Finite Group Databasebeta

← #32014823

Subgroups — #32014823

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#22596998C211yesmaximal, characteristic, complemented
2#22596789C211yesmaximal, characteristic
3#22589053C211yesmaximal, characteristic, complemented
4#22589046C211yesmaximal, characteristic, complemented
5#22588990C211yesmaximal, characteristic, complemented
6#22588990C211yesmaximal, characteristic, complemented
7#22588617C211yesmaximal, characteristic, complemented
8#22588617C211yesmaximal, characteristic, complemented
9#22588439C211yesmaximal, characteristic, complemented
10#22588382C211yesmaximal, characteristic, complemented
11#22588284C211yesmaximal, characteristic
12#22588187C211yesmaximal, characteristic, complemented
13#22588180C211yesmaximal, characteristic, complemented
14#22588121C211yesmaximal, characteristic, complemented
15C71×#2896C211yesmaximal, characteristic
16C2×#14556135C2211yescharacteristic
17C2×#14556135C2211yescharacteristic
18#17986060—21no—
19#17986060—21no—
20#17986056—21no—
21#17986052—21no—
22C2×#14556064C2211yescharacteristic, complemented
23C2×#14556064C2211yescharacteristic, complemented
24#17986026C2211yescharacteristic, complemented
25#17986026C2211yescharacteristic, complemented
26C2×#14556055C2211yescharacteristic
27C2×#14556055C2211yescharacteristic
28C2×#14556055C2211yescharacteristic
29C2×#14556055C2211yescharacteristic
30#17985966—21no—
31#17985966—21no—
32#17985966C2211yescharacteristic
33#17985966C2211yescharacteristic
34#17985963—21no—
35#17985963C2211yescharacteristic
36#17985963C2211yescharacteristic
37C2×C22⋊(C71⋊C8)—21no—
38C2×C22⋊(C71⋊C8)C2211yescharacteristic
39#17985955C2211yescharacteristic, complemented
40#17985955C2211yescharacteristic, complemented
41C2×#14556038C2211yescharacteristic, complemented
42C2×C8×Dic71C2211yescharacteristic, complemented
43C4×C22⋊Dic71C2211yescharacteristic
44#17985764C2211yescharacteristic, complemented
45#17985764C2211yescharacteristic, complemented
46#17985758C2211yescharacteristic, complemented
47#17985758C2211yescharacteristic, complemented
48#17985758C2211yescharacteristic, complemented
49#17985758C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52C22×#41×C71C2211yescharacteristic
53C22×M16×C71C2211yescharacteristic
54C2×#117×C71C2211yescharacteristic
55#419×C71C411yescharacteristic, complemented
56#419×C71C411yescharacteristic, complemented
57#418×C71C411yescharacteristic, complemented
58#418×C71C411yescharacteristic, complemented
59#417×C71C411yescharacteristic, complemented
60#417×C71C411yescharacteristic, complemented
61#417×C71C411yescharacteristic, complemented
62#417×C71C411yescharacteristic, complemented
63#416×C71C2211yescharacteristic
64#416×C71C2211yescharacteristic
65#416×C71C2211yescharacteristic
66#416×C71C2211yescharacteristic
67#14556135—22no—
68#14556135—22no—
69#14556135—41no—
70#14556135—41no—
71C2×#11765849—21no—
72C2×#11765849—21no—
73C2×#11765849C2311yescharacteristic
74C2×#11765849C2311yescharacteristic
75C2×#11765849C2311yescharacteristic
76C2×#11765849C2311yescharacteristic
77C22×C71⋊C8—21no—
78C22×C71⋊C8—21no—
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C2×C22⋊Dic71—21no—
82C2×C4×Dic71C2311yescharacteristic
83C2×C4×Dic71C2311yescharacteristic
84#14556064—41no—
85#14556064—41no—
