Finite Group Databasebeta

← #30622843

Subgroups — #30622843

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462353C211yesmaximal, characteristic, complemented
2#21462349C211yesmaximal, characteristic
3#21461999C211yesmaximal, characteristic, complemented
4#21461986C211yesmaximal, characteristic
5#21461911C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic, complemented
9#21461782C211yesmaximal, characteristic, complemented
10#21461782C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12#21461617C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic, complemented
15#490×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28#16840714—21no—
29#16840714C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713—21no—
32#16840713C2211yescharacteristic
33#16840713C2211yescharacteristic
34#16840711—21no—
35#16840711—21no—
36#16840710—21no—
37#16840710—21no—
38C4⋊C4×#6923—21no—
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C4⋊#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44#16840636C2211yescharacteristic
45#16840636C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#127×D61C2211yescharacteristic
53#125×D61C2211yescharacteristic
54#16840128C411yescharacteristic, complemented
55#16840127C411yescharacteristic, complemented
56#16840126C411yescharacteristic, complemented
57#16840125C411yescharacteristic, complemented
58#16840125C411yescharacteristic, complemented
59#16840125C411yescharacteristic, complemented
60#16840125C411yescharacteristic, complemented
61#102×D61C2211yescharacteristic
62#102×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#490C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
75D4×#6923—44no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923D411yescharacteristic
79C2×C4⋊#6923D411yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519845—22no—
98#14519844—21no—
99C4⋊#92420—21no—
100#14519839—22no—
101#14519839—22no—
102#14519839—41no—
103#14519839—41no—
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×D4×D61—21no—
115C2×D4×D61—21no—
116C2×D4×D61C2311yescharacteristic
117C2×D4×D61C2311yescharacteristic
118C2×C8×D61C2311yescharacteristic
119C2×C8×D61C2311yescharacteristic
120#14519774C2×C411yescharacteristic
121#14519773—21no—
122#14519773—21no—
123#14519773C2×C411yescharacteristic
124#14519773C2×C411yescharacteristic
125#14519769C2×C411yescharacteristic, complemented
126#14519768C2×C411yescharacteristic, complemented
127#14519768C2×C411yescharacteristic, complemented
128#14519767—21no—
129#14519767—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C42×D61C2311yescharacteristic
135#14519699C2×C411yescharacteristic, complemented
136#14519699C2×C411yescharacteristic, complemented
137#14519699C2×C411yescharacteristic, complemented
138#14519699C2×C411yescharacteristic, complemented
139#14519698C2×C411yescharacteristic, complemented
140#14519698C2×C411yescharacteristic, complemented
141#14519698C2×C411yescharacteristic, complemented
142#14519698C2×C411yescharacteristic, complemented
143#14519697C2×C411yescharacteristic, complemented
144#14519697C2×C411yescharacteristic, complemented
145#14519697C2×C411yescharacteristic, complemented
146#14519697C2×C411yescharacteristic, complemented
147#14519688C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149#14519687C2×C411yescharacteristic, complemented
150#127×C61C2×C411yescharacteristic
151#125×C61C2×C411yescharacteristic, complemented
152#102×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic, complemented
154#102×C61C2×C411yescharacteristic, complemented
155#102×C61C2×C411yescharacteristic, complemented
156#97×C61C2×C411yescharacteristic, complemented
157C23×D61—21no—
158C23×D61—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—42no—
164C22×#6923—42no—
165C22×#6923—42no—
