Finite Group Databasebeta

← #32170228

Subgroups — #32170228

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#22596633C211yesmaximal, characteristic, complemented
2#22596629C211yesmaximal, characteristic, complemented
3#22596628C211yesmaximal, characteristic, complemented
4#22596621C211yesmaximal, characteristic
5#22594309C211yesmaximal, characteristic, complemented
6#22594294C211yesmaximal, characteristic, complemented
7#22594292C211yesmaximal, characteristic, complemented
8#22594267C211yesmaximal, characteristic, complemented
9#22592897C211yesmaximal, characteristic, complemented
10#22592893C211yesmaximal, characteristic, complemented
11#22592848C211yesmaximal, characteristic, complemented
12#22592836C211yesmaximal, characteristic, complemented
13#22592729C211yesmaximal, characteristic, complemented
14#22592727C211yesmaximal, characteristic, complemented
15#22592666C211yesmaximal, characteristic, complemented
16#22592664C211yesmaximal, characteristic, complemented
17#22592169C211yesmaximal, characteristic, complemented
18#22592165C211yesmaximal, characteristic, complemented
19#22592093C211yesmaximal, characteristic, complemented
20#22592089C211yesmaximal, characteristic, complemented
21#22591887C211yesmaximal, characteristic, complemented
22#22591885C211yesmaximal, characteristic, complemented
23#22591823C211yesmaximal, characteristic, complemented
24#22591069C211yesmaximal, characteristic, complemented
25#22591037C211yesmaximal, characteristic, complemented
26#22590972C211yesmaximal, characteristic, complemented
27#22590969C211yesmaximal, characteristic, complemented
28#22590841C211yesmaximal, characteristic, complemented
29C4×#14556096C211yesmaximal, characteristic, complemented
30C2×#95×D71C211yesmaximal, characteristic, complemented
31C71×#2419C211yesmaximal, characteristic, complemented
32C23×C4×D71C2211yescharacteristic
33C23×C4×D71C2211yescharacteristic
34C23×C4×D71C2211yescharacteristic
35C2×#14556112C2211yescharacteristic
36C2×#14556111C2211yescharacteristic
37C2×#14556109C2211yescharacteristic
38C2×#14556108C2211yescharacteristic
39C2×#14556108C2211yescharacteristic
40C2×#14556107C2211yescharacteristic
41C2×#14556101C2211yescharacteristic
42C2×#14556101C2211yescharacteristic
43C2×#14556100C2211yescharacteristic
44C2×#14556098C2211yescharacteristic
45C2×#14556096C2211yescharacteristic
46C2×#14556090C2211yescharacteristic
47C2×#14556090C2211yescharacteristic
48C2×C4×C22⋊D71C2211yescharacteristic
49C2×C4×C22⋊D71C2211yescharacteristic
50C2×(C22⋊D71)⋊C4C2211yescharacteristic
51C71⋊#401C2211yescharacteristic, complemented
52C71⋊#401C2211yescharacteristic, complemented
53#17985941C2211yescharacteristic, complemented
54#17985941C2211yescharacteristic, complemented
55#17985941C2211yescharacteristic, complemented
56#17985941C2211yescharacteristic, complemented
57#17985941C2211yescharacteristic, complemented
58#17985940C2211yescharacteristic, complemented
59#17985940C2211yescharacteristic, complemented
60#17985940C2211yescharacteristic, complemented
61#17985939C2211yescharacteristic, complemented
62#17985938C2211yescharacteristic, complemented
63#17985937C2211yescharacteristic, complemented
64#17985932C2211yescharacteristic, complemented
65#17985930C2211yescharacteristic, complemented
66#17985929C2211yescharacteristic, complemented
67#17985928C2211yescharacteristic, complemented
68#17985928C2211yescharacteristic, complemented
69#17985927C2211yescharacteristic, complemented
70#17985925C2211yescharacteristic, complemented
71#17985925C2211yescharacteristic, complemented
