Finite Group Databasebeta

← #32170262

Subgroups — #32170262

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#22596671C211yesmaximal, characteristic, complemented
2#22596662C211yesmaximal, characteristic, complemented
3#22596655C211yesmaximal, characteristic, complemented
4#22596641C211yesmaximal, characteristic, complemented
5#22594397C211yesmaximal, characteristic, complemented
6#22594337C211yesmaximal, characteristic, complemented
7#22594322C211yesmaximal, characteristic, complemented
8#22594322C211yesmaximal, characteristic, complemented
9#22592998C211yesmaximal, characteristic, complemented
10#22592992C211yesmaximal, characteristic, complemented
11#22592900C211yesmaximal, characteristic, complemented
12#22592894C211yesmaximal, characteristic, complemented
13#22592835C211yesmaximal, characteristic, complemented
14#22592666C211yesmaximal, characteristic, complemented
15#22592586C211yesmaximal, characteristic, complemented
16#22592466C211yesmaximal, characteristic, complemented
17#22592391C211yesmaximal, characteristic, complemented
18#22592277C211yesmaximal, characteristic, complemented
19#22592090C211yesmaximal, characteristic, complemented
20#22592001C211yesmaximal, characteristic, complemented
21#22591891C211yesmaximal, characteristic, complemented
22#22591736C211yesmaximal, characteristic, complemented
23#22591708C211yesmaximal, characteristic
24#22591667C211yesmaximal, characteristic, complemented
25#22591068C211yesmaximal, characteristic, complemented
26#22591000C211yesmaximal, characteristic, complemented
27#22590967C211yesmaximal, characteristic, complemented
28#22590935C211yesmaximal, characteristic, complemented
29C4×#14556097C211yesmaximal, characteristic, complemented
30C2×#17985878C211yesmaximal, characteristic, complemented
31C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
32C23×C22⋊D71C2211yescharacteristic
33C2×#14556122C2211yescharacteristic, complemented
34C2×#14556116C2211yescharacteristic, complemented
35C2×#14556111C2211yescharacteristic
36C2×#14556111C2211yescharacteristic
37C2×#14556111C2211yescharacteristic, complemented
38C2×#14556107C2211yescharacteristic, complemented
39C2×#14556105C2211yescharacteristic
40C2×#14556102C2211yescharacteristic
41C2×#14556102C2211yescharacteristic
42C2×#14556098C2211yescharacteristic
43C2×#14556097C2211yescharacteristic
44C2×C4×C22⋊D71C2211yescharacteristic
45C2×C4×C22⋊D71C2211yescharacteristic, complemented
46C2×C4×C22⋊D71C2211yescharacteristic, complemented
47C22×C22⋊Dic71C2211yescharacteristic
48C22×(C2×D71)⋊C4C2211yescharacteristic
49C22×(C2×D71)⋊C4C2211yescharacteristic
50C71⋊#401C2211yescharacteristic, complemented
51#17985941C2211yescharacteristic, complemented
52#17985941C2211yescharacteristic, complemented
53#17985941C2211yescharacteristic, complemented
54#17985940C2211yescharacteristic, complemented
55#17985935C2211yescharacteristic, complemented
56#17985933C2211yescharacteristic, complemented
57#17985928C2211yescharacteristic, complemented
58#17985928C2211yescharacteristic, complemented
59#17985928C2211yescharacteristic, complemented
60#17985928C2211yescharacteristic, complemented
61#17985928C2211yescharacteristic, complemented
62#17985927C2211yescharacteristic, complemented
63#17985927C2211yescharacteristic, complemented
64#17985926C2211yescharacteristic, complemented
65#17985923C2211yescharacteristic, complemented
66#17985922C2211yescharacteristic, complemented
67#17985922C2211yescharacteristic, complemented
68#17985917C2211yescharacteristic, complemented
69#17985917C2211yescharacteristic, complemented
70#17985915C2211yescharacteristic
71#17985915C2211yescharacteristic
72#17985914C2211yescharacteristic
73#17985914C2211yescharacteristic
74#17985914C2211yescharacteristic
75#17985914C2211yescharacteristic
