Finite Group Databasebeta

← #32002600

Subgroups — #32002600

Order 18176.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986060C211yesmaximal, characteristic, complemented
2#22590696C211yesmaximal, characteristic, complemented
3#22589293C211yesmaximal, characteristic, complemented
4#22589289C211yesmaximal, characteristic, complemented
5#22589273C211yesmaximal, characteristic, complemented
6#22589273C211yesmaximal, characteristic, complemented
7#22588663C211yesmaximal, characteristic
8#22588658C211yesmaximal, characteristic
9#22588653C211yesmaximal, characteristic, complemented
10#22588648C211yesmaximal, characteristic, complemented
11#22588170C211yesmaximal, characteristic, complemented
12#22588165C211yesmaximal, characteristic, complemented
13C4×#14556052C211yesmaximal, characteristic, complemented
14C4×#14556049C211yesmaximal, characteristic, complemented
15C2×#542×C71C211yesmaximal, characteristic
16C2×#14556087C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18#17986060—24no—
19C2×C4⋊(C71⋊C8)C2211yescharacteristic
20C2×C4⋊(C71⋊C8)C2211yescharacteristic
21C2×#14556052C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556052C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26C2×#14556049C2211yescharacteristic
27C2×#14556049C2211yescharacteristic
28C2×#14556049C2211yescharacteristic
29C2×C22⋊(C71⋊C8)C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×#14556039C2211yescharacteristic
32C2×C4×C71⋊C8C2211yescharacteristic
33C4⋊C4×Dic71—21no—
34C4⋊C4×Dic71—21no—
35C4×C4⋊Dic71C2211yescharacteristic
36C4×C4⋊Dic71C2211yescharacteristic
37C4×C4⋊Dic71C2211yescharacteristic
38C4×C4⋊Dic71C2211yescharacteristic
39C22⋊C4×Dic71—21no—
40C22⋊C4×Dic71—21no—
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
62C23×Dic71—21no—
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C22×C71⋊C8C2311yescharacteristic
67#14556087—22no—
68#14556087—22no—
69C2×C4⋊Dic71—22no—
70C2×C4⋊Dic71—22no—
71C2×C4⋊Dic71—21no—
72C2×C4⋊Dic71C2311yescharacteristic
73C2×C4⋊Dic71C2311yescharacteristic
74C2×C4⋊Dic71C2311yescharacteristic
75C2×C4⋊Dic71C2311yescharacteristic
76C2×C22⋊Dic71—21no—
77C2×C4×Dic71—21no—
78C2×C4×Dic71—21no—
79C2×C4×Dic71—21no—
80C2×C4×Dic71—21no—
81C2×C4×Dic71—21no—
82C4⋊(C71⋊C8)—22no—
83C4⋊(C71⋊C8)—22no—
84#14556052—22no—
85#14556052—22no—
86#14556052—22no—
87#14556052—22no—
88#14556049—22no—
89#14556049—22no—
90#14556049—22no—
91#14556049—22no—
92C22⋊(C71⋊C8)—22no—
93C22⋊(C71⋊C8)—22no—
94#14556039—22no—
95C4×C71⋊C8—22no—
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×C414yescomplemented
108#126×C71—28no—
109#124×C71—28no—
110#124×C71—22no—
111#124×C71C2×C414yescomplemented
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×C414yescomplemented
120C4×D4×C71—22no—
121C4×D4×C71C2×C414yescomplemented
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—
145C22×Dic71—24no—
146C22×Dic71—81no—
147C22×Dic71—81no—
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—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C4⋊Dic71—24no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71#4112yes—
166C4⋊Dic71#4112yes—
167C4⋊Dic71#4112yes—
168C4⋊Dic71#4112yes—
169C22⋊Dic71—24no—
170C4×Dic71—24no—
171C4×Dic71—81no—
