Finite Group Databasebeta

← #32004852

Subgroups — #32004852

Order 18176.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597044C211yesmaximal, characteristic
2#22596759C211yesmaximal, characteristic, complemented
3#22588990C211yesmaximal, characteristic, complemented
4#22588990C211yesmaximal, characteristic, complemented
5#22588941C211yesmaximal, characteristic, complemented
6#22588941C211yesmaximal, characteristic, complemented
7#22588643C211yesmaximal, characteristic
8#22588547C211yesmaximal, characteristic, complemented
9#22588439C211yesmaximal, characteristic, complemented
10#22588226C211yesmaximal, characteristic, complemented
11#22588221C211yesmaximal, characteristic, complemented
12#22588187C211yesmaximal, characteristic, complemented
13#22588180C211yesmaximal, characteristic, complemented
14#22588126C211yesmaximal, characteristic, complemented
15C71×#3091C211yesmaximal, characteristic
16C2×#14556135C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19#17986077—21no—
20#17986077—21no—
21#17986071—21no—
22#17986071—21no—
23C2×#14556064C2211yescharacteristic
24C2×#14556064C2211yescharacteristic
25#17986026C2211yescharacteristic
26C2×#14556055C2211yescharacteristic
27C2×#14556055C2211yescharacteristic
28#17985966C2211yescharacteristic
29#17985963C2211yescharacteristic
30#17985955—21no—
31#17985955—21no—
32#17985955C2211yescharacteristic
33#17985955C2211yescharacteristic
34#17985955C2211yescharacteristic
35#17985955C2211yescharacteristic
36#17985955C2211yescharacteristic
37C4×#11765849—21no—
38C4×#11765849—21no—
39C2×#14556038C2211yescharacteristic
40C2×C8×Dic71C2211yescharacteristic
41C4×C22⋊Dic71C2211yescharacteristic
42#17985764C2211yescharacteristic
43#17985764C2211yescharacteristic
44#17985758C2211yescharacteristic
45#17985758C2211yescharacteristic
46#17985758C2211yescharacteristic
47#17985758C2211yescharacteristic
48#17985758C2211yescharacteristic
49#17985758C2211yescharacteristic
50#17985753C2211yescharacteristic
51#17985753C2211yescharacteristic
52#525×C71C2211yescharacteristic
53C2×#117×C71C2211yescharacteristic
54#485×C71C411yescharacteristic, complemented
55#485×C71C411yescharacteristic, complemented
56#484×C71C411yescharacteristic, complemented
57#483×C71C411yescharacteristic, complemented
58#482×C71C411yescharacteristic, complemented
59#482×C71C411yescharacteristic, complemented
60#481×C71C411yescharacteristic, complemented
61#480×C71C411yescharacteristic, complemented
62#427×C71C2211yescharacteristic
63#427×C71C2211yescharacteristic
64#416×C71C2211yescharacteristic
65#416×C71C2211yescharacteristic
66C2×C22⋊C8×C71C2211yescharacteristic
67#14556135—22no—
68#14556135—22no—
69C2×#11765849—22no—
70C2×#11765849—22no—
71C2×#11765849—21no—
72C2×#11765849—22no—
73C2×#11765849—22no—
74C2×#11765849—21no—
75C2×#11765849D411yescharacteristic
76C2×#11765849D411yescharacteristic
77C2×#11765849D411yescharacteristic
78C2×#11765849D411yescharacteristic
79C2×#11765849C2311yescharacteristic
80C2×#11765849C2311yescharacteristic
81C2×#11765849C2311yescharacteristic
82C2×#11765849C2311yescharacteristic
83C22×C71⋊C8—21no—
84C22×C71⋊C8—21no—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C2×C22⋊Dic71—21no—
88C2×C4×Dic71C2311yescharacteristic
89C2×C4×Dic71C2311yescharacteristic
90#14556064—22no—
91#14556064—22no—
92C4⋊(C71⋊C8)—21no—
93C4⋊(C71⋊C8)—21no—
