Finite Group Databasebeta

← #30620358

Subgroups — #30620358

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic, complemented
2#21462335C211yesmaximal, characteristic, complemented
3#21462003C211yesmaximal, characteristic, complemented
4#21461998C211yesmaximal, characteristic, complemented
5#21461835C211yesmaximal, characteristic, complemented
6#21461833C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic, complemented
8#21461806C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461724C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13#21461508C211yesmaximal, characteristic, complemented
14#21461504C211yesmaximal, characteristic, complemented
15#555×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×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
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#16840478C411yescharacteristic, complemented
53#16840477C411yescharacteristic, complemented
54#16840477C411yescharacteristic, complemented
55#16840476—21no—
56#16840476C411yescharacteristic, complemented
57#16840476C411yescharacteristic, complemented
58#16840475—21no—
59#16840475C411yescharacteristic, complemented
60#16840475C411yescharacteristic, complemented
61#16840474—21no—
62#16840474—21no—
63C4⋊Q8×D61C2211yescharacteristic
64#124×D61—21no—
65#124×D61—21no—
66#121×D61—21no—
67#121×D61C2211yescharacteristic
68#121×D61C2211yescharacteristic
69C4×D4×D61C2211yescharacteristic
70C4×D4×D61C2211yescharacteristic
71#117×D61—21no—
72#117×D61C2211yescharacteristic
73#117×D61C2211yescharacteristic
74C61×#555C411yescharacteristic, 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#14519839—22no—
105#14519839—22no—
106#14519839—41no—
107#14519839—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×D4×D61—21no—
121C2×D4×D61—21no—
122C2×D4×D61D411yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61—21no—
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127#14519777C2×C411yescharacteristic, complemented
128#14519776—21no—
129#14519776C2×C411yescharacteristic, complemented
130#14519776C2×C411yescharacteristic, complemented
131#14519775—21no—
132#14519766—21no—
133#14519766—21no—
134#14519765—21no—
135#14519765—21no—
136#14519764—21no—
137#14519764—21no—
138#14519763—21no—
139#14519763—21no—
140#14519763—21no—
141#14519763—21no—
142#14519763—21no—
143#14519763—21no—
144#14519763—21no—
145#14519763—21no—
146#14519752—21no—
147#14519752C2×C411yescharacteristic
148#14519752C2×C411yescharacteristic, complemented
149#14519751—21no—
150#14519751C2×C411yescharacteristic
151#14519751C2×C411yescharacteristic, complemented
152#14519750—21no—
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519749—21no—
157#14519749—21no—
158#14519749—21no—
159#14519749—21no—
160#14519748—21no—
161#14519748C2×C411yescharacteristic
162#14519748C2×C411yescharacteristic, complemented
163C4×D244C2×C411yescharacteristic
164C4×D244C2×C411yescharacteristic, complemented
165D4×Dic61C2×C411yescharacteristic, complemented
166D4×Dic61D411yescharacteristic
167#14519739C2×C411yescharacteristic, complemented
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61C2×C411yescharacteristic
171C4×C22⋊D61C2×C411yescharacteristic
172#14519737—21no—
173#14519737D411yescharacteristic
174#14519737D411yescharacteristic
175#14519736—21no—
176#14519736C2×C411yescharacteristic
177#14519736C2×C411yescharacteristic, complemented
178#14519735—21no—
179#14519735—21no—
180#14519735C2×C411yescharacteristic
181#14519735C2×C411yescharacteristic
182#14519735C2×C411yescharacteristic, complemented
183#14519735C2×C411yescharacteristic, complemented
184#14519734—21no—
185#14519734—21no—
186#14519734—21no—
187#14519734—21no—
188#14519733—21no—
189#14519733—21no—
190#14519733—21no—
191#14519733—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61D411yescharacteristic
194C4⋊C4×D61C2311yescharacteristic
195C4⋊C4×D61C2311yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61D411yescharacteristic
203C22⋊C4×D61D411yescharacteristic
204C42×D61—21no—
205C42×D61—21no—
206C42×D61C2311yescharacteristic
207C4⋊Q8×C61C2×C411yescharacteristic, complemented
208#124×C61—21no—
209#124×C61—21no—
210#121×C61—21no—
211#121×C61C2×C411yescharacteristic
212#121×C61C2×C411yescharacteristic, complemented
213C4×D4×C61C2×C411yescharacteristic
214C4×D4×C61C2×C411yescharacteristic, complemented
215#117×C61—21no—
216#117×C61C2×C411yescharacteristic
217#117×C61C2×C411yescharacteristic, complemented
218C23×D61—21no—
219C23×D61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—42no—
226C22×#6923—42no—
227C22×#6923—81no—
228C2×Q8×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61C22⋊C411yescharacteristic
232C2×D4×C61C22×C411yescharacteristic
233C22×C4×C61—21no—
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C22×C411yescharacteristic
