Finite Group Databasebeta

← #32002725

Subgroups — #32002725

Order 18176.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985955C211yesmaximal, characteristic, complemented
2#22590949C211yesmaximal, characteristic, complemented
3#22589314C211yesmaximal, characteristic, complemented
4#22589302C211yesmaximal, characteristic, complemented
5#22589157C211yesmaximal, characteristic, complemented
6#22589152C211yesmaximal, characteristic, complemented
7#22588779C211yesmaximal, characteristic
8#22588774C211yesmaximal, characteristic, complemented
9#22588769C211yesmaximal, characteristic
10#22588764C211yesmaximal, characteristic, complemented
11#22588170C211yesmaximal, characteristic, complemented
12#22588165C211yesmaximal, characteristic, complemented
13C4×#14556052C211yesmaximal, characteristic, complemented
14C4×#14556049C211yesmaximal, characteristic, complemented
15C2×#542×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556052C2211yescharacteristic
19C2×#14556052C2211yescharacteristic
20C2×#14556052C2211yescharacteristic
21C2×#14556052C2211yescharacteristic
22C2×#14556049C2211yescharacteristic
23C2×#14556049C2211yescharacteristic
24C2×#14556049C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26#17985955—24no—
27C2×#14556039C2211yescharacteristic
28C2×#14556039C2211yescharacteristic
29C2×C4×C71⋊C8C2211yescharacteristic
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
49#542×C71—24no—
50#542×C71C418yescomplemented
51C2×C4⋊Q8×C71C2211yescharacteristic
52C2×#126×C71—21no—
53C2×#124×C71—21no—
54C2×#124×C71C2211yescharacteristic
55C2×#123×C71—21no—
56C2×C22⋊Q8×C71—21no—
57C2×C22⋊Q8×C71C2211yescharacteristic
58C2×#121×C71C2211yescharacteristic
59C2×C4×Q8×C71C2211yescharacteristic
60C2×C4×D4×C71C2211yescharacteristic
61C2×#117×C71C2211yescharacteristic
62C2×#11765849—22no—
63C2×#11765849—22no—
64C2×#11765849—22no—
65C22×C71⋊C8—22no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8C2311yescharacteristic
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C2×C4⋊Dic71—21no—
73C2×C4⋊Dic71—21no—
74C2×C4⋊Dic71C2311yescharacteristic
75C2×C4⋊Dic71C2311yescharacteristic
76C2×C4⋊Dic71C2311yescharacteristic
77C2×C4⋊Dic71C2311yescharacteristic
78C2×C22⋊Dic71—21no—
79C2×C22⋊Dic71—21no—
80C2×C4×Dic71—21no—
81C2×C4×Dic71—21no—
82#14556052—22no—
83#14556052—22no—
84#14556052—22no—
85#14556052—22no—
86#14556049—22no—
87#14556049—22no—
88#14556049—22no—
89#14556049—22no—
90#14556039—22no—
91#14556039—22no—
92C4×C71⋊C8—22no—
93C4×C71⋊C8—22no—
94C71⋊#95—21no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71—21no—
101C22×Q8×C71C2311yescharacteristic
102C22×D4×C71—21no—
103C22×D4×C71C2311yescharacteristic
104C23×C4×C71—21no—
105C23×C4×C71C2311yescharacteristic
106C4⋊Q8×C71—22no—
107C4⋊Q8×C71C2×C414yes—
108#126×C71—28no—
109#124×C71—28no—
110#124×C71—22no—
111#124×C71C2×C414yes—
112#123×C71—28no—
113C22⋊Q8×C71—22no—
114C22⋊Q8×C71—28no—
115C22⋊Q8×C71C2×C414yes—
116#121×C71—22no—
117#121×C71C2×C414yes—
118C4×Q8×C71—22no—
119C4×Q8×C71C2×C414yes—
120C4×D4×C71—22no—
121C4×D4×C71C2×C414yes—
122#117×C71C2×C414yes—
123#117×C71D414yes—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71D411yescharacteristic
