Finite Group Databasebeta

← #32013755

Subgroups — #32013755

Order 18176.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic, complemented
2#22591269C211yesmaximal, characteristic, complemented
3#22589314C211yesmaximal, characteristic, complemented
4#22589293C211yesmaximal, characteristic, complemented
5#22588779C211yesmaximal, characteristic, complemented
6#22588769C211yesmaximal, characteristic, complemented
7#22588663C211yesmaximal, characteristic, complemented
8#22588658C211yesmaximal, characteristic, complemented
9#22588435C211yesmaximal, characteristic, complemented
10#22588435C211yesmaximal, characteristic, complemented
11#22588350C211yesmaximal, characteristic, complemented
12#22588165C211yesmaximal, characteristic, complemented
13#22588061C211yesmaximal, characteristic, complemented
14#22588056C211yesmaximal, characteristic, complemented
15C2×#555×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20#17986071—24no—
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×#14556049C2211yescharacteristic
23C2×#14556049C2211yescharacteristic
24C2×#14556049C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×#14556039C2211yescharacteristic
29#17985892—21no—
30#17985885—21no—
31#17985879—21no—
32#17985865C2211yescharacteristic
33#17985859C2211yescharacteristic
34#17985859C2211yescharacteristic
35C4×C4⋊Dic71C2211yescharacteristic
36C22⋊C4×Dic71—21no—
37#17985761C2211yescharacteristic
38#17985761C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#555×C71—24no—
50#555×C71C418yescomplemented
51C2×C4⋊Q8×C71C2211yescharacteristic
52C2×#124×C71—21no—
53C2×#124×C71—21no—
54C2×#121×C71—21no—
55C2×#121×C71C2211yescharacteristic
56C2×#121×C71C2211yescharacteristic
57C2×C4×D4×C71C2211yescharacteristic
58C2×C4×D4×C71C2211yescharacteristic
59C2×#117×C71—21no—
60C2×#117×C71C2211yescharacteristic
61C2×#117×C71C2211yescharacteristic
62C23×Dic71—21no—
63C2×#11765849—22no—
64C2×#11765849—22no—
65C2×#11765849—41no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8—41no—
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73#14556087—22no—
74#14556087—41no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—41no—
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C4×Dic71—21no—
86C2×C4×Dic71—21no—
87C4⋊(C71⋊C8)—22no—
88#14556049—22no—
89#14556049—22no—
90#14556049—41no—
91#14556049—41no—
92C22⋊(C71⋊C8)—22no—
93C22⋊(C71⋊C8)—22no—
94#14556039—22no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71—21no—
101C22×D4×C71—21no—
102C22×D4×C71—21no—
103C22×D4×C71D411yescharacteristic
104C22×D4×C71C2311yescharacteristic
105C23×C4×C71—21no—
106C23×C4×C71C2311yescharacteristic
107C23×C4×C71C2311yescharacteristic
108C4⋊Q8×C71—22no—
109C4⋊Q8×C71C2×C414yescomplemented
110#124×C71—28no—
111#124×C71—28no—
112#121×C71—28no—
113#121×C71—22no—
114#121×C71—22no—
115#121×C71C2×C414yes—
116#121×C71C2×C414yescomplemented
117C4×D4×C71—22no—
118C4×D4×C71C2×C414yes—
119C4×D4×C71C2×C414yescomplemented
120C4×D4×C71D414yes—
121#117×C71—22no—
122#117×C71—22no—
123#117×C71—28no—
124#117×C71C2×C414yes—
125#117×C71C2×C414yescomplemented
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71D411yescharacteristic
128C2×C4⋊C4×C71C2311yescharacteristic
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×C71—21no—
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—42no—
146C22×Dic71—42no—
147C22×Dic71—81no—
148#11765849—44no—
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—
160C2×C71⋊C8—44no—
161C2×C71⋊C8#4112yes—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—42no—
170C4⋊Dic71#4112yes—
171C22⋊Dic71—42no—
