Finite Group Databasebeta

← #31997562

Subgroups — #31997562

Order 18176.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986060C211yesmaximal, characteristic, complemented
2#22590949C211yesmaximal, characteristic, complemented
3#22588430C211yesmaximal, characteristic, complemented
4#22588426C211yesmaximal, characteristic, complemented
5#22588355C211yesmaximal, characteristic, complemented
6#22588350C211yesmaximal, characteristic, complemented
7#22588345C211yesmaximal, characteristic, complemented
8#22588340C211yesmaximal, characteristic, complemented
9#22588280C211yesmaximal, characteristic
10#22588280C211yesmaximal, characteristic
11#22588170C211yesmaximal, characteristic, complemented
12#22588165C211yesmaximal, characteristic, complemented
13C4×#14556052C211yesmaximal, characteristic, complemented
14C4×#14556049C211yesmaximal, characteristic, complemented
15C2×#520×C71C211yesmaximal, characteristic
16#17986060—24no—
17C2×C4⋊(C71⋊C8)C2211yescharacteristic
18C2×C4⋊(C71⋊C8)C2211yescharacteristic
19C2×#14556052C2211yescharacteristic
20C2×#14556052C2211yescharacteristic
21C2×#14556052C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556049C2211yescharacteristic
24C2×#14556049C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26C2×#14556049C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×#14556039C2211yescharacteristic
30C2×C4×C71⋊C8C2211yescharacteristic
31#17985892—21no—
32#17985892—21no—
33#17985885—21no—
34#17985885—21no—
35#17985869C2211yescharacteristic
36#17985865C2211yescharacteristic
37#17985859C2211yescharacteristic
38#17985859C2211yescharacteristic
39C4×C4⋊Dic71C2211yescharacteristic
40C4×C4⋊Dic71C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49C22×#41×C71C2211yescharacteristic
50#520×C71—24no—
51#520×C71C418yescomplemented
52C2×C4×Q8×C71C2211yescharacteristic
53C2×C4×Q8×C71C2211yescharacteristic
54C2×C4×D4×C71—21no—
55C2×C4×D4×C71—21no—
56C2×C4×D4×C71C2211yescharacteristic
57C2×C4×D4×C71C2211yescharacteristic
58C2×#117×C71—21no—
59C2×#117×C71C2211yescharacteristic
60C22×C4⋊C4×C71—21no—
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C71⋊C8C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C2×C4⋊Dic71—21no—
67C2×C4⋊Dic71—21no—
68C2×C4⋊Dic71C2311yescharacteristic
69C2×C4⋊Dic71C2311yescharacteristic
70C2×C4⋊Dic71C2311yescharacteristic
71C2×C4⋊Dic71C2311yescharacteristic
72C2×C22⋊Dic71—21no—
73C2×C22⋊Dic71—21no—
74C2×C4×Dic71—21no—
75C2×C4×Dic71—21no—
76C4⋊(C71⋊C8)—22no—
77C4⋊(C71⋊C8)—22no—
78#14556052—22no—
79#14556052—22no—
80#14556052—22no—
81#14556052—22no—
82#14556049—22no—
83#14556049—22no—
84#14556049—22no—
85#14556049—22no—
86C22⋊(C71⋊C8)—22no—
87C22⋊(C71⋊C8)—22no—
88#14556039—22no—
89C4×C71⋊C8—22no—
90C71⋊#95—21no—
91C71⋊#95—21no—
92C71⋊#95—21no—
93C71⋊#95—21no—
94C71⋊#95—21no—
95C71⋊#95—21no—
96C2×#41×C71—22no—
97C2×#41×C71—22no—
98C2×#41×C71—22no—
99C2×#41×C71—22no—
100C2×#41×C71—22no—
101C2×#41×C71C2×C414yes—
102C22×Q8×C71C2311yescharacteristic
103C22×D4×C71—21no—
