Finite Group Databasebeta

← #30620615

Subgroups — #30620615

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462327C211yesmaximal, 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#21461723C211yesmaximal, 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×#14519856—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26C2×#14519831C2211yescharacteristic
27C2×C8×#6923C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840711—21no—
33#16840711—21no—
34#16840710—21no—
35#16840710—21no—
36#16840705—21no—
37#16840705—21no—
38#16840704C2211yescharacteristic
39#16840704C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
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—
75#14519856—44no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923D411yescharacteristic
87C2×C22⋊#6923D411yescharacteristic
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923C2311yescharacteristic
91C2×C4×#6923C2311yescharacteristic
92#14519846—41no—
93#14519845—41no—
94#14519840—41no—
95#14519840—41no—
96#14519839—22no—
97#14519839—22no—
98#14519834—21no—
99C22⋊#92420—21no—
100#14519831—41no—
101C8×#6923—41no—
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)⋊C4—21no—
112(C2×#6923)⋊C4D411yescharacteristic
113(C2×#6923)⋊C4D411yescharacteristic
114C2×#11758226C2×C411yescharacteristic
115C2×#11758222—21no—
116C2×#11758222C2×C411yescharacteristic
117C2×#11758224—21no—
118C2×#11758224C2×C411yescharacteristic
119#41×D61—22no—
120#41×D61—22no—
121#41×D61—41no—
122#41×D61—41no—
123C2×Q8×D61C2311yescharacteristic
124C2×D4×D61—21no—
125C2×D4×D61C2311yescharacteristic
126C22×C4×D61—21no—
127C22×C4×D61—21no—
128C22×C4×D61C2311yescharacteristic
129C2×#11758194C2×C411yescharacteristic, complemented
130C2×#11758189C2×C411yescharacteristic, complemented
131C2×#11758189C2×C411yescharacteristic, complemented
132M16×D61—41no—
133M16×D61—41no—
134C2×C8×D61C2311yescharacteristic
135C2×C8×D61C2311yescharacteristic
136C2×C4⋊Dic61C2×C411yescharacteristic, complemented
137C2×#11758196—21no—
138C4⋊C4×D61—21no—
139C4⋊C4×D61—21no—
140C4⋊C4×D61C2×C411yescharacteristic, complemented
141C4⋊C4×D61C2×C411yescharacteristic, complemented
142C4⋊C4×D61C2311yescharacteristic
143C4⋊C4×D61C2311yescharacteristic
144#14519702C2×C411yescharacteristic, complemented
145#14519702C2×C411yescharacteristic, complemented
146#14519701C2×C411yescharacteristic, complemented
147#14519701C2×C411yescharacteristic, complemented
148#14519700C2×C411yescharacteristic, complemented
149#14519700C2×C411yescharacteristic, complemented
150#14519699C2×C411yescharacteristic
151#14519699C2×C411yescharacteristic
152#14519698C2×C411yescharacteristic
153#14519698C2×C411yescharacteristic
154#14519697C2×C411yescharacteristic
155#14519697C2×C411yescharacteristic
156C2×#41×C61C2×C411yescharacteristic
157C2×M16×C61C2×C411yescharacteristic, complemented
158C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
159#103×C61C2×C411yescharacteristic, complemented
160#103×C61C2×C411yescharacteristic, complemented
161#102×C61C2×C411yescharacteristic
162#102×C61C2×C411yescharacteristic
163C23×D61—21no—
164C23×D61C2×D411yescharacteristic
165C22×#6923—21no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—21no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923—42no—
173C22×#6923—81no—
174C22×#6923—81no—
175C22×#6923C2×D411yescharacteristic
176C22×#6923C2×D411yescharacteristic
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179#41×C61—22no—
180#41×C61—41no—
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C22×C411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61#4111yescharacteristic
193#11758226—22no—
194#11758226—41no—
195Q8×D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61—21no—
199#11758224—22no—