172C4×Dic71—81no—
173C4×Dic71—81no—
174C4×Dic71—81no—
175C24×C71—21no—
176C24×C71C2×D411yescharacteristic
177C2×Q8×C71—24no—
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—21no—
182C2×Q8×C71—21no—
183C2×Q8×C71—81no—
184C2×Q8×C71—81no—
185C2×Q8×C71C22×C412yes—
186C2×D4×C71—24no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—21no—
190C2×D4×C71—21no—
191C2×D4×C71—21no—
192C2×D4×C71—81no—
193C2×D4×C71—81no—
194C2×D4×C71C22×C412yes—
195C22×C4×C71—21no—
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—81no—
204C22×C4×C71—81no—
205C22×C4×C71C22×C412yes—
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×D412yes—
212C22×C4×C71C2411yescharacteristic
213C4⋊C4×C71—24no—
214C4⋊C4×C71—24no—
215C4⋊C4×C71—24no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71C22⋊C414yes—
219C4⋊C4×C71C22⋊C414yes—
220C4⋊C4×C71C22×C412yes—
221C4⋊C4×C71C22×C412yes—
222C22⋊C4×C71—24no—
223C22⋊C4×C71—24no—
224C22⋊C4×C71—24no—
225C22⋊C4×C71—24no—
226C22⋊C4×C71—24no—
227C22⋊C4×C71C22⋊C414yes—
228C22⋊C4×C71C22⋊C414yes—
229C42×C71—24no—
230C42×C71C22×C412yes—
231C42×C71C22×C412yes—
232C42×C71C2×D412yes—
233C42×C71C2×D412yes—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—22no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71—41no—
246C23×C71—41no—
247C23×C71C2×C22⋊C412yes—
248C23×C71C22×D411yescharacteristic
249Q8×C71—22no—
250Q8×C71—22no—
251Q8×C71—41no—
252Q8×C71—41no—
253Q8×C71—84no—
254D4×C71—22no—
255D4×C71—22no—
256D4×C71—41no—
257D4×C71—41no—
258D4×C71—84no—
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—21no—
268C2×C4×C71—21no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71—84no—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C2×C22⋊C412yes—
287C2×C4×C71C2×C22⋊C412yes—
288C2×C4×C71C23×C411yescharacteristic
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C2×#4111yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71C2×#4111yescharacteristic
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—41no—
305C2×Dic71—41no—
306C2×Dic71—84no—
307C71⋊C8—41no—
308C71⋊C8—41no—
309C71⋊C8—41no—
310C71⋊C8—41no—
311C22×C71—22no—
312C22×C71—22no—
313C22×C71—22no—
314C22×C71—41no—
315C22×C71—41no—
316C22×C71—41no—
317C22×C71—41no—
318C22×C71—42no—
319C22×C71—42no—
320C22×C71—42no—
321C22×C71—81no—
322C22×C71—81no—
323C22×C71—81no—
324C22×C71—81no—
325C22×C71C22×C22⋊C411yescharacteristic
326C22×C71#52511yescharacteristic
327C22×C71#52511yescharacteristic
328C22×C71#57611yescharacteristic
329C22×C71#57711yescharacteristic
330C22×C71#57711yescharacteristic
331C22×C71#57811yescharacteristic
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—22no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71C4×#4111yescharacteristic
341C4×C71C4×#4111yescharacteristic
342C4×C71#53211yescharacteristic
343C4×C71#53211yescharacteristic
344Dic71—42no—
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348#21397—711nomaximal, Sylow
349C2×C71—42no—
350C2×C71—82no—
351C2×C71#229711yescharacteristic
352C2×C71#289711yescharacteristic
353C2×C71#289811yescharacteristic
354C2×C71#311811yescharacteristic
355C2×C71#312111yescharacteristic
356C2×C71#312411yescharacteristic
357C2×C71#312511yescharacteristic
358C2×#542D7111yescharacteristic
