Finite Group Databasebeta

← #32170249

Subgroups — #32170249

Order 18176.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596673C211yesmaximal, characteristic, complemented
2#22596660C211yesmaximal, characteristic, complemented
3#22596656C211yesmaximal, characteristic, complemented
4#22596638C211yesmaximal, characteristic, complemented
5#22594396C211yesmaximal, characteristic, complemented
6#22594344C211yesmaximal, characteristic, complemented
7#22594331C211yesmaximal, characteristic, complemented
8#22594321C211yesmaximal, characteristic, complemented
9#22592992C211yesmaximal, characteristic, complemented
10#22592907C211yesmaximal, characteristic, complemented
11#22592905C211yesmaximal, characteristic, complemented
12#22592846C211yesmaximal, characteristic, complemented
13#22592663C211yesmaximal, characteristic, complemented
14#22592590C211yesmaximal, characteristic, complemented
15#22592464C211yesmaximal, characteristic, complemented
16#22592391C211yesmaximal, characteristic, complemented
17#22592279C211yesmaximal, characteristic, complemented
18#22592095C211yesmaximal, characteristic, complemented
19#22592002C211yesmaximal, characteristic, complemented
20#22591896C211yesmaximal, characteristic, complemented
21#22591729C211yesmaximal, characteristic, complemented
22#22591709C211yesmaximal, characteristic
23#22591662C211yesmaximal, characteristic, complemented
24#22591069C211yesmaximal, characteristic, complemented
25#22591002C211yesmaximal, characteristic, complemented
26#22590976C211yesmaximal, characteristic, complemented
27#22590934C211yesmaximal, characteristic, complemented
28C4×#14556098C211yesmaximal, characteristic, complemented
29#386×D71C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D71C211yesmaximal, characteristic, complemented
31C71×#2518C211yesmaximal, characteristic, complemented
32C22×D4×D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C2×#14556122C2211yescharacteristic, complemented
35C2×#14556114C2211yescharacteristic, complemented
36C2×#14556113C2211yescharacteristic
37C2×#14556113C2211yescharacteristic, complemented
38C2×#14556110C2211yescharacteristic
39C2×#14556108C2211yescharacteristic
40C2×#14556106C2211yescharacteristic, complemented
41C2×#14556103C2211yescharacteristic
42C2×#14556101C2211yescharacteristic
43C2×#14556098C2211yescharacteristic
44C2×#14556098C2211yescharacteristic
45C2×C4×D284C2211yescharacteristic
46C2×C4×D284C2211yescharacteristic, complemented
47C2×C4×C22⋊D71C2211yescharacteristic, complemented
48C2×C22⋊C4×D71C2211yescharacteristic
49C2×C22⋊C4×D71C2211yescharacteristic
50C2×C22⋊C4×D71C2211yescharacteristic
51C2×C22⋊C4×D71C2211yescharacteristic
52C2×C22⋊C4×D71C2211yescharacteristic
53C2×C42×D71C2211yescharacteristic, complemented
54C2×C42×D71C2211yescharacteristic, complemented
55C71⋊#401C2211yescharacteristic, complemented
56#17985940C2211yescharacteristic, complemented
57#17985938C2211yescharacteristic, complemented
58#17985938C2211yescharacteristic, complemented
59#17985937C2211yescharacteristic, complemented
60#17985935C2211yescharacteristic, complemented
61#17985932C2211yescharacteristic, complemented
62#17985928C2211yescharacteristic, complemented
63#17985927C2211yescharacteristic, complemented
64#17985927C2211yescharacteristic, complemented
65#17985926C2211yescharacteristic, complemented
66#17985926C2211yescharacteristic, complemented
67#17985925C2211yescharacteristic, complemented
68#17985924C2211yescharacteristic, complemented
69#17985922C2211yescharacteristic, complemented
70#17985922C2211yescharacteristic, complemented
71#17985916C2211yescharacteristic, complemented
72#17985915C2211yescharacteristic
73#17985915C2211yescharacteristic, complemented
74#17985915C2211yescharacteristic, complemented
75#17985914C2211yescharacteristic
76#17985914C2211yescharacteristic
77#17985914C2211yescharacteristic, complemented
78#17985913C2211yescharacteristic
79#17985912C2211yescharacteristic, complemented
80#17985911C2211yescharacteristic, complemented
81#17985908C2211yescharacteristic
82#17985907C2211yescharacteristic
83#17985903C2211yescharacteristic, complemented
84#17985903C2211yescharacteristic, complemented
85#17985901C2211yescharacteristic, complemented
86#17985900C2211yescharacteristic, complemented
87#17985899C2211yescharacteristic, complemented
88#17985897C2211yescharacteristic, complemented
89#17985895C2211yescharacteristic, complemented
90#17985893C2211yescharacteristic, complemented
91#17985893C2211yescharacteristic, complemented
92#17985892C2211yescharacteristic, complemented
93#17985892C2211yescharacteristic, complemented
94#17985891C2211yescharacteristic, complemented
95#17985891C2211yescharacteristic, complemented
96#17985891C2211yescharacteristic, complemented
97#17985890C2211yescharacteristic, complemented
