirect product factor
752#2574—711no—
753#2574—711no—
754#2574—711no—
755#2574—711no—
756#2574—711no—
757#2574—711no—
758#2574—711no—
759#2574—711no—
760#2574—711no—
761#2574—711no—
762#2574—711no—
763#2574—711no—
764#2574—711no—
765#2574—711no—
766#2574—711no—
767#2574D7111yescharacteristic, direct product factor
768C2×#398—711no—
769C2×#396—711no—
770C2×#395—711no—
771C2×#393—711no—
772C2×#391—711no—
773C2×#388—711no—
774C2×#388—711no—
775C2×#387—711no—
776C2×#387—711no—
777C2×#387—711no—
778C2×#385—711no—
779C2×#382—711no—
780C2×#380—711no—
781C2×C4×C4⋊C4—711no—
782C2×C4×C22⋊C4—711no—
783C71C2×#257411yescharacteristic, complemented, Sylow
784C23×Q8—711no—
785C24×C4—711no—
786C22×C4⋊C4—711no—
787C22×C4⋊C4—711no—
788C22×C4⋊C4—711no—
789C22×C4⋊C4—711no—
790C22×C4⋊C4—711no—
791C22×C4⋊C4—711no—
792C22×C4⋊C4—711no—
793C22×C4⋊C4—711no—
794C22×C4⋊C4—711no—
795C22×C22⋊C4—711no—
796C22×C22⋊C4—711no—
797C22×C22⋊C4—711no—
798C22×C22⋊C4—711no—
799C22×C22⋊C4—711no—
800C22×C22⋊C4—711no—
801C22×C42—711no—
802C22×C42—711no—
803C22×C42—711no—
804C22×C42—711no—
805#398—711no—
806#398—711no—
807#398—711no—
808#398—711no—
809#398—711no—
810#398—711no—
811#398—711no—
812#398C2×D7111yescharacteristic, complemented
813#396—711no—
814#396—711no—
815#396—711no—
816#396—711no—
817#396—711no—
818#396—711no—
819#396—711no—
820#396C2×D7111yescharacteristic
821#395—711no—
822#395—711no—
823#395—711no—
824#395—711no—
825#395—711no—
826#395—711no—
827#395—711no—
828#395C2×D7111yescharacteristic, complemented
829#393—711no—
830#393—711no—
831#393—711no—
832#393—711no—
833#393—711no—
834#393—711no—
835#393—711no—
836#393C2×D7111yescharacteristic
837#391—711no—
838#391—711no—
839#391—711no—
840#391—711no—
841#391—711no—
842#391—711no—
843#391—711no—
844#391C2×D7111yescharacteristic, complemented
845#388—711no—
846#388—711no—
847#388—711no—
848#388—711no—
849#388—711no—
850#388—711no—
851#388—711no—
852#388—711no—
853#388—711no—
854#388—711no—
855#388—711no—
856#388—711no—
857#388—711no—
858#388—711no—
859#388C2×D7111yescharacteristic
860#388C2×D7111yescharacteristic
861#387—711no—
862#387—711no—
863#387—711no—
864#387—711no—
865#387—711no—
866#387—711no—
867#387—711no—
868#387—711no—
869#387—711no—
870#387—711no—
871#387—711no—
872#387—711no—
873#387—711no—
874#387—711no—
875#387—711no—
876#387—711no—
877#387—711no—
878#387—711no—
879#387—711no—
880#387—711no—
881#387—711no—
882#387C2×D7111yescharacteristic, complemented
883#387C2×D7111yescharacteristic, complemented
884#387C2×D7111yescharacteristic, complemented
885#385—711no—
886#385—711no—
887#385—711no—
888#385—711no—
889#385—711no—
890#385—711no—
891#385—711no—
892#385C2×D7111yescharacteristic
893#382—711no—
894#382—711no—
895#382—711no—
896#382—711no—
897#382—711no—
898#382—711no—
899#382—711no—
900#382C2×D7111yescharacteristic, complemented
901#380—711no—
902#380—711no—
903#380—711no—
904#380—711no—
905#380—711no—
906#380—711no—
