Finite Group Databasebeta

← #29700872

Subgroups — #29700872

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839931C211yesmaximal, characteristic
2#21454654C211yesmaximal, characteristic, complemented
3#21454653C211yesmaximal, characteristic, complemented
4#21454346C211yesmaximal, characteristic, complemented
5#21454341C211yesmaximal, characteristic, complemented
6#21446625C211yesmaximal, characteristic, complemented
7#21446482C211yesmaximal, characteristic, complemented
8#21446481C211yesmaximal, characteristic, complemented
9#21446327C211yesmaximal, characteristic, complemented
10#21446326C211yesmaximal, characteristic, complemented
11#21446216C211yesmaximal, characteristic, complemented
12#21446047C211yesmaximal, characteristic, complemented
13#21446046C211yesmaximal, characteristic, complemented
14#21445656C211yesmaximal, characteristic, complemented
15C61×#1764C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17C2×#14519805C2211yescharacteristic
18C2×#14519802C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×#14519774C2211yescharacteristic
21#16840245C2211yescharacteristic
22#16840242C2211yescharacteristic
23#16840236C2211yescharacteristic, complemented
24#16839931C418yescomplemented
25#16839875—21no—
26#16839871—21no—
27#16839865—21no—
28#16839864—21no—
29C4×#11758190—21no—
30#16839847—21no—
31C4×D488—21no—
32#16839842—21no—
33#16839805C2211yescharacteristic, complemented
34#16839804C2211yescharacteristic, complemented
35C2×#14519705C2211yescharacteristic
36#16839768—21no—
37#16839768C2211yescharacteristic
38#16839766C2211yescharacteristic
39#16839765—21no—
40#16839764—21no—
41#16839764C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839762—21no—
44#16839759—21no—
45#16839759C2211yescharacteristic
46#16839757—21no—
47C2×#14519699—21no—
48C2×#14519699C2211yescharacteristic
49C2×#14519699C2211yescharacteristic
50C2×#14519699C2211yescharacteristic, complemented
51C2×#14519699C2211yescharacteristic, complemented
52#102×D61—21no—
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic, complemented
55#16839717C2211yescharacteristic, complemented
56#16839632C2211yescharacteristic, complemented
57#16839530C2211yescharacteristic, complemented
58#16839530C2211yescharacteristic, complemented
59#16839527C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61C2×#131×C61C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C61×#416C2211yescharacteristic
64C61×#405C2211yescharacteristic, complemented
65C2×C4×C8×C61C2211yescharacteristic, complemented
66C61×#341C2211yescharacteristic, complemented
67C61×#339C2211yescharacteristic, complemented
68#14519823—22no—
69#14519823—22no—
70#14519823—41no—
71#14519823C2×C414yescomplemented
72C2×#11758226—21no—
73C2×#11758222—21no—
74C2×#11758222C2311yescharacteristic
75C22×D244—21no—
76C22×D244—41no—
77C22×D244C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61—41no—
81#14519805—22no—
82#14519805C2×C414yescomplemented
83#14519802—22no—
84#14519802C2×C414yescomplemented
85C2×#11758190—21no—
86C2×#11758201—21no—
87C2×D488—21no—
88C2×#11758199—21no—
89#14519783—22no—
90#14519783—41no—
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758189—21no—
94C2×C8×D61—21no—
95#14519774—41no—
96#14519774C2×C414yescomplemented
97Q8×Dic61—21no—
98C4×Dic122—21no—
99C4×D244—21no—
100C4×D244—21no—
101C4×D244—21no—
102D4×Dic61—21no—
103D4×Dic61—41no—
104#14519739—21no—
105#14519739—21no—
106#14519737—41no—
107#14519736—21no—
108#14519736C2311yescharacteristic