72#17985924C2211yescharacteristic, complemented
73#17985922C2211yescharacteristic, complemented
74#17985921C2211yescharacteristic, complemented
75#17985915C2211yescharacteristic, complemented
76#17985915C2211yescharacteristic, complemented
77#17985912C2211yescharacteristic, complemented
78#17985911C2211yescharacteristic, complemented
79#17985903C2211yescharacteristic, complemented
80#17985903C2211yescharacteristic, complemented
81#17985897C2211yescharacteristic, complemented
82#17985895C2211yescharacteristic, complemented
83#17985892C2211yescharacteristic, complemented
84#17985891C2211yescharacteristic, complemented
85#17985890C2211yescharacteristic, complemented
86#17985888C2211yescharacteristic, complemented
87#17985887C2211yescharacteristic, complemented
88#17985887C2211yescharacteristic, complemented
89#17985886C2211yescharacteristic, complemented
90#17985886C2211yescharacteristic, complemented
91#17985885C2211yescharacteristic, complemented
92#17985885C2211yescharacteristic, complemented
93#17985884C2211yescharacteristic, complemented
94#17985882C2211yescharacteristic, complemented
95#17985881C2211yescharacteristic, complemented
96#17985880C2211yescharacteristic, complemented
97#17985879C2211yescharacteristic
98#17985878C2211yescharacteristic
99#17985878C2211yescharacteristic
100#17985878C2211yescharacteristic, complemented
101#17985877C2211yescharacteristic
102#17985877C2211yescharacteristic
103#17985877C2211yescharacteristic
104#17985877C2211yescharacteristic
105#17985877C2211yescharacteristic
106#17985877C2211yescharacteristic
107#17985877C2211yescharacteristic
108#17985877C2211yescharacteristic
109#17985875C2211yescharacteristic
110#17985875C2211yescharacteristic
111#17985875C2211yescharacteristic
112#17985875C2211yescharacteristic
113#17985875C2211yescharacteristic
114#17985875C2211yescharacteristic
115#17985875C2211yescharacteristic
116#17985875C2211yescharacteristic
117#17985875C2211yescharacteristic, complemented
118#17985874C2211yescharacteristic
119#17985874C2211yescharacteristic
120#17985873C2211yescharacteristic
121#17985873C2211yescharacteristic
122#17985873C2211yescharacteristic
123#17985873C2211yescharacteristic
124#17985873C2211yescharacteristic
125#17985873C2211yescharacteristic
126#17985873C2211yescharacteristic
127#17985873C2211yescharacteristic
128#17985871C2211yescharacteristic
129#17985870C2211yescharacteristic
130#17985870C2211yescharacteristic
131#17985870C2211yescharacteristic
132#17985870C2211yescharacteristic
133#17985870C2211yescharacteristic
134#17985870C2211yescharacteristic
135#17985870C2211yescharacteristic
136#17985870C2211yescharacteristic
137#17985870C2211yescharacteristic, complemented
138#17985866C2211yescharacteristic, complemented
139#17985866C2211yescharacteristic, complemented
140#17985863C2211yescharacteristic, complemented
141#17985863C2211yescharacteristic, complemented
142#17985862C2211yescharacteristic
143#17985861C2211yescharacteristic, complemented
144#17985860C2211yescharacteristic
145#17985860C2211yescharacteristic
146#17985859C2211yescharacteristic, complemented
147#17985858C2211yescharacteristic
148#17985858C2211yescharacteristic
149#17985857C2211yescharacteristic
150#17985856C2211yescharacteristic
151#17985856C2211yescharacteristic
152#17985856C2211yescharacteristic, complemented
153#17985854C2211yescharacteristic
154#17985854C2211yescharacteristic
155C22⋊C4×Dic71C2211yescharacteristic
156C4×(C2×D71)⋊C4C2211yescharacteristic
157C4×(C2×D71)⋊C4C2211yescharacteristic
158C4×C22⋊Dic71C2211yescharacteristic
