Finite Group Databasebeta

← #30620616

Subgroups — #30620616

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462327C211yesmaximal, characteristic, complemented
2#21462324C211yesmaximal, characteristic
3#21461911C211yesmaximal, characteristic, complemented
4#21461909C211yesmaximal, characteristic, complemented
5#21461897C211yesmaximal, characteristic, complemented
6#21461896C211yesmaximal, characteristic, complemented
7#21461785C211yesmaximal, characteristic, complemented
8#21461783C211yesmaximal, characteristic, complemented
9#21461723C211yesmaximal, characteristic, complemented
10#21461697C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#417×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519856—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28#16840714—21no—
29#16840714—21no—
30#16840714C2211yescharacteristic
31#16840714C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840713C2211yescharacteristic
34#16840711—21no—
35#16840711—21no—
36#16840705—21no—
37#16840704—21no—
38#16840704C2211yescharacteristic
39#16840704C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C22⋊#6923—21no—
43C4×C22⋊#6923C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×#41×D61C2211yescharacteristic
53C2×M16×D61C2211yescharacteristic
54C2×C4⋊C4×D61C2211yescharacteristic
55#16839764C411yescharacteristic, complemented
56#16839763C411yescharacteristic, complemented
57#16839762C411yescharacteristic, complemented
58#16839762C411yescharacteristic, complemented
59#16839761C411yescharacteristic, complemented
60#16839760C411yescharacteristic, complemented
61#16839760C411yescharacteristic, complemented
62#103×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#417C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—41no—
73#14519856—44no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923D411yescharacteristic
89C2×C22⋊#6923D411yescharacteristic
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—41no—
97#14519845—41no—
98#14519840—22no—
99#14519840—22no—
100#14519839—41no—
101#14519839—41no—
102#14519834—21no—
103C22⋊#92420—21no—
104#14519831—41no—
105C8×#6923—41no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4D411yescharacteristic
113(C2×#6923)⋊C4D411yescharacteristic
114C2×#11758226C2×C411yescharacteristic
115C2×#11758222—21no—
116C2×#11758222C2×C411yescharacteristic
117C2×#11758224—21no—
118C2×#11758224C2×C411yescharacteristic
119#41×D61—22no—
120#41×D61—22no—
121#41×D61—41no—
122#41×D61—41no—
123C2×Q8×D61C2311yescharacteristic
124C2×D4×D61—21no—
125C2×D4×D61C2311yescharacteristic
126C22×C4×D61—21no—
127C22×C4×D61—21no—
128C22×C4×D61C2311yescharacteristic
129C2×#11758194C2×C411yescharacteristic
130C2×#11758189C2×C411yescharacteristic
131C2×#11758189C2×C411yescharacteristic
132M16×D61—41no—
133M16×D61—41no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136C2×C4⋊Dic61C2×C411yescharacteristic
137C2×#11758196—21no—
138C4⋊C4×D61—21no—
139C4⋊C4×D61—21no—
140C4⋊C4×D61C2×C411yescharacteristic
141C4⋊C4×D61C2×C411yescharacteristic
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144#14519702C2×C411yescharacteristic
145#14519702C2×C411yescharacteristic
146#14519701C2×C411yescharacteristic
147#14519701C2×C411yescharacteristic
148#14519700C2×C411yescharacteristic
149#14519700C2×C411yescharacteristic
150#14519699C2×C411yescharacteristic
151#14519699C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155#14519697C2×C411yescharacteristic
156C2×#41×C61C2×C411yescharacteristic
157C2×M16×C61C2×C411yescharacteristic
158C2×C4⋊C4×C61C2×C411yescharacteristic
