Finite Group Databasebeta

← #32170250

Subgroups — #32170250

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#22596667C211yesmaximal, characteristic, complemented
2#22596660C211yesmaximal, characteristic, complemented
3#22596654C211yesmaximal, characteristic, complemented
4#22596638C211yesmaximal, characteristic, complemented
5#22594401C211yesmaximal, characteristic, complemented
6#22594339C211yesmaximal, characteristic, complemented
7#22594326C211yesmaximal, characteristic, complemented
8#22594324C211yesmaximal, characteristic, complemented
9#22592996C211yesmaximal, characteristic, complemented
10#22592995C211yesmaximal, characteristic, complemented
11#22592899C211yesmaximal, characteristic, complemented
12#22592896C211yesmaximal, characteristic, complemented
13#22592837C211yesmaximal, characteristic, complemented
14#22592671C211yesmaximal, characteristic, complemented
15#22592585C211yesmaximal, characteristic, complemented
16#22592463C211yesmaximal, characteristic, complemented
17#22592390C211yesmaximal, characteristic, complemented
18#22592282C211yesmaximal, characteristic, complemented
19#22592097C211yesmaximal, characteristic, complemented
20#22592008C211yesmaximal, characteristic, complemented
21#22591896C211yesmaximal, characteristic, complemented
22#22591733C211yesmaximal, characteristic, complemented
23#22591716C211yesmaximal, characteristic
24#22591665C211yesmaximal, characteristic, complemented
25#22591068C211yesmaximal, characteristic, complemented
26#22590998C211yesmaximal, characteristic, complemented
27#22590967C211yesmaximal, characteristic, complemented
28C4×#14556098C211yesmaximal, characteristic, complemented
29C2×#17985875C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D71C211yesmaximal, characteristic, complemented
31C71×#2312C211yesmaximal, characteristic, complemented
32C23×C22⋊D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C2×#14556121C2211yescharacteristic, complemented
35C2×#14556114C2211yescharacteristic, complemented
36C2×#14556113C2211yescharacteristic, complemented
37C2×#14556110C2211yescharacteristic
38C2×#14556110C2211yescharacteristic
39C2×#14556106C2211yescharacteristic, complemented
40C2×#14556105C2211yescharacteristic
41C2×#14556101C2211yescharacteristic
42C2×#14556101C2211yescharacteristic
43C2×#14556098C2211yescharacteristic
44C2×#14556097C2211yescharacteristic
45C2×C4×D284C2211yescharacteristic, complemented
46C2×C4×D284C2211yescharacteristic, complemented
47C2×C4×C22⋊D71C2211yescharacteristic
48C22×C22⋊Dic71C2211yescharacteristic
49C22×(C2×D71)⋊C4C2211yescharacteristic
50C2×C22⋊C4×D71C2211yescharacteristic
51C2×C22⋊C4×D71C2211yescharacteristic
52C2×C42×D71C2211yescharacteristic, complemented
53C2×C42×D71C2211yescharacteristic, complemented
54C71⋊#401C2211yescharacteristic, complemented
55#17985940C2211yescharacteristic, complemented
56#17985939C2211yescharacteristic, complemented
57#17985938C2211yescharacteristic, complemented
58#17985937C2211yescharacteristic, complemented
59#17985934C2211yescharacteristic, complemented
60#17985932C2211yescharacteristic, complemented
61#17985928C2211yescharacteristic, complemented
62#17985927C2211yescharacteristic, complemented
63#17985927C2211yescharacteristic, complemented
64#17985927C2211yescharacteristic, complemented
65#17985926C2211yescharacteristic, complemented
66#17985925C2211yescharacteristic, complemented
67#17985925C2211yescharacteristic, complemented
68#17985924C2211yescharacteristic, complemented
69#17985923C2211yescharacteristic, complemented
70#17985922C2211yescharacteristic, complemented
71#17985921C2211yescharacteristic, complemented
72#17985917C2211yescharacteristic, complemented
73#17985916C2211yescharacteristic, complemented
74#17985915C2211yescharacteristic
75#17985915C2211yescharacteristic
76#17985915C2211yescharacteristic, complemented
77#17985914C2211yescharacteristic
78#17985914C2211yescharacteristic
79#17985914C2211yescharacteristic
80#17985914C2211yescharacteristic
81#17985914C2211yescharacteristic, complemented
82#17985912C2211yescharacteristic, complemented