166C22×#6923—42no—
167C22×#6923—81no—
168C22×#6923—81no—
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61C22×C411yescharacteristic
176C2×D4×C61C22×C411yescharacteristic
177C2×C22⋊D61—21no—
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183D4×D61—21no—
184D4×D61—21no—
185D4×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190D4×D61—21no—
191D4×D61—42no—
192D4×D61—42no—
193D4×D61—81no—
194D4×D61—81no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244C22×C411yescharacteristic
198C2×D244C22×C411yescharacteristic
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61C2×D411yescharacteristic
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2411yescharacteristic
204C22⋊#6923—42no—
205C22⋊#6923—42no—
206C22⋊#6923—42no—
207C22⋊#6923—42no—
208C22⋊#6923—81no—
209C22⋊#6923—81no—
210C2×#92420—21no—
211C2×#92420—21no—
212C4⋊#6923—22no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—41no—
220C4⋊#6923—42no—
221C4⋊#6923—81no—
222C4⋊#6923#4112yes—
223C4⋊#6923#4112yes—
224C4×#6923—21no—
225C4×#6923—21no—
226C4×#6923—21no—
227C4×#6923—21no—
228C4×#6923—42no—
229C4×#6923—42no—
230C4×#6923—81no—
231C4×#6923—81no—
232D61⋊C8—21no—
233D61⋊C8—21no—
234D61⋊C8—21no—
235D61⋊C8—21no—
236C2×C8×C61C22×C411yescharacteristic
237C2×C8×C61C22×C411yescharacteristic
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C22×C411yescharacteristic
241C4⋊C4×C61C22×C411yescharacteristic
242C42×C61C22×C411yescharacteristic
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61C22×C411yescharacteristic
246C4⋊Dic61C22×C411yescharacteristic
247#11758196—21no—
248#11758196—21no—
249#11758196—21no—
250#11758196—21no—
251#11758196—21no—
252#11758196—21no—
253C4×Dic61C22×C411yescharacteristic
254C4×Dic61#4111yescharacteristic
255C4×Dic61#4111yescharacteristic
256C2×#92418C22×C411yescharacteristic
257C2×#92418C22×C411yescharacteristic
258C8×D61—21no—
259C8×D61—21no—
260C8×D61—21no—
261C8×D61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61C22×D411yescharacteristic
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—22no—
285C2×#6923—22no—
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—41no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—84no—
303C2×#6923—84no—
304C2×#6923AGL(1,ℤ/8)12yes—
305D4×C61—21no—
306D4×C61—21no—
307D4×C61—21no—
308D4×C61—21no—
309D4×C61—42no—
310D4×C61—81no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C23×C411yescharacteristic
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—41no—
319C22⋊D61—41no—
320C22⋊D61—41no—
321C22⋊D61—41no—
322C22⋊D61—81no—
323C22⋊D61—81no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61C4×D411yescharacteristic
327C2×Dic61C4×D411yescharacteristic
328C2×Dic61C2×#4111yescharacteristic
329D244—21no—
330D244—21no—
331D244—21no—
332D244—21no—
333D244—42no—
334D244—81no—
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61C2×#4111yescharacteristic
344C4×D61C2×#4111yescharacteristic
345C4×D61H(5,𝔽2)11yescharacteristic
346C4×D612−1+411yescharacteristic
347#92420—41no—
348#92420—41no—
349C8×C61—21no—
350C8×C61—21no—
351#92418—21no—
352#92418—21no—
353#23229—611nomaximal, Sylow
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61C2×C4×D411yescharacteristic
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C2×D61—81no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61#54611yescharacteristic
376C2×D61#54811yescharacteristic
377C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
378C2×D61#57511yescharacteristic
379C2×D61#57611yescharacteristic
380C2×D61#57711yescharacteristic
381#6923—22no—
382#6923—42no—
383#6923—41no—
384#6923—41no—
385#6923—41no—
386#6923—42no—
387#6923—81no—
388#6923—81no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61C4×#4111yescharacteristic
394C4×C61#52011yescharacteristic