98#17985890C2211yescharacteristic, complemented
99#17985890C2211yescharacteristic, complemented
100#17985889C2211yescharacteristic, complemented
101#17985889C2211yescharacteristic, complemented
102#17985889C2211yescharacteristic, complemented
103#17985888C2211yescharacteristic, complemented
104#17985888C2211yescharacteristic, complemented
105#17985888C2211yescharacteristic, complemented
106#17985887C2211yescharacteristic, complemented
107#17985886C2211yescharacteristic, complemented
108#17985885C2211yescharacteristic, complemented
109#17985884C2211yescharacteristic, complemented
110#17985884C2211yescharacteristic, complemented
111#17985884C2211yescharacteristic, complemented
112#17985884C2211yescharacteristic, complemented
113#17985883C2211yescharacteristic, complemented
114#17985882C2211yescharacteristic, complemented
115#17985879C2211yescharacteristic
116#17985878C2211yescharacteristic
117#17985877C2211yescharacteristic
118#17985877C2211yescharacteristic
119#17985877C2211yescharacteristic
120#17985877C2211yescharacteristic
121#17985877C2211yescharacteristic
122#17985877C2211yescharacteristic
123#17985877C2211yescharacteristic
124#17985877C2211yescharacteristic
125#17985877C2211yescharacteristic, complemented
126#17985877C2211yescharacteristic, complemented
127#17985877C2211yescharacteristic, complemented
128#17985876C2211yescharacteristic
129#17985876C2211yescharacteristic, complemented
130#17985875C2211yescharacteristic
131#17985875C2211yescharacteristic
132#17985875C2211yescharacteristic
133#17985875C2211yescharacteristic
134#17985875C2211yescharacteristic, complemented
135#17985874C2211yescharacteristic, complemented
136#17985873C2211yescharacteristic
137#17985873C2211yescharacteristic
138#17985873C2211yescharacteristic, complemented
139#17985873C2211yescharacteristic, complemented
140#17985873C2211yescharacteristic, complemented
141#17985870C2211yescharacteristic
142#17985870C2211yescharacteristic
143#17985870C2211yescharacteristic
144#17985870C2211yescharacteristic
145#17985870C2211yescharacteristic, complemented
146#17985867C2211yescharacteristic, complemented
147#17985863C2211yescharacteristic, complemented
148#17985861C2211yescharacteristic, complemented
149#17985861C2211yescharacteristic, complemented
150#17985858C2211yescharacteristic
151#17985858C2211yescharacteristic
152#17985858C2211yescharacteristic, complemented
153#17985856C2211yescharacteristic
154#17985856C2211yescharacteristic, complemented
155#17985854C2211yescharacteristic
156#17985854C2211yescharacteristic
157#17985854C2211yescharacteristic
158#17985854C2211yescharacteristic
159C22⋊C4×Dic71C2211yescharacteristic, complemented
160C22⋊C4×Dic71C2211yescharacteristic, complemented
161C4×(C2×D71)⋊C4C2211yescharacteristic
162C4×(C2×D71)⋊C4C2211yescharacteristic
163C4×(C2×D71)⋊C4C2211yescharacteristic
164C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
165C4×C22⋊Dic71C2211yescharacteristic, complemented
166#17985846C2211yescharacteristic
167#17985846C2211yescharacteristic
168#95×D71C2211yescharacteristic
169#95×D71C2211yescharacteristic
170#95×D71C2211yescharacteristic, complemented
171#95×D71C2211yescharacteristic, complemented
172#397×C71C2211yescharacteristic, complemented
173#396×C71C2211yescharacteristic, complemented
174#394×C71C2211yescharacteristic
175#394×C71C2211yescharacteristic
176#389×C71C2211yescharacteristic, complemented
177#388×C71C2211yescharacteristic, complemented
178#388×C71C2211yescharacteristic, complemented
179#388×C71C2211yescharacteristic, complemented
180#388×C71C2211yescharacteristic, complemented
181#387×C71C2211yescharacteristic, complemented
182#386×C71C2211yescharacteristic
183#383×C71C2211yescharacteristic, complemented
184#382×C71C2211yescharacteristic, complemented
185C4×C22⋊C4×C71C2211yescharacteristic, complemented
186C4×C22⋊C4×C71C2211yescharacteristic, complemented
187C24×D71C2311yescharacteristic
188C24×D71C2311yescharacteristic
189C22×Dic142C2311yescharacteristic
190C22×D284C2311yescharacteristic
191C22×D284C2311yescharacteristic
192C22×D284C2311yescharacteristic
193C22×D284C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C22×C22⋊D71C2311yescharacteristic
197C22×C22⋊D71C2311yescharacteristic
198C2×D4×D71—24no—
199C2×D4×D71—42no—
200C2×D4×D71—42no—
201C23×Dic71C2311yescharacteristic
202C22×C4×D71—24no—
203C22×C4×D71—42no—
204C22×C4×D71—42no—
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
214C22×C4×D71C2311yescharacteristic
215C22×C4×D71C2311yescharacteristic
216C22×C4×D71C2311yescharacteristic
217#14556122—42no—
218#14556114—42no—
219#14556113—42no—
220#14556113—42no—
221#14556110—42no—
222#14556108—24no—
223#14556106—42no—
224#14556103—42no—
225#14556101—42no—
226#14556098—24no—
227#14556098—24no—
228C4×D284—24no—
229C4×D284—42no—
230C4×C22⋊D71—42no—
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