83#17985911C2211yescharacteristic, complemented
84#17985908C2211yescharacteristic
85#17985908C2211yescharacteristic
86#17985905C2211yescharacteristic, complemented
87#17985903C2211yescharacteristic, complemented
88#17985899C2211yescharacteristic, complemented
89#17985899C2211yescharacteristic, complemented
90#17985899C2211yescharacteristic, complemented
91#17985897C2211yescharacteristic, complemented
92#17985896C2211yescharacteristic, complemented
93#17985894C2211yescharacteristic, complemented
94#17985893C2211yescharacteristic, complemented
95#17985893C2211yescharacteristic, complemented
96#17985893C2211yescharacteristic, complemented
97#17985892C2211yescharacteristic, complemented
98#17985892C2211yescharacteristic, complemented
99#17985891C2211yescharacteristic, complemented
100#17985890C2211yescharacteristic, complemented
101#17985890C2211yescharacteristic, complemented
102#17985889C2211yescharacteristic, complemented
103#17985887C2211yescharacteristic, complemented
104#17985887C2211yescharacteristic, complemented
105#17985887C2211yescharacteristic, complemented
106#17985887C2211yescharacteristic, complemented
107#17985886C2211yescharacteristic, complemented
108#17985885C2211yescharacteristic, complemented
109#17985885C2211yescharacteristic, complemented
110#17985884C2211yescharacteristic, complemented
111#17985883C2211yescharacteristic, complemented
112#17985883C2211yescharacteristic, complemented
113#17985883C2211yescharacteristic, complemented
114#17985883C2211yescharacteristic, complemented
115#17985882C2211yescharacteristic, complemented
116#17985878C2211yescharacteristic
117#17985877C2211yescharacteristic, complemented
118#17985877C2211yescharacteristic, complemented
119#17985877C2211yescharacteristic, complemented
120#17985876C2211yescharacteristic
121#17985876C2211yescharacteristic
122#17985876C2211yescharacteristic
123#17985875C2211yescharacteristic
124#17985875C2211yescharacteristic
125#17985875C2211yescharacteristic
126#17985875C2211yescharacteristic
127#17985875C2211yescharacteristic
128#17985875C2211yescharacteristic
129#17985875C2211yescharacteristic
130#17985875C2211yescharacteristic
131#17985875C2211yescharacteristic
132#17985875C2211yescharacteristic
133#17985875C2211yescharacteristic
134#17985875C2211yescharacteristic
135#17985875C2211yescharacteristic, complemented
136#17985875C2211yescharacteristic, complemented
137#17985874C2211yescharacteristic
138#17985874C2211yescharacteristic
139#17985873C2211yescharacteristic, complemented
140#17985873C2211yescharacteristic, complemented
141#17985873C2211yescharacteristic, complemented
142#17985872C2211yescharacteristic
143#17985871C2211yescharacteristic
144#17985871C2211yescharacteristic
145#17985871C2211yescharacteristic
146#17985870C2211yescharacteristic, complemented
147#17985870C2211yescharacteristic, complemented
148#17985866C2211yescharacteristic, complemented
149#17985866C2211yescharacteristic, complemented
150#17985863C2211yescharacteristic, complemented
151#17985863C2211yescharacteristic, complemented
152#17985861C2211yescharacteristic, complemented
153#17985861C2211yescharacteristic, complemented
154#17985858C2211yescharacteristic, complemented
155#17985858C2211yescharacteristic, complemented
156#17985857C2211yescharacteristic
157#17985855C2211yescharacteristic
158#17985854C2211yescharacteristic
159C22⋊C4×Dic71C2211yescharacteristic
160C22⋊C4×Dic71C2211yescharacteristic
161C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
163C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
164C4×(C2×D71)⋊C4C2211yescharacteristic, complemented
165C4×C22⋊Dic71C2211yescharacteristic
166#17985846C2211yescharacteristic, complemented
167#17985846C2211yescharacteristic, complemented
168C2×C71⋊#95C2211yescharacteristic
169C2×C71⋊#95C2211yescharacteristic
170#95×D71C2211yescharacteristic, complemented
171#95×D71C2211yescharacteristic, complemented
172C22×C22⋊C4×C71C2211yescharacteristic
173#388×C71C2211yescharacteristic, complemented
174#388×C71C2211yescharacteristic, complemented