86C4⋊(C71⋊C8)—21no—
87C4⋊(C71⋊C8)—21no—
88C4⋊(C71⋊C8)—21no—
89C4⋊(C71⋊C8)—21no—
90#14556055—22no—
91#14556055—22no—
92#14556055—41no—
93#14556055—41no—
94C22⋊(C71⋊C8)—21no—
95C22⋊(C71⋊C8)—21no—
96C22⋊(C71⋊C8)—21no—
97C22⋊(C71⋊C8)—21no—
98C22⋊(C71⋊C8)—21no—
99C22⋊(C71⋊C8)—21no—
100C22⋊(C71⋊C8)—21no—
101C22⋊(C71⋊C8)—21no—
102C22⋊(C71⋊C8)D411yescharacteristic
103C22⋊(C71⋊C8)D411yescharacteristic
104C22⋊(C71⋊C8)D411yescharacteristic
105C22⋊(C71⋊C8)D411yescharacteristic
106#14556039—21no—
107#14556039—21no—
108#14556038—41no—
109C4×C71⋊C8—21no—
110C4×C71⋊C8—21no—
111C8×Dic71—41no—
112C71⋊#95—21no—
113C2×#41×C71—21no—
114C2×#41×C71—21no—
115C2×#41×C71—22no—
116C2×#41×C71—22no—
117C2×#41×C71—41no—
118C2×#41×C71—41no—
119C2×#41×C71C2×C411yescharacteristic
120C2×#41×C71C2×C411yescharacteristic
121C2×#41×C71C2311yescharacteristic
122C2×#41×C71C2311yescharacteristic
123C22×Q8×C71C2×C411yescharacteristic
124C22×D4×C71—21no—
125C22×D4×C71C2×C411yescharacteristic
126C23×C4×C71—21no—
127C23×C4×C71C2311yescharacteristic
128C2×M16×C71—41no—
129C2×M16×C71—41no—
130C2×M16×C71C2×C411yescharacteristic
131C2×M16×C71C2×C411yescharacteristic
132C2×M16×C71C2×C411yescharacteristic
133C2×M16×C71C2×C411yescharacteristic
134C22×C8×C71C2311yescharacteristic
135C22×C8×C71C2311yescharacteristic
136#117×C71—21no—
137#117×C71—21no—
138#117×C71C2×C411yescharacteristic
139#117×C71C2×C411yescharacteristic
140#117×C71C2311yescharacteristic
141#117×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2×C411yescharacteristic
143C2×C4⋊C4×C71C2×C411yescharacteristic
144C2×C22⋊C4×C71—21no—
145C2×C42×C71—21no—
146#103×C71C2×C411yescharacteristic
147#103×C71C2×C411yescharacteristic
148#103×C71C2×C411yescharacteristic
149#103×C71C2×C411yescharacteristic
150#103×C71C2×C411yescharacteristic
151#103×C71C2×C411yescharacteristic
152#103×C71C2×C411yescharacteristic
153#103×C71C2×C411yescharacteristic
154#102×C71C2×C411yescharacteristic
155#102×C71C2×C411yescharacteristic
156#102×C71C2×C411yescharacteristic
157#102×C71C2×C411yescharacteristic
158#102×C71C2×C411yescharacteristic
159#102×C71C2×C411yescharacteristic
160#102×C71C2×C411yescharacteristic
161#102×C71C2×C411yescharacteristic
162C22×Dic71—21no—
163C22×Dic71—21no—
164#11765849—21no—
165#11765849—21no—
166#11765849—21no—
167#11765849—21no—
168#11765849—21no—
169#11765849—21no—
170#11765849—21no—
171#11765849—21no—
172#11765849—42no—
173#11765849—42no—
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⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—42no—
183C2×C71⋊C8—42no—
184C2×C71⋊C8C2×D411yescharacteristic
185C2×C71⋊C8C2×D411yescharacteristic
186C2×C71⋊C8C2×D411yescharacteristic
187C2×C71⋊C8C2×D411yescharacteristic
188C22⋊Dic71—42no—
189C4×Dic71—21no—
190C4×Dic71—21no—
191C4×Dic71—21no—
192C4×Dic71—21no—
193C24×C71—21no—
194C24×C71#4111yescharacteristic
195#41×C71—21no—
196#41×C71—21no—
197#41×C71—22no—
198#41×C71—22no—
199#41×C71—21no—
200#41×C71—21no—
201#41×C71—21no—
202#41×C71—21no—
203#41×C71—42no—
204#41×C71—42no—
205#41×C71—41no—
206#41×C71—41no—
207#41×C71—42no—
208#41×C71—42no—
209#41×C71#4112yes—
210#41×C71#4112yes—
211C2×Q8×C71—21no—
212C2×Q8×C71—22no—
213C2×Q8×C71—41no—
214C2×Q8×C71C22×C411yescharacteristic
215C2×Q8×C71C22×C411yescharacteristic
216C2×D4×C71—21no—
217C2×D4×C71—22no—
218C2×D4×C71—21no—
