Finite Group Databasebeta

← #32170233

Subgroups — #32170233

Order 18176.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596632C211yesmaximal, characteristic, complemented
2#22596625C211yesmaximal, characteristic, complemented
3#22596620C211yesmaximal, characteristic
4#22594312C211yesmaximal, characteristic, complemented
5#22594296C211yesmaximal, characteristic, complemented
6#22594295C211yesmaximal, characteristic, complemented
7#22594270C211yesmaximal, characteristic, complemented
8#22592906C211yesmaximal, characteristic, complemented
9#22592898C211yesmaximal, characteristic, complemented
10#22592847C211yesmaximal, characteristic, complemented
11#22592839C211yesmaximal, characteristic, complemented
12#22592729C211yesmaximal, characteristic, complemented
13#22592721C211yesmaximal, characteristic, complemented
14#22592670C211yesmaximal, characteristic, complemented
15#22592662C211yesmaximal, characteristic, complemented
16#22592170C211yesmaximal, characteristic, complemented
17#22592162C211yesmaximal, characteristic, complemented
18#22592096C211yesmaximal, characteristic, complemented
19#22592088C211yesmaximal, characteristic, complemented
20#22591895C211yesmaximal, characteristic, complemented
21#22591887C211yesmaximal, characteristic, complemented
22#22591821C211yesmaximal, characteristic, complemented
23#22591813C211yesmaximal, characteristic, complemented
24#22591071C211yesmaximal, characteristic, complemented
25#22591041C211yesmaximal, characteristic, complemented
26#22590968C211yesmaximal, characteristic, complemented
27#22590966C211yesmaximal, characteristic, complemented
28#120×Dic71C211yesmaximal, characteristic, complemented
29#22590839C211yesmaximal, characteristic, complemented
30C22×C71⋊#95C211yesmaximal, characteristic, complemented
31C71×#2849C211yesmaximal, characteristic, complemented
32C24×Dic71C2211yescharacteristic
33C24×Dic71C2211yescharacteristic
34C2×#14556111C2211yescharacteristic
35C2×#14556111C2211yescharacteristic
36C2×#14556105C2211yescharacteristic
37C2×#14556105C2211yescharacteristic
38C2×#14556105C2211yescharacteristic
39C2×#14556100C2211yescharacteristic
40C2×#14556100C2211yescharacteristic
41C2×#14556100C2211yescharacteristic
42C2×#14556097C2211yescharacteristic
43C2×D4×Dic71C2211yescharacteristic
44C2×D4×Dic71C2211yescharacteristic
45C2×D4×Dic71C2211yescharacteristic
46C2×(C22⋊D71)⋊C4C2211yescharacteristic
47C2×(C22⋊D71)⋊C4C2211yescharacteristic
48C2×(C22⋊D71)⋊C4C2211yescharacteristic
49C71⋊#401C2211yescharacteristic, complemented
50C71⋊#401C2211yescharacteristic, complemented
51#17985941C2211yescharacteristic, complemented
52#17985941C2211yescharacteristic, complemented
53#17985941C2211yescharacteristic, complemented
54#17985940C2211yescharacteristic, complemented
55#17985940C2211yescharacteristic, complemented
56#17985940C2211yescharacteristic, complemented
57#17985940C2211yescharacteristic, complemented
58#17985939C2211yescharacteristic, complemented
59#17985939C2211yescharacteristic, complemented
60#17985938C2211yescharacteristic, complemented
61#17985937C2211yescharacteristic, complemented
62#17985937C2211yescharacteristic, complemented
63#17985933C2211yescharacteristic, complemented
64#17985932C2211yescharacteristic, complemented
65#17985930C2211yescharacteristic, complemented
66#17985929C2211yescharacteristic, complemented
67#17985928C2211yescharacteristic, complemented
68#17985928C2211yescharacteristic, complemented
69#17985927C2211yescharacteristic, complemented
70#17985927C2211yescharacteristic, complemented
71#17985927C2211yescharacteristic, complemented
72#17985926C2211yescharacteristic, complemented
73#17985925C2211yescharacteristic, complemented
74#17985924C2211yescharacteristic, complemented
75#17985922C2211yescharacteristic, complemented
76#17985921C2211yescharacteristic, complemented
77#17985915C2211yescharacteristic, complemented
78#17985914C2211yescharacteristic, complemented
79#17985912C2211yescharacteristic, complemented
80#17985911C2211yescharacteristic, complemented
81#17985904C2211yescharacteristic, complemented
82#17985903C2211yescharacteristic, complemented
83#17985895C2211yescharacteristic, complemented
84#17985894C2211yescharacteristic, complemented
85#17985893C2211yescharacteristic, complemented
86#17985893C2211yescharacteristic, complemented
87#17985891C2211yescharacteristic, complemented
88#17985889C2211yescharacteristic, complemented
89#17985888C2211yescharacteristic, complemented
90#17985887C2211yescharacteristic, complemented