159#103×C61C2×C411yescharacteristic
160#103×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162#102×C61C2×C411yescharacteristic
163C23×D61—21no—
164C23×D61C2×D411yescharacteristic
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173#41×C61—22no—
174#41×C61—41no—
175C2×Q8×C61C22×C411yescharacteristic
176C2×D4×C61—21no—
177C2×D4×C61C22×C411yescharacteristic
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61C22×C411yescharacteristic
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—21no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61#4111yescharacteristic
187#11758226—22no—
188#11758226—41no—
189Q8×D61—21no—
190Q8×D61—21no—
191Q8×D61#4112yes—
192Q8×D61#4112yes—
193#11758224—22no—
194#11758224—41no—
195#11758224—42no—
196#11758224—42no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61—21no—
200D4×D61—21no—
201D4×D61—42no—
202D4×D61—42no—
203#11758222—22no—
204#11758222—42no—
205#11758222—42no—
206#11758222—41no—
207C2×D244—21no—
208C2×D244C22×C411yescharacteristic
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—42no—
224C2×C4×D61C22×C411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61#4111yescharacteristic
227C2×C4×D61C2411yescharacteristic
228C2×Dic122—21no—
229C2×Dic122C22×C411yescharacteristic
230C22⋊#6923—22no—
231C22⋊#6923—41no—
232C22⋊#6923—42no—
233C22⋊#6923—42no—
234C22⋊#6923—42no—
235C22⋊#6923—81no—
236C22⋊#6923—81no—
237C22⋊#6923—81no—
238C2×#92420—21no—
239C2×#92420—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—21no—
243C4⋊#6923—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—42no—
249C4⋊#6923—42no—
250C4⋊#6923—42no—
251C4⋊#6923—42no—
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923—21no—
256C4×#6923—42no—
257C4×#6923—42no—
258C4×#6923—42no—
259C4×#6923—42no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263D61⋊C8—21no—
264M16×C61—41no—
265C2×C8×C61C22×C411yescharacteristic
266C2×C8×C61C22×C411yescharacteristic
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊Dic61—21no—
271C4⋊Dic61C22×C411yescharacteristic
272C4⋊Dic61C22×C411yescharacteristic
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758194—41no—
278C2×#92418C22×C411yescharacteristic
279C2×#92418C22×C411yescharacteristic
280#11758189—41no—
281#11758189—41no—
282C8×D61—21no—
283C8×D61—21no—
284C8×D61—21no—
285C8×D61—21no—
286C23×C61—21no—
287C23×C61C4×D411yescharacteristic
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61C4×D411yescharacteristic
302C22×D61C22×D411yescharacteristic
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923AGL(1,ℤ/8)12yes—
327Q8×C61—21no—
328Q8×C61#11712yescomplemented
329D4×C61—21no—
330D4×C61—21no—
331D4×C61—42no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61C4×D411yescharacteristic
340C2×C4×C61C23×C411yescharacteristic
341C22⋊D61—42no—
342C22⋊D61—42no—
343C22⋊D61—41no—
344C22⋊D61—41no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C4×D411yescharacteristic
353C2×Dic61C2×#4111yescharacteristic
354D244—21no—
355D244—21no—
356D244—42no—
357C4×D61—22no—
358C4×D61—22no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61C2×#4111yescharacteristic
374C4×D61C2×#4111yescharacteristic
375C4×D61H(5,𝔽2)11yescharacteristic
376C4×D61H(5,𝔽2)11yescharacteristic
377Dic122—21no—
378Dic122—22no—
379Dic122—22no—
380Dic122#11712yescomplemented
381#92420—41no—
382#92420—41no—
383C8×C61—21no—
384C8×C61—21no—
385#92418—21no—
386#92418—21no—
387#22583—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61C2×C4×D411yescharacteristic
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—81no—
