Finite Group Databasebeta

← #30620363

Subgroups — #30620363

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic
2#21462335C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic, complemented
4#21461998C211yesmaximal, characteristic, complemented
5#21461834C211yesmaximal, characteristic, complemented
6#21461832C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461804C211yesmaximal, characteristic, complemented
9#21461723C211yesmaximal, characteristic, complemented
10#21461722C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461506C211yesmaximal, characteristic, complemented
14C2×#16840635C211yesmaximal, characteristic, complemented
15#554×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31#16840721C2211yescharacteristic
32#16840712—21no—
33#16840711—21no—
34#16840710—21no—
35#16840706C2211yescharacteristic
36#16840704C2211yescharacteristic
37#16840704C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C22⋊C4×#6923—21no—
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840473C411yescharacteristic, complemented
53#16840472C411yescharacteristic, complemented
54#16840471—21no—
55#16840470C411yescharacteristic, complemented
56#16840470C411yescharacteristic, complemented
57#16840469C411yescharacteristic, complemented
58#16840468—21no—
59#16840467C411yescharacteristic, complemented
60#16840467C411yescharacteristic, complemented
61#16840466—21no—
62#16840466—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#125×D61—21no—
65C22⋊Q8×D61—21no—
66C22⋊Q8×D61—21no—
67C22⋊Q8×D61C2211yescharacteristic
68C22⋊Q8×D61C2211yescharacteristic
69C4×Q8×D61C2211yescharacteristic
70C4×D4×D61—21no—
71C4×D4×D61C2211yescharacteristic
72C2×C4⋊C4×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#554C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77D61⋊M16—22no—
78D61⋊M16—41no—
79C2×#11758217—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—21no—
82C2×D61⋊C8—41no—
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C22×#92420—21no—
88#14519856—22no—
89#14519856—41no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—41no—
93C2×C4⋊#6923C2311yescharacteristic
94C2×C4⋊#6923C2311yescharacteristic
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519840—22no—
105#14519840—22no—
106#14519840—41no—
107#14519840—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112#14519832—21no—
113#14519832—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×Q8×D61—21no—
120C2×Q8×D61C2311yescharacteristic
121C2×D4×D61D411yescharacteristic
122C22×C4×D61—21no—
123C22×C4×D61—21no—
124C22×C4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126#14519777C2×C411yescharacteristic, complemented
127#14519776—21no—
128#14519776C2×C411yescharacteristic, complemented
129#14519776C2×C411yescharacteristic, complemented
130#14519775—21no—
131#14519769—21no—
132#14519768—21no—
133#14519768—21no—
134#14519767—21no—
135#14519767—21no—
136#14519767—21no—
137#14519767—21no—
138#14519757—21no—
139#14519757—21no—
140#14519757C2×C411yescharacteristic
141#14519757C2×C411yescharacteristic, complemented
142#14519756—21no—
143#14519756—21no—
144#14519756C2×C411yescharacteristic
145#14519756C2×C411yescharacteristic, complemented
146#14519755—21no—
147#14519755—21no—
148#14519755—21no—
149#14519755—21no—
150#14519755—21no—
151#14519755—21no—
152#14519754—21no—
153#14519754—21no—
154#14519754—21no—
155#14519754—21no—
156#14519754—21no—
157#14519754—21no—
158#14519753—21no—
159#14519753—21no—