76#17985914C2211yescharacteristic, complemented
77#17985914C2211yescharacteristic, complemented
78#17985912C2211yescharacteristic, complemented
79#17985911C2211yescharacteristic, complemented
80#17985908C2211yescharacteristic
81#17985908C2211yescharacteristic
82#17985905C2211yescharacteristic, complemented
83#17985903C2211yescharacteristic, complemented
84#17985901C2211yescharacteristic, complemented
85#17985901C2211yescharacteristic, complemented
86#17985901C2211yescharacteristic, complemented
87#17985897C2211yescharacteristic, complemented
88#17985897C2211yescharacteristic, complemented
89#17985896C2211yescharacteristic, complemented
90#17985891C2211yescharacteristic, complemented
91#17985891C2211yescharacteristic, complemented
92#17985890C2211yescharacteristic, complemented
93#17985890C2211yescharacteristic, complemented
94#17985890C2211yescharacteristic, complemented
95#17985890C2211yescharacteristic, complemented
96#17985890C2211yescharacteristic, complemented
97#17985890C2211yescharacteristic, complemented
98#17985890C2211yescharacteristic, complemented
99#17985890C2211yescharacteristic, complemented
100#17985890C2211yescharacteristic, complemented
101#17985890C2211yescharacteristic, complemented
102#17985890C2211yescharacteristic, complemented
103#17985890C2211yescharacteristic, complemented
104#17985890C2211yescharacteristic, complemented
105#17985890C2211yescharacteristic, complemented
106#17985890C2211yescharacteristic, complemented
107#17985888C2211yescharacteristic, complemented
108#17985888C2211yescharacteristic, complemented
109#17985888C2211yescharacteristic, complemented
110#17985888C2211yescharacteristic, complemented
111#17985886C2211yescharacteristic, complemented
112#17985883C2211yescharacteristic, complemented
113#17985883C2211yescharacteristic, complemented
114#17985883C2211yescharacteristic, complemented
115#17985883C2211yescharacteristic, complemented
116#17985883C2211yescharacteristic, complemented
117#17985883C2211yescharacteristic, complemented
118#17985883C2211yescharacteristic, complemented
119#17985882C2211yescharacteristic, complemented
120#17985878C2211yescharacteristic
121#17985878C2211yescharacteristic
122#17985878C2211yescharacteristic
123#17985878C2211yescharacteristic
124#17985878C2211yescharacteristic
125#17985878C2211yescharacteristic
126#17985878C2211yescharacteristic
127#17985878C2211yescharacteristic
128#17985878C2211yescharacteristic
129#17985878C2211yescharacteristic
130#17985878C2211yescharacteristic
131#17985878C2211yescharacteristic
132#17985878C2211yescharacteristic
133#17985878C2211yescharacteristic, complemented
134#17985878C2211yescharacteristic, complemented
135#17985878C2211yescharacteristic, complemented
136#17985877C2211yescharacteristic, complemented
137#17985877C2211yescharacteristic, complemented
138#17985876C2211yescharacteristic
139#17985876C2211yescharacteristic
140#17985876C2211yescharacteristic
141#17985874C2211yescharacteristic
142#17985874C2211yescharacteristic
143#17985872C2211yescharacteristic
144#17985872C2211yescharacteristic, complemented
145#17985872C2211yescharacteristic, complemented
146#17985872C2211yescharacteristic, complemented
147#17985872C2211yescharacteristic, complemented
148#17985872C2211yescharacteristic, complemented
149#17985871C2211yescharacteristic
150#17985871C2211yescharacteristic
151#17985871C2211yescharacteristic
152#17985867C2211yescharacteristic, complemented
153#17985866C2211yescharacteristic, complemented
154#17985865C2211yescharacteristic, complemented
155#17985863C2211yescharacteristic, complemented
156#17985862C2211yescharacteristic, complemented
157#17985861C2211yescharacteristic, complemented
158#17985859C2211yescharacteristic, complemented
159#17985858C2211yescharacteristic, complemented
160#17985857C2211yescharacteristic