104C22×D4×C71C2311yescharacteristic
105C23×C4×C71—21no—
106C23×C4×C71—21no—
107C23×C4×C71—21no—
108C23×C4×C71—21no—
109C23×C4×C71C2311yescharacteristic
110C4×Q8×C71—22no—
111C4×Q8×C71—22no—
112C4×Q8×C71C2×C414yes—
113C4×Q8×C71C2×C414yes—
114C4×D4×C71—28no—
115C4×D4×C71—28no—
116C4×D4×C71—22no—
117C4×D4×C71—22no—
118C4×D4×C71C2×C414yes—
119C4×D4×C71C2×C414yes—
120#117×C71—28no—
121#117×C71C2×C414yes—
122#117×C71D414yes—
123C2×C4⋊C4×C71—21no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—22no—
127C2×C4⋊C4×C71—28no—
128C2×C4⋊C4×C71C2×C414yes—
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71D411yescharacteristic
131C2×C4⋊C4×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2311yescharacteristic
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71D411yescharacteristic
136C2×C22⋊C4×C71D411yescharacteristic
137C2×C42×C71—21no—
138C2×C42×C71—21no—
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C2×C71⋊C8—21no—
146C2×C71⋊C8—21no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C4⋊Dic71—21no—
158C4⋊Dic71—21no—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—81no—
166C4⋊Dic71—81no—
167C22⋊Dic71—81no—
168C22⋊Dic71—81no—
169C4×Dic71—81no—
170C4×Dic71—81no—
171C24×C71—21no—
172C24×C71C2×D411yescharacteristic
173#41×C71—28no—
174#41×C71—28no—
175#41×C71—28no—
176#41×C71—28no—
177C2×Q8×C71—21no—
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71C22×C412yes—
181C2×Q8×C71#4112yes—
182C2×Q8×C71#4112yes—
183C2×D4×C71—24no—
184C2×D4×C71—24no—
185C2×D4×C71—24no—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71C22×C412yes—
190C2×D4×C71#4112yes—
191C2×D4×C71#4112yes—
192C22×C4×C71—24no—
193C22×C4×C71—24no—
194C22×C4×C71—21no—
195C22×C4×C71—24no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—24no—
203C22×C4×C71—24no—
204C22×C4×C71—24no—
205C22×C4×C71—81no—
206C22×C4×C71—81no—
207C22×C4×C71—81no—
208C22×C4×C71—81no—
209C22×C4×C71—81no—
210C22×C4×C71—81no—
211C22×C4×C71C22×C412yes—
212C22×C4×C71C2×D411yescharacteristic
213C22×C4×C71C2×D411yescharacteristic
214C22×C4×C71C2×D411yescharacteristic
215C22×C4×C71C2×D411yescharacteristic
216C22×C4×C71C2×D411yescharacteristic
217C22×C4×C71C2×D412yes—
218C22×C4×C71C2411yescharacteristic
219C4⋊C4×C71—24no—
220C4⋊C4×C71—24no—
221C4⋊C4×C71—24no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71C22⋊C414yes—
225C4⋊C4×C71C22⋊C414yes—
226C4⋊C4×C71C22×C412yes—
227C4⋊C4×C71C22×C412yes—
228C22⋊C4×C71—24no—
229C22⋊C4×C71—24no—
230C22⋊C4×C71C22⋊C414yes—
231C22⋊C4×C71C22⋊C414yes—
232C42×C71—24no—
233C42×C71—24no—
234C42×C71C22×C412yes—
235C42×C71C22×C412yes—
236C42×C71C2×D412yes—
237C42×C71C2×D412yes—
238C23×C71—22no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—22no—
242C23×C71—22no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—41no—
248C23×C71—41no—
249C23×C71—41no—
250C23×C71—41no—
251C23×C71C2×C22⋊C412yes—
252C23×C71C22×D411yescharacteristic
253Q8×C71—22no—
254Q8×C71—22no—
255Q8×C71—22no—
256Q8×C71#11714yes—
257D4×C71—216no—