91#17985886C2211yescharacteristic, complemented
92#17985886C2211yescharacteristic, complemented
93#17985884C2211yescharacteristic, complemented
94#17985884C2211yescharacteristic, complemented
95#17985882C2211yescharacteristic, complemented
96#17985881C2211yescharacteristic, complemented
97#17985881C2211yescharacteristic, complemented
98#17985881C2211yescharacteristic, complemented
99#17985880C2211yescharacteristic, complemented
100#17985880C2211yescharacteristic, complemented
101#17985879C2211yescharacteristic
102#17985879C2211yescharacteristic
103#17985879C2211yescharacteristic
104#17985879C2211yescharacteristic
105#17985879C2211yescharacteristic
106#17985879C2211yescharacteristic
107#17985878C2211yescharacteristic
108#17985878C2211yescharacteristic
109#17985878C2211yescharacteristic
110#17985878C2211yescharacteristic
111#17985876C2211yescharacteristic
112#17985876C2211yescharacteristic
113#17985876C2211yescharacteristic
114#17985876C2211yescharacteristic
115#17985876C2211yescharacteristic
116#17985876C2211yescharacteristic
117#17985876C2211yescharacteristic, complemented
118#17985875C2211yescharacteristic, complemented
119#17985874C2211yescharacteristic
120#17985874C2211yescharacteristic
121#17985874C2211yescharacteristic
122#17985874C2211yescharacteristic
123#17985874C2211yescharacteristic
124#17985874C2211yescharacteristic
125#17985873C2211yescharacteristic, complemented
126#17985872C2211yescharacteristic
127#17985872C2211yescharacteristic
128#17985872C2211yescharacteristic
129#17985872C2211yescharacteristic
130#17985871C2211yescharacteristic
131#17985871C2211yescharacteristic
132#17985871C2211yescharacteristic
133#17985871C2211yescharacteristic
134#17985871C2211yescharacteristic
135#17985871C2211yescharacteristic
136#17985871C2211yescharacteristic, complemented
137#17985866C2211yescharacteristic, complemented
138#17985866C2211yescharacteristic, complemented
139#17985864C2211yescharacteristic, complemented
140#17985863C2211yescharacteristic, complemented
141#17985862C2211yescharacteristic
142#17985862C2211yescharacteristic
143#17985861C2211yescharacteristic, complemented
144#17985860C2211yescharacteristic, complemented
145#17985857C2211yescharacteristic
146#17985857C2211yescharacteristic
147#17985857C2211yescharacteristic
148#17985857C2211yescharacteristic
149#17985857C2211yescharacteristic
150#17985857C2211yescharacteristic
151#17985857C2211yescharacteristic, complemented
152#17985856C2211yescharacteristic, complemented
153#17985855C2211yescharacteristic
154C22⋊C4×Dic71C2211yescharacteristic
155C22⋊C4×Dic71C2211yescharacteristic
156C22⋊C4×Dic71C2211yescharacteristic
157C22⋊C4×Dic71C2211yescharacteristic
158C22⋊C4×Dic71C2211yescharacteristic
159C22⋊C4×Dic71C2211yescharacteristic
160C2×C71⋊#95C2211yescharacteristic
161C2×C71⋊#95C2211yescharacteristic
162C2×C71⋊#95C2211yescharacteristic
163C2×C71⋊#95C2211yescharacteristic
164C2×C71⋊#95C2211yescharacteristic
165C2×C71⋊#95C2211yescharacteristic
166C2×C71⋊#95C2211yescharacteristic
167C2×C71⋊#95C2211yescharacteristic
168C2×C71⋊#95C2211yescharacteristic
169C2×C71⋊#95C2211yescharacteristic
170C2×C71⋊#95C2211yescharacteristic
171C2×C71⋊#95C2211yescharacteristic
172C24×C4×C71C2211yescharacteristic
173C2×#123×C71C2211yescharacteristic
174C2×#123×C71C2211yescharacteristic
175C2×#120×C71C2211yescharacteristic
176#386×C71C2211yescharacteristic
177#386×C71C2211yescharacteristic
178#386×C71C2211yescharacteristic
179#386×C71C2211yescharacteristic
180#385×C71C2211yescharacteristic
181#385×C71C2211yescharacteristic
182#385×C71C2211yescharacteristic
183#385×C71C2211yescharacteristic
184#381×C71C2211yescharacteristic
185#381×C71C2211yescharacteristic
186#379×C71C2211yescharacteristic
187C22×Dic142C2311yescharacteristic
188C22×C22⋊D71C2311yescharacteristic
189C22×C22⋊D71C2311yescharacteristic
190C22×C22⋊D71C2311yescharacteristic
191C22×C22⋊D71C2311yescharacteristic
192C23×Dic71—24no—
193C23×Dic71—24no—
194C23×Dic71—42no—
195C23×Dic71—42no—
196C23×Dic71—42no—
197C23×Dic71—42no—
198C23×Dic71C2311yescharacteristic
199C23×Dic71C2311yescharacteristic
200C23×Dic71C2311yescharacteristic
201C23×Dic71C2311yescharacteristic
202C23×Dic71C2311yescharacteristic
203C23×Dic71C2311yescharacteristic
204C23×Dic71C2311yescharacteristic
205C23×Dic71C2311yescharacteristic
206C23×Dic71C2311yescharacteristic
207C23×Dic71C2311yescharacteristic
208C23×Dic71C2311yescharacteristic
209C23×Dic71C2311yescharacteristic
210C23×Dic71C2311yescharacteristic