161#17985857C2211yescharacteristic
162#17985857C2211yescharacteristic
163#17985855C2211yescharacteristic
164#17985854C2211yescharacteristic
165#17985854C2211yescharacteristic
166#17985854C2211yescharacteristic
167C4×C22⋊Dic71C2211yescharacteristic
168C4×C22⋊Dic71C2211yescharacteristic, complemented
169C4×C22⋊Dic71C2211yescharacteristic, complemented
170C2×C71⋊#95C2211yescharacteristic
171C2×C71⋊#95C2211yescharacteristic
172C24×C4×C71C2211yescharacteristic
173C22×C22⋊C4×C71C2211yescharacteristic
174C22×C22⋊C4×C71C2211yescharacteristic
175C22×C42×C71C2211yescharacteristic, complemented
176C22×C42×C71C2211yescharacteristic, complemented
177C4×C22⋊C4×C71C2211yescharacteristic
178C4×C22⋊C4×C71C2211yescharacteristic
179C4×C22⋊C4×C71C2211yescharacteristic
180C4×C22⋊C4×C71C2211yescharacteristic
181C4×C22⋊C4×C71C2211yescharacteristic, complemented
182C4×C22⋊C4×C71C2211yescharacteristic, complemented
183C4×C22⋊C4×C71C2211yescharacteristic, complemented
184C4×C22⋊C4×C71C2211yescharacteristic, complemented
185C2×#95×C71C2211yescharacteristic, complemented
186C2×#95×C71C2211yescharacteristic, complemented
187C24×D71C2311yescharacteristic
188C22×Dic142C2311yescharacteristic
189C22×D284C2311yescharacteristic
190C22×D284C2311yescharacteristic
191C22×C22⋊D71—24no—
192C22×C22⋊D71—42no—
193C22×C22⋊D71—42no—
194C22×C22⋊D71C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C22×C22⋊D71C2311yescharacteristic
197C22×C22⋊D71C2311yescharacteristic
198C22×C22⋊D71C2311yescharacteristic
199C22×C22⋊D71C2311yescharacteristic
200C22×C22⋊D71C2311yescharacteristic
201C23×Dic71C2311yescharacteristic
202C23×Dic71C2311yescharacteristic
203C23×Dic71C2311yescharacteristic
204C22×C4×D71C2311yescharacteristic
205#14556122—42no—
206#14556116—42no—
207#14556111—42no—
208#14556111—42no—
209#14556111—42no—
210#14556107—42no—
211#14556105—24no—
212#14556102—42no—
213#14556102—42no—
214#14556098—24no—
215#14556097—24no—
216C4×C22⋊D71—24no—
217C4×C22⋊D71—42no—
218C4×C22⋊D71—42no—
219C2×C4⋊Dic71C2311yescharacteristic
220C2×C4⋊Dic71C2311yescharacteristic
221C2×C4⋊Dic71C2311yescharacteristic
222C2×C4⋊Dic71C2311yescharacteristic
223C2×C4⋊Dic71C2311yescharacteristic
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
241C2×C22⋊Dic71—42no—
242C2×C22⋊Dic71C2311yescharacteristic
243C2×C22⋊Dic71C2311yescharacteristic
244C2×C22⋊Dic71C2311yescharacteristic
245C2×C22⋊Dic71C2311yescharacteristic
246C2×C22⋊Dic71C2311yescharacteristic
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×(C2×D71)⋊C4—24no—
256C2×(C2×D71)⋊C4—42no—
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×C4×Dic71C2311yescharacteristic
289C2×C4×Dic71C2311yescharacteristic
290C2×C4×Dic71C2311yescharacteristic
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
327C25×C71C2311yescharacteristic
328C23×C4×C71—24no—
329C23×C4×C71—42no—
330C23×C4×C71—42no—
331C23×C4×C71C2311yescharacteristic
332C23×C4×C71C2311yescharacteristic
333C23×C4×C71C2311yescharacteristic
334C23×C4×C71C2311yescharacteristic
335C23×C4×C71C2311yescharacteristic
336C23×C4×C71C2311yescharacteristic
337C23×C4×C71C2311yescharacteristic
338C23×C4×C71C2311yescharacteristic
339C23×C4×C71C2311yescharacteristic
340C23×C4×C71C2311yescharacteristic
341C2×C22⋊C4×C71—24no—
342C2×C22⋊C4×C71—24no—
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×C42×C71—42no—
352C2×C42×C71—42no—
353C2×C42×C71C2311yescharacteristic
354C2×C42×C71C2311yescharacteristic
355C2×C42×C71C2311yescharacteristic
356C2×C42×C71C2311yescharacteristic
357C2×C42×C71C2311yescharacteristic
358C2×C42×C71C2311yescharacteristic
359C2×C42×C71C2311yescharacteristic
360C2×C42×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—41no—
373C23×D71—41no—
374C23×D71—41no—
375C23×D71—41no—
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C23×D71C2411yescharacteristic