408C2×D61—81no—
409C2×D61#54611yescharacteristic
410C2×D61#54611yescharacteristic
411C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
412C2×D61#57511yescharacteristic
413C2×D61#57711yescharacteristic
414C2×D61#57811yescharacteristic
415#6923—22no—
416#6923—41no—
417#6923—41no—
418#6923—41no—
419#6923—81no—
420#6923—81no—
421#6923—81no—
422#6923—81no—
423C4×C61—22no—
424C4×C61—21no—
425C4×C61—41no—
426C4×C61—41no—
427C4×C61C2×#11711yescharacteristic
428C4×C61#51811yescharacteristic
429Dic61—22no—
430Dic61—21no—
431Dic61—41no—
432Dic61—41no—
433Dic61#55111yescharacteristic
434Dic61#55111yescharacteristic
435C2×#417—611no—
436#2344—611no—
437#2341—611no—
438#1936—611no—
439#1934—611no—
440#1926—611no—
441#1925—611no—
442#1865—611no—
443#1863—611no—
444#1824—611no—
445#1809—611no—
446#1788—611no—
447#1763—611no—
448C4×#103—611no—
449#1753—611no—
450C2×C61—41no—
451C2×C61—81no—
452C2×C61#234211yescharacteristic
453C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
454C2×C61#294711yescharacteristic
455D61—41no—
456D61—81no—
457D61#330811yescharacteristic
458D61#331711yescharacteristic
459D61#332711yescharacteristic
460D61#333211yescharacteristic
461C22×#41—611no—
462C22×M16—611no—
463C2×C4×Q8—611no—
464C2×C4×Q8—611no—
465C2×#117—1221no—
466C22×C4⋊C4—611no—
467C2×#107—611no—
468C2×#106—611no—
469#417—611no—
470#417—611no—
471#417—611no—
472#417—611no—
473#417—611no—
474#417—611no—
475#417—611no—
476#417#692311yescharacteristic, complemented
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×C22⋊C8—611no—
486C2×#97—611no—
487C2×C4×C8—611no—
488#390—611no—
489#390—611no—
490#390—1221no—
491#390—1221no—
492#389—611no—
493#389—611no—
494#387—1221no—
495#387—1221no—
496#381—1221no—
497#380—611no—
498#380—611no—
499#380—1221no—
500C4×C4⋊C4—611no—
501C4×C4⋊C4—611no—
502C4×C22⋊C4—611no—
503C4×C22⋊C4—1221no—
504#340—611no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#340—611no—
510#336—611no—
511#336—611no—
512C61#2258311yescharacteristic, complemented, Sylow
513C2×#41—611no—
514C2×#41—611no—
515C2×#41—611no—
516C2×#41—1221no—
517C2×#41—1221no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—2441no—
521C2×#41—2441no—
522C2×#41C2×#692311yescharacteristic
523C22×Q8—611no—
524C22×D4—611no—
525C22×D4—1221no—
526C23×C4—611no—
527C23×C4—1221no—
528C23×C4—1221no—
529C2×M16—611no—
530C2×M16—611no—
531C2×M16—611no—
532C2×M16—2441no—
533C2×M16—2441no—
534C2×M16C2×#692311yescharacteristic
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C4×Q8—1222no—
540C4×Q8—1222no—
541C4×Q8—2441no—
542C4×Q8—2441no—
543#117—2444no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4C2×#692311yescharacteristic
561C2×C22⋊C4—611no—
562C2×C22⋊C4—611no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42—1221no—
574C2×C42—1221no—
575#107—2441no—
576#106—2441no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#103—611no—
582#103—611no—
583#103—1222no—
584#103—1222no—
585#103C2×#692311yescharacteristic
586#103C2×#692311yescharacteristic
587#102—611no—
588#102—611no—
589#102—611no—
590#102—611no—
591#102—611no—
592#102—611no—
593#102—2441no—
594#102—2441no—
595#102C2×#692311yescharacteristic
596#102C2×#692311yescharacteristic
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599#97—2441no—
600C4×C8—2441no—
601#95—611no—
602#95—611no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609C24—611no—
610C24—1221no—
611#41—22no—
612#41—41no—
613#41—1222no—
614#41—1222no—
615#41—1222no—
616#41—2441no—
617#41—2442no—
618#41—2442no—
619#41—2441no—
620#41—2442no—
