Finite Group Databasebeta

← #32014819

Subgroups — #32014819

Order 18176.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596994C211yesmaximal, characteristic, complemented
2#22596859C211yesmaximal, characteristic
3#22589054C211yesmaximal, characteristic, complemented
4#22589047C211yesmaximal, characteristic, complemented
5#22588985C211yesmaximal, characteristic, complemented
6#22588985C211yesmaximal, characteristic, complemented
7#22588615C211yesmaximal, characteristic, complemented
8#22588615C211yesmaximal, characteristic, complemented
9#22588437C211yesmaximal, characteristic, complemented
10#22588380C211yesmaximal, characteristic, complemented
11#22588284C211yesmaximal, characteristic
12#22588182C211yesmaximal, characteristic, complemented
13#22588175C211yesmaximal, characteristic, complemented
14#22588126C211yesmaximal, characteristic, complemented
15C71×#2880C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C2×#14556087C2211yescharacteristic
18#17986057—21no—
19#17986057—21no—
20#17986053—21no—
21#17986049—21no—
22C2×#14556063C2211yescharacteristic, complemented
23C2×#14556063C2211yescharacteristic, complemented
24#17986025C2211yescharacteristic, complemented
25#17986025C2211yescharacteristic, complemented
26C2×#14556055C2211yescharacteristic
27C2×#14556055C2211yescharacteristic
28C2×#14556055C2211yescharacteristic
29C2×#14556055C2211yescharacteristic
30#17986008C411yescharacteristic, complemented
31#17986008C411yescharacteristic, complemented
32#17986004C411yescharacteristic, complemented
33#17986004C411yescharacteristic, complemented
34#17986000C411yescharacteristic, complemented
35#17986000C411yescharacteristic, complemented
36#17986000C411yescharacteristic, complemented
37#17986000C411yescharacteristic, complemented
38#17985995C2211yescharacteristic
39#17985995C2211yescharacteristic
40#17985995C2211yescharacteristic
41#17985995C2211yescharacteristic
42#17985963C2211yescharacteristic
43#17985954C2211yescharacteristic, complemented
44#17985954C2211yescharacteristic, complemented
45C2×#14556038C2211yescharacteristic, complemented
46C2×C8×Dic71C2211yescharacteristic, complemented
47C4×C22⋊Dic71C2211yescharacteristic
48#17985763C2211yescharacteristic, complemented
49#17985763C2211yescharacteristic, complemented
50#17985760C2211yescharacteristic, complemented
51#17985760C2211yescharacteristic, complemented
52#17985760C2211yescharacteristic, complemented
53#17985760C2211yescharacteristic, complemented
54#17985753C2211yescharacteristic, complemented
55#17985753C2211yescharacteristic, complemented
56C22×#41×C71C2211yescharacteristic
57C2×#131×C71C2211yescharacteristic
58C2×#131×C71C2211yescharacteristic
59#408×C71—21no—
60#408×C71—21no—
61#408×C71C2211yescharacteristic
62#408×C71C2211yescharacteristic
63#407×C71—21no—
64#407×C71C2211yescharacteristic
65C2×C22⋊C8×C71—21no—
66C2×C22⋊C8×C71C2211yescharacteristic
67C2×#11765849—41no—
68C2×#11765849—41no—