379C2×Dic142—22no—
380C2×Dic142—41no—
381C2×Dic142—41no—
382C2×D284—22no—
383C2×D284—22no—
384C2×D284—41no—
385C2×D284—41no—
386C2×D284—41no—
387C2×D284—41no—
388C2×C22⋊D71—22no—
389C2×C22⋊D71—22no—
390C2×C22⋊D71—22no—
391C2×C22⋊D71—22no—
392C2×C22⋊D71—22no—
393C2×C22⋊D71—22no—
394C2×C22⋊D71—22no—
395C2×C22⋊D71—22no—
396C2×C22⋊D71—22no—
397C2×C22⋊D71—22no—
398C2×C22⋊D71—22no—
399C2×C22⋊D71—22no—
400C2×C22⋊D71—22no—
401C2×C22⋊D71—22no—
402C2×C22⋊D71—22no—
403C2×C22⋊D71—41no—
404C2×C22⋊D71—41no—
405C2×C22⋊D71—41no—
406C2×C22⋊D71—41no—
407C2×C22⋊D71—41no—
408C2×C22⋊D71—41no—
409C2×C22⋊D71—416no—
410C22×Dic71—22no—
411C22×Dic71—22no—
412C22×Dic71—22no—
413C22×Dic71—41no—
414C22×Dic71—41no—
415C22×Dic71—41no—
416C22×Dic71—41no—
417C22×Dic71—41no—
418C22×Dic71—41no—
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C22×Dic71C2411yescharacteristic
423C22×Dic71C2411yescharacteristic
424C22×Dic71C2411yescharacteristic
425C22×Dic71C2411yescharacteristic
426C22×Dic71C2411yescharacteristic
427C22×Dic71C2411yescharacteristic
428C22×Dic71C2411yescharacteristic
429C22×Dic71C2411yescharacteristic
430C22×Dic71C2411yescharacteristic
431C22×Dic71C2411yescharacteristic
432C2×C4×D71—22no—
433C2×C4×D71—41no—
434C2×C4×D71—41no—
435C4⋊Dic71—22no—
436C4⋊Dic71—41no—
437C4⋊Dic71—41no—
438C4⋊Dic71—41no—
439C4⋊Dic71—41no—
440Dic71⋊C4—22no—
441Dic71⋊C4—22no—
442Dic71⋊C4—22no—
443Dic71⋊C4—22no—
444Dic71⋊C4—41no—
445Dic71⋊C4—41no—
446Dic71⋊C4—41no—
447Dic71⋊C4—41no—
448Dic71⋊C4—41no—
449Dic71⋊C4—41no—
450Dic71⋊C4—41no—
451Dic71⋊C4—41no—
452Dic71⋊C4—41no—
453Dic71⋊C4—41no—
454Dic71⋊C4—41no—
455Dic71⋊C4—41no—
456Dic71⋊C4—41no—
457C22⋊Dic71—22no—
458C22⋊Dic71—22no—
459C22⋊Dic71—22no—
460C22⋊Dic71—22no—
461C22⋊Dic71—22no—
462C22⋊Dic71—22no—
463C22⋊Dic71—22no—
464C22⋊Dic71—22no—
465C22⋊Dic71—22no—
466C22⋊Dic71—41no—
467C22⋊Dic71—41no—
468C22⋊Dic71—41no—
469C22⋊Dic71—41no—
470(C2×D71)⋊C4—22no—
471(C2×D71)⋊C4—22no—
472(C2×D71)⋊C4—22no—
473(C2×D71)⋊C4—22no—
474(C2×D71)⋊C4—22no—
475(C2×D71)⋊C4—22no—
476(C2×D71)⋊C4—22no—
477(C2×D71)⋊C4—22no—
478(C2×D71)⋊C4—22no—
479(C2×D71)⋊C4—22no—
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)⋊C4—41no—
499(C2×D71)⋊C4—41no—
500(C2×D71)⋊C4—41no—
501C4×Dic71—22no—
502C4×Dic71—41no—
503C4×Dic71—41no—
504C24×C71—22no—
505C24×C71—22no—
506C24×C71—22no—
507C24×C71—22no—
508C24×C71—41no—
509C24×C71—41no—
510C24×C71#4114yes—
511C24×C71C2411yescharacteristic
512C24×C71C2411yescharacteristic
513C24×C71C2411yescharacteristic
514C22×C4×C71—22no—
515C22×C4×C71—22no—
516C22×C4×C71—22no—
517C22×C4×C71—22no—
518C22×C4×C71—22no—
519C22×C4×C71—22no—
520C22×C4×C71—22no—
521C22×C4×C71—22no—
522C22×C4×C71—22no—
523C22×C4×C71—22no—
524C22×C4×C71—22no—
525C22×C4×C71—22no—
526C22×C4×C71—22no—
527C22×C4×C71—22no—
528C22×C4×C71—22no—
529C22×C4×C71—22no—
530C22×C4×C71—22no—
531C22×C4×C71—22no—
532C22×C4×C71—41no—
533C22×C4×C71—41no—
534C22×C4×C71—41no—
535C22×C4×C71—41no—
536C22×C4×C71—41no—
537C22×C4×C71—41no—
538C22×C4×C71—41no—
539C22×C4×C71—41no—
540C22×C4×C71—41no—
541C22×C4×C71—41no—
542C22×C4×C71—41no—
543C22×C4×C71—416no—
544C22×C4×C71#4114yes—
545C22×C4×C71C2411yescharacteristic
546C22×C4×C71C2411yescharacteristic
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C22×C4×C71C2411yescharacteristic
550C22×C4×C71C2411yescharacteristic
551C22×C4×C71C2411yescharacteristic
552C22×C4×C71C2411yescharacteristic
553C22×C4×C71C2411yescharacteristic
554C22×C4×C71C2411yescharacteristic
555C22×C4×C71C2411yescharacteristic
556C22×C4×C71C2411yescharacteristic
557C22⋊C4×C71—22no—
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#4114yes—
565C42×C71—22no—
566C42×C71—22no—
567C42×C71—41no—
568C42×C71—41no—
569C42×C71—41no—
570C42×C71—41no—
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—28no—
582C23×C71—28no—
583C23×C71—21no—