109#14519735—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61—41no—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C4⋊C4×D61—21no—
115C22⋊C4×D61—41no—
116#14519711—21no—
117#14519710—21no—
118#14519709—21no—
119#14519708—21no—
120#14519705C2×C414yescomplemented
121#14519702—21no—
122#14519702D411yescharacteristic, complemented
123#14519702D411yescharacteristic, complemented
124#14519701—21no—
125#14519699—21no—
126#14519699—21no—
127#14519699—21no—
128#14519699—21no—
129#14519699—21no—
130#14519699—21no—
131#14519699—21no—
132#14519699—21no—
133#14519699—21no—
134#14519699—21no—
135#14519699—21no—
136#14519699D411yescharacteristic, complemented
137#14519699D411yescharacteristic, complemented
138#14519698—21no—
139#14519697—21no—
140#14519697—21no—
141#14519693—41no—
142#14519693C2×C414yescomplemented
143#14519687—21no—
144C8×Dic61—21no—
145C2×#41×C61C2311yescharacteristic
146#131×C61—22no—
147#131×C61—41no—
148C2×M16×C61—21no—
149C2×M16×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C22×C8×C61—21no—
152C22×C8×C61C2311yescharacteristic
153C22×C8×C61C2311yescharacteristic
154#117×C61C2311yescharacteristic
155C2×C42×C61C2311yescharacteristic
156#104×C61C2×C414yescomplemented
157#103×C61D411yescharacteristic, complemented
158#103×C61D411yescharacteristic, complemented
159#102×C61D411yescharacteristic, complemented
160#102×C61D411yescharacteristic, complemented
161#97×C61—21no—
162C4×C8×C61—21no—
163C4×C8×C61—41no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—41no—
167#41×C61—21no—
168#41×C61—21no—
169#41×C61C22×C412yes—
170#41×C61#4112yes—
171C2×Q8×C61C2×D411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61C2×D411yescharacteristic
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—21no—
178C2×C22⋊D61—41no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—41no—
182#11758226—24no—
183#11758226—42no—
184D4×D61—24no—
185D4×D61—42no—
186D4×D61—44no—
187D4×D61—44no—
188#11758222—21no—
189#11758222—21no—
190#11758222—24no—
191#11758222—42no—
192#11758222C22×C412yes—
193#11758222#4112yes—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—24no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—42no—
206C2×D244—41no—
207C2×D244—44no—
208C2×D244—82no—
209C2×D244—82no—
210C2×D244C22×C412yes—
211C2×D244C22×C412yes—
212C2×D244C2×D411yescharacteristic
213C2×C4×D61—21no—
214C2×C4×D61—41no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61—41no—
218C2×Dic122C2×D411yescharacteristic
219M16×C61—21no—
220M16×C61—21no—
221M16×C61—21no—
222M16×C61—42no—
223M16×C61C22×C412yes—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—42no—
231C2×C8×C61C2×D411yescharacteristic
232C2×C8×C61C2×D411yescharacteristic
233C2×C8×C61C2×D411yescharacteristic
234C2×C8×C61C2×D411yescharacteristic
235C4⋊C4×C61C2×D411yescharacteristic
236C4⋊C4×C61C2×D411yescharacteristic
237C22⋊C4×C61—21no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61C22×C412yes—
241C22⋊Dic61—21no—
242C22⋊Dic61—41no—
243#11758201—24no—
244#11758199—24no—
245#11758198—41no—
246#11758198—41no—
247#11758198—41no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—41no—
253C4⋊Dic61—82no—
254C4⋊Dic61C2×D411yescharacteristic
255C4⋊Dic61C2×D411yescharacteristic
256#11758196—41no—
257C4×Dic61—21no—
258C4×Dic61—41no—
259C4×Dic61—41no—
260#11758194—21no—
261#11758194—21no—
262#11758194—21no—
263#11758194C22×C412yes—
264C2×#92418—21no—
265C2×#92418—21no—
266D488—24no—
267#11758190—24no—
268#11758189—42no—
269C8×D61—42no—
270C23×C61—21no—
271C23×C61H(5,𝔽2)11yescharacteristic