159#17985846C2211yescharacteristic
160#17985846C2211yescharacteristic
161C2×C71⋊#95C2211yescharacteristic
162C2×C71⋊#95C2211yescharacteristic
163C2×C71⋊#95C2211yescharacteristic
164#95×D71C2211yescharacteristic
165#95×D71C2211yescharacteristic
166#95×D71C2211yescharacteristic
167#95×D71C2211yescharacteristic
168#95×D71C2211yescharacteristic
169#95×D71C2211yescharacteristic
170#95×D71C2211yescharacteristic
171#95×D71C2211yescharacteristic
172C2×#123×C71C2211yescharacteristic
173C2×C4×D4×C71C2211yescharacteristic
174#400×C71C2211yescharacteristic, complemented
175#398×C71C2211yescharacteristic, complemented
176#397×C71C2211yescharacteristic, complemented
177#397×C71C2211yescharacteristic, complemented
178#387×C71C2211yescharacteristic, complemented
179#387×C71C2211yescharacteristic, complemented
180#386×C71C2211yescharacteristic
181#385×C71C2211yescharacteristic
182#385×C71C2211yescharacteristic, complemented
183#381×C71C2211yescharacteristic
184#381×C71C2211yescharacteristic, complemented
185#380×C71C2211yescharacteristic
186C2×#95×C71C2211yescharacteristic
187C24×D71C2311yescharacteristic
188C22×Dic142C2311yescharacteristic
189C22×D284C2311yescharacteristic
190C22×D284C2311yescharacteristic
191C22×C22⋊D71C2311yescharacteristic
192C22×C22⋊D71C2311yescharacteristic
193C22×C22⋊D71C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C23×Dic71C2311yescharacteristic
196C23×Dic71C2311yescharacteristic
197C23×Dic71C2311yescharacteristic
198C22×C4×D71—24no—
199C22×C4×D71—24no—
200C22×C4×D71—24no—
201C22×C4×D71—42no—
202C22×C4×D71—42no—
203C22×C4×D71—42no—
204C22×C4×D71—42no—
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
216C22×C4×D71C2311yescharacteristic
217C22×C4×D71C2311yescharacteristic
218C22×C4×D71C2311yescharacteristic
219C22×C4×D71C2311yescharacteristic
220#14556112—42no—
221#14556111—42no—
222#14556109—42no—
223#14556108—24no—
224#14556108—42no—
225#14556107—42no—
226#14556101—24no—
227#14556101—42no—
228#14556100—42no—
229#14556098—24no—
230#14556096—24no—
231#14556090—24no—
232#14556090—42no—
233C4×C22⋊D71—24no—
234C4×C22⋊D71—42no—
235(C22⋊D71)⋊C4—42no—
236C2×C4⋊Dic71C2311yescharacteristic
237C2×C4⋊Dic71C2311yescharacteristic
238C2×C4⋊Dic71C2311yescharacteristic
239C2×C4⋊Dic71C2311yescharacteristic
240C2×C4⋊Dic71C2311yescharacteristic
241C2×C4⋊Dic71C2311yescharacteristic
242C2×C4⋊Dic71C2311yescharacteristic
243C2×Dic71⋊C4C2311yescharacteristic
244C2×Dic71⋊C4C2311yescharacteristic
245C2×Dic71⋊C4C2311yescharacteristic
246C2×Dic71⋊C4C2311yescharacteristic
247C2×Dic71⋊C4C2311yescharacteristic
248C2×Dic71⋊C4C2311yescharacteristic
249C2×Dic71⋊C4C2311yescharacteristic
250C2×Dic71⋊C4C2311yescharacteristic
251C2×Dic71⋊C4C2311yescharacteristic
252C2×Dic71⋊C4C2311yescharacteristic
253C2×Dic71⋊C4C2311yescharacteristic
254C2×Dic71⋊C4C2311yescharacteristic
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×(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×C4×Dic71C2311yescharacteristic
286C2×C4×Dic71C2311yescharacteristic
287C2×C4×Dic71C2311yescharacteristic
288C2×C4×Dic71C2311yescharacteristic
289C2×C4×Dic71C2311yescharacteristic
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
328C71⋊#95C2311yescharacteristic
329C71⋊#95C2311yescharacteristic
330C71⋊#95C2311yescharacteristic
331C71⋊#95C2311yescharacteristic
332C22×D4×C71C2311yescharacteristic
333C23×C4×C71C2311yescharacteristic
334C23×C4×C71C2311yescharacteristic
335C23×C4×C71C2311yescharacteristic
336C23×C4×C71C2311yescharacteristic
337#123×C71—42no—
338C4×D4×C71—42no—
