Finite Group Databasebeta

← #32161816

Subgroups — #32161816

Order 18176.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986588C211yesmaximal, characteristic
2#22591532C211yesmaximal, characteristic, complemented
3#22591505C211yesmaximal, characteristic, complemented
4#22591485C211yesmaximal, characteristic, complemented
5#22591480C211yesmaximal, characteristic, complemented
6#22591465C211yesmaximal, characteristic, complemented
7#22591459C211yesmaximal, characteristic, complemented
8#22591448C211yesmaximal, characteristic, complemented
9#22591414C211yesmaximal, characteristic, complemented
10#22591368C211yesmaximal, characteristic, complemented
11#22591339C211yesmaximal, characteristic, complemented
12#22591322C211yesmaximal, characteristic, complemented
13#22591287C211yesmaximal, characteristic, complemented
14#22591281C211yesmaximal, characteristic, complemented
15#22591187C211yesmaximal, characteristic, complemented
16#22591184C211yesmaximal, characteristic, complemented
17#22591153C211yesmaximal, characteristic, complemented
18#22591137C211yesmaximal, characteristic, complemented
19#22591104C211yesmaximal, characteristic, complemented
20#22591104C211yesmaximal, characteristic, complemented
21#22591051C211yesmaximal, characteristic, complemented
22#22591044C211yesmaximal, characteristic, complemented
23#22591034C211yesmaximal, characteristic, complemented
24#22591032C211yesmaximal, characteristic, complemented
25#22591002C211yesmaximal, characteristic, complemented
26#22591000C211yesmaximal, characteristic, complemented
27#22590979C211yesmaximal, characteristic, complemented
28C4×#14556110C211yesmaximal, characteristic, complemented
29C4×#14556103C211yesmaximal, characteristic, complemented
30#22590778C211yesmaximal, characteristic, complemented
31C71×#2373C211yesmaximal, characteristic, complemented
32#17986588C4116yescomplemented
33C2×#14556123C2211yescharacteristic
34C2×#14556116C2211yescharacteristic
35C2×#14556114C2211yescharacteristic
36C2×#14556113C2211yescharacteristic
37C2×#14556110C2211yescharacteristic
38C2×#14556106C2211yescharacteristic
39C2×#14556103C2211yescharacteristic
40C2×#14556103C2211yescharacteristic
41C2×#14556101C2211yescharacteristic
42C2×#14556098C2211yescharacteristic
43C2×#14556098C2211yescharacteristic
44C2×C4×Dic142C2211yescharacteristic, complemented
45C2×C4×D284C2211yescharacteristic
46C2×C4×D284C2211yescharacteristic
47C2×C4×D284C2211yescharacteristic
48C2×C4×D284C2211yescharacteristic, complemented
49C2×#14556090C2211yescharacteristic
50C2×C4×C22⋊D71C2211yescharacteristic
51C2×(C22⋊D71)⋊C4C2211yescharacteristic
52C2×#14556086C2211yescharacteristic
53C2×#14556086C2211yescharacteristic, complemented
54C2×#14556085C2211yescharacteristic
55C22×(C2×D71)⋊C4C2211yescharacteristic
56C2×C22⋊C4×D71C2211yescharacteristic
57C2×C22⋊C4×D71C2211yescharacteristic
58C2×C42×D71C2211yescharacteristic, complemented
59#17985905C2211yescharacteristic, complemented
60#17985903C2211yescharacteristic, complemented
61#17985903C2211yescharacteristic, complemented
62#17985901C2211yescharacteristic
63#17985901C2211yescharacteristic
64#17985901C2211yescharacteristic
65#17985901C2211yescharacteristic
66#17985900C2211yescharacteristic
67#17985900C2211yescharacteristic
68#17985900C2211yescharacteristic, complemented
69#17985899C2211yescharacteristic
70#17985899C2211yescharacteristic
71#17985898C2211yescharacteristic, complemented
72#17985898C2211yescharacteristic, complemented
73#17985898C2211yescharacteristic, complemented
74#17985894C2211yescharacteristic, complemented
75#17985894C2211yescharacteristic, complemented
76#17985893C2211yescharacteristic
77#17985892C2211yescharacteristic
78#17985892C2211yescharacteristic
79#17985892C2211yescharacteristic
80#17985891C2211yescharacteristic
81#17985891C2211yescharacteristic
82#17985891C2211yescharacteristic
83#17985891C2211yescharacteristic
84#17985891C2211yescharacteristic
85#17985891C2211yescharacteristic
86#17985891C2211yescharacteristic
87#17985891C2211yescharacteristic, complemented
88#17985891C2211yescharacteristic, complemented
89#17985891C2211yescharacteristic, complemented
90#17985891C2211yescharacteristic, complemented
91#17985890C2211yescharacteristic
92#17985890C2211yescharacteristic
93#17985890C2211yescharacteristic
94#17985890C2211yescharacteristic
95#17985890C2211yescharacteristic
96#17985890C2211yescharacteristic, complemented
97#17985890C2211yescharacteristic, complemented
98#17985889C2211yescharacteristic
99#17985889C2211yescharacteristic
100#17985889C2211yescharacteristic
101#17985889C2211yescharacteristic, complemented
102#17985889C2211yescharacteristic, complemented
103#17985888C2211yescharacteristic