69C2×#11765849C2×C411yescharacteristic
70C2×#11765849C2×C411yescharacteristic
71C2×#11765849C2×C411yescharacteristic
72C2×#11765849C2×C411yescharacteristic
73C2×#11765849C2311yescharacteristic
74C2×#11765849C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77#14556087—21no—
78#14556087—21no—
79#14556087C2×C411yescharacteristic
80#14556087C2×C411yescharacteristic
81#14556087C2311yescharacteristic
82#14556087C2311yescharacteristic
83C2×C4⋊Dic71C2×C411yescharacteristic
84C2×C4⋊Dic71C2×C411yescharacteristic
85C2×C22⋊Dic71—21no—
86C2×C22⋊Dic71—21no—
87C2×C4×Dic71—21no—
88C2×C4×Dic71C2311yescharacteristic
89C2×C4×Dic71C2311yescharacteristic
90#14556063—41no—
91#14556063—41no—
92Dic71⋊C8—21no—
93Dic71⋊C8—21no—
94Dic71⋊C8—21no—
95Dic71⋊C8—21no—
96#14556055—22no—
97#14556055—22no—
98#14556055—41no—
99#14556055—41no—
100#14556052C2×C411yescharacteristic
101#14556052C2×C411yescharacteristic
102#14556052C2×C411yescharacteristic
103#14556052C2×C411yescharacteristic
104#14556052C2×C411yescharacteristic
105#14556052C2×C411yescharacteristic
106#14556052C2×C411yescharacteristic
107#14556052C2×C411yescharacteristic
108#14556049C2×C411yescharacteristic
109#14556049C2×C411yescharacteristic
110#14556049C2×C411yescharacteristic
111#14556049C2×C411yescharacteristic
112#14556049C2×C411yescharacteristic
113#14556049C2×C411yescharacteristic
114#14556049C2×C411yescharacteristic
115#14556049C2×C411yescharacteristic
116C22⋊(C71⋊C8)—21no—
117C22⋊(C71⋊C8)—21no—
118#14556038—21no—
119#14556038—21no—
120#14556038—41no—
121C8×Dic71—21no—
122C8×Dic71—21no—
123C8×Dic71—41no—
124C71⋊#95—21no—
125C2×#41×C71—21no—
126C2×#41×C71—21no—
127C2×#41×C71—22no—
128C2×#41×C71—22no—
129C2×#41×C71—41no—
130C2×#41×C71—41no—
131C2×#41×C71C2×C411yescharacteristic
132C2×#41×C71C2×C411yescharacteristic
133C2×#41×C71C2311yescharacteristic
134C2×#41×C71C2311yescharacteristic
135C22×Q8×C71C2×C411yescharacteristic
136C22×D4×C71—21no—
137C22×D4×C71C2×C411yescharacteristic
138C23×C4×C71—21no—
139C23×C4×C71C2311yescharacteristic
140#131×C71—22no—
141#131×C71—22no—
142#131×C71—41no—
143#131×C71—41no—
144C2×M16×C71—21no—
145C2×M16×C71—21no—
146C2×M16×C71C2311yescharacteristic
147C2×M16×C71C2311yescharacteristic
148C22×C8×C71—21no—
149C22×C8×C71—21no—
150C22×C8×C71C2311yescharacteristic
151C22×C8×C71C2311yescharacteristic
152C22⋊C8×C71—21no—
153C22⋊C8×C71—21no—
154C22⋊C8×C71—21no—
155C22⋊C8×C71—21no—
156C22⋊C8×C71—21no—
157C22⋊C8×C71—21no—
158C22⋊C8×C71D411yescharacteristic
159C22⋊C8×C71D411yescharacteristic
160C22⋊C8×C71D411yescharacteristic
161C22⋊C8×C71D411yescharacteristic
162C22×Dic71—21no—
163C22×Dic71—21no—
164C22×Dic71—21no—
165C22×Dic71—21no—
166#11765849—21no—
167#11765849—21no—
168#11765849—21no—
169#11765849—21no—
170#11765849—41no—
171#11765849—41no—
172#11765849—41no—
173#11765849—41no—
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8C22×C411yescharacteristic
181C2×C71⋊C8C22×C411yescharacteristic
182C2×C71⋊C8C22×C411yescharacteristic