172C22⋊Dic71—42no—
173C22⋊Dic71—81no—
174C4×Dic71—42no—
175C4×Dic71—81no—
176C24×C71—21no—
177C24×C71C2×D411yescharacteristic
178C24×C71C2×D411yescharacteristic
179C2×Q8×C71—24no—
180C2×Q8×C71—81no—
181C2×Q8×C71—81no—
182C2×D4×C71—24no—
183C2×D4×C71—24no—
184C2×D4×C71—21no—
185C2×D4×C71—21no—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—41no—
190C2×D4×C71—41no—
191C2×D4×C71—81no—
192C2×D4×C71—81no—
193C2×D4×C71—81no—
194C2×D4×C71—81no—
195C2×D4×C71C22⋊C414yes—
196C2×D4×C71C22×C412yes—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—24no—
209C22×C4×C71—42no—
210C22×C4×C71—42no—
211C22×C4×C71C22×C412yes—
212C22×C4×C71C22×C412yes—
213C22×C4×C71C2×D411yescharacteristic
214C22×C4×C71C2×D411yescharacteristic
215C22×C4×C71C2×D411yescharacteristic
216C22×C4×C71C2×D411yescharacteristic
217C22×C4×C71C2×D412yes—
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2411yescharacteristic
220C4⋊C4×C71—24no—
221C4⋊C4×C71—21no—
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71C22⋊C414yes—
225C4⋊C4×C71C22×C412yes—
226C4⋊C4×C71C22×C412yes—
227C4⋊C4×C71C22×C412yes—
228C22⋊C4×C71—24no—
229C22⋊C4×C71—24no—
230C22⋊C4×C71—24no—
231C22⋊C4×C71—24no—
232C22⋊C4×C71—24no—
233C22⋊C4×C71C22⋊C414yes—
234C22⋊C4×C71C22⋊C414yes—
235C42×C71—24no—
236C42×C71—24no—
237C42×C71C22×C412yes—
238C42×C71C2×D412yes—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—22no—
252C23×C71—41no—
253C23×C71—41no—
254C23×C71—41no—
255C23×C71—41no—
256C23×C71—41no—
257C23×C71—41no—
258C23×C71C2×C22⋊C412yes—
259C23×C71C2×C22⋊C412yes—
260C23×C71C22×D411yescharacteristic
261Q8×C71—84no—
262D4×C71—22no—
263D4×C71—22no—
264D4×C71—44no—
265D4×C71—41no—
266D4×C71—41no—
267D4×C71—84no—
268D4×C71—84no—
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—21no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—48no—
289C2×C4×C71—41no—
290C2×C4×C71—41no—
291C2×C4×C71—41no—
292C2×C4×C71—41no—
293C2×C4×C71—41no—
294C2×C4×C71—41no—
295C2×C4×C71C2×C22⋊C412yes—
296C2×C4×C71C2×C22⋊C412yes—
297C2×C4×C71C2×C22⋊C412yes—
298C2×C4×C71C2×C22⋊C412yes—
299C2×C4×C71C23×C411yescharacteristic
300C2×C4×C71C22×D411yescharacteristic
301C2×C4×C71C2×#4111yescharacteristic
302C2×C4×C71C2×#4111yescharacteristic
303C2×C4×C71H(5,𝔽2)11yescharacteristic
304C2×C4×C712−1+411yescharacteristic
305C2×Dic71—22no—
306C2×Dic71—41no—
307C2×Dic71—41no—
308C2×Dic71—41no—
309C2×Dic71—41no—
310C2×Dic71—41no—
311C2×Dic71—41no—
312C2×Dic71—41no—
313C2×Dic71—41no—
314C2×Dic71—41no—
315C2×Dic71—41no—
316C2×Dic71—41no—
317C2×Dic71—84no—
318C71⋊C8—22no—
319C71⋊C8—41no—
320C71⋊C8—41no—
321C71⋊C8—41no—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—22no—
325C22×C71—22no—
326C22×C71—22no—
327C22×C71—22no—
328C22×C71—41no—
329C22×C71—41no—
330C22×C71—41no—
331C22×C71—41no—
332C22×C71—41no—
333C22×C71—41no—
334C22×C71—41no—
335C22×C71—41no—
336C22×C71—42no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—81no—
340C22×C71—81no—
341C22×C71—81no—
342C22×C71—81no—
343C22×C71C22×C22⋊C411yescharacteristic
344C22×C71#54611yescharacteristic
345C22×C71#54711yescharacteristic
346C22×C71#57511yescharacteristic
347C22×C71#57511yescharacteristic
348C22×C71#57611yescharacteristic
349C22×C71#57711yescharacteristic
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71C4×#4111yescharacteristic
358C4×C71#52011yescharacteristic
359C4×C71#54611yescharacteristic
360C4×C71#54711yescharacteristic
361Dic71—42no—
362Dic71—81no—
363Dic71—81no—
364Dic71—81no—
365#22492—711nomaximal, Sylow
366C2×C71—42no—
367C2×C71—42no—
368C2×C71—82no—
369C2×C71#233911yescharacteristic
370C2×C71#289611yescharacteristic