128C2×C4⋊C4×C71D411yescharacteristic
129C2×C4⋊C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C22⋊C4×C71D411yescharacteristic
137C2×C22⋊C4×C71D411yescharacteristic
138C2×C42×C71—21no—
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145#11765849—28no—
146C2×C71⋊C8—28no—
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#4112yes—
156C2×C71⋊C8#4112yes—
157C2×C71⋊C8#4112yes—
158C2×C71⋊C8#4112yes—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—81no—
168C4⋊Dic71—81no—
169C22⋊Dic71—81no—
170C22⋊Dic71—81no—
171C4×Dic71—81no—
172C4×Dic71—81no—
173C24×C71—21no—
174C24×C71C2×D411yescharacteristic
175C2×Q8×C71—24no—
176C2×Q8×C71—21no—
177C2×Q8×C71—21no—
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—81no—
182C2×Q8×C71—81no—
183C2×Q8×C71C22×C412yes—
184C2×D4×C71—24no—
185C2×D4×C71—21no—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—21no—
190C2×D4×C71—81no—
191C2×D4×C71—81no—
192C2×D4×C71C22×C412yes—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—24no—
201C22×C4×C71—81no—
202C22×C4×C71—81no—
203C22×C4×C71C22×C412yes—
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D412yes—
210C22×C4×C71C2411yescharacteristic
211C4⋊C4×C71—24no—
212C4⋊C4×C71—24no—
213C4⋊C4×C71—24no—
214C4⋊C4×C71—21no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71C22⋊C414yes—
217C4⋊C4×C71C22⋊C414yes—
218C4⋊C4×C71C22×C412yes—
219C4⋊C4×C71C22×C412yes—
220C22⋊C4×C71—24no—
221C22⋊C4×C71—24no—
222C22⋊C4×C71—24no—
223C22⋊C4×C71—24no—
224C22⋊C4×C71—24no—
225C22⋊C4×C71C22⋊C414yes—
226C22⋊C4×C71C22⋊C414yes—
227C42×C71—24no—
228C42×C71C22×C412yes—
229C42×C71C22×C412yes—
230C42×C71C2×D412yes—
231C42×C71C2×D412yes—
232C23×C71—21no—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—22no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71C2×C22⋊C412yes—
246C23×C71C22×D411yescharacteristic
247Q8×C71—22no—
248Q8×C71—22no—
249Q8×C71—41no—
250Q8×C71—41no—
251Q8×C71—84no—
252D4×C71—22no—
253D4×C71—22no—
254D4×C71—41no—
255D4×C71—41no—
256D4×C71—84no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—84no—
281C2×C4×C71C2×C22⋊C412yes—
282C2×C4×C71C2×C22⋊C412yes—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C23×C411yescharacteristic
287C2×C4×C71C22×D411yescharacteristic
288C2×C4×C71C2×#4111yescharacteristic
289C2×C4×C71C2×#4111yescharacteristic
290C2×C4×C71C2×#4111yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C71⋊C8—22no—
305C71⋊C8—22no—
306C71⋊C8—22no—
307C71⋊C8—22no—
308C22×C71—22no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—41no—
312C22×C71—41no—
313C22×C71—41no—
314C22×C71—41no—
315C22×C71—42no—
316C22×C71—42no—
317C22×C71—42no—
318C22×C71—81no—
319C22×C71—81no—
320C22×C71—81no—
321C22×C71—81no—
322C22×C71C22×C22⋊C411yescharacteristic
323C22×C71#53211yescharacteristic
324C22×C71#53211yescharacteristic
325C22×C71#57611yescharacteristic
326C22×C71#57711yescharacteristic
327C22×C71#57711yescharacteristic
328C22×C71#57811yescharacteristic
329C4×C71—22no—
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71C4×#4111yescharacteristic
338C4×C71C4×#4111yescharacteristic
339C4×C71#52511yescharacteristic
340C4×C71#52511yescharacteristic
341Dic71—81no—
342Dic71—81no—
343Dic71—81no—
344Dic71—81no—