175#388×C71C2211yescharacteristic, complemented
176#388×C71C2211yescharacteristic, complemented
177#388×C71C2211yescharacteristic, complemented
178#388×C71C2211yescharacteristic, complemented
179#388×C71C2211yescharacteristic, complemented
180#388×C71C2211yescharacteristic, complemented
181#380×C71C2211yescharacteristic
182#380×C71C2211yescharacteristic
183#379×C71C2211yescharacteristic
184#379×C71C2211yescharacteristic
185C4×C22⋊C4×C71C2211yescharacteristic
186C4×C22⋊C4×C71C2211yescharacteristic
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×D71—24no—
205C22×C4×D71—42no—
206C22×C4×D71—42no—
207C22×C4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209C22×C4×D71C2311yescharacteristic
210C22×C4×D71C2311yescharacteristic
211C22×C4×D71C2311yescharacteristic
212C22×C4×D71C2311yescharacteristic
213C22×C4×D71C2311yescharacteristic
214C22×C4×D71C2311yescharacteristic
215C22×C4×D71C2311yescharacteristic
216#14556121—42no—
217#14556114—42no—
218#14556113—42no—
219#14556110—42no—
220#14556110—42no—
221#14556106—42no—
222#14556105—24no—
223#14556101—42no—
224#14556101—42no—
225#14556098—24no—
226#14556097—24no—
227C4×D284—42no—
228C4×D284—42no—
229C4×C22⋊D71—24no—
230C2×C4⋊Dic71C2311yescharacteristic
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
233C2×C4⋊Dic71C2311yescharacteristic
234C2×C4⋊Dic71C2311yescharacteristic
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×C22⋊Dic71—42no—
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×(C2×D71)⋊C4—42no—
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
286C22⋊C4×D71—24no—
287C22⋊C4×D71—24no—
288C2×C4×Dic71C2311yescharacteristic
289C2×C4×Dic71C2311yescharacteristic
290C2×C4×Dic71C2311yescharacteristic
291C2×C4×Dic71C2311yescharacteristic
292C2×C4×Dic71C2311yescharacteristic
293C2×C4×Dic71C2311yescharacteristic
294C2×C4×Dic71C2311yescharacteristic
295C42×D71—42no—
296C42×D71—42no—
297C71⋊#95C2311yescharacteristic
298C71⋊#95C2311yescharacteristic
299C71⋊#95C2311yescharacteristic
300C71⋊#95C2311yescharacteristic
301C71⋊#95C2311yescharacteristic
302C71⋊#95C2311yescharacteristic
303C71⋊#95C2311yescharacteristic
304C71⋊#95C2311yescharacteristic
305C71⋊#95C2311yescharacteristic
306C71⋊#95C2311yescharacteristic
307C71⋊#95C2311yescharacteristic
308C71⋊#95C2311yescharacteristic
309C71⋊#95C2311yescharacteristic
310C71⋊#95C2311yescharacteristic
311C71⋊#95C2311yescharacteristic
312C71⋊#95C2311yescharacteristic
313C71⋊#95C2311yescharacteristic
314C71⋊#95C2311yescharacteristic
315C71⋊#95C2311yescharacteristic
316C71⋊#95C2311yescharacteristic
317C71⋊#95C2311yescharacteristic
318C71⋊#95C2311yescharacteristic
319C71⋊#95C2311yescharacteristic
320C71⋊#95C2311yescharacteristic
321C71⋊#95C2311yescharacteristic
322C71⋊#95C2311yescharacteristic
323C71⋊#95C2311yescharacteristic
324C71⋊#95C2311yescharacteristic
325C71⋊#95C2311yescharacteristic
326C71⋊#95C2311yescharacteristic
327C71⋊#95C2311yescharacteristic
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C71⋊#95C2311yescharacteristic
331C71⋊#95C2311yescharacteristic
332C71⋊#95C2311yescharacteristic
333C25×C71C2311yescharacteristic
334C23×C4×C71C2311yescharacteristic
335C23×C4×C71C2311yescharacteristic
336C2×C4⋊C4×C71C2311yescharacteristic
337C2×C4⋊C4×C71C2311yescharacteristic
338C2×C4⋊C4×C71C2311yescharacteristic
339C2×C4⋊C4×C71C2311yescharacteristic
340C2×C22⋊C4×C71—24no—
341C2×C22⋊C4×C71C2311yescharacteristic
342C2×C22⋊C4×C71C2311yescharacteristic
343C2×C22⋊C4×C71C2311yescharacteristic
344C2×C22⋊C4×C71C2311yescharacteristic
345C2×C22⋊C4×C71C2311yescharacteristic
346C2×C22⋊C4×C71C2311yescharacteristic
347C2×C22⋊C4×C71C2311yescharacteristic
348C2×C22⋊C4×C71C2311yescharacteristic
349C2×C22⋊C4×C71C2311yescharacteristic
350C2×C22⋊C4×C71C2311yescharacteristic
351C2×C22⋊C4×C71C2311yescharacteristic
352C2×C22⋊C4×C71C2311yescharacteristic
353C2×C22⋊C4×C71C2311yescharacteristic
354C2×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C22⋊C4×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—22no—
373C23×D71—41no—
374C23×D71—41no—
375C23×D71#4114yes—
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C23×D71C2411yescharacteristic