584C23×C71—21no—
585C23×C71—21no—
586C23×C71—21no—
587C23×C71—21no—
588C23×C71—21no—
589C23×C71—44no—
590C23×C71—44no—
591C23×C71—44no—
592C23×C71—44no—
593C23×C71—44no—
594C23×C71C2×#4112yes—
595C23×C71C2×#4112yes—
596C23×C71C2×#4112yes—
597C23×C71C2×#4112yes—
598C23×C71C2×#4112yes—
599C23×C71H(5,𝔽2)12yes—
600C23×C71H(5,𝔽2)12yes—
601C23×C71C2511yescharacteristic
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—21no—
613C22×D71—21no—
614C22×D71—21no—
615C22×D71—21no—
616C22×D71—21no—
617C22×D71—21no—
618C22×D71—21no—
619C22×D71—21no—
620C22×D71—21no—
621C22×D71—21no—
622C22×D71—21no—
623C22×D71—44no—
624C22×D71—44no—
625C22×D71—44no—
626C22×D71—82no—
627C22×D71—82no—
628C22×D71—82no—
629C22×D71—82no—
630C2×C4×C71—28no—
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—44no—
663C2×C4×C71—44no—
664C2×C4×C71—44no—
665C2×C4×C71—44no—
666C2×C4×C71—44no—
667C2×C4×C71—44no—
668C2×C4×C71—44no—
669C2×C4×C71—44no—
670C2×C4×C71—44no—
671C2×C4×C71C2×#4112yes—
672C2×C4×C71C2×#4112yes—
673C2×C4×C71C2×#4112yes—
674C2×C4×C71C2×#4112yes—
675C2×C4×C71H(5,𝔽2)12yes—
676C22⋊D71—44no—
677C22⋊D71—44no—
678C22⋊D71—44no—
679C22⋊D71—44no—
680C22⋊D71—44no—
681C22⋊D71—44no—
682C22⋊D71—44no—
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—21no—
710C2×Dic71—21no—
711C2×Dic71—21no—
712C2×Dic71—21no—
713C2×Dic71—21no—
714C2×Dic71—21no—
715C2×Dic71—21no—
716C2×Dic71—21no—
717C2×Dic71—21no—
718C2×Dic71—21no—
719C2×Dic71—21no—
720C2×Dic71—21no—
721C2×Dic71—21no—
722C2×Dic71—44no—
723C2×Dic71—82no—
724C2×Dic71—82no—
725D284—82no—
726D284—82no—
727C4×D71—82no—
728Dic142—82no—
729C22×C71—22no—
730C22×C71—22no—
731C22×C71—22no—
732C22×C71—22no—
733C22×C71—22no—
734C22×C71—22no—
735C22×C71—22no—
736C22×C71—22no—
737C22×C71—22no—
738C22×C71—22no—
739C22×C71—22no—
740C22×C71—22no—
741C22×C71—22no—
742C22×C71—22no—
743C22×C71—22no—
744C22×C71—416no—
745C22×C71—41no—
746C22×C71—41no—
747C22×C71—41no—
748C22×C71—41no—
749C22×C71#52914yes—
750C22×C71#53814yes—
751C22×C71C22×#4111yescharacteristic
752C22×C71C22×#4111yescharacteristic
753C22×C71C22×#4111yescharacteristic
754C22×C71C2×H(5,𝔽2)11yescharacteristic
755C22×C71C2×H(5,𝔽2)11yescharacteristic
756C22×C71C2×H(5,𝔽2)11yescharacteristic
757C22×C71#58511yescharacteristic
758C2×D71—41no—
759C2×D71—41no—
760C2×D71—41no—
761C2×D71—41no—
762C2×D71—41no—
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—41no—
778C2×D71—41no—
779C2×D71—88no—
780C4×C71—22no—
781C4×C71—22no—
782C4×C71—22no—
783C4×C71—22no—
784C4×C71—22no—
785C4×C71—41no—
786C4×C71—41no—
787C4×C71—41no—
788C4×C71—41no—
789C4×C71—41no—
790C4×C71—41no—
791C4×C71—41no—
792Dic71—41no—
793Dic71—41no—
794Dic71—41no—
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—24no—
807C2×C71—24no—
808C2×C71—42no—
809C2×C71C2×#52911yescharacteristic
810C2×C71C2×#53811yescharacteristic
811C2×C71#345911yescharacteristic
812C2×C71#349011yescharacteristic
813C2×C71#349411yescharacteristic
814C2×C71#351311yescharacteristic
815C2×C71#351911yescharacteristic
816D71—81no—
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#2518—711no—
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⋊C4D7111yescharacteristic, complemented
850C71#3499811yescharacteristic, complemented, Sylow
851C23×D4—711no—
852C24×C4C2×D7111yescharacteristic
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⋊C4C2×D7111yescharacteristic
871C22×C22⋊C4C2×D7111yescharacteristic
872C22×C42C2×D7111yescharacteristic, complemented
873C22×C42C2×D7111yescharacteristic, complemented
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#397—711no—
889#396—711no—
890#396—711no—
891#396—711no—
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#394—711no—
901#394—711no—
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#389—711no—
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#388—711no—