371C2×C71#289711yescharacteristic
372C2×C71#331911yescharacteristic
373C2×C71#332111yescharacteristic
374C2×C71#334711yescharacteristic
375C2×C71#334811yescharacteristic
376C2×#555D7111yescharacteristic
377C2×#435—711no—
378#2352—711no—
379#1993—711no—
380#1988—711no—
381#1895—711no—
382#1893—711no—
383#1875—711no—
384#1874—711no—
385#1825—711no—
386#1825—711no—
387#1804—711no—
388#1762—711no—
389#1736—711no—
390#1735—711no—
391C71#2249211yescharacteristic, complemented, Sylow
392C22×M16—711no—
393C23×C8—711no—
394#555—24no—
395#555Dic7118yescomplemented
396C2×C4⋊Q8C2×D7111yescharacteristic
397C2×#124—21no—
398C2×#124—21no—
399C2×#121—21no—
400C2×#121C2×D7111yescharacteristic
401C2×#121C2×D7111yescharacteristic
402C2×C4×D4C2×D7111yescharacteristic
403C2×C4×D4C2×D7111yescharacteristic
404C2×#117—21no—
405C2×#117—711no—
406C2×#117C2×D7111yescharacteristic
407C2×#117C2×D7111yescharacteristic
408C22×C4⋊C4—711no—
409#435—1424no—
410C2×C4⋊C8—711no—
411C2×#102—711no—
412C2×#102—711no—
413C2×#102—711no—
414C2×#102—711no—
415C2×C22⋊C8—711no—
416C2×C22⋊C8—711no—
417C2×#97—711no—
418#388—1421no—
419#387—1421no—
420#386—1421no—
421#382—711no—
422#380—711no—
423#380—711no—
424C4×C4⋊C4—711no—
425C4×C22⋊C4—1421no—
426#340—711no—
427#340—711no—
428#340—711no—
429#340—711no—
430#340—711no—
431#340—711no—
432#340—711no—
433#340—711no—
434#340—711no—
435#340—711no—
436#340—711no—
437#340—711no—
438C22×Q8—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22⋊D7111yescharacteristic
442C22×D4C22×D7111yescharacteristic
443C23×C4—21no—
444C23×C4—1421no—
445C23×C4C22×D7111yescharacteristic
446C23×C4C22×D7111yescharacteristic
447C2×M16—2841no—
448C2×M16—1422no—
449C2×M16—1422no—
450C22×C8—2841no—
451C22×C8—711no—
452C22×C8—711no—
453C22×C8—711no—
454C22×C8—711no—
455C22×C8—1422no—
456C22×C8—1422no—
457C4⋊Q8—22no—
458C4⋊Q8C2×Dic7114yescomplemented
459#124—28no—
460#124—28no—
461#121—28no—
462#121—22no—
463#121—22no—
464#121C2×Dic7114yes—
465#121C2×Dic7114yescomplemented
466C4×D4—22no—
467C4×D4C2×Dic7114yes—
468C4×D4C2×Dic7114yescomplemented
469C4×D4C22⋊D7114yes—
470#117—22no—
471#117—22no—
472#117—28no—
473#117—2841no—
474#117—1422no—
475#117C2×Dic7114yes—
476#117C2×Dic7114yescomplemented
477C2×C4⋊C4—21no—
478C2×C4⋊C4—2841no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—711no—
481C2×C4⋊C4—711no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1422no—
485C2×C4⋊C4C22⋊D7111yescharacteristic
486C2×C4⋊C4C22×D7111yescharacteristic
487C2×C4⋊C4C22×D7111yescharacteristic
488C2×C4⋊C4C22×D7111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1421no—
495C2×C22⋊C4—1421no—
496C2×C22⋊C4—1421no—
497C2×C22⋊C4C22⋊D7111yescharacteristic
498C2×C22⋊C4C22⋊D7111yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—1421no—
502C2×C42—1421no—
503C2×C42C22×D7111yescharacteristic
504C4⋊C8—1422no—
505#102—2841no—
506#102—2841no—
507#102—1422no—
508#102—1422no—
509C22⋊C8—1422no—
510C22⋊C8—1422no—
511#97—1422no—
512#95—1421no—
513#95—1421no—
514#95—1421no—
515#95—1421no—
516#95—1421no—
517C24—21no—
518C24C2×C22⋊D7111yescharacteristic
519C24C2×C22⋊D7111yescharacteristic
520C2×Q8—24no—
521C2×Q8—81no—
522C2×Q8—81no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4C22⋊Dic7114yes—
537C2×D4C22×Dic7112yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—2842no—
553C22×C4—2842no—
554C22×C4—5681no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1421no—
559C22×C4C22×Dic7112yes—
560C22×C4C22×Dic7112yes—
561C22×C4C2×C22⋊D7112yes—
562C22×C4C2×C22⋊D7112yes—
563C22×C4C2×C22⋊D7111yescharacteristic
564C22×C4C2×C22⋊D7111yescharacteristic