345#21412—711nomaximal, Sylow
346C2×C71—42no—
347C2×C71—82no—
348C2×C71#229711yescharacteristic
349C2×C71#289711yescharacteristic
350C2×C71#289811yescharacteristic
351C2×C71#317311yescharacteristic
352C2×C71#317511yescharacteristic
353C2×C71#317811yescharacteristic
354C2×C71#317911yescharacteristic
355C2×#542D7111yescharacteristic
356C2×#405—711no—
357#2314—711no—
358#1993—711no—
359#1990—711no—
360#1959—711no—
361#1958—711no—
362#1895—711no—
363#1894—711no—
364#1893—711no—
365#1892—711no—
366#1763—711no—
367#1762—711no—
368C4×#103—711no—
369C4×#102—711no—
370C71#2141211yescharacteristic, complemented, Sylow
371C22×M16—711no—
372C23×C8—711no—
373#542—24no—
374#542Dic7118yescomplemented
375C2×C4⋊Q8C2×D7111yescharacteristic
376C2×#126—21no—
377C2×#124—21no—
378C2×#124C2×D7111yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D7111yescharacteristic
382C2×#121C2×D7111yescharacteristic
383C2×C4×Q8C2×D7111yescharacteristic
384C2×C4×D4C2×D7111yescharacteristic
385C2×#117C2×D7111yescharacteristic
386C2×#103—711no—
387C2×#103—711no—
388C2×#103—711no—
389C2×#103—711no—
390C2×#102—711no—
391C2×#102—711no—
392C2×#102—711no—
393C2×#102—711no—
394#405—1424no—
395C2×#97—711no—
396C2×#97—711no—
397C2×C4×C8—711no—
398C2×C4×C8—711no—
399#388—1421no—
400#388—1421no—
401#387—1421no—
402#387—1421no—
403#384—711no—
404#382—711no—
405#380—711no—
406#380—711no—
407C4×C4⋊C4—711no—
408C4×C4⋊C4—711no—
409#340—711no—
410#340—711no—
411#340—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417C22×Q8—21no—
418C22×Q8C22×D7111yescharacteristic
419C22×D4—21no—
420C22×D4C22×D7111yescharacteristic
421C23×C4—21no—
422C23×C4C22×D7111yescharacteristic
423C2×M16—1422no—
424C2×M16—1422no—
425C2×M16—1422no—
426C22×C8—711no—
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—1422no—
431C22×C8—1422no—
432C22×C8—1422no—
433C4⋊Q8—22no—
434C4⋊Q8C2×Dic7114yes—
435#126—28no—
436#124—28no—
437#124—22no—
438#124C2×Dic7114yes—
439#123—28no—
440C22⋊Q8—22no—
441C22⋊Q8—28no—
442C22⋊Q8C2×Dic7114yes—
443#121—22no—
444#121C2×Dic7114yes—
445C4×Q8—22no—
446C4×Q8C2×Dic7114yes—
447C4×D4—22no—
448C4×D4C2×Dic7114yes—
449#117C2×Dic7114yes—
450#117C22⋊D7114yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—711no—
456C2×C4⋊C4—711no—
457C2×C4⋊C4—711no—
458C2×C4⋊C4—1421no—
459C2×C4⋊C4—1421no—
460C2×C4⋊C4C22⋊D7111yescharacteristic
461C2×C4⋊C4C22⋊D7111yescharacteristic
462C2×C4⋊C4C22×D7111yescharacteristic
463C2×C4⋊C4C22×D7111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—1421no—
470C2×C22⋊C4—1421no—
471C2×C22⋊C4C22⋊D7111yescharacteristic
472C2×C22⋊C4C22⋊D7111yescharacteristic
473C2×C42—21no—
474C2×C42—1421no—
475C2×C42—1421no—
476C2×C42C22×D7111yescharacteristic
477C2×C42C22×D7111yescharacteristic
478#103—1422no—
479#103—1422no—
480#103—1422no—
481#103—1422no—
482#102—1422no—
483#102—1422no—
484#102—1422no—
485#102—1422no—
486#97—1422no—
487#97—1422no—
488C4×C8—1422no—
489C4×C8—1422no—
490#95—1421no—
491#95—1421no—
492#95—1421no—
493#95—1421no—
494#95—1421no—
495#95—1421no—
496C24—21no—
497C24C2×C22⋊D7111yescharacteristic
498C2×Q8—21no—