219C2×D4×C71—21no—
220C2×D4×C71—21no—
221C2×D4×C71—21no—
222C2×D4×C71—41no—
223C2×D4×C71—42no—
224C2×D4×C71—42no—
225C2×D4×C71C22×C411yescharacteristic
226C2×D4×C71C22×C411yescharacteristic
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—42no—
239C22×C4×C71—42no—
240C22×C4×C71C22×C411yescharacteristic
241C22×C4×C71C22×C411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71#4111yescharacteristic
245C22×C4×C71C2411yescharacteristic
246M16×C71—41no—
247M16×C71—41no—
248M16×C71—41no—
249M16×C71—41no—
250C2×C8×C71—21no—
251C2×C8×C71—21no—
252C2×C8×C71—21no—
253C2×C8×C71—21no—
254C2×C8×C71C22×C411yescharacteristic
255C2×C8×C71C22×C411yescharacteristic
256C2×C8×C71C22×C411yescharacteristic
257C2×C8×C71C22×C411yescharacteristic
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71C22×C411yescharacteristic
261C4⋊C4×C71C22×C411yescharacteristic
262C4⋊C4×C71C22×C411yescharacteristic
263C4⋊C4×C71C22×C411yescharacteristic
264C22⋊C4×C71—21no—
265C22⋊C4×C71—21no—
266C22⋊C4×C71—21no—
267C22⋊C4×C71—21no—
268C42×C71—21no—
269C42×C71—21no—
270C42×C71—21no—
271C42×C71—21no—
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—21no—
308C2×C4×C71—21no—
309C2×C4×C71—21no—
310C2×C4×C71—21no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—21no—
314C2×C4×C71—21no—
315C2×C4×C71—21no—
316C2×C4×C71—21no—
317C2×C4×C71—21no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—41no—
323C2×C4×C71—41no—
324C2×C4×C71—81no—
325C2×C4×C71C4×D411yescharacteristic
326C2×C4×C71C4×D411yescharacteristic
327C2×C4×C71C23×C411yescharacteristic
328C2×C4×C71C22×D411yescharacteristic
329C2×C4×C71C2×#4111yescharacteristic
330C2×C4×C71C2×#4111yescharacteristic
331C2×C4×C71H(5,𝔽2)11yescharacteristic
332C2×C4×C71H(5,𝔽2)11yescharacteristic
333C2×Dic71—22no—
334C2×Dic71—41no—
335C2×Dic71—41no—
336C2×Dic71—41no—
337C2×Dic71—41no—
338C2×Dic71—41no—
339C8×C71—21no—
340C8×C71—21no—
341C8×C71—21no—
342C8×C71—21no—
343C71⋊C8—21no—
344C71⋊C8—21no—
345C71⋊C8—21no—
346C71⋊C8—21no—
347C71⋊C8—41no—
348C71⋊C8—41no—
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×C71—41no—
376C4×C71—41no—
377C4×C71—41no—
378C4×C71—41no—
379C4×C71C2×#11711yescharacteristic
380C4×C71#51811yescharacteristic
381C4×C71#54611yescharacteristic
382C4×C71#54611yescharacteristic
383Dic71—42no—
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#2896D7111yescharacteristic
397#2880—711no—
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×#131—711no—
413C2×#131—711no—
414C22×M16C2×D7111yescharacteristic
415C2×#117C2×D7111yescharacteristic
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#419Dic7111yescharacteristic, complemented
429#419Dic7111yescharacteristic, complemented
430#418Dic7111yescharacteristic, complemented
431#418Dic7111yescharacteristic, complemented
432#417Dic7111yescharacteristic, complemented
433#417Dic7111yescharacteristic, complemented
434#417Dic7111yescharacteristic, complemented
435#417Dic7111yescharacteristic, complemented
436#416C2×D7111yescharacteristic
437#416C2×D7111yescharacteristic
438#416C2×D7111yescharacteristic
439#416C2×D7111yescharacteristic
440#408—711no—
441#408—711no—
442#408—1421no—
443#408—1421no—
444#407—711no—
445#407—711no—
446#407—1421no—
447C2×C22⋊C8—711no—
448C2×C22⋊C8—1421no—
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×#41C2×Dic7111yescharacteristic