104#17985887C2211yescharacteristic
105#17985886C2211yescharacteristic, complemented
106#17985886C2211yescharacteristic, complemented
107#17985885C2211yescharacteristic, complemented
108#17985885C2211yescharacteristic, complemented
109#17985885C2211yescharacteristic, complemented
110#17985883C2211yescharacteristic, complemented
111#17985882C2211yescharacteristic, complemented
112#17985882C2211yescharacteristic, complemented
113#17985881C2211yescharacteristic, complemented
114#17985878C2211yescharacteristic
115#17985877C2211yescharacteristic
116#17985877C2211yescharacteristic
117#17985877C2211yescharacteristic
118#17985877C2211yescharacteristic
119#17985877C2211yescharacteristic
120#17985877C2211yescharacteristic
121#17985877C2211yescharacteristic
122#17985877C2211yescharacteristic
123#17985877C2211yescharacteristic, complemented
124#17985877C2211yescharacteristic, complemented
125#17985876C2211yescharacteristic
126#17985875C2211yescharacteristic
127#17985875C2211yescharacteristic
128#17985874C2211yescharacteristic
129#17985874C2211yescharacteristic
130#17985874C2211yescharacteristic
131#17985873C2211yescharacteristic
132#17985873C2211yescharacteristic
133#17985873C2211yescharacteristic, complemented
134#17985873C2211yescharacteristic, complemented
135#17985873C2211yescharacteristic, complemented
136#17985870C2211yescharacteristic
137#17985870C2211yescharacteristic
138#17985870C2211yescharacteristic, complemented
139#17985869C2211yescharacteristic, complemented
140#17985867C2211yescharacteristic, complemented
141#17985861C2211yescharacteristic
142#17985861C2211yescharacteristic
143#17985861C2211yescharacteristic, complemented
144#17985858C2211yescharacteristic, complemented
145#17985856C2211yescharacteristic
146#17985856C2211yescharacteristic
147#17985856C2211yescharacteristic, complemented
148#17985856C2211yescharacteristic, complemented
149#17985854C2211yescharacteristic
150#17985854C2211yescharacteristic
151C4⋊C4×Dic71C2211yescharacteristic, complemented
152C4×Dic71⋊C4C2211yescharacteristic, complemented
153C4×C4⋊Dic71C2211yescharacteristic, complemented
154C4×C4⋊Dic71C2211yescharacteristic, complemented
155#17985850C2211yescharacteristic, complemented
156#17985850C2211yescharacteristic, complemented
157C22⋊C4×Dic71C2211yescharacteristic
158C4×(C2×D71)⋊C4C2211yescharacteristic
159C4×(C2×D71)⋊C4C2211yescharacteristic
160C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
161C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
163C4×C22⋊Dic71C2211yescharacteristic
164#17985846C2211yescharacteristic
165#17985846C2211yescharacteristic
166#17985846C2211yescharacteristic
167#17985846C2211yescharacteristic
168#17985846C2211yescharacteristic, complemented
169#17985846C2211yescharacteristic, complemented
170#17985845C2211yescharacteristic, complemented
171#17985844C2211yescharacteristic, complemented
172#95×D71C2211yescharacteristic, complemented
173C2×#126×C71C2211yescharacteristic
174#389×C71C2211yescharacteristic, complemented
175#388×C71C2211yescharacteristic
176#388×C71C2211yescharacteristic
177#388×C71C2211yescharacteristic
178#387×C71C2211yescharacteristic, complemented
179#387×C71C2211yescharacteristic, complemented
180#387×C71C2211yescharacteristic, complemented
181#385×C71C2211yescharacteristic
182C4×C4⋊C4×C71C2211yescharacteristic, complemented
183C4×C4⋊C4×C71C2211yescharacteristic, complemented
184C4×C4⋊C4×C71C2211yescharacteristic, complemented
185C4×C22⋊C4×C71C2211yescharacteristic
186C4×C22⋊C4×C71C2211yescharacteristic
187#376×C71C2211yescharacteristic, complemented
188C24×D71C2311yescharacteristic
189C22×Dic142C2311yescharacteristic
190C22×D284C2311yescharacteristic
191C22×D284C2311yescharacteristic
192C22×D284C2311yescharacteristic
193C22×D284C2311yescharacteristic
194C22×D284C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C22×C22⋊D71C2311yescharacteristic
197C23×Dic71C2311yescharacteristic
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
208#14556123C2×C418yescomplemented
209#14556116C2×C418yescomplemented
210#14556114C2×C418yescomplemented
211#14556113C2×C418yescomplemented
212#14556110C2×C418yescomplemented
213#14556106C2×C418yescomplemented
214#14556103C2×C418yescomplemented
215#14556103C2×C418yescomplemented
216#14556101C2×C418yescomplemented
217#14556098C2×C418yescomplemented
218#14556098C2×C418yescomplemented
219C4×Dic142—42no—
220C4×D284—42no—
221C4×D284—42no—
222C4×D284—42no—
223C4×D284C2×C418yescomplemented
224#14556090C2×C418yescomplemented
225C4×C22⋊D71—42no—
226(C22⋊D71)⋊C4—42no—
227#14556086—42no—
228#14556086—42no—
229#14556085—42no—
230C2×C4⋊Dic71C2311yescharacteristic
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
233C2×C4⋊Dic71C2311yescharacteristic