94#14556055—22no—
95#14556055—22no—
96C22⋊(C71⋊C8)—21no—
97C22⋊(C71⋊C8)—21no—
98C22⋊(C71⋊C8)—21no—
99C22⋊(C71⋊C8)—21no—
100#14556039—21no—
101#14556039—21no—
102#14556039—21no—
103#14556039—21no—
104#14556039—21no—
105#14556038—22no—
106C4×C71⋊C8—21no—
107C4×C71⋊C8—21no—
108C4×C71⋊C8—21no—
109C4×C71⋊C8—21no—
110C4×C71⋊C8—21no—
111C8×Dic71—22no—
112C71⋊#95—21no—
113C2×#41×C71C2311yescharacteristic
114C23×C4×C71C2311yescharacteristic
115C22×C8×C71C2311yescharacteristic
116C22×C8×C71C2311yescharacteristic
117#123×C71—21no—
118C22⋊Q8×C71C2×C411yescharacteristic
119C22⋊Q8×C71C2×C411yescharacteristic
120#121×C71C2×C411yescharacteristic
121#121×C71C2×C411yescharacteristic
122#120×C71—21no—
123C4×D4×C71—21no—
124C4×D4×C71—21no—
125#117×C71—21no—
126#117×C71—21no—
127#117×C71C2×C411yescharacteristic
128#117×C71C2×C411yescharacteristic
129#117×C71C2311yescharacteristic
130#117×C71C2311yescharacteristic
131#117×C71C2311yescharacteristic
132C2×C4⋊C4×C71C2×C411yescharacteristic
133C2×C4⋊C4×C71C2×C411yescharacteristic
134C2×C22⋊C4×C71—21no—
135C2×C42×C71—21no—
136#107×C71C2×C411yescharacteristic
137#107×C71C2×C411yescharacteristic
138#107×C71C2×C411yescharacteristic
139#107×C71C2×C411yescharacteristic
140#106×C71C2×C411yescharacteristic
141#106×C71C2×C411yescharacteristic
142#106×C71C2×C411yescharacteristic
143#106×C71C2×C411yescharacteristic
144#103×C71C2×C411yescharacteristic
145#103×C71C2×C411yescharacteristic
146#103×C71C2×C411yescharacteristic
147#103×C71C2×C411yescharacteristic
148#102×C71C2×C411yescharacteristic
149#102×C71C2×C411yescharacteristic
150#102×C71C2×C411yescharacteristic
151#102×C71C2×C411yescharacteristic
152C22⋊C8×C71C2×C411yescharacteristic
153C22⋊C8×C71C2×C411yescharacteristic
154C22⋊C8×C71C2×C411yescharacteristic
155C22⋊C8×C71C2×C411yescharacteristic
156C22×Dic71—21no—
157C22×Dic71—21no—
158#11765849—24no—
159#11765849—21no—
160#11765849—21no—
161#11765849—22no—
162#11765849—22no—
163#11765849—22no—
164#11765849—22no—
165#11765849—21no—
166#11765849—21no—
167#11765849—21no—
168#11765849—21no—
169#11765849—42no—
170#11765849#4112yes—
171#11765849#4112yes—
172C2×C71⋊C8—24no—
173C2×C71⋊C8—21no—
174C2×C71⋊C8—21no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
179C2×C71⋊C8—42no—
180C2×C71⋊C8C2×D411yescharacteristic
181C2×C71⋊C8C2×D411yescharacteristic
182C2×C71⋊C8C2×D411yescharacteristic
183C2×C71⋊C8C2×D411yescharacteristic
184C2×C71⋊C8#4112yes—
185C2×C71⋊C8#4112yes—
186C22⋊Dic71—42no—
187C4×Dic71—21no—
188C4×Dic71—21no—
189C4×Dic71—21no—
190C4×Dic71—21no—
191C24×C71#4111yescharacteristic
192#41×C71—21no—
193#41×C71—21no—
194#41×C71—21no—
195#41×C71—21no—
196C2×Q8×C71C22×C411yescharacteristic
197C2×D4×C71—21no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71C22×C411yescharacteristic
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×C71C22×C411yescharacteristic
209C22×C4×C71C22×C411yescharacteristic
210C22×C4×C71C2×D411yescharacteristic
211C22×C4×C71C2×D411yescharacteristic
212C22×C4×C71#4111yescharacteristic
213C22×C4×C71C2411yescharacteristic
214C2×C8×C71—21no—
215C2×C8×C71—21no—
216C2×C8×C71—21no—
217C2×C8×C71—21no—
218C2×C8×C71C22×C411yescharacteristic
219C2×C8×C71C22×C411yescharacteristic
220C2×C8×C71C22×C411yescharacteristic
221C2×C8×C71C22×C411yescharacteristic
222C4⋊C4×C71—21no—
223C4⋊C4×C71—21no—
224C4⋊C4×C71—21no—
225C4⋊C4×C71—21no—