907#380—711no—
908#380C2×D7111yescharacteristic
909C4×C4⋊C4—711no—
910C4×C4⋊C4—711no—
911C4×C4⋊C4—711no—
912C4×C4⋊C4—711no—
913C4×C4⋊C4—711no—
914C4×C4⋊C4—711no—
915C4×C4⋊C4—711no—
916C4×C4⋊C4C2×D7111yescharacteristic, complemented
917C4×C22⋊C4—711no—
918C4×C22⋊C4—711no—
919C4×C22⋊C4—711no—
920C4×C22⋊C4—711no—
921C4×C22⋊C4—711no—
922C4×C22⋊C4—711no—
923C4×C22⋊C4—711no—
924C4×C22⋊C4C2×D7111yescharacteristic
925C2×#95—711no—
926C2×#95—711no—
927C2×#95—711no—
928C2×#95—711no—
929C2×#95—711no—
930C2×#95—711no—
931C2×#95—711no—
932C2×#95—711no—
933C2×#95—711no—
934C2×#95—711no—
935C2×#95—711no—
936C2×#95—711no—
937C2×#95—711no—
938C2×#95—711no—
939C25—711no—
940C22×Q8—2842no—
941C22×Q8—2842no—
942C22×Q8—711no—
943C22×Q8—711no—
944C22×Q8—711no—
945C22×Q8—1424no—
946C22×Q8C22×D7111yescharacteristic
947C23×C4—2842no—
948C23×C4—711no—
949C23×C4—711no—
950C23×C4—711no—
951C23×C4—711no—
952C23×C4—711no—
953C23×C4—711no—
954C23×C4—711no—
955C23×C4—711no—
956C23×C4—711no—
957C23×C4—711no—
958C23×C4—711no—
959C23×C4—711no—
960C23×C4—711no—
961C23×C4—711no—
962C23×C4—711no—
963C23×C4—711no—
964C23×C4—711no—
965C23×C4—1424no—
966C23×C4—1424no—
967C23×C4C22×D7111yescharacteristic
968C2×C4⋊C4—2842no—
969C2×C4⋊C4—2842no—
970C2×C4⋊C4—2842no—
971C2×C4⋊C4—2842no—
972C2×C4⋊C4—711no—
973C2×C4⋊C4—711no—
974C2×C4⋊C4—711no—
975C2×C4⋊C4—711no—
976C2×C4⋊C4—711no—
977C2×C4⋊C4—711no—
978C2×C4⋊C4—711no—
979C2×C4⋊C4—711no—
980C2×C4⋊C4—711no—
981C2×C4⋊C4—711no—
982C2×C4⋊C4—711no—
983C2×C4⋊C4—711no—
984C2×C4⋊C4—711no—
985C2×C4⋊C4—711no—
986C2×C4⋊C4—711no—
987C2×C4⋊C4—711no—
988C2×C4⋊C4—711no—
989C2×C4⋊C4—711no—
990C2×C4⋊C4—711no—
991C2×C4⋊C4—711no—
992C2×C4⋊C4—711no—
993C2×C4⋊C4—711no—
994C2×C4⋊C4—711no—
995C2×C4⋊C4—711no—
996C2×C4⋊C4—711no—
997C2×C4⋊C4—711no—
998C2×C4⋊C4—711no—
999C2×C4⋊C4—1424no—
1000C2×C4⋊C4—1424no—
1001C2×C4⋊C4—1424no—
1002C2×C4⋊C4—1424no—
1003C2×C4⋊C4—1424no—
1004C2×C4⋊C4C22×D7111yescharacteristic
1005C2×C4⋊C4C22×D7111yescharacteristic
1006C2×C4⋊C4C22×D7111yescharacteristic
1007C2×C4⋊C4C22×D7111yescharacteristic
1008C2×C4⋊C4C22×D7111yescharacteristic
1009C2×C4⋊C4C22×D7111yescharacteristic
1010C2×C4⋊C4C22×D7111yescharacteristic
1011C2×C4⋊C4C22×D7111yescharacteristic
1012C2×C4⋊C4C22×D7111yescharacteristic
1013C2×C22⋊C4—2842no—
1014C2×C22⋊C4—2842no—
1015C2×C22⋊C4—2842no—
1016C2×C22⋊C4—711no—
1017C2×C22⋊C4—711no—
1018C2×C22⋊C4—711no—
1019C2×C22⋊C4—711no—
1020C2×C22⋊C4—711no—
1021C2×C22⋊C4—711no—
1022C2×C22⋊C4—711no—
1023C2×C22⋊C4—711no—
1024C2×C22⋊C4—711no—
1025C2×C22⋊C4—711no—
1026C2×C22⋊C4—711no—
1027C2×C22⋊C4—711no—
1028C2×C22⋊C4—718no—
1029C2×C22⋊C4—711no—
1030C2×C22⋊C4—711no—
1031C2×C22⋊C4—711no—
1032C2×C22⋊C4—711no—
1033C2×C22⋊C4—711no—
1034C2×C22⋊C4—711no—
1035C2×C22⋊C4—1424no—
1036C2×C22⋊C4—1424no—
1037C2×C22⋊C4C22×D7111yescharacteristic
1038C2×C22⋊C4C22×D7111yescharacteristic
1039C2×C22⋊C4C22×D7111yescharacteristic
1040C2×C22⋊C4C22×D7111yescharacteristic