234C2×C4⋊Dic71C2311yescharacteristic
235C2×C4⋊Dic71C2311yescharacteristic
236C2×C4⋊Dic71C2311yescharacteristic
237C2×C4⋊Dic71C2311yescharacteristic
238C2×C4⋊Dic71C2311yescharacteristic
239C2×C4⋊Dic71C2311yescharacteristic
240C2×Dic71⋊C4C2311yescharacteristic
241C2×Dic71⋊C4C2311yescharacteristic
242C2×Dic71⋊C4C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×Dic71⋊C4C2311yescharacteristic
248C2×C22⋊Dic71C2311yescharacteristic
249C2×C22⋊Dic71C2311yescharacteristic
250C2×C22⋊Dic71C2311yescharacteristic
251C2×C22⋊Dic71C2311yescharacteristic
252C2×(C2×D71)⋊C4—42no—
253C2×(C2×D71)⋊C4C2311yescharacteristic
254C2×(C2×D71)⋊C4C2311yescharacteristic
255C2×(C2×D71)⋊C4C2311yescharacteristic
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
288C2×(C2×D71)⋊C4C2311yescharacteristic
289C22⋊C4×D71—42no—
290C22⋊C4×D71C2×C418yescomplemented
291C2×C4×Dic71C2311yescharacteristic
292C2×C4×Dic71C2311yescharacteristic
293C2×C4×Dic71C2311yescharacteristic
294C2×C4×Dic71C2311yescharacteristic
295C2×C4×Dic71C2311yescharacteristic
296C2×C4×Dic71C2311yescharacteristic
297C2×C4×Dic71C2311yescharacteristic
298C2×C4×Dic71C2311yescharacteristic
299C2×C4×Dic71C2311yescharacteristic
300C2×C4×Dic71C2311yescharacteristic
301C2×C4×Dic71C2311yescharacteristic
302C2×C4×Dic71C2311yescharacteristic
303C2×C4×Dic71C2311yescharacteristic
304C2×C4×Dic71C2311yescharacteristic
305C42×D71—42no—
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
334C23×C4×C71C2311yescharacteristic
335#126×C71C2×C418yescomplemented
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×C4⋊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×C42×C71C2311yescharacteristic
351C2×C42×C71C2311yescharacteristic
352C2×C42×C71C2311yescharacteristic
353C2×C42×C71C2311yescharacteristic
354C2×C42×C71C2311yescharacteristic
355C2×C42×C71C2311yescharacteristic
356C2×C42×C71C2311yescharacteristic
357C2×C42×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
369#95×C71C2311yescharacteristic
370C23×D71—41no—
371C23×D71—41no—
372C23×D71—41no—
373C23×D71—41no—
374C23×D71—41no—
375C23×D71—41no—
376C23×D71C22×C414yes—
377C23×D71C2411yescharacteristic
378C23×D71C2411yescharacteristic
379C23×D71C2411yescharacteristic
380C23×D71C2411yescharacteristic
381C2×Dic142—41no—
382C2×Dic142—41no—
383C2×Dic142C22×C414yes—
384C2×D284—41no—
385C2×D284—41no—
386C2×D284—41no—
387C2×D284—41no—
388C2×D284—41no—
389C2×D284—41no—
390C2×D284—41no—
391C2×D284—41no—
392C2×D284—41no—
393C2×D284—41no—
394C2×D284C22×C414yes—
395C2×D284C22×C414yes—
396C2×D284C22×C414yes—
397C2×D284C22×C414yes—
398C2×D284C22×C414yes—
399C2×C22⋊D71—41no—
400C2×C22⋊D71—41no—
401C2×C22⋊D71—41no—
402C2×C22⋊D71—41no—
403C2×C22⋊D71C22×C414yes—
404C2×C22⋊D71C22×C414yes—
405C22×Dic71—41no—
406C22×Dic71—41no—
407C22×Dic71—41no—
408C22×Dic71C2411yescharacteristic
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C2×C4×D71—22no—
421C2×C4×D71—22no—
422C2×C4×D71—22no—
423C2×C4×D71—22no—
424C2×C4×D71—41no—
425C2×C4×D71—41no—
426C2×C4×D71—41no—
427C2×C4×D71—41no—
428C2×C4×D71—41no—
429C2×C4×D71—41no—
430C2×C4×D71—41no—
431C2×C4×D71—41no—
432C2×C4×D71—41no—
433C2×C4×D71—41no—
434C2×C4×D71—41no—
435C2×C4×D71—41no—
436C2×C4×D71—41no—
437C2×C4×D71—41no—
438C2×C4×D71—41no—
439C2×C4×D71—41no—
440C2×C4×D71—41no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—41no—
445C2×C4×D71—41no—
446C2×C4×D71C22×C414yes—
447C2×C4×D71C22×C414yes—
448C2×C4×D71C22×C414yes—
449C2×C4×D71C22×C414yes—
450C4⋊Dic71—41no—
451C4⋊Dic71—41no—
452C4⋊Dic71—41no—
453C4⋊Dic71—41no—
454C4⋊Dic71—41no—
455C4⋊Dic71—41no—
456C4⋊Dic71—41no—
457C4⋊Dic71—41no—
458C4⋊Dic71—41no—
459C4⋊Dic71C22×C414yes—
460Dic71⋊C4—22no—
461Dic71⋊C4—22no—
462Dic71⋊C4—41no—
463Dic71⋊C4—41no—
464Dic71⋊C4—41no—
465Dic71⋊C4—41no—
466Dic71⋊C4C22×C414yes—
467Dic71⋊C4C22×C414yes—
468C22⋊Dic71—41no—
469C22⋊Dic71—41no—
470C22⋊Dic71—41no—
471C22⋊Dic71C22×C414yes—
472(C2×D71)⋊C4—22no—
473(C2×D71)⋊C4—22no—
474(C2×D71)⋊C4—22no—
475(C2×D71)⋊C4—22no—
476(C2×D71)⋊C4—41no—
477(C2×D71)⋊C4—41no—
478(C2×D71)⋊C4—41no—
479(C2×D71)⋊C4—41no—
480(C2×D71)⋊C4—41no—
481(C2×D71)⋊C4—41no—
482(C2×D71)⋊C4—41no—
483(C2×D71)⋊C4—41no—
484(C2×D71)⋊C4—41no—
485(C2×D71)⋊C4—41no—
486(C2×D71)⋊C4—41no—
487(C2×D71)⋊C4—41no—
488(C2×D71)⋊C4—41no—
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)⋊C4—41no—
496(C2×D71)⋊C4—41no—
497(C2×D71)⋊C4—41no—
498(C2×D71)⋊C4C22×C414yes—
499(C2×D71)⋊C4C22×C414yes—
500(C2×D71)⋊C4C22×C414yes—
501(C2×D71)⋊C4C22×C414yes—
502(C2×D71)⋊C4C22×C414yes—
503(C2×D71)⋊C4C22×C414yes—
504(C2×D71)⋊C4C22×C414yes—
505(C2×D71)⋊C4C22×C414yes—
506(C2×D71)⋊C4C22×C414yes—
507(C2×D71)⋊C4C22×C414yes—
508C4×Dic71—22no—
509C4×Dic71—22no—
510C4×Dic71—41no—
511C4×Dic71—41no—
512C4×Dic71—41no—
513C4×Dic71—41no—
