Finite Group Databasebeta

← #32204631

Subgroups — #32204631

Order 18176.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596628C211yesmaximal, characteristic, complemented
2#22596621C211yesmaximal, characteristic
3#22595544C211yesmaximal, characteristic, complemented
4#22595532C211yesmaximal, characteristic, complemented
5#22595471C211yesmaximal, characteristic, complemented
6#22595464C211yesmaximal, characteristic, complemented
7#22595457C211yesmaximal, characteristic, complemented
8#22595449C211yesmaximal, characteristic, complemented
9#22595176C211yesmaximal, characteristic, complemented
10#22594972C211yesmaximal, characteristic, complemented
11#22594968C211yesmaximal, characteristic, complemented
12#22594843C211yesmaximal, characteristic, complemented
13#22594839C211yesmaximal, characteristic, complemented
14#22594823C211yesmaximal, characteristic, complemented
15#22594819C211yesmaximal, characteristic, complemented
16#22594591C211yesmaximal, characteristic, complemented
17#22594586C211yesmaximal, characteristic, complemented
18#22594453C211yesmaximal, characteristic, complemented
19#22594267C211yesmaximal, characteristic, complemented
20#22592599C211yesmaximal, characteristic, complemented
21#22592596C211yesmaximal, characteristic, complemented
22#22592462C211yesmaximal, characteristic, complemented
23#22592459C211yesmaximal, characteristic, complemented
24#22592148C211yesmaximal, characteristic, complemented
25#22592142C211yesmaximal, characteristic, complemented
26#22591803C211yesmaximal, characteristic, complemented
27#22591799C211yesmaximal, characteristic, complemented
28#22591069C211yesmaximal, characteristic, complemented
29#22591037C211yesmaximal, characteristic, complemented
30#380×D71C211yesmaximal, characteristic, complemented
31C71×#2717C211yesmaximal, characteristic, complemented
32C23×C4×D71C2211yescharacteristic
33C2×#14556123C2211yescharacteristic, complemented
34C2×#14556121C2211yescharacteristic, complemented
35C2×#14556114C2211yescharacteristic
36C2×#14556110C2211yescharacteristic
37C2×#14556108C2211yescharacteristic
38C2×#14556108C2211yescharacteristic
39C2×#14556107C2211yescharacteristic
40C2×#14556107C2211yescharacteristic, complemented
41C2×#14556106C2211yescharacteristic
42C2×#14556104C2211yescharacteristic
43C2×#14556104C2211yescharacteristic, complemented
44C2×#14556101C2211yescharacteristic
45C2×#14556101C2211yescharacteristic
46C2×#14556100C2211yescharacteristic
47C2×#14556098C2211yescharacteristic
48C2×#14556096C2211yescharacteristic
49C2×#14556090C2211yescharacteristic
50C2×C4×C22⋊D71C2211yescharacteristic
51C2×C4⋊C4×D71C2211yescharacteristic
52C2×C4⋊C4×D71C2211yescharacteristic
53C2×C22⋊C4×D71C2211yescharacteristic
54C2×C22⋊C4×D71C2211yescharacteristic
55#17985941C2211yescharacteristic, complemented
56#17985941C2211yescharacteristic, complemented
57#17985940C2211yescharacteristic, complemented
58#17985939C2211yescharacteristic, complemented
59#17985939C2211yescharacteristic, complemented
60#17985937C2211yescharacteristic, complemented
61#17985935C2211yescharacteristic, complemented
62#17985934C2211yescharacteristic
63#17985934C2211yescharacteristic
64#17985934C2211yescharacteristic, complemented
65#17985933C2211yescharacteristic, complemented
66#17985933C2211yescharacteristic, complemented
67#17985932C2211yescharacteristic, complemented
68#17985932C2211yescharacteristic, complemented
69#17985931C2211yescharacteristic, complemented
70#17985929C2211yescharacteristic, complemented
71#17985927C2211yescharacteristic
72#17985927C2211yescharacteristic
73#17985926C2211yescharacteristic, complemented
74#17985925C2211yescharacteristic, complemented
75#17985922C2211yescharacteristic, complemented
76#17985922C2211yescharacteristic, complemented
77#17985921C2211yescharacteristic, complemented
78#17985921C2211yescharacteristic, complemented
79#17985920C2211yescharacteristic, complemented
80#17985919C2211yescharacteristic, complemented
81#17985919C2211yescharacteristic, complemented
82#17985918C2211yescharacteristic, complemented
83#17985917C2211yescharacteristic
84#17985917C2211yescharacteristic
85#17985915C2211yescharacteristic
86#17985915C2211yescharacteristic
87#17985915C2211yescharacteristic, complemented
88#17985915C2211yescharacteristic, complemented
89#17985914C2211yescharacteristic
90#17985914C2211yescharacteristic
91#17985913C2211yescharacteristic
92#17985913C2211yescharacteristic
93#17985912C2211yescharacteristic
94#17985912C2211yescharacteristic, complemented
95#17985911C2211yescharacteristic, complemented