233C2×C4⋊Dic71C2311yescharacteristic
234C2×C4⋊Dic71C2311yescharacteristic
235C2×C4⋊Dic71C2311yescharacteristic
236C2×C4⋊Dic71C2311yescharacteristic
237C2×Dic71⋊C4C2311yescharacteristic
238C2×Dic71⋊C4C2311yescharacteristic
239C2×Dic71⋊C4C2311yescharacteristic
240C2×Dic71⋊C4C2311yescharacteristic
241C2×Dic71⋊C4C2311yescharacteristic
242C2×Dic71⋊C4C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×C22⋊Dic71C2311yescharacteristic
248C2×C22⋊Dic71C2311yescharacteristic
249C2×C22⋊Dic71C2311yescharacteristic
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
268C2×(C2×D71)⋊C4C2311yescharacteristic
269C2×(C2×D71)⋊C4C2311yescharacteristic
270C2×(C2×D71)⋊C4C2311yescharacteristic
271C2×(C2×D71)⋊C4C2311yescharacteristic
272C2×(C2×D71)⋊C4C2311yescharacteristic
273C2×(C2×D71)⋊C4C2311yescharacteristic
274C2×(C2×D71)⋊C4C2311yescharacteristic
275C2×(C2×D71)⋊C4C2311yescharacteristic
276C2×(C2×D71)⋊C4C2311yescharacteristic
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
288C22⋊C4×D71—24no—
289C22⋊C4×D71—24no—
290C22⋊C4×D71—24no—
291C22⋊C4×D71—42no—
292C22⋊C4×D71—42no—
293C2×C4×Dic71C2311yescharacteristic
294C2×C4×Dic71C2311yescharacteristic
295C2×C4×Dic71C2311yescharacteristic
296C2×C4×Dic71C2311yescharacteristic
297C2×C4×Dic71C2311yescharacteristic
298C2×C4×Dic71C2311yescharacteristic
299C2×C4×Dic71C2311yescharacteristic
300C42×D71—42no—
301C42×D71—42no—
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
332C71⋊#95C2311yescharacteristic
333C71⋊#95C2311yescharacteristic
334C22×D4×C71C2311yescharacteristic
335C23×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×C22⋊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×C22⋊C4×C71C2311yescharacteristic
350C2×C22⋊C4×C71C2311yescharacteristic
351C2×C22⋊C4×C71C2311yescharacteristic
352C2×C22⋊C4×C71C2311yescharacteristic
353C2×C42×C71C2311yescharacteristic
354C2×C42×C71C2311yescharacteristic
355C2×C42×C71C2311yescharacteristic
356C2×C42×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
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C23×D71—22no—
370C23×D71—22no—
371C23×D71—22no—
372C23×D71—22no—
373C23×D71—22no—
374C23×D71—22no—
375C23×D71—22no—
376C23×D71—41no—
377C23×D71—41no—
378C23×D71—41no—
379C23×D71—41no—
380C23×D71—41no—
381C23×D71—41no—
382C23×D71#4114yes—
383C23×D71C2411yescharacteristic
384C23×D71C2411yescharacteristic
385C23×D71C2411yescharacteristic
386C23×D71C2411yescharacteristic
387C2×Dic142—22no—
388C2×Dic142—41no—
389C2×Dic142—41no—
390C2×D284—22no—
391C2×D284—22no—
392C2×D284—22no—
393C2×D284—22no—
394C2×D284—22no—
395C2×D284—22no—
396C2×D284—22no—
397C2×D284—22no—
398C2×D284—22no—
399C2×D284—22no—
400C2×D284—41no—
401C2×D284—41no—
402C2×C22⋊D71—22no—
403C2×C22⋊D71—22no—
404C2×C22⋊D71—22no—
405C2×C22⋊D71—22no—
406C2×C22⋊D71—22no—
407C2×C22⋊D71—22no—
408C2×C22⋊D71—41no—
409C2×C22⋊D71—41no—
410C2×C22⋊D71—41no—
411C2×C22⋊D71—41no—
412C2×C22⋊D71—41no—
413C2×C22⋊D71—41no—
414D4×D71—416no—
415C22×Dic71—22no—
416C22×Dic71—41no—
417C22×Dic71—41no—
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C22×Dic71C2411yescharacteristic
424C22×Dic71C2411yescharacteristic
425C22×Dic71C2411yescharacteristic
426C22×Dic71C2411yescharacteristic
427C22×Dic71C2411yescharacteristic
428C22×Dic71C2411yescharacteristic
429C22×Dic71C2411yescharacteristic
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—22no—
444C2×C4×D71—22no—
445C2×C4×D71—22no—
446C2×C4×D71—22no—
447C2×C4×D71—22no—
448C2×C4×D71—22no—
449C2×C4×D71—416no—
450C2×C4×D71—41no—
451C2×C4×D71—41no—
452C2×C4×D71—41no—
453C2×C4×D71—41no—
454C2×C4×D71—41no—
455C2×C4×D71—41no—
456C2×C4×D71—41no—
457C2×C4×D71—41no—
458C2×C4×D71—41no—
459C2×C4×D71—41no—
460C2×C4×D71—41no—
461C2×C4×D71—41no—
462C2×C4×D71—41no—
463C2×C4×D71—41no—
464C2×C4×D71—41no—
465C2×C4×D71—41no—
466C2×C4×D71#4114yes—
467C4⋊Dic71—22no—
468C4⋊Dic71—22no—
469C4⋊Dic71—22no—
470C4⋊Dic71—41no—
471C4⋊Dic71—41no—
472C4⋊Dic71—41no—
473Dic71⋊C4—22no—
474Dic71⋊C4—41no—
475Dic71⋊C4—41no—
476Dic71⋊C4—41no—
477Dic71⋊C4—41no—
478Dic71⋊C4—41no—
479Dic71⋊C4—41no—
480Dic71⋊C4—41no—
481Dic71⋊C4—41no—
482Dic71⋊C4—41no—
483C22⋊Dic71—22no—
484C22⋊Dic71—22no—
485C22⋊Dic71—22no—
486C22⋊Dic71—41no—
487C22⋊Dic71—41no—
488C22⋊Dic71—41no—
489C22⋊Dic71—41no—
490C22⋊Dic71—41no—
491C22⋊Dic71—41no—
492(C2×D71)⋊C4—22no—
493(C2×D71)⋊C4—22no—
494(C2×D71)⋊C4—22no—
495(C2×D71)⋊C4—22no—
496(C2×D71)⋊C4—22no—
497(C2×D71)⋊C4—22no—
498(C2×D71)⋊C4—22no—
499(C2×D71)⋊C4—22no—
500(C2×D71)⋊C4—22no—
501(C2×D71)⋊C4—22no—
502(C2×D71)⋊C4—22no—
503(C2×D71)⋊C4—22no—
504(C2×D71)⋊C4—22no—
505(C2×D71)⋊C4—22no—
506(C2×D71)⋊C4—22no—
507(C2×D71)⋊C4—22no—
508(C2×D71)⋊C4—22no—
509(C2×D71)⋊C4—41no—
510(C2×D71)⋊C4—41no—
511(C2×D71)⋊C4—41no—
512(C2×D71)⋊C4—41no—
513(C2×D71)⋊C4—41no—
514(C2×D71)⋊C4—41no—
515(C2×D71)⋊C4—41no—
516(C2×D71)⋊C4—41no—
517(C2×D71)⋊C4—41no—