211C22×C4×D71C2311yescharacteristic
212#14556111—42no—
213#14556111—42no—
214#14556105—24no—
215#14556105—42no—
216#14556105—42no—
217#14556100—24no—
218#14556100—42no—
219#14556100—42no—
220#14556097—24no—
221D4×Dic71—24no—
222D4×Dic71—42no—
223D4×Dic71—42no—
224(C22⋊D71)⋊C4—24no—
225(C22⋊D71)⋊C4—42no—
226(C22⋊D71)⋊C4—42no—
227C2×C4⋊Dic71C2311yescharacteristic
228C2×C4⋊Dic71C2311yescharacteristic
229C2×C4⋊Dic71C2311yescharacteristic
230C2×C4⋊Dic71C2311yescharacteristic
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
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×Dic71⋊C4C2311yescharacteristic
242C2×Dic71⋊C4C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×Dic71⋊C4C2311yescharacteristic
248C2×Dic71⋊C4C2311yescharacteristic
249C2×C22⋊Dic71C2311yescharacteristic
250C2×C22⋊Dic71C2311yescharacteristic
251C2×C22⋊Dic71C2311yescharacteristic
252C2×C22⋊Dic71C2311yescharacteristic
253C2×C22⋊Dic71C2311yescharacteristic
254C2×C22⋊Dic71C2311yescharacteristic
255C2×C22⋊Dic71C2311yescharacteristic
256C2×C22⋊Dic71C2311yescharacteristic
257C2×C22⋊Dic71C2311yescharacteristic
258C2×C22⋊Dic71C2311yescharacteristic
259C2×C22⋊Dic71C2311yescharacteristic
260C2×C22⋊Dic71C2311yescharacteristic
261C2×C22⋊Dic71C2311yescharacteristic
262C2×C22⋊Dic71C2311yescharacteristic
263C2×C22⋊Dic71C2311yescharacteristic
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×C4×Dic71C2311yescharacteristic
275C2×C4×Dic71C2311yescharacteristic
276C2×C4×Dic71C2311yescharacteristic
277C2×C4×Dic71C2311yescharacteristic
278C2×C4×Dic71C2311yescharacteristic
279C2×C4×Dic71C2311yescharacteristic
280C71⋊#95C2311yescharacteristic
281C71⋊#95C2311yescharacteristic
282C71⋊#95C2311yescharacteristic
283C71⋊#95C2311yescharacteristic
284C71⋊#95C2311yescharacteristic
285C71⋊#95C2311yescharacteristic
286C71⋊#95C2311yescharacteristic
287C71⋊#95C2311yescharacteristic
288C71⋊#95C2311yescharacteristic
289C71⋊#95C2311yescharacteristic
290C71⋊#95C2311yescharacteristic
291C71⋊#95C2311yescharacteristic
292C71⋊#95C2311yescharacteristic
293C71⋊#95C2311yescharacteristic
294C71⋊#95C2311yescharacteristic
295C71⋊#95C2311yescharacteristic
296C71⋊#95C2311yescharacteristic
297C71⋊#95C2311yescharacteristic
298C71⋊#95C2311yescharacteristic
299C71⋊#95C2311yescharacteristic
300C71⋊#95C2311yescharacteristic
301C71⋊#95C2311yescharacteristic
302C71⋊#95C2311yescharacteristic
303C71⋊#95C2311yescharacteristic
304C71⋊#95C2311yescharacteristic
305C71⋊#95C2311yescharacteristic
306C71⋊#95C2311yescharacteristic
307C71⋊#95C2311yescharacteristic
308C71⋊#95C2311yescharacteristic
309C71⋊#95C2311yescharacteristic
310C71⋊#95C2311yescharacteristic
311C71⋊#95C2311yescharacteristic
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C25×C71C2311yescharacteristic
329C22×D4×C71C2311yescharacteristic
330C22×D4×C71C2311yescharacteristic
331C22×D4×C71C2311yescharacteristic
332C23×C4×C71—24no—
333C23×C4×C71—42no—
334C23×C4×C71—42no—
335C23×C4×C71C2311yescharacteristic
336C23×C4×C71C2311yescharacteristic
337C23×C4×C71C2311yescharacteristic
338C23×C4×C71C2311yescharacteristic
339C23×C4×C71C2311yescharacteristic
340C23×C4×C71C2311yescharacteristic
341#123×C71—42no—
342#123×C71—42no—
343#120×C71—24no—
344C2×C4⋊C4×C71C2311yescharacteristic
345C2×C4⋊C4×C71C2311yescharacteristic
346C2×C4⋊C4×C71C2311yescharacteristic
347C2×C4⋊C4×C71C2311yescharacteristic
348C2×C22⋊C4×C71C2311yescharacteristic
349C2×C22⋊C4×C71C2311yescharacteristic
350C2×C22⋊C4×C71C2311yescharacteristic
351C2×C22⋊C4×C71C2311yescharacteristic
352C2×C22⋊C4×C71C2311yescharacteristic
353C2×C22⋊C4×C71C2311yescharacteristic
354C2×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C22⋊C4×C71C2311yescharacteristic
357C2×C22⋊C4×C71C2311yescharacteristic
358C2×C22⋊C4×C71C2311yescharacteristic
359C2×C22⋊C4×C71C2311yescharacteristic
360C2×C22⋊C4×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×D71C2411yescharacteristic
370C2×Dic142—22no—
371C2×Dic142—41no—
372C2×Dic142—41no—
373C2×C22⋊D71—22no—
374C2×C22⋊D71—22no—
375C2×C22⋊D71—22no—
376C2×C22⋊D71—22no—
377C2×C22⋊D71—22no—
378C2×C22⋊D71—22no—
379C2×C22⋊D71—22no—
380C2×C22⋊D71—22no—
381C2×C22⋊D71—22no—
382C2×C22⋊D71—22no—
383C2×C22⋊D71—41no—
384C2×C22⋊D71—41no—
385C22×Dic71—22no—
386C22×Dic71—22no—
387C22×Dic71—22no—
388C22×Dic71—22no—
389C22×Dic71—22no—
390C22×Dic71—22no—
391C22×Dic71—22no—
392C22×Dic71—22no—
393C22×Dic71—22no—
394C22×Dic71—22no—
395C22×Dic71—22no—
396C22×Dic71—22no—
397C22×Dic71—22no—
398C22×Dic71—22no—
399C22×Dic71—22no—
400C22×Dic71—22no—
