Finite Group Databasebeta

← #30620611

Subgroups — #30620611

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C211yesmaximal, characteristic, complemented
2#21462322C211yesmaximal, characteristic
3#21461910C211yesmaximal, characteristic, complemented
4#21461908C211yesmaximal, characteristic, complemented
5#21461899C211yesmaximal, characteristic, complemented
6#21461898C211yesmaximal, characteristic, complemented
7#21461784C211yesmaximal, characteristic, complemented
8#21461782C211yesmaximal, characteristic, complemented
9#21461722C211yesmaximal, characteristic, complemented
10#21461697C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic
12#21461590C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461559C211yesmaximal, characteristic, complemented
15#417×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×#14519831C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840711—21no—
32#16840711—21no—
33#16840710—21no—
34#16840710—21no—
35#16840705—21no—
36#16840704—21no—
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39C4⋊C4×#6923C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4×C22⋊#6923—21no—
42C4×C22⋊#6923C2211yescharacteristic
43C2×(C2×#6923)⋊C4—21no—
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
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—41no—
74D4×#6923—41no—
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×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923D411yescharacteristic
86C2×C22⋊#6923D411yescharacteristic
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923C2311yescharacteristic
90C2×C4×#6923C2311yescharacteristic
91#14519846—41no—
92#14519845—41no—
93#14519840—41no—
94#14519840—41no—
95#14519839—22no—
96#14519839—22no—
97#14519834—21no—
98C22⋊#92420—21no—
99#14519831—41no—
100C8×#6923—41no—
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)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4D411yescharacteristic
112(C2×#6923)⋊C4D411yescharacteristic
113C2×#11758226C2×C411yescharacteristic
114C2×#11758222—21no—
115C2×#11758222C2×C411yescharacteristic
116C2×#11758224—21no—
117C2×#11758224C2×C411yescharacteristic
118#41×D61—22no—
119#41×D61—22no—
120#41×D61—41no—
121#41×D61—41no—
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C22×C4×D61—21no—
126C22×C4×D61—21no—
127C22×C4×D61C2311yescharacteristic
128C2×#11758194C2×C411yescharacteristic, complemented
129C2×#11758189C2×C411yescharacteristic, complemented
130C2×#11758189C2×C411yescharacteristic, complemented
131M16×D61—41no—
132M16×D61—41no—
133C2×C8×D61C2311yescharacteristic
134C2×C8×D61C2311yescharacteristic
135C2×C4⋊Dic61C2×C411yescharacteristic, complemented
136C2×#11758196—21no—
137C4⋊C4×D61—21no—
138C4⋊C4×D61—21no—
139C4⋊C4×D61C2×C411yescharacteristic, complemented
140C4⋊C4×D61C2×C411yescharacteristic, complemented
141C4⋊C4×D61C2311yescharacteristic
142C4⋊C4×D61C2311yescharacteristic
143#14519702C2×C411yescharacteristic, complemented
144#14519702C2×C411yescharacteristic, complemented
145#14519701C2×C411yescharacteristic, complemented
146#14519701C2×C411yescharacteristic, complemented
147#14519700C2×C411yescharacteristic, complemented
148#14519700C2×C411yescharacteristic, complemented
149#14519699C2×C411yescharacteristic
150#14519699C2×C411yescharacteristic
151#14519698C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519697C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155C2×#41×C61C2×C411yescharacteristic
156C2×M16×C61C2×C411yescharacteristic, complemented
157C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
158#103×C61C2×C411yescharacteristic, complemented
159#103×C61C2×C411yescharacteristic, complemented
160#102×C61C2×C411yescharacteristic
161#102×C61C2×C411yescharacteristic
162C23×D61—21no—
163C23×D61C2×D411yescharacteristic
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—42no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—81no—
173C22×#6923—81no—
174C22×#6923C2×D411yescharacteristic
175C22×#6923C2×D411yescharacteristic
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178#41×C61—22no—
179#41×C61—41no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61#4111yescharacteristic
192#11758226—22no—
193#11758226—41no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198#11758224—22no—
199#11758224—41no—
200#11758224—42no—
201#11758224—42no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—42no—
205D4×D61—42no—
206D4×D61#4112yes—
207D4×D61#4112yes—
208#11758222—22no—
209#11758222—41no—
210#11758222—42no—
211#11758222—42no—
212C2×D244—21no—
213C2×D244C22×C411yescharacteristic
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—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—81no—
228C2×C4×D61—81no—
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61#4111yescharacteristic
232C2×C4×D61C2411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122C22×C411yescharacteristic
235C22⋊#6923—22no—
236C22⋊#6923—41no—