183C2×C71⋊C8C22×C411yescharacteristic
184C4⋊Dic71—21no—
185C4⋊Dic71—21no—
186C4⋊Dic71C22×C411yescharacteristic
187C4⋊Dic71C22×C411yescharacteristic
188C4⋊Dic71C22×C411yescharacteristic
189C4⋊Dic71C22×C411yescharacteristic
190C22⋊Dic71—21no—
191C22⋊Dic71—21no—
192C22⋊Dic71—21no—
193C22⋊Dic71—21no—
194C22⋊Dic71—42no—
195C4×Dic71—21no—
196C4×Dic71—21no—
197C4×Dic71—21no—
198C4×Dic71—21no—
199C4×Dic71—21no—
200C4×Dic71—21no—
201C4×Dic71—21no—
202C4×Dic71—21no—
203C24×C71—21no—
204C24×C71#4111yescharacteristic
205#41×C71—21no—
206#41×C71—21no—
207#41×C71—22no—
208#41×C71—22no—
209#41×C71—21no—
210#41×C71—21no—
211#41×C71—21no—
212#41×C71—21no—
213#41×C71—42no—
214#41×C71—42no—
215#41×C71—41no—
216#41×C71—41no—
217#41×C71—42no—
218#41×C71—42no—
219#41×C71#4112yes—
220#41×C71#4112yes—
221C2×Q8×C71—21no—
222C2×Q8×C71—22no—
223C2×Q8×C71—41no—
224C2×Q8×C71C22×C411yescharacteristic
225C2×Q8×C71C22×C411yescharacteristic
226C2×D4×C71—21no—
227C2×D4×C71—22no—
228C2×D4×C71—21no—
229C2×D4×C71—21no—
230C2×D4×C71—21no—
231C2×D4×C71—21no—
232C2×D4×C71—41no—
233C2×D4×C71—42no—
234C2×D4×C71—42no—
235C2×D4×C71C22×C411yescharacteristic
236C2×D4×C71C22×C411yescharacteristic
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—42no—
247C22×C4×C71—42no—
248C22×C4×C71C22×C411yescharacteristic
249C22×C4×C71C22×C411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71#4111yescharacteristic
253C22×C4×C71C2411yescharacteristic
254M16×C71—21no—
255M16×C71—21no—
256M16×C71—21no—
257M16×C71—21no—
258M16×C71—42no—
259M16×C71—42no—
260C2×C8×C71—21no—
261C2×C8×C71—21no—
262C2×C8×C71—21no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
266C2×C8×C71—42no—
267C2×C8×C71—42no—
268C2×C8×C71C2×D411yescharacteristic
269C2×C8×C71C2×D411yescharacteristic
270C2×C8×C71C2×D411yescharacteristic
271C2×C8×C71C2×D411yescharacteristic
272C23×C71—21no—
273C23×C71—21no—
274C23×C71—21no—
275C23×C71—21no—
276C23×C71—41no—
277C23×C71—41no—
278C23×C71—42no—
279C23×C71—42no—
280C23×C71—81no—
281C23×C71C4×D411yescharacteristic
282C23×C71C4×D411yescharacteristic
283C23×C71C2×#4111yescharacteristic
284Q8×C71—21no—
285Q8×C71—21no—
286Q8×C71—21no—
287Q8×C71—42no—
288Q8×C71#11712yes—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—21no—
292D4×C71—21no—
293D4×C71—21no—
294D4×C71—42no—
295D4×C71—42no—
296D4×C71—42no—
297D4×C71—41no—
298D4×C71—41no—
299D4×C71#11712yes—
300C2×C4×C71—21no—
301C2×C4×C71—21no—
302C2×C4×C71—21no—
303C2×C4×C71—21no—
304C2×C4×C71—21no—
305C2×C4×C71—21no—
306C2×C4×C71—21no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—21no—
310C2×C4×C71—21no—
311C2×C4×C71—21no—
312C2×C4×C71—21no—
313C2×C4×C71—21no—
314C2×C4×C71—42no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71—41no—
318C2×C4×C71—41no—
319C2×C4×C71C4×D411yescharacteristic
320C2×C4×C71C4×D411yescharacteristic
321C2×C4×C71C23×C411yescharacteristic
322C2×C4×C71C22×D411yescharacteristic
323C2×C4×C71C2×#4111yescharacteristic