499C2×Q8—24no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8C22×Dic7112yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C22×Dic7112yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4C22×Dic7112yes—
531C22×C4C2×C22⋊D7112yes—
532C22×C4C2×C22⋊D7111yescharacteristic
533C22×C4C2×C22⋊D7111yescharacteristic
534C22×C4C2×C22⋊D7111yescharacteristic
535C22×C4C2×C22⋊D7111yescharacteristic
536C22×C4C2×C22⋊D7111yescharacteristic
537C22×C4C23×D7111yescharacteristic
538M16—1428no—
539C2×C8—712no—
540C2×C8—712no—
541C2×C8—712no—
542C2×C8—712no—
543C2×C8—1428no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—5681no—
558C4⋊C4—5681no—
559C4⋊C4—1421no—
560C4⋊C4—1421no—
561C4⋊C4—1421no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4C22⋊Dic7114yes—
568C4⋊C4C22⋊Dic7114yes—
569C4⋊C4C22×Dic7112yes—
570C4⋊C4C22×Dic7112yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—5681no—
577C22⋊C4—5681no—
578C22⋊C4C22⋊Dic7114yes—
579C22⋊C4C22⋊Dic7114yes—
580C42—24no—
581C42—5681no—
582C42—5681no—
583C42C22×Dic7112yes—
584C42C22×Dic7112yes—
585C42C2×C22⋊D7112yes—
586C42C2×C22⋊D7112yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C22⋊Dic7112yes—
601C23C22×C22⋊D7111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—2841no—
637C2×C4—2841no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4C2×C22⋊Dic7112yes—
649C2×C4C2×C22⋊Dic7112yes—
650C2×C4C2×C22⋊Dic7112yes—
651C2×C4C2×C22⋊Dic7112yes—
652C2×C4C2×C22⋊Dic7112yes—
653C2×C4C23×Dic7111yescharacteristic
654C2×C4C22×C22⋊D7111yescharacteristic
655C2×C4#41×D7111yescharacteristic
656C2×C4#41×D7111yescharacteristic
657C2×C4#41×D7111yescharacteristic
658C2×C4#41×D7111yescharacteristic
659C8—1422no—
660C8—1422no—
661C8—1422no—
662C8—1422no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C22⋊Dic7111yescharacteristic
678C22#1798654511yescharacteristic
679C22#1798654511yescharacteristic
680C22#1798680211yescharacteristic
681C22#1798680711yescharacteristic
682C22#1798681011yescharacteristic
683C22#1798681411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—5681no—
693C4—5681no—
694C4—5681no—
695C4—5681no—
696C4#41×Dic7111yescharacteristic
697C4#41×Dic7111yescharacteristic
698C4#1798650611yescharacteristic
699C4#1798650611yescharacteristic
700C2—42no—
701C2—82no—
702C2#2259083111yescharacteristic
703C2#2259686611yescharacteristic
704C2#2259687311yescharacteristic
705C2#2259895111yescharacteristic
706C2#2259897311yescharacteristic
707C2#2259900211yescharacteristic
708C2#2259901711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
prime radicalC2×#121×C71C22
cosocleC22×C4×C71C24
hypercenterC2×#542D71
hypocenterC71#21412
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17985955C2semidirect
2. #22590949C2semidirect
3. #22589314C2semidirect
4. #22589302C2semidirect
5. #22589157C2semidirect
6. #22589152C2semidirect
8. #22588774C2semidirect
10. #22588764C2semidirect
11. #22588170C2semidirect
12. #22588165C2semidirect
13. C4×#14556052C2semidirect
14. C4×#14556049C2semidirect
50. #542×C71C4semidirect
370. C71#21412semidirect
374. #542Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179859552
#225909492
#225893142
#225893022
#225891572
#225891522
#225887792
#225887742
#225887692
#225887642
#225881702
#225881652
C4×#145560522
C4×#145560492
C2×#542×C712
#2141271