Finite Group Databasebeta

← #30617319

Subgroups — #30617319

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462313C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic
3#21461999C211yesmaximal, characteristic, complemented
4#21461931C211yesmaximal, characteristic, complemented
5#21461881C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461784C211yesmaximal, characteristic
8#21461784C211yesmaximal, characteristic
9#21461687C211yesmaximal, characteristic
10#21461634C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12#21461608C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic
14#102×#6923C211yesmaximal, characteristic
15#478×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519845C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20D61⋊(C4⋊C8)C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25#16840713—21no—
26#16840713—21no—
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840711—21no—
30#16840711—21no—
31#16840708C2211yescharacteristic
32C4⋊C4×#6923C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C4×C22⋊#6923—21no—
40#16840698C2211yescharacteristic
41C2×(C2×#6923)⋊C4—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#125×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840065C411yescharacteristic, complemented
55#16840064C411yescharacteristic, complemented
56#16840063C411yescharacteristic, complemented
57#16840062C411yescharacteristic, complemented
58#16840061C411yescharacteristic, complemented
59#16840060C411yescharacteristic, complemented
60#16840059C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#478C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923Q814yes—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519845—22no—
93#14519845—22no—
94#14519844—21no—
95C4⋊#92420—21no—
96#14519839—22no—
97#14519839—22no—
98#14519831—22no—
99C8×#6923—22no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×D4×D61C2311yescharacteristic
112C22×C4×D61—21no—
113C2×C8×D61C2311yescharacteristic
114C2×C8×D61C2311yescharacteristic
115#14519769C2×C411yescharacteristic, complemented
116#14519768C2×C411yescharacteristic, complemented
117#14519768C2×C411yescharacteristic, complemented
118#14519767—21no—
119#14519767—21no—
120C4×D244C2×C411yescharacteristic
121D4×Dic61C2×C411yescharacteristic
122#14519739C2×C411yescharacteristic
123C4×C22⋊D61—21no—
124#14519737—21no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C22⋊C4×D61—21no—
131C42×D61C2311yescharacteristic
132#14519711C2×C411yescharacteristic, complemented
133#14519710C2×C411yescharacteristic, complemented
134#14519710C2×C411yescharacteristic, complemented
135#14519709C2×C411yescharacteristic, complemented
136#14519708C2×C411yescharacteristic, complemented
137#14519708C2×C411yescharacteristic, complemented
138C4⋊#92418C2×C411yescharacteristic, complemented
139#14519706C2×C411yescharacteristic, complemented
140#14519706C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic
142#14519699C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#125×C61C2×C411yescharacteristic, complemented
148C4×D4×C61C2×C411yescharacteristic
149#107×C61C2×C411yescharacteristic, complemented
150#106×C61C2×C411yescharacteristic, complemented
151C4⋊C8×C61C2×C411yescharacteristic, complemented
152#102×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154C23×D61—21no—
155C22×#6923—21no—
156C22×#6923—21no—
157C22×#6923—24no—
158C22×#6923—24no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—81no—
162C22×#6923—81no—
163C22×#6923—81no—
164C22×#6923—81no—
165C22×#6923C2×D411yescharacteristic
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C2×D4×C61C22×C411yescharacteristic
170C22×C4×C61—21no—
171C2×C22⋊D61—21no—
172C22×Dic61—21no—
173D4×D61—21no—
174D4×D61—21no—
175D4×D61C2×Q812yes—
176D4×D61#4112yes—
177C2×D244C22×C411yescharacteristic
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—81no—
184C2×C4×D61—81no—
185C2×C4×D61C2×D411yescharacteristic
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2411yescharacteristic
188C22⋊#6923—24no—
189C22⋊#6923—24no—
190C2×#92420—21no—
191C2×#92420—21no—
192C4⋊#6923—21no—
193C4⋊#6923—21no—
194C4⋊#6923—21no—
195C4⋊#6923—21no—
196C4⋊#6923—21no—
197C4⋊#6923—21no—
198C4⋊#6923—81no—
199C4⋊#6923—81no—
200C4⋊#6923—81no—
201C4⋊#6923—81no—
202C4⋊#6923C2×Q812yes—
203C4⋊#6923#4112yes—
204C4×#6923—21no—
205C4×#6923—21no—
206C4×#6923—81no—
207C4×#6923—81no—
208C4×#6923—81no—
209C4×#6923—81no—
210C4×#6923—81no—
211C4×#6923C2×Q812yes—
212C4×#6923#4112yes—
213D61⋊C8—21no—
214D61⋊C8—21no—
215D61⋊C8—21no—
216D61⋊C8—21no—
217C2×C8×C61C22×C411yescharacteristic
218C2×C8×C61C22×C411yescharacteristic
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C4⋊C4×C61C22×C411yescharacteristic