96#17985910C2211yescharacteristic
97#17985903C2211yescharacteristic, complemented
98#17985903C2211yescharacteristic, complemented
99#17985900C2211yescharacteristic
100#17985899C2211yescharacteristic
101#17985897C2211yescharacteristic, complemented
102#17985896C2211yescharacteristic, complemented
103#17985895C2211yescharacteristic, complemented
104#17985894C2211yescharacteristic, complemented
105#17985893C2211yescharacteristic
106#17985892C2211yescharacteristic
107#17985892C2211yescharacteristic
108#17985892C2211yescharacteristic, complemented
109#17985891C2211yescharacteristic
110#17985891C2211yescharacteristic, complemented
111#17985890C2211yescharacteristic
112#17985890C2211yescharacteristic, complemented
113#17985889C2211yescharacteristic
114#17985888C2211yescharacteristic
115#17985887C2211yescharacteristic
116#17985887C2211yescharacteristic, complemented
117#17985886C2211yescharacteristic, complemented
118#17985885C2211yescharacteristic, complemented
119#17985884C2211yescharacteristic, complemented
120#17985884C2211yescharacteristic, complemented
121#17985882C2211yescharacteristic, complemented
122#17985882C2211yescharacteristic, complemented
123#17985882C2211yescharacteristic, complemented
124#17985881C2211yescharacteristic, complemented
125#17985881C2211yescharacteristic, complemented
126#17985880C2211yescharacteristic, complemented
127#17985878C2211yescharacteristic
128#17985878C2211yescharacteristic
129#17985878C2211yescharacteristic, complemented
130#17985877C2211yescharacteristic
131#17985877C2211yescharacteristic
132#17985877C2211yescharacteristic
133#17985877C2211yescharacteristic
134#17985877C2211yescharacteristic
135#17985877C2211yescharacteristic
136#17985875C2211yescharacteristic
137#17985875C2211yescharacteristic
138#17985875C2211yescharacteristic
139#17985875C2211yescharacteristic
140#17985875C2211yescharacteristic
141#17985875C2211yescharacteristic, complemented
142#17985874C2211yescharacteristic
143#17985874C2211yescharacteristic
144#17985873C2211yescharacteristic
145#17985873C2211yescharacteristic
146#17985873C2211yescharacteristic
147#17985873C2211yescharacteristic
148#17985873C2211yescharacteristic
149#17985873C2211yescharacteristic, complemented
150#17985870C2211yescharacteristic
151#17985870C2211yescharacteristic, complemented
152#17985859C2211yescharacteristic
153#17985858C2211yescharacteristic
154#17985858C2211yescharacteristic
155#17985858C2211yescharacteristic
156#17985858C2211yescharacteristic
157#17985858C2211yescharacteristic
158#17985857C2211yescharacteristic
159#17985857C2211yescharacteristic
160#17985857C2211yescharacteristic
161#17985856C2211yescharacteristic
162#17985856C2211yescharacteristic
163#17985856C2211yescharacteristic
164#17985856C2211yescharacteristic
165#17985856C2211yescharacteristic
166#17985854C2211yescharacteristic
167#17985854C2211yescharacteristic
168C4×(C2×D71)⋊C4C2211yescharacteristic
169#17985846C2211yescharacteristic
170#95×D71C2211yescharacteristic
171#95×D71C2211yescharacteristic
172C2×#124×C71C2211yescharacteristic
173C2×#123×C71C2211yescharacteristic
174#397×C71C2211yescharacteristic
175#397×C71C2211yescharacteristic
176#397×C71C2211yescharacteristic, complemented
177#397×C71C2211yescharacteristic, complemented
178#395×C71C2211yescharacteristic, complemented
179#395×C71C2211yescharacteristic, complemented
180#387×C71C2211yescharacteristic, complemented
181#387×C71C2211yescharacteristic, complemented
182#386×C71C2211yescharacteristic
183#385×C71C2211yescharacteristic, complemented
184#385×C71C2211yescharacteristic, complemented
185#380×C71C2211yescharacteristic
186#380×C71C2211yescharacteristic
187C24×D71C2311yescharacteristic
188C22×Dic142C2311yescharacteristic
189C22×Dic142C2311yescharacteristic
190C22×D284C2311yescharacteristic
191C22×D284C2311yescharacteristic
192C22×C22⋊D71C2311yescharacteristic
193C22×C22⋊D71C2311yescharacteristic
194C22×C22⋊D71C2311yescharacteristic
195C22×C22⋊D71C2311yescharacteristic
196C23×Dic71C2311yescharacteristic
197C22×C4×D71—24no—
198C22×C4×D71—42no—
199C22×C4×D71—42no—
200C22×C4×D71C2311yescharacteristic
201C22×C4×D71C2311yescharacteristic
202C22×C4×D71C2311yescharacteristic
203C22×C4×D71C2311yescharacteristic
204C22×C4×D71C2311yescharacteristic
205C22×C4×D71C2311yescharacteristic
206C22×C4×D71C2311yescharacteristic
207C22×C4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209#14556123—42no—
210#14556121—42no—
211#14556114—42no—
212#14556110—42no—
213#14556108—24no—
214#14556108—42no—
215#14556107—42no—
216#14556107—42no—
217#14556106—42no—