359C2×#433—711no—
360#2274—711no—
361#1988—711no—
362#1987—711no—
363#1983—711no—
364#1983—711no—
365#1875—711no—
366#1874—711no—
367#1873—711no—
368#1872—711no—
369#1763—711no—
370#1762—711no—
371C4×#103—711no—
372C4×#102—711no—
373C71#2139711yescharacteristic, complemented, Sylow
374#542—24no—
375#542Dic7118yescomplemented
376C2×C4⋊Q8C2×D7111yescharacteristic
377C2×#126—21no—
378C2×#124—21no—
379C2×#124C2×D7111yescharacteristic
380C2×#123—21no—
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8C2×D7111yescharacteristic
383C2×#121C2×D7111yescharacteristic
384C2×C4×Q8C2×D7111yescharacteristic
385C2×C4×D4C2×D7111yescharacteristic
386C2×#117—711no—
387C2×#117C2×D7111yescharacteristic
388C22×C4⋊C4—711no—
389#433—1424no—
390C2×C4⋊C8—711no—
391C2×C4⋊C8—711no—
392C2×#103—711no—
393C2×#103—711no—
394C2×#103—711no—
395C2×#103—711no—
396C2×#102—711no—
397C2×#102—711no—
398C2×#102—711no—
399C2×#102—711no—
400C2×C22⋊C8—711no—
401C2×C22⋊C8—711no—
402C2×#97—711no—
403C2×C4×C8—711no—
404C4×C4⋊C4—711no—
405C4×C4⋊C4—711no—
406C4×C4⋊C4—711no—
407C4×C4⋊C4—711no—
408C4×C4⋊C4—1421no—
409C4×C4⋊C4—1421no—
410C4×C22⋊C4—1421no—
411C4×C22⋊C4—1421no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417#340—711no—
418#340—711no—
419#340—711no—
420C22×Q8—21no—
421C22×Q8C22×D7111yescharacteristic
422C22×D4—21no—
423C22×D4C22×D7111yescharacteristic
424C23×C4—21no—
425C23×C4—1421no—
426C23×C4C22×D7111yescharacteristic
427C22×C8—711no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—711no—
431C4⋊Q8—22no—
432C4⋊Q8C2×Dic7114yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×Dic7114yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×Dic7114yes—
441#121—22no—
442#121C2×Dic7114yes—
443C4×Q8—22no—
444C4×Q8C2×Dic7114yescomplemented
445C4×D4—22no—
446C4×D4C2×Dic7114yescomplemented
447#117—1422no—
448#117—1422no—
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—1422no—
459C2×C4⋊C4—1422no—
460C2×C4⋊C4—1421no—
461C2×C4⋊C4C22⋊D7111yescharacteristic
462C2×C4⋊C4C22⋊D7111yescharacteristic
463C2×C4⋊C4C22×D7111yescharacteristic
464C2×C4⋊C4C22×D7111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—1421no—
471C2×C22⋊C4C22⋊D7111yescharacteristic
472C2×C22⋊C4C22⋊D7111yescharacteristic
473C2×C42—21no—
474C2×C42—1421no—
475C2×C42—1421no—
476C2×C42—1421no—
477C2×C42—1421no—
478C2×C42—1421no—
479C2×C42C22×D7111yescharacteristic
480C2×C42C22×D7111yescharacteristic
481C4⋊C8—1422no—
482C4⋊C8—1422no—
483#103—1422no—
484#103—1422no—
485#103—1422no—
486#103—1422no—
487#102—1422no—
488#102—1422no—
489#102—1422no—
490#102—1422no—
491C22⋊C8—1422no—
492C22⋊C8—1422no—
493#97—1422no—
494C4×C8—1422no—
495#95—1421no—
496#95—1421no—
497#95—1421no—
498#95—1421no—
499C24—21no—
500C24C2×C22⋊D7111yescharacteristic
501C2×Q8—21no—
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×Dic7112yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×Dic7112yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—5681no—
530C22×C4—5681no—
531C22×C4—1421no—
532C22×C4—1421no—
533C22×C4—1421no—
534C22×C4—1421no—
535C22×C4—1424no—
536C22×C4C22×Dic7112yes—
537C22×C4C2×C22⋊D7112yes—
538C22×C4C2×C22⋊D7111yescharacteristic
539C22×C4C2×C22⋊D7111yescharacteristic