1041C2×C22⋊C4C22×D7111yescharacteristic
1042C2×C22⋊C4C22×D7111yescharacteristic
1043C2×C42—2842no—
1044C2×C42—2842no—
1045C2×C42—711no—
1046C2×C42—711no—
1047C2×C42—711no—
1048C2×C42—711no—
1049C2×C42—711no—
1050C2×C42—711no—
1051C2×C42—711no—
1052C2×C42—711no—
1053C2×C42—711no—
1054C2×C42—711no—
1055C2×C42—711no—
1056C2×C42—711no—
1057C2×C42—1424no—
1058C2×C42—1424no—
1059C2×C42C22×D7111yescharacteristic
1060C2×C42C22×D7111yescharacteristic
1061C2×C42C22×D7111yescharacteristic
1062C2×C42C22×D7111yescharacteristic
1063#95—711no—
1064#95—711no—
1065#95—711no—
1066#95—711no—
1067#95—711no—
1068#95—711no—
1069#95—711no—
1070#95—711no—
1071#95—711no—
1072#95—711no—
1073#95—711no—
1074#95—711no—
1075#95—711no—
1076#95—711no—
1077#95—711no—
1078#95—711no—
1079#95—711no—
1080#95—711no—
1081#95—711no—
1082#95—711no—
1083#95—711no—
1084#95—711no—
1085#95—711no—
1086#95—711no—
1087#95—711no—
1088#95—711no—
1089#95—711no—
1090#95—711no—
1091#95—711no—
1092#95—711no—
1093#95—711no—
1094#95—711no—
1095#95—711no—
1096#95—711no—
1097#95—711no—
1098#95—711no—
1099#95—711no—
1100#95—711no—
1101#95—711no—
1102#95—711no—
1103#95—711no—
1104#95—711no—
1105#95C22×D7111yescharacteristic
1106#95C22×D7111yescharacteristic
1107#95C22×D7111yescharacteristic
1108#95C22×D7111yescharacteristic
1109#95C22×D7111yescharacteristic
1110#95C22×D7111yescharacteristic
1111#95C22×D7111yescharacteristic
1112#95C22×D7111yescharacteristic
1113#95C22×D7111yescharacteristic
1114#95C22×D7111yescharacteristic
1115#95C22×D7111yescharacteristic
1116#95C22×D7111yescharacteristic
1117#95C22×D7111yescharacteristic
1118#95C22×D7111yescharacteristic
1119C24—711no—
1120C24—714no—
1121C24—711no—
1122C24—1422no—
1123C24—1422no—
1124C24—1422no—
1125C24—1422no—
1126C24—1422no—
1127C24—1422no—
1128C24C23×D7111yescharacteristic
1129C2×Q8—22no—
1130C2×Q8—41no—
1131C2×Q8—41no—
1132C2×Q8—2841no—
1133C2×Q8—2841no—
1134C2×Q8—2841no—
1135C2×Q8—2841no—
1136C2×Q8—2841no—
1137C2×Q8—2841no—
1138C2×Q8—28416no—
1139C2×Q8—1422no—
1140C2×Q8—1422no—
1141C2×Q8—1422no—
1142C22×C4—22no—
1143C22×C4—22no—
1144C22×C4—41no—
1145C22×C4—2841no—
1146C22×C4—2841no—
1147C22×C4—28416no—
1148C22×C4—2841no—
1149C22×C4—711no—
1150C22×C4—711no—
1151C22×C4—711no—
1152C22×C4—711no—
1153C22×C4—711no—
1154C22×C4—711no—
1155C22×C4—714no—
1156C22×C4—714no—
1157C22×C4—714no—
1158C22×C4—714no—
1159C22×C4—714no—
1160C22×C4—714no—
1161C22×C4—711no—
1162C22×C4—711no—
1163C22×C4—711no—
1164C22×C4—711no—
1165C22×C4—711no—
1166C22×C4—711no—
1167C22×C4—711no—
1168C22×C4—711no—
1169C22×C4—1422no—
1170C22×C4—1422no—
1171C22×C4—1422no—
1172C22×C4—1422no—
1173C22×C4—1422no—
1174C22×C4—1422no—
1175C22×C4—1422no—
1176C22×C4—1422no—
1177C22×C4—1422no—
1178C22×C4—1422no—
1179C22×C4—1422no—
1180C22×C4—1422no—
1181C22×C4—1422no—
1182C22×C4—1422no—
1183C22×C4—1422no—
1184C22×C4—1422no—
1185C22×C4—1422no—
1186C22×C4—1422no—
1187C22×C4—1422no—
1188C22×C4—1422no—
1189C22×C4—1422no—