324C2×C4×C71C2×#4111yescharacteristic
325C2×C4×C71H(5,𝔽2)11yescharacteristic
326C2×C4×C71H(5,𝔽2)11yescharacteristic
327C2×Dic71—22no—
328C2×Dic71—21no—
329C2×Dic71—21no—
330C2×Dic71—21no—
331C2×Dic71—21no—
332C2×Dic71—41no—
333C2×Dic71—42no—
334C2×Dic71—41no—
335C2×Dic71—41no—
336C2×Dic71—41no—
337C2×Dic71—41no—
338C2×Dic71—81no—
339C8×C71—21no—
340C8×C71—21no—
341C8×C71—21no—
342C8×C71—21no—
343C8×C71—41no—
344C8×C71—41no—
345C71⋊C8—21no—
346C71⋊C8—21no—
347C71⋊C8—21no—
348C71⋊C8—21no—
349C71⋊C8—41no—
350C71⋊C8—41no—
351C22×C71—21no—
352C22×C71—21no—
353C22×C71—21no—
354C22×C71—21no—
355C22×C71—22no—
356C22×C71—21no—
357C22×C71—21no—
358C22×C71—21no—
359C22×C71—21no—
360C22×C71—41no—
361C22×C71—41no—
362C22×C71—41no—
363C22×C71—41no—
364C22×C71—41no—
365C22×C71—81no—
366C22×C71—81no—
367C22×C71—84no—
368C22×C71C2×C4×D411yescharacteristic
369C22×C71#55111yescharacteristic
370C22×C71#55111yescharacteristic
371C4×C71—21no—
372C4×C71—21no—
373C4×C71—22no—
374C4×C71—41no—
375C4×C71C2×#11711yescharacteristic
376C4×C71#51811yescharacteristic
377C4×C71#54611yescharacteristic
378C4×C71#54611yescharacteristic
379Dic71—42no—
380Dic71—41no—
381Dic71—41no—
382Dic71—41no—
383Dic71—41no—
384Dic71—81no—
385#22588—711nomaximal, Sylow
386C2×C71—21no—
387C2×C71—21no—
388C2×C71—41no—
389C2×C71—41no—
390C2×C71—42no—
391C2×C71—81no—
392C2×C71#234211yescharacteristic
393C2×C71#295511yescharacteristic
394C2×C71#295611yescharacteristic
395#2924—711no—
396#2896—711no—
397#2880D7111yescharacteristic
398#1938—711no—
399#1937—711no—
400#1929—711no—
401#1929—711no—
402#1866—711no—
403#1866—711no—
404#1826—711no—
405#1811—711no—
406#1789—711no—
407#1765—711no—
408#1764—711no—
409#1753—711no—
410C71#2258811yescharacteristic, complemented, Sylow
411C22×#41C2×D7111yescharacteristic
412C2×#131C2×D7111yescharacteristic
413C2×#131C2×D7111yescharacteristic
414C22×M16—711no—
415C2×#117—711no—
416#433—1421no—
417#433—1421no—
418#432—1421no—
419#431—1421no—
420C2×#108—711no—
421C2×#108—711no—
422#424—711no—
423#424—711no—
424C2×#104—711no—
425C2×#104—711no—
426C2×#104—711no—
427C2×#104—711no—
428#419—711no—
429#419—711no—
430#418—711no—
431#418—711no—
432#417—711no—
433#417—711no—
434#417—711no—
435#417—711no—
436#416—711no—
437#416—711no—
438#416—711no—
439#416—711no—
440#408—21no—
441#408—21no—
442#408C2×D7111yescharacteristic
443#408C2×D7111yescharacteristic
444#407—21no—
445#407—711no—
446#407C2×D7111yescharacteristic
447C2×C22⋊C8—21no—
448C2×C22⋊C8C2×D7111yescharacteristic
449#405—711no—
450#405—711no—
451C2×#97—711no—
452C2×C4×C8—711no—
453C4×C22⋊C4—711no—
454#341—711no—
455#341—711no—
456#339—711no—
457#339—711no—
458#339—711no—
459#339—711no—
460#336—711no—
461#336—711no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C4×D7111yescharacteristic
469C2×#41C4×D7111yescharacteristic
470C2×#41C22×D7111yescharacteristic
471C2×#41C22×D7111yescharacteristic
472C22×Q8C4×D7111yescharacteristic
473C22×D4—21no—