226C4⋊C4×C71C22×C411yescharacteristic
227C4⋊C4×C71C22×C411yescharacteristic
228C4⋊C4×C71C22×C411yescharacteristic
229C4⋊C4×C71C22×C411yescharacteristic
230C4⋊C4×C71C22×C411yescharacteristic
231C4⋊C4×C71C22×C411yescharacteristic
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—21no—
239C22⋊C4×C71—21no—
240C22⋊C4×C71—21no—
241C42×C71—21no—
242C42×C71—21no—
243C42×C71—21no—
244C42×C71—21no—
245C42×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—41no—
250C23×C71—41no—
251C23×C71C4×D411yescharacteristic
252C23×C71C4×D411yescharacteristic
253C23×C71C2×#4111yescharacteristic
254Q8×C71—21no—
255Q8×C71—21no—
256D4×C71—21no—
257D4×C71—21no—
258D4×C71—41no—
259D4×C71—41no—
260D4×C71—81no—
261D4×C71—81no—
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—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—21no—
278C2×C4×C71—21no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—81no—
282C2×C4×C71—81no—
283C2×C4×C71C4×D411yescharacteristic
284C2×C4×C71C4×D411yescharacteristic
285C2×C4×C71C23×C411yescharacteristic
286C2×C4×C71C22×D411yescharacteristic
287C2×C4×C71C2×#4111yescharacteristic
288C2×C4×C71C2×#4111yescharacteristic
289C2×C4×C71C2×#4111yescharacteristic
290C2×C4×C71C2×#4111yescharacteristic
291C2×Dic71—22no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C8×C71—21no—
298C8×C71—21no—
299C8×C71—21no—
300C8×C71—21no—
301C71⋊C8—21no—
302C71⋊C8—21no—
303C71⋊C8—22no—
304C71⋊C8—22no—
305C71⋊C8—41no—
306C71⋊C8—41no—
307C71⋊C8#12312yes—
308C71⋊C8#12312yes—
309C22×C71—21no—
310C22×C71—21no—
311C22×C71—21no—
312C22×C71—21no—
313C22×C71—21no—
314C22×C71—21no—
315C22×C71—21no—
316C22×C71—21no—
317C22×C71—41no—
318C22×C71—41no—
319C22×C71—41no—
320C22×C71—81no—
321C22×C71—81no—
322C22×C71C2×C4×D411yescharacteristic
323C22×C71#52911yescharacteristic
324C22×C71#52911yescharacteristic
325C4×C71—21no—
326C4×C71—21no—
327C4×C71—41no—
328C4×C71—41no—
329C4×C71—41no—
330C4×C71—41no—
331C4×C71—41no—
332C4×C71—41no—
333C4×C71—41no—
334C4×C71C4×#4111yescharacteristic
335C4×C71C4×#4111yescharacteristic
336C4×C71C2×#12311yescharacteristic
337C4×C71#52511yescharacteristic
338Dic71—42no—
339Dic71—81no—
340#21594—711nomaximal, Sylow
341C2×C71—21no—
342C2×C71—21no—
343C2×C71—41no—
344C2×C71—41no—
345C2×C71—81no—
346C2×C71C4×#12311yescharacteristic
347C2×C71#295611yescharacteristic
348C2×C71#295711yescharacteristic
349#3091D7111yescharacteristic
350#2930—711no—
351#2873—711no—
352#1929—711no—
353#1929—711no—
354#1922—711no—
355#1922—711no—
356#1871—711no—
357#1855—711no—
358#1826—711no—
359#1773—711no—
360#1772—711no—
361#1765—711no—
362#1764—711no—
363#1753—711no—
364C71#2159411yescharacteristic, complemented, Sylow
365C2×#131—711no—
366C22×M16—711no—
367C22×M16—711no—
368#525C2×D7111yescharacteristic
369C2×#117C2×D7111yescharacteristic
370#485Dic7111yescharacteristic, complemented
371#485Dic7111yescharacteristic, complemented
372#484Dic7111yescharacteristic, complemented
373#483Dic7111yescharacteristic, complemented
374#482Dic7111yescharacteristic, complemented
375#482Dic7111yescharacteristic, complemented
376#481Dic7111yescharacteristic, complemented
377#480Dic7111yescharacteristic, complemented
378#436—1421no—
379#436—1421no—
380#435—1421no—
381#435—1421no—
382C2×#108—711no—
383C2×#108—711no—
384#427C2×D7111yescharacteristic
385#427C2×D7111yescharacteristic
386#424—711no—
