Finite Group Databasebeta

← #30622466

Subgroups — #30622466

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462350C211yesmaximal, characteristic, complemented
2#21462340C211yesmaximal, characteristic, complemented
3#21461966C211yesmaximal, characteristic
4#21461964C211yesmaximal, characteristic, complemented
5#21461948C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic
11#21461612C211yesmaximal, characteristic, complemented
12#103×#6923C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14C4×#14519839C211yesmaximal, characteristic, complemented
15#463×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C4×D61⋊C8C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28C2×C8×#6923C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840714C2211yescharacteristic
32#16840714C2211yescharacteristic
33#16840712—21no—
34#16840712—21no—
35#16840712—21no—
36#16840712—21no—
37#16840709—21no—
38#16840706C2211yescharacteristic
39#16840705—21no—
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C22⋊C4×#6923—21no—
45C4×C22⋊#6923—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C2×D8×D61C2211yescharacteristic
54#124×D61C2211yescharacteristic
55C4×D4×D61C2211yescharacteristic
56#16839980C411yescharacteristic, complemented
57#16839979C411yescharacteristic, complemented
58#16839978C411yescharacteristic, complemented
59#16839977C411yescharacteristic, complemented
60#16839976C411yescharacteristic, complemented
61#16839975C411yescharacteristic, complemented
62#16839974C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#463C411yescharacteristic, complemented
67C23×#6923—21no—
68C2×D61⋊C8C2311yescharacteristic
69C2×D61⋊C8C2311yescharacteristic
70Q8×#6923—22no—
71Q8×#6923—41no—
72D4×#6923—22no—
73D4×#6923—41no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923D411yescharacteristic
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
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×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923C2311yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94#14519846—41no—
95#14519845—41no—
96#14519840—22no—
97#14519840—41no—
98#14519839—22no—
99#14519839—22no—
100#14519839—22no—
101#14519839—41no—
102C4×#92420—21no—
103C4×#92420—21no—
104C8×#6923—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)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×D4×D61C2311yescharacteristic
117C2×D4×D61C2311yescharacteristic
118C22×C4×D61—21no—
119C2×#11758190C2×C411yescharacteristic, complemented
120C2×#11758200C2×C411yescharacteristic, complemented
121C2×#11758201C2×C411yescharacteristic, complemented
122SD16×D61—41no—
123SD16×D61—41no—
124C2×D488C2×C411yescharacteristic
125C2×#11758199C2×C411yescharacteristic
126C2×#11758199C2×C411yescharacteristic
127D8×D61—41no—
128D8×D61—41no—
129C2×C8×D61C2311yescharacteristic
130C2×C8×D61C2311yescharacteristic
131#14519766C2×C411yescharacteristic
132#14519765C2×C411yescharacteristic
133#14519764C2×C411yescharacteristic
134#14519763—21no—
135#14519763—21no—
136C4×D244C2×C411yescharacteristic, complemented
137D4×Dic61C2×C411yescharacteristic, complemented
138#14519739C2×C411yescharacteristic, complemented
139C4×C22⋊D61—21no—
140#14519737—21no—
141C4⋊C4×D61C2311yescharacteristic
142C22⋊C4×D61—21no—
143C22⋊C4×D61—21no—
144C22⋊C4×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic, complemented
147#14519706C2×C411yescharacteristic, complemented
148#14519706C2×C411yescharacteristic, complemented
149#14519702C2×C411yescharacteristic, complemented
150#14519701C2×C411yescharacteristic, complemented
151#14519700C2×C411yescharacteristic, complemented
152#14519699C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×SD16×C61C2×C411yescharacteristic, complemented
156C2×D8×C61C2×C411yescharacteristic
157#124×C61C2×C411yescharacteristic
158C4×D4×C61C2×C411yescharacteristic, complemented