474C22×D4C4×D7111yescharacteristic
475C23×C4—21no—
476C23×C4C22×D7111yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—2841no—
484C2×M16—2841no—
485C2×M16—711no—
486C2×M16—711no—
487C2×M16—711no—
488C2×M16—711no—
489C2×M16—711no—
490C2×M16—711no—
491C2×M16C22×D7111yescharacteristic
492C2×M16C22×D7111yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—711no—
496C22×C8—711no—
497C22×C8C22×D7111yescharacteristic
498C22×C8C22×D7111yescharacteristic
499#117—711no—
500#117—711no—
501#117—711no—
502#117—711no—
503#117—1421no—
504#117—1421no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—711no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C42—711no—
510C2×C42—711no—
511C2×C42—1421no—
512#108—2841no—
513#108—2841no—
514C4⋊C8—1421no—
515C4⋊C8—1421no—
516C4⋊C8—1421no—
517C4⋊C8—1421no—
518#104—2841no—
519#104—2841no—
520#104—1422no—
521#104—1422no—
522#103—711no—
523#103—711no—
524#103—711no—
525#103—711no—
526#103—711no—
527#103—711no—
528#103—711no—
529#103—711no—
530#102—711no—
531#102—711no—
532#102—711no—
533#102—711no—
534#102—711no—
535#102—711no—
536#102—711no—
537#102—711no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—1421no—
545C22⋊C8—1421no—
546C22⋊C8C22⋊D7111yescharacteristic
547C22⋊C8C22⋊D7111yescharacteristic
548C22⋊C8C22⋊D7111yescharacteristic
549C22⋊C8C22⋊D7111yescharacteristic
550#97—2841no—
551#97—1421no—
552#97—1421no—
553C4×C8—2841no—
554C4×C8—1421no—
555C4×C8—1421no—
556#95—1421no—
557C24—21no—
558C24#1176586511yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#1176586412yes—
574#41#1176586412yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C2×C4×D7111yescharacteristic
579C2×Q8C2×C4×D7111yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C2×C4×D7111yescharacteristic
590C2×D4C2×C4×D7111yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—1421no—
603C22×C4—1421no—
604C22×C4—1421no—
605C22×C4—1421no—
606C22×C4C2×C4×D7111yescharacteristic
607C22×C4C2×C4×D7111yescharacteristic
608C22×C4C2×C22⋊D7111yescharacteristic
609C22×C4C2×C22⋊D7111yescharacteristic
610C22×C4#1176586511yescharacteristic
611C22×C4C23×D7111yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—42no—
618M16—2841no—
619M16—2841no—
620M16—2841no—
621M16—2841no—
622M16—1421no—
623M16—1421no—
624M16—1421no—
625M16—1421no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—42no—
633C2×C8—42no—
634C2×C8—711no—
635C2×C8—711no—
636C2×C8—711no—
637C2×C8—711no—
638C2×C8—1421no—
639C2×C8—1421no—
640C2×C8—1421no—
641C2×C8—1421no—
642C2×C8—1421no—
643C2×C8—1421no—
644C2×C8C2×C22⋊D7111yescharacteristic
645C2×C8C2×C22⋊D7111yescharacteristic
646C2×C8C2×C22⋊D7111yescharacteristic
647C2×C8C2×C22⋊D7111yescharacteristic
648C4⋊C4—711no—
649C4⋊C4—711no—
650C4⋊C4—711no—
651C4⋊C4—711no—
652C4⋊C4—1421no—
653C4⋊C4—1421no—
654C22⋊C4—2842no—
655C22⋊C4—1421no—
656C22⋊C4—1421no—
657C22⋊C4—1421no—
658C22⋊C4—1421no—
659C42—1421no—
660C42—1421no—
661C42—1421no—
662C42—1421no—
663C42—1421no—
664C42—1421no—