1190C22×C4—1422no—
1191C22×C4—1422no—
1192C22×C4—1422no—
1193C22×C4—1422no—
1194C22×C4—1422no—
1195C22×C4—1422no—
1196C22×C4—1422no—
1197C22×C4—1422no—
1198C22×C4—1422no—
1199C22×C4—1422no—
1200C22×C4—1422no—
1201C22×C4—1422no—
1202C22×C4—1422no—
1203C22×C4—1422no—
1204C22×C4—1422no—
1205C22×C4—1422no—
1206C22×C4—1422no—
1207C22×C4—1422no—
1208C22×C4—1422no—
1209C22×C4—1422no—
1210C22×C4—1422no—
1211C22×C4C23×D7111yescharacteristic
1212C22×C4C23×D7111yescharacteristic
1213C22×C4C23×D7111yescharacteristic
1214C22×C4C23×D7111yescharacteristic
1215C22×C4C23×D7111yescharacteristic
1216C22×C4C23×D7111yescharacteristic
1217C22×C4C23×D7111yescharacteristic
1218C22×C4C23×D7111yescharacteristic
1219C22×C4C23×D7111yescharacteristic
1220C22×C4C23×D7111yescharacteristic
1221C22×C4C23×D7111yescharacteristic
1222C22×C4C23×D7111yescharacteristic
1223C22×C4C23×D7111yescharacteristic
1224C22×C4C23×D7111yescharacteristic
1225C4⋊C4—22no—
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—41no—
1231C4⋊C4—41no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—2841no—
1235C4⋊C4—2841no—
1236C4⋊C4—2841no—
1237C4⋊C4—2841no—
1238C4⋊C4—2841no—
1239C4⋊C4—2841no—
1240C4⋊C4—2841no—
1241C4⋊C4—2841no—
1242C4⋊C4—2841no—
1243C4⋊C4—2841no—
1244C4⋊C4—2841no—
1245C4⋊C4—2841no—
1246C4⋊C4—1422no—
1247C4⋊C4—1422no—
1248C4⋊C4—1422no—
1249C4⋊C4—1422no—
1250C4⋊C4—1422no—
1251C4⋊C4—1422no—
1252C4⋊C4—1422no—
1253C4⋊C4—1422no—
1254C4⋊C4—1422no—
1255C4⋊C4—1422no—
1256C4⋊C4—1422no—
1257C4⋊C4—1422no—
1258C4⋊C4—1422no—
1259C4⋊C4—1422no—
1260C4⋊C4—1422no—
1261C22⋊C4—22no—
1262C22⋊C4—22no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—2841no—
1267C22⋊C4—2841no—
1268C22⋊C4—2841no—
1269C22⋊C4—2841no—
1270C22⋊C4—2841no—
1271C22⋊C4—2841no—
1272C22⋊C4—2841no—
1273C22⋊C4—2841no—
1274C22⋊C4—2841no—
1275C22⋊C4—714no—
1276C22⋊C4—714no—
1277C22⋊C4—714no—
1278C22⋊C4—1422no—
1279C22⋊C4—1422no—
1280C22⋊C4—1422no—
1281C22⋊C4—1422no—
1282C22⋊C4—1422no—
1283C22⋊C4—1422no—
1284C22⋊C4Q8×D7114yescomplemented
1285C42—22no—
1286C42—22no—
1287C42—41no—
1288C42—41no—
1289C42—2841no—
1290C42—2841no—
1291C42—2841no—
1292C42—2841no—
1293C42—2841no—
1294C42—2841no—
1295C42—1422no—
1296C42—1422no—
1297C42—1422no—
1298C42—1422no—
1299C42—1422no—
1300C42—1422no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—2844no—
1308C23—2844no—
1309C23—2844no—
1310C23—2844no—
1311C23—712no—
1312C23—712no—
1313C23—712no—
1314C23—712no—
1315C23—712no—
1316C23—712no—
1317C23—712no—
1318C23—712no—
1319C23—1428no—
1320C23—1428no—
1321C23—1428no—
1322C23—1421no—
1323C23—1421no—
1324C23—1421no—
1325C23—1421no—
1326C23—1421no—
1327C23—1421no—
1328C23C2×Q8×D7112yes—
1329C23C24×D7111yescharacteristic
1330Q8—44no—
1331Q8—2844no—
1332Q8—2844no—
1333Q8—2844no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—44no—
1371C2×C4—2844no—
1372C2×C4—2844no—
1373C2×C4—2844no—
1374C2×C4—2844no—
1375C2×C4—2844no—
1376C2×C4—2844no—
1377C2×C4—2844no—