514C4×Dic71—41no—
515C4×Dic71—41no—
516C4×Dic71—41no—
517C4×Dic71—41no—
518C4×Dic71—41no—
519C4×Dic71—41no—
520C4×Dic71—41no—
521C4×Dic71C22×C414yes—
522C24×C71C2411yescharacteristic
523C22×C4×C71—22no—
524C22×C4×C71—41no—
525C22×C4×C71—41no—
526C22×C4×C71C2411yescharacteristic
527C22×C4×C71C2411yescharacteristic
528C22×C4×C71C2411yescharacteristic
529C22×C4×C71C2411yescharacteristic
530C22×C4×C71C2411yescharacteristic
531C22×C4×C71C2411yescharacteristic
532C22×C4×C71C2411yescharacteristic
533C22×C4×C71C2411yescharacteristic
534C22×C4×C71C2411yescharacteristic
535C22×C4×C71C2411yescharacteristic
536C22×C4×C71C2411yescharacteristic
537C22×C4×C71C2411yescharacteristic
538C22×C4×C71C2411yescharacteristic
539C22×C4×C71C2411yescharacteristic
540C4⋊C4×C71—22no—
541C4⋊C4×C71—41no—
542C4⋊C4×C71—41no—
543C4⋊C4×C71—41no—
544C4⋊C4×C71—41no—
545C4⋊C4×C71C22×C414yes—
546C4⋊C4×C71C22×C414yes—
547C4⋊C4×C71C22×C414yes—
548C22⋊C4×C71—22no—
549C22⋊C4×C71—41no—
550C22⋊C4×C71—41no—
551C22⋊C4×C71C22×C414yes—
552C22⋊C4×C71C22×C414yes—
553C22⋊C4×C71C22×C414yes—
554C42×C71—22no—
555C42×C71—22no—
556C42×C71—22no—
557C42×C71—41no—
558C42×C71—41no—
559C42×C71—41no—
560C42×C71—41no—
561C42×C71C22×C414yes—
562C23×C71—21no—
563C23×C71—21no—
564C23×C71—21no—
565C23×C71—21no—
566C23×C71—21no—
567C23×C71—21no—
568C23×C71C23×C412yes—
569C23×C71C2511yescharacteristic
570C22×D71—21no—
571C22×D71—21no—
572C22×D71—21no—
573C22×D71—21no—
574C22×D71—21no—
575C22×D71—21no—
576C22×D71—21no—
577C22×D71—21no—
578C22×D71—21no—
579C22×D71—21no—
580C22×D71—21no—
581C22×D71—21no—
582C22×D71—21no—
583C22×D71—21no—
584C22×D71—21no—
585C22×D71—21no—
586C22×D71—21no—
587C22×D71—21no—
588C22×D71—21no—
589C22×D71—21no—
590C22×D71—21no—
591C22×D71—21no—
592C22×D71—21no—
593C22×D71—21no—
594C22×D71—44no—
595C22×D71—44no—
596C22×D71—44no—
597C22×D71—82no—
598C22×D71—82no—
599C22×D71—82no—
600C22×D71—82no—
601C22×D71C23×C412yes—
602C22×D71C23×C412yes—
603C22×D71C23×C412yes—
604C22×D71C23×C412yes—
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—21no—
616C2×C4×C71—21no—
617C2×C4×C71—21no—
618C2×C4×C71—21no—
619C2×C4×C71—21no—
620C2×C4×C71—21no—
621C2×C4×C71—21no—
622C2×C4×C71—21no—
623C2×C4×C71—21no—
624C2×C4×C71—21no—
625C2×C4×C71—21no—
626C2×C4×C71—21no—
627C2×C4×C71—21no—
628C2×C4×C71—21no—
629C2×C4×C71—21no—
630C2×C4×C71—21no—
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—82no—
640C2×C4×C71C23×C412yes—
641C2×C4×C71C23×C412yes—
642C2×C4×C71C23×C412yes—
643C2×C4×C71C23×C412yes—
644C2×C4×C71C23×C412yes—
645C2×C4×C71C23×C412yes—
646C2×C4×C71H(5,𝔽2)12yes—
647C2×C4×C71H(5,𝔽2)12yes—
648C22⋊D71—44no—
649C22⋊D71—44no—
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—21no—
659C2×Dic71—21no—
660C2×Dic71—21no—
661C2×Dic71—21no—
662C2×Dic71—21no—
663C2×Dic71—21no—
664C2×Dic71—21no—
665C2×Dic71—21no—
666C2×Dic71—21no—
667C2×Dic71—21no—
668C2×Dic71—21no—
669C2×Dic71—21no—
670C2×Dic71—21no—
671C2×Dic71—21no—
672C2×Dic71—21no—
673C2×Dic71—21no—
674C2×Dic71—21no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—82no—
683C2×Dic71C23×C412yes—
684C2×Dic71C23×C412yes—
685C2×Dic71C23×C412yes—
686C2×Dic71C23×C412yes—
687D284—44no—
688D284—44no—
689D284—44no—
690D284—44no—
691D284—44no—
692C4×D71—44no—
693C4×D71—44no—
694C4×D71—44no—
695C4×D71—44no—
696C4×D71—44no—
697C4×D71—44no—
698C4×D71—82no—
699C4×D71—82no—
700C4×D71—82no—
701C4×D71—82no—
702Dic142—44no—
703C22×C71—22no—
704C22×C71—22no—
705C22×C71—22no—
706C22×C71—41no—
707C22×C71—41no—
708C22×C71—41no—
709C22×C71—41no—
710C22×C71C24×C411yescharacteristic
711C22×C71C2×H(5,𝔽2)11yescharacteristic
712C22×C71C2×H(5,𝔽2)11yescharacteristic
713C22×C71#58511yescharacteristic
714C22×C71#58511yescharacteristic
715C22×C71#58511yescharacteristic
716C22×C71#58511yescharacteristic
717C2×D71—22no—
718C2×D71—22no—
719C2×D71—22no—
720C2×D71—22no—
721C2×D71—22no—
722C2×D71—22no—
723C2×D71—22no—
724C2×D71—22no—
725C2×D71—22no—
726C2×D71—22no—
727C2×D71—22no—
728C2×D71—22no—
729C2×D71—41no—
730C2×D71—41no—
731C2×D71—41no—
732C2×D71—41no—
733C2×D71—41no—
734C2×D71—41no—
735C2×D71—41no—
736C2×D71—41no—
737C2×D71—41no—
738C2×D71—41no—
739C2×D71—41no—
740C2×D71—41no—
741C2×D71—41no—
742C2×D71—41no—
743C2×D71—41no—
744C2×D71—41no—
745C2×D71—88no—
746C4×C71—22no—
747C4×C71—22no—
748C4×C71—22no—
749C4×C71—22no—
750C4×C71—22no—
751C4×C71—22no—
752C4×C71—22no—
753C4×C71—22no—
754C4×C71—41no—
755C4×C71—41no—
756C4×C71—41no—
757C4×C71—41no—
758C4×C71—41no—
759C4×C71—41no—
760Dic71—22no—
761Dic71—22no—
762Dic71—22no—
763Dic71—22no—
764Dic71—41no—
765Dic71—41no—
766Dic71—41no—
767Dic71—41no—
768Dic71—41no—
769Dic71—41no—
770Dic71—41no—
771Dic71—41no—
772#34451—711nomaximal, Sylow
773C2×C71—42no—
774C2×C71#342811yescharacteristic