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—44no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—81no—
281C22×D61—81no—
282C22×D61—81no—
283C22×D61—81no—
284C22×D61—161no—
285C22×D61—161no—
286Q8×C61—21no—
287Q8×C61C4×D412yes—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—21no—
291D4×C61C4×D412yes—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61H(5,𝔽2)11yescharacteristic
306C22⋊D61—22no—
307C22⋊D61—22no—
308C22⋊D61—44no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—81no—
315C2×Dic61—81no—
316C2×Dic61—161no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244—22no—
321D244—21no—
322D244—44no—
323D244—41no—
324D244—41no—
325D244—41no—
326D244—41no—
327D244—88no—
328D244C4×D412yes—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—44no—
332C4×D61—161no—
333C4×D61—161no—
334C4×D61—161no—
335Dic122—21no—
336Dic122C4×D412yes—
337C8×C61—22no—
338C8×C61—21no—
339C8×C61—21no—
340C8×C61—21no—
341C8×C61—21no—
342C8×C61—41no—
343#92418—22no—
344#92418—41no—
345#22897—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—22no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61#51811yescharacteristic
352C22×C61D4211yescharacteristic
353C22×C61#55111yescharacteristic
354C2×D61—22no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C2×D61—82no—
364C2×D61—82no—
365C2×D61—164no—
366C2×D61—161no—
367C2×D61—161no—
368C4×C61—24no—
369C4×C61—22no—
370C4×C61—41no—
371C4×C61—41no—
372C4×C61C2×C4×D411yescharacteristic
373C4×C61C2×C4×D411yescharacteristic
374C4×C61#54611yescharacteristic
375C4×C61#54611yescharacteristic
376Dic61—22no—
377Dic61—41no—
378Dic61—41no—
379Dic61—81no—
380Dic61—81no—
381C2×#453—611no—
382#2946—611no—
383#2946—611no—
384#2897—611no—
385#2897—611no—
386#1957—611no—
387#1931—611no—
388#1931—611no—
389#1907—611no—
390#1907—611no—
391#1887—611no—
392#1859—611no—
393#1859—611no—
394#1764—611no—
395#1764D6111yescharacteristic, complemented
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—42no—
399C2×C61#235811yescharacteristic
400C2×C61#329111yescharacteristic
401C2×C61#329211yescharacteristic
402D61—42no—
403D61—82no—
404D61—82no—
405C2×H(5,𝔽2)—611no—
406C2×AGL(1,ℤ/8)—611no—
407C2×AGL(1,ℤ/8)—611no—
408C2×#131—611no—
409C2×#131C2×D6111yescharacteristic
410C2×#127—611no—
411#520—611no—
412#520—611no—
413#518—611no—
414#453—618no—
415#442—1221no—
416#442—1221no—
417#440—1221no—
418#440—1221no—
419C4×SD16—1221no—
420C4×SD16—1221no—
421C4×D8—1221no—
422C4×D8—1221no—
423#428—611no—
424#428—611no—
425C2×#104—611no—
426C2×#104C2×D6111yescharacteristic
427#418—611no—
428#418—611no—
429#418—1221no—
430#418—1221no—
431#417—611no—
432#417—611no—
433#417—1221no—
434#417—1221no—
435#416—611no—
436#416—1221no—
437#416—1221no—
438#416C2×D6111yescharacteristic
439C2×#102—611no—
440C2×#102—611no—
441C2×#102—611no—
442C2×#102—611no—
443C2×#102—1221no—
444C2×#102—1221no—
445C2×#100—611no—
446C2×#100—611no—
447#405—611no—
448#405C2×D6111yescharacteristic, complemented
449C2×C4×C8C2×D6111yescharacteristic, complemented
450#384—611no—
451#343—611no—
452#343—611no—
453#341—611no—
454#341C2×D6111yescharacteristic, complemented
455#339—611no—
456#339C2×D6111yescharacteristic, complemented
457C61#2289711yescharacteristic, complemented, Sylow
458H(5,𝔽2)—614no—
459H(5,𝔽2)—1222no—
460H(5,𝔽2)—1222no—
461H(5,𝔽2)—2441no—
462C2×#41—611no—
463C2×#41—1221no—
464C2×#41—1221no—
465C2×#41C22×D6111yescharacteristic
466C22×D4—611no—
467C22×D4—611no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—2441no—
471C22×D4—2441no—
472AGL(1,ℤ/8)—614no—
473AGL(1,ℤ/8)—614no—