518(C2×D71)⋊C4—41no—
519(C2×D71)⋊C4—41no—
520(C2×D71)⋊C4—41no—
521(C2×D71)⋊C4—41no—
522(C2×D71)⋊C4—41no—
523(C2×D71)⋊C4#4114yes—
524C4×Dic71—22no—
525C4×Dic71—41no—
526C4×Dic71—41no—
527C4×Dic71—41no—
528C4×Dic71—41no—
529C4×Dic71—41no—
530C4×Dic71—41no—
531C24×C71C2411yescharacteristic
532C24×C71C2411yescharacteristic
533C2×D4×C71—22no—
534C2×D4×C71—41no—
535C2×D4×C71—41no—
536C22×C4×C71—22no—
537C22×C4×C71—22no—
538C22×C4×C71—41no—
539C22×C4×C71C2411yescharacteristic
540C22×C4×C71C2411yescharacteristic
541C22×C4×C71C2411yescharacteristic
542C22×C4×C71C2411yescharacteristic
543C22×C4×C71C2411yescharacteristic
544C22×C4×C71C2411yescharacteristic
545C22×C4×C71C2411yescharacteristic
546C22×C4×C71C2411yescharacteristic
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C22×C4×C71C2411yescharacteristic
550C22×C4×C71C2411yescharacteristic
551C22×C4×C71C2411yescharacteristic
552C4⋊C4×C71—22no—
553C4⋊C4×C71—41no—
554C4⋊C4×C71—41no—
555C4⋊C4×C71—41no—
556C4⋊C4×C71—41no—
557C4⋊C4×C71—41no—
558C22⋊C4×C71—22no—
559C22⋊C4×C71—22no—
560C22⋊C4×C71—22no—
561C22⋊C4×C71—22no—
562C22⋊C4×C71—22no—
563C22⋊C4×C71—22no—
564C22⋊C4×C71—41no—
565C22⋊C4×C71—41no—
566C22⋊C4×C71—41no—
567C22⋊C4×C71—41no—
568C22⋊C4×C71—41no—
569C42×C71—22no—
570C42×C71—22no—
571C42×C71—41no—
572C42×C71—41no—
573C23×C71—21no—
574C23×C71—21no—
575C23×C71—21no—
576C23×C71—21no—
577C23×C71—21no—
578C23×C71—21no—
579C23×C71—21no—
580C23×C71—21no—
581C23×C71—21no—
582C23×C71—21no—
583C23×C71—21no—
584C23×C71—21no—
585C23×C71—21no—
586C23×C71C2×#4112yes—
587C23×C71C2511yescharacteristic
588C22×D71—21no—
589C22×D71—21no—
590C22×D71—21no—
591C22×D71—21no—
592C22×D71—21no—
593C22×D71—21no—
594C22×D71—21no—
595C22×D71—21no—
596C22×D71—28no—
597C22×D71—28no—
598C22×D71—21no—
599C22×D71—21no—
600C22×D71—21no—
601C22×D71—21no—
602C22×D71—21no—
603C22×D71—21no—
604C22×D71—21no—
605C22×D71—21no—
606C22×D71—21no—
607C22×D71—21no—
608C22×D71—21no—
609C22×D71—21no—
610C22×D71—21no—
611C22×D71—21no—
612C22×D71—44no—
613C22×D71—44no—
614C22×D71—44no—
615C22×D71—44no—
616C22×D71—44no—
617C22×D71—44no—
618C22×D71—44no—
619C22×D71—44no—
620C22×D71—82no—
621C22×D71—82no—
622C22×D71—82no—
623C22×D71—82no—
624C22×D71C2×#4112yes—
625C22×D71C2×#4112yes—
626C22×D71C2×#4112yes—
627C22×D71C2×#4112yes—
628C22×D71H(5,𝔽2)12yes—
629C22×D71H(5,𝔽2)12yes—
630D4×C71—44no—
631C2×C4×C71—21no—
632C2×C4×C71—21no—
633C2×C4×C71—21no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—21no—
645C2×C4×C71—21no—
646C2×C4×C71—21no—
647C2×C4×C71—21no—
648C2×C4×C71—21no—
649C2×C4×C71—21no—
650C2×C4×C71—21no—
651C2×C4×C71—21no—
652C2×C4×C71—21no—
653C2×C4×C71—21no—
654C2×C4×C71—21no—
655C2×C4×C71—21no—
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—44no—
668C2×C4×C71C2×#4112yes—
669C2×C4×C71C2×#4112yes—
670C2×C4×C71H(5,𝔽2)12yes—
671C22⋊D71—44no—
672C22⋊D71—44no—
673C22⋊D71—44no—
674C22⋊D71—82no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—21no—
690C2×Dic71—21no—
691C2×Dic71—21no—
692C2×Dic71—21no—
693C2×Dic71—21no—
694C2×Dic71—21no—
695C2×Dic71—21no—
696C2×Dic71—21no—
697C2×Dic71—21no—
698C2×Dic71—21no—
699C2×Dic71—21no—
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—44no—
710C2×Dic71C2×#4112yes—
711C2×Dic71C2×#4112yes—
712D284—44no—
713D284—44no—
714D284—44no—
715D284—82no—
716C4×D71—28no—
717C4×D71—44no—
718C4×D71—44no—
719C4×D71—44no—
720C4×D71—44no—
721C4×D71—44no—
722C4×D71—44no—
723C4×D71—44no—
724C4×D71—44no—
725C4×D71—82no—
726C4×D71—82no—
727C4×D71—82no—
728Dic142—82no—
729C22×C71—22no—
730C22×C71—22no—
731C22×C71—22no—
732C22×C71—41no—
733C22×C71—41no—
734C22×C71—41no—
735C22×C71—41no—
736C22×C71—41no—
737C22×C71—41no—
738C22×C71—41no—
739C22×C71—41no—
740C22×C71—41no—
741C22×C71—41no—
742C22×C71—41no—
743C22×C71C22×#4111yescharacteristic
744C22×C71C22×#4111yescharacteristic
745C22×C71C22×#4111yescharacteristic
746C22×C71C2×H(5,𝔽2)11yescharacteristic
747C22×C71C2×H(5,𝔽2)11yescharacteristic
748C22×C71C2×H(5,𝔽2)11yescharacteristic
749C22×C71#58511yescharacteristic
750C2×D71—22no—
751C2×D71—22no—
752C2×D71—22no—
753C2×D71—22no—
754C2×D71—22no—
755C2×D71—22no—
756C2×D71—22no—
757C2×D71—22no—
758C2×D71—22no—
759C2×D71—22no—
760C2×D71—22no—
761C2×D71—22no—
762C2×D71—416no—
763C2×D71—41no—
764C2×D71—41no—
765C2×D71—41no—
766C2×D71—41no—
767C2×D71—41no—
768C2×D71—41no—
769C2×D71—41no—
770C2×D71—41no—
771C2×D71—41no—
772C2×D71—41no—
773C2×D71—41no—
774C2×D71—41no—
775C2×D71—41no—
776C2×D71—41no—
777C2×D71—88no—
778C2×D71#52914yes—
779C2×D71#53814yes—
780C4×C71—22no—
781C4×C71—22no—
782C4×C71—22no—
783C4×C71—41no—
784C4×C71—41no—
785C4×C71—41no—
786C4×C71—41no—
787C4×C71—41no—
788C4×C71—41no—
789C4×C71—41no—
790C4×C71—41no—
791C4×C71—41no—
792C4×C71—41no—
793Dic71—22no—
794Dic71—22no—
795Dic71—41no—
796Dic71—41no—
797Dic71—41no—
798Dic71—41no—
799Dic71—41no—
800Dic71—41no—