621#41—2442no—
622#41—2441no—
623C2×Q8—612no—
624C2×Q8—612no—
625C2×Q8—611no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8C22×#692311yescharacteristic
630C2×D4—21no—
631C2×D4—611no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—2442no—
641C2×D4—2442no—
642C2×D4C22×#692311yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4C22×#692311yescharacteristic
676M16—41no—
677M16—2441no—
678M16—2441no—
679M16—2441no—
680C2×C8—611no—
681C2×C8—611no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8C22×#692311yescharacteristic
693C2×C8C22×#692311yescharacteristic
694C4⋊C4—21no—
695C4⋊C4—611no—
696C4⋊C4—611no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—2442no—
711C4⋊C4—2442no—
712C4⋊C4—2442no—
713C4⋊C4—2442no—
714C4⋊C4C22×#692311yescharacteristic
715C4⋊C4C22×#692311yescharacteristic
716C22⋊C4—1222no—
717C22⋊C4—4881no—
718C22⋊C4—4881no—
719C22⋊C4—4881no—
720C22⋊C4—2442no—
721C22⋊C4—2441no—
722C22⋊C4—2442no—
723C22⋊C4—2442no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C42—2442no—
729C42—2442no—
730C42—2442no—
731C42—2442no—
732C23—21no—
733C23—611no—
734C23—611no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23D4×#692311yescharacteristic
749Q8—21no—
750Q8—612no—
751Q8—1222no—
752Q8—1222no—
753Q8—1221no—
754Q8#1451985612yescomplemented
755D4—21no—
756D4—21no—
757D4—42no—
758D4—1221no—
759D4—1221no—
760D4—2442no—
761D4—2441no—
762D4—2441no—
763D4—2442no—
764D4—2442no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—612no—
778C2×C4—611no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2442no—
825C2×C4D4×#692311yescharacteristic
826C2×C4C23×#692311yescharacteristic
827C8—21no—
828C8—21no—
829C8—1221no—
830C8—1221no—
831C8—2441no—
832C8—2441no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—611no—
840C22—611no—
841C22—611no—
842C22—611no—
843C22—611no—
844C22—611no—
845C22—1221no—
846C22—1221no—
847C22—1221no—
848C22—4881no—
849C22—4881no—
850C22—4881no—
851C22—4881no—
852C22—2441no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22C2×D4×#692311yescharacteristic
860C4—21no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—611no—
865C4—611no—
866C4—1222no—
867C4—1221no—
868C4—1222no—
869C4—4881no—
870C4—4881no—
871C4—4881no—
872C4—4881no—
873C4—2441no—
874C4—2441no—
875C4—2441no—
876C4—2441no—
877C4—2441no—
878C4C2×#1451985611yescharacteristic
879C4#1684082911yescharacteristic
880C2—41no—
881C2—81no—
882C2—611no—
883C2—611no—
884C2—611no—
885C2—611no—
886C2—4881no—
887C2—2441no—
888C2#2146232511yescharacteristic
889C2AGL(1,ℤ/8)×#692311yescharacteristic
890C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#417#6923
hypocenterC61#22583
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #21462327C2semidirect
3. #21461911C2semidirect
4. #21461909C2semidirect
5. #21461897C2semidirect
6. #21461896C2semidirect
7. #21461785C2semidirect
8. #21461783C2semidirect
9. #21461723C2semidirect
10. #21461697C2semidirect
12. #21461592C2semidirect
13. #103×#6923C2semidirect
14. #21461559C2semidirect
55. #16839764C4semidirect
56. #16839763C4semidirect
57. #16839762C4semidirect
58. #16839762C4semidirect
59. #16839761C4semidirect
60. #16839760C4semidirect
61. #16839760C4semidirect
66. C61×#417C4semidirect
328. Q8×C61#117semidirect
380. Dic122#117semidirect
476. #417#6923semidirect
512. C61#22583semidirect
754. Q8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214623272
#214623242
#214619112
#214619092
#214618972
#214618962
#214617852
#214617832
#214617232
#214616972
#214616592
#214615922
#103×#69232
#214615592
#417×D612
#2258361