775C2×C71C4×H(5,𝔽2)11yescharacteristic
776C2×C71C4×H(5,𝔽2)11yescharacteristic
777C2×C71#353311yescharacteristic
778C2×C71#354211yescharacteristic
779C2×C71#355111yescharacteristic
780C2×C71#356811yescharacteristic
781D71—42no—
782D71—42no—
783D71—42no—
784D71—42no—
785C2×#538—711no—
786#2383—711no—
787#2378—711no—
788#2376—711no—
789#2375—711no—
790#2373—711no—
791#2373—711no—
792#2373D7111yescharacteristic, complemented
793#2372—711no—
794#2367—711no—
795#2362—711no—
796#2359—711no—
797#2358—711no—
798#2354—711no—
799#2353—711no—
800#2342—711no—
801#2342—711no—
802#2337—711no—
803#2335—711no—
804#2333—711no—
805#2333—711no—
806#2326—711no—
807#2325—711no—
808#2324—711no—
809#2324—711no—
810#2321—711no—
811#2321—711no—
812#2319—711no—
813C4×#123—711no—
814C4×#121—711no—
815#2290—711no—
816C71#3445111yescharacteristic, complemented, Sylow
817#538—7116no—
818C2×#126—711no—
819C2×#126C2×D7111yescharacteristic
820C2×#124—711no—
821C2×#124—711no—
822C2×#123—711no—
823C2×#123—711no—
824C2×C22⋊Q8—711no—
825C2×#121—711no—
826C2×#121—711no—
827C2×#121—711no—
828C2×#120—711no—
829C2×#120—711no—
830C2×C4×Q8—711no—
831C2×C4×D4—711no—
832C2×C4×D4—711no—
833C2×C4×D4—711no—
834C2×C4×D4—711no—
835C2×C4×D4—711no—
836C2×C4×D4—711no—
837C2×C4×D4—711no—
838C2×#117—711no—
839C2×#117—711no—
840C2×#117—711no—
841C22×C22⋊C4—711no—
842C22×C22⋊C4—711no—
843C22×C22⋊C4—711no—
844C22×C42—711no—
845#391—711no—
846#391—711no—
847#391—711no—
848#390—711no—
849#390—711no—
850#390—711no—
851#390—711no—
852#390—711no—
853#390—711no—
854#390—711no—
855#390—711no—
856#390—711no—
857#389—711no—
858#389—711no—
859#389—711no—
860#389—711no—
861#389—711no—
862#389C2×D7111yescharacteristic, complemented
863#388—711no—
864#388—711no—
865#388—711no—
866#388—711no—
867#388—711no—
868#388—711no—
869#388—711no—
870#388—711no—
871#388—711no—
872#388—711no—
873#388—711no—
874#388—711no—
875#388—711no—
876#388—711no—
877#388—711no—
878#388—711no—
879#388—711no—
880#388—711no—
881#388—711no—
882#388—711no—
883#388—711no—
884#388—711no—
885#388—711no—
886#388—711no—
887#388—711no—
888#388—711no—
889#388—711no—
890#388—711no—
891#388—711no—
892#388C2×D7111yescharacteristic
893#388C2×D7111yescharacteristic
894#388C2×D7111yescharacteristic
895#387—711no—
896#387—711no—
897#387—711no—
898#387—711no—
899#387—711no—
900#387—711no—
901#387—711no—
902#387—711no—
903#387—711no—
904#387C2×D7111yescharacteristic, complemented
905#387C2×D7111yescharacteristic, complemented
906#387C2×D7111yescharacteristic, complemented
907#386—711no—
908#386—711no—
909#386—711no—
910#386—711no—
911#386—711no—
912#386—711no—
913#386—711no—
914#386—711no—
915#386—711no—
916#386—711no—
917#386—711no—
918#386—711no—
919#386—711no—
920#386—711no—
921#385—711no—
922#385—711no—
923#385—711no—
924#385—711no—
925#385—711no—
926#385—711no—
927#385—711no—
928#385—711no—
929#385—711no—
930#385—711no—
931#385—711no—
932#385C2×D7111yescharacteristic
933#384—711no—
934#383—711no—
935#381—711no—
936#381—711no—
937#381—711no—
938#380—711no—
939#380—711no—
940#380—711no—
941#380—711no—
942#380—711no—
943#379—711no—
944#379—711no—
945C4×C4⋊C4—711no—
946C4×C4⋊C4—711no—
947C4×C4⋊C4—711no—
948C4×C4⋊C4—711no—
949C4×C4⋊C4—711no—
950C4×C4⋊C4—711no—
951C4×C4⋊C4C2×D7111yescharacteristic, complemented
952C4×C4⋊C4C2×D7111yescharacteristic, complemented
953C4×C4⋊C4C2×D7111yescharacteristic, complemented
954C4×C22⋊C4—711no—
955C4×C22⋊C4—711no—
956C4×C22⋊C4—711no—
957C4×C22⋊C4—711no—
958C4×C22⋊C4—711no—
959C4×C22⋊C4—711no—
960C4×C22⋊C4—711no—
961C4×C22⋊C4—711no—
962C4×C22⋊C4—711no—
963C4×C22⋊C4—711no—
964C4×C22⋊C4—711no—
965C4×C22⋊C4—711no—
966C4×C22⋊C4—711no—
967C4×C22⋊C4C2×D7111yescharacteristic
968C4×C22⋊C4C2×D7111yescharacteristic
969#376—711no—
970#376—711no—
971#376C2×D7111yescharacteristic, complemented
972C2×#95—711no—
973C25—711no—
974C22×Q8—711no—
975C22×D4—711no—
976C22×D4—711no—
977C22×D4—711no—
978C22×D4—711no—
979C22×D4—711no—
980C22×D4—711no—
981C22×D4—711no—
982C23×C4—711no—
983C23×C4—711no—
984C23×C4—711no—
985C23×C4—711no—
986C23×C4—711no—
987C23×C4—711no—
988C23×C4—711no—
989C23×C4—711no—
990C23×C4—711no—
991C23×C4—711no—
992C23×C4—711no—
993C23×C4C22×D7111yescharacteristic
994#126—718no—
995#126C4×D7118yescomplemented
996#124—718no—
997#124—718no—
998#123—718no—
999#123—718no—
1000C22⋊Q8—718no—
1001#121—718no—
1002#121—718no—
1003#121—718no—
1004#120—718no—
1005#120—718no—
1006C4×Q8—2842no—
1007C4×D4—2842no—
1008C4×D4—2842no—
1009C4×D4—2842no—
1010C4×D4—2842no—
1011C4×D4—2842no—
1012C4×D4—718no—
1013C4×D4—718no—
1014#117—2842no—
1015#117—2842no—
1016#117—2842no—
1017C2×C4⋊C4—711no—
1018C2×C4⋊C4—711no—
1019C2×C4⋊C4—711no—
1020C2×C4⋊C4—711no—
1021C2×C4⋊C4—711no—