258D4×C71—22no—
259D4×C71—22no—
260D4×C71—22no—
261D4×C71#11714yes—
262C2×C4×C71—216no—
263C2×C4×C71—22no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—41no—
283C2×C4×C71—41no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—84no—
287C2×C4×C71—84no—
288C2×C4×C71—84no—
289C2×C4×C71C2×C22⋊C412yes—
290C2×C4×C71C2×C22⋊C412yes—
291C2×C4×C71C2×C22⋊C412yes—
292C2×C4×C71C2×C22⋊C412yes—
293C2×C4×C71C2×C22⋊C412yes—
294C2×C4×C71C23×C411yescharacteristic
295C2×C4×C71C22×D411yescharacteristic
296C2×C4×C71C2×#4111yescharacteristic
297C2×C4×C71C2×#4111yescharacteristic
298C2×C4×C71C2×#4111yescharacteristic
299C2×C4×C71C2×#4111yescharacteristic
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—41no—
305C2×Dic71—41no—
306C2×Dic71—41no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—41no—
310C2×Dic71—41no—
311C2×Dic71—41no—
312C71⋊C8—41no—
313C71⋊C8—41no—
314C71⋊C8—41no—
315C71⋊C8—41no—
316C22×C71—22no—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—24no—
320C22×C71—41no—
321C22×C71—42no—
322C22×C71—41no—
323C22×C71—42no—
324C22×C71—41no—
325C22×C71—42no—
326C22×C71—41no—
327C22×C71—42no—
328C22×C71—42no—
329C22×C71—42no—
330C22×C71C22×C22⋊C411yescharacteristic
331C22×C71#52511yescharacteristic
332C22×C71#52511yescharacteristic
333C22×C71#57611yescharacteristic
334C22×C71#57711yescharacteristic
335C22×C71#57711yescharacteristic
336C22×C71#57811yescharacteristic
337C4×C71—22no—
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—22no—
341C4×C71—22no—
342C4×C71—24no—
343C4×C71—42no—
344C4×C71—42no—
345C4×C71C2×#11711yescharacteristic
346C4×C71C2×#11711yescharacteristic
347C4×C71#52511yescharacteristic
348C4×C71#52511yescharacteristic
349Dic71—81no—
350Dic71—81no—
351Dic71—81no—
352Dic71—81no—
353#20746—711nomaximal, Sylow
354C2×C71—42no—
355C2×C71—44no—
356C2×C71#228011yescharacteristic
357C2×C71#289711yescharacteristic
358C2×C71#289811yescharacteristic
359C2×C71#311911yescharacteristic
360C2×C71#312011yescharacteristic
361C2×C71#312411yescharacteristic
362C2×C71#312511yescharacteristic
363C2×#520D7111yescharacteristic
364C2×#433—711no—
365#2314—711no—
366#1824—711no—
367#1823—711no—
368#1805—711no—
369#1804—711no—
370#1803—711no—
371#1802—711no—
372#1788—711no—
373#1788—711no—
374#1763—711no—
375#1762—711no—
376C4×#103—711no—
377C4×#102—711no—
378C71#2074611yescharacteristic, complemented, Sylow
379C22×#41C2×D7111yescharacteristic
380#520—24no—
381#520Dic7118yescomplemented
382C2×C4×Q8C2×D7111yescharacteristic
383C2×C4×Q8C2×D7111yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4—21no—
386C2×C4×D4C2×D7111yescharacteristic
387C2×C4×D4C2×D7111yescharacteristic
388C2×#117—21no—
389C2×#117C2×D7111yescharacteristic
390C22×C4⋊C4—21no—
391C22×C4⋊C4C2×D7111yescharacteristic
392#433—1424no—
393C2×C4⋊C8—711no—
394C2×C4⋊C8—711no—
395C2×#103—711no—
396C2×#103—711no—
397C2×#103—711no—
398C2×#103—711no—
399C2×#102—711no—
400C2×#102—711no—
401C2×#102—711no—
402C2×#102—711no—
403C2×C22⋊C8—711no—
404C2×C22⋊C8—711no—