160#14519753C2×C411yescharacteristic
161#14519753C2×C411yescharacteristic, complemented
162Q8×Dic61C2×C411yescharacteristic, complemented
163C4×Dic122—21no—
164C4×Dic122C2×C411yescharacteristic, complemented
165#14519742—21no—
166#14519742C2×C411yescharacteristic, complemented
167C4×D244—21no—
168C4×D244C2×C411yescharacteristic
169D4×Dic61—21no—
170D4×Dic61D411yescharacteristic
171#14519739—21no—
172#14519739D411yescharacteristic
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181C2×C4⋊Dic61C2×C411yescharacteristic
182C2×C4⋊Dic61C2×C411yescharacteristic, complemented
183C2×#11758196—21no—
184C2×#11758196—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61C2×C411yescharacteristic
194C4⋊C4×D61C2×C411yescharacteristic
195C4⋊C4×D61C2×C411yescharacteristic, complemented
196C4⋊C4×D61C2×C411yescharacteristic, complemented
197C4⋊C4×D61D411yescharacteristic
198C4⋊C4×D61C2311yescharacteristic
199C4⋊C4×D61C2311yescharacteristic
200C4⋊C4×D61C2311yescharacteristic
201C22⋊C4×D61—21no—
202C22⋊C4×D61—21no—
203C22⋊C4×D61D411yescharacteristic
204C22⋊C4×D61D411yescharacteristic
205C42×D61—21no—
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic, complemented
208#125×C61—21no—
209C22⋊Q8×C61—21no—
210C22⋊Q8×C61—21no—
211C22⋊Q8×C61C2×C411yescharacteristic
212C22⋊Q8×C61C2×C411yescharacteristic, complemented
213C4×Q8×C61C2×C411yescharacteristic, complemented
214C4×D4×C61—21no—
215C4×D4×C61C2×C411yescharacteristic
216C2×C4⋊C4×C61C2×C411yescharacteristic
217C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—42no—
225C22×#6923—42no—
226C22×#6923—81no—
227C2×Q8×C61—21no—
228C2×Q8×C61C22×C411yescharacteristic
229C2×D4×C61C22⋊C411yescharacteristic
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61C22×C411yescharacteristic
233C22×C4×C61C22×C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240Q8×D61—21no—
241Q8×D61—21no—
242Q8×D61—21no—
243Q8×D61—21no—
244Q8×D61—81no—
245Q8×D61—81no—
246D4×D61—22no—
247D4×D61—22no—
248C2×D244C22⋊C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—81no—
266C2×C4×D61—81no—
267C2×C4×D61—81no—
268C2×C4×D61—81no—
269C2×C4×D61C22×C411yescharacteristic
270C2×C4×D61C22×C411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2×D411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×C4×D61C2×D411yescharacteristic
277C2×C4×D61C2411yescharacteristic
278C2×Dic122—21no—
279C2×Dic122—21no—
280C2×Dic122—21no—
281C2×Dic122—21no—
282C2×Dic122C22×C411yescharacteristic
283C22⋊#6923—42no—
284C22⋊#6923—42no—
285C22⋊#6923—81no—
286#11758217—42no—
287C2×#92420—21no—
288C2×#92420—21no—
289C2×#92420—21no—
290C2×#92420—21no—
291C2×#92420—42no—
292C4⋊#6923—21no—
293C4⋊#6923—21no—
294C4⋊#6923—21no—
295C4⋊#6923—21no—
296C4⋊#6923—21no—
297C4⋊#6923—21no—
298C4⋊#6923—21no—
299C4⋊#6923—42no—
300C4⋊#6923#4112yes—
301C4×#6923—42no—
302C4×#6923—81no—
303#11758213—42no—
304D61⋊C8—21no—
305D61⋊C8—21no—
306D61⋊C8—21no—
307D61⋊C8—21no—
308D61⋊C8—21no—
309D61⋊C8—21no—
310D61⋊C8—21no—
311D61⋊C8—42no—
312D61⋊C8#4112yes—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61—21no—
318C4⋊C4×C61—21no—
319C4⋊C4×C61C22⋊C411yescharacteristic
320C4⋊C4×C61C22×C411yescharacteristic
321C4⋊C4×C61C22×C411yescharacteristic
322C4⋊C4×C61C22×C411yescharacteristic
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61C22⋊C411yescharacteristic
326C22⋊C4×C61C22⋊C411yescharacteristic
327C42×C61—21no—
328C42×C61C22×C411yescharacteristic
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331C22⋊Dic61C22⋊C411yescharacteristic