1022C2×C4⋊C4—711no—
1023C2×C4⋊C4—711no—
1024C2×C4⋊C4—711no—
1025C2×C4⋊C4—711no—
1026C2×C4⋊C4—711no—
1027C2×C4⋊C4—711no—
1028C2×C4⋊C4—711no—
1029C2×C4⋊C4—711no—
1030C2×C4⋊C4—711no—
1031C2×C4⋊C4—711no—
1032C2×C4⋊C4—711no—
1033C2×C4⋊C4—711no—
1034C2×C4⋊C4—711no—
1035C2×C4⋊C4C22×D7111yescharacteristic
1036C2×C4⋊C4C22×D7111yescharacteristic
1037C2×C4⋊C4C22×D7111yescharacteristic
1038C2×C4⋊C4C22×D7111yescharacteristic
1039C2×C4⋊C4C22×D7111yescharacteristic
1040C2×C4⋊C4C22×D7111yescharacteristic
1041C2×C4⋊C4C22×D7111yescharacteristic
1042C2×C4⋊C4C22×D7111yescharacteristic
1043C2×C22⋊C4—2842no—
1044C2×C22⋊C4—2842no—
1045C2×C22⋊C4—711no—
1046C2×C22⋊C4—711no—
1047C2×C22⋊C4—711no—
1048C2×C22⋊C4—711no—
1049C2×C22⋊C4—711no—
1050C2×C22⋊C4—711no—
1051C2×C22⋊C4—711no—
1052C2×C22⋊C4—711no—
1053C2×C22⋊C4—711no—
1054C2×C22⋊C4—711no—
1055C2×C22⋊C4—711no—
1056C2×C22⋊C4—711no—
1057C2×C22⋊C4—711no—
1058C2×C22⋊C4—711no—
1059C2×C22⋊C4—711no—
1060C2×C22⋊C4—711no—
1061C2×C22⋊C4—711no—
1062C2×C22⋊C4—711no—
1063C2×C22⋊C4—711no—
1064C2×C22⋊C4—711no—
1065C2×C22⋊C4—711no—
1066C2×C22⋊C4—711no—
1067C2×C22⋊C4—711no—
1068C2×C22⋊C4—711no—
1069C2×C22⋊C4—711no—
1070C2×C22⋊C4—711no—
1071C2×C22⋊C4—711no—
1072C2×C22⋊C4—711no—
1073C2×C22⋊C4—711no—
1074C2×C22⋊C4—711no—
1075C2×C22⋊C4—711no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—718no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4C22×D7111yescharacteristic
1087C2×C22⋊C4C22×D7111yescharacteristic
1088C2×C22⋊C4C22×D7111yescharacteristic
1089C2×C22⋊C4C22×D7111yescharacteristic
1090C2×C22⋊C4C22×D7111yescharacteristic
1091C2×C22⋊C4C22×D7111yescharacteristic
1092C2×C42—2842no—
1093C2×C42—711no—
1094C2×C42—711no—
1095C2×C42—711no—
1096C2×C42—711no—
1097C2×C42—711no—
1098C2×C42—711no—
1099C2×C42—711no—
1100C2×C42—711no—
1101C2×C42—711no—
1102C2×C42—711no—
1103C2×C42—711no—
1104C2×C42—711no—
1105C2×C42—711no—
1106C2×C42—711no—
1107C2×C42C22×D7111yescharacteristic
1108C2×C42C22×D7111yescharacteristic
1109C2×C42C22×D7111yescharacteristic
1110C2×C42C22×D7111yescharacteristic
1111C2×C42C22×D7111yescharacteristic
1112C2×C42C22×D7111yescharacteristic
1113C2×C42C22×D7111yescharacteristic
1114C2×C42C22×D7111yescharacteristic
1115#95—711no—
1116#95—711no—
1117#95—711no—
1118#95—711no—
1119#95—711no—
1120#95—711no—
1121#95—711no—
1122#95—711no—
1123#95—711no—
1124#95—711no—
1125#95—711no—
1126#95—711no—
1127#95—711no—
1128#95—711no—
1129#95—711no—
1130#95—711no—
1131#95—711no—
1132#95—711no—
1133#95—711no—
1134#95—711no—
1135#95—711no—
1136#95—711no—
1137#95—711no—
1138#95—711no—
1139#95—711no—
1140#95—711no—
1141#95—711no—
1142#95—711no—
1143#95C22×D7111yescharacteristic
1144#95C22×D7111yescharacteristic
1145#95C22×D7111yescharacteristic
1146#95C22×D7111yescharacteristic
1147#95C22×D7111yescharacteristic
1148#95C22×D7111yescharacteristic
1149#95C22×D7111yescharacteristic
1150#95C22×D7111yescharacteristic
1151#95C22×D7111yescharacteristic
1152#95C22×D7111yescharacteristic
1153#95C22×D7111yescharacteristic
1154#95C22×D7111yescharacteristic
1155C24—2841no—
1156C24—2841no—
1157C24—2841no—
1158C24—2841no—
1159C24—2841no—
1160C24—2841no—
1161C24—714no—
1162C24—711no—
1163C24—711no—
1164C24—711no—
1165C24—711no—
1166C24C23×D7111yescharacteristic
1167C2×Q8—2841no—
1168C2×Q8—2841no—
1169C2×Q8—714no—
1170C2×D4—2841no—
1171C2×D4—2841no—
1172C2×D4—2841no—
1173C2×D4—2841no—
1174C2×D4—2841no—
1175C2×D4—2841no—
1176C2×D4—2841no—
1177C2×D4—2841no—
1178C2×D4—2841no—
1179C2×D4—2841no—
1180C2×D4—2841no—
1181C2×D4—2841no—
1182C2×D4—2841no—
1183C2×D4—2841no—
1184C2×D4—714no—
1185C2×D4—714no—
1186C2×D4—714no—
1187C2×D4—714no—
1188C2×D4—714no—
1189C2×D4—714no—
1190C2×D4—714no—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—2841no—
1195C22×C4—2841no—
1196C22×C4—2841no—
1197C22×C4—2841no—
1198C22×C4—2841no—
1199C22×C4—2841no—
1200C22×C4—2841no—
1201C22×C4—2841no—
1202C22×C4—2841no—
1203C22×C4—2841no—
1204C22×C4—2841no—
1205C22×C4—2841no—
1206C22×C4—2841no—
1207C22×C4—2841no—
1208C22×C4—2841no—
1209C22×C4—2841no—
1210C22×C4—2841no—
1211C22×C4—2841no—
1212C22×C4—2841no—
1213C22×C4—2841no—
1214C22×C4—2841no—
1215C22×C4—2841no—
1216C22×C4—2841no—
1217C22×C4—2841no—
1218C22×C4—2841no—
1219C22×C4—714no—
1220C22×C4—714no—
1221C22×C4—714no—
1222C22×C4—714no—
1223C22×C4—711no—
1224C22×C4—711no—
1225C22×C4—711no—
1226C22×C4—711no—
1227C22×C4—711no—
1228C22×C4—711no—
1229C22×C4—711no—
1230C22×C4—711no—
1231C22×C4—711no—
1232C22×C4—711no—
1233C22×C4—711no—
1234C22×C4—711no—
1235C22×C4—1422no—
1236C22×C4—1422no—
1237C22×C4—1422no—
1238C22×C4—1422no—
1239C22×C4C23×D7111yescharacteristic
1240C22×C4C23×D7111yescharacteristic
1241C22×C4C23×D7111yescharacteristic
1242C22×C4C23×D7111yescharacteristic
1243C22×C4C23×D7111yescharacteristic