405C2×#97—711no—
406C2×C4×C8—711no—
407#388—1421no—
408#388—1421no—
409#387—1421no—
410#387—1421no—
411#384—711no—
412#382—711no—
413#380—711no—
414#380—711no—
415C4×C4⋊C4—711no—
416C4×C4⋊C4—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420#340—711no—
421#340—711no—
422#340—711no—
423#340—711no—
424#340—711no—
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41C2×Dic7114yes—
431C22×Q8C22×D7111yescharacteristic
432C22×D4—21no—
433C22×D4C22×D7111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C22×D7111yescharacteristic
439C22×C8—711no—
440C22×C8—711no—
441C22×C8—711no—
442C22×C8—711no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8C2×Dic7114yes—
446C4×Q8C2×Dic7114yes—
447C4×D4—28no—
448C4×D4—28no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4C2×Dic7114yes—
452C4×D4C2×Dic7114yes—
453#117—28no—
454#117C2×Dic7114yes—
455#117C22⋊D7114yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—28no—
461C2×C4⋊C4—711no—
462C2×C4⋊C4—711no—
463C2×C4⋊C4—711no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—1421no—
466C2×C4⋊C4—1421no—
467C2×C4⋊C4C2×Dic7114yes—
468C2×C4⋊C4C22⋊D7111yescharacteristic
469C2×C4⋊C4C22⋊D7111yescharacteristic
470C2×C4⋊C4C22×D7111yescharacteristic
471C2×C4⋊C4C22×D7111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1421no—
475C2×C22⋊C4—1421no—
476C2×C22⋊C4C22⋊D7111yescharacteristic
477C2×C22⋊C4C22⋊D7111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—1421no—
481C2×C42—1421no—
482C2×C42C22×D7111yescharacteristic
483C2×C42C22×D7111yescharacteristic
484C4⋊C8—1422no—
485C4⋊C8—1422no—
486#103—1422no—
487#103—1422no—
488#103—1422no—
489#103—1422no—
490#102—1422no—
491#102—1422no—
492#102—1422no—
493#102—1422no—
494C22⋊C8—1422no—
495C22⋊C8—1422no—
496#97—1422no—
497C4×C8—1422no—
498#95—1421no—
499#95—1421no—
500#95—1421no—
501#95—1421no—
502#95—1421no—
503#95—1421no—
504C24—21no—
505C24C2×C22⋊D7111yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C22×Dic7112yes—
514C2×Q8#1176586512yes—
515C2×Q8#1176586512yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4C22×Dic7112yes—
523C2×D4#1176586512yes—
524C2×D4#1176586512yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—1421no—
545C22×C4—1421no—
546C22×C4—1421no—
547C22×C4—1421no—
548C22×C4C22×Dic7112yes—
549C22×C4C2×C22⋊D7112yes—
550C22×C4C2×C22⋊D7111yescharacteristic
551C22×C4C2×C22⋊D7111yescharacteristic
552C22×C4C2×C22⋊D7111yescharacteristic
553C22×C4C2×C22⋊D7111yescharacteristic
554C22×C4C2×C22⋊D7111yescharacteristic
555C22×C4C23×D7111yescharacteristic
556C2×C8—1421no—
557C2×C8—1421no—
558C2×C8—1421no—
559C2×C8—1421no—
560C2×C8—1421no—
561C2×C8—1421no—
562C2×C8—1421no—
563C2×C8—1421no—
564C2×C8—1421no—
565C2×C8—1421no—
566C2×C8—1421no—
567C2×C8—1421no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—5681no—
574C4⋊C4—5681no—
575C4⋊C4—1421no—
576C4⋊C4—1421no—
577C4⋊C4—1421no—
578C4⋊C4—1421no—
579C4⋊C4—1421no—
580C4⋊C4—1421no—
581C4⋊C4—1421no—
582C4⋊C4—1421no—
583C4⋊C4C22⋊Dic7114yes—
584C4⋊C4C22⋊Dic7114yes—