332C22⋊Dic61C22⋊C411yescharacteristic
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198C22⋊C411yescharacteristic
338#11758198C22⋊C411yescharacteristic
339#11758198C22⋊C411yescharacteristic
340#11758198C22⋊C411yescharacteristic
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4⋊Dic61—21no—
346C4⋊Dic61—21no—
347C4⋊Dic61C22⋊C411yescharacteristic
348C4⋊Dic61C22×C411yescharacteristic
349C4⋊Dic61C22×C411yescharacteristic
350C4⋊Dic61C22×C411yescharacteristic
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196—21no—
357#11758196—21no—
358#11758196—21no—
359#11758196—21no—
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363#11758196—21no—
364#11758196—21no—
365#11758196—21no—
366#11758196C22⋊C411yescharacteristic
367#11758196C22⋊C411yescharacteristic
368C4×Dic61—21no—
369C4×Dic61—21no—
370C4×Dic61—21no—
371C4×Dic61C22×C411yescharacteristic
372C4×Dic61C2×D411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C23×C61C2×C22⋊C411yescharacteristic
375C23×C61C2×C22⋊C411yescharacteristic
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61C2×C22⋊C411yescharacteristic
387C22×D61C2×C22⋊C411yescharacteristic
388C22×D61#13712yes—
389C22×D61#13712yes—
390C22×D61C22×D411yescharacteristic
391C2×#6923—22no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—84no—
404Q8×C61—21no—
405Q8×C61—21no—
406Q8×C61—81no—
407D4×C61—22no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—81no—
417C2×C4×C61—81no—
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61C23×C411yescharacteristic
423C22⋊D61—22no—
424C22⋊D61—22no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—81no—
434C2×Dic61—81no—
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440D244—22no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—41no—
464C4×D61—41no—
465C4×D61—81no—
466C4×D61—81no—
467C4×D61—81no—
468C4×D61—81no—
469C4×D61C2×#4111yescharacteristic
470C4×D61C2×#4111yescharacteristic
471C4×D61H(5,𝔽2)11yescharacteristic
472C4×D612−1+411yescharacteristic
473Dic122—21no—
474Dic122—21no—
475Dic122—41no—
476Dic122—41no—
477Dic122—81no—
478Dic122—81no—
479Dic122—81no—
480#92420—22no—
481#92420—41no—
482#92420—41no—
483#92420—41no—
484#22497—611nomaximal, Sylow
485C22×C61—21no—
486C22×C61—21no—
487C22×C61—21no—
488C22×C61—21no—
489C22×C61—21no—
490C22×C61#41912yes—
491C22×C61C22×C22⋊C411yescharacteristic
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—22no—
495C2×D61—22no—
496C2×D61—22no—
497C2×D61—22no—
498C2×D61—21no—
499C2×D61—21no—
500C2×D61—21no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—41no—
504C2×D61—41no—
505C2×D61#41912yes—
506C2×D61#54611yescharacteristic
507C2×D61#54711yescharacteristic
508C2×D61C2×#13711yescharacteristic
509C2×D61C2×#13711yescharacteristic
510C2×D61#57611yescharacteristic
511C2×D61#57711yescharacteristic
512#6923—42no—
513#6923—81no—
514#6923—81no—
515#6923—81no—
516C4×C61—21no—
517C4×C61—21no—
518C4×C61—21no—
519C4×C61—21no—
520C4×C61—41no—
521C4×C61—41no—
522C4×C61—41no—
523C4×C61—41no—
524C4×C61C4×#4111yescharacteristic
525C4×C61#52011yescharacteristic
526Dic61—21no—
527Dic61—21no—
528Dic61—21no—
529Dic61—21no—
530Dic61—41no—
531Dic61—41no—
532Dic61—41no—
533Dic61—41no—
534Dic61#54611yescharacteristic
535Dic61#54711yescharacteristic
536C2×#554—611no—
537C2×#435—611no—
538#2352—611no—
539#1993—611no—
540#1988—611no—
541#1894—611no—
542#1892—611no—
543#1873—611no—
544#1872—611no—
545#1824—611no—
546#1823—611no—
547#1805—611no—
548#1763—611no—
549#1736—611no—
