Finite Group Databasebeta

← #30617323

Subgroups — #30617323

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462314C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic
3#21461998C211yesmaximal, characteristic, complemented
4#21461932C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461784C211yesmaximal, characteristic
8#21461782C211yesmaximal, characteristic
9#21461689C211yesmaximal, characteristic
10#21461635C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12#21461608C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic
14#102×#6923C211yesmaximal, characteristic
15#476×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20D61⋊(C4⋊C8)C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25(C2×#6923)⋊Q8—21no—
26(C2×#6923)⋊Q8—21no—
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840711—21no—
30#16840711—21no—
31#16840706C2211yescharacteristic
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
52C4⋊Q8×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840053C411yescharacteristic, complemented
55#16840052C411yescharacteristic, complemented
56#16840051C411yescharacteristic, complemented
57#16840051C411yescharacteristic, complemented
58#16840050C411yescharacteristic, complemented
59#16840050C411yescharacteristic, complemented
60#16840049C411yescharacteristic, complemented
61#106×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#476C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923Q814yescomplemented
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923C2311yescharacteristic
89C2×C4×#6923C2311yescharacteristic
90#14519846—22no—
91#14519845—22no—
92#14519844—21no—
93C4⋊#92420—21no—
94#14519839—22no—
95#14519839—22no—
96#14519831—22no—
97C8×#6923—22no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
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×Q8×D61—21no—
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×C8×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116#14519777C2×C411yescharacteristic, complemented
117#14519776—21no—
118#14519776C2×C411yescharacteristic, complemented
119#14519776C2×C411yescharacteristic, complemented
120#14519775—21no—
121C4×D244C2×C411yescharacteristic
122D4×Dic61C2×C411yescharacteristic
123#14519739C2×C411yescharacteristic
124C4×C22⋊D61—21no—
125#14519737—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61C2311yescharacteristic
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C22⋊C4×D61—21no—
131C42×D61C2311yescharacteristic
132#14519709C2×C411yescharacteristic, complemented
133#14519709C2×C411yescharacteristic, complemented
134#14519708C2×C411yescharacteristic, complemented
135#14519708C2×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
147C4⋊Q8×C61C2×C411yescharacteristic, complemented
148C4×D4×C61C2×C411yescharacteristic
149#106×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×Q8×C61—21no—
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C2×C22⋊D61—21no—
173C22×Dic61—21no—
174Q8×D61—81no—
175Q8×D61—81no—
176D4×D61—21no—
177D4×D61—21no—
178D4×D61C2×Q812yes—
179D4×D61#4112yes—
180C2×D244C22×C411yescharacteristic
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—81no—
187C2×C4×D61—81no—
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2411yescharacteristic
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C22⋊#6923—24no—
195C22⋊#6923—24no—
196C2×#92420—21no—
197C2×#92420—21no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—81no—
205C4⋊#6923—81no—
206C4⋊#6923C2×Q812yes—
207C4⋊#6923#4112yes—
208C4×#6923—21no—
209C4×#6923—21no—
210C4×#6923—81no—
211C4×#6923—81no—
212C4×#6923—81no—
213C4×#6923—81no—
214C4×#6923—81no—
215C4×#6923C2×Q812yes—
216C4×#6923#4112yes—
217D61⋊C8—21no—
218D61⋊C8—21no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221C2×C8×C61C22×C411yescharacteristic
222C2×C8×C61C22×C411yescharacteristic
223C4⋊C4×C61—21no—
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C4⋊C4×C61C22×C411yescharacteristic
227C22⋊C4×C61—21no—
228C42×C61C22×C411yescharacteristic
229C22⋊Dic61—21no—
230#11758198—21no—
231#11758198—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C411yescharacteristic
234C4⋊Dic61C22×C411yescharacteristic
235C4⋊Dic61C22×C411yescharacteristic
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—