200#11758224—41no—
201#11758224—42no—
202#11758224—42no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—42no—
206D4×D61—42no—
207D4×D61#4112yes—
208D4×D61#4112yes—
209#11758222—22no—
210#11758222—41no—
211#11758222—42no—
212#11758222—42no—
213C2×D244—21no—
214C2×D244C22×C411yescharacteristic
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—21no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61#4111yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122C22×C411yescharacteristic
236C22⋊#6923—22no—
237C22⋊#6923—41no—
238C22⋊#6923—42no—
239C22⋊#6923—42no—
240C22⋊#6923—42no—
241C22⋊#6923—81no—
242C2×#92420—21no—
243C2×#92420—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—21no—
252C4⋊#6923—42no—
253C4⋊#6923—42no—
254C4×#6923—21no—
255C4×#6923—21no—
256C4×#6923—21no—
257C4×#6923—21no—
258C4×#6923—42no—
259C4×#6923—42no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263D61⋊C8—21no—
264M16×C61—41no—
265C2×C8×C61C22×C411yescharacteristic
266C2×C8×C61C22×C411yescharacteristic
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22×C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊Dic61—21no—
271C4⋊Dic61C22×C411yescharacteristic
272C4⋊Dic61C22×C411yescharacteristic
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758194—41no—
278C2×#92418C22×C411yescharacteristic
279C2×#92418C22×C411yescharacteristic
280#11758189—41no—
281#11758189—41no—
282C8×D61—21no—
283C8×D61—21no—
284C8×D61—21no—
285C8×D61—21no—
286C23×C61—21no—
287C23×C61C4×D411yescharacteristic
288C22×D61—21no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61C4×D411yescharacteristic
302C22×D61C22×D411yescharacteristic
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—21no—
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—41no—
326C2×#6923—84no—
327C2×#6923—84no—
328C2×#6923AGL(1,ℤ/8)12yes—
329Q8×C61—21no—
330Q8×C61—21no—
331D4×C61—21no—
332D4×C61—42no—
333D4×C61#11712yescomplemented
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61C4×D411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—22no—
344C22⋊D61—22no—
345C22⋊D61—42no—
346C22⋊D61—42no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—42no—
353C2×Dic61—42no—
354C2×Dic61C4×D411yescharacteristic
355C2×Dic61C2×#4111yescharacteristic
356D244—21no—
357D244—42no—
358D244#11712yescomplemented
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—42no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—41no—
374C4×D61—41no—
375C4×D61C2×#4111yescharacteristic
376C4×D61C2×#4111yescharacteristic
377C4×D61H(5,𝔽2)11yescharacteristic
378C4×D61H(5,𝔽2)11yescharacteristic
379Dic122—21no—
380Dic122—21no—
381Dic122—41no—
382Dic122—41no—
383#92420—41no—
384#92420—41no—
385C8×C61—21no—
386C8×C61—21no—
387#92418—21no—
388#92418—21no—
389#22582—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—22no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61C2×C4×D411yescharacteristic
397C2×D61—21no—
398C2×D61—22no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—41no—
411C2×D61#54611yescharacteristic
412C2×D61#54611yescharacteristic
413C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
414C2×D61#57511yescharacteristic
415C2×D61#57711yescharacteristic
416C2×D61#57811yescharacteristic
417#6923—22no—
418#6923—41no—
419#6923—41no—
420#6923—41no—
421#6923—81no—
422#6923—81no—
423#6923—81no—
424#6923—81no—
425C4×C61—21no—
426C4×C61—41no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61C2×#11711yescharacteristic
430C4×C61#51811yescharacteristic
431Dic61—21no—
432Dic61—41no—
433Dic61—41no—
434Dic61—41no—
435Dic61#55111yescharacteristic
436Dic61#55111yescharacteristic
437C2×#417—611no—
438#2344—611no—
439#2339—611no—
440#1935—611no—
441#1933—611no—
442#1928—611no—
443#1927—611no—