218#14556104—42no—
219#14556104—42no—
220#14556101—24no—
221#14556101—42no—
222#14556100—42no—
223#14556098—42no—
224#14556096—42no—
225#14556090—42no—
226C4×C22⋊D71—42no—
227C2×C4⋊Dic71C2311yescharacteristic
228C2×C4⋊Dic71C2311yescharacteristic
229C2×C4⋊Dic71C2311yescharacteristic
230C2×C4⋊Dic71C2311yescharacteristic
231C2×C4⋊Dic71C2311yescharacteristic
232C2×C4⋊Dic71C2311yescharacteristic
233C2×C4⋊Dic71C2311yescharacteristic
234C2×C4⋊Dic71C2311yescharacteristic
235C2×C4⋊Dic71C2311yescharacteristic
236C2×C4⋊Dic71C2311yescharacteristic
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×Dic71⋊C4C2311yescharacteristic
250C2×Dic71⋊C4C2311yescharacteristic
251C2×Dic71⋊C4C2311yescharacteristic
252C2×Dic71⋊C4C2311yescharacteristic
253C2×Dic71⋊C4C2311yescharacteristic
254C2×Dic71⋊C4C2311yescharacteristic
255C4⋊C4×D71—42no—
256C4⋊C4×D71—42no—
257C2×C22⋊Dic71C2311yescharacteristic
258C2×C22⋊Dic71C2311yescharacteristic
259C2×C22⋊Dic71C2311yescharacteristic
260C2×C22⋊Dic71C2311yescharacteristic
261C2×C22⋊Dic71C2311yescharacteristic
262C2×C22⋊Dic71C2311yescharacteristic
263C2×C22⋊Dic71C2311yescharacteristic
264C2×C22⋊Dic71C2311yescharacteristic
265C2×C22⋊Dic71C2311yescharacteristic
266C2×C22⋊Dic71C2311yescharacteristic
267C2×(C2×D71)⋊C4C2311yescharacteristic
268C2×(C2×D71)⋊C4C2311yescharacteristic
269C2×(C2×D71)⋊C4C2311yescharacteristic
270C2×(C2×D71)⋊C4C2311yescharacteristic
271C2×(C2×D71)⋊C4C2311yescharacteristic
272C2×(C2×D71)⋊C4C2311yescharacteristic
273C2×(C2×D71)⋊C4C2311yescharacteristic
274C2×(C2×D71)⋊C4C2311yescharacteristic
275C2×(C2×D71)⋊C4C2311yescharacteristic
276C2×(C2×D71)⋊C4C2311yescharacteristic
277C2×(C2×D71)⋊C4C2311yescharacteristic
278C2×(C2×D71)⋊C4C2311yescharacteristic
279C2×(C2×D71)⋊C4C2311yescharacteristic
280C2×(C2×D71)⋊C4C2311yescharacteristic
281C2×(C2×D71)⋊C4C2311yescharacteristic
282C2×(C2×D71)⋊C4C2311yescharacteristic
283C2×(C2×D71)⋊C4C2311yescharacteristic
284C2×(C2×D71)⋊C4C2311yescharacteristic
285C2×(C2×D71)⋊C4C2311yescharacteristic
286C2×(C2×D71)⋊C4C2311yescharacteristic
287C2×(C2×D71)⋊C4C2311yescharacteristic
288C2×(C2×D71)⋊C4C2311yescharacteristic
289C2×(C2×D71)⋊C4C2311yescharacteristic
290C2×(C2×D71)⋊C4C2311yescharacteristic
291C2×(C2×D71)⋊C4C2311yescharacteristic
292C2×(C2×D71)⋊C4C2311yescharacteristic
293C22⋊C4×D71—42no—
294C22⋊C4×D71—42no—
295C2×C4×Dic71C2311yescharacteristic
296C2×C4×Dic71C2311yescharacteristic
297C2×C4×Dic71C2311yescharacteristic
298C2×C4×Dic71C2311yescharacteristic
299C2×C4×Dic71C2311yescharacteristic
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×Q8×C71C2311yescharacteristic
333C22×D4×C71C2311yescharacteristic
334C23×C4×C71C2311yescharacteristic
335C23×C4×C71C2311yescharacteristic
336#124×C71—42no—
337#123×C71—42no—
338C2×C4⋊C4×C71C2311yescharacteristic
339C2×C4⋊C4×C71C2311yescharacteristic
340C2×C4⋊C4×C71C2311yescharacteristic
341C2×C4⋊C4×C71C2311yescharacteristic
342C2×C4⋊C4×C71C2311yescharacteristic
343C2×C4⋊C4×C71C2311yescharacteristic
344C2×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×C22⋊C4×C71C2311yescharacteristic
355C2×C22⋊C4×C71C2311yescharacteristic
356C2×C42×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—41no—
375C23×D71—41no—
376C23×D71C2411yescharacteristic
377C23×D71C2411yescharacteristic
378C23×D71C2411yescharacteristic
379C2×Dic142—22no—
380C2×Dic142—41no—
381C2×Dic142—41no—
382C2×Dic142—41no—
383C2×Dic142—41no—
384C2×Dic142—41no—
385C2×D284—22no—
386C2×D284—22no—
387C2×D284—22no—
388C2×D284—22no—
389C2×D284—41no—
390C2×D284—41no—
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—41no—
398C2×C22⋊D71—41no—
399C2×C22⋊D71—41no—
400C2×C22⋊D71—41no—
401C2×C22⋊D71—41no—
402C2×C22⋊D71—41no—
403C22×Dic71—22no—
404C22×Dic71—22no—
405C22×Dic71—41no—
406C22×Dic71C2411yescharacteristic
407C22×Dic71C2411yescharacteristic
408C22×Dic71C2411yescharacteristic
409C22×Dic71C2411yescharacteristic
410C22×Dic71C2411yescharacteristic
411C22×Dic71C2411yescharacteristic
412C22×Dic71C2411yescharacteristic
413C22×Dic71C2411yescharacteristic
414C22×Dic71C2411yescharacteristic
415C22×Dic71C2411yescharacteristic
416C22×Dic71C2411yescharacteristic
417C22×Dic71C2411yescharacteristic
418C22×Dic71C2411yescharacteristic
419C2×C4×D71—22no—
420C2×C4×D71—22no—
421C2×C4×D71—22no—
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—416no—
431C2×C4×D71—41no—
432C2×C4×D71—41no—
433C2×C4×D71—41no—
434C2×C4×D71—41no—
435C2×C4×D71—41no—
436C2×C4×D71—41no—
437C2×C4×D71—41no—
438C2×C4×D71—41no—
439C2×C4×D71—41no—
440C2×C4×D71—41no—
441C2×C4×D71—41no—
442C2×C4×D71—41no—
443C2×C4×D71—41no—