159C4⋊C8×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—42no—
169C22×#6923—42no—
170C22×#6923—81no—
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C22×#6923C2×D411yescharacteristic
175C2×Q8×C61C22×C411yescharacteristic
176C2×D4×C61C22×C411yescharacteristic
177C2×D4×C61C22×C411yescharacteristic
178C22×C4×C61—21no—
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C22×Dic61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185Q8×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61—21no—
190D4×D61—21no—
191D4×D61—21no—
192D4×D61—21no—
193D4×D61—21no—
194C2×D244C22×C411yescharacteristic
195C2×D244C22×C411yescharacteristic
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2411yescharacteristic
205C2×Dic122—21no—
206C2×Dic122C22×C411yescharacteristic
207C22⋊#6923—42no—
208C22⋊#6923—42no—
209C22⋊#6923—42no—
210C22⋊#6923—42no—
211C22⋊#6923—81no—
212C22⋊#6923—81no—
213C22⋊#6923—81no—
214C2×#92420—21no—
215C2×#92420—21no—
216C4⋊#6923—22no—
217C4⋊#6923—22no—
218C4⋊#6923—21no—
219C4⋊#6923—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—42no—
226C4⋊#6923#4112yes—
227C4×#6923—21no—
228C4×#6923—21no—
229C4×#6923—21no—
230C4×#6923—21no—
231C4×#6923—42no—
232C4×#6923—81no—
233C4×#6923—81no—
234C4×#6923—81no—
235D61⋊C8—21no—
236D61⋊C8—21no—
237D61⋊C8—21no—
238D61⋊C8#4112yes—
239SD16×C61—41no—
240D8×C61—41no—
241C2×C8×C61C22×C411yescharacteristic
242C2×C8×C61C22×C411yescharacteristic
243C4⋊C4×C61C22×C411yescharacteristic
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C42×C61C22×C411yescharacteristic
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251#11758201—41no—
252#11758200—41no—
253#11758199—41no—
254#11758199—41no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61C22×C411yescharacteristic
262#11758196—21no—
263C4×Dic61C22×C411yescharacteristic
264C4×Dic61#4111yescharacteristic
265C4×Dic61#4111yescharacteristic
266C2×#92418C22×C411yescharacteristic
267C2×#92418C22×C411yescharacteristic
268D488—41no—
269#11758190—41no—
270C8×D61—21no—
271C8×D61—21no—
272C8×D61—21no—
273C8×D61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61C22×D411yescharacteristic
291C2×#6923—21no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—22no—
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—84no—
314C2×#6923#13512yes—
315C2×#6923#13512yes—
316Q8×C61—21no—
317Q8×C61—21no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—81no—
325C2×C4×C61C4×D411yescharacteristic
326C2×C4×C61C4×D411yescharacteristic
327C2×C4×C61C23×C411yescharacteristic
328C22⋊D61—41no—
329C22⋊D61—41no—
330C22⋊D61—41no—
331C22⋊D61—41no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—81no—
335C2×Dic61C4×D411yescharacteristic
336C2×Dic61C4×D411yescharacteristic
337C2×Dic61C2×#4111yescharacteristic
338D244—21no—
339D244—21no—
340D244—21no—
341D244—21no—
342C4×D61—21no—
343C4×D61—21no—
344C4×D61—21no—
345C4×D61—21no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—81no—
351C4×D61—81no—
352C4×D61C2×#4111yescharacteristic
353C4×D61C2×#4111yescharacteristic
354C4×D61H(5,𝔽2)11yescharacteristic
355C4×D61H(5,𝔽2)11yescharacteristic
356Dic122—21no—
357Dic122—21no—
358Dic122—41no—
359Dic122—41no—
360#92420—22no—
361#92420—41no—
362C8×C61—21no—
363C8×C61—21no—
364#92418—21no—
365#92418—21no—
366#23098—611nomaximal, Sylow
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61C2×C4×D411yescharacteristic
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61—81no—
383C2×D61—81no—
384C2×D61—81no—
385C2×D61—81no—
386C2×D61—81no—
387C2×D61—81no—
388C2×D61#54611yescharacteristic
389C2×D61#55011yescharacteristic
390C2×D61C2×#13511yescharacteristic
391C2×D61C2×#13511yescharacteristic
392C2×D61#57611yescharacteristic
393C2×D61#57711yescharacteristic
394#6923—22no—
395#6923—22no—
396#6923—41no—
397#6923—42no—
398#6923—41no—
399#6923—81no—
400#6923—81no—