550C2×#340—611no—
551C2×C61—22no—
552C2×C61—41no—
553C2×C61#233911yescharacteristic
554C2×C61C2×#41911yescharacteristic
555C2×C61#289711yescharacteristic
556D61—22no—
557D61—41no—
558D61#331411yescharacteristic
559D61#331611yescharacteristic
560D61#334411yescharacteristic
561D61#334611yescharacteristic
562C22×M16—611no—
563C23×C8—611no—
564#554—611no—
565#554—611no—
566#554—611no—
567#554—611no—
568#554—611no—
569#554—611no—
570#554—611no—
571#554—1221no—
572#554—1221no—
573#554—1221no—
574#554—1221no—
575#554#692311yescharacteristic, complemented
576C2×C4⋊Q8—611no—
577C2×#125—1221no—
578C2×C22⋊Q8—611no—
579C2×C22⋊Q8—611no—
580C2×C22⋊Q8—1221no—
581C2×C22⋊Q8—1221no—
582C2×C4×Q8—611no—
583C2×C4×D4—611no—
584C2×C4×D4—1221no—
585C2×#117—611no—
586C22×C4⋊C4—611no—
587C22×C4⋊C4—611no—
588C22×C4⋊C4—611no—
589#435—1221no—
590#435—1221no—
591#435—1221no—
592#435—1221no—
593C2×C4⋊C8—611no—
594C2×#103—611no—
595C2×#103—611no—
596C2×#103—611no—
597C2×#103—611no—
598C2×C22⋊C8—611no—
599C2×C22⋊C8—611no—
600C2×#97—611no—
601#388—1221no—
602#387—1221no—
603#386—1221no—
604#382—611no—
605#380—611no—
606#380—611no—
607C4×C4⋊C4—611no—
608C4×C22⋊C4—1221no—
609#340—611no—
610#340—611no—
611#340—611no—
612#340—611no—
613#340—611no—
614#340—611no—
615#340—611no—
616#340—611no—
617#340—611no—
618#340—611no—
619#340—611no—
620#340—611no—
621C61#2249711yescharacteristic, complemented, Sylow
622C22×Q8—611no—
623C22×Q8—1221no—
624C22×D4—611no—
625C23×C4—611no—
626C23×C4—611no—
627C23×C4—1221no—
628C23×C4—1221no—
629C23×C4—1221no—
630C2×M16—1222no—
631C2×M16—1221no—
632C2×M16—1221no—
633C2×M16—2441no—
634C22×C8—611no—
635C22×C8—611no—
636C22×C8—611no—
637C22×C8—611no—
638C22×C8—1222no—
639C22×C8—1221no—
640C22×C8—1221no—
641C22×C8—2441no—
642C4⋊Q8—611no—
643C4⋊Q8—611no—
644C4⋊Q8—611no—
645C4⋊Q8—1221no—
646C4⋊Q8—1221no—
647C4⋊Q8C2×#692311yescharacteristic, complemented
648#125—21no—
649#125—1221no—
650#125—1221no—
651#125—1221no—
652#125—1221no—
653#125—1221no—
654#125—1221no—
655#125—1221no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—611no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—1221no—
665C22⋊Q8—1221no—
666C22⋊Q8—1221no—
667C22⋊Q8—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8—1221no—
678C22⋊Q8—1221no—
679C22⋊Q8—1221no—
680C22⋊Q8—1221no—
681C22⋊Q8—1221no—
682C22⋊Q8C2×#692311yescharacteristic
683C22⋊Q8C2×#692311yescharacteristic, complemented
684C4×Q8—611no—
685C4×Q8—611no—
686C4×Q8—611no—
687C4×Q8—1221no—
688C4×Q8—1221no—
689C4×Q8C2×#692311yescharacteristic, complemented
690C4×D4—21no—
691C4×D4—611no—
692C4×D4—611no—
693C4×D4—611no—
694C4×D4—611no—
695C4×D4—611no—
696C4×D4—611no—
697C4×D4—611no—
698C4×D4—1221no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4C2×#692311yescharacteristic
706#117—1222no—
707#117—2441no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—611no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—611no—
717C2×C4⋊C4—611no—
718C2×C4⋊C4—611no—
719C2×C4⋊C4—611no—
720C2×C4⋊C4—611no—
721C2×C4⋊C4—611no—
722C2×C4⋊C4—1221no—
723C2×C4⋊C4—1221no—
724C2×C4⋊C4—1221no—
725C2×C4⋊C4—1221no—
726C2×C4⋊C4—1221no—
727C2×C4⋊C4—1221no—
728C2×C4⋊C4—1221no—
729C2×C4⋊C4—1221no—
730C2×C4⋊C4—1222no—
731C2×C4⋊C4—1221no—
732C2×C4⋊C4—1221no—
733C2×C4⋊C4—1221no—
734C2×C4⋊C4—2441no—
735C2×C4⋊C4C2×#692311yescharacteristic
736C2×C4⋊C4C2×#692311yescharacteristic, complemented
737C2×C22⋊C4—611no—
738C2×C22⋊C4—611no—
739C2×C22⋊C4—1221no—
740C2×C22⋊C4—1221no—
741C2×C22⋊C4—1221no—