339C2×C4⋊C4×C71C2311yescharacteristic
340C2×C4⋊C4×C71C2311yescharacteristic
341C2×C4⋊C4×C71C2311yescharacteristic
342C2×C4⋊C4×C71C2311yescharacteristic
343C2×C4⋊C4×C71C2311yescharacteristic
344C2×C4⋊C4×C71C2311yescharacteristic
345C2×C4⋊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×C42×C71C2311yescharacteristic
355#95×C71C2311yescharacteristic
356#95×C71C2311yescharacteristic
357#95×C71C2311yescharacteristic
358#95×C71C2311yescharacteristic
359#95×C71C2311yescharacteristic
360#95×C71C2311yescharacteristic
361#95×C71C2311yescharacteristic
362#95×C71C2311yescharacteristic
363#95×C71C2311yescharacteristic
364#95×C71C2311yescharacteristic
365#95×C71C2311yescharacteristic
366#95×C71C2311yescharacteristic
367#95×C71C2311yescharacteristic
368#95×C71C2311yescharacteristic
369C23×D71—22no—
370C23×D71—22no—
371C23×D71—22no—
372C23×D71—22no—
373C23×D71—22no—
374C23×D71—22no—
375C23×D71#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—22no—
387C2×D284—22no—
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—41no—
399C2×C22⋊D71—41no—
400C22×Dic71—22no—
401C22×Dic71—22no—
402C22×Dic71—22no—
403C22×Dic71—22no—
404C22×Dic71—22no—
405C22×Dic71—22no—
406C22×Dic71—22no—
407C22×Dic71—41no—
408C22×Dic71—41no—
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C22×Dic71C2411yescharacteristic
420C22×Dic71C2411yescharacteristic
421C22×Dic71C2411yescharacteristic
422C2×C4×D71—22no—
423C2×C4×D71—22no—
424C2×C4×D71—22no—
425C2×C4×D71—22no—
426C2×C4×D71—22no—
427C2×C4×D71—22no—
428C2×C4×D71—22no—
429C2×C4×D71—22no—
430C2×C4×D71—22no—
431C2×C4×D71—22no—
432C2×C4×D71—22no—
433C2×C4×D71—22no—
434C2×C4×D71—22no—
435C2×C4×D71—22no—
436C2×C4×D71—22no—
437C2×C4×D71—41no—
438C2×C4×D71—41no—
439C2×C4×D71—41no—
440C2×C4×D71—41no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—41no—
445C2×C4×D71—41no—
446C2×C4×D71—41no—
447C2×C4×D71—41no—
448C2×C4×D71—41no—
449C2×C4×D71—41no—
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—416no—
458C2×C4×D71—416no—
459C2×C4×D71—416no—
460C2×C4×D71—41no—
461C2×C4×D71—41no—
462C2×C4×D71#4114yes—
463C2×C4×D71#4114yes—
464C4⋊Dic71—22no—
465C4⋊Dic71—22no—
466C4⋊Dic71—41no—
467C4⋊Dic71—41no—
468C4⋊Dic71—41no—
469C4⋊Dic71—41no—
470C4⋊Dic71—41no—
471Dic71⋊C4—22no—
472Dic71⋊C4—22no—
473Dic71⋊C4—41no—
474Dic71⋊C4—41no—
475Dic71⋊C4—41no—
476Dic71⋊C4—41no—
477Dic71⋊C4—41no—
478Dic71⋊C4—41no—
479Dic71⋊C4—41no—
480Dic71⋊C4—41no—
481Dic71⋊C4—41no—
482Dic71⋊C4—41no—
483C22⋊Dic71—22no—
484C22⋊Dic71—22no—
485C22⋊Dic71—22no—
486C22⋊Dic71—22no—
487C22⋊Dic71—41no—
488C22⋊Dic71—41no—
489C22⋊Dic71—41no—
490C22⋊Dic71—41no—
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—22no—
504(C2×D71)⋊C4—22no—
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—
513C4×Dic71—22no—
514C4×Dic71—22no—
515C4×Dic71—41no—
516C4×Dic71—41no—
517C4×Dic71—41no—
518C24×C71C2411yescharacteristic
519C24×C71C2411yescharacteristic
520C2×D4×C71—22no—
521C2×D4×C71—22no—
522C2×D4×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—41no—
532C22×C4×C71—41no—
533C22×C4×C71—41no—
534C22×C4×C71—41no—
535C22×C4×C71C2411yescharacteristic
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
547C22×C4×C71C2411yescharacteristic
548C4⋊C4×C71—22no—
549C4⋊C4×C71—22no—
550C4⋊C4×C71—41no—
551C4⋊C4×C71—41no—
552C4⋊C4×C71—41no—
553C4⋊C4×C71—41no—
554C4⋊C4×C71—41no—
555C22⋊C4×C71—22no—
556C22⋊C4×C71—22no—
557C22⋊C4×C71—22no—
558C22⋊C4×C71—22no—
559C22⋊C4×C71—41no—
560C22⋊C4×C71—41no—
561C22⋊C4×C71—41no—
562C22⋊C4×C71—41no—
563C42×C71—41no—
564C23×C71—21no—
565C23×C71—21no—
566C23×C71—21no—
567C23×C71—21no—