401C22×Dic71—22no—
402C22×Dic71—22no—
403C22×Dic71—22no—
404C22×Dic71—41no—
405C22×Dic71—41no—
406C22×Dic71—41no—
407C22×Dic71—41no—
408C22×Dic71—41no—
409C22×Dic71—41no—
410C22×Dic71—41no—
411C22×Dic71—41no—
412C22×Dic71—41no—
413C22×Dic71—41no—
414C22×Dic71—41no—
415C22×Dic71—41no—
416C22×Dic71—41no—
417C22×Dic71—41no—
418C22×Dic71—41no—
419C22×Dic71—41no—
420C22×Dic71—41no—
421C22×Dic71—41no—
422C22×Dic71—416no—
423C22×Dic71—416no—
424C22×Dic71#4114yes—
425C22×Dic71#4114yes—
426C22×Dic71C2411yescharacteristic
427C22×Dic71C2411yescharacteristic
428C22×Dic71C2411yescharacteristic
429C22×Dic71C2411yescharacteristic
430C22×Dic71C2411yescharacteristic
431C22×Dic71C2411yescharacteristic
432C22×Dic71C2411yescharacteristic
433C22×Dic71C2411yescharacteristic
434C22×Dic71C2411yescharacteristic
435C22×Dic71C2411yescharacteristic
436C22×Dic71C2411yescharacteristic
437C22×Dic71C2411yescharacteristic
438C22×Dic71C2411yescharacteristic
439C22×Dic71C2411yescharacteristic
440C22×Dic71C2411yescharacteristic
441C2×C4×D71—22no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C4⋊Dic71—22no—
445C4⋊Dic71—22no—
446C4⋊Dic71—41no—
447C4⋊Dic71—41no—
448C4⋊Dic71—41no—
449C4⋊Dic71—41no—
450Dic71⋊C4—22no—
451Dic71⋊C4—22no—
452Dic71⋊C4—22no—
453Dic71⋊C4—22no—
454Dic71⋊C4—41no—
455Dic71⋊C4—41no—
456Dic71⋊C4—41no—
457Dic71⋊C4—41no—
458Dic71⋊C4—41no—
459Dic71⋊C4—41no—
460Dic71⋊C4—41no—
461Dic71⋊C4—41no—
462Dic71⋊C4—41no—
463Dic71⋊C4—41no—
464Dic71⋊C4—41no—
465Dic71⋊C4—41no—
466C22⋊Dic71—22no—
467C22⋊Dic71—22no—
468C22⋊Dic71—22no—
469C22⋊Dic71—22no—
470C22⋊Dic71—22no—
471C22⋊Dic71—22no—
472C22⋊Dic71—22no—
473C22⋊Dic71—22no—
474C22⋊Dic71—22no—
475C22⋊Dic71—22no—
476C22⋊Dic71—22no—
477C22⋊Dic71—41no—
478C22⋊Dic71—41no—
479C22⋊Dic71—41no—
480C22⋊Dic71—41no—
481(C2×D71)⋊C4—22no—
482(C2×D71)⋊C4—22no—
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—
491C4×Dic71—22no—
492C4×Dic71—22no—
493C4×Dic71—41no—
494C4×Dic71—41no—
495C4×Dic71—41no—
496C4×Dic71—41no—
497C24×C71—22no—
498C24×C71—22no—
499C24×C71—22no—
500C24×C71—22no—
501C24×C71—22no—
502C24×C71—22no—
503C24×C71#4114yes—
504C24×C71C2411yescharacteristic
505C24×C71C2411yescharacteristic
506C24×C71C2411yescharacteristic
507C24×C71C2411yescharacteristic
508C2×D4×C71—22no—
509C2×D4×C71—22no—
510C2×D4×C71—22no—
511C2×D4×C71—22no—
512C2×D4×C71—22no—
513C2×D4×C71—22no—
514C2×D4×C71—22no—
515C2×D4×C71—22no—
516C2×D4×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—41no—
528C22×C4×C71—41no—
529C22×C4×C71—41no—
530C22×C4×C71—41no—
531C22×C4×C71—41no—
532C22×C4×C71—41no—
533C22×C4×C71—41no—
534C22×C4×C71—41no—
535C22×C4×C71—416no—
536C22×C4×C71C2411yescharacteristic
537C22×C4×C71C2411yescharacteristic
538C22×C4×C71C2411yescharacteristic
539C22×C4×C71C2411yescharacteristic
540C22×C4×C71C2411yescharacteristic
541C22×C4×C71C2411yescharacteristic
542C22×C4×C71C2411yescharacteristic
543C22×C4×C71C2411yescharacteristic
544C22×C4×C71C2411yescharacteristic
545C22×C4×C71C2411yescharacteristic
546C22×C4×C71C2411yescharacteristic
547C4⋊C4×C71—41no—
548C4⋊C4×C71—41no—
549C4⋊C4×C71—41no—
550C4⋊C4×C71—41no—
551C22⋊C4×C71—22no—
552C22⋊C4×C71—22no—
553C22⋊C4×C71—22no—
554C22⋊C4×C71—22no—
555C22⋊C4×C71—22no—
556C22⋊C4×C71—22no—
557C22⋊C4×C71—22no—
558C22⋊C4×C71—22no—
559C22⋊C4×C71—22no—
560C22⋊C4×C71—41no—
561C22⋊C4×C71—41no—
562C22⋊C4×C71—41no—
563C22⋊C4×C71—41no—
564C23×C71—28no—
565C23×C71—28no—
566C23×C71—28no—
567C23×C71—28no—
568C23×C71—28no—
569C23×C71—28no—
570C23×C71—28no—
571C23×C71—21no—
572C23×C71—21no—
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×C71—21no—
587C23×C71—21no—
588C23×C71—21no—
589C23×C71—21no—
590C23×C71C2×#4112yes—
591C23×C71C2×#4112yes—
592C23×C71C2×#4112yes—
593C23×C71C2×#4112yes—
594C23×C71C2×#4112yes—
595C23×C71H(5,𝔽2)12yes—
596C23×C71H(5,𝔽2)12yes—
597C23×C71H(5,𝔽2)12yes—
598C23×C712−1+412yes—
599C23×C71C2511yescharacteristic
600C22×D71—21no—
601C22×D71—21no—
602C22×D71—21no—
603C22×D71—21no—
604C22×D71—21no—
605C22×D71—21no—
606C22×D71—21no—
607D4×C71—44no—
608D4×C71—44no—
609D4×C71—44no—
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—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—44no—
644C2×C4×C71—44no—
645C2×C4×C71—44no—
646C2×C4×C71—44no—
647C2×C4×C71—44no—
648C2×C4×C71—44no—
649C22⋊D71—44no—
650C22⋊D71—44no—
651C22⋊D71—44no—
652C22⋊D71—82no—
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—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—44no—
695C2×Dic71—44no—
696C2×Dic71—44no—
697C2×Dic71—44no—
698C2×Dic71—44no—