742C2×C22⋊C4—1221no—
743C2×C22⋊C4—1221no—
744C2×C42—611no—
745C2×C42—1221no—
746C2×C42—1221no—
747C2×C42—1221no—
748C4⋊C8—1221no—
749C4⋊C8—1221no—
750#103—1222no—
751#103—1222no—
752#103—2441no—
753#103—2441no—
754C22⋊C8—1221no—
755C22⋊C8—1221no—
756C22⋊C8—1221no—
757C22⋊C8—1221no—
758#97—1221no—
759#97—1221no—
760#95—1221no—
761#95—1221no—
762#95—1221no—
763#95—1221no—
764#95—1221no—
765C24—611no—
766C24—611no—
767C2×Q8—21no—
768C2×Q8—611no—
769C2×Q8—1221no—
770C2×Q8—1221no—
771C2×Q8—1221no—
772C2×Q8—1221no—
773C2×Q8—1221no—
774C2×Q8—1221no—
775C2×Q8—1221no—
776C2×Q8—1221no—
777C2×Q8—4881no—
778C2×Q8—4881no—
779C2×Q8C22×#692311yescharacteristic
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—1222no—
784C2×D4—1222no—
785C2×D4C22⋊#692311yescharacteristic
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—611no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—611no—
797C22×C4—611no—
798C22×C4—611no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—1221no—
807C22×C4—1221no—
808C22×C4—1221no—
809C22×C4—1221no—
810C22×C4—1221no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—4881no—
822C22×C4—4881no—
823C22×C4—4881no—
824C22×C4—4881no—
825C22×C4—4881no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4C22×#692311yescharacteristic
829C22×C4C22×#692311yescharacteristic
830M16—2442no—
831M16—2442no—
832C2×C8—612no—
833C2×C8—1221no—
834C2×C8—1221no—
835C2×C8—1221no—
836C2×C8—1221no—
837C2×C8—1221no—
838C2×C8—1221no—
839C2×C8—1221no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—2442no—
845C2×C8—2442no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—611no—
853C4⋊C4—611no—
854C4⋊C4—611no—
855C4⋊C4—612no—
856C4⋊C4—611no—
857C4⋊C4—611no—
858C4⋊C4—611no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4—1221no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—1221no—
874C4⋊C4—1221no—
875C4⋊C4—1221no—
876C4⋊C4—1221no—
877C4⋊C4—1221no—
878C4⋊C4—1221no—
879C4⋊C4—1221no—
880C4⋊C4—1221no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4—2442no—
888C4⋊C4C22⋊#692311yescharacteristic
889C4⋊C4C22×#692311yescharacteristic
890C4⋊C4C22×#692311yescharacteristic
891C4⋊C4C22×#692311yescharacteristic
892C22⋊C4—21no—
893C22⋊C4—21no—
894C22⋊C4—611no—
895C22⋊C4—611no—
896C22⋊C4—611no—
897C22⋊C4—611no—
898C22⋊C4—611no—
899C22⋊C4—611no—
900C22⋊C4—1221no—
901C22⋊C4—1221no—
902C22⋊C4—1221no—
903C22⋊C4—1221no—
904C22⋊C4—1221no—
905C22⋊C4—1221no—
906C22⋊C4—4881no—
907C22⋊C4—2442no—
908C22⋊C4—2442no—
909C22⋊C4C22⋊#692311yescharacteristic
910C22⋊C4C22⋊#692311yescharacteristic
911C42—21no—
912C42—611no—
913C42—611no—
914C42—611no—
915C42—1221no—
916C42—1221no—
917C42—1221no—
918C42—4881no—
919C42—2442no—
920C42C22×#692311yescharacteristic
921C23—611no—
922C23—612no—
923C23—612no—
924C23—611no—
925C23—611no—
926C23—1221no—
927C23—1221no—
928C23—1221no—
929C23—1221no—
930C23—1221no—
931C23—1221no—
932C23—1221no—
933C23—1221no—
934C23—1221no—
935C23—1221no—
936C23C2×C22⋊#692311yescharacteristic
937C23C2×C22⋊#692311yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—81no—
941Q8—1221no—
942Q8—1221no—
943Q8—4881no—
944Q8—4881no—
945Q8—4881no—
946Q8—2441no—
947Q8—2441no—
948D4—22no—
949D4—1222no—
950D4—1222no—
951D4—1222no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—81no—
961C2×C4—81no—
962C2×C4—611no—
963C2×C4—611no—
964C2×C4—611no—
965C2×C4—611no—
966C2×C4—611no—
967C2×C4—611no—
968C2×C4—611no—
969C2×C4—611no—