474AGL(1,ℤ/8)—1222no—
475AGL(1,ℤ/8)—1222no—
476C2×SD16—1221no—
477C2×SD16—1221no—
478C2×D8—1221no—
479C2×D8—1221no—
480#131—22no—
481#131—41no—
482#131—1222no—
483#131—2441no—
484C2×M16—21no—
485C2×M16—611no—
486C2×M16—611no—
487C2×M16—1221no—
488C2×M16C22×D6111yescharacteristic
489C2×M16C22×D6111yescharacteristic
490C22×C8—21no—
491C22×C8—1221no—
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494#127—614no—
495#127—2441no—
496C4×Q8—1221no—
497C4×Q8—1221no—
498C4×D4—1221no—
499C4×D4—1221no—
500C4×D4—1221no—
501C4×D4—1221no—
502C4×D4—1221no—
503C4×D4—1221no—
504C4×D4—2441no—
505C4×D4—2441no—
506#117—611no—
507#117—1221no—
508#117—1221no—
509#117C22×D6111yescharacteristic
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—2441no—
515C2×C22⋊C4—2441no—
516C2×C42C22×D6111yescharacteristic
517#107—1221no—
518#107—1221no—
519#106—1221no—
520#106—1221no—
521#104—614no—
522#104C4×D6114yescomplemented
523#103—611no—
524#103—611no—
525#103—1221no—
526#103—1221no—
527#103D24411yescharacteristic, complemented
528#103D24411yescharacteristic, complemented
529#102—611no—
530#102—611no—
531#102—1221no—
532#102—1221no—
533#102—1221no—
534#102—1221no—
535#102—1221no—
536#102—1221no—
537#102—1221no—
538#102—1221no—
539#102—1221no—
540#102—1221no—
541#102—1221no—
542#102—1221no—
543#102—1221no—
544#102—1221no—
545#102D24411yescharacteristic, complemented
546#102D24411yescharacteristic, complemented
547#100—614no—
548#100—2441no—
549#97—21no—
550#97—1221no—
551C4×C8—21no—
552C4×C8—41no—
553C4×C8—1221no—
554C24—1221no—
555C24—1221no—
556C24—2441no—
557#41—21no—
558#41—21no—
559#41—612no—
560#41—612no—
561#41—1224no—
562#41—1221no—
563#41—1221no—
564#41—1224no—
565#41—2442no—
566#41—2442no—
567#41C2×C4×D6112yes—
568#41#1175822212yes—
569C2×Q8—611no—
570C2×Q8C2×D24411yescharacteristic
571C2×D4—21no—
572C2×D4—612no—
573C2×D4—612no—
574C2×D4—611no—
575C2×D4—1224no—
576C2×D4—1221no—
577C2×D4—1224no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—4882no—
589C2×D4—4882no—
590C2×D4—2442no—
591C2×D4—2444no—
592C2×D4—2441no—
593C2×D4—2442no—
594C2×D4—2441no—
595C2×D4—2444no—
596C2×D4—2444no—
597C2×D4C2×D24411yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2441no—
604C22×C4—2441no—
605C22×C4—2441no—
606C22×C4—2441no—
607C22×C4—2441no—
608C22×C4C23×D6111yescharacteristic
609SD16—1224no—
610SD16—1224no—
611D8—1224no—
612D8—1224no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—612no—
618M16—1221no—
619M16—1221no—
620M16—1221no—
621M16—2442no—
622M16C2×C4×D6112yes—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—42no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—2442no—
633C2×C8C2×D24411yescharacteristic
634C2×C8C2×D24411yescharacteristic
635C2×C8D4×D6111yescharacteristic
636C2×C8D4×D6111yescharacteristic
637C4⋊C4—611no—
638C4⋊C4—611no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—4882no—
644C4⋊C4—2441no—
645C4⋊C4—2441no—
646C4⋊C4C2×D24411yescharacteristic
647C4⋊C4C2×D24411yescharacteristic
648C22⋊C4—21no—
649C22⋊C4—1221no—
650C22⋊C4—2441no—
651C22⋊C4—2441no—
652C22⋊C4—2441no—
653C22⋊C4—2441no—
654C42—21no—
655C42—21no—
656C42—1221no—
657C42—2441no—
658C42—2441no—
659C42C2×C4×D6112yes—
660C23—21no—
661C23—1221no—
662C23—1222no—
663C23—1222no—
664C23—9761no—
665C23—9761no—
666C23—4881no—
667C23—4881no—
668C23—4881no—
669C23—4881no—
670C23—2444no—
671C23—2441no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23#1451982311yescharacteristic
676Q8—21no—
677Q8—612no—
678Q8—1221no—
679Q8C4×D24412yes—
680D4—22no—
681D4—22no—
682D4—21no—