1378C2×C4—2844no—
1379C2×C4—2844no—
1380C2×C4—2844no—
1381C2×C4—2844no—
1382C2×C4—712no—
1383C2×C4—712no—
1384C2×C4—712no—
1385C2×C4—712no—
1386C2×C4—712no—
1387C2×C4—712no—
1388C2×C4—1428no—
1389C2×C4—1428no—
1390C2×C4—1428no—
1391C2×C4—1428no—
1392C2×C4—1428no—
1393C2×C4—1428no—
1394C2×C4—1421no—
1395C2×C4—1421no—
1396C2×C4—1421no—
1397C2×C4—1421no—
1398C2×C4—1421no—
1399C2×C4—1421no—
1400C2×C4—1421no—
1401C2×C4—1421no—
1402C2×C4—1421no—
1403C2×C4—1421no—
1404C2×C4—1421no—
1405C2×C4—1421no—
1406C2×C4—1421no—
1407C2×C4—1421no—
1408C2×C4—1421no—
1409C2×C4—1421no—
1410C2×C4—1421no—
1411C2×C4—1421no—
1412C2×C4—1421no—
1413C2×C4—1421no—
1414C2×C4—1421no—
1415C2×C4—1421no—
1416C2×C4—1421no—
1417C2×C4—1421no—
1418C2×C4—1421no—
1419C2×C4—1421no—
1420C2×C4—1421no—
1421C2×C4—1421no—
1422C2×C4—1421no—
1423C2×C4—1421no—
1424C2×C4—1421no—
1425C2×C4—1421no—
1426C2×C4—1421no—
1427C2×C4—1421no—
1428C2×C4—1421no—
1429C2×C4—1421no—
1430C2×C4C2×Q8×D7112yes—
1431C2×C4C2×Q8×D7112yes—
1432C2×C4#41×D7112yes—
1433C2×C4#41×D7112yes—
1434C2×C4#41×D7112yes—
1435C2×C4#41×D7112yes—
1436C22—22no—
1437C22—22no—
1438C22—22no—
1439C22—41no—
1440C22—41no—
1441C22—41no—
1442C22—41no—
1443C22—28416no—
1444C22—2841no—
1445C22—2841no—
1446C22—2841no—
1447C22—2841no—
1448C22—714no—
1449C22—714no—
1450C22—714no—
1451C22—714no—
1452C22—714no—
1453C22—714no—
1454C22—714no—
1455C22—1422no—
1456C22—1422no—
1457C22—1422no—
1458C22C22×Q8×D7111yescharacteristic
1459C22C2×#41×D7111yescharacteristic
1460C22C2×#41×D7111yescharacteristic
1461C22C2×#41×D7111yescharacteristic
1462C22C2×#41×D7111yescharacteristic
1463C22H(5,𝔽2)×D7111yescharacteristic
1464C22H(5,𝔽2)×D7111yescharacteristic
1465C4—22no—
1466C4—22no—
1467C4—22no—
1468C4—22no—
1469C4—22no—
1470C4—22no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—41no—
1479C4—2841no—
1480C4—2841no—
1481C4—2841no—
1482C4—2841no—
1483C4—2841no—
1484C4—2841no—
1485C4—2841no—
1486C4—2841no—
1487C4—1422no—
1488C4—1422no—
1489C4—1422no—
1490C4—1422no—
1491C4—1422no—
1492C4—1422no—
1493C2—42no—
1494C2—2842no—
1495C2—718no—
1496C2#529×D7111yescharacteristic
1497C2#533×D7111yescharacteristic
1498C2#538×D7111yescharacteristic
1499C2#551×D7111yescharacteristic
1500C2#554×D7111yescharacteristic
1501C2#554×D7111yescharacteristic
1502C2#555×D7111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2574C2
prime radicalC24×D71C23
hypercenter#2574D71
hypocenterC71C2×#2574
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2574

Complements

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

NH ≅ G/Ntype
1. #22593621C2semidirect
2. #22593620C2semidirect
3. #22593619C2semidirect
4. #22593618C2semidirect
5. #22593617C2semidirect
6. #22593616C2semidirect
7. #22593615C2semidirect
8. #22593614C2semidirect
9. #22593613C2semidirect
10. #22593612C2semidirect
11. #22593611C2semidirect
12. #22593610C2semidirect
13. #22593609C2semidirect
14. #22593608C2semidirect