665C42—1421no—
666C42—1421no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×C22⋊D7111yescharacteristic
677C23C4×C22⋊D7111yescharacteristic
678C23C2×#1176586511yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1455608412yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1455608412yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—2841no—
715C2×C4—2842no—
716C2×C4—2841no—
717C2×C4—2841no—
718C2×C4—2841no—
719C2×C4—2841no—
720C2×C4—5681no—
721C2×C4—1422no—
722C2×C4—1421no—
723C2×C4—1421no—
724C2×C4—1421no—
725C2×C4—1421no—
726C2×C4C4×C22⋊D7111yescharacteristic
727C2×C4C4×C22⋊D7111yescharacteristic
728C2×C4C22×C4×D7111yescharacteristic
729C2×C4C22×C22⋊D7111yescharacteristic
730C2×C4C2×#1176586411yescharacteristic
731C2×C4C2×#1176586411yescharacteristic
732C2×C4#1455617311yescharacteristic
733C2×C4#1455617311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—2841no—
741C8—2841no—
742C8—1421no—
743C8—1421no—
744C8—1421no—
745C8—1421no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×C22⋊D7111yescharacteristic
764C22#1798667511yescharacteristic
765C22#1798667511yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—2842no—
771C4—2841no—
772C4—2841no—
773C4—2841no—
774C4—2841no—
775C4—5681no—
776C4C2×#1455608411yescharacteristic
777C4#1798647211yescharacteristic
778C4#1798664311yescharacteristic
779C4#1798664311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2259118511yescharacteristic
787C2#2259724111yescharacteristic
788C2#2259724711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2880C2
socleC22×C71C2×C4×D4
prime radicalC22×#41×C71C22
cosocleC22×C4×C71C24
hypercenter#2880D71
hypocenterC71#22588
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. #22596994C2semidirect
3. #22589054C2semidirect
4. #22589047C2semidirect
5. #22588985C2semidirect
6. #22588985C2semidirect
7. #22588615C2semidirect
8. #22588615C2semidirect
9. #22588437C2semidirect
10. #22588380C2semidirect
12. #22588182C2semidirect
13. #22588175C2semidirect
14. #22588126C2semidirect
22. C2×#14556063C22semidirect
23. C2×#14556063C22semidirect
24. #17986025C22semidirect
25. #17986025C22semidirect
30. #17986008C4semidirect
31. #17986008C4semidirect
32. #17986004C4semidirect
33. #17986004C4semidirect
34. #17986000C4semidirect
35. #17986000C4semidirect
36. #17986000C4semidirect
37. #17986000C4semidirect
43. #17985954C22semidirect
44. #17985954C22semidirect
45. C2×#14556038C22semidirect
46. C2×C8×Dic71C22semidirect
48. #17985763C22semidirect
49. #17985763C22semidirect
50. #17985760C22semidirect
51. #17985760C22semidirect
52. #17985760C22semidirect
53. #17985760C22semidirect
54. #17985753C22semidirect
55. #17985753C22semidirect
410. C71#22588semidirect

Maximal subgroups

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

subgroupindex
#225969942
#225968592
#225890542
#225890472
#225889852
#225886152
#225884372
#225883802
#225882842
#225881822
#225881752
#225881262
C71×#28802
#2258871