469C2×#41C2×Dic7111yescharacteristic
470C2×#41C22×D7111yescharacteristic
471C2×#41C22×D7111yescharacteristic
472C22×Q8C2×Dic7111yescharacteristic
473C22×D4—21no—
474C22×D4C2×Dic7111yescharacteristic
475C23×C4—21no—
476C23×C4C22×D7111yescharacteristic
477#131—2841no—
478#131—2841no—
479#131—1422no—
480#131—1422no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—711no—
484C2×M16—711no—
485C2×M16—711no—
486C2×M16—711no—
487C2×M16—1421no—
488C2×M16—1421no—
489C2×M16C2×Dic7111yescharacteristic
490C2×M16C2×Dic7111yescharacteristic
491C2×M16C2×Dic7111yescharacteristic
492C2×M16C2×Dic7111yescharacteristic
493C22×C8—711no—
494C22×C8—711no—
495C22×C8—1421no—
496C22×C8—1421no—
497C22×C8C22×D7111yescharacteristic
498C22×C8C22×D7111yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×Dic7111yescharacteristic
502#117C2×Dic7111yescharacteristic
503#117C22×D7111yescharacteristic
504#117C22×D7111yescharacteristic
505C2×C4⋊C4C2×Dic7111yescharacteristic
506C2×C4⋊C4C2×Dic7111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1421no—
509C2×C42—21no—
510C2×C42—711no—
511C2×C42—711no—
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#103C2×Dic7111yescharacteristic
523#103C2×Dic7111yescharacteristic
524#103C2×Dic7111yescharacteristic
525#103C2×Dic7111yescharacteristic
526#103C2×Dic7111yescharacteristic
527#103C2×Dic7111yescharacteristic
528#103C2×Dic7111yescharacteristic
529#103C2×Dic7111yescharacteristic
530#102C2×Dic7111yescharacteristic
531#102C2×Dic7111yescharacteristic
532#102C2×Dic7111yescharacteristic
533#102C2×Dic7111yescharacteristic
534#102C2×Dic7111yescharacteristic
535#102C2×Dic7111yescharacteristic
536#102C2×Dic7111yescharacteristic
537#102C2×Dic7111yescharacteristic
538C22⋊C8—711no—
539C22⋊C8—711no—
540C22⋊C8—711no—
541C22⋊C8—711no—
542C22⋊C8—1421no—
543C22⋊C8—1421no—
544C22⋊C8—1421no—
545C22⋊C8—1421no—
546C22⋊C8—1421no—
547C22⋊C8—1421no—
548C22⋊C8—1421no—
549C22⋊C8—1421no—
550#97—2841no—
551#97—1421no—
552#97—1421no—
553C4×C8—2841no—
554C4×C8—1421no—
555C4×C8—1421no—
556#95—1421no—
557C24—21no—
558C24#1176586411yescharacteristic
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#1176586512yes—
574#41#1176586512yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×Dic7111yescharacteristic
579C2×Q8C22×Dic7111yescharacteristic
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×D4C22×Dic7111yescharacteristic
590C2×D4C22×Dic7111yescharacteristic
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—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—1421no—
605C22×C4—1421no—
606C22×C4C22×Dic7111yescharacteristic
607C22×C4C22×Dic7111yescharacteristic
608C22×C4D4×D7111yescharacteristic
609C22×C4D4×D7111yescharacteristic
610C22×C4#1176586411yescharacteristic
611C22×C4C23×D7111yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—2842no—
617M16—2842no—
618M16—1421no—
619M16—1421no—
620M16—1421no—
621M16—1421no—
622M16—1421no—
623M16—1421no—
624M16—1421no—
625M16—1421no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—2842no—
631C2×C8—2842no—
632C2×C8—711no—
633C2×C8—711no—
634C2×C8—711no—
635C2×C8—711no—
636C2×C8—1421no—
637C2×C8—1421no—
638C2×C8—1421no—
639C2×C8—1421no—
640C2×C8—1421no—
641C2×C8—1421no—
642C2×C8—1421no—
643C2×C8—1421no—
644C2×C8C22×Dic7111yescharacteristic
645C2×C8C22×Dic7111yescharacteristic