801Dic71—41no—
802Dic71—41no—
803Dic71—41no—
804Dic71—41no—
805#34998—711nomaximal, Sylow
806C2×C71—42no—
807C2×C71—81no—
808C2×C71C2×#52911yescharacteristic
809C2×C71C2×#53811yescharacteristic
810C2×C71#345911yescharacteristic
811C2×C71#349011yescharacteristic
812C2×C71#349411yescharacteristic
813C2×C71#351311yescharacteristic
814C2×C71#351911yescharacteristic
815D71—24no—
816D71—24no—
817D71—81no—
818D71—81no—
819#2854—711no—
820#2853—711no—
821#2852—711no—
822#2850—711no—
823#2653—711no—
824#2649—711no—
825#2648—711no—
826#2648—711no—
827#2518—711no—
828#2518D7111yescharacteristic, complemented
829#2510—711no—
830#2510—711no—
831#2505—711no—
832#2488—711no—
833#2480—711no—
834#2472—711no—
835#2467—711no—
836#2459—711no—
837#2444—711no—
838#2437—711no—
839#2425—711no—
840#2412—711no—
841#2410—711no—
842#2405—711no—
843#2329—711no—
844#2321—711no—
845#2318—711no—
846#2312—711no—
847C4×#120—711no—
848C2×#386—711no—
849C2×C4×C22⋊C4—711no—
850C71#3499811yescharacteristic, complemented, Sylow
851C23×D4—711no—
852C24×C4—711no—
853C2×#126—711no—
854C2×#124—711no—
855C2×#123—711no—
856C2×#123—711no—
857C2×#123—711no—
858C2×C22⋊Q8—711no—
859C2×C22⋊Q8—711no—
860C2×#121—711no—
861C2×#121—711no—
862C2×#120—711no—
863C2×#120—711no—
864C2×C4×D4—711no—
865C2×C4×D4—711no—
866C2×C4×D4—711no—
867C22×C22⋊C4—711no—
868C22×C22⋊C4—711no—
869C22×C22⋊C4—711no—
870C22×C22⋊C4—711no—
871C22×C22⋊C4—711no—
872C22×C42—711no—
873C22×C42—711no—
874#401—711no—
875#400—711no—
876#400—711no—
877#400—711no—
878#400—711no—
879#399—711no—
880#398—711no—
881#397—711no—
882#397—711no—
883#397—711no—
884#397—711no—
885#397—711no—
886#397—711no—
887#397—711no—
888#397C2×D7111yescharacteristic, complemented
889#396—711no—
890#396—711no—
891#396C2×D7111yescharacteristic, complemented
892#394—711no—
893#394—711no—
894#394—711no—
895#394—711no—
896#394—711no—
897#394—711no—
898#394—711no—
899#394—711no—
900#394C2×D7111yescharacteristic
901#394C2×D7111yescharacteristic
902#393—711no—
903#393—711no—
904#392—711no—
905#392—711no—
906#391—711no—
907#391—711no—
908#390—711no—
909#390—711no—
910#390—711no—
911#389—711no—
912#389—711no—
913#389C2×D7111yescharacteristic, complemented
914#388—711no—
915#388—711no—
916#388—711no—
917#388—711no—
918#388—711no—
919#388—711no—
920#388—711no—
921#388—711no—
922#388—711no—
923#388—711no—
924#388—711no—
925#388—711no—
926#388—711no—
927#388—711no—
928#388—711no—
929#388—711no—
930#388—711no—
931#388C2×D7111yescharacteristic, complemented
932#388C2×D7111yescharacteristic, complemented
933#388C2×D7111yescharacteristic, complemented
934#388C2×D7111yescharacteristic, complemented
935#387—711no—
936#387—711no—
937#387—711no—
938#387—711no—
939#387—711no—
940#387—711no—
941#387—711no—
942#387—711no—
943#387C2×D7111yescharacteristic, complemented
944#386—711no—
945#386—711no—
946#386—711no—
947#386—711no—
948#386—711no—
949#386—711no—
950#386—711no—
951#386—711no—
952#386—711no—
953#386—711no—
954#386—711no—
955#386—711no—
956#386—711no—
957#386—711no—
958#386—711no—
959#386—711no—
960#386—711no—
961#386—711no—
962#386—711no—
963#386—711no—
964#386C2×D7111yescharacteristic
965#385—711no—
966#385—711no—
967#385—711no—
968#385—711no—
969#385—711no—
970#385—711no—
971#385—711no—
972#385—711no—
973#385—711no—
974#385—711no—
975#385—711no—
976#383—711no—
977#383C2×D7111yescharacteristic, complemented
978#382—711no—
979#382C2×D7111yescharacteristic, complemented
980#381—711no—
981#381—711no—
982#380—711no—
983#380—711no—
984#380—711no—
985#380—711no—
986#380—711no—
987#379—711no—
988#379—711no—
989#379—711no—
990#379—711no—
991C4×C22⋊C4—711no—
992C4×C22⋊C4—711no—
993C4×C22⋊C4—711no—
994C4×C22⋊C4—711no—
995C4×C22⋊C4—711no—
996C4×C22⋊C4—711no—
997C4×C22⋊C4—711no—
998C4×C22⋊C4—711no—
999C4×C22⋊C4—711no—
1000C4×C22⋊C4C2×D7111yescharacteristic, complemented
1001C4×C22⋊C4C2×D7111yescharacteristic, complemented
1002C2×#95—711no—
1003C2×#95—711no—
1004C2×#95—711no—
1005C2×#95—711no—
1006C25—711no—
1007C25—711no—
1008C22×Q8—711no—
1009C22×D4—2842no—
1010C22×D4—2842no—
1011C22×D4—711no—
1012C22×D4—711no—
1013C22×D4—711no—
1014C22×D4—711no—
1015C22×D4—711no—
1016C22×D4—711no—
1017C22×D4—711no—
1018C22×D4—711no—
1019C22×D4—1424no—
1020C22×D4C22×D7111yescharacteristic
1021C23×C4—2842no—
1022C23×C4—2842no—
1023C23×C4—711no—
1024C23×C4—711no—
1025C23×C4—711no—
1026C23×C4—711no—
1027C23×C4—711no—
1028C23×C4—711no—
1029C23×C4—711no—
1030C23×C4—711no—
1031C23×C4—711no—
1032C23×C4—711no—
1033C23×C4—711no—
1034C23×C4—711no—
1035C23×C4—711no—
1036C23×C4—1424no—
1037C23×C4C22×D7111yescharacteristic
1038#126—2842no—
1039#124—2842no—
1040#123—2842no—
1041#123—2842no—
1042#123—2842no—
1043C22⋊Q8—2842no—
1044C22⋊Q8—1424no—
1045#121—2842no—
1046#121—2842no—
1047#120—1424no—
1048#120—1424no—
1049C4×D4—2842no—
1050C4×D4—2842no—
1051C4×D4—1424no—