699C2×Dic71—44no—
700C2×Dic71—44no—
701C2×Dic71—44no—
702C2×Dic71—44no—
703C2×Dic71—44no—
704C2×Dic71—44no—
705C2×Dic71—44no—
706C2×Dic71—82no—
707C2×Dic71C2×#4112yes—
708C2×Dic71C2×#4112yes—
709C2×Dic71C2×#4112yes—
710C2×Dic71C2×#4112yes—
711C4×D71—82no—
712Dic142—82no—
713C22×C71—232no—
714C22×C71—22no—
715C22×C71—22no—
716C22×C71—22no—
717C22×C71—22no—
718C22×C71—22no—
719C22×C71—22no—
720C22×C71—22no—
721C22×C71—22no—
722C22×C71—22no—
723C22×C71—22no—
724C22×C71—22no—
725C22×C71—22no—
726C22×C71—22no—
727C22×C71—22no—
728C22×C71—22no—
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#52914yes—
740C22×C71#53814yes—
741C22×C71#53914yes—
742C22×C71C22×#4111yescharacteristic
743C22×C71C22×#4111yescharacteristic
744C22×C71C22×#4111yescharacteristic
745C22×C71C2×H(5,𝔽2)11yescharacteristic
746C22×C71C2×H(5,𝔽2)11yescharacteristic
747C22×C71C2×H(5,𝔽2)11yescharacteristic
748C22×C71C2×2−1+411yescharacteristic
749C2×D71—41no—
750C2×D71—41no—
751C2×D71—41no—
752C2×D71—41no—
753C2×D71—41no—
754C2×D71—41no—
755C2×D71—41no—
756C4×C71—41no—
757C4×C71—41no—
758C4×C71—41no—
759C4×C71—41no—
760C4×C71—41no—
761C4×C71—41no—
762C4×C71—41no—
763C4×C71—41no—
764C4×C71—41no—
765C4×C71—41no—
766C4×C71—41no—
767Dic71—22no—
768Dic71—22no—
769Dic71—22no—
770Dic71—22no—
771Dic71—41no—
772Dic71—41no—
773Dic71—41no—
774Dic71—41no—
775Dic71—41no—
776Dic71—41no—
777Dic71—41no—
778Dic71—41no—
779Dic71—41no—
780Dic71—41no—
781Dic71—41no—
782#34997—711nomaximal, Sylow
783C2×C71—24no—
784C2×C71—24no—
785C2×C71—24no—
786C2×C71—81no—
787C2×C71C2×#52911yescharacteristic
788C2×C71C2×#53811yescharacteristic
789C2×C71C2×#53911yescharacteristic
790C2×C71#349011yescharacteristic
791C2×C71#349011yescharacteristic
792C2×C71#349211yescharacteristic
793C2×C71#349211yescharacteristic
794D71—81no—
795#2849—711no—
796#2849D7111yescharacteristic, complemented
797#2848—711no—
798#2847—711no—
799#2646—711no—
800#2643—711no—
801#2643—711no—
802#2639—711no—
803#2510—711no—
804#2510—711no—
805#2505—711no—
806#2505—711no—
807#2493—711no—
808#2493—711no—
809#2488—711no—
810#2488—711no—
811#2450—711no—
812#2450—711no—
813#2444—711no—
814#2444—711no—
815#2425—711no—
816#2425—711no—
817#2419—711no—
818#2419—711no—
819#2329—711no—
820#2325—711no—
821#2318—711no—
822#2318—711no—
823C4×#120—711no—
824C4×#120—711no—
825C22×#95—711no—
826C71#3499711yescharacteristic, complemented, Sylow
827C24×C4—711no—
828C24×C4—711no—
829C24×C4C2×D7111yescharacteristic
830C2×#123—711no—
831C2×#123—711no—
832C2×#123C2×D7111yescharacteristic
833C2×#123C2×D7111yescharacteristic
834C2×C22⋊Q8—711no—
835C2×C22⋊Q8—711no—
836C2×C22⋊Q8—711no—
837C2×#121—711no—
838C2×#121—711no—
839C2×#121—711no—
840C2×#120—711no—
841C2×#120C2×D7111yescharacteristic
842C2×C4×D4—711no—
843C2×C4×D4—711no—
844C2×C4×D4—711no—
845C2×C4×D4—711no—
846C2×C4×D4—711no—
847C2×C4×D4—711no—
848#401—711no—
849#401—711no—
850#400—711no—
851#400—711no—
852#400—711no—
853#400—711no—
854#400—711no—
855#400—711no—
856#400—711no—
857#400—711no—
858#400—711no—
859#400—711no—
860#400—711no—
861#400—711no—
862#398—711no—
863#398—711no—
864#398—711no—
865#398—711no—
866#397—711no—
867#397—711no—
868#397—711no—
869#397—711no—
870#397—711no—
871#397—711no—
872#397—711no—
873#397—711no—
874#396—711no—
875#396—711no—
876#394—711no—
877#394—711no—
878#393—711no—
879#393—711no—
880#391—711no—
881#391—711no—
882#389—711no—
883#389—711no—
884#388—711no—
885#388—711no—
886#388—711no—
887#388—711no—
888#388—711no—
889#388—711no—
890#387—711no—
891#387—711no—
892#387—711no—
893#387—711no—
894#387—711no—
895#387—711no—
896#387—711no—
897#387—711no—
898#387—711no—
899#387—711no—
900#386—711no—
901#386—711no—
902#386—711no—
903#386—711no—
904#386—711no—
905#386—711no—
906#386—711no—
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#386C2×D7111yescharacteristic
919#386C2×D7111yescharacteristic
920#386C2×D7111yescharacteristic
921#386C2×D7111yescharacteristic
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#385—711no—
933#385—711no—
934#385—711no—
935#385—711no—
936#385—711no—
937#385—711no—
938#385—711no—
939#385—711no—
940#385C2×D7111yescharacteristic
941#385C2×D7111yescharacteristic
942#385C2×D7111yescharacteristic
943#385C2×D7111yescharacteristic
944#383—711no—
945#383—711no—
946#382—711no—
947#382—711no—
948#381—711no—
949#381—711no—
950#381—711no—
951#381—711no—
952#381C2×D7111yescharacteristic
953#381C2×D7111yescharacteristic
954#380—711no—
955#380—711no—
956#380—711no—
957#380—711no—
958#380—711no—