379C2×Dic142—22no—
380C2×Dic142—41no—
381C2×Dic142—41no—
382C2×D284—22no—
383C2×D284—22no—
384C2×D284—22no—
385C2×D284—22no—
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—41no—
402C2×C22⋊D71—41no—
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—22no—
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—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—22no—
437C2×C4×D71—22no—
438C2×C4×D71—22no—
439C2×C4×D71—22no—
440C2×C4×D71—22no—
441C2×C4×D71—22no—
442C2×C4×D71—22no—
443C2×C4×D71—22no—
444C2×C4×D71—22no—
445C2×C4×D71—22no—
446C2×C4×D71—22no—
447C2×C4×D71—22no—
448C2×C4×D71—22no—
449C2×C4×D71—416no—
450C2×C4×D71—41no—
451C2×C4×D71—41no—
452C2×C4×D71—41no—
453C2×C4×D71—41no—
454C2×C4×D71—41no—
455C2×C4×D71—41no—
456C2×C4×D71—41no—
457C2×C4×D71—41no—
458C2×C4×D71—41no—
459C2×C4×D71—41no—
460C4⋊Dic71—22no—
461C4⋊Dic71—22no—
462C4⋊Dic71—41no—
463C4⋊Dic71—41no—
464C4⋊Dic71—41no—
465Dic71⋊C4—22no—
466Dic71⋊C4—22no—
467Dic71⋊C4—22no—
468Dic71⋊C4—41no—
469Dic71⋊C4—41no—
470Dic71⋊C4—41no—
471Dic71⋊C4—41no—
472Dic71⋊C4—41no—
473Dic71⋊C4—41no—
474Dic71⋊C4—41no—
475Dic71⋊C4—41no—
476Dic71⋊C4—41no—
477Dic71⋊C4—41no—
478C22⋊Dic71—22no—
479C22⋊Dic71—22no—
480C22⋊Dic71—22no—
481C22⋊Dic71—22no—
482C22⋊Dic71—22no—
483C22⋊Dic71—22no—
484C22⋊Dic71—41no—
485C22⋊Dic71—41no—
486C22⋊Dic71—41no—
487C22⋊Dic71—41no—
488C22⋊Dic71—41no—
489C22⋊Dic71—41no—
490C22⋊Dic71#4114yes—
491(C2×D71)⋊C4—22no—
492(C2×D71)⋊C4—22no—
493(C2×D71)⋊C4—22no—
494(C2×D71)⋊C4—22no—
495(C2×D71)⋊C4—22no—
496(C2×D71)⋊C4—22no—
497(C2×D71)⋊C4—22no—
498(C2×D71)⋊C4—22no—
499(C2×D71)⋊C4—22no—
500(C2×D71)⋊C4—22no—
501(C2×D71)⋊C4—22no—
502(C2×D71)⋊C4—22no—
503(C2×D71)⋊C4—41no—
504(C2×D71)⋊C4—41no—
505(C2×D71)⋊C4—41no—
506(C2×D71)⋊C4—41no—
507(C2×D71)⋊C4—41no—
508(C2×D71)⋊C4—41no—
509(C2×D71)⋊C4—41no—
510(C2×D71)⋊C4—41no—
511(C2×D71)⋊C4—41no—
512(C2×D71)⋊C4—41no—
513(C2×D71)⋊C4—41no—
514C4×Dic71—22no—
515C4×Dic71—22no—
516C4×Dic71—22no—
517C4×Dic71—41no—
518C4×Dic71—41no—
519C4×Dic71—41no—
520C4×Dic71—41no—
521C24×C71—22no—
522C24×C71—22no—
523C24×C71—22no—
524C24×C71—41no—
525C24×C71—41no—
526C24×C71—41no—
527C24×C71—41no—
528C24×C71C2411yescharacteristic
529C24×C71C2411yescharacteristic
530C24×C71C2411yescharacteristic
531C22×C4×C71—22no—
532C22×C4×C71—41no—
533C22×C4×C71—41no—
534C22×C4×C71—41no—
535C22×C4×C71—41no—
536C22×C4×C71#4114yes—
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
547C22×C4×C71C2411yescharacteristic
548C22×C4×C71C2411yescharacteristic
549C4⋊C4×C71—41no—
550C4⋊C4×C71—41no—
551C4⋊C4×C71—41no—
552C4⋊C4×C71—41no—
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—22no—
561C22⋊C4×C71—41no—
562C22⋊C4×C71—41no—
563C22⋊C4×C71—41no—
564C22⋊C4×C71—41no—
565C22⋊C4×C71—41no—
566C22⋊C4×C71—41no—
567C22⋊C4×C71—41no—
568C22⋊C4×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—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×C71—21no—
591C23×C71—44no—
592C23×C71—44no—
593C23×C71—44no—
594C23×C71—82no—
595C23×C71—82no—
596C23×C71—82no—
597C23×C71—82no—
598C23×C71C2×#4112yes—
599C23×C71C2×#4112yes—
600C23×C71C2×#4112yes—
601C23×C71C2511yescharacteristic
602C22×D71—21no—
603C22×D71—21no—
604C22×D71—21no—
605C22×D71—21no—
606C22×D71—28no—
607C22×D71—21no—
608C22×D71—21no—
609C22×D71—21no—
610C22×D71—21no—
611C22×D71—21no—
612C22×D71—21no—
613C22×D71—28no—
614C22×D71—21no—
615C22×D71—21no—
616C22×D71—21no—
617C22×D71—21no—
618C22×D71—21no—
619C22×D71—21no—
620C22×D71—21no—
621C22×D71—44no—
622C22×D71—44no—
623C22×D71—44no—
624C22×D71—44no—
625C22×D71—44no—
626C22×D71C2×#4112yes—
627C22×D71C2×#4112yes—
628C22×D71H(5,𝔽2)12yes—
629C22×D71H(5,𝔽2)12yes—
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—21no—
644C2×C4×C71—21no—
645C2×C4×C71—21no—
646C2×C4×C71—21no—
647C2×C4×C71—21no—
648C2×C4×C71—21no—
649C2×C4×C71—21no—
650C2×C4×C71—21no—
651C2×C4×C71—21no—
652C2×C4×C71—21no—
653C2×C4×C71—21no—
654C2×C4×C71—21no—
655C2×C4×C71—21no—
656C2×C4×C71—21no—
657C2×C4×C71—21no—
658C2×C4×C71—21no—
659C2×C4×C71—21no—
660C2×C4×C71—21no—
661C2×C4×C71—21no—
662C2×C4×C71—21no—