444C2×C4×D71—41no—
445C2×C4×D71—41no—
446C2×C4×D71#4114yes—
447C4⋊Dic71—22no—
448C4⋊Dic71—22no—
449C4⋊Dic71—22no—
450C4⋊Dic71—22no—
451C4⋊Dic71—22no—
452C4⋊Dic71—41no—
453C4⋊Dic71—41no—
454C4⋊Dic71—41no—
455C4⋊Dic71—41no—
456C4⋊Dic71—41no—
457Dic71⋊C4—22no—
458Dic71⋊C4—22no—
459Dic71⋊C4—22no—
460Dic71⋊C4—22no—
461Dic71⋊C4—22no—
462Dic71⋊C4—41no—
463Dic71⋊C4—41no—
464Dic71⋊C4—41no—
465Dic71⋊C4—41no—
466Dic71⋊C4—41no—
467Dic71⋊C4—41no—
468Dic71⋊C4—41no—
469Dic71⋊C4—41no—
470Dic71⋊C4—41no—
471Dic71⋊C4—41no—
472Dic71⋊C4—41no—
473Dic71⋊C4—41no—
474Dic71⋊C4—41no—
475C22⋊Dic71—22no—
476C22⋊Dic71—22no—
477C22⋊Dic71—22no—
478C22⋊Dic71—41no—
479C22⋊Dic71—41no—
480C22⋊Dic71—41no—
481C22⋊Dic71—41no—
482C22⋊Dic71—41no—
483C22⋊Dic71—41no—
484C22⋊Dic71—41no—
485(C2×D71)⋊C4—22no—
486(C2×D71)⋊C4—22no—
487(C2×D71)⋊C4—22no—
488(C2×D71)⋊C4—22no—
489(C2×D71)⋊C4—22no—
490(C2×D71)⋊C4—22no—
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—41no—
497(C2×D71)⋊C4—41no—
498(C2×D71)⋊C4—41no—
499(C2×D71)⋊C4—41no—
500(C2×D71)⋊C4—41no—
501(C2×D71)⋊C4—41no—
502(C2×D71)⋊C4—41no—
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—
511C4×Dic71—41no—
512C4×Dic71—41no—
513C4×Dic71—41no—
514C4×Dic71—41no—
515C4×Dic71—41no—
516C24×C71C2411yescharacteristic
517C24×C71C2411yescharacteristic
518C2×Q8×C71—41no—
519C2×Q8×C71—41no—
520C2×Q8×C71—41no—
521C2×D4×C71—22no—
522C2×D4×C71—41no—
523C2×D4×C71—41no—
524C22×C4×C71—22no—
525C22×C4×C71—22no—
526C22×C4×C71—41no—
527C22×C4×C71—41no—
528C22×C4×C71—41no—
529C22×C4×C71—41no—
530C22×C4×C71C2411yescharacteristic
531C22×C4×C71C2411yescharacteristic
532C22×C4×C71C2411yescharacteristic
533C22×C4×C71C2411yescharacteristic
534C22×C4×C71C2411yescharacteristic
535C22×C4×C71C2411yescharacteristic
536C22×C4×C71C2411yescharacteristic
537C22×C4×C71C2411yescharacteristic
538C22×C4×C71C2411yescharacteristic
539C22×C4×C71C2411yescharacteristic
540C22×C4×C71C2411yescharacteristic
541C22×C4×C71C2411yescharacteristic
542C22×C4×C71C2411yescharacteristic
543C4⋊C4×C71—22no—
544C4⋊C4×C71—22no—
545C4⋊C4×C71—41no—
546C4⋊C4×C71—41no—
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—41no—
558C22⋊C4×C71—41no—
559C22⋊C4×C71—41no—
560C22⋊C4×C71—41no—
561C42×C71—41no—
562C23×C71—21no—
563C23×C71—21no—
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×C71H(5,𝔽2)12yes—
576C23×C71C2511yescharacteristic
577C22×D71—21no—
578C22×D71—21no—
579C22×D71—21no—
580C22×D71—21no—
581C22×D71—28no—
582C22×D71—21no—
583C22×D71—21no—
584C22×D71—21no—
585C22×D71—21no—
586C22×D71—21no—
587C22×D71—21no—
588C22×D71—21no—
589C22×D71—21no—
590C22×D71—21no—
591C22×D71—21no—
592C22×D71—21no—
593C22×D71—21no—
594C22×D71—21no—
595C22×D71—44no—
596C22×D71—44no—
597C22×D71—44no—
598C22×D71—44no—
599C22×D71—44no—
600C22×D71—44no—
601C22×D71C2×#4112yes—
602C22×D71H(5,𝔽2)12yes—
603C22×D712−1+412yes—
604C22×D712−1+412yes—
605Q8×C71—82no—
606D4×C71—82no—
607C2×C4×C71—21no—
608C2×C4×C71—21no—
609C2×C4×C71—21no—
610C2×C4×C71—21no—
611C2×C4×C71—21no—
612C2×C4×C71—21no—
613C2×C4×C71—21no—
614C2×C4×C71—21no—
615C2×C4×C71—21no—
616C2×C4×C71—21no—
617C2×C4×C71—21no—
618C2×C4×C71—21no—
619C2×C4×C71—21no—
620C2×C4×C71—21no—
621C2×C4×C71—21no—
622C2×C4×C71—21no—
623C2×C4×C71—21no—
624C2×C4×C71—21no—
625C2×C4×C71—21no—
626C2×C4×C71—21no—
627C2×C4×C71—21no—
628C2×C4×C71—21no—
629C2×C4×C71—21no—
630C2×C4×C71—21no—
631C2×C4×C71—21no—
632C2×C4×C71—21no—
633C2×C4×C71—21no—
634C2×C4×C71—21no—
635C2×C4×C71—21no—
636C2×C4×C71—21no—
637C2×C4×C71—21no—
638C2×C4×C71—21no—
639C2×C4×C71—21no—
640C2×C4×C71—21no—
641C2×C4×C71—21no—
642C2×C4×C71—21no—
643C2×C4×C71—21no—
644C2×C4×C71—44no—
645C2×C4×C71—82no—
646C2×C4×C71C2×#4112yes—
647C2×C4×C71H(5,𝔽2)12yes—
648C22⋊D71—44no—
649C22⋊D71—82no—
650C22⋊D71—82no—
651C22⋊D71—82no—
652C2×Dic71—21no—
653C2×Dic71—21no—
654C2×Dic71—21no—
655C2×Dic71—21no—
656C2×Dic71—21no—
657C2×Dic71—21no—
658C2×Dic71—21no—
659C2×Dic71—21no—
660C2×Dic71—21no—
661C2×Dic71—21no—
662C2×Dic71—21no—
663C2×Dic71—21no—
664C2×Dic71—21no—
665C2×Dic71—21no—
666C2×Dic71—21no—
667C2×Dic71—21no—
668C2×Dic71—21no—
669C2×Dic71—21no—
670C2×Dic71—21no—
671C2×Dic71—21no—
672C2×Dic71—21no—
673C2×Dic71—21no—
674C2×Dic71—21no—
675C2×Dic71—21no—
676C2×Dic71—21no—
677C2×Dic71—21no—
678C2×Dic71—21no—
679C2×Dic71—21no—
680C2×Dic71—21no—
681C2×Dic71—21no—
682C2×Dic71—21no—
683C2×Dic71—21no—
684C2×Dic71—21no—
685C2×Dic71—21no—
686C2×Dic71—21no—
687C2×Dic71—21no—
688C2×Dic71—21no—
689C2×Dic71—44no—
690C2×Dic71C2×#4112yes—
691C2×Dic71H(5,𝔽2)12yes—
692D284—44no—
693D284—82no—
694C4×D71—28no—
695C4×D71—44no—
696C4×D71—44no—