395Dic61—21no—
396Dic61—21no—
397Dic61—41no—
398Dic61—41no—
399Dic61#55611yescharacteristic
400Dic61#55911yescharacteristic
401C2×#490—611no—
402#2370—611no—
403#2366—611no—
404#1989—611no—
405#1982—611no—
406#1936—611no—
407#1934—611no—
408#1926—611no—
409#1926—611no—
410#1862—611no—
411#1862—611no—
412#1776—611no—
413#1771—611no—
414#1762—611no—
415C4×#102—611no—
416C2×C61—81no—
417C2×C61—81no—
418C2×C61#236711yescharacteristic
419C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
420C2×C61#294611yescharacteristic
421D61—81no—
422D61—81no—
423D61#331711yescharacteristic
424D61#331811yescharacteristic
425D61#336811yescharacteristic
426D61#337011yescharacteristic
427C2×#127—611no—
428C2×#125—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432#490—611no—
433#490—611no—
434#490—611no—
435#490—611no—
436#490—611no—
437#490—611no—
438#490—611no—
439#490#692311yescharacteristic, complemented
440C2×#107—611no—
441C2×#106—611no—
442C2×C4⋊C8—611no—
443C2×#102—611no—
444C2×#102—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#97—611no—
452C2×#97—611no—
453C2×C4×C8—611no—
454#390—611no—
455#390—611no—
456#390—1221no—
457#389—611no—
458#389—611no—
459#389—1221no—
460#387—1221no—
461#387—1221no—
462#386—1221no—
463#386—1221no—
464C4×C4⋊C4—611no—
465C4×C4⋊C4—611no—
466C4×C4⋊C4—611no—
467C4×C4⋊C4—611no—
468C4×C4⋊C4—611no—
469C4×C4⋊C4—1221no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476#336—611no—
477#336—611no—
478C61#2322911yescharacteristic, complemented, Sylow
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489#127—611no—
490#127—611no—
491#127—611no—
492#127—1221no—
493#127—1221no—
494#127C2×#692311yescharacteristic
495#125—611no—
496#125—611no—
497#125—611no—
498#125—1221no—
499#125—1221no—
500#125C2×#692311yescharacteristic, complemented
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—2441no—
504C4×D4—2441no—
505C4×D4—2444no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C42—611no—
525C2×C42—611no—
526C2×C42—611no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531#107—1222no—
532#106—1222no—
533C4⋊C8—1221no—
534C4⋊C8—1221no—
535#102—611no—
536#102—611no—
537#102—611no—
538#102—611no—
539#102—611no—
540#102—611no—
541#102—611no—
542#102—611no—
543#102—611no—
544#102—611no—
545#102—611no—
546#102—611no—
547#102—1222no—
548#102—1222no—
549#102—2441no—
550#102—2441no—
551#102C2×#692311yescharacteristic, complemented
552#102C2×#692311yescharacteristic, complemented
553#102C2×#692311yescharacteristic, complemented
554#102C2×#692311yescharacteristic, complemented
555#97—611no—
556#97—611no—
557#97—611no—
558#97—2441no—
559#97C2×#692311yescharacteristic, complemented
560C4×C8—2441no—
561#95—611no—
562#95—611no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—1221no—
570C24—1221no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—611no—
574C2×D4—611no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
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—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—4881no—
592C2×D4—4881no—
593C2×D4—2442no—
594C2×D4—2442no—
595C2×D4C22×#692311yescharacteristic
596C2×D4C22×#692311yescharacteristic
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—4881no—
611C22×C4—4881no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2442no—
616C2×C8—611no—
617C2×C8—611no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8C22×#692311yescharacteristic
629C2×C8C22×#692311yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—612no—
633C4⋊C4—612no—
634C4⋊C4—611no—
635C4⋊C4—611no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C4⋊C4—1222no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—4881no—
652C4⋊C4—2442no—
653C4⋊C4—2441no—
654C4⋊C4C22×#692311yescharacteristic
655C4⋊C4C22×#692311yescharacteristic