401#6923—81no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61C4×#4111yescharacteristic
407C4×C61#51811yescharacteristic
408Dic61—21no—
409Dic61—21no—
410Dic61—41no—
411Dic61—41no—
412Dic61#55311yescharacteristic
413Dic61#55511yescharacteristic
414C2×#463—611no—
415#2367—611no—
416#2357—611no—
417#1970—611no—
418#1968—611no—
419#1958—611no—
420#1949—611no—
421#1928—611no—
422#1926—611no—
423#1880—611no—
424#1879—611no—
425C8×C4⋊C4—611no—
426C4×#103—611no—
427C4×#102—611no—
428C4×#102—611no—
429C2×C61—81no—
430C2×C61—81no—
431C2×C61#236311yescharacteristic
432C2×C61C4×#13511yescharacteristic
433C2×C61#294611yescharacteristic
434D61—81no—
435D61—81no—
436D61#329711yescharacteristic
437D61#330111yescharacteristic
438D61#339411yescharacteristic
439D61#339611yescharacteristic
440C22×SD16—611no—
441C22×D8—611no—
442C2×#124—611no—
443C2×C4×Q8—611no—
444C2×C4×D4—611no—
445C2×C4×D4—611no—
446#463—611no—
447#463—611no—
448#463—611no—
449#463—611no—
450#463—611no—
451#463—611no—
452#463—611no—
453#463#692311yescharacteristic, complemented
454C2×#107—611no—
455C2×#106—611no—
456C2×C4⋊C8—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×C4×C8—611no—
466C2×C4×C8—611no—
467C2×C4×C8—611no—
468#391—611no—
469#390—611no—
470#390—611no—
471#390—611no—
472#388—1221no—
473#388—1221no—
474#388—1221no—
475#388—1221no—
476#385—1221no—
477#382—611no—
478#381—1221no—
479C4×C4⋊C4—611no—
480C4×C4⋊C4—611no—
481C4×C4⋊C4—611no—
482C4×C4⋊C4—611no—
483C4×C22⋊C4—1221no—
484C4×C22⋊C4—1221no—
485#340—611no—
486#340—611no—
487#340—611no—
488#340—611no—
489#336—611no—
490#336—611no—
491C61#2309811yescharacteristic, complemented, Sylow
492C22×Q8—611no—
493C22×D4—611no—
494C22×D4—611no—
495C23×C4—1221no—
496C23×C4—1221no—
497C2×SD16—611no—
498C2×SD16—611no—
499C2×SD16—611no—
500C2×SD16—2441no—
501C2×SD16—2441no—
502C2×SD16C2×#692311yescharacteristic, complemented
503C2×D8—611no—
504C2×D8—611no—
505C2×D8—611no—
506C2×D8—2441no—
507C2×D8—2441no—
508C2×D8C2×#692311yescharacteristic
509C22×C8—611no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513#124—611no—
514#124—611no—
515#124—611no—
516#124—1221no—
517#124—1221no—
518#124C2×#692311yescharacteristic
519C4×Q8—1222no—
520C4×Q8—2441no—
521C4×D4—611no—
522C4×D4—611no—
523C4×D4—611no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1222no—
527C4×D4—2441no—
528C4×D4C2×#692311yescharacteristic, complemented
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—1221no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42—1221no—
554#107—2441no—
555#106—2441no—
556C4⋊C8—611no—
557C4⋊C8—611no—
558C4⋊C8—611no—
559C4⋊C8C2×#692311yescharacteristic, complemented
560#103—611no—
561#103—611no—
562#103—611no—
563#103—1222no—
564#103—2441no—
565#103C2×#692311yescharacteristic, complemented
566#102—611no—
567#102—611no—
568#102—611no—
569#102—1222no—
570#102—1222no—
571#102—1222no—
572#102—2441no—
573#102C2×#692311yescharacteristic
574C4×C8—1221no—
575C4×C8—1221no—
576C4×C8—2441no—
577C4×C8—2441no—
578#95—611no—
579#95—611no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584#95—1221no—
585#95—1221no—
586#95—1221no—
587C24—1221no—
588C24—1221no—
589C2×Q8—611no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8C22×#692311yescharacteristic
596C2×D4—611no—
597C2×D4—611no—
598C2×D4—1221no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4C22×#692311yescharacteristic
609C2×D4C22×#692311yescharacteristic
610C22×C4—21no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—4881no—
628C22×C4—4881no—
629C22×C4—4881no—
630C22×C4—2442no—
631C22×C4—2442no—
632SD16—41no—
633SD16—2441no—
634SD16—2441no—
635SD16—2441no—
636D8—41no—
637D8—2441no—
638D8—2441no—
639D8—2441no—
640C2×C8—612no—
641C2×C8—611no—
642C2×C8—611no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8C22×#692311yescharacteristic
653C2×C8C22×#692311yescharacteristic
654C4⋊C4—612no—