444#1864—611no—
445#1862—611no—
446#1824—611no—
447#1809—611no—
448#1788—611no—
449#1762—611no—
450C4×#102—611no—
451#1753—611no—
452C2×C61—41no—
453C2×C61—42no—
454C2×C61#234211yescharacteristic
455C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
456C2×C61#294711yescharacteristic
457D61—41no—
458D61—42no—
459D61#330611yescharacteristic
460D61#331511yescharacteristic
461D61#332311yescharacteristic
462D61#333011yescharacteristic
463C22×#41—611no—
464C22×M16—611no—
465C2×C4×D4—611no—
466C2×C4×D4—611no—
467C2×#117—1221no—
468C22×C4⋊C4—611no—
469C2×#107—611no—
470C2×#106—611no—
471#417—611no—
472#417—611no—
473#417—611no—
474#417—611no—
475#417—611no—
476#417—611no—
477#417—611no—
478#417#692311yescharacteristic, complemented
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×C22⋊C8—611no—
488C2×#97—611no—
489C2×C4×C8—611no—
490#391—611no—
491#391—611no—
492#389—611no—
493#389—611no—
494#387—1221no—
495#387—1221no—
496#386—1221no—
497#386—1221no—
498#381—1221no—
499#381—1221no—
500#380—611no—
501#380—611no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—611no—
504C4×C22⋊C4—611no—
505C2×#95—1221no—
506#340—611no—
507#340—611no—
508#340—611no—
509#340—611no—
510#340—611no—
511#340—611no—
512#336—611no—
513#336—611no—
514C61#2258211yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—611no—
518C2×#41—1221no—
519C2×#41—1221no—
520C2×#41—1222no—
521C2×#41—1222no—
522C2×#41—2441no—
523C2×#41—2441no—
524C2×#41C2×#692311yescharacteristic
525C22×Q8—611no—
526C22×D4—611no—
527C22×D4—1221no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533C2×M16—611no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—2441no—
537C2×M16—2441no—
538C2×M16C2×#692311yescharacteristic, complemented
539C22×C8—611no—
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—611no—
543C4×D4—1222no—
544C4×D4—1222no—
545C4×D4—2441no—
546C4×D4—2441no—
547#117—2444no—
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—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4C2×#692311yescharacteristic, complemented
563C2×C22⋊C4—611no—
564C2×C22⋊C4—611no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—1221no—
572C2×C42—1221no—
573#107—2441no—
574#106—2441no—
575#103—611no—
576#103—611no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#103—2441no—
582#103—2441no—
583#103C2×#692311yescharacteristic, complemented
584#103C2×#692311yescharacteristic, complemented
585#102—611no—
586#102—611no—
587#102—611no—
588#102—611no—
589#102—611no—
590#102—611no—
591#102—1222no—
592#102—1222no—
593#102C2×#692311yescharacteristic
594#102C2×#692311yescharacteristic
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597#97—2441no—
598C4×C8—2441no—
599#95—611no—
600#95—611no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609#95—1221no—
610#95—1221no—
611C24—611no—
612C24—1221no—
613#41—22no—
614#41—41no—
615#41—1222no—
616#41—1222no—
617#41—1222no—
618#41—2441no—
619#41—2442no—
620#41—2442no—
621#41—2441no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625C2×Q8—611no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8C22×#692311yescharacteristic
632C2×D4—21no—
633C2×D4—612no—
634C2×D4—612no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—2442no—
643C2×D4—2442no—
644C2×D4C22×#692311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
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—1221no—
672C22×C4—1221no—
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×C4—2442no—
682C22×C4—2442no—
683C22×C4C22×#692311yescharacteristic
684M16—41no—
685M16—2441no—
686M16—2441no—
687M16—2441no—
688C2×C8—611no—
689C2×C8—611no—
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×C8—1221no—
699C2×C8—1221no—
700C2×C8C22×#692311yescharacteristic
701C2×C8C22×#692311yescharacteristic