697C4×D71—44no—
698C4×D71—82no—
699C4×D71—82no—
700C4×D71—82no—
701C4×D71—82no—
702C4×D71—82no—
703Dic142—82no—
704Dic142—82no—
705C22×C71—22no—
706C22×C71—22no—
707C22×C71—22no—
708C22×C71—41no—
709C22×C71—41no—
710C22×C71—41no—
711C22×C71—41no—
712C22×C71—41no—
713C22×C71—41no—
714C22×C71—41no—
715C22×C71—41no—
716C22×C71—41no—
717C22×C71—41no—
718C22×C71—41no—
719C22×C71C22×#4111yescharacteristic
720C22×C71C2×H(5,𝔽2)11yescharacteristic
721C22×C71C2×H(5,𝔽2)11yescharacteristic
722C22×C71C2×H(5,𝔽2)11yescharacteristic
723C22×C71C2×H(5,𝔽2)11yescharacteristic
724C22×C71C2×2−1+411yescharacteristic
725C22×C71C2×2−1+411yescharacteristic
726C2×D71—22no—
727C2×D71—22no—
728C2×D71—22no—
729C2×D71—22no—
730C2×D71—22no—
731C2×D71—22no—
732C2×D71—22no—
733C2×D71—22no—
734C2×D71—22no—
735C2×D71—416no—
736C2×D71—41no—
737C2×D71—41no—
738C2×D71—41no—
739C2×D71—41no—
740C2×D71—41no—
741C2×D71—41no—
742C2×D71—41no—
743C2×D71—41no—
744C2×D71—41no—
745C2×D71—41no—
746C2×D71—41no—
747C2×D71#54214yes—
748C4×C71—22no—
749C4×C71—22no—
750C4×C71—41no—
751C4×C71—41no—
752C4×C71—41no—
753C4×C71—41no—
754C4×C71—41no—
755C4×C71—41no—
756C4×C71—41no—
757C4×C71—41no—
758C4×C71—41no—
759C4×C71—41no—
760C4×C71—41no—
761Dic71—22no—
762Dic71—22no—
763Dic71—41no—
764Dic71—41no—
765Dic71—41no—
766Dic71—41no—
767Dic71—41no—
768Dic71—41no—
769Dic71—41no—
770Dic71—41no—
771Dic71—41no—
772Dic71—41no—
773Dic71—41no—
774#36729—711nomaximal, Sylow
775C2×C71—42no—
776C2×C71—81no—
777C2×C71C2×#54211yescharacteristic
778C2×C71#349011yescharacteristic
779C2×C71#349211yescharacteristic
780C2×C71#353611yescharacteristic
781C2×C71#353611yescharacteristic
782C2×C71#353711yescharacteristic
783C2×C71#353811yescharacteristic
784D71—24no—
785D71—42no—
786D71—81no—
787#2848—711no—
788#2847—711no—
789#2747—711no—
790#2747—711no—
791#2742—711no—
792#2742—711no—
793#2741—711no—
794#2741—711no—
795#2717—711no—
796#2717D7111yescharacteristic, complemented
797#2702—711no—
798#2702—711no—
799#2692—711no—
800#2692—711no—
801#2691—711no—
802#2691—711no—
803#2672—711no—
804#2672—711no—
805#2659—711no—
806#2639—711no—
807#2481—711no—
808#2481—711no—
809#2472—711no—
810#2472—711no—
811#2449—711no—
812#2449—711no—
813#2418—711no—
814#2418—711no—
815#2329—711no—
816#2325—711no—
817C2×#380—711no—
818C71#3672911yescharacteristic, complemented, Sylow
819C24×C4—711no—
820C2×#126—711no—
821C2×#126—711no—
822C2×#124—711no—
823C2×#124C2×D7111yescharacteristic
824C2×#123—711no—
825C2×#123C2×D7111yescharacteristic
826C2×C22⋊Q8—711no—
827C2×C22⋊Q8—711no—
828C2×C22⋊Q8—711no—
829C2×C22⋊Q8—711no—
830C2×C22⋊Q8—711no—
831C2×C22⋊Q8—711no—
832C2×C22⋊Q8—711no—
833C2×#121—711no—
834C2×#121—711no—
835C2×#121—711no—
836C2×#120—711no—
837C2×#120—711no—
838C2×C4×D4—711no—
839C2×C4×D4—711no—
840C22×C4⋊C4—711no—
841C22×C4⋊C4—711no—
842C22×C22⋊C4—711no—
843C22×C22⋊C4—711no—
844#400—711no—
845#400—711no—
846#400—711no—
847#400—711no—
848#400—711no—
849#400—711no—
850#399—711no—
851#399—711no—
852#399—711no—
853#399—711no—
854#398—711no—
855#398—711no—
856#398—711no—
857#398—711no—
858#398—711no—
859#398—711no—
860#397—711no—
861#397—711no—
862#397—711no—
863#397—711no—
864#397C2×D7111yescharacteristic
865#397C2×D7111yescharacteristic
866#397C2×D7111yescharacteristic, complemented
867#397C2×D7111yescharacteristic, complemented
868#396—711no—
869#396—711no—
870#396—711no—
871#396—711no—
872#395—711no—
873#395—711no—
874#395—711no—
875#395—711no—
876#395C2×D7111yescharacteristic, complemented
877#395C2×D7111yescharacteristic, complemented
878#394—711no—
879#394—711no—
880#394—711no—
881#394—711no—
882#394—711no—
883#394—711no—
884#394—711no—
885#394—711no—
886#394—711no—
887#394—711no—
888#393—711no—
889#393—711no—
890#393—711no—
891#393—711no—
892#391—711no—
893#391—711no—
894#390—711no—
895#390—711no—
896#389—711no—
897#389—711no—
898#389—711no—
899#389—711no—
900#388—711no—
901#388—711no—
902#388—711no—
903#388—711no—
904#388—711no—
905#388—711no—
906#388—711no—
907#388—711no—
908#388—711no—
909#388—711no—
910#388—711no—
911#388—711no—
912#387—711no—
913#387—711no—
914#387—711no—
915#387—711no—
916#387—711no—
917#387—711no—
918#387—711no—
919#387—711no—
920#387—711no—
921#387—711no—
922#387C2×D7111yescharacteristic, complemented
923#387C2×D7111yescharacteristic, complemented
924#386—711no—
925#386—711no—
926#386—711no—
927#386—711no—
928#386—711no—
929#386—711no—
930#386—711no—
931#386—711no—
932#386—711no—
933#386—711no—
934#386—711no—
935#386—711no—
936#386—711no—
937#386—711no—
938#386—711no—
939#386C2×D7111yescharacteristic