655C4⋊C4—611no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1222no—
659C4⋊C4—1222no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—2442no—
667C4⋊C4C22×#692311yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—4881no—
681C22⋊C4—4881no—
682C22⋊C4—4881no—
683C22⋊C4—2442no—
684C22⋊C4—2442no—
685C22⋊C4—2442no—
686C22⋊C4—2442no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—1221no—
691C42—1221no—
692C42—1221no—
693C42—1221no—
694C42—4881no—
695C42—4881no—
696C42—4881no—
697C42—2442no—
698C42C22×#692311yescharacteristic
699C23—21no—
700C23—21no—
701C23—611no—
702C23—1221no—
703C23—1221no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2441no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716Q8—21no—
717Q8—21no—
718Q8—1221no—
719Q8—1221no—
720Q8—2441no—
721Q8—2441no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—21no—
726D4—1221no—
727D4—1221no—
728D4—1221no—
729D4—1221no—
730D4—2441no—
731D4—2441no—
732D4—2441no—
733D4—2441no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—81no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1222no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—4881no—
764C2×C4—4881no—
765C2×C4—4881no—
766C2×C4—4884no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4D4×#692311yescharacteristic
783C2×C4D4×#692311yescharacteristic
784C2×C4C23×#692311yescharacteristic
785C8—21no—
786C8—21no—
787C8—1222no—
788C8—1221no—
789C8—1221no—
790C8—2441no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—611no—
798C22—611no—
799C22—611no—
800C22—611no—
801C22—611no—
802C22—611no—
803C22—4881no—
804C22—4881no—
805C22—4881no—
806C22—4881no—
807C22—4881no—
808C22—4881no—
809C22—4881no—
810C22—4881no—
811C22—2441no—
812C22—2441no—
813C22—2441no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22C2×D4×#692311yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—611no—
823C4—611no—
824C4—1222no—
825C4—1222no—
826C4—1221no—
827C4—1221no—
828C4—4881no—
829C4—4881no—
830C4—4881no—
831C4—2441no—
832C4—2441no—
833C4—2442no—
834C4—2441no—
835C4—2441no—
836C4#41×#692311yescharacteristic
837C4#1684082911yescharacteristic
838C2—81no—
839C2—81no—
840C2—611no—
841C2—611no—
842C2—611no—
843C2—611no—
844C2—4881no—
845C2—4881no—
846C2#2146234611yescharacteristic
847C2#135×#692311yescharacteristic
848C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#463C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#463#6923
hypocenterC61#23098
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #21462350C2semidirect
2. #21462340C2semidirect
4. #21461964C2semidirect
5. #21461948C2semidirect
6. #21461932C2semidirect
7. #21461899C2semidirect
8. #21461897C2semidirect
9. #21461815C2semidirect
11. #21461612C2semidirect
12. #103×#6923C2semidirect
13. #102×#6923C2semidirect
14. C4×#14519839C2semidirect
56. #16839980C4semidirect
57. #16839979C4semidirect
58. #16839978C4semidirect
59. #16839977C4semidirect
60. #16839976C4semidirect
61. #16839975C4semidirect
62. #16839974C4semidirect
66. C61×#463C4semidirect
119. C2×#11758190C2×C4semidirect
120. C2×#11758200C2×C4semidirect
121. C2×#11758201C2×C4semidirect
136. C4×D244C2×C4semidirect
137. D4×Dic61C2×C4semidirect
138. #14519739C2×C4semidirect
146. C4⋊#92418C2×C4semidirect
147. #14519706C2×C4semidirect
148. #14519706C2×C4semidirect
149. #14519702C2×C4semidirect
150. #14519701C2×C4semidirect
151. #14519700C2×C4semidirect
155. C2×SD16×C61C2×C4semidirect
158. C4×D4×C61C2×C4semidirect
159. C4⋊C8×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
453. #463#6923semidirect
491. C61#23098semidirect
502. C2×SD16C2×#6923semidirect
528. C4×D4C2×#6923semidirect
559. C4⋊C8C2×#6923semidirect
565. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623502
#214623402
#214619662
#214619642
#214619482
#214619322
#214618992
#214618972
#214618152
#214618142
#214616122
#103×#69232
#102×#69232
C4×#145198392
#463×D612
#2309861