1244C22×C4C23×D7111yescharacteristic
1245C22×C4C23×D7111yescharacteristic
1246C22×C4C23×D7111yescharacteristic
1247C22×C4C23×D7111yescharacteristic
1248C22×C4C23×D7111yescharacteristic
1249C22×C4C23×D7111yescharacteristic
1250C22×C4C23×D7111yescharacteristic
1251C22×C4C23×D7111yescharacteristic
1252C22×C4C23×D7111yescharacteristic
1253C4⋊C4—22no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—41no—
1258C4⋊C4—2841no—
1259C4⋊C4—2841no—
1260C4⋊C4—2841no—
1261C4⋊C4—2841no—
1262C4⋊C4—2841no—
1263C4⋊C4—2841no—
1264C4⋊C4—2841no—
1265C4⋊C4—2841no—
1266C4⋊C4—2841no—
1267C4⋊C4—2841no—
1268C4⋊C4—2841no—
1269C4⋊C4—2841no—
1270C4⋊C4—2841no—
1271C4⋊C4—714no—
1272C4⋊C4—714no—
1273C4⋊C4—714no—
1274C4⋊C4—1422no—
1275C4⋊C4—1422no—
1276C4⋊C4C2×C4×D7114yes—
1277C4⋊C4C2×C4×D7114yes—
1278C4⋊C4C2×C4×D7114yes—
1279C22⋊C4—22no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—2841no—
1283C22⋊C4—2841no—
1284C22⋊C4—2841no—
1285C22⋊C4—2841no—
1286C22⋊C4—2841no—
1287C22⋊C4—2841no—
1288C22⋊C4—2841no—
1289C22⋊C4—2841no—
1290C22⋊C4—2841no—
1291C22⋊C4—2841no—
1292C22⋊C4—2841no—
1293C22⋊C4—2841no—
1294C22⋊C4—2841no—
1295C22⋊C4—2841no—
1296C22⋊C4—2841no—
1297C22⋊C4—2841no—
1298C22⋊C4—2841no—
1299C22⋊C4—2841no—
1300C22⋊C4—2841no—
1301C22⋊C4—2841no—
1302C22⋊C4—2841no—
1303C22⋊C4—2841no—
1304C22⋊C4—2841no—
1305C22⋊C4—2841no—
1306C22⋊C4—2841no—
1307C22⋊C4—714no—
1308C22⋊C4—714no—
1309C22⋊C4—714no—
1310C22⋊C4—714no—
1311C22⋊C4—714no—
1312C22⋊C4—714no—
1313C22⋊C4—714no—
1314C22⋊C4—714no—
1315C22⋊C4—714no—
1316C22⋊C4—714no—
1317C22⋊C4—714no—
1318C22⋊C4—1422no—
1319C22⋊C4—1422no—
1320C22⋊C4—1422no—
1321C22⋊C4—1422no—
1322C22⋊C4C2×C4×D7114yes—
1323C22⋊C4C2×C4×D7114yes—
1324C22⋊C4C2×C4×D7114yes—
1325C42—22no—
1326C42—22no—
1327C42—22no—
1328C42—41no—
1329C42—41no—
1330C42—41no—
1331C42—41no—
1332C42—2841no—
1333C42—2841no—
1334C42—2841no—
1335C42—2841no—
1336C42—2841no—
1337C42—2841no—
1338C42—2841no—
1339C42—2841no—
1340C42—2841no—
1341C42—2841no—
1342C42—2841no—
1343C42—714no—
1344C42—1422no—
1345C42—1422no—
1346C42C2×C4×D7114yes—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—2844no—
1354C23—2844no—
1355C23—2844no—
1356C23—5682no—
1357C23—5682no—
1358C23—5682no—
1359C23—5682no—
1360C23—712no—
1361C23—712no—
1362C23—712no—
1363C23—712no—
1364C23—1421no—
1365C23—1421no—
1366C23—1421no—
1367C23—1421no—
1368C23—1421no—
1369C23—1421no—
1370C23—1421no—
1371C23—1421no—
1372C23—1421no—
1373C23—1421no—
1374C23—1421no—
1375C23—1421no—
1376C23—1421no—
1377C23—1421no—
1378C23—1421no—
1379C23—1421no—
1380C23—1421no—
1381C23—1421no—
1382C23—1421no—
1383C23—1421no—
1384C23—1421no—
1385C23—1421no—
1386C23—1421no—
1387C23—1421no—
1388C23C22×C4×D7112yes—
1389C23C24×D7111yescharacteristic
1390Q8—2844no—
1391D4—2844no—
1392D4—2844no—
1393D4—2844no—
1394D4—2844no—
1395D4—2844no—
1396D4—2844no—
1397D4—2844no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—82no—
1433C2×C4—2844no—
1434C2×C4—2844no—
1435C2×C4—2844no—
1436C2×C4—2844no—
1437C2×C4—2844no—
1438C2×C4—2844no—
1439C2×C4—5682no—
1440C2×C4—5682no—
1441C2×C4—5682no—
1442C2×C4—5682no—
1443C2×C4—5682no—
1444C2×C4—712no—
1445C2×C4—712no—
1446C2×C4—712no—
1447C2×C4—712no—
1448C2×C4—1421no—
1449C2×C4—1421no—
1450C2×C4—1421no—
1451C2×C4—1421no—
1452C2×C4—1421no—
1453C2×C4—1421no—
1454C2×C4—1421no—
1455C2×C4—1421no—
1456C2×C4—1421no—
1457C2×C4—1421no—
1458C2×C4—1421no—
1459C2×C4—1421no—
1460C2×C4—1421no—
1461C2×C4—1421no—
1462C2×C4—1421no—
1463C2×C4—1421no—
1464C2×C4—1421no—
1465C2×C4—1421no—
1466C2×C4—1421no—
1467C2×C4—1421no—
1468C2×C4—1421no—
1469C2×C4—1421no—
1470C2×C4—1421no—
1471C2×C4—1421no—
1472C2×C4—1421no—
1473C2×C4—1421no—
1474C2×C4—1421no—
1475C2×C4—1421no—
1476C2×C4—1421no—
1477C2×C4—1421no—
1478C2×C4—1421no—
1479C2×C4—1421no—
1480C2×C4C22×C4×D7112yes—
1481C2×C4C22×C4×D7112yes—
1482C2×C4C22×C4×D7112yes—
1483C2×C4C22×C4×D7112yes—
1484C2×C4C22×C4×D7112yes—
1485C2×C4C22×C4×D7112yes—
1486C2×C4#1455617412yes—
1487C2×C4#1455617412yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—41no—
1492C22—41no—
1493C22—41no—
1494C22—41no—
1495C22—2841no—
1496C22—2841no—
1497C22—2841no—
1498C22—2841no—
1499C22—2841no—
1500C22—2841no—
1501C22—2841no—
1502C22—2841no—
1503C22—2841no—
1504C22—2841no—
1505C22—2841no—
1506C22—2841no—
1507C22—2841no—
1508C22—2841no—
1509C22—2841no—
1510C22—2841no—
1511C22—5688no—
1512C22—1422no—
1513C22—1422no—
1514C22—1422no—
1515C22—1422no—
1516C22—1422no—
1517C22—1422no—
1518C22—1422no—
1519C22—1422no—
1520C22—1422no—
1521C22—1422no—
1522C22—1422no—
1523C22—1422no—
1524C22C23×C4×D7111yescharacteristic
1525C22C2×#1455617411yescharacteristic
1526C22C2×#1455617411yescharacteristic
1527C22#1798683411yescharacteristic
1528C22#1798683511yescharacteristic