940#385—711no—
941#385—711no—
942#385—711no—
943#385—711no—
944#385—711no—
945#385—711no—
946#385—711no—
947#385—711no—
948#385—711no—
949#385—711no—
950#385C2×D7111yescharacteristic, complemented
951#385C2×D7111yescharacteristic, complemented
952#380—711no—
953#380—711no—
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#380—711no—
963#380—711no—
964#380—711no—
965#380—711no—
966#380C2×D7111yescharacteristic
967#380C2×D7111yescharacteristic
968#379—711no—
969#379—711no—
970C4×C22⋊C4—711no—
971C4×C22⋊C4—711no—
972C2×#95—711no—
973C2×#95—711no—
974C25—711no—
975C22×Q8—711no—
976C22×Q8—711no—
977C22×Q8C22×D7111yescharacteristic
978C22×D4—711no—
979C22×D4—711no—
980C22×D4—711no—
981C22×D4—711no—
982C22×D4—711no—
983C22×D4—711no—
984C22×D4C22×D7111yescharacteristic
985C23×C4—2842no—
986C23×C4—2842no—
987C23×C4—711no—
988C23×C4—711no—
989C23×C4—711no—
990C23×C4—711no—
991C23×C4—711no—
992C23×C4—711no—
993C23×C4—711no—
994C23×C4—711no—
995C23×C4—711no—
996C23×C4—711no—
997C23×C4—1424no—
998C23×C4C22×D7111yescharacteristic
999C23×C4C22×D7111yescharacteristic
1000#126—2842no—
1001#126—2842no—
1002#124—42no—
1003#124—2842no—
1004#123—42no—
1005#123—2842no—
1006C22⋊Q8—2842no—
1007C22⋊Q8—2842no—
1008C22⋊Q8—2842no—
1009C22⋊Q8—2842no—
1010C22⋊Q8—2842no—
1011C22⋊Q8—2842no—
1012C22⋊Q8—1424no—
1013#121—2842no—
1014#121—2842no—
1015#121—1424no—
1016#120—2842no—
1017#120—2842no—
1018C4×D4—2842no—
1019C4×D4—2842no—
1020C2×C4⋊C4—2842no—
1021C2×C4⋊C4—2842no—
1022C2×C4⋊C4—711no—
1023C2×C4⋊C4—711no—
1024C2×C4⋊C4—711no—
1025C2×C4⋊C4—711no—
1026C2×C4⋊C4—711no—
1027C2×C4⋊C4—711no—
1028C2×C4⋊C4—711no—
1029C2×C4⋊C4—711no—
1030C2×C4⋊C4—711no—
1031C2×C4⋊C4—711no—
1032C2×C4⋊C4—711no—
1033C2×C4⋊C4—711no—
1034C2×C4⋊C4—711no—
1035C2×C4⋊C4—711no—
1036C2×C4⋊C4—711no—
1037C2×C4⋊C4—711no—
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⋊C4C22×D7111yescharacteristic
1051C2×C4⋊C4C22×D7111yescharacteristic
1052C2×C4⋊C4C22×D7111yescharacteristic
1053C2×C4⋊C4C22×D7111yescharacteristic
1054C2×C4⋊C4C22×D7111yescharacteristic
1055C2×C4⋊C4C22×D7111yescharacteristic
1056C2×C4⋊C4C22×D7111yescharacteristic
1057C2×C4⋊C4C22×D7111yescharacteristic
1058C2×C22⋊C4—2842no—
1059C2×C22⋊C4—2842no—
1060C2×C22⋊C4—711no—
1061C2×C22⋊C4—711no—
1062C2×C22⋊C4—711no—
1063C2×C22⋊C4—711no—
1064C2×C22⋊C4—711no—
1065C2×C22⋊C4—711no—
1066C2×C22⋊C4—711no—
1067C2×C22⋊C4—711no—
1068C2×C22⋊C4—711no—
1069C2×C22⋊C4—711no—
1070C2×C22⋊C4—711no—
1071C2×C22⋊C4—711no—
1072C2×C22⋊C4—711no—
1073C2×C22⋊C4—711no—
1074C2×C22⋊C4—711no—
1075C2×C22⋊C4—711no—
1076C2×C22⋊C4—711no—
1077C2×C22⋊C4—711no—
1078C2×C22⋊C4—711no—
1079C2×C22⋊C4—711no—
1080C2×C22⋊C4—711no—
1081C2×C22⋊C4—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⋊C4C22×D7111yescharacteristic
1097C2×C22⋊C4C22×D7111yescharacteristic
1098C2×C22⋊C4C22×D7111yescharacteristic
1099C2×C22⋊C4C22×D7111yescharacteristic
1100C2×C22⋊C4C22×D7111yescharacteristic
1101C2×C22⋊C4C22×D7111yescharacteristic
1102C2×C22⋊C4C22×D7111yescharacteristic
1103C2×C22⋊C4C22×D7111yescharacteristic
1104C2×C22⋊C4C22×D7111yescharacteristic
1105C2×C22⋊C4C22×D7111yescharacteristic
1106C2×C42—711no—
1107C2×C42—711no—
1108C2×C42—711no—
1109C2×C42—711no—
1110C2×C42—711no—
1111C2×C42C22×D7111yescharacteristic
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#95C22×D7111yescharacteristic
1145#95C22×D7111yescharacteristic
1146#95C22×D7111yescharacteristic
1147#95C22×D7111yescharacteristic
1148#95C22×D7111yescharacteristic
1149#95C22×D7111yescharacteristic
1150#95C22×D7111yescharacteristic
1151#95C22×D7111yescharacteristic
1152#95C22×D7111yescharacteristic
1153#95C22×D7111yescharacteristic
1154#95C22×D7111yescharacteristic
1155#95C22×D7111yescharacteristic
1156C24—2841no—
1157C24—2841no—
1158C24—711no—
1159C24—711no—
1160C24—711no—
1161C24—1422no—
1162C24—1422no—
1163C24—1422no—
1164C24—1422no—
1165C24—1422no—
1166C24C23×D7111yescharacteristic
1167C24C23×D7111yescharacteristic
1168C2×Q8—41no—
1169C2×Q8—41no—
1170C2×Q8—41no—
1171C2×Q8—2841no—
1172C2×Q8—2841no—
1173C2×Q8—2841no—
1174C2×Q8—2841no—
1175C2×Q8—2841no—
1176C2×Q8—1422no—
1177C2×D4—22no—
1178C2×D4—41no—
1179C2×D4—41no—
1180C2×D4—2841no—
1181C2×D4—2841no—
1182C2×D4—2841no—
1183C2×D4—2841no—
1184C2×D4—2841no—
1185C2×D4—2841no—
1186C2×D4—2841no—
1187C2×D4—2841no—
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—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—41no—
1201C22×C4—41no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—2841no—
1205C22×C4—2841no—
1206C22×C4—2841no—
1207C22×C4—2841no—
1208C22×C4—2841no—
1209C22×C4—2841no—