585C4⋊C4C22×Dic7112yes—
586C4⋊C4C22×Dic7112yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—5681no—
590C22⋊C4—5681no—
591C22⋊C4C22⋊Dic7114yes—
592C22⋊C4C22⋊Dic7114yes—
593C42—24no—
594C42—24no—
595C42—5681no—
596C42—5681no—
597C42C22×Dic7112yes—
598C42C22×Dic7112yes—
599C42C2×C22⋊D7112yes—
600C42C2×C22⋊D7112yes—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C2×C22⋊Dic7112yes—
615C23C22×C22⋊D7111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#1455608714yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#1455608714yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—84no—
652C2×C4—2841no—
653C2×C4—2841no—
654C2×C4—2841no—
655C2×C4—2841no—
656C2×C4—2841no—
657C2×C4—2841no—
658C2×C4—2841no—
659C2×C4—2841no—
660C2×C4—2841no—
661C2×C4—2841no—
662C2×C4—2841no—
663C2×C4—2841no—
664C2×C4C2×C22⋊Dic7112yes—
665C2×C4C2×C22⋊Dic7112yes—
666C2×C4C2×C22⋊Dic7112yes—
667C2×C4C2×C22⋊Dic7112yes—
668C2×C4C2×C22⋊Dic7112yes—
669C2×C4C23×Dic7111yescharacteristic
670C2×C4C22×C22⋊D7111yescharacteristic
671C2×C4C2×#1176586511yescharacteristic
672C2×C4C2×#1176586511yescharacteristic
673C2×C4C2×#1176586511yescharacteristic
674C2×C4C2×#1176586511yescharacteristic
675C8—2841no—
676C8—2841no—
677C8—2841no—
678C8—2841no—
679C22—22no—
680C22—22no—
681C22—24no—
682C22—22no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—41no—
692C22—42no—
693C22C22×C22⋊Dic7111yescharacteristic
694C22#1798651011yescharacteristic
695C22#1798651011yescharacteristic
696C22#1798680211yescharacteristic
697C22#1798680711yescharacteristic
698C22#1798681011yescharacteristic
699C22#1798681411yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—24no—
704C4—22no—
705C4—22no—
706C4—42no—
707C4—42no—
708C4—5681no—
709C4—5681no—
710C4—5681no—
711C4—5681no—
712C4C2×#1455608711yescharacteristic
713C4C2×#1455608711yescharacteristic
714C4#1798651011yescharacteristic
715C4#1798651011yescharacteristic
716C2—42no—
717C2—44no—
718C2#2259072311yescharacteristic
719C2#2259686611yescharacteristic
720C2#2259687311yescharacteristic
721C2#2259853911yescharacteristic
722C2#2259855411yescharacteristic
723C2#2259860211yescharacteristic
724C2#2259861711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#520×C71C2
socleC23×C71C22×D4
prime radicalC22×#41×C71C22
cosocleC22×C4×C71C24
hypercenterC2×#520D71
hypocenterC71#20746
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#17986060C2semidirect
2. #22590949C2semidirect
3. #22588430C2semidirect
4. #22588426C2semidirect
5. #22588355C2semidirect
6. #22588350C2semidirect
7. #22588345C2semidirect
8. #22588340C2semidirect
11. #22588170C2semidirect
12. #22588165C2semidirect
13. C4×#14556052C2semidirect
14. C4×#14556049C2semidirect
51. #520×C71C4semidirect
378. C71#20746semidirect
381. #520Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860602
#225909492
#225884302
#225884262
#225883552
#225883502
#225883452
#225883402
#225882802
#225881702
#225881652
C4×#145560522
C4×#145560492
C2×#520×C712
#2074671