683D4—612no—
684D4—1222no—
685D4—1222no—
686D4—1222no—
687D4—1222no—
688D4—1222no—
689D4—1222no—
690D4—1221no—
691D4—4888no—
692D4—2444no—
693D4—2444no—
694D4—2441no—
695D4—2441no—
696D4—2441no—
697D4—2441no—
698D4C4×D24412yes—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—1221no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—9761no—
713C2×C4—9761no—
714C2×C4—9761no—
715C2×C4—9761no—
716C2×C4—4881no—
717C2×C4—4881no—
718C2×C4—2444no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C22×D24411yescharacteristic
724C2×C4#41×D6111yescharacteristic
725C2×C4C2×#1175822211yescharacteristic
726C2×C4#1451982211yescharacteristic
727C8—22no—
728C8—21no—
729C8—21no—
730C8—21no—
731C8—21no—
732C8—41no—
733C8—1222no—
734C8—2441no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—1222no—
741C22—9761no—
742C22—9761no—
743C22—9764no—
744C22—4882no—
745C22—4882no—
746C22—4881no—
747C22—4881no—
748C22—4881no—
749C22—4881no—
750C22—2442no—
751C22—2442no—
752C22—2441no—
753C22—2441no—
754C22#1684023411yescharacteristic
755C22D4×D24411yescharacteristic
756C22#1684043611yescharacteristic
757C4—24no—
758C4—22no—
759C4—41no—
760C4—41no—
761C4—1222no—
762C4—4881no—
763C4—4881no—
764C4—2441no—
765C4—2441no—
766C4C4×D4×D6111yescharacteristic
767C4C2×C4×D24411yescharacteristic
768C4#1684040211yescharacteristic
769C4#1684040711yescharacteristic
770C2—21no—
771C2—21no—
772C2—42no—
773C2—4882no—
774C2—4882no—
775C2—2442no—
776C2#2144880111yescharacteristic
777C2#2145761311yescharacteristic
778C2#2145761911yescharacteristic
subgroupG/H
centerC22D4×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1764C2
socleC22×C61D42
prime radicalC2×#16839931C2
cosocleC22×C4×C61C24
hypercenter#1764D61
hypocenterC61#22897
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #21454654C2semidirect
3. #21454653C2semidirect
4. #21454346C2semidirect
5. #21454341C2semidirect
6. #21446625C2semidirect
7. #21446482C2semidirect
8. #21446481C2semidirect
9. #21446327C2semidirect
10. #21446326C2semidirect
11. #21446216C2semidirect
12. #21446047C2semidirect
13. #21446046C2semidirect
14. #21445656C2semidirect
15. C61×#1764C2semidirect
23. #16840236C22semidirect
24. #16839931C4semidirect
33. #16839805C22semidirect
34. #16839804C22semidirect
50. C2×#14519699C22semidirect
51. C2×#14519699C22semidirect
54. C2×#14519693C22semidirect
55. #16839717C22semidirect
56. #16839632C22semidirect
57. #16839530C22semidirect
58. #16839530C22semidirect
59. #16839527C22semidirect
60. #16839522C22semidirect
64. C61×#405C22semidirect
65. C2×C4×C8×C61C22semidirect
66. C61×#341C22semidirect
67. C61×#339C22semidirect
71. #14519823C2×C4semidirect
82. #14519805C2×C4semidirect
84. #14519802C2×C4semidirect
96. #14519774C2×C4semidirect
120. #14519705C2×C4semidirect
122. #14519702D4semidirect
123. #14519702D4semidirect
136. #14519699D4semidirect
137. #14519699D4semidirect
142. #14519693C2×C4semidirect
156. #104×C61C2×C4semidirect
157. #103×C61D4semidirect
158. #103×C61D4semidirect
159. #102×C61D4semidirect
160. #102×C61D4semidirect
395. #1764D61semidirect
448. #405C2×D61semidirect
449. C2×C4×C8C2×D61semidirect
454. #341C2×D61semidirect
456. #339C2×D61semidirect
457. C61#22897semidirect
522. #104C4×D61semidirect
527. #103D244semidirect
528. #103D244semidirect
545. #102D244semidirect
546. #102D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168399312
#214546542
#214546532
#214543462
#214543412
#214466252
#214464822
#214464812
#214463272
#214463262
#214462162
#214460472
#214460462
#214456562
C61×#17642
#2289761