540C22×C4C2×C22⋊D7111yescharacteristic
541C22×C4C2×C22⋊D7111yescharacteristic
542C22×C4C2×C22⋊D7111yescharacteristic
543C22×C4C23×D7111yescharacteristic
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C2×C8—1421no—
553C2×C8—1421no—
554C2×C8—1421no—
555C2×C8—1421no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—712no—
562C4⋊C4—712no—
563C4⋊C4—712no—
564C4⋊C4—712no—
565C4⋊C4—1424no—
566C4⋊C4—1421no—
567C4⋊C4—1421no—
568C4⋊C4—1421no—
569C4⋊C4—1421no—
570C4⋊C4C22⋊Dic7114yes—
571C4⋊C4C22⋊Dic7114yes—
572C4⋊C4C22×Dic7112yes—
573C4⋊C4C22×Dic7112yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—1424no—
580C22⋊C4C22⋊Dic7114yes—
581C22⋊C4C22⋊Dic7114yes—
582C42—24no—
583C42—5681no—
584C42—5681no—
585C42—5681no—
586C42—5681no—
587C42—1424no—
588C42C22×Dic7112yes—
589C42C22×Dic7112yes—
590C42C2×C22⋊D7112yes—
591C42C2×C22⋊D7112yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic7112yes—
606C23C22×C22⋊D7111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4—2841no—
649C2×C4—5684no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4—1422no—
653C2×C4—1422no—
654C2×C4C2×C22⋊Dic7112yes—
655C2×C4C2×C22⋊Dic7112yes—
656C2×C4C2×C22⋊Dic7112yes—
657C2×C4C2×C22⋊Dic7112yes—
658C2×C4C2×C22⋊Dic7112yes—
659C2×C4C23×Dic7111yescharacteristic
660C2×C4C22×C22⋊D7111yescharacteristic
661C2×C4#41×D7111yescharacteristic
662C2×C4#41×D7111yescharacteristic
663C2×C4#41×D7111yescharacteristic
664C2×C4#41×D7111yescharacteristic
665C8—2841no—
666C8—2841no—
667C8—2841no—
668C8—2841no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic7111yescharacteristic
684C22#1798650611yescharacteristic
685C22#1798650611yescharacteristic
686C22#1798680211yescharacteristic
687C22#1798680711yescharacteristic
688C22#1798681011yescharacteristic
689C22#1798681411yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2842no—
699C4—2842no—
700C4—2842no—
701C4—2842no—
702C4#41×Dic7111yescharacteristic
703C4#41×Dic7111yescharacteristic
704C4#1798654511yescharacteristic
705C4#1798654511yescharacteristic
706C2—42no—
707C2—82no—
708C2#2259083111yescharacteristic
709C2#2259686611yescharacteristic
710C2#2259687311yescharacteristic
711C2#2259851811yescharacteristic
712C2#2259856311yescharacteristic
713C2#2259859611yescharacteristic
714C2#2259861111yescharacteristic
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#21397
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×#17986060C2semidirect
2. #22590696C2semidirect
3. #22589293C2semidirect
4. #22589289C2semidirect
5. #22589273C2semidirect
6. #22589273C2semidirect
9. #22588653C2semidirect
10. #22588648C2semidirect
11. #22588170C2semidirect
12. #22588165C2semidirect
13. C4×#14556052C2semidirect
14. C4×#14556049C2semidirect
50. #542×C71C4semidirect
107. C4⋊Q8×C71C2×C4semidirect
111. #124×C71C2×C4semidirect
119. C4×Q8×C71C2×C4semidirect
121. C4×D4×C71C2×C4semidirect
373. C71#21397semidirect
375. #542Dic71semidirect
432. C4⋊Q8C2×Dic71semidirect
436. #124C2×Dic71semidirect
444. C4×Q8C2×Dic71semidirect
446. C4×D4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860602
#225906962
#225892932
#225892892
#225892732
#225886632
#225886582
#225886532
#225886482
#225881702
#225881652
C4×#145560522
C4×#145560492
C2×#542×C712
#2139771