932#388—711no—
933#388—711no—
934#388—711no—
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#387—711no—
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#386—711no—
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#383—711no—
978#382—711no—
979#382—711no—
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⋊C4C2×D7111yescharacteristic
995C4×C22⋊C4C2×D7111yescharacteristic
996C4×C22⋊C4C2×D7111yescharacteristic
997C4×C22⋊C4C2×D7111yescharacteristic
998C4×C22⋊C4C2×D7111yescharacteristic, complemented
999C4×C22⋊C4C2×D7111yescharacteristic, complemented
1000C4×C22⋊C4C2×D7111yescharacteristic, complemented
1001C4×C22⋊C4C2×D7111yescharacteristic, complemented
1002C2×#95—711no—
1003C2×#95—711no—
1004C2×#95C2×D7111yescharacteristic, complemented
1005C2×#95C2×D7111yescharacteristic, complemented
1006C25—711no—
1007C25C22×D7111yescharacteristic
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—711no—
1020C22×D4—1424no—
1021C23×C4—24no—
1022C23×C4—42no—
1023C23×C4—42no—
1024C23×C4—711no—
1025C23×C4—711no—
1026C23×C4—711no—
1027C23×C4—711no—
1028C23×C4C22×D7111yescharacteristic
1029C23×C4C22×D7111yescharacteristic
1030C23×C4C22×D7111yescharacteristic
1031C23×C4C22×D7111yescharacteristic
1032C23×C4C22×D7111yescharacteristic
1033C23×C4C22×D7111yescharacteristic
1034C23×C4C22×D7111yescharacteristic
1035C23×C4C22×D7111yescharacteristic
1036C23×C4C22×D7111yescharacteristic
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⋊C4—711no—
1069C2×C4⋊C4—711no—
1070C2×C4⋊C4—711no—
1071C2×C4⋊C4—711no—
1072C2×C4⋊C4—711no—
1073C2×C4⋊C4—711no—
1074C2×C22⋊C4—24no—
1075C2×C22⋊C4—24no—
1076C2×C22⋊C4—2842no—
1077C2×C22⋊C4—2842no—
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—711no—
1118C2×C22⋊C4—711no—
1119C2×C22⋊C4—711no—
1120C2×C22⋊C4—711no—
1121C2×C22⋊C4—711no—
1122C2×C22⋊C4—1424no—
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—42no—
1132C2×C42—42no—
1133C2×C42—711no—
1134C2×C42—711no—
1135C2×C42—711no—
1136C2×C42C22×D7111yescharacteristic
1137C2×C42C22×D7111yescharacteristic
1138C2×C42C22×D7111yescharacteristic
1139C2×C42C22×D7111yescharacteristic
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#95—711no—
1177#95—711no—
1178#95—711no—
1179#95—711no—
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—22no—
1189C24—22no—
1190C24—22no—
1191C24—22no—
1192C24—41no—
1193C24—41no—
1194C24—2841no—
1195C24—2841no—
1196C24—2841no—
1197C24—2841no—
1198C24—711no—
1199C24—711no—
1200C24—711no—
1201C24—1422no—
1202C24—1422no—
1203C24—1422no—
1204C24#1176586514yes—
1205C24C23×D7111yescharacteristic
1206C24C23×D7111yescharacteristic
1207C24C23×D7111yescharacteristic
1208C2×Q8—2841no—
1209C2×Q8—2841no—
1210C2×Q8—1422no—
1211C2×D4—2841no—
1212C2×D4—2841no—
1213C2×D4—2841no—
1214C2×D4—2841no—
1215C2×D4—28416no—
1216C2×D4—2841no—
1217C2×D4—2841no—
1218C2×D4—2841no—
1219C2×D4—2841no—
1220C2×D4—2841no—
1221C2×D4—2841no—
1222C2×D4—1422no—
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—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—416no—
1269C22×C4—2841no—
1270C22×C4—2841no—
1271C22×C4—2841no—
1272C22×C4—2841no—
1273C22×C4—2841no—
1274C22×C4—2841no—
1275C22×C4—2841no—
1276C22×C4—2841no—
1277C22×C4—711no—
1278C22×C4—711no—
1279C22×C4—711no—
1280C22×C4—711no—
1281C22×C4—711no—
1282C22×C4—711no—
1283C22×C4—711no—
1284C22×C4—711no—
1285C22×C4—711no—
1286C22×C4—711no—
1287C22×C4—711no—
1288C22×C4—711no—
1289C22×C4—711no—
1290C22×C4—1422no—
1291C22×C4—1422no—
1292C22×C4—1422no—
1293C22×C4—1422no—
1294C22×C4#1176586514yes—
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—2841no—
1308C4⋊C4—2841no—
1309C4⋊C4—2841no—
1310C4⋊C4—2841no—
1311C4⋊C4—2841no—
1312C4⋊C4—2841no—
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—1422no—
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—22no—