237C22⋊#6923—42no—
238C22⋊#6923—42no—
239C22⋊#6923—42no—
240C22⋊#6923—81no—
241C2×#92420—21no—
242C2×#92420—21no—
243C4⋊#6923—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—81no—
252C4⋊#6923—81no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923—21no—
256C4×#6923—21no—
257C4×#6923—81no—
258C4×#6923—81no—
259D61⋊C8—21no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263M16×C61—41no—
264C2×C8×C61C22×C411yescharacteristic
265C2×C8×C61C22×C411yescharacteristic
266C4⋊C4×C61—21no—
267C4⋊C4×C61C22×C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758194—41no—
277C2×#92418C22×C411yescharacteristic
278C2×#92418C22×C411yescharacteristic
279#11758189—41no—
280#11758189—41no—
281C8×D61—21no—
282C8×D61—21no—
283C8×D61—21no—
284C8×D61—21no—
285C23×C61—21no—
286C23×C61C4×D411yescharacteristic
287C22×D61—21no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61C4×D411yescharacteristic
301C22×D61C22×D411yescharacteristic
302C2×#6923—21no—
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—41no—
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—84no—
326C2×#6923—84no—
327C2×#6923#13712yes—
328Q8×C61—21no—
329Q8×C61—21no—
330D4×C61—21no—
331D4×C61—42no—
332D4×C61#11712yes—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—42no—
339C2×C4×C61—81no—
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C23×C411yescharacteristic
342C22⋊D61—22no—
343C22⋊D61—22no—
344C22⋊D61—42no—
345C22⋊D61—42no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—42no—
352C2×Dic61—81no—
353C2×Dic61C4×D411yescharacteristic
354C2×Dic61C2×#4111yescharacteristic
355D244—21no—
356D244—42no—
357D244#11712yes—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—42no—
365C4×D61—42no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—81no—
373C4×D61—81no—
374C4×D61C2×#4111yescharacteristic
375C4×D61C2×#4111yescharacteristic
376C4×D61H(5,𝔽2)11yescharacteristic
377C4×D61H(5,𝔽2)11yescharacteristic
378Dic122—21no—
379Dic122—21no—
380Dic122—41no—
381Dic122—41no—
382#92420—41no—
383#92420—41no—
384C8×C61—21no—
385C8×C61—21no—
386#92418—21no—
387#92418—21no—
388#22578—611nomaximal, Sylow
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61C2×C4×D411yescharacteristic
396C2×D61—21no—
397C2×D61—22no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—42no—
404C2×D61—41no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—41no—
410C2×D61#54611yescharacteristic
411C2×D61#54611yescharacteristic
412C2×D61C2×#13711yescharacteristic
413C2×D61#57511yescharacteristic
414C2×D61#57611yescharacteristic
415C2×D61#57711yescharacteristic
416#6923—22no—
417#6923—41no—
418#6923—41no—
419#6923—41no—
420#6923—81no—
421#6923—81no—
422#6923—81no—
423#6923—81no—
424C4×C61—21no—
425C4×C61—41no—
426C4×C61—41no—
427C4×C61—41no—
428C4×C61C2×#11711yescharacteristic
429C4×C61#51811yescharacteristic
430Dic61—21no—
431Dic61—41no—
432Dic61—41no—
433Dic61—41no—
434Dic61#55111yescharacteristic
435Dic61#55111yescharacteristic
436C2×#417—611no—
437#2345—611no—
438#2339—611no—
439#1935—611no—
440#1933—611no—
441#1928—611no—
442#1927—611no—
443#1864—611no—
444#1862—611no—
445#1823—611no—
446#1809—611no—
447#1788—611no—
448#1762—611no—
449C4×#102—611no—
450#1753—611no—
451C2×C61—41no—
452C2×C61—42no—
453C2×C61#234211yescharacteristic
454C2×C61C4×#13711yescharacteristic
455C2×C61#294611yescharacteristic
456D61—41no—
457D61—42no—
458D61#330711yescharacteristic
459D61#331411yescharacteristic
460D61#332211yescharacteristic
461D61#333111yescharacteristic
462C22×#41—611no—
463C22×M16—611no—
464C2×C4×D4—611no—
465C2×C4×D4—611no—
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#391—611no—
489#391—611no—
490#389—611no—
491#389—611no—
492#387—1221no—
493#387—1221no—
494#386—1221no—
495#386—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—
504C2×#95—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#340—611no—
510#340—611no—
511#336—611no—
512#336—611no—
513C61#2257811yescharacteristic, complemented, Sylow
514C2×#41—611no—
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—1221no—
518C2×#41—1221no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—2441no—
522C2×#41—2441no—
523C2×#41C2×#692311yescharacteristic
524C22×Q8—611no—
525C22×D4—611no—
526C22×D4—1221no—
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C2×M16—611no—
533C2×M16—611no—
534C2×M16—611no—
535C2×M16—2441no—
536C2×M16—2441no—
537C2×M16C2×#692311yescharacteristic, complemented
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8—611no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4—2441no—
545C4×D4—2441no—
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—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4C2×#692311yescharacteristic, complemented
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×C42—611no—
568C2×C42—611no—
569C2×C42—1221no—
570C2×C42—1221no—
571#107—2441no—
572#106—2441no—
573#103—611no—
574#103—611no—
575#103—611no—
576#103—611no—