1210C22×C4—2841no—
1211C22×C4—2841no—
1212C22×C4—2841no—
1213C22×C4—2841no—
1214C22×C4—2841no—
1215C22×C4—2841no—
1216C22×C4—2841no—
1217C22×C4—2841no—
1218C22×C4—2841no—
1219C22×C4—28416no—
1220C22×C4—2841no—
1221C22×C4—714no—
1222C22×C4—711no—
1223C22×C4—711no—
1224C22×C4—711no—
1225C22×C4—711no—
1226C22×C4—711no—
1227C22×C4—711no—
1228C22×C4—711no—
1229C22×C4—711no—
1230C22×C4—711no—
1231C22×C4—711no—
1232C22×C4—711no—
1233C22×C4—711no—
1234C22×C4—711no—
1235C22×C4—1422no—
1236C22×C4—1422no—
1237C22×C4—1422no—
1238C22×C4—1422no—
1239C22×C4—1422no—
1240C22×C4—1422no—
1241C22×C4—1422no—
1242C22×C4—1422no—
1243C22×C4—1422no—
1244C22×C4—1422no—
1245C22×C4—1422no—
1246C22×C4—1422no—
1247C22×C4—1422no—
1248C22×C4C23×D7111yescharacteristic
1249C22×C4C23×D7111yescharacteristic
1250C22×C4C23×D7111yescharacteristic
1251C22×C4C23×D7111yescharacteristic
1252C22×C4C23×D7111yescharacteristic
1253C22×C4C23×D7111yescharacteristic
1254C22×C4C23×D7111yescharacteristic
1255C22×C4C23×D7111yescharacteristic
1256C22×C4C23×D7111yescharacteristic
1257C22×C4C23×D7111yescharacteristic
1258C22×C4C23×D7111yescharacteristic
1259C22×C4C23×D7111yescharacteristic
1260C22×C4C23×D7111yescharacteristic
1261C4⋊C4—22no—
1262C4⋊C4—22no—
1263C4⋊C4—41no—
1264C4⋊C4—41no—
1265C4⋊C4—41no—
1266C4⋊C4—41no—
1267C4⋊C4—41no—
1268C4⋊C4—41no—
1269C4⋊C4—2841no—
1270C4⋊C4—2841no—
1271C4⋊C4—2841no—
1272C4⋊C4—2841no—
1273C4⋊C4—2841no—
1274C4⋊C4—2841no—
1275C4⋊C4—2841no—
1276C4⋊C4—2841no—
1277C4⋊C4—2841no—
1278C4⋊C4—2841no—
1279C4⋊C4—2841no—
1280C4⋊C4—2841no—
1281C4⋊C4—2841no—
1282C4⋊C4—2841no—
1283C4⋊C4—2841no—
1284C4⋊C4—2841no—
1285C4⋊C4—2841no—
1286C4⋊C4—2841no—
1287C4⋊C4—1422no—
1288C4⋊C4—1422no—
1289C4⋊C4—1422no—
1290C4⋊C4—1422no—
1291C4⋊C4—1422no—
1292C4⋊C4—1422no—
1293C4⋊C4—1422no—
1294C4⋊C4—1422no—
1295C4⋊C4—1422no—
1296C4⋊C4—1422no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—22no—
1301C22⋊C4—22no—
1302C22⋊C4—22no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—2841no—
1308C22⋊C4—2841no—
1309C22⋊C4—2841no—
1310C22⋊C4—2841no—
1311C22⋊C4—2841no—
1312C22⋊C4—2841no—
1313C22⋊C4—2841no—
1314C22⋊C4—2841no—
1315C22⋊C4—2841no—
1316C22⋊C4—2841no—
1317C22⋊C4—2841no—
1318C22⋊C4—2841no—
1319C22⋊C4—2841no—
1320C22⋊C4—2841no—
1321C22⋊C4—2841no—
1322C22⋊C4—2841no—
1323C22⋊C4—2841no—
1324C22⋊C4—2841no—
1325C22⋊C4—2841no—
1326C22⋊C4—2841no—
1327C22⋊C4—2841no—
1328C22⋊C4—2841no—
1329C22⋊C4—1422no—
1330C22⋊C4—1422no—
1331C22⋊C4—1422no—
1332C22⋊C4—1422no—
1333C22⋊C4—1422no—
1334C22⋊C4—1422no—
1335C22⋊C4—1422no—
1336C22⋊C4—1422no—
1337C22⋊C4—1422no—
1338C22⋊C4—1422no—
1339C22⋊C4—1422no—
1340C22⋊C4—1422no—
1341C22⋊C4—1422no—
1342C22⋊C4—1422no—
1343C42—41no—
1344C42—2841no—
1345C42—2841no—
1346C42—2841no—
1347C42—2841no—
1348C42—2841no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—2844no—
1363C23—2844no—
1364C23—2844no—
1365C23—2844no—
1366C23—2844no—
1367C23—2844no—
1368C23—712no—
1369C23—712no—
1370C23—712no—
1371C23—712no—
1372C23—1428no—
1373C23—1421no—
1374C23—1421no—
1375C23—1421no—
1376C23—1421no—
1377C23—1421no—
1378C23—1421no—
1379C23—1421no—
1380C23—1421no—
1381C23—1421no—
1382C23—1421no—
1383C23—1421no—
1384C23—1421no—
1385C23—1421no—
1386C23—1421no—
1387C23—1421no—
1388C23—1421no—
1389C23—1421no—
1390C23#1455617312yes—
1391C23C24×D7111yescharacteristic
1392Q8—82no—
1393Q8—5682no—
1394Q8—5682no—
1395D4—82no—
1396D4—2844no—
1397D4—2844no—
1398D4—5682no—
1399D4—5682no—
1400D4—5682no—
1401D4—5682no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—44no—
1440C2×C4—82no—
1441C2×C4—2844no—
1442C2×C4—2844no—
1443C2×C4—2844no—
1444C2×C4—2844no—
1445C2×C4—5682no—
1446C2×C4—5682no—
1447C2×C4—5682no—
1448C2×C4—5682no—
1449C2×C4—5682no—
1450C2×C4—712no—
1451C2×C4—712no—
1452C2×C4—1428no—
1453C2×C4—1421no—
1454C2×C4—1421no—
1455C2×C4—1421no—
1456C2×C4—1421no—
1457C2×C4—1421no—
1458C2×C4—1421no—
1459C2×C4—1421no—
1460C2×C4—1421no—
1461C2×C4—1421no—
1462C2×C4—1421no—
1463C2×C4—1421no—
1464C2×C4—1421no—
1465C2×C4—1421no—
1466C2×C4—1421no—
1467C2×C4—1421no—
1468C2×C4—1421no—
1469C2×C4—1421no—
1470C2×C4—1421no—
1471C2×C4—1421no—
1472C2×C4—1421no—
1473C2×C4—1421no—
1474C2×C4—1421no—
1475C2×C4—1421no—
1476C2×C4—1421no—
1477C2×C4—1421no—
1478C2×C4—1421no—
1479C2×C4—1421no—
1480C2×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#41×D7112yes—
1491C2×C4#1455617412yes—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—28416no—
1507C22—2841no—
1508C22—2841no—
1509C22—2841no—
1510C22—2841no—
1511C22—2841no—
1512C22—2841no—
1513C22—2841no—
1514C22—2841no—
1515C22—2841no—
1516C22—2841no—