15. #22593607C2semidirect
16. #398×D71C2semidirect
18. #395×D71C2semidirect
20. #391×D71C2semidirect
23. #387×D71C2semidirect
24. #387×D71C2semidirect
25. #387×D71C2semidirect
27. #382×D71C2semidirect
29. C4×C4⋊C4×D71C2semidirect
31. C71×#2574C2semidirect
53. #17985933C22semidirect
54. #17985933C22semidirect
55. #17985932C22semidirect
56. #17985932C22semidirect
57. #17985931C22semidirect
58. #17985930C22semidirect
59. #17985929C22semidirect
67. #17985920C22semidirect
68. #17985920C22semidirect
69. #17985920C22semidirect
70. #17985919C22semidirect
71. #17985919C22semidirect
72. #17985919C22semidirect
73. #17985918C22semidirect
81. #17985906C22semidirect
82. #17985905C22semidirect
83. #17985904C22semidirect
84. #17985903C22semidirect
85. #17985903C22semidirect
86. #17985903C22semidirect
87. #17985903C22semidirect
102. #17985886C22semidirect
103. #17985886C22semidirect
104. #17985886C22semidirect
105. #17985885C22semidirect
106. #17985885C22semidirect
107. #17985885C22semidirect
108. #17985884C22semidirect
109. #17985884C22semidirect
110. #17985884C22semidirect
111. #17985883C22semidirect
112. #17985883C22semidirect
113. #17985883C22semidirect
114. #17985882C22semidirect
115. #17985882C22semidirect
116. #17985882C22semidirect
117. #17985881C22semidirect
118. #17985881C22semidirect
119. #17985881C22semidirect
120. #17985880C22semidirect
121. #17985880C22semidirect
122. #17985880C22semidirect
130. #17985865C22semidirect
131. #17985864C22semidirect
132. #17985864C22semidirect
133. #17985863C22semidirect
134. #17985863C22semidirect
135. #17985863C22semidirect
136. #17985863C22semidirect
144. C4⋊C4×Dic71C22semidirect
145. C4⋊C4×Dic71C22semidirect
146. C4×Dic71⋊C4C22semidirect
147. C4×Dic71⋊C4C22semidirect
148. C4×C4⋊Dic71C22semidirect
149. #17985850C22semidirect
150. #17985850C22semidirect
172. #398×C71C22semidirect
174. #395×C71C22semidirect
176. #391×C71C22semidirect
179. #387×C71C22semidirect
180. #387×C71C22semidirect
181. #387×C71C22semidirect
183. #382×C71C22semidirect
185. C4×C4⋊C4×C71C22semidirect
273. C22⋊C4×D71Q8semidirect
484. C22⋊Dic71C2×Q8semidirect
495. (C2×D71)⋊C4C2×Q8semidirect
496. (C2×D71)⋊C4C2×Q8semidirect
544. C22⋊C4×C71C2×Q8semidirect
751. D71#2574direct (N × H)
767. #2574D71direct (N × H)
783. C71C2×#2574semidirect
812. #398C2×D71semidirect
828. #395C2×D71semidirect
844. #391C2×D71semidirect
882. #387C2×D71semidirect
883. #387C2×D71semidirect
884. #387C2×D71semidirect
900. #382C2×D71semidirect
916. C4×C4⋊C4C2×D71semidirect
1284. C22⋊C4Q8×D71semidirect

Maximal subgroups

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

subgroupindex
#225936212
#225936202
#225936192
#225936182
#225936172
#225936162
#225936152
#225936142
#225936132
#225936122
#225936112
#225936102
#225936092
#225936082
#225936072
#398×D712
#396×D712
#395×D712
#393×D712
#391×D712
#388×D712
#387×D712
#385×D712
#382×D712
#380×D712
C4×C4⋊C4×D712
C4×C22⋊C4×D712
C71×#25742
C2×#257471