663C2×C4×C71—21no—
664C2×C4×C71—44no—
665C2×C4×C71—82no—
666C2×C4×C71C2×#4112yes—
667C2×C4×C71C2×#4112yes—
668C22⋊D71—44no—
669C22⋊D71—44no—
670C22⋊D71—44no—
671C22⋊D71—44no—
672C22⋊D71—44no—
673C22⋊D71—82no—
674C22⋊D71—82no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—21no—
690C2×Dic71—21no—
691C2×Dic71—21no—
692C2×Dic71—21no—
693C2×Dic71—21no—
694C2×Dic71—21no—
695C2×Dic71—21no—
696C2×Dic71—21no—
697C2×Dic71—21no—
698C2×Dic71—21no—
699C2×Dic71—21no—
700C2×Dic71—21no—
701C2×Dic71—21no—
702C2×Dic71—21no—
703C2×Dic71—21no—
704C2×Dic71—21no—
705C2×Dic71—21no—
706C2×Dic71—21no—
707C2×Dic71—21no—
708C2×Dic71—21no—
709C2×Dic71—21no—
710C2×Dic71—21no—
711C2×Dic71—44no—
712C2×Dic71—44no—
713C2×Dic71—82no—
714C2×Dic71C2×#4112yes—
715C2×Dic71C2×#4112yes—
716C2×Dic71H(5,𝔽2)12yes—
717D284—44no—
718D284—44no—
719C4×D71—28no—
720C4×D71—44no—
721C4×D71—44no—
722C4×D71—44no—
723C4×D71—44no—
724C4×D71—44no—
725C4×D71—44no—
726C4×D71—44no—
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—41no—
736C22×C71—41no—
737C22×C71—41no—
738C22×C71—41no—
739C22×C71—41no—
740C22×C71—41no—
741C22×C71—41no—
742C22×C71—41no—
743C22×C71—41no—
744C22×C71—41no—
745C22×C71—41no—
746C22×C71—41no—
747C22×C71—41no—
748C22×C71—41no—
749C22×C71—88no—
750C22×C71#52914yes—
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—22no—
759C2×D71—22no—
760C2×D71—22no—
761C2×D71—22no—
762C2×D71—22no—
763C2×D71—22no—
764C2×D71—22no—
765C2×D71—22no—
766C2×D71—22no—
767C2×D71—416no—
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#53814yes—
780C4×C71—22no—
781C4×C71—22no—
782C4×C71—41no—
783C4×C71—41no—
784C4×C71—41no—
785C4×C71—41no—
786C4×C71—41no—
787C4×C71—41no—
788C4×C71—41no—
789C4×C71—41no—
790C4×C71—41no—
791C4×C71—41no—
792Dic71—22no—
793Dic71—22no—
794Dic71—22no—
795Dic71—41no—
796Dic71—41no—
797Dic71—41no—
798Dic71—41no—
799Dic71—41no—
800Dic71—41no—
801Dic71—41no—
802Dic71—41no—
803Dic71—41no—
804Dic71—41no—
805#34998—711nomaximal, Sylow
806C2×C71—24no—
807C2×C71—81no—
808C2×C71—81no—
809C2×C71C2×#52911yescharacteristic
810C2×C71C2×#53811yescharacteristic
811C2×C71#345911yescharacteristic
812C2×C71#349011yescharacteristic
813C2×C71#349411yescharacteristic
814C2×C71#351311yescharacteristic
815C2×C71#351911yescharacteristic
816D71—24no—
817D71—42no—
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#2312D7111yescharacteristic, complemented
847C4×#120—711no—
848C2×#386—711no—
849C2×C4×C22⋊C4—711no—
850C71#3499811yescharacteristic, complemented, Sylow
851C23×D4—711no—
852C24×C4—711no—
853C2×#126—711no—
854C2×#124—711no—
855C2×#123—711no—
856C2×#123—711no—
857C2×#123—711no—
858C2×C22⋊Q8—711no—
859C2×C22⋊Q8—711no—
860C2×#121—711no—
861C2×#121—711no—
862C2×#120—711no—
863C2×#120—711no—
864C2×C4×D4—711no—
865C2×C4×D4—711no—
866C2×C4×D4—711no—
867C22×C22⋊C4—711no—
868C22×C22⋊C4—711no—
869C22×C22⋊C4—711no—
870C22×C22⋊C4—711no—
871C22×C22⋊C4C2×D7111yescharacteristic
872C22×C42—711no—
873C22×C42—711no—
874#401—711no—
875#400—711no—
876#400—711no—
877#400—711no—
878#400—711no—
879#399—711no—
880#398—711no—
881#397—711no—
882#397—711no—
883#397—711no—
884#397—711no—
885#397—711no—
886#397—711no—
887#397—711no—
888#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#388C2×D7111yescharacteristic, complemented
928#388C2×D7111yescharacteristic, complemented
929#388C2×D7111yescharacteristic, complemented
930#388C2×D7111yescharacteristic, complemented
931#388C2×D7111yescharacteristic, complemented
932#388C2×D7111yescharacteristic, complemented
933#388C2×D7111yescharacteristic, complemented
934#388C2×D7111yescharacteristic, complemented
935#387—711no—
936#387—711no—
937#387—711no—
938#387—711no—
939#387—711no—
940#387—711no—
941#387—711no—
942#387—711no—
943#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#380C2×D7111yescharacteristic
986#380C2×D7111yescharacteristic
987#379—711no—
988#379—711no—
989#379C2×D7111yescharacteristic
990#379C2×D7111yescharacteristic
991C4×C22⋊C4—711no—
992C4×C22⋊C4—711no—
993C4×C22⋊C4—711no—
994C4×C22⋊C4—711no—
995C4×C22⋊C4—711no—
996C4×C22⋊C4—711no—
997C4×C22⋊C4—711no—