1529C22#1798683511yescharacteristic
1530C22#1798683611yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—22no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—2841no—
1546C4—2841no—
1547C4—2841no—
1548C4—2841no—
1549C4—2841no—
1550C4—2841no—
1551C4—2841no—
1552C4—2841no—
1553C4—1422no—
1554C4—1422no—
1555C4—1422no—
1556C4—1422no—
1557C2—42no—
1558C2—2842no—
1559C2—2842no—
1560C2—2842no—
1561C2—2842no—
1562C2#2260154011yescharacteristic
1563C2C4×#1455617411yescharacteristic
1564C2C4×#1455617411yescharacteristic
1565C2#2260251211yescharacteristic
1566C2#2260265011yescharacteristic
1567C2#2260276611yescharacteristic
1568C2#2260303511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2373C2
socle, cosocleC23×C71C25
prime radicalC2×#17986588C2
hypercenter#2373D71
hypocenterC71#34451
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2373

Complements

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

NH ≅ G/Ntype
2. #22591532C2semidirect
3. #22591505C2semidirect
4. #22591485C2semidirect
5. #22591480C2semidirect
6. #22591465C2semidirect
7. #22591459C2semidirect
8. #22591448C2semidirect
9. #22591414C2semidirect
10. #22591368C2semidirect
11. #22591339C2semidirect
12. #22591322C2semidirect
13. #22591287C2semidirect
14. #22591281C2semidirect
15. #22591187C2semidirect
16. #22591184C2semidirect
17. #22591153C2semidirect
18. #22591137C2semidirect
19. #22591104C2semidirect
20. #22591104C2semidirect
21. #22591051C2semidirect
22. #22591044C2semidirect
23. #22591034C2semidirect
24. #22591032C2semidirect
25. #22591002C2semidirect
26. #22591000C2semidirect
27. #22590979C2semidirect
28. C4×#14556110C2semidirect
29. C4×#14556103C2semidirect
30. #22590778C2semidirect
31. C71×#2373C2semidirect
32. #17986588C4semidirect
44. C2×C4×Dic142C22semidirect
48. C2×C4×D284C22semidirect
53. C2×#14556086C22semidirect
58. C2×C42×D71C22semidirect
59. #17985905C22semidirect
60. #17985903C22semidirect
61. #17985903C22semidirect
68. #17985900C22semidirect
71. #17985898C22semidirect
72. #17985898C22semidirect
73. #17985898C22semidirect
74. #17985894C22semidirect
75. #17985894C22semidirect
87. #17985891C22semidirect
88. #17985891C22semidirect
89. #17985891C22semidirect
90. #17985891C22semidirect
96. #17985890C22semidirect
97. #17985890C22semidirect
101. #17985889C22semidirect
102. #17985889C22semidirect
105. #17985886C22semidirect
106. #17985886C22semidirect
107. #17985885C22semidirect
108. #17985885C22semidirect
109. #17985885C22semidirect
110. #17985883C22semidirect
111. #17985882C22semidirect
112. #17985882C22semidirect
113. #17985881C22semidirect
123. #17985877C22semidirect
124. #17985877C22semidirect
133. #17985873C22semidirect
134. #17985873C22semidirect
135. #17985873C22semidirect
138. #17985870C22semidirect
139. #17985869C22semidirect
140. #17985867C22semidirect
143. #17985861C22semidirect
144. #17985858C22semidirect
147. #17985856C22semidirect
148. #17985856C22semidirect
151. C4⋊C4×Dic71C22semidirect
152. C4×Dic71⋊C4C22semidirect
153. C4×C4⋊Dic71C22semidirect
154. C4×C4⋊Dic71C22semidirect
155. #17985850C22semidirect
156. #17985850C22semidirect
160. C4×(C2×D71)⋊C4C22semidirect
161. C4×(C2×D71)⋊C4C22semidirect
162. C4×(C2×D71)⋊C4C22semidirect
168. #17985846C22semidirect
169. #17985846C22semidirect
170. #17985845C22semidirect
171. #17985844C22semidirect
172. #95×D71C22semidirect
174. #389×C71C22semidirect
178. #387×C71C22semidirect
179. #387×C71C22semidirect
180. #387×C71C22semidirect
182. C4×C4⋊C4×C71C22semidirect
183. C4×C4⋊C4×C71C22semidirect
184. C4×C4⋊C4×C71C22semidirect
187. #376×C71C22semidirect
208. #14556123C2×C4semidirect
209. #14556116C2×C4semidirect
210. #14556114C2×C4semidirect
211. #14556113C2×C4semidirect
212. #14556110C2×C4semidirect
213. #14556106C2×C4semidirect
214. #14556103C2×C4semidirect
215. #14556103C2×C4semidirect
216. #14556101C2×C4semidirect
217. #14556098C2×C4semidirect
218. #14556098C2×C4semidirect
223. C4×D284C2×C4semidirect
224. #14556090C2×C4semidirect
290. C22⋊C4×D71C2×C4semidirect
335. #126×C71C2×C4semidirect
792. #2373D71semidirect
816. C71#34451semidirect
862. #389C2×D71semidirect
904. #387C2×D71semidirect
905. #387C2×D71semidirect
906. #387C2×D71semidirect
951. C4×C4⋊C4C2×D71semidirect
952. C4×C4⋊C4C2×D71semidirect
953. C4×C4⋊C4C2×D71semidirect
971. #376C2×D71semidirect
995. #126C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865882
#225915322
#225915052
#225914852
#225914802
#225914652
#225914592
#225914482
#225914142
#225913682
#225913392
#225913222
#225912872
#225912812
#225911872
#225911842
#225911532
#225911372
#225911042
#225910512
#225910442
#225910342
#225910322
#225910022
#225910002
#225909792
C4×#145561102
C4×#145561032
#225907782
C71×#23732
#3445171