1052C2×C4⋊C4—711no—
1053C2×C4⋊C4—711no—
1054C2×C4⋊C4—711no—
1055C2×C4⋊C4—711no—
1056C2×C4⋊C4—711no—
1057C2×C4⋊C4—711no—
1058C2×C4⋊C4—711no—
1059C2×C4⋊C4—711no—
1060C2×C4⋊C4—711no—
1061C2×C4⋊C4—711no—
1062C2×C4⋊C4—711no—
1063C2×C4⋊C4—711no—
1064C2×C4⋊C4—711no—
1065C2×C4⋊C4—711no—
1066C2×C4⋊C4—711no—
1067C2×C4⋊C4—711no—
1068C2×C4⋊C4C22×D7111yescharacteristic
1069C2×C4⋊C4C22×D7111yescharacteristic
1070C2×C4⋊C4C22×D7111yescharacteristic
1071C2×C4⋊C4C22×D7111yescharacteristic
1072C2×C4⋊C4C22×D7111yescharacteristic
1073C2×C4⋊C4C22×D7111yescharacteristic
1074C2×C22⋊C4—2842no—
1075C2×C22⋊C4—2842no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4—711no—
1087C2×C22⋊C4—711no—
1088C2×C22⋊C4—711no—
1089C2×C22⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
1094C2×C22⋊C4—711no—
1095C2×C22⋊C4—711no—
1096C2×C22⋊C4—711no—
1097C2×C22⋊C4—711no—
1098C2×C22⋊C4—711no—
1099C2×C22⋊C4—711no—
1100C2×C22⋊C4—711no—
1101C2×C22⋊C4—711no—
1102C2×C22⋊C4—711no—
1103C2×C22⋊C4—711no—
1104C2×C22⋊C4—711no—
1105C2×C22⋊C4—711no—
1106C2×C22⋊C4—711no—
1107C2×C22⋊C4—711no—
1108C2×C22⋊C4—711no—
1109C2×C22⋊C4—711no—
1110C2×C22⋊C4—711no—
1111C2×C22⋊C4—711no—
1112C2×C22⋊C4—711no—
1113C2×C22⋊C4—711no—
1114C2×C22⋊C4—711no—
1115C2×C22⋊C4—711no—
1116C2×C22⋊C4—711no—
1117C2×C22⋊C4—1424no—
1118C2×C22⋊C4—1424no—
1119C2×C22⋊C4—1424no—
1120C2×C22⋊C4C22×D7111yescharacteristic
1121C2×C22⋊C4C22×D7111yescharacteristic
1122C2×C22⋊C4C22×D7111yescharacteristic
1123C2×C22⋊C4C22×D7111yescharacteristic
1124C2×C22⋊C4C22×D7111yescharacteristic
1125C2×C22⋊C4C22×D7111yescharacteristic
1126C2×C22⋊C4C22×D7111yescharacteristic
1127C2×C22⋊C4C22×D7111yescharacteristic
1128C2×C22⋊C4C22×D7111yescharacteristic
1129C2×C22⋊C4C22×D7111yescharacteristic
1130C2×C22⋊C4C22×D7111yescharacteristic
1131C2×C42—2842no—
1132C2×C42—2842no—
1133C2×C42—711no—
1134C2×C42—711no—
1135C2×C42—711no—
1136C2×C42—711no—
1137C2×C42—711no—
1138C2×C42—711no—
1139C2×C42—711no—
1140C2×C42C22×D7111yescharacteristic
1141C2×C42C22×D7111yescharacteristic
1142C2×C42C22×D7111yescharacteristic
1143C2×C42C22×D7111yescharacteristic
1144#95—711no—
1145#95—711no—
1146#95—711no—
1147#95—711no—
1148#95—711no—
1149#95—711no—
1150#95—711no—
1151#95—711no—
1152#95—711no—
1153#95—711no—
1154#95—711no—
1155#95—711no—
1156#95—711no—
1157#95—711no—
1158#95—711no—
1159#95—711no—
1160#95—711no—
1161#95—711no—
1162#95—711no—
1163#95—711no—
1164#95—711no—
1165#95—711no—
1166#95—711no—
1167#95—711no—
1168#95—711no—
1169#95—711no—
1170#95—711no—
1171#95—711no—
1172#95—711no—
1173#95—711no—
1174#95—711no—
1175#95—711no—
1176#95C22×D7111yescharacteristic
1177#95C22×D7111yescharacteristic
1178#95C22×D7111yescharacteristic
1179#95C22×D7111yescharacteristic
1180#95C22×D7111yescharacteristic
1181#95C22×D7111yescharacteristic
1182#95C22×D7111yescharacteristic
1183#95C22×D7111yescharacteristic
1184#95C22×D7111yescharacteristic
1185#95C22×D7111yescharacteristic
1186#95C22×D7111yescharacteristic
1187#95C22×D7111yescharacteristic
1188C24—2841no—
1189C24—2841no—
1190C24—2841no—
1191C24—2841no—
1192C24—2841no—
1193C24—2841no—
1194C24—714no—
1195C24—711no—
1196C24—711no—
1197C24—711no—
1198C24—711no—
1199C24—1422no—
1200C24—1422no—
1201C24—1422no—
1202C24—1422no—
1203C24—1422no—
1204C24—1422no—
1205C24—1422no—
1206C24C23×D7111yescharacteristic
1207C24C23×D7111yescharacteristic
1208C2×Q8—2841no—
1209C2×Q8—2841no—
1210C2×Q8—1422no—
1211C2×D4—22no—
1212C2×D4—41no—
1213C2×D4—41no—
1214C2×D4—2841no—
1215C2×D4—2841no—
1216C2×D4—28416no—
1217C2×D4—2841no—
1218C2×D4—2841no—
1219C2×D4—2841no—
1220C2×D4—2841no—
1221C2×D4—2841no—
1222C2×D4—2841no—
1223C2×D4—1422no—
1224C2×D4—1422no—
1225C2×D4—1422no—
1226C2×D4—1422no—
1227C2×D4—1422no—
1228C2×D4—1422no—
1229C2×D4—1422no—
1230C2×D4—1422no—
1231C2×D4—1422no—
1232C2×D4—1422no—
1233C2×D4—1422no—
1234C2×D4—1422no—
1235C2×D4—1422no—
1236C2×D4—1422no—
1237C2×D4—1422no—
1238C2×D4—1422no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—41no—
1242C22×C4—2841no—
1243C22×C4—2841no—
1244C22×C4—2841no—
1245C22×C4—2841no—
1246C22×C4—2841no—
1247C22×C4—2841no—
1248C22×C4—2841no—
1249C22×C4—2841no—
1250C22×C4—2841no—
1251C22×C4—2841no—
1252C22×C4—2841no—
1253C22×C4—2841no—
1254C22×C4—2841no—
1255C22×C4—2841no—
1256C22×C4—2841no—
1257C22×C4—2841no—
1258C22×C4—28416no—
1259C22×C4—2841no—
1260C22×C4—2841no—
1261C22×C4—714no—
1262C22×C4—711no—
1263C22×C4—711no—
1264C22×C4—711no—
1265C22×C4—711no—
1266C22×C4—711no—
1267C22×C4—711no—
1268C22×C4—711no—
1269C22×C4—711no—
1270C22×C4—711no—
1271C22×C4—711no—
1272C22×C4—711no—
1273C22×C4—711no—
1274C22×C4—1422no—
1275C22×C4—1422no—
1276C22×C4—1422no—
1277C22×C4—1422no—
1278C22×C4—1422no—
1279C22×C4—1422no—
1280C22×C4—1422no—
1281C22×C4—1422no—
1282C22×C4—1422no—
1283C22×C4—1422no—
1284C22×C4—1422no—
1285C22×C4—1422no—
1286C22×C4—1422no—
1287C22×C4—1422no—