568C23×C71—21no—
569C23×C71—21no—
570C23×C71—21no—
571C23×C71—21no—
572C23×C71—21no—
573C23×C71—21no—
574C23×C71—21no—
575C23×C71C2×#4112yes—
576C23×C71H(5,𝔽2)12yes—
577C23×C71H(5,𝔽2)12yes—
578C23×C71C2511yescharacteristic
579C22×D71—28no—
580C22×D71—28no—
581C22×D71—28no—
582C22×D71—28no—
583C22×D71—28no—
584C22×D71—21no—
585C22×D71—21no—
586C22×D71—21no—
587C22×D71—21no—
588C22×D71—21no—
589C22×D71—21no—
590C22×D71—21no—
591C22×D71—21no—
592C22×D71—28no—
593C22×D71—28no—
594C22×D71—21no—
595C22×D71—21no—
596C22×D71—21no—
597C22×D71—21no—
598C22×D71—21no—
599C22×D71—21no—
600C22×D71—21no—
601C22×D71C2×#4112yes—
602C22×D71C2×#4112yes—
603C22×D71C2×#4112yes—
604C22×D71C2×#4112yes—
605C22×D71H(5,𝔽2)12yes—
606C22×D712−1+412yes—
607D4×C71—44no—
608C2×C4×C71—21no—
609C2×C4×C71—21no—
610C2×C4×C71—21no—
611C2×C4×C71—21no—
612C2×C4×C71—21no—
613C2×C4×C71—21no—
614C2×C4×C71—21no—
615C2×C4×C71—21no—
616C2×C4×C71—21no—
617C2×C4×C71—21no—
618C2×C4×C71—21no—
619C2×C4×C71—21no—
620C2×C4×C71—21no—
621C2×C4×C71—21no—
622C2×C4×C71—21no—
623C2×C4×C71—21no—
624C2×C4×C71—21no—
625C2×C4×C71—21no—
626C2×C4×C71—21no—
627C2×C4×C71—21no—
628C2×C4×C71—21no—
629C2×C4×C71—21no—
630C2×C4×C71—21no—
631C2×C4×C71—21no—
632C2×C4×C71—21no—
633C2×C4×C71—21no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—21no—
645C2×C4×C71—44no—
646C2×C4×C71—44no—
647C2×C4×C71—44no—
648C2×C4×C71—82no—
649C2×C4×C71C2×#4112yes—
650C2×C4×C71C2×#4112yes—
651C22⋊D71—44no—
652C22⋊D71—44no—
653C22⋊D71—44no—
654C22⋊D71—82no—
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—44no—
693C2×Dic71—44no—
694C2×Dic71—44no—
695C2×Dic71C2×#4112yes—
696C2×Dic71C2×#4112yes—
697D284—44no—
698D284—44no—
699C4×D71—44no—
700C4×D71—44no—
701C4×D71—44no—
702C4×D71—44no—
703C4×D71—44no—
704C4×D71—44no—
705C4×D71—44no—
706C4×D71—44no—
707C4×D71—44no—
708C4×D71—44no—
709C4×D71—44no—
710C4×D71—44no—
711C4×D71—82no—
712Dic142—82no—
713C22×C71—22no—
714C22×C71—22no—
715C22×C71—22no—
716C22×C71—22no—
717C22×C71—22no—
718C22×C71—22no—
719C22×C71—41no—
720C22×C71—41no—
721C22×C71—41no—
722C22×C71—41no—
723C22×C71—41no—
724C22×C71—41no—
725C22×C71—41no—
726C22×C71#53814yes—
727C22×C71C22×#4111yescharacteristic
728C22×C71C22×#4111yescharacteristic
729C22×C71C22×#4111yescharacteristic
730C22×C71C2×H(5,𝔽2)11yescharacteristic
731C22×C71C2×H(5,𝔽2)11yescharacteristic
732C22×C71C2×H(5,𝔽2)11yescharacteristic
733C22×C71C2×2−1+411yescharacteristic
734C2×D71—232no—
735C2×D71—22no—
736C2×D71—22no—
737C2×D71—22no—
738C2×D71—22no—
739C2×D71—22no—
740C2×D71—22no—
741C2×D71—22no—
742C2×D71—22no—
743C2×D71—22no—
744C2×D71—22no—
745C2×D71—22no—
746C2×D71—22no—
747C2×D71—41no—
748C2×D71—41no—
749C2×D71—41no—
750C2×D71—41no—
751C2×D71—41no—
752C2×D71—41no—
753C2×D71—41no—
754C2×D71#52914yes—
755C2×D71#53914yes—
756C4×C71—22no—
757C4×C71—22no—
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—
767C4×C71—41no—
768C4×C71—41no—
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—81no—
785C2×C71C2×#52911yescharacteristic
786C2×C71C2×#53811yescharacteristic
787C2×C71C2×#53911yescharacteristic
788C2×C71#349011yescharacteristic
789C2×C71#349011yescharacteristic
790C2×C71#349211yescharacteristic
791C2×C71#349211yescharacteristic
792D71—24no—
793D71—24no—
794D71—81no—
795#2849—711no—
796#2849—711no—
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#2419D7111yescharacteristic, complemented
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×C4—711no—
830C2×#123—711no—
831C2×#123—711no—
832C2×#123—711no—
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×#120—711no—