702C4⋊C4—21no—
703C4⋊C4—611no—
704C4⋊C4—611no—
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—1221no—
717C4⋊C4—1221no—
718C4⋊C4—2442no—
719C4⋊C4—2442no—
720C4⋊C4C22×#692311yescharacteristic
721C4⋊C4C22×#692311yescharacteristic
722C22⋊C4—1222no—
723C22⋊C4—4881no—
724C22⋊C4—2441no—
725C22⋊C4—2442no—
726C22⋊C4—2442no—
727C22⋊C4—2442no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C42—2442no—
734C23—21no—
735C23—611no—
736C23—611no—
737C23—1221no—
738C23—1221no—
739C23—1222no—
740C23—1222no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—2441no—
747C23—2441no—
748C23—2441no—
749C23—2441no—
750C23D4×#692311yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—1221no—
754Q8—1221no—
755Q8—2441no—
756Q8—2441no—
757D4—21no—
758D4—42no—
759D4—612no—
760D4—1222no—
761D4—1222no—
762D4—1221no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766D4#1451985612yescomplemented
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—612no—
780C2×C4—611no—
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—1221no—
802C2×C4—1221no—
803C2×C4—4884no—
804C2×C4—4884no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
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×C4—2441no—
828C2×C4—2442no—
829C2×C4D4×#692311yescharacteristic
830C2×C4C23×#692311yescharacteristic
831C8—21no—
832C8—21no—
833C8—1221no—
834C8—1221no—
835C8—2441no—
836C8—2441no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—22no—
841C22—41no—
842C22—41no—
843C22—611no—
844C22—611no—
845C22—611no—
846C22—611no—
847C22—611no—
848C22—611no—
849C22—1221no—
850C22—1221no—
851C22—1221no—
852C22—1222no—
853C22—2442no—
854C22—2442no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22—2441no—
859C22—2442no—
860C22—2442no—
861C22—2441no—
862C22—2441no—
863C22C2×D4×#692311yescharacteristic
864C4—21no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—611no—
869C4—611no—
870C4—1222no—
871C4—1221no—
872C4—4881no—
873C4—4881no—
874C4—4881no—
875C4—4881no—
876C4—2441no—
877C4—2441no—
878C4—2441no—
879C4—2441no—
880C4—2441no—
881C4—2441no—
882C4C2×#1451985611yescharacteristic
883C4#1684082911yescharacteristic
884C2—41no—
885C2—42no—
886C2—611no—
887C2—611no—
888C2—611no—
889C2—611no—
890C2—2441no—
891C2—2442no—
892C2#2146232511yescharacteristic
893C2AGL(1,ℤ/8)×#692311yescharacteristic
894C2#2146257711yescharacteristic
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#22582
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. #21462327C2semidirect
3. #21461910C2semidirect
4. #21461908C2semidirect
5. #21461899C2semidirect
6. #21461898C2semidirect
7. #21461784C2semidirect
8. #21461782C2semidirect
9. #21461723C2semidirect
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
129. C2×#11758194C2×C4semidirect
130. C2×#11758189C2×C4semidirect
131. C2×#11758189C2×C4semidirect
136. C2×C4⋊Dic61C2×C4semidirect
140. C4⋊C4×D61C2×C4semidirect
141. C4⋊C4×D61C2×C4semidirect
144. #14519702C2×C4semidirect
145. #14519702C2×C4semidirect
146. #14519701C2×C4semidirect
147. #14519701C2×C4semidirect
148. #14519700C2×C4semidirect
149. #14519700C2×C4semidirect
157. C2×M16×C61C2×C4semidirect
158. C2×C4⋊C4×C61C2×C4semidirect
159. #103×C61C2×C4semidirect
160. #103×C61C2×C4semidirect
333. D4×C61#117semidirect
358. D244#117semidirect
478. #417#6923semidirect
514. C61#22582semidirect
538. C2×M16C2×#6923semidirect
562. C2×C4⋊C4C2×#6923semidirect
583. #103C2×#6923semidirect
584. #103C2×#6923semidirect
766. D4#14519856semidirect

Maximal subgroups

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

subgroupindex
#214623272
#214623222
#214619102
#214619082
#214618992
#214618982
#214617842
#214617822
#214617232
#214616972
#214616592
#214615902
#102×#69232
#214615592
#417×D612
#2258261