656C22⋊C4—4881no—
657C22⋊C4—4881no—
658C22⋊C4—2442no—
659C22⋊C4—2442no—
660C22⋊C4—2442no—
661C22⋊C4—2442no—
662C42—611no—
663C42—611no—
664C42—611no—
665C42—1221no—
666C42—1221no—
667C42—1221no—
668C42—1221no—
669C42—4881no—
670C42—4881no—
671C42—2442no—
672C42—2442no—
673C42C22×#692311yescharacteristic
674C23—21no—
675C23—21no—
676C23—611no—
677C23—1221no—
678C23—1221no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—42no—
696D4—81no—
697D4—1221no—
698D4—1221no—
699D4—1221no—
700D4—1221no—
701D4—4881no—
702D4—4881no—
703D4—4881no—
704D4—2442no—
705D4—2441no—
706D4—2441no—
707D4—2441no—
708D4—2441no—
709D4—2442no—
710D4—2442no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—612no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1222no—
734C2×C4—1221no—
735C2×C4—1222no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—4884no—
741C2×C4—4884no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4D4×#692311yescharacteristic
757C2×C4D4×#692311yescharacteristic
758C2×C4C23×#692311yescharacteristic
759C8—21no—
760C8—21no—
761C8—1221no—
762C8—1221no—
763C8—2441no—
764C8—2441no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—611no—
772C22—611no—
773C22—611no—
774C22—611no—
775C22—611no—
776C22—611no—
777C22—4881no—
778C22—4881no—
779C22—4881no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—4881no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22C2×D4×#692311yescharacteristic
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—611no—
797C4—611no—
798C4—1222no—
799C4—1221no—
800C4—1221no—
801C4—4881no—
802C4—4881no—
803C4—2441no—
804C4—2441no—
805C4—2441no—
806C4—2442no—
807C4—2442no—
808C4—2441no—
809C4—2441no—
810C4#41×#692311yescharacteristic
811C4#1684083111yescharacteristic
812C2—81no—
813C2—81no—
814C2—611no—
815C2—611no—
816C2—611no—
817C2—611no—
818C2—4881no—
819C2—4881no—
820C2#2146235011yescharacteristic
821C2AGL(1,ℤ/8)×#692311yescharacteristic
822C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#490C4
socleC22×C61C2×C4×D4
prime radical#127×D61C22
cosocleC2×C4×D61C24
hypercenter#490#6923
hypocenterC61#23229
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #21462353C2semidirect
3. #21461999C2semidirect
5. #21461911C2semidirect
6. #21461909C2semidirect
7. #21461897C2semidirect
8. #21461897C2semidirect
9. #21461782C2semidirect
10. #21461782C2semidirect
11. #21461633C2semidirect
12. #21461617C2semidirect
13. #21461590C2semidirect
14. #102×#6923C2semidirect
54. #16840128C4semidirect
55. #16840127C4semidirect
56. #16840126C4semidirect
57. #16840125C4semidirect
58. #16840125C4semidirect
59. #16840125C4semidirect
60. #16840125C4semidirect
66. C61×#490C4semidirect
125. #14519769C2×C4semidirect
126. #14519768C2×C4semidirect
127. #14519768C2×C4semidirect
135. #14519699C2×C4semidirect
136. #14519699C2×C4semidirect
137. #14519699C2×C4semidirect
138. #14519699C2×C4semidirect
139. #14519698C2×C4semidirect
140. #14519698C2×C4semidirect
141. #14519698C2×C4semidirect
142. #14519698C2×C4semidirect
143. #14519697C2×C4semidirect
144. #14519697C2×C4semidirect
145. #14519697C2×C4semidirect
146. #14519697C2×C4semidirect
147. #14519688C2×C4semidirect
148. #14519687C2×C4semidirect
149. #14519687C2×C4semidirect
151. #125×C61C2×C4semidirect
152. #102×C61C2×C4semidirect
153. #102×C61C2×C4semidirect
154. #102×C61C2×C4semidirect
155. #102×C61C2×C4semidirect
156. #97×C61C2×C4semidirect
439. #490#6923semidirect
478. C61#23229semidirect
500. #125C2×#6923semidirect
551. #102C2×#6923semidirect
552. #102C2×#6923semidirect
553. #102C2×#6923semidirect
554. #102C2×#6923semidirect
559. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623532
#214623492
#214619992
#214619862
#214619112
#214619092
#214618972
#214617822
#214616332
#214616172
#214615902
#102×#69232
#490×D612
#2322961