387C2×#104—711no—
388C2×#104—711no—
389#416C2×D7111yescharacteristic
390#416C2×D7111yescharacteristic
391#408—711no—
392#407—711no—
393C2×C22⋊C8C2×D7111yescharacteristic
394#405—711no—
395#405—711no—
396#405—711no—
397#405—711no—
398#405—711no—
399#405—1421no—
400#405—1421no—
401C4×M16—1421no—
402C4×M16—1421no—
403C2×#97—711no—
404C2×C4×C8—711no—
405C4×C22⋊C4—711no—
406#341—711no—
407#341—711no—
408#339—711no—
409#339—711no—
410#339—711no—
411#339—711no—
412#339—711no—
413#339—711no—
414#336—711no—
415#336—711no—
416C2×#41C22×D7111yescharacteristic
417C23×C4C22×D7111yescharacteristic
418#131—1422no—
419#131—1422no—
420C2×M16—711no—
421C2×M16—711no—
422C2×M16—711no—
423C2×M16—711no—
424C2×M16—711no—
425C2×M16—711no—
426C2×M16—711no—
427C2×M16—711no—
428C2×M16—1421no—
429C2×M16—1422no—
430C2×M16—1422no—
431C2×M16—1422no—
432C2×M16—1422no—
433C2×M16—1421no—
434C22×C8—711no—
435C22×C8—711no—
436C22×C8—1421no—
437C22×C8—1421no—
438C22×C8C22×D7111yescharacteristic
439C22×C8C22×D7111yescharacteristic
440#123—21no—
441C22⋊Q8C2×Dic7111yescharacteristic
442C22⋊Q8C2×Dic7111yescharacteristic
443#121C2×Dic7111yescharacteristic
444#121C2×Dic7111yescharacteristic
445#120—21no—
446C4×D4—21no—
447C4×D4—21no—
448#117—21no—
449#117—21no—
450#117C2×Dic7111yescharacteristic
451#117C2×Dic7111yescharacteristic
452#117C22×D7111yescharacteristic
453#117C22×D7111yescharacteristic
454#117C22×D7111yescharacteristic
455C2×C4⋊C4C2×Dic7111yescharacteristic
456C2×C4⋊C4C2×Dic7111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—1421no—
459C2×C42—21no—
460C2×C42—711no—
461C2×C42—711no—
462#108—1422no—
463#108—1422no—
464#107C2×Dic7111yescharacteristic
465#107C2×Dic7111yescharacteristic
466#107C2×Dic7111yescharacteristic
467#107C2×Dic7111yescharacteristic
468#106C2×Dic7111yescharacteristic
469#106C2×Dic7111yescharacteristic
470#106C2×Dic7111yescharacteristic
471#106C2×Dic7111yescharacteristic
472C4⋊C8—1421no—
473C4⋊C8—1421no—
474#104—1422no—
475#104—1422no—
476#103C2×Dic7111yescharacteristic
477#103C2×Dic7111yescharacteristic
478#103C2×Dic7111yescharacteristic
479#103C2×Dic7111yescharacteristic
480#102C2×Dic7111yescharacteristic
481#102C2×Dic7111yescharacteristic
482#102C2×Dic7111yescharacteristic
483#102C2×Dic7111yescharacteristic
484C22⋊C8—1421no—
485C22⋊C8—1421no—
486C22⋊C8—1421no—
487C22⋊C8—1421no—
488C22⋊C8C2×Dic7111yescharacteristic
489C22⋊C8C2×Dic7111yescharacteristic
490C22⋊C8C2×Dic7111yescharacteristic
491C22⋊C8C2×Dic7111yescharacteristic
492#97—1421no—
493#97—1421no—
494#97—1421no—
495#97—1421no—
496#97—1421no—
497#97—1422no—
498C4×C8—1421no—
499C4×C8—1421no—
500C4×C8—1421no—
501C4×C8—1421no—
502C4×C8—1421no—
503C4×C8—1422no—
504#95—1421no—
505C24#1176586411yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×Dic7111yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×Dic7111yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—1421no—
523C22×C4—1421no—
524C22×C4C22×Dic7111yescharacteristic
525C22×C4C22×Dic7111yescharacteristic
526C22×C4D4×D7111yescharacteristic
527C22×C4D4×D7111yescharacteristic
528C22×C4#1176586411yescharacteristic
529C22×C4C23×D7111yescharacteristic
530M16—2842no—
531M16—712no—
532M16—712no—
533M16—1421no—
534M16—1421no—
535M16—1421no—
536M16—1421no—
537M16—1422no—
538M16—1422no—
539M16—1422no—
540M16—1422no—
541M16—1424no—
542M16—1421no—