1288C22×C4—1422no—
1289C22×C4—1422no—
1290C22×C4—1422no—
1291C22×C4—1422no—
1292C22×C4—1422no—
1293C22×C4—1422no—
1294C22×C4C23×D7111yescharacteristic
1295C22×C4C23×D7111yescharacteristic
1296C22×C4C23×D7111yescharacteristic
1297C22×C4C23×D7111yescharacteristic
1298C22×C4C23×D7111yescharacteristic
1299C22×C4C23×D7111yescharacteristic
1300C22×C4C23×D7111yescharacteristic
1301C22×C4C23×D7111yescharacteristic
1302C22×C4C23×D7111yescharacteristic
1303C22×C4C23×D7111yescharacteristic
1304C22×C4C23×D7111yescharacteristic
1305C22×C4C23×D7111yescharacteristic
1306C22×C4C23×D7111yescharacteristic
1307C4⋊C4—22no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—41no—
1312C4⋊C4—41no—
1313C4⋊C4—2841no—
1314C4⋊C4—2841no—
1315C4⋊C4—2841no—
1316C4⋊C4—2841no—
1317C4⋊C4—2841no—
1318C4⋊C4—2841no—
1319C4⋊C4—2841no—
1320C4⋊C4—2841no—
1321C4⋊C4—2841no—
1322C4⋊C4—2841no—
1323C4⋊C4—2841no—
1324C4⋊C4—2841no—
1325C4⋊C4—1422no—
1326C4⋊C4—1422no—
1327C4⋊C4—1422no—
1328C4⋊C4—1422no—
1329C22⋊C4—22no—
1330C22⋊C4—22no—
1331C22⋊C4—22no—
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—2841no—
1341C22⋊C4—2841no—
1342C22⋊C4—2841no—
1343C22⋊C4—2841no—
1344C22⋊C4—2841no—
1345C22⋊C4—2841no—
1346C22⋊C4—2841no—
1347C22⋊C4—2841no—
1348C22⋊C4—2841no—
1349C22⋊C4—2841no—
1350C22⋊C4—2841no—
1351C22⋊C4—2841no—
1352C22⋊C4—2841no—
1353C22⋊C4—2841no—
1354C22⋊C4—2841no—
1355C22⋊C4—2841no—
1356C22⋊C4—2841no—
1357C22⋊C4—2841no—
1358C22⋊C4—2841no—
1359C22⋊C4—2841no—
1360C22⋊C4—714no—
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⋊C4—1422no—
1376C22⋊C4—1422no—
1377C22⋊C4—1422no—
1378C22⋊C4—1422no—
1379C22⋊C4—1422no—
1380C22⋊C4—1422no—
1381C42—22no—
1382C42—22no—
1383C42—41no—
1384C42—41no—
1385C42—2841no—
1386C42—2841no—
1387C42—2841no—
1388C42—2841no—
1389C42—2841no—
1390C42—2841no—
1391C42—1422no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—2844no—
1406C23—2844no—
1407C23—2844no—
1408C23—2844no—
1409C23—2844no—
1410C23—2844no—
1411C23—2844no—
1412C23—2844no—
1413C23—5682no—
1414C23—5682no—
1415C23—5682no—
1416C23—5682no—
1417C23—712no—
1418C23—712no—
1419C23—712no—
1420C23—712no—
1421C23—712no—
1422C23—712no—
1423C23—1428no—
1424C23—1428no—
1425C23—1421no—
1426C23—1421no—
1427C23—1421no—
1428C23—1421no—
1429C23—1421no—
1430C23—1421no—
1431C23—1421no—
1432C23—1421no—
1433C23—1421no—
1434C23—1421no—
1435C23—1421no—
1436C23—1421no—
1437C23—1421no—
1438C23—1421no—
1439C23—1421no—
1440C23—1421no—
1441C23—1421no—
1442C23—1421no—
1443C23—1421no—
1444C23—1421no—
1445C23—1421no—
1446C23—1421no—
1447C23#41×D7112yes—
1448C23C24×D7111yescharacteristic
1449Q8—5682no—
1450D4—44no—
1451D4—2844no—
1452D4—2844no—
1453D4—2844no—
1454D4—2844no—
1455D4—2844no—
1456D4—2844no—
1457D4—5682no—
1458D4—5682no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—44no—
1496C2×C4—2844no—
1497C2×C4—2844no—
1498C2×C4—2844no—
1499C2×C4—2844no—
1500C2×C4—2844no—
1501C2×C4—2844no—
1502C2×C4—2844no—
1503C2×C4—2844no—
1504C2×C4—2844no—
1505C2×C4—5682no—
1506C2×C4—5682no—
1507C2×C4—5682no—
1508C2×C4—712no—
1509C2×C4—712no—
1510C2×C4—1428no—
1511C2×C4—1421no—
1512C2×C4—1421no—
1513C2×C4—1421no—
1514C2×C4—1421no—
1515C2×C4—1421no—
1516C2×C4—1421no—
1517C2×C4—1421no—
1518C2×C4—1421no—
1519C2×C4—1421no—
1520C2×C4—1421no—
1521C2×C4—1421no—
1522C2×C4—1421no—
1523C2×C4—1421no—
1524C2×C4—1421no—
1525C2×C4—1421no—
1526C2×C4—1421no—
1527C2×C4—1421no—
1528C2×C4—1421no—
1529C2×C4—1421no—
1530C2×C4—1421no—
1531C2×C4—1421no—
1532C2×C4—1421no—
1533C2×C4—1421no—
1534C2×C4—1421no—
1535C2×C4—1421no—
1536C2×C4—1421no—
1537C2×C4—1421no—
1538C2×C4—1421no—
1539C2×C4—1421no—
1540C2×C4—1421no—
1541C2×C4—1421no—
1542C2×C4—1421no—
1543C2×C4—1421no—
1544C2×C4—1421no—
1545C2×C4#41×D7112yes—
1546C2×C4#41×D7112yes—
1547C2×C4#1455617412yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—28416no—
1563C22—2841no—
1564C22—2841no—
1565C22—2841no—
1566C22—2841no—
1567C22—2841no—
1568C22—2841no—
1569C22—2841no—
1570C22—2841no—
1571C22—2841no—
1572C22—2841no—
1573C22—2841no—
1574C22—2841no—
1575C22—2841no—
1576C22—2841no—
1577C22—5688no—
1578C22—714no—
1579C22—714no—
1580C22—1422no—
1581C22—1422no—
1582C22—1422no—
1583C22—1422no—
1584C22—1422no—
1585C22—1422no—
1586C22—1422no—
1587C22—1422no—
1588C22—1422no—
1589C22—1422no—
1590C22—1422no—
1591C22—1422no—
1592C22C2×#41×D7111yescharacteristic
1593C22C2×#41×D7111yescharacteristic
1594C22C2×#41×D7111yescharacteristic
1595C22H(5,𝔽2)×D7111yescharacteristic
1596C22H(5,𝔽2)×D7111yescharacteristic
1597C22C2×#1455617411yescharacteristic
1598C22#1798683511yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—22no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—41no—
1611C4—41no—
1612C4—2841no—
1613C4—2841no—
1614C4—2841no—
1615C4—2841no—
1616C4—2841no—
1617C4—2841no—
1618C4—2841no—
1619C4—2841no—
1620C4—2841no—
1621C4—2841no—
1622C4—1422no—
1623C4—1422no—