998C4×C22⋊C4—711no—
999C4×C22⋊C4—711no—
1000C4×C22⋊C4C2×D7111yescharacteristic
1001C4×C22⋊C4C2×D7111yescharacteristic
1002C2×#95—711no—
1003C2×#95—711no—
1004C2×#95—711no—
1005C2×#95—711no—
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—2842no—
1022C23×C4—2842no—
1023C23×C4—711no—
1024C23×C4—711no—
1025C23×C4—711no—
1026C23×C4—711no—
1027C23×C4—711no—
1028C23×C4—711no—
1029C23×C4—711no—
1030C23×C4—711no—
1031C23×C4—711no—
1032C23×C4—711no—
1033C23×C4—711no—
1034C23×C4—711no—
1035C23×C4—1424no—
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⋊C4C22×D7111yescharacteristic
1071C2×C4⋊C4C22×D7111yescharacteristic
1072C2×C4⋊C4C22×D7111yescharacteristic
1073C2×C4⋊C4C22×D7111yescharacteristic
1074C2×C22⋊C4—24no—
1075C2×C22⋊C4—2842no—
1076C2×C22⋊C4—2842no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—711no—
1082C2×C22⋊C4—711no—
1083C2×C22⋊C4—711no—
1084C2×C22⋊C4—711no—
1085C2×C22⋊C4—711no—
1086C2×C22⋊C4—711no—
1087C2×C22⋊C4—711no—
1088C2×C22⋊C4—711no—
1089C2×C22⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
1094C2×C22⋊C4—711no—
1095C2×C22⋊C4—711no—
1096C2×C22⋊C4—711no—
1097C2×C22⋊C4—711no—
1098C2×C22⋊C4—711no—
1099C2×C22⋊C4—711no—
1100C2×C22⋊C4—711no—
1101C2×C22⋊C4—711no—
1102C2×C22⋊C4—711no—
1103C2×C22⋊C4—711no—
1104C2×C22⋊C4—711no—
1105C2×C22⋊C4—711no—
1106C2×C22⋊C4—711no—
1107C2×C22⋊C4—711no—
1108C2×C22⋊C4—711no—
1109C2×C22⋊C4—711no—
1110C2×C22⋊C4—711no—
1111C2×C22⋊C4—711no—
1112C2×C22⋊C4—711no—
1113C2×C22⋊C4—1424no—
1114C2×C22⋊C4—1424no—
1115C2×C22⋊C4C22×D7111yescharacteristic
1116C2×C22⋊C4C22×D7111yescharacteristic
1117C2×C22⋊C4C22×D7111yescharacteristic
1118C2×C22⋊C4C22×D7111yescharacteristic
1119C2×C22⋊C4C22×D7111yescharacteristic
1120C2×C22⋊C4C22×D7111yescharacteristic
1121C2×C22⋊C4C22×D7111yescharacteristic
1122C2×C22⋊C4C22×D7111yescharacteristic
1123C2×C22⋊C4C22×D7111yescharacteristic
1124C2×C22⋊C4C22×D7111yescharacteristic
1125C2×C22⋊C4C22×D7111yescharacteristic
1126C2×C22⋊C4C22×D7111yescharacteristic
1127C2×C22⋊C4C22×D7111yescharacteristic
1128C2×C22⋊C4C22×D7111yescharacteristic
1129C2×C22⋊C4C22×D7111yescharacteristic
1130C2×C22⋊C4C22×D7111yescharacteristic
1131C2×C42—2842no—
1132C2×C42—2842no—
1133C2×C42—711no—
1134C2×C42—711no—
1135C2×C42—711no—
1136C2×C42—711no—
1137C2×C42—711no—
1138C2×C42—711no—
1139C2×C42—711no—
1140C2×C42C22×D7111yescharacteristic
1141C2×C42C22×D7111yescharacteristic
1142C2×C42C22×D7111yescharacteristic
1143C2×C42C22×D7111yescharacteristic
1144#95—711no—
1145#95—711no—
1146#95—711no—
1147#95—711no—
1148#95—711no—
1149#95—711no—
1150#95—711no—
1151#95—711no—
1152#95—711no—
1153#95—711no—
1154#95—711no—
1155#95—711no—
1156#95—711no—
1157#95—711no—
1158#95—711no—
1159#95—711no—
1160#95—711no—
1161#95—711no—
1162#95—711no—
1163#95—711no—
1164#95—711no—
1165#95—711no—
1166#95—711no—
1167#95—711no—
1168#95—711no—
1169#95—711no—
1170#95—711no—
1171#95—711no—
1172#95—711no—
1173#95—711no—
1174#95—711no—
1175#95—711no—
1176#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—41no—
1192C24—41no—
1193C24—41no—
1194C24—41no—
1195C24—2841no—
1196C24—2841no—
1197C24—714no—
1198C24—711no—
1199C24—711no—
1200C24—711no—
1201C24—1422no—
1202C24—1422no—
1203C24—1422no—
1204C24—1422no—
1205C24C23×D7111yescharacteristic
1206C24C23×D7111yescharacteristic
1207C24C23×D7111yescharacteristic
1208C2×Q8—2841no—
1209C2×Q8—2841no—
1210C2×Q8—1422no—
1211C2×D4—2841no—
1212C2×D4—2841no—
1213C2×D4—28416no—
1214C2×D4—2841no—
1215C2×D4—2841no—
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—41no—
1241C22×C4—41no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—2841no—
1245C22×C4—2841no—
1246C22×C4—2841no—
1247C22×C4—2841no—
1248C22×C4—2841no—
1249C22×C4—2841no—
1250C22×C4—2841no—
1251C22×C4—2841no—
1252C22×C4—2841no—
1253C22×C4—2841no—
1254C22×C4—28416no—
1255C22×C4—2841no—
1256C22×C4—2841no—
1257C22×C4—2841no—
1258C22×C4—2841no—
1259C22×C4—2841no—
1260C22×C4—711no—
1261C22×C4—711no—
1262C22×C4—711no—
1263C22×C4—711no—
1264C22×C4—711no—
1265C22×C4—711no—
1266C22×C4—711no—
1267C22×C4—711no—
1268C22×C4—711no—
1269C22×C4—711no—
1270C22×C4—711no—