224C22⋊C4×C61—21no—
225C42×C61C22×C411yescharacteristic
226C22⋊Dic61—21no—
227#11758198—21no—
228#11758198—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61C22×C411yescharacteristic
232C4⋊Dic61C22×C411yescharacteristic
233C4⋊Dic61C22×C411yescharacteristic
234#11758196—21no—
235#11758196—21no—
236#11758196—21no—
237#11758196—21no—
238#11758196—21no—
239#11758196—21no—
240#11758196—21no—
241C4×Dic61C22×C411yescharacteristic
242C4×Dic61#4111yescharacteristic
243C4×Dic61#4111yescharacteristic
244C2×#92418C22×C411yescharacteristic
245C2×#92418C22×C411yescharacteristic
246C8×D61—21no—
247C8×D61—21no—
248C8×D61—21no—
249C8×D61—21no—
250C23×C61—21no—
251C22×D61—21no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61C22×D411yescharacteristic
259C2×#6923—21no—
260C2×#6923—21no—
261C2×#6923—21no—
262C2×#6923—21no—
263C2×#6923—22no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—22no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—41no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—84no—
282C2×#6923—84no—
283C2×#6923C22⋊Q812yes—
284C2×#6923C22⋊Q812yes—
285D4×C61—21no—
286D4×C61C4×Q812yes—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—81no—
291C2×C4×C61C4×D411yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C23×C411yescharacteristic
294C22⋊D61—22no—
295C22⋊D61—22no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—81no—
300C2×Dic61C4×D411yescharacteristic
301C2×Dic61C4×D411yescharacteristic
302C2×Dic61C2×#4111yescharacteristic
303D244—21no—
304D244C4×Q812yes—
305C4×D61—21no—
306C4×D61—21no—
307C4×D61—21no—
308C4×D61—21no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—81no—
316C4×D61—81no—
317C4×D61C22×Q811yescharacteristic
318C4×D61C2×#4111yescharacteristic
319C4×D61C2×#4111yescharacteristic
320C4×D61C2×#4111yescharacteristic
321#92420—41no—
322#92420—41no—
323C8×C61—21no—
324C8×C61—21no—
325#92418—21no—
326#92418—21no—
327#21619—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61C2×C4×D411yescharacteristic
332C2×D61—22no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—42no—
336C2×D61—42no—
337C2×D61—42no—
338C2×D61—42no—
339C2×D61C2×C22⋊Q811yescharacteristic
340C2×D61#52511yescharacteristic
341C2×D61#57611yescharacteristic
342C2×D61#57711yescharacteristic
343C2×D61#57711yescharacteristic
344C2×D61#57711yescharacteristic
345#6923—22no—
346#6923—22no—
347#6923—42no—
348#6923—41no—
349#6923—41no—
350#6923—42no—
351#6923—81no—
352#6923—81no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61C2×C4×Q811yescharacteristic
359C4×C61C4×#4111yescharacteristic
360Dic61—21no—
361Dic61—21no—
362Dic61—41no—
363Dic61—41no—
364Dic61—41no—
365Dic61#52911yescharacteristic
366Dic61#53311yescharacteristic
367C2×#478—611no—
368#2330—611no—
369#2275—611no—
370#1989—611no—
371#1948—611no—
372#1919—611no—
373#1918—611no—
374#1864—611no—
375#1864—611no—
376#1802—611no—
377#1776—611no—
378C4×#106—611no—
379#1768—611no—
380#1762—611no—
381C4×#102—611no—
382C2×C61—42no—
383C2×C61C4×C22⋊Q811yescharacteristic
384C2×C61#294611yescharacteristic
385C2×C61#295211yescharacteristic
386D61—42no—
387D61#308111yescharacteristic
388D61#308411yescharacteristic
389D61#311911yescharacteristic
390D61#312311yescharacteristic
391C2×#125—611no—
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C2×C4×D4—611no—
395#478—611no—
396#478—611no—
397#478—611no—
398#478—611no—
399#478—611no—
400#478—611no—
401#478—611no—
402#478#692311yescharacteristic, complemented
403C2×#107—611no—
404C2×#106—611no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#97—611no—
414C2×C4×C8—611no—
415#389—611no—
416#389—611no—
417#389—1221no—
418#389—1221no—
419#387—1221no—
420#387—1221no—
421#384—611no—
422C4×C4⋊C4—611no—
423C4×C4⋊C4—611no—
424C4×C4⋊C4—611no—
425C4×C4⋊C4—611no—
426C4×C4⋊C4—611no—
427C4×C22⋊C4—1221no—
428C4×C22⋊C4—1221no—
429C4×C22⋊C4—1221no—
430#376—611no—
431C2×#95—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2161911yescharacteristic, complemented, Sylow
443C22×D4—611no—
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451#125—611no—
452#125—611no—
453#125—611no—
454#125—1221no—
455#125—1221no—
456#125C2×#692311yescharacteristic, complemented
457C4×D4—614no—
458C4×D4—611no—
459C4×D4—611no—
460C4×D4—611no—
461C4×D4—1221no—
462C4×D4—1221no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4C2×#692311yescharacteristic
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—1221no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491#107—611no—
492#107—611no—
493#107—611no—
494#107C2×#692311yescharacteristic, complemented
495#106—611no—
496#106—611no—
497#106—611no—
498#106—1222no—
499#106—1222no—
500#106C2×#692311yescharacteristic, complemented