285Q8×C61—81no—
286D4×C61—21no—
287D4×C61C4×Q812yes—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—81no—
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C23×C411yescharacteristic
295C22⋊D61—22no—
296C22⋊D61—22no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—81no—
301C2×Dic61C4×D411yescharacteristic
302C2×Dic61C4×D411yescharacteristic
303C2×Dic61C2×#4111yescharacteristic
304D244—21no—
305D244C4×Q812yes—
306C4×D61—21no—
307C4×D61—21no—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—41no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—81no—
317C4×D61—81no—
318C4×D61C22×Q811yescharacteristic
319C4×D61C2×#4111yescharacteristic
320C4×D61C2×#4111yescharacteristic
321C4×D61C2×#4111yescharacteristic
322Dic122—81no—
323Dic122—81no—
324Dic122—81no—
325#92420—41no—
326#92420—41no—
327C8×C61—21no—
328C8×C61—21no—
329#92418—21no—
330#92418—21no—
331#21623—611nomaximal, Sylow
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61C2×C4×D411yescharacteristic
336C2×D61—22no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61C2×C22⋊Q811yescharacteristic
344C2×D61#52511yescharacteristic
345C2×D61#57611yescharacteristic
346C2×D61#57711yescharacteristic
347C2×D61#57711yescharacteristic
348C2×D61#57711yescharacteristic
349#6923—22no—
350#6923—22no—
351#6923—42no—
352#6923—41no—
353#6923—42no—
354#6923—41no—
355#6923—81no—
356#6923—81no—
357C4×C61—21no—
358C4×C61—21no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61C2×C4×Q811yescharacteristic
363C4×C61C4×#4111yescharacteristic
364Dic61—21no—
365Dic61—21no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61#52911yescharacteristic
370Dic61#53311yescharacteristic
371C2×#476—611no—
372#2331—611no—
373#2275—611no—
374#1988—611no—
375#1949—611no—
376#1920—611no—
377#1919—611no—
378#1864—611no—
379#1862—611no—
380#1804—611no—
381#1776—611no—
382C4×#106—611no—
383#1768—611no—
384#1762—611no—
385C4×#102—611no—
386C2×C61—42no—
387C2×C61C4×C22⋊Q811yescharacteristic
388C2×C61#294611yescharacteristic
389C2×C61#294911yescharacteristic
390D61—42no—
391D61#308111yescharacteristic
392D61#308411yescharacteristic
393D61#311811yescharacteristic
394D61#312511yescharacteristic
395C2×C4⋊Q8—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399#476—611no—
400#476—611no—
401#476—611no—
402#476—611no—
403#476—611no—
404#476—611no—
405#476—611no—
406#476#692311yescharacteristic, complemented
407C2×#107—611no—
408C2×#106—611no—
409C2×#106—611no—
410C2×#106—611no—
411C2×C4⋊C8—611no—
412C2×C4⋊C8—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#97—611no—
418C2×C4×C8—611no—
419#391—1221no—
420#391—1221no—
421#389—611no—
422#389—611no—
423#387—1221no—
424#387—1221no—
425#382—611no—
426C4×C4⋊C4—611no—
427C4×C4⋊C4—611no—
428C4×C4⋊C4—611no—
429C4×C4⋊C4—611no—
430C4×C4⋊C4—611no—
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C4×C22⋊C4—1221no—
434#376—611no—
435C2×#95—1221no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#336—611no—
445#336—611no—
446C61#2162311yescharacteristic, complemented, Sylow
447C22×Q8—1221no—
448C22×D4—611no—
449C23×C4—1221no—
450C23×C4—1221no—
451C23×C4—1221no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C4⋊Q8—611no—
457C4⋊Q8—611no—
458C4⋊Q8—611no—
459C4⋊Q8—1221no—
460C4⋊Q8—1221no—
461C4⋊Q8C2×#692311yescharacteristic, complemented
462C4×D4—614no—
463C4×D4—611no—
464C4×D4—611no—
465C4×D4—611no—
466C4×D4—1221no—
467C4×D4—1221no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4C2×#692311yescharacteristic
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493#107—1222no—
494#106—611no—
495#106—611no—
496#106—611no—
497#106—611no—
498#106—611no—
499#106—611no—
500#106—1222no—
501#106C2×#692311yescharacteristic, complemented
502#106C2×#692311yescharacteristic, complemented
503C4⋊C8—611no—
504C4⋊C8—611no—
505C4⋊C8—611no—
506C4⋊C8—1221no—
507C4⋊C8—1221no—
508C4⋊C8C2×#692311yescharacteristic, complemented
509#102—611no—
510#102—611no—
511#102—611no—
512#102—611no—
513#102—611no—
514#102—611no—
515#102—1222no—
516#102—1222no—
517#102C2×#692311yescharacteristic
518#102C2×#692311yescharacteristic
519#97—1222no—
520C4×C8—1222no—
521#95—611no—
522#95—611no—
523#95—611no—
524#95—611no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534C24—1221no—