646C2×C8C22×Dic7111yescharacteristic
647C2×C8C22×Dic7111yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×Dic7111yescharacteristic
651C4⋊C4C22×Dic7111yescharacteristic
652C4⋊C4C22×Dic7111yescharacteristic
653C4⋊C4C22×Dic7111yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—2842no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
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—
676C23D4×Dic7111yescharacteristic
677C23D4×Dic7111yescharacteristic
678C23C2×#1176586411yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#1455608712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#1455608712yes—
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—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—2841no—
721C2×C4—2841no—
722C2×C4—2841no—
723C2×C4—2841no—
724C2×C4—2841no—
725C2×C4—1422no—
726C2×C4D4×Dic7111yescharacteristic
727C2×C4D4×Dic7111yescharacteristic
728C2×C4C23×Dic7111yescharacteristic
729C2×C4C2×D4×D7111yescharacteristic
730C2×C4C2×#1176586511yescharacteristic
731C2×C4C2×#1176586511yescharacteristic
732C2×C4#1455617311yescharacteristic
733C2×C4#1455617311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—2841no—
739C8—2841no—
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×D4×Dic7111yescharacteristic
764C22#1798667511yescharacteristic
765C22#1798667511yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—2842no—
775C4—5681no—
776C4C2×#1455608711yescharacteristic
777C4#1798647411yescharacteristic
778C4#1798663911yescharacteristic
779C4#1798663911yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#2259118911yescharacteristic
787C2#2259724311yescharacteristic
788C2#2259725011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#2896C2
socleC22×C71C2×C4×D4
prime radicalC22×#41×C71C22
cosocleC22×C4×C71C24
hypercenter#2896D71
hypocenterC71#22588
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #22596998C2semidirect
3. #22589053C2semidirect
4. #22589046C2semidirect
5. #22588990C2semidirect
6. #22588990C2semidirect
7. #22588617C2semidirect
8. #22588617C2semidirect
9. #22588439C2semidirect
10. #22588382C2semidirect
12. #22588187C2semidirect
13. #22588180C2semidirect
14. #22588121C2semidirect
22. C2×#14556064C22semidirect
23. C2×#14556064C22semidirect
24. #17986026C22semidirect
25. #17986026C22semidirect
39. #17985955C22semidirect
40. #17985955C22semidirect
41. C2×#14556038C22semidirect
42. C2×C8×Dic71C22semidirect
44. #17985764C22semidirect
45. #17985764C22semidirect
46. #17985758C22semidirect
47. #17985758C22semidirect
48. #17985758C22semidirect
49. #17985758C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
55. #419×C71C4semidirect
56. #419×C71C4semidirect
57. #418×C71C4semidirect
58. #418×C71C4semidirect
59. #417×C71C4semidirect
60. #417×C71C4semidirect
61. #417×C71C4semidirect
62. #417×C71C4semidirect
410. C71#22588semidirect
428. #419Dic71semidirect
429. #419Dic71semidirect
430. #418Dic71semidirect
431. #418Dic71semidirect
432. #417Dic71semidirect
433. #417Dic71semidirect
434. #417Dic71semidirect
435. #417Dic71semidirect

Maximal subgroups

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

subgroupindex
#225969982
#225967892
#225890532
#225890462
#225889902
#225886172
#225884392
#225883822
#225882842
#225881872
#225881802
#225881212
C71×#28962
#2258871