842C2×C4×D4—711no—
843C2×C4×D4—711no—
844C2×C4×D4—711no—
845C2×C4×D4—711no—
846C2×C4×D4—711no—
847C2×C4×D4C2×D7111yescharacteristic
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#400C2×D7111yescharacteristic, complemented
862#398—711no—
863#398—711no—
864#398—711no—
865#398C2×D7111yescharacteristic, complemented
866#397—711no—
867#397—711no—
868#397—711no—
869#397—711no—
870#397—711no—
871#397—711no—
872#397C2×D7111yescharacteristic, complemented
873#397C2×D7111yescharacteristic, complemented
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#387C2×D7111yescharacteristic, complemented
899#387C2×D7111yescharacteristic, complemented
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#386—711no—
919#386—711no—
920#386—711no—
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#385—711no—
941#385—711no—
942#385C2×D7111yescharacteristic
943#385C2×D7111yescharacteristic, complemented
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, complemented
954#380—711no—
955#380—711no—
956#380—711no—
957#380—711no—
958#380—711no—
959#380—711no—
960#380—711no—
961#380C2×D7111yescharacteristic
962#379—711no—
963#379—711no—
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×#95C2×D7111yescharacteristic
982C25—711no—
983C22×Q8—711no—
984C22×D4—711no—
985C22×D4—711no—
986C22×D4—711no—
987C22×D4—711no—
988C22×D4—711no—
989C22×D4—711no—
990C22×D4C22×D7111yescharacteristic
991C23×C4—2842no—
992C23×C4—2842no—
993C23×C4—2842no—
994C23×C4—2842no—
995C23×C4—2842no—
996C23×C4—2842no—
997C23×C4—711no—
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—711no—
1013C23×C4—1424no—
1014C23×C4—1424no—
1015C23×C4—1424no—
1016C23×C4C22×D7111yescharacteristic
1017C23×C4C22×D7111yescharacteristic
1018C23×C4C22×D7111yescharacteristic
1019C23×C4C22×D7111yescharacteristic
1020#123—42no—
1021#123—2842no—
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—1424no—
1031#120—1424no—
1032C4×D4—42no—
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⋊C4C22×D7111yescharacteristic
1058C2×C4⋊C4C22×D7111yescharacteristic
1059C2×C4⋊C4C22×D7111yescharacteristic
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⋊C4—711no—
1090C2×C22⋊C4—711no—
1091C2×C22⋊C4—711no—
1092C2×C22⋊C4—711no—
1093C2×C22⋊C4—711no—
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×C42C22×D7111yescharacteristic
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#95C22×D7111yescharacteristic
1151#95C22×D7111yescharacteristic
1152#95C22×D7111yescharacteristic
1153#95C22×D7111yescharacteristic
1154#95C22×D7111yescharacteristic
1155#95C22×D7111yescharacteristic
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—711no—
1165C24—711no—
1166C24—714no—
1167C24—711no—
1168C24—1422no—
1169C24—1422no—
1170C24—1422no—
1171C24—1422no—
1172C24—1422no—
1173C24—1422no—
1174C24C23×D7111yescharacteristic
1175C24C23×D7111yescharacteristic
1176C2×Q8—2841no—
1177C2×Q8—2841no—
1178C2×Q8—1422no—
1179C2×D4—22no—
1180C2×D4—22no—
1181C2×D4—22no—
1182C2×D4—2841no—
1183C2×D4—2841no—
1184C2×D4—1422no—
1185C2×D4—1422no—
1186C2×D4—1422no—
1187C2×D4—1422no—
1188C2×D4—1422no—
1189C2×D4—1422no—
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—41no—
1209C22×C4—41no—
1210C22×C4—41no—
1211C22×C4—41no—
1212C22×C4—2841no—
1213C22×C4—2841no—
1214C22×C4—2841no—
1215C22×C4—2841no—
1216C22×C4—2841no—
1217C22×C4—2841no—
1218C22×C4—2841no—
1219C22×C4—2841no—
1220C22×C4—2841no—
1221C22×C4—2841no—
1222C22×C4—2841no—
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—28416no—
1235C22×C4—28416no—
1236C22×C4—28416no—
1237C22×C4—2841no—