535C2×Q8—21no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—4881no—
540C2×Q8—4881no—
541C2×D4—612no—
542C2×D4—612no—
543C2×D4—611no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4C22×#692311yescharacteristic
548C22×C4—21no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1224no—
562C22×C4—1224no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—4881no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—4881no—
573C22×C4—4881no—
574C2×C8—611no—
575C2×C8—611no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8C22×#692311yescharacteristic
587C2×C8C22×#692311yescharacteristic
588C4⋊C4—21no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—611no—
592C4⋊C4—611no—
593C4⋊C4—611no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—4881no—
607C4⋊C4—4881no—
608C4⋊C4C22×#692311yescharacteristic
609C4⋊C4C22×#692311yescharacteristic
610C4⋊C4C22×#692311yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—1221no—
613C22⋊C4—1221no—
614C22⋊C4—1224no—
615C22⋊C4—1224no—
616C22⋊C4—1221no—
617C42—612no—
618C42—612no—
619C42—611no—
620C42—611no—
621C42—611no—
622C42—1221no—
623C42—1221no—
624C42—4881no—
625C42—4881no—
626C42—4881no—
627C42—4881no—
628C42—4881no—
629C42C22×#692311yescharacteristic
630C23—21no—
631C23—611no—
632C23—1222no—
633C23—1222no—
634C23—1221no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639Q8—81no—
640Q8—4881no—
641Q8—4881no—
642Q8—4881no—
643D4—21no—
644D4—612no—
645D4—1222no—
646D4—1222no—
647D4—1221no—
648D4Q8×#692312yes—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—81no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—4881no—
682C2×C4—4881no—
683C2×C4—4881no—
684C2×C4—4884no—
685C2×C4—4884no—
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×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4D4×#692311yescharacteristic
703C2×C4D4×#692311yescharacteristic
704C2×C4C23×#692311yescharacteristic
705C8—21no—
706C8—21no—
707C8—1221no—
708C8—1221no—
709C8—2441no—
710C8—2441no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—611no—
715C22—611no—
716C22—611no—
717C22—611no—
718C22—611no—
719C22—611no—
720C22—1222no—
721C22—2442no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2441no—
726C22—2441no—
727C22C2×D4×#692311yescharacteristic
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—611no—
734C4—611no—
735C4—1222no—
736C4—1222no—
737C4—1221no—
738C4—1221no—
739C4—4881no—
740C4—4881no—
741C4—2441no—
742C4—2441no—
743C4—2442no—
744C4—2442no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4C2×Q8×#692311yescharacteristic
749C4#41×#692311yescharacteristic
750C2—42no—
751C2—611no—
752C2—611no—
753C2—611no—
754C2—611no—
755C2—2442no—
756C2C22⋊Q8×#692311yescharacteristic
757C2#2146257611yescharacteristic
758C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#476C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#476#6923
hypocenterC61#21623
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #21462314C2semidirect
3. #21461998C2semidirect
4. #21461932C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
10. #21461635C2semidirect
11. #106×#6923C2semidirect
12. #21461608C2semidirect
54. #16840053C4semidirect
55. #16840052C4semidirect
56. #16840051C4semidirect
57. #16840051C4semidirect
58. #16840050C4semidirect
59. #16840050C4semidirect
60. #16840049C4semidirect
66. C61×#476C4semidirect
74. D4×#6923Q8semidirect
116. #14519777C2×C4semidirect
118. #14519776C2×C4semidirect
119. #14519776C2×C4semidirect
132. #14519709C2×C4semidirect
133. #14519709C2×C4semidirect
134. #14519708C2×C4semidirect
135. #14519708C2×C4semidirect
136. #14519708C2×C4semidirect
137. #14519708C2×C4semidirect
138. C4⋊#92418C2×C4semidirect
139. #14519706C2×C4semidirect
140. #14519706C2×C4semidirect
147. C4⋊Q8×C61C2×C4semidirect
149. #106×C61C2×C4semidirect
150. #106×C61C2×C4semidirect
151. C4⋊C8×C61C2×C4semidirect
406. #476#6923semidirect
446. C61#21623semidirect
461. C4⋊Q8C2×#6923semidirect
501. #106C2×#6923semidirect
502. #106C2×#6923semidirect
508. C4⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623142
#214622582
#214619982
#214619322
#214618822
#214618812
#214617842
#214617822
#214616892
#214616352
#106×#69232
#214616082
#214615902
#102×#69232
#476×D612
#2162361