1517C22—2841no—
1518C22—714no—
1519C22—1422no—
1520C22—1422no—
1521C22—1422no—
1522C22—1422no—
1523C22—1422no—
1524C22—1422no—
1525C22—1422no—
1526C22—1422no—
1527C22—1422no—
1528C22C2×#41×D7111yescharacteristic
1529C22H(5,𝔽2)×D7111yescharacteristic
1530C22H(5,𝔽2)×D7111yescharacteristic
1531C22C2×#1455617311yescharacteristic
1532C22C2×#1455617411yescharacteristic
1533C222−1+4×D7111yescharacteristic
1534C222−1+4×D7111yescharacteristic
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—41no—
1548C4—2841no—
1549C4—2841no—
1550C4—2841no—
1551C4—2841no—
1552C4—2841no—
1553C4—2841no—
1554C4—2841no—
1555C4—2841no—
1556C4—2841no—
1557C4—2841no—
1558C4—2841no—
1559C4—1422no—
1560C4—1422no—
1561C2—42no—
1562C2—81no—
1563C2—2842no—
1564C2—5681no—
1565C2—1424no—
1566C2#542×D7111yescharacteristic
1567C2#2260202411yescharacteristic
1568C2#2260204211yescharacteristic
1569C2#2260256311yescharacteristic
1570C2#2260256511yescharacteristic
1571C2#2260257711yescharacteristic
1572C2#2260258411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutator, socle, cosocleC23×C71C25
FittingC71×#2717C2
prime radical#22596621C2
hypercenter#2717D71
hypocenterC71#36729
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2717

Complements

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

NH ≅ G/Ntype
1. #22596628C2semidirect
3. #22595544C2semidirect
4. #22595532C2semidirect
5. #22595471C2semidirect
6. #22595464C2semidirect
7. #22595457C2semidirect
8. #22595449C2semidirect
9. #22595176C2semidirect
10. #22594972C2semidirect
11. #22594968C2semidirect
12. #22594843C2semidirect
13. #22594839C2semidirect
14. #22594823C2semidirect
15. #22594819C2semidirect
16. #22594591C2semidirect
17. #22594586C2semidirect
18. #22594453C2semidirect
19. #22594267C2semidirect
20. #22592599C2semidirect
21. #22592596C2semidirect
22. #22592462C2semidirect
23. #22592459C2semidirect
24. #22592148C2semidirect
25. #22592142C2semidirect
26. #22591803C2semidirect
27. #22591799C2semidirect
28. #22591069C2semidirect
29. #22591037C2semidirect
30. #380×D71C2semidirect
31. C71×#2717C2semidirect
33. C2×#14556123C22semidirect
34. C2×#14556121C22semidirect
40. C2×#14556107C22semidirect
43. C2×#14556104C22semidirect
55. #17985941C22semidirect
56. #17985941C22semidirect
57. #17985940C22semidirect
58. #17985939C22semidirect
59. #17985939C22semidirect
60. #17985937C22semidirect
61. #17985935C22semidirect
64. #17985934C22semidirect
65. #17985933C22semidirect
66. #17985933C22semidirect
67. #17985932C22semidirect
68. #17985932C22semidirect
69. #17985931C22semidirect
70. #17985929C22semidirect
73. #17985926C22semidirect
74. #17985925C22semidirect
75. #17985922C22semidirect
76. #17985922C22semidirect
77. #17985921C22semidirect
78. #17985921C22semidirect
79. #17985920C22semidirect
80. #17985919C22semidirect
81. #17985919C22semidirect
82. #17985918C22semidirect
87. #17985915C22semidirect
88. #17985915C22semidirect
94. #17985912C22semidirect
95. #17985911C22semidirect
97. #17985903C22semidirect
98. #17985903C22semidirect
101. #17985897C22semidirect
102. #17985896C22semidirect
103. #17985895C22semidirect
104. #17985894C22semidirect
108. #17985892C22semidirect
110. #17985891C22semidirect
112. #17985890C22semidirect
116. #17985887C22semidirect
117. #17985886C22semidirect
118. #17985885C22semidirect
119. #17985884C22semidirect
120. #17985884C22semidirect
121. #17985882C22semidirect
122. #17985882C22semidirect
123. #17985882C22semidirect
124. #17985881C22semidirect
125. #17985881C22semidirect
126. #17985880C22semidirect
129. #17985878C22semidirect
141. #17985875C22semidirect
149. #17985873C22semidirect
151. #17985870C22semidirect
176. #397×C71C22semidirect
177. #397×C71C22semidirect
178. #395×C71C22semidirect
179. #395×C71C22semidirect
180. #387×C71C22semidirect
181. #387×C71C22semidirect
183. #385×C71C22semidirect
184. #385×C71C22semidirect
796. #2717D71semidirect
818. C71#36729semidirect
866. #397C2×D71semidirect
867. #397C2×D71semidirect
876. #395C2×D71semidirect
877. #395C2×D71semidirect
922. #387C2×D71semidirect
923. #387C2×D71semidirect
950. #385C2×D71semidirect
951. #385C2×D71semidirect

Maximal subgroups

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

subgroupindex
#225966282
#225966212
#225955442
#225955322
#225954712
#225954642
#225954572
#225954492
#225951762
#225949722
#225949682
#225948432
#225948392
#225948232
#225948192
#225945912
#225945862
#225944532
#225942672
#225925992
#225925962
#225924622
#225924592
#225921482
#225921422
#225918032
#225917992
#225910692
#225910372
#380×D712
C71×#27172
#3672971