1238C22×C4—2841no—
1239C22×C4—714no—
1240C22×C4—714no—
1241C22×C4—711no—
1242C22×C4—711no—
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—1422no—
1255C22×C4—1422no—
1256C22×C4—1422no—
1257C22×C4—1422no—
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×C4C23×D7111yescharacteristic
1277C22×C4C23×D7111yescharacteristic
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—22no—
1290C4⋊C4—22no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
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—2841no—
1310C4⋊C4—2841no—
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—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—2841no—
1324C22⋊C4—2841no—
1325C22⋊C4—2841no—
1326C22⋊C4—2841no—
1327C22⋊C4—2841no—
1328C22⋊C4—2841no—
1329C22⋊C4—2841no—
1330C22⋊C4—2841no—
1331C22⋊C4—2841no—
1332C22⋊C4—2841no—
1333C22⋊C4—2841no—
1334C22⋊C4—2841no—
1335C22⋊C4—1422no—
1336C22⋊C4—1422no—
1337C22⋊C4—1422no—
1338C22⋊C4—1422no—
1339C22⋊C4—1422no—
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—41no—
1354C42—2841no—
1355C42—2841no—
1356C42—2841no—
1357C42—1422no—
1358C42—1422no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—712no—
1371C23—712no—
1372C23—712no—
1373C23—712no—
1374C23—712no—
1375C23—712no—
1376C23—1428no—
1377C23—1428no—
1378C23—1428no—
1379C23—1428no—
1380C23—1428no—
1381C23—1428no—
1382C23—1421no—
1383C23—1421no—
1384C23—1421no—
1385C23—1421no—
1386C23—1421no—
1387C23—1421no—
1388C23—1421no—
1389C23—1421no—
1390C23—1421no—
1391C23—1421no—
1392C23—1421no—
1393C23—1421no—
1394C23—1421no—
1395C23—1421no—
1396C23—1421no—
1397C23—1428no—
1398C23#41×D7112yes—
1399C23#1455617312yes—
1400C23#1455617412yes—
1401C23C24×D7111yescharacteristic
1402Q8—5682no—
1403D4—44no—
1404D4—2844no—
1405D4—2844no—
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—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—44no—
1448C2×C4—44no—
1449C2×C4—44no—
1450C2×C4—82no—
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—2844no—
1462C2×C4—2844no—
1463C2×C4—2844no—
1464C2×C4—2844no—
1465C2×C4—2844no—
1466C2×C4—5682no—
1467C2×C4—712no—
1468C2×C4—712no—
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#41×D7112yes—
1507C2×C4#41×D7112yes—
1508C22—22no—
1509C22—22no—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—41no—
1515C22—41no—
1516C22—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—2841no—
1522C22—2841no—
1523C22—2841no—
1524C22—2841no—
1525C22—2841no—
1526C22—2841no—
1527C22—2841no—
1528C22—714no—
1529C22—714no—
1530C22—14232no—
1531C22—1422no—
1532C22—1422no—
1533C22—1422no—
1534C22—1422no—
1535C22—1422no—
1536C22—1422no—
1537C22—1422no—
1538C22—1422no—
1539C22—1422no—
1540C22—1422no—
1541C22—1422no—
1542C22—1422no—
1543C22#1798658514yes—
1544C22C2×#41×D7111yescharacteristic
1545C22C2×#41×D7111yescharacteristic
1546C22C2×#41×D7111yescharacteristic
1547C22H(5,𝔽2)×D7111yescharacteristic
1548C22C2×#1455617311yescharacteristic
1549C22C2×#1455617411yescharacteristic
1550C222−1+4×D7111yescharacteristic
1551C4—22no—
1552C4—22no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—41no—
1557C4—41no—
1558C4—41no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—2841no—
1565C4—2841no—
1566C4—2841no—
1567C4—2841no—
1568C4—2841no—
1569C4—2841no—
1570C4—2841no—
1571C4—2841no—
1572C4—2841no—
1573C4—2841no—
1574C4—2841no—
1575C4—1422no—
1576C4—1422no—
1577C2—24no—
1578C2—81no—
1579C2—5681no—
1580C2—1424no—
1581C2—1424no—
1582C2#529×D7111yescharacteristic
1583C2C2×#1798658511yescharacteristic
1584C2#539×D7111yescharacteristic
1585C2#2260202211yescharacteristic