565C22×C4C2×C22⋊D7111yescharacteristic
566C22×C4C2×C22⋊D7111yescharacteristic
567C22×C4C23×D7111yescharacteristic
568M16—2844no—
569C2×C8—2844no—
570C2×C8—712no—
571C2×C8—1421no—
572C2×C8—1421no—
573C2×C8—1421no—
574C2×C8—1421no—
575C2×C8—1421no—
576C2×C8—1421no—
577C2×C8—1421no—
578C2×C8—1421no—
579C2×C8—1421no—
580C2×C8—1421no—
581C2×C8—1421no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—2842no—
587C4⋊C4—712no—
588C4⋊C4—1421no—
589C4⋊C4—1421no—
590C4⋊C4—1421no—
591C4⋊C4—1421no—
592C4⋊C4—1421no—
593C4⋊C4—1421no—
594C4⋊C4—1421no—
595C4⋊C4C22⋊Dic7114yes—
596C4⋊C4C22×Dic7112yes—
597C4⋊C4C22×Dic7112yes—
598C4⋊C4C22×Dic7112yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—2842no—
605C22⋊C4—2842no—
606C22⋊C4—5681no—
607C22⋊C4C22⋊Dic7114yes—
608C22⋊C4C22⋊Dic7114yes—
609C42—24no—
610C42—24no—
611C42—2842no—
612C42—5681no—
613C42C22×Dic7112yes—
614C42C2×C22⋊D7112yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C2×C22⋊Dic7112yes—
635C23C2×C22⋊Dic7112yes—
636C23C22×C22⋊D7111yescharacteristic
637Q8—84no—
638D4—22no—
639D4—22no—
640D4—44no—
641D4—41no—
642D4—41no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—2841no—
672C2×C4—2841no—
673C2×C4—2841no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
678C2×C4—2841no—
679C2×C4—2841no—
680C2×C4—2841no—
681C2×C4—2841no—
682C2×C4—5684no—
683C2×C4—1422no—
684C2×C4C2×C22⋊Dic7112yes—
685C2×C4C2×C22⋊Dic7112yes—
686C2×C4C2×C22⋊Dic7112yes—
687C2×C4C2×C22⋊Dic7112yes—
688C2×C4C23×Dic7111yescharacteristic
689C2×C4C22×C22⋊D7111yescharacteristic
690C2×C4#41×D7111yescharacteristic
691C2×C4#41×D7111yescharacteristic
692C2×C4#1455617411yescharacteristic
693C2×C4#1455617511yescharacteristic
694C8—2841no—
695C8—2841no—
696C8—2841no—
697C8—1422no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C22×C22⋊Dic7111yescharacteristic
720C22#1798663711yescharacteristic
721C22#1798664811yescharacteristic
722C22#1798679711yescharacteristic
723C22#1798679711yescharacteristic
724C22#1798680211yescharacteristic
725C22#1798681011yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—2842no—
734C4—5681no—
735C4—5681no—
736C4—5681no—
737C4#41×Dic7111yescharacteristic
738C4#1798648211yescharacteristic
739C4#1798663711yescharacteristic
740C4#1798664811yescharacteristic
741C2—42no—
742C2—42no—
743C2—82no—
744C2#2259117011yescharacteristic
745C2#2259685911yescharacteristic
746C2#2259686611yescharacteristic
747C2#2260049011yescharacteristic
748C2#2260052011yescharacteristic
749C2#2260084011yescharacteristic
750C2#2260085511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC2×#555×C71C2
socleC23×C71C22×D4
cosocleC22×C4×C71C24
hypercenterC2×#555D71
hypocenterC71#22492
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#17986071C2semidirect
2. #22591269C2semidirect
3. #22589314C2semidirect
4. #22589293C2semidirect
5. #22588779C2semidirect
6. #22588769C2semidirect
7. #22588663C2semidirect
8. #22588658C2semidirect
9. #22588435C2semidirect
10. #22588435C2semidirect
11. #22588350C2semidirect
12. #22588165C2semidirect
13. #22588061C2semidirect
14. #22588056C2semidirect
50. #555×C71C4semidirect
109. C4⋊Q8×C71C2×C4semidirect
116. #121×C71C2×C4semidirect
119. C4×D4×C71C2×C4semidirect
125. #117×C71C2×C4semidirect
391. C71#22492semidirect
395. #555Dic71semidirect
458. C4⋊Q8C2×Dic71semidirect
465. #121C2×Dic71semidirect
468. C4×D4C2×Dic71semidirect
476. #117C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
#225912692
#225893142
#225892932
#225887792
#225887692
#225886632
#225886582
#225884352
#225883502
#225881652
#225880612
#225880562
C2×#555×C712
#2249271