1336C22⋊C4—2841no—
1337C22⋊C4—2841no—
1338C22⋊C4—2841no—
1339C22⋊C4—2841no—
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—2841no—
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#1176586514yes—
1381C42—22no—
1382C42—22no—
1383C42—41no—
1384C42—41no—
1385C42—41no—
1386C42—41no—
1387C42—41no—
1388C42—41no—
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—21no—
1406C23—28no—
1407C23—28no—
1408C23—44no—
1409C23—44no—
1410C23—44no—
1411C23—44no—
1412C23—44no—
1413C23—2844no—
1414C23—2844no—
1415C23—2844no—
1416C23—5682no—
1417C23—5682no—
1418C23—5682no—
1419C23—5682no—
1420C23—1421no—
1421C23—1421no—
1422C23—1421no—
1423C23—1421no—
1424C23—1421no—
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—
1441C23C2×#1176586512yes—
1442C23C2×#1176586512yes—
1443C23C2×#1176586512yes—
1444C23C2×#1176586512yes—
1445C23C2×#1176586512yes—
1446C23#1455617312yes—
1447C23#1455617412yes—
1448C23C24×D7111yescharacteristic
1449Q8—5682no—
1450D4—2844no—
1451D4—2844no—
1452D4—2844no—
1453D4—2844no—
1454D4—2844no—
1455D4—2844no—
1456D4—2844no—
1457D4—5682no—
1458D4—5682no—
1459C2×C4—28no—
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—44no—
1492C2×C4—44no—
1493C2×C4—44no—
1494C2×C4—44no—
1495C2×C4—44no—
1496C2×C4—44no—
1497C2×C4—44no—
1498C2×C4—44no—
1499C2×C4—44no—
1500C2×C4—2844no—
1501C2×C4—5682no—
1502C2×C4—5682no—
1503C2×C4—5682no—
1504C2×C4—1421no—
1505C2×C4—1421no—
1506C2×C4—1421no—
1507C2×C4—1421no—
1508C2×C4—1421no—
1509C2×C4—1421no—
1510C2×C4—1421no—
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×C4C2×#1176586512yes—
1544C2×C4C2×#1176586512yes—
1545C2×C4C2×#1176586512yes—
1546C2×C4C2×#1176586512yes—
1547C2×C4#1455617312yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—22no—
1555C22—22no—
1556C22—22no—
1557C22—22no—
1558C22—22no—
1559C22—22no—
1560C22—22no—
1561C22—22no—
1562C22—22no—
1563C22—416no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—2841no—
1569C22—2841no—
1570C22—2841no—
1571C22—2841no—
1572C22—2841no—
1573C22—2841no—
1574C22—2841no—
1575C22—2841no—
1576C22—2841no—
1577C22—2841no—
1578C22—2841no—
1579C22—2841no—
1580C22—2841no—
1581C22—2841no—
1582C22—2841no—
1583C22—2841no—
1584C22—2841no—
1585C22—2841no—
1586C22—2841no—
1587C22—2841no—
1588C22—2841no—
1589C22—5688no—
1590C22#1798653314yes—
1591C22#1798658214yes—
1592C22C22×#1176586511yescharacteristic
1593C22C22×#1176586511yescharacteristic
1594C22C22×#1176586511yescharacteristic
1595C22C2×#1455617311yescharacteristic
1596C22C2×#1455617311yescharacteristic
1597C22C2×#1455617411yescharacteristic
1598C22#1798683511yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—22no—
1602C4—22no—
1603C4—22no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—41no—
1611C4—2841no—
1612C4—2841no—
1613C4—2841no—
1614C4—2841no—
1615C4—2841no—
1616C4—2841no—
1617C4—2841no—
1618C4—2841no—
1619C4—2841no—
1620C4—2841no—
1621C4—2841no—
1622C4—2841no—
1623C4—2841no—
1624C2—24no—
1625C2—24no—
1626C2—42no—
1627C2—5681no—
1628C2—5681no—
1629C2—5681no—
1630C2C2×#1798653311yescharacteristic
1631C2C2×#1798658211yescharacteristic
1632C2#2260174911yescharacteristic
1633C2#2260202911yescharacteristic
1634C2#2260207511yescharacteristic
1635C2#2260228011yescharacteristic
1636C2#2260237211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC2×C4×C22⋊C4×C71C2
prime radical#22591708C2
hypercenterC2×C4×C22⋊C4D71
hypocenterC71#34998
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #22596671C2semidirect
2. #22596662C2semidirect
3. #22596655C2semidirect
4. #22596641C2semidirect
5. #22594397C2semidirect
6. #22594337C2semidirect
7. #22594322C2semidirect
8. #22594322C2semidirect
9. #22592998C2semidirect
10. #22592992C2semidirect
11. #22592900C2semidirect
12. #22592894C2semidirect
13. #22592835C2semidirect
14. #22592666C2semidirect
15. #22592586C2semidirect