959#380—711no—
960#380—711no—
961#380—711no—
962#379—711no—
963#379C2×D7111yescharacteristic
964C4×C22⋊C4—711no—
965C4×C22⋊C4—711no—
966C4×C22⋊C4—711no—
967C4×C22⋊C4—711no—
968C4×C22⋊C4—711no—
969C4×C22⋊C4—711no—
970C2×#95—711no—
971C2×#95—711no—
972C2×#95—711no—
973C2×#95—711no—
974C2×#95—711no—
975C2×#95—711no—
976C2×#95—711no—
977C2×#95—711no—
978C2×#95—711no—
979C2×#95—711no—
980C2×#95—711no—
981C2×#95—711no—
982C25C22×D7111yescharacteristic
983C22×Q8—711no—
984C22×D4—711no—
985C22×D4—711no—
986C22×D4—711no—
987C22×D4—711no—
988C22×D4C22×D7111yescharacteristic
989C22×D4C22×D7111yescharacteristic
990C22×D4C22×D7111yescharacteristic
991C23×C4—24no—
992C23×C4—42no—
993C23×C4—42no—
994C23×C4—2842no—
995C23×C4—2842no—
996C23×C4—2842no—
997C23×C4—2842no—
998C23×C4—711no—
999C23×C4—711no—
1000C23×C4—711no—
1001C23×C4—711no—
1002C23×C4—711no—
1003C23×C4—711no—
1004C23×C4—711no—
1005C23×C4—711no—
1006C23×C4—711no—
1007C23×C4—711no—
1008C23×C4—711no—
1009C23×C4—711no—
1010C23×C4—711no—
1011C23×C4—711no—
1012C23×C4—1424no—
1013C23×C4—1424no—
1014C23×C4C22×D7111yescharacteristic
1015C23×C4C22×D7111yescharacteristic
1016C23×C4C22×D7111yescharacteristic
1017C23×C4C22×D7111yescharacteristic
1018C23×C4C22×D7111yescharacteristic
1019C23×C4C22×D7111yescharacteristic
1020#123—42no—
1021#123—42no—
1022#123—2842no—
1023#123—2842no—
1024C22⋊Q8—2842no—
1025C22⋊Q8—2842no—
1026C22⋊Q8—1424no—
1027#121—2842no—
1028#121—2842no—
1029#121—1424no—
1030#120—24no—
1031#120—1424no—
1032C4×D4—2842no—
1033C4×D4—2842no—
1034C4×D4—2842no—
1035C4×D4—2842no—
1036C4×D4—1424no—
1037C4×D4—1424no—
1038C2×C4⋊C4—711no—
1039C2×C4⋊C4—711no—
1040C2×C4⋊C4—711no—
1041C2×C4⋊C4—711no—
1042C2×C4⋊C4—711no—
1043C2×C4⋊C4—711no—
1044C2×C4⋊C4—711no—
1045C2×C4⋊C4—711no—
1046C2×C4⋊C4—711no—
1047C2×C4⋊C4—711no—
1048C2×C4⋊C4—711no—
1049C2×C4⋊C4—711no—
1050C2×C4⋊C4—711no—
1051C2×C4⋊C4—711no—
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⋊C4C22×D7111yescharacteristic
1061C2×C4⋊C4C22×D7111yescharacteristic
1062C2×C4⋊C4C22×D7111yescharacteristic
1063C2×C4⋊C4C22×D7111yescharacteristic
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—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⋊C4C22×D7111yescharacteristic
1090C2×C22⋊C4C22×D7111yescharacteristic
1091C2×C22⋊C4C22×D7111yescharacteristic
1092C2×C22⋊C4C22×D7111yescharacteristic
1093C2×C22⋊C4C22×D7111yescharacteristic
1094C2×C22⋊C4C22×D7111yescharacteristic
1095C2×C22⋊C4C22×D7111yescharacteristic
1096C2×C22⋊C4C22×D7111yescharacteristic
1097C2×C22⋊C4C22×D7111yescharacteristic
1098C2×C22⋊C4C22×D7111yescharacteristic
1099C2×C22⋊C4C22×D7111yescharacteristic
1100C2×C22⋊C4C22×D7111yescharacteristic
1101C2×C22⋊C4C22×D7111yescharacteristic
1102C2×C42—711no—
1103C2×C42—711no—
1104C2×C42—711no—
1105C2×C42—711no—
1106C2×C42—711no—
1107C2×C42—711no—
1108#95—711no—
1109#95—711no—
1110#95—711no—
1111#95—711no—
1112#95—711no—
1113#95—711no—
1114#95—711no—
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#95—711no—
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#95C22×D7111yescharacteristic
1157#95C22×D7111yescharacteristic
1158#95C22×D7111yescharacteristic
1159#95C22×D7111yescharacteristic
1160#95C22×D7111yescharacteristic
1161#95C22×D7111yescharacteristic
1162#95C22×D7111yescharacteristic
1163#95C22×D7111yescharacteristic
1164C24—22no—
1165C24—22no—
1166C24—22no—
1167C24—22no—
1168C24—22no—
1169C24—22no—
1170C24—711no—
1171C24#1176586414yes—
1172C24C23×D7111yescharacteristic
1173C24C23×D7111yescharacteristic
1174C24C23×D7111yescharacteristic
1175C24C23×D7111yescharacteristic
1176C2×Q8—2841no—
1177C2×Q8—2841no—
1178C2×Q8—1422no—
1179C2×D4—22no—
1180C2×D4—22no—
1181C2×D4—22no—
1182C2×D4—22no—
1183C2×D4—22no—
1184C2×D4—22no—
1185C2×D4—22no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—2841no—
1189C2×D4—2841no—
1190C2×D4—1422no—
1191C2×D4—1422no—
1192C2×D4—1422no—
1193C2×D4—1422no—
1194C2×D4—1422no—
1195C2×D4—1422no—
1196C2×D4—1422no—
1197C2×D4—1422no—
1198C2×D4—1422no—
1199C2×D4—1422no—
1200C22×C4—22no—
1201C22×C4—22no—
1202C22×C4—22no—
1203C22×C4—22no—
1204C22×C4—22no—
1205C22×C4—22no—
1206C22×C4—22no—
1207C22×C4—22no—
1208C22×C4—22no—
1209C22×C4—22no—
1210C22×C4—41no—
1211C22×C4—41no—
1212C22×C4—41no—
1213C22×C4—41no—
1214C22×C4—41no—
1215C22×C4—41no—
1216C22×C4—41no—
1217C22×C4—41no—
1218C22×C4—416no—
1219C22×C4—2841no—
1220C22×C4—2841no—
1221C22×C4—28416no—
1222C22×C4—28416no—
1223C22×C4—2841no—
1224C22×C4—2841no—
1225C22×C4—2841no—
1226C22×C4—2841no—
1227C22×C4—2841no—