543M16—1421no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—2842no—
549C2×C8—711no—
550C2×C8—711no—
551C2×C8—712no—
552C2×C8—712no—
553C2×C8—711no—
554C2×C8—711no—
555C2×C8—1421no—
556C2×C8—1421no—
557C2×C8—1424no—
558C2×C8—1421no—
559C2×C8—1421no—
560C2×C8—1421no—
561C2×C8—1421no—
562C2×C8C22×Dic7111yescharacteristic
563C2×C8C22×Dic7111yescharacteristic
564C2×C8C22×Dic7111yescharacteristic
565C2×C8C22×Dic7111yescharacteristic
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4C22×Dic7111yescharacteristic
571C4⋊C4C22×Dic7111yescharacteristic
572C4⋊C4C22×Dic7111yescharacteristic
573C4⋊C4C22×Dic7111yescharacteristic
574C4⋊C4C22×Dic7111yescharacteristic
575C4⋊C4C22×Dic7111yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—2842no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—1421no—
592C42—1421no—
593C42—1421no—
594C42—1421no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23D4×Dic7111yescharacteristic
601C23D4×Dic7111yescharacteristic
602C23C2×#1176586411yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
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—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—2841no—
633C2×C4—2841no—
634C2×C4—2841no—
635C2×C4—2841no—
636C2×C4—2841no—
637C2×C4—1422no—
638C2×C4D4×Dic7111yescharacteristic
639C2×C4D4×Dic7111yescharacteristic
640C2×C4C23×Dic7111yescharacteristic
641C2×C4C2×D4×D7111yescharacteristic
642C2×C4#41×D7111yescharacteristic
643C2×C4#41×D7111yescharacteristic
644C2×C4#41×D7111yescharacteristic
645C2×C4#41×D7111yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—2841no—
651C8—2841no—
652C8—712no—
653C8—712no—
654C8—1421no—
655C8—1421no—
656C8—1422no—
657C8—1422no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×D4×Dic7111yescharacteristic
672C22#1798652611yescharacteristic
673C22#1798652611yescharacteristic
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—2842no—
684C4—5681no—
685C4#41×Dic7111yescharacteristic
686C4#41×Dic7111yescharacteristic
687C4#123×D7111yescharacteristic
688C4#1798650711yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2#123×Dic7111yescharacteristic
695C2#2259725011yescharacteristic
696C2#2259725711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#3091C2
socleC22×C71C2×C4×D4
prime radical#525×C71C22
cosocleC22×C4×C71C24
hypercenter#3091D71
hypocenterC71#21594
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. #22596759C2semidirect
3. #22588990C2semidirect
4. #22588990C2semidirect
5. #22588941C2semidirect
6. #22588941C2semidirect
8. #22588547C2semidirect
9. #22588439C2semidirect
10. #22588226C2semidirect
11. #22588221C2semidirect
12. #22588187C2semidirect
13. #22588180C2semidirect
14. #22588126C2semidirect
54. #485×C71C4semidirect
55. #485×C71C4semidirect
56. #484×C71C4semidirect
57. #483×C71C4semidirect
58. #482×C71C4semidirect
59. #482×C71C4semidirect
60. #481×C71C4semidirect
61. #480×C71C4semidirect
364. C71#21594semidirect
370. #485Dic71semidirect
371. #485Dic71semidirect
372. #484Dic71semidirect
373. #483Dic71semidirect
374. #482Dic71semidirect
375. #482Dic71semidirect
376. #481Dic71semidirect
377. #480Dic71semidirect

Maximal subgroups

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

subgroupindex
#225970442
#225967592
#225889902
#225889412
#225886432
#225885472
#225884392
#225882262
#225882212
#225881872
#225881802
#225881262
C71×#30912
#2159471