16. #22592466C2semidirect
17. #22592391C2semidirect
18. #22592277C2semidirect
19. #22592090C2semidirect
20. #22592001C2semidirect
21. #22591891C2semidirect
22. #22591736C2semidirect
24. #22591667C2semidirect
25. #22591068C2semidirect
26. #22591000C2semidirect
27. #22590967C2semidirect
28. #22590935C2semidirect
29. C4×#14556097C2semidirect
30. C2×#17985878C2semidirect
31. C2×C4×C22⋊C4×C71C2semidirect
33. C2×#14556122C22semidirect
34. C2×#14556116C22semidirect
37. C2×#14556111C22semidirect
38. C2×#14556107C22semidirect
45. C2×C4×C22⋊D71C22semidirect
46. C2×C4×C22⋊D71C22semidirect
50. C71⋊#401C22semidirect
51. #17985941C22semidirect
52. #17985941C22semidirect
53. #17985941C22semidirect
54. #17985940C22semidirect
55. #17985935C22semidirect
56. #17985933C22semidirect
57. #17985928C22semidirect
58. #17985928C22semidirect
59. #17985928C22semidirect
60. #17985928C22semidirect
61. #17985928C22semidirect
62. #17985927C22semidirect
63. #17985927C22semidirect
64. #17985926C22semidirect
65. #17985923C22semidirect
66. #17985922C22semidirect
67. #17985922C22semidirect
68. #17985917C22semidirect
69. #17985917C22semidirect
76. #17985914C22semidirect
77. #17985914C22semidirect
78. #17985912C22semidirect
79. #17985911C22semidirect
82. #17985905C22semidirect
83. #17985903C22semidirect
84. #17985901C22semidirect
85. #17985901C22semidirect
86. #17985901C22semidirect
87. #17985897C22semidirect
88. #17985897C22semidirect
89. #17985896C22semidirect
90. #17985891C22semidirect
91. #17985891C22semidirect
92. #17985890C22semidirect
93. #17985890C22semidirect
94. #17985890C22semidirect
95. #17985890C22semidirect
96. #17985890C22semidirect
97. #17985890C22semidirect
98. #17985890C22semidirect
99. #17985890C22semidirect
100. #17985890C22semidirect
101. #17985890C22semidirect
102. #17985890C22semidirect
103. #17985890C22semidirect
104. #17985890C22semidirect
105. #17985890C22semidirect
106. #17985890C22semidirect
107. #17985888C22semidirect
108. #17985888C22semidirect
109. #17985888C22semidirect
110. #17985888C22semidirect
111. #17985886C22semidirect
112. #17985883C22semidirect
113. #17985883C22semidirect
114. #17985883C22semidirect
115. #17985883C22semidirect
116. #17985883C22semidirect
117. #17985883C22semidirect
118. #17985883C22semidirect
119. #17985882C22semidirect
133. #17985878C22semidirect
134. #17985878C22semidirect
135. #17985878C22semidirect
136. #17985877C22semidirect
137. #17985877C22semidirect
144. #17985872C22semidirect
145. #17985872C22semidirect
146. #17985872C22semidirect
147. #17985872C22semidirect
148. #17985872C22semidirect
152. #17985867C22semidirect
153. #17985866C22semidirect
154. #17985865C22semidirect
155. #17985863C22semidirect
156. #17985862C22semidirect
157. #17985861C22semidirect
158. #17985859C22semidirect
159. #17985858C22semidirect
168. C4×C22⋊Dic71C22semidirect
169. C4×C22⋊Dic71C22semidirect
175. C22×C42×C71C22semidirect
176. C22×C42×C71C22semidirect
181. C4×C22⋊C4×C71C22semidirect
182. C4×C22⋊C4×C71C22semidirect
183. C4×C22⋊C4×C71C22semidirect
184. C4×C22⋊C4×C71C22semidirect
185. C2×#95×C71C22semidirect
186. C2×#95×C71C22semidirect
849. C2×C4×C22⋊C4D71semidirect
850. C71#34998semidirect
872. C22×C42C2×D71semidirect
873. C22×C42C2×D71semidirect
998. C4×C22⋊C4C2×D71semidirect
999. C4×C22⋊C4C2×D71semidirect
1000. C4×C22⋊C4C2×D71semidirect
1001. C4×C22⋊C4C2×D71semidirect
1004. C2×#95C2×D71semidirect
1005. C2×#95C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966712
#225966622
#225966552
#225966412
#225943972
#225943372
#225943222
#225929982
#225929922
#225929002
#225928942
#225928352
#225926662
#225925862
#225924662
#225923912
#225922772
#225920902
#225920012
#225918912
#225917362
#225917082
#225916672
#225910682
#225910002
#225909672
#225909352
C4×#145560972
C2×#179858782
C2×C4×C22⋊C4×C712
#3499871