1624C2—42no—
1625C2—81no—
1626C2—5681no—
1627C2—5681no—
1628C2—1424no—
1629C2—1424no—
1630C2#529×D7111yescharacteristic
1631C2#538×D7111yescharacteristic
1632C2#2260175011yescharacteristic
1633C2#2260202411yescharacteristic
1634C2#2260206811yescharacteristic
1635C2#2260227111yescharacteristic
1636C2#2260237511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2518C2
prime radical#22591709C2
hypercenter#2518D71
hypocenterC71#34998
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2518

Complements

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

NH ≅ G/Ntype
1. #22596673C2semidirect
2. #22596660C2semidirect
3. #22596656C2semidirect
4. #22596638C2semidirect
5. #22594396C2semidirect
6. #22594344C2semidirect
7. #22594331C2semidirect
8. #22594321C2semidirect
9. #22592992C2semidirect
10. #22592907C2semidirect
11. #22592905C2semidirect
12. #22592846C2semidirect
13. #22592663C2semidirect
14. #22592590C2semidirect
15. #22592464C2semidirect
16. #22592391C2semidirect
17. #22592279C2semidirect
18. #22592095C2semidirect
19. #22592002C2semidirect
20. #22591896C2semidirect
21. #22591729C2semidirect
23. #22591662C2semidirect
24. #22591069C2semidirect
25. #22591002C2semidirect
26. #22590976C2semidirect
27. #22590934C2semidirect
28. C4×#14556098C2semidirect
29. #386×D71C2semidirect
30. C4×C22⋊C4×D71C2semidirect
31. C71×#2518C2semidirect
34. C2×#14556122C22semidirect
35. C2×#14556114C22semidirect
37. C2×#14556113C22semidirect
40. C2×#14556106C22semidirect
46. C2×C4×D284C22semidirect
47. C2×C4×C22⋊D71C22semidirect
53. C2×C42×D71C22semidirect
54. C2×C42×D71C22semidirect
55. C71⋊#401C22semidirect
56. #17985940C22semidirect
57. #17985938C22semidirect
58. #17985938C22semidirect
59. #17985937C22semidirect
60. #17985935C22semidirect
61. #17985932C22semidirect
62. #17985928C22semidirect
63. #17985927C22semidirect
64. #17985927C22semidirect
65. #17985926C22semidirect
66. #17985926C22semidirect
67. #17985925C22semidirect
68. #17985924C22semidirect
69. #17985922C22semidirect
70. #17985922C22semidirect
71. #17985916C22semidirect
73. #17985915C22semidirect
74. #17985915C22semidirect
77. #17985914C22semidirect
79. #17985912C22semidirect
80. #17985911C22semidirect
83. #17985903C22semidirect
84. #17985903C22semidirect
85. #17985901C22semidirect
86. #17985900C22semidirect
87. #17985899C22semidirect
88. #17985897C22semidirect
89. #17985895C22semidirect
90. #17985893C22semidirect
91. #17985893C22semidirect
92. #17985892C22semidirect
93. #17985892C22semidirect
94. #17985891C22semidirect
95. #17985891C22semidirect
96. #17985891C22semidirect
97. #17985890C22semidirect
98. #17985890C22semidirect
99. #17985890C22semidirect
100. #17985889C22semidirect
101. #17985889C22semidirect
102. #17985889C22semidirect
103. #17985888C22semidirect
104. #17985888C22semidirect
105. #17985888C22semidirect
106. #17985887C22semidirect
107. #17985886C22semidirect
108. #17985885C22semidirect
109. #17985884C22semidirect
110. #17985884C22semidirect
111. #17985884C22semidirect
112. #17985884C22semidirect
113. #17985883C22semidirect
114. #17985882C22semidirect
125. #17985877C22semidirect
126. #17985877C22semidirect
127. #17985877C22semidirect
129. #17985876C22semidirect
134. #17985875C22semidirect
135. #17985874C22semidirect
138. #17985873C22semidirect
139. #17985873C22semidirect
140. #17985873C22semidirect
145. #17985870C22semidirect
146. #17985867C22semidirect
147. #17985863C22semidirect
148. #17985861C22semidirect
149. #17985861C22semidirect
152. #17985858C22semidirect
154. #17985856C22semidirect
159. C22⋊C4×Dic71C22semidirect
160. C22⋊C4×Dic71C22semidirect
164. C4×(C2×D71)⋊C4C22semidirect
165. C4×C22⋊Dic71C22semidirect
170. #95×D71C22semidirect
171. #95×D71C22semidirect
172. #397×C71C22semidirect
173. #396×C71C22semidirect
176. #389×C71C22semidirect
177. #388×C71C22semidirect
178. #388×C71C22semidirect
179. #388×C71C22semidirect
180. #388×C71C22semidirect
181. #387×C71C22semidirect
183. #383×C71C22semidirect
184. #382×C71C22semidirect
185. C4×C22⋊C4×C71C22semidirect
186. C4×C22⋊C4×C71C22semidirect
828. #2518D71semidirect
850. C71#34998semidirect
888. #397C2×D71semidirect
891. #396C2×D71semidirect
913. #389C2×D71semidirect
931. #388C2×D71semidirect
932. #388C2×D71semidirect
933. #388C2×D71semidirect
934. #388C2×D71semidirect
943. #387C2×D71semidirect
977. #383C2×D71semidirect
979. #382C2×D71semidirect
1000. C4×C22⋊C4C2×D71semidirect
1001. C4×C22⋊C4C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966732
#225966602
#225966562
#225966382
#225943962
#225943442
#225943312
#225943212
#225929922
#225929072
#225929052
#225928462
#225926632
#225925902
#225924642
#225923912
#225922792
#225920952
#225920022
#225918962
#225917292
#225917092
#225916622
#225910692
#225910022
#225909762
#225909342
C4×#145560982
#386×D712
C4×C22⋊C4×D712
C71×#25182
#3499871