1271C22×C4—711no—
1272C22×C4—711no—
1273C22×C4—1422no—
1274C22×C4—1422no—
1275C22×C4—1422no—
1276C22×C4—1422no—
1277C22×C4—1422no—
1278C22×C4—1422no—
1279C22×C4—1422no—
1280C22×C4—1422no—
1281C22×C4—1422no—
1282C22×C4—1422no—
1283C22×C4—1422no—
1284C22×C4—1422no—
1285C22×C4—1422no—
1286C22×C4—1422no—
1287C22×C4—1422no—
1288C22×C4—1422no—
1289C22×C4—1422no—
1290C22×C4—1422no—
1291C22×C4—1422no—
1292C22×C4—1422no—
1293C22×C4—1422no—
1294C22×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—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
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—22no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—41no—
1341C22⋊C4—41no—
1342C22⋊C4—41no—
1343C22⋊C4—41no—
1344C22⋊C4—41no—
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—2841no—
1362C22⋊C4—714no—
1363C22⋊C4—1422no—
1364C22⋊C4—1422no—
1365C22⋊C4—1422no—
1366C22⋊C4—1422no—
1367C22⋊C4—1422no—
1368C22⋊C4—1422no—
1369C22⋊C4—1422no—
1370C22⋊C4—1422no—
1371C22⋊C4—1422no—
1372C22⋊C4—1422no—
1373C22⋊C4—1422no—
1374C22⋊C4—1422no—
1375C22⋊C4—1422no—
1376C22⋊C4—1422no—
1377C22⋊C4—1422no—
1378C22⋊C4—1422no—
1379C22⋊C4—1422no—
1380C22⋊C4—1422no—
1381C42—41no—
1382C42—41no—
1383C42—41no—
1384C42—41no—
1385C42—2841no—
1386C42—2841no—
1387C42—2841no—
1388C42—2841no—
1389C42—1422no—
1390C42—1422no—
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—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—44no—
1411C23—44no—
1412C23—44no—
1413C23—82no—
1414C23—82no—
1415C23—82no—
1416C23—82no—
1417C23—2844no—
1418C23—2844no—
1419C23—2844no—
1420C23—2844no—
1421C23—2844no—
1422C23—712no—
1423C23—712no—
1424C23—712no—
1425C23—712no—
1426C23—1428no—
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—1428no—
1441C23—1421no—
1442C23—1421no—
1443C23—1421no—
1444C23—1421no—
1445C23#41×D7112yes—
1446C23#41×D7112yes—
1447C23C2×#1176586512yes—
1448C23C24×D7111yescharacteristic
1449Q8—5682no—
1450D4—2844no—
1451D4—2844no—
1452D4—2844no—
1453D4—2844no—
1454D4—2844no—
1455D4—2844no—
1456D4—2844no—
1457D4—5682no—
1458D4—5682no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—44no—
1494C2×C4—82no—
1495C2×C4—2844no—
1496C2×C4—2844no—
1497C2×C4—2844no—
1498C2×C4—2844no—
1499C2×C4—2844no—
1500C2×C4—2844no—
1501C2×C4—2844no—
1502C2×C4—2844no—
1503C2×C4—2844no—
1504C2×C4—5682no—
1505C2×C4—5682no—
1506C2×C4—712no—
1507C2×C4—712no—
1508C2×C4—712no—
1509C2×C4—1428no—
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×C4—1421no—
1544C2×C4—1421no—
1545C2×C4—1421no—
1546C2×C4C2×#1176586512yes—
1547C2×C4C2×#1176586512yes—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—88no—
1569C22—28416no—
1570C22—2841no—
1571C22—2841no—
1572C22—2841no—
1573C22—2841no—
1574C22—2841no—
1575C22—2841no—
1576C22—2841no—
1577C22—2841no—
1578C22—2841no—
1579C22—2841no—
1580C22—2841no—
1581C22—714no—
1582C22—1422no—
1583C22—1422no—
1584C22—1422no—
1585C22—1422no—
1586C22—1422no—
1587C22—1422no—
1588C22—1422no—
1589C22—1422no—
1590C22—1422no—
1591C22#1798652714yes—
1592C22C2×#41×D7111yescharacteristic
1593C22C2×#41×D7111yescharacteristic
1594C22C22×#1176586511yescharacteristic
1595C22H(5,𝔽2)×D7111yescharacteristic
1596C22H(5,𝔽2)×D7111yescharacteristic
1597C22H(5,𝔽2)×D7111yescharacteristic
1598C22#1798683411yescharacteristic
1599C4—22no—
1600C4—22no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
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—1422no—
1622C4—1422no—
1623C4—1422no—
1624C2—24no—
1625C2—81no—
1626C2—81no—
1627C2—2842no—
1628C2—5681no—
1629C2—1424no—
1630C2C2×#1798652711yescharacteristic
1631C2#538×D7111yescharacteristic
1632C2#2260175111yescharacteristic
1633C2#2260202511yescharacteristic
1634C2#2260206511yescharacteristic
1635C2#2260227611yescharacteristic
1636C2#2260236411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2312C2
prime radical#22591716C2
hypercenter#2312D71
hypocenterC71#34998
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2312

Complements

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

NH ≅ G/Ntype
1. #22596667C2semidirect
2. #22596660C2semidirect