1586C2#2260202411yescharacteristic
1587C2#2260204011yescharacteristic
1588C2#2260204211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2419C2
prime radical#22596621C2
hypercenter#2419D71
hypocenterC71#34997
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2419

Complements

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

NH ≅ G/Ntype
1. #22596633C2semidirect
2. #22596629C2semidirect
3. #22596628C2semidirect
5. #22594309C2semidirect
6. #22594294C2semidirect
7. #22594292C2semidirect
8. #22594267C2semidirect
9. #22592897C2semidirect
10. #22592893C2semidirect
11. #22592848C2semidirect
12. #22592836C2semidirect
13. #22592729C2semidirect
14. #22592727C2semidirect
15. #22592666C2semidirect
16. #22592664C2semidirect
17. #22592169C2semidirect
18. #22592165C2semidirect
19. #22592093C2semidirect
20. #22592089C2semidirect
21. #22591887C2semidirect
22. #22591885C2semidirect
23. #22591823C2semidirect
24. #22591069C2semidirect
25. #22591037C2semidirect
26. #22590972C2semidirect
27. #22590969C2semidirect
28. #22590841C2semidirect
29. C4×#14556096C2semidirect
30. C2×#95×D71C2semidirect
31. C71×#2419C2semidirect
51. C71⋊#401C22semidirect
52. C71⋊#401C22semidirect
53. #17985941C22semidirect
54. #17985941C22semidirect
55. #17985941C22semidirect
56. #17985941C22semidirect
57. #17985941C22semidirect
58. #17985940C22semidirect
59. #17985940C22semidirect
60. #17985940C22semidirect
61. #17985939C22semidirect
62. #17985938C22semidirect
63. #17985937C22semidirect
64. #17985932C22semidirect
65. #17985930C22semidirect
66. #17985929C22semidirect
67. #17985928C22semidirect
68. #17985928C22semidirect
69. #17985927C22semidirect
70. #17985925C22semidirect
71. #17985925C22semidirect
72. #17985924C22semidirect
73. #17985922C22semidirect
74. #17985921C22semidirect
75. #17985915C22semidirect
76. #17985915C22semidirect
77. #17985912C22semidirect
78. #17985911C22semidirect
79. #17985903C22semidirect
80. #17985903C22semidirect
81. #17985897C22semidirect
82. #17985895C22semidirect
83. #17985892C22semidirect
84. #17985891C22semidirect
85. #17985890C22semidirect
86. #17985888C22semidirect
87. #17985887C22semidirect
88. #17985887C22semidirect
89. #17985886C22semidirect
90. #17985886C22semidirect
91. #17985885C22semidirect
92. #17985885C22semidirect
93. #17985884C22semidirect
94. #17985882C22semidirect
95. #17985881C22semidirect
96. #17985880C22semidirect
100. #17985878C22semidirect
117. #17985875C22semidirect
137. #17985870C22semidirect
138. #17985866C22semidirect
139. #17985866C22semidirect
140. #17985863C22semidirect
141. #17985863C22semidirect
143. #17985861C22semidirect
146. #17985859C22semidirect
152. #17985856C22semidirect
174. #400×C71C22semidirect
175. #398×C71C22semidirect
176. #397×C71C22semidirect
177. #397×C71C22semidirect
178. #387×C71C22semidirect
179. #387×C71C22semidirect
182. #385×C71C22semidirect
184. #381×C71C22semidirect
818. #2419D71semidirect
826. C71#34997semidirect
861. #400C2×D71semidirect
865. #398C2×D71semidirect
872. #397C2×D71semidirect
873. #397C2×D71semidirect
898. #387C2×D71semidirect
899. #387C2×D71semidirect
943. #385C2×D71semidirect
953. #381C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966332
#225966292
#225966282
#225966212
#225943092
#225942942
#225942922
#225942672
#225928972
#225928932
#225928482
#225928362
#225927292
#225927272
#225926662
#225926642
#225921692
#225921652
#225920932
#225920892
#225918872
#225918852
#225918232
#225910692
#225910372
#225909722
#225909692
#225908412
C4×#145560962
C2×#95×D712
C71×#24192
#3499771