501C4⋊C8—611no—
502C4⋊C8—611no—
503C4⋊C8—611no—
504C4⋊C8—1221no—
505C4⋊C8—1221no—
506C4⋊C8C2×#692311yescharacteristic, complemented
507#102—611no—
508#102—611no—
509#102—611no—
510#102—611no—
511#102—611no—
512#102—611no—
513#102—1222no—
514#102—1222no—
515#102C2×#692311yescharacteristic
516#102C2×#692311yescharacteristic
517#97—1222no—
518C4×C8—1222no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95—611no—
523#95—1221no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—1221no—
531C2×D4—612no—
532C2×D4—612no—
533C2×D4—611no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4C22×#692311yescharacteristic
538C22×C4—21no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1224no—
552C22×C4—1224no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—4881no—
559C22×C4—4881no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—4881no—
563C22×C4—4881no—
564C2×C8—611no—
565C2×C8—611no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8C22×#692311yescharacteristic
577C2×C8C22×#692311yescharacteristic
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—612no—
581C4⋊C4—612no—
582C4⋊C4—611no—
583C4⋊C4—611no—
584C4⋊C4—611no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—4881no—
601C4⋊C4—4881no—
602C4⋊C4—4881no—
603C4⋊C4—4881no—
604C4⋊C4C22×#692311yescharacteristic
605C4⋊C4C22×#692311yescharacteristic
606C4⋊C4C22×#692311yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—1221no—
609C22⋊C4—1221no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C22⋊C4—1221no—
613C42—612no—
614C42—612no—
615C42—611no—
616C42—611no—
617C42—611no—
618C42—1221no—
619C42—1221no—
620C42—4881no—
621C42—4881no—
622C42—4881no—
623C42—4881no—
624C42—4881no—
625C42C22×#692311yescharacteristic
626C23—21no—
627C23—611no—
628C23—1222no—
629C23—1222no—
630C23—1221no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635D4—21no—
636D4—612no—
637D4—1222no—
638D4—1222no—
639D4—1221no—
640D4Q8×#692312yes—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—81no—
645C2×C4—611no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—612no—
651C2×C4—612no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—4881no—
674C2×C4—4881no—
675C2×C4—4881no—
676C2×C4—4884no—
677C2×C4—4884no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4D4×#692311yescharacteristic
695C2×C4D4×#692311yescharacteristic
696C2×C4C23×#692311yescharacteristic
697C8—21no—
698C8—21no—
699C8—1221no—
700C8—1221no—
701C8—2441no—
702C8—2441no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—611no—
707C22—611no—
708C22—611no—
709C22—611no—
710C22—611no—
711C22—611no—
712C22—1222no—
713C22—2442no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22—2441no—
718C22—2441no—
719C22C2×D4×#692311yescharacteristic
720C4—21no—
721C4—21no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—611no—
726C4—611no—
727C4—1222no—
728C4—1222no—
729C4—1221no—
730C4—1221no—
731C4—4881no—
732C4—4881no—
733C4—2441no—
734C4—2441no—
735C4—2442no—
736C4—2442no—
737C4—2441no—
738C4—2441no—
739C4—2441no—
740C4C2×Q8×#692311yescharacteristic
741C4#41×#692311yescharacteristic
742C2—42no—
743C2—611no—
744C2—611no—
745C2—611no—
746C2—611no—
747C2—2442no—
748C2C22⋊Q8×#692311yescharacteristic
749C2#2146257611yescharacteristic
750C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#478C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#478#6923
hypocenterC61#21619
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #21462313C2semidirect
3. #21461999C2semidirect
4. #21461931C2semidirect
5. #21461881C2semidirect
6. #21461880C2semidirect
10. #21461634C2semidirect
11. #106×#6923C2semidirect
12. #21461608C2semidirect
54. #16840065C4semidirect
55. #16840064C4semidirect
56. #16840063C4semidirect
57. #16840062C4semidirect
58. #16840061C4semidirect
59. #16840060C4semidirect
60. #16840059C4semidirect
66. C61×#478C4semidirect
115. #14519769C2×C4semidirect
116. #14519768C2×C4semidirect
117. #14519768C2×C4semidirect
132. #14519711C2×C4semidirect
133. #14519710C2×C4semidirect
134. #14519710C2×C4semidirect
135. #14519709C2×C4semidirect
136. #14519708C2×C4semidirect
137. #14519708C2×C4semidirect
138. C4⋊#92418C2×C4semidirect
139. #14519706C2×C4semidirect
140. #14519706C2×C4semidirect
147. #125×C61C2×C4semidirect
149. #107×C61C2×C4semidirect
150. #106×C61C2×C4semidirect
151. C4⋊C8×C61C2×C4semidirect
402. #478#6923semidirect
442. C61#21619semidirect
456. #125C2×#6923semidirect
494. #107C2×#6923semidirect
500. #106C2×#6923semidirect
506. C4⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623132
#214622582
#214619992
#214619312
#214618812
#214618802
#214617842
#214616872
#214616342
#106×#69232
#214616082
#214615902
#102×#69232
#478×D612
#2161961