970C2×C4—611no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1221no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—1221no—
987C2×C4—1221no—
988C2×C4—1221no—
989C2×C4—1221no—
990C2×C4—1221no—
991C2×C4—1222no—
992C2×C4—1221no—
993C2×C4—1221no—
994C2×C4—1221no—
995C2×C4—1221no—
996C2×C4—4881no—
997C2×C4—4881no—
998C2×C4—4881no—
999C2×C4—4881no—
1000C2×C4—4884no—
1001C2×C4—4881no—
1002C2×C4—4881no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2441no—
1010C2×C4—2441no—
1011C2×C4—2441no—
1012C2×C4—2441no—
1013C2×C4—2441no—
1014C2×C4—2441no—
1015C2×C4—2441no—
1016C2×C4—2441no—
1017C2×C4—2441no—
1018C2×C4—2441no—
1019C2×C4—2441no—
1020C2×C4—2441no—
1021C2×C4—2441no—
1022C2×C4C2×C22⋊#692311yescharacteristic
1023C2×C4C2×C22⋊#692311yescharacteristic
1024C2×C4C2×C22⋊#692311yescharacteristic
1025C2×C4C2×C22⋊#692311yescharacteristic
1026C2×C4C23×#692311yescharacteristic
1027C8—1222no—
1028C8—2441no—
1029C8—2441no—
1030C8—2441no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—611no—
1037C22—611no—
1038C22—611no—
1039C22—611no—
1040C22—611no—
1041C22—611no—
1042C22—612no—
1043C22—1222no—
1044C22—1222no—
1045C22—1222no—
1046C22—1222no—
1047C22—1221no—
1048C22—1221no—
1049C22—1221no—
1050C22—1221no—
1051C22—1221no—
1052C22—2441no—
1053C22—2441no—
1054C22—2441no—
1055C22—2441no—
1056C22#1684075512yes—
1057C22C22×C22⋊#692311yescharacteristic
1058C4—21no—
1059C4—21no—
1060C4—21no—
1061C4—21no—
1062C4—41no—
1063C4—41no—
1064C4—41no—
1065C4—41no—
1066C4—611no—
1067C4—611no—
1068C4—1221no—
1069C4—1221no—
1070C4—1221no—
1071C4—1221no—
1072C4—4881no—
1073C4—4881no—
1074C4—4881no—
1075C4—2442no—
1076C4—2441no—
1077C4—2441no—
1078C4—2441no—
1079C4—2441no—
1080C4#41×#692311yescharacteristic
1081C4#1684083111yescharacteristic
1082C2—22no—
1083C2—41no—
1084C2—611no—
1085C2—611no—
1086C2—611no—
1087C2—611no—
1088C2—1222no—
1089C2—2441no—
1090C2#2146232211yescharacteristic
1091C2C2×#1684075511yescharacteristic
1092C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#554C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenter#554#6923
hypocenterC61#22497
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
3. #21462003C2semidirect
4. #21461998C2semidirect
5. #21461834C2semidirect
6. #21461832C2semidirect
7. #21461805C2semidirect
8. #21461804C2semidirect
9. #21461723C2semidirect
10. #21461722C2semidirect
11. #21461690C2semidirect
12. #21461591C2semidirect
13. #21461506C2semidirect
14. C2×#16840635C2semidirect
52. #16840473C4semidirect
53. #16840472C4semidirect
55. #16840470C4semidirect
56. #16840470C4semidirect
57. #16840469C4semidirect
59. #16840467C4semidirect
60. #16840467C4semidirect
74. C61×#554C4semidirect
126. #14519777C2×C4semidirect
128. #14519776C2×C4semidirect
129. #14519776C2×C4semidirect
141. #14519757C2×C4semidirect
145. #14519756C2×C4semidirect
161. #14519753C2×C4semidirect
162. Q8×Dic61C2×C4semidirect
164. C4×Dic122C2×C4semidirect
166. #14519742C2×C4semidirect
182. C2×C4⋊Dic61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
196. C4⋊C4×D61C2×C4semidirect
207. C4⋊Q8×C61C2×C4semidirect
212. C22⋊Q8×C61C2×C4semidirect
213. C4×Q8×C61C2×C4semidirect
217. C2×C4⋊C4×C61C2×C4semidirect
575. #554#6923semidirect
621. C61#22497semidirect
647. C4⋊Q8C2×#6923semidirect
683. C22⋊Q8C2×#6923semidirect
689. C4×Q8C2×#6923semidirect
736. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
#214623352
#214620032
#214619982
#214618342
#214618322
#214618052
#214618042
#214617232
#214617222
#214616902
#214615912
#214615062
C2×#168406352
#554×D612
#2249761