1228C22×C4—2841no—
1229C22×C4—2841no—
1230C22×C4—2841no—
1231C22×C4—2841no—
1232C22×C4—2841no—
1233C22×C4—2841no—
1234C22×C4—2841no—
1235C22×C4—2841no—
1236C22×C4—2841no—
1237C22×C4—2841no—
1238C22×C4—2841no—
1239C22×C4—2841no—
1240C22×C4—2841no—
1241C22×C4—714no—
1242C22×C4—714no—
1243C22×C4—711no—
1244C22×C4—711no—
1245C22×C4—711no—
1246C22×C4—711no—
1247C22×C4—711no—
1248C22×C4—711no—
1249C22×C4—711no—
1250C22×C4—711no—
1251C22×C4—711no—
1252C22×C4—711no—
1253C22×C4—711no—
1254C22×C4—711no—
1255C22×C4—711no—
1256C22×C4—711no—
1257C22×C4—711no—
1258C22×C4—1422no—
1259C22×C4—1422no—
1260C22×C4—1422no—
1261C22×C4—1422no—
1262C22×C4—1422no—
1263C22×C4—1422no—
1264C22×C4—1422no—
1265C22×C4—1422no—
1266C22×C4—1422no—
1267C22×C4—1422no—
1268C22×C4—1422no—
1269C22×C4—1422no—
1270C22×C4—1422no—
1271C22×C4—1422no—
1272C22×C4—1422no—
1273C22×C4—1422no—
1274C22×C4—1422no—
1275C22×C4—1422no—
1276C22×C4—1422no—
1277C22×C4—1422no—
1278C22×C4C23×D7111yescharacteristic
1279C22×C4C23×D7111yescharacteristic
1280C22×C4C23×D7111yescharacteristic
1281C22×C4C23×D7111yescharacteristic
1282C22×C4C23×D7111yescharacteristic
1283C22×C4C23×D7111yescharacteristic
1284C22×C4C23×D7111yescharacteristic
1285C22×C4C23×D7111yescharacteristic
1286C22×C4C23×D7111yescharacteristic
1287C22×C4C23×D7111yescharacteristic
1288C22×C4C23×D7111yescharacteristic
1289C4⋊C4—41no—
1290C4⋊C4—41no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—2841no—
1294C4⋊C4—2841no—
1295C4⋊C4—2841no—
1296C4⋊C4—2841no—
1297C4⋊C4—2841no—
1298C4⋊C4—2841no—
1299C4⋊C4—2841no—
1300C4⋊C4—2841no—
1301C4⋊C4—2841no—
1302C4⋊C4—2841no—
1303C4⋊C4—2841no—
1304C4⋊C4—2841no—
1305C4⋊C4—2841no—
1306C4⋊C4—2841no—
1307C4⋊C4—2841no—
1308C4⋊C4—2841no—
1309C4⋊C4—1422no—
1310C4⋊C4—1422no—
1311C4⋊C4—1422no—
1312C4⋊C4—1422no—
1313C4⋊C4—1422no—
1314C4⋊C4—1422no—
1315C22⋊C4—22no—
1316C22⋊C4—22no—
1317C22⋊C4—22no—
1318C22⋊C4—22no—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—22no—
1322C22⋊C4—22no—
1323C22⋊C4—22no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—41no—
1328C22⋊C4—2841no—
1329C22⋊C4—2841no—
1330C22⋊C4—2841no—
1331C22⋊C4—2841no—
1332C22⋊C4—2841no—
1333C22⋊C4—2841no—
1334C22⋊C4—2841no—
1335C22⋊C4—2841no—
1336C22⋊C4—2841no—
1337C22⋊C4—2841no—
1338C22⋊C4—2841no—
1339C22⋊C4—2841no—
1340C22⋊C4—1422no—
1341C22⋊C4—1422no—
1342C22⋊C4—1422no—
1343C22⋊C4—1422no—
1344C22⋊C4—1422no—
1345C22⋊C4—1422no—
1346C22⋊C4—1422no—
1347C22⋊C4—1422no—
1348C22⋊C4—1422no—
1349C22⋊C4—1422no—
1350C22⋊C4—1422no—
1351C22⋊C4—1422no—
1352C22⋊C4—1422no—
1353C42—2841no—
1354C42—2841no—
1355C42—2841no—
1356C42—2841no—
1357C42—1422no—
1358C42—1422no—
1359C23—28no—
1360C23—28no—
1361C23—28no—
1362C23—28no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—21no—
1375C23—28no—
1376C23—28no—
1377C23—28no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—1421no—
1386C23—1421no—
1387C23—1421no—
1388C23—1421no—
1389C23—1421no—
1390C23—1421no—
1391C23—1421no—
1392C23#41×D7112yes—
1393C23#41×D7112yes—
1394C23C2×#1176586412yes—
1395C23C2×#1176586412yes—
1396C23C2×#1176586412yes—
1397C23#1455617312yes—
1398C23#1455617312yes—
1399C23#1455617412yes—
1400C23#1455617512yes—
1401C23C24×D7111yescharacteristic
1402Q8—5682no—
1403D4—44no—
1404D4—44no—
1405D4—44no—
1406D4—2844no—
1407D4—2844no—
1408D4—2844no—
1409D4—5682no—
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—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—44no—
1444C2×C4—44no—
1445C2×C4—44no—
1446C2×C4—44no—
1447C2×C4—44no—
1448C2×C4—44no—
1449C2×C4—2844no—
1450C2×C4—2844no—
1451C2×C4—2844no—
1452C2×C4—2844no—
1453C2×C4—2844no—
1454C2×C4—2844no—
1455C2×C4—2844no—
1456C2×C4—2844no—
1457C2×C4—2844no—
1458C2×C4—2844no—
1459C2×C4—2844no—
1460C2×C4—2844no—
1461C2×C4—5682no—
1462C2×C4—5682no—
1463C2×C4—712no—
1464C2×C4—712no—
1465C2×C4—712no—
1466C2×C4—712no—
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×C4—1421no—
1481C2×C4—1421no—
1482C2×C4—1421no—
1483C2×C4—1421no—
1484C2×C4—1421no—
1485C2×C4—1421no—
1486C2×C4—1421no—
1487C2×C4—1421no—
1488C2×C4—1421no—
1489C2×C4—1421no—
1490C2×C4—1421no—
1491C2×C4—1421no—
1492C2×C4—1421no—
1493C2×C4—1421no—
1494C2×C4—1421no—
1495C2×C4—1421no—
1496C2×C4—1421no—
1497C2×C4—1421no—
1498C2×C4—1421no—
1499C2×C4—1421no—
1500C2×C4—1421no—
1501C2×C4—1421no—
1502C2×C4—1421no—
1503C2×C4—1421no—
1504C2×C4—1421no—
1505C2×C4—1421no—
1506C2×C4—1421no—
1507C2×C4—1421no—
1508C22—232no—
1509C22—22no—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—22no—
1515C22—22no—
1516C22—22no—
1517C22—22no—