577#103—611no—
578#103—611no—
579#103—2441no—
580#103—2441no—
581#103C2×#692311yescharacteristic, complemented
582#103C2×#692311yescharacteristic, complemented
583#102—611no—
584#102—611no—
585#102—611no—
586#102—611no—
587#102—611no—
588#102—611no—
589#102—1222no—
590#102—1222no—
591#102C2×#692311yescharacteristic
592#102C2×#692311yescharacteristic
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595#97—2441no—
596C4×C8—2441no—
597#95—611no—
598#95—611no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
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—611no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8C22×#692311yescharacteristic
630C2×D4—21no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—611no—
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—4881no—
672C22×C4—4881no—
673C22×C4—4881no—
674C22×C4—4881no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4C22×#692311yescharacteristic
682M16—41no—
683M16—2441no—
684M16—2441no—
685M16—2441no—
686C2×C8—611no—
687C2×C8—611no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8C22×#692311yescharacteristic
699C2×C8C22×#692311yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—4881no—
717C4⋊C4—4881no—
718C4⋊C4C22×#692311yescharacteristic
719C4⋊C4C22×#692311yescharacteristic
720C22⋊C4—1222no—
721C22⋊C4—4881no—
722C22⋊C4—2441no—
723C22⋊C4—2442no—
724C22⋊C4—2442no—
725C22⋊C4—2442no—
726C42—1221no—
727C42—1221no—
728C42—1221no—
729C42—1221no—
730C42—4881no—
731C42—4881no—
732C23—21no—
733C23—611no—
734C23—611no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1222no—
739C23—1222no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23D4×#692311yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—1221no—
752Q8—1221no—
753Q8—2441no—
754Q8—2441no—
755D4—21no—
756D4—42no—
757D4—612no—
758D4—1222no—
759D4—1222no—
760D4—1221no—
761D4—2442no—
762D4—2442no—
763D4—2442no—
764D4#1451985612yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—42no—
771C2×C4—81no—
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—1221no—
782C2×C4—1221no—
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—4881no—
802C2×C4—4881no—
803C2×C4—4884no—
804C2×C4—4884no—
805C2×C4—4881no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2442no—
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—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4D4×#692311yescharacteristic
828C2×C4C23×#692311yescharacteristic
829C8—21no—
830C8—21no—
831C8—1221no—
832C8—1221no—
833C8—2441no—
834C8—2441no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—611no—
842C22—611no—
843C22—611no—
844C22—611no—
845C22—611no—
846C22—611no—
847C22—1221no—
848C22—1221no—
849C22—1221no—
850C22—1222no—
851C22—2442no—
852C22—2442no—
853C22—2441no—
854C22—2441no—
855C22—2441no—
856C22—2441no—
857C22—2442no—
858C22—2442no—
859C22—2441no—
860C22—2441no—
861C22C2×D4×#692311yescharacteristic
862C4—21no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—611no—
867C4—611no—
868C4—1222no—
869C4—1221no—
870C4—4881no—
871C4—4881no—
872C4—4881no—
873C4—4881no—
874C4—2441no—
875C4—2441no—
876C4—2441no—
877C4—2441no—
878C4—2441no—
879C4—2441no—
880C4C2×#1451985611yescharacteristic
881C4#1684082911yescharacteristic
882C2—41no—
883C2—42no—
884C2—611no—
885C2—611no—
886C2—611no—
887C2—611no—
888C2—2441no—
889C2—2442no—
890C2#2146232511yescharacteristic
891C2#137×#692311yescharacteristic
892C2#2146257611yescharacteristic
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#22578
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. #21462328C2semidirect
3. #21461910C2semidirect
4. #21461908C2semidirect
5. #21461899C2semidirect
6. #21461898C2semidirect
7. #21461784C2semidirect
8. #21461782C2semidirect
9. #21461722C2semidirect
10. #21461697C2semidirect
12. #21461590C2semidirect
13. #102×#6923C2semidirect
14. #21461559C2semidirect
55. #16839764C4semidirect
56. #16839763C4semidirect
57. #16839762C4semidirect
58. #16839762C4semidirect
59. #16839761C4semidirect
60. #16839760C4semidirect
61. #16839760C4semidirect
66. C61×#417C4semidirect
128. C2×#11758194C2×C4semidirect
129. C2×#11758189C2×C4semidirect
130. C2×#11758189C2×C4semidirect
135. C2×C4⋊Dic61C2×C4semidirect
139. C4⋊C4×D61C2×C4semidirect
140. C4⋊C4×D61C2×C4semidirect
143. #14519702C2×C4semidirect
144. #14519702C2×C4semidirect
145. #14519701C2×C4semidirect
146. #14519701C2×C4semidirect
147. #14519700C2×C4semidirect
148. #14519700C2×C4semidirect
156. C2×M16×C61C2×C4semidirect
157. C2×C4⋊C4×C61C2×C4semidirect
158. #103×C61C2×C4semidirect
159. #103×C61C2×C4semidirect
476. #417#6923semidirect
513. C61#22578semidirect
537. C2×M16C2×#6923semidirect
560. C2×C4⋊C4C2×#6923semidirect
581. #103C2×#6923semidirect
582. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214623222
#214619102
#214619082
#214618992
#214618982
#214617842
#214617822
#214617222
#214616972
#214616592
#214615902
#102×#69232
#214615592
#417×D612
#2257861