3. #22596654C2semidirect
4. #22596638C2semidirect
5. #22594401C2semidirect
6. #22594339C2semidirect
7. #22594326C2semidirect
8. #22594324C2semidirect
9. #22592996C2semidirect
10. #22592995C2semidirect
11. #22592899C2semidirect
12. #22592896C2semidirect
13. #22592837C2semidirect
14. #22592671C2semidirect
15. #22592585C2semidirect
16. #22592463C2semidirect
17. #22592390C2semidirect
18. #22592282C2semidirect
19. #22592097C2semidirect
20. #22592008C2semidirect
21. #22591896C2semidirect
22. #22591733C2semidirect
24. #22591665C2semidirect
25. #22591068C2semidirect
26. #22590998C2semidirect
27. #22590967C2semidirect
28. C4×#14556098C2semidirect
29. C2×#17985875C2semidirect
30. C4×C22⋊C4×D71C2semidirect
31. C71×#2312C2semidirect
34. C2×#14556121C22semidirect
35. C2×#14556114C22semidirect
36. C2×#14556113C22semidirect
39. C2×#14556106C22semidirect
45. C2×C4×D284C22semidirect
46. C2×C4×D284C22semidirect
52. C2×C42×D71C22semidirect
53. C2×C42×D71C22semidirect
54. C71⋊#401C22semidirect
55. #17985940C22semidirect
56. #17985939C22semidirect
57. #17985938C22semidirect
58. #17985937C22semidirect
59. #17985934C22semidirect
60. #17985932C22semidirect
61. #17985928C22semidirect
62. #17985927C22semidirect
63. #17985927C22semidirect
64. #17985927C22semidirect
65. #17985926C22semidirect
66. #17985925C22semidirect
67. #17985925C22semidirect
68. #17985924C22semidirect
69. #17985923C22semidirect
70. #17985922C22semidirect
71. #17985921C22semidirect
72. #17985917C22semidirect
73. #17985916C22semidirect
76. #17985915C22semidirect
81. #17985914C22semidirect
82. #17985912C22semidirect
83. #17985911C22semidirect
86. #17985905C22semidirect
87. #17985903C22semidirect
88. #17985899C22semidirect
89. #17985899C22semidirect
90. #17985899C22semidirect
91. #17985897C22semidirect
92. #17985896C22semidirect
93. #17985894C22semidirect
94. #17985893C22semidirect
95. #17985893C22semidirect
96. #17985893C22semidirect
97. #17985892C22semidirect
98. #17985892C22semidirect
99. #17985891C22semidirect
100. #17985890C22semidirect
101. #17985890C22semidirect
102. #17985889C22semidirect
103. #17985887C22semidirect
104. #17985887C22semidirect
105. #17985887C22semidirect
106. #17985887C22semidirect
107. #17985886C22semidirect
108. #17985885C22semidirect
109. #17985885C22semidirect
110. #17985884C22semidirect
111. #17985883C22semidirect
112. #17985883C22semidirect
113. #17985883C22semidirect
114. #17985883C22semidirect
115. #17985882C22semidirect
117. #17985877C22semidirect
118. #17985877C22semidirect
119. #17985877C22semidirect
135. #17985875C22semidirect
136. #17985875C22semidirect
139. #17985873C22semidirect
140. #17985873C22semidirect
141. #17985873C22semidirect
146. #17985870C22semidirect
147. #17985870C22semidirect
148. #17985866C22semidirect
149. #17985866C22semidirect
150. #17985863C22semidirect
151. #17985863C22semidirect
152. #17985861C22semidirect
153. #17985861C22semidirect
154. #17985858C22semidirect
155. #17985858C22semidirect
161. C4×(C2×D71)⋊C4C22semidirect
162. C4×(C2×D71)⋊C4C22semidirect
163. C4×(C2×D71)⋊C4C22semidirect
164. C4×(C2×D71)⋊C4C22semidirect
166. #17985846C22semidirect
167. #17985846C22semidirect
170. #95×D71C22semidirect
171. #95×D71C22semidirect
173. #388×C71C22semidirect
174. #388×C71C22semidirect
175. #388×C71C22semidirect
176. #388×C71C22semidirect
177. #388×C71C22semidirect
178. #388×C71C22semidirect
179. #388×C71C22semidirect
180. #388×C71C22semidirect
846. #2312D71semidirect
850. C71#34998semidirect
927. #388C2×D71semidirect
928. #388C2×D71semidirect
929. #388C2×D71semidirect
930. #388C2×D71semidirect
931. #388C2×D71semidirect
932. #388C2×D71semidirect
933. #388C2×D71semidirect
934. #388C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966672
#225966602
#225966542
#225966382
#225944012
#225943392
#225943262
#225943242
#225929962
#225929952
#225928992
#225928962
#225928372
#225926712
#225925852
#225924632
#225923902
#225922822
#225920972
#225920082
#225918962
#225917332
#225917162
#225916652
#225910682
#225909982
#225909672
C4×#145560982
C2×#179858752
C4×C22⋊C4×D712
C71×#23122
#3499871