1518C22—22no—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—22no—
1523C22—22no—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22—41no—
1533C22—41no—
1534C22—2841no—
1535C22—2841no—
1536C22—2841no—
1537C22—2841no—
1538C22—2841no—
1539C22—2841no—
1540C22—2841no—
1541C22#1798652614yes—
1542C22#1798658414yes—
1543C22#1798659314yes—
1544C22C2×#41×D7111yescharacteristic
1545C22C2×#41×D7111yescharacteristic
1546C22C22×#1176586411yescharacteristic
1547C22C2×#1455617311yescharacteristic
1548C22C2×#1455617311yescharacteristic
1549C22C2×#1455617411yescharacteristic
1550C22C2×#1455617511yescharacteristic
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—2841no—
1563C4—2841no—
1564C4—2841no—
1565C4—2841no—
1566C4—2841no—
1567C4—2841no—
1568C4—2841no—
1569C4—2841no—
1570C4—2841no—
1571C4—2841no—
1572C4—2841no—
1573C4—1422no—
1574C4—1422no—
1575C4—1422no—
1576C4—1422no—
1577C2—24no—
1578C2—24no—
1579C2—24no—
1580C2—81no—
1581C2—5681no—
1582C2C2×#1798652611yescharacteristic
1583C2C2×#1798658411yescharacteristic
1584C2C2×#1798659311yescharacteristic
1585C2#2260202311yescharacteristic
1586C2#2260202311yescharacteristic
1587C2#2260204111yescharacteristic
1588C2#2260204111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2849C2
prime radical#22596620C2
hypercenter#2849D71
hypocenterC71#34997
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2849

Complements

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

NH ≅ G/Ntype
1. #22596632C2semidirect
2. #22596625C2semidirect
4. #22594312C2semidirect
5. #22594296C2semidirect
6. #22594295C2semidirect
7. #22594270C2semidirect
8. #22592906C2semidirect
9. #22592898C2semidirect
10. #22592847C2semidirect
11. #22592839C2semidirect
12. #22592729C2semidirect
13. #22592721C2semidirect
14. #22592670C2semidirect
15. #22592662C2semidirect
16. #22592170C2semidirect
17. #22592162C2semidirect
18. #22592096C2semidirect
19. #22592088C2semidirect
20. #22591895C2semidirect
21. #22591887C2semidirect
22. #22591821C2semidirect
23. #22591813C2semidirect
24. #22591071C2semidirect
25. #22591041C2semidirect
26. #22590968C2semidirect
27. #22590966C2semidirect
28. #120×Dic71C2semidirect
29. #22590839C2semidirect
30. C22×C71⋊#95C2semidirect
31. C71×#2849C2semidirect
49. C71⋊#401C22semidirect
50. C71⋊#401C22semidirect
51. #17985941C22semidirect
52. #17985941C22semidirect
53. #17985941C22semidirect
54. #17985940C22semidirect
55. #17985940C22semidirect
56. #17985940C22semidirect
57. #17985940C22semidirect
58. #17985939C22semidirect
59. #17985939C22semidirect
60. #17985938C22semidirect
61. #17985937C22semidirect
62. #17985937C22semidirect
63. #17985933C22semidirect
64. #17985932C22semidirect
65. #17985930C22semidirect
66. #17985929C22semidirect
67. #17985928C22semidirect
68. #17985928C22semidirect
69. #17985927C22semidirect
70. #17985927C22semidirect
71. #17985927C22semidirect
72. #17985926C22semidirect
73. #17985925C22semidirect
74. #17985924C22semidirect
75. #17985922C22semidirect
76. #17985921C22semidirect
77. #17985915C22semidirect
78. #17985914C22semidirect
79. #17985912C22semidirect
80. #17985911C22semidirect
81. #17985904C22semidirect
82. #17985903C22semidirect
83. #17985895C22semidirect
84. #17985894C22semidirect
85. #17985893C22semidirect
86. #17985893C22semidirect
87. #17985891C22semidirect
88. #17985889C22semidirect
89. #17985888C22semidirect
90. #17985887C22semidirect
91. #17985886C22semidirect
92. #17985886C22semidirect
93. #17985884C22semidirect
94. #17985884C22semidirect
95. #17985882C22semidirect
96. #17985881C22semidirect
97. #17985881C22semidirect
98. #17985881C22semidirect
99. #17985880C22semidirect
100. #17985880C22semidirect
117. #17985876C22semidirect
118. #17985875C22semidirect
125. #17985873C22semidirect
136. #17985871C22semidirect
137. #17985866C22semidirect
138. #17985866C22semidirect
139. #17985864C22semidirect
140. #17985863C22semidirect
143. #17985861C22semidirect
144. #17985860C22semidirect
151. #17985857C22semidirect
152. #17985856C22semidirect
796. #2849D71semidirect
826. C71#34997semidirect

Maximal subgroups

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

subgroupindex
#225966322
#225966252
#225966202
#225943122
#225942962
#225942952
#225942702
#225929062
#225928982
#225928472
#225928392
#225927292
#225927212
#225926702
#225926622
#225921702
#225921622
#225920962
#225920882
#225918952
#225918872
#225918212
#225918132
#225910712
#225910412
#225909682
#225909662
#120×Dic712
#225908392
C22×C71⋊#952
C71×#28492
#3499771