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246Q8×D61—81no—
247Q8×D61—81no—
248D4×D61—21no—
249D4×D61—21no—
250D4×D61—21no—
251D4×D61—21no—
252D4×D61—41no—
253D4×D61—41no—
254D4×D61—81no—
255D4×D61—81no—
256D4×D61—81no—
257D4×D61—81no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244C22⋊C411yescharacteristic
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61C22×C411yescharacteristic
278C2×C4×D61C22×C411yescharacteristic
279C2×C4×D61C2×D411yescharacteristic
280C2×C4×D61C2×D411yescharacteristic
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2411yescharacteristic
286C2×Dic122—21no—
287C2×Dic122—21no—
288C2×Dic122—21no—
289C22⋊#6923—42no—
290C22⋊#6923—42no—
291C22⋊#6923—81no—
292#11758217—42no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—21no—
297C2×#92420—42no—
298C4⋊#6923—21no—
299C4⋊#6923—21no—
300C4⋊#6923—21no—
301C4⋊#6923—21no—
302C4⋊#6923—21no—
303C4⋊#6923—21no—
304C4⋊#6923—21no—
305C4⋊#6923—42no—
306C4⋊#6923#4112yes—
307C4×#6923—42no—
308C4×#6923—81no—
309#11758213—42no—
310D61⋊C8—21no—
311D61⋊C8—21no—
312D61⋊C8—21no—
313D61⋊C8—21no—
314D61⋊C8—21no—
315D61⋊C8—21no—
316D61⋊C8—21no—
317D61⋊C8—42no—
318D61⋊C8#4112yes—
319C4⋊C4×C61—21no—
320C4⋊C4×C61C22⋊C411yescharacteristic
321C4⋊C4×C61C22×C411yescharacteristic
322C4⋊C4×C61C22×C411yescharacteristic
323C4⋊C4×C61C22×C411yescharacteristic
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61C22⋊C411yescharacteristic
330C22⋊C4×C61C22⋊C411yescharacteristic
331C42×C61—21no—
332C42×C61—21no—
333C42×C61C22×C411yescharacteristic
334C22⋊Dic61—21no—
335C22⋊Dic61—21no—
336C22⋊Dic61—21no—
337C22⋊Dic61—21no—
338C22⋊Dic61—21no—
339C22⋊Dic61C22⋊C411yescharacteristic
340C22⋊Dic61C22⋊C411yescharacteristic
341#11758198—21no—
342#11758198—21no—
343#11758198—21no—
344#11758198—21no—
345#11758198—21no—
346#11758198—21no—
347#11758198—21no—
348#11758198—21no—
349#11758198—21no—
350#11758198—21no—
351#11758198C22⋊C411yescharacteristic
352#11758198C22⋊C411yescharacteristic
353#11758198C22⋊C411yescharacteristic
354#11758198C22⋊C411yescharacteristic
355C4⋊Dic61—21no—
356C4⋊Dic61C22⋊C411yescharacteristic
357C4⋊Dic61C22×C411yescharacteristic
358C4⋊Dic61C22×C411yescharacteristic
359C4⋊Dic61C22×C411yescharacteristic
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363#11758196—21no—
364#11758196—21no—
365#11758196C22⋊C411yescharacteristic
366#11758196C22⋊C411yescharacteristic
367C4×Dic61—21no—
368C4×Dic61—21no—
369C4×Dic61—21no—
370C4×Dic61—21no—
371C4×Dic61—21no—
372C4×Dic61—21no—
373C4×Dic61C22×C411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C4×Dic61C2×D411yescharacteristic
376C23×C61—21no—
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—21no—
389C22×D61—21no—
390C22×D61—21no—
391C22×D61—21no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61C2×C22⋊C411yescharacteristic
399C22×D61C2×C22⋊C411yescharacteristic
400C22×D61C22×D411yescharacteristic
401C2×#6923—22no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—41no—
405C2×#6923—41no—
406C2×#6923—41no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—84no—
414Q8×C61—81no—
415D4×C61—21no—
416D4×C61—21no—
417D4×C61—41no—
418D4×C61—81no—
419D4×C61—81no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—42no—
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C2×C22⋊C411yescharacteristic
431C2×C4×C61C2×C22⋊C411yescharacteristic
432C2×C4×C61C23×C411yescharacteristic
433C22⋊D61—41no—
434C22⋊D61—41no—
435C22⋊D61—41no—
436C22⋊D61—41no—
437C22⋊D61—81no—
438C22⋊D61—81no—
439C22⋊D61—81no—
440C22⋊D61—81no—
441C2×Dic61—21no—
442C2×Dic61—21no—
443C2×Dic61—21no—
444C2×Dic61—21no—
445C2×Dic61—21no—
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—42no—
449C2×Dic61C2×C22⋊C411yescharacteristic
450C2×Dic61C2×C22⋊C411yescharacteristic
451C2×Dic61C2×C22⋊C411yescharacteristic
452C2×Dic61C2×C22⋊C411yescharacteristic
453C2×Dic61C22×D411yescharacteristic
454D244—21no—
455D244—21no—
456D244—41no—
457D244—81no—
458D244—81no—
459C4×D61—21no—
460C4×D61—21no—
461C4×D61—21no—
462C4×D61—21no—
463C4×D61—21no—
464C4×D61—21no—
465C4×D61—21no—
466C4×D61—21no—
467C4×D61—21no—
468C4×D61—21no—
469C4×D61—21no—
470C4×D61—21no—
471C4×D61—21no—
472C4×D61—21no—
473C4×D61—21no—
474C4×D61—21no—
475C4×D61—42no—
476C4×D61—42no—
477C4×D61—41no—
478C4×D61—41no—
479C4×D61—41no—
480C4×D61—41no—
481C4×D61—41no—
482C4×D61—41no—
483C4×D61C2×#4111yescharacteristic
484C4×D61C2×#4111yescharacteristic
485C4×D61H(5,𝔽2)11yescharacteristic
486C4×D612−1+411yescharacteristic
487Dic122—81no—
488Dic122—81no—
489Dic122—81no—
490#92420—22no—
491#92420—41no—
492#92420—41no—
493#92420—41no—
494#22492—611nomaximal, Sylow
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—21no—
498C22×C61—21no—
499C22×C61—21no—
500C22×C61—21no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—41no—
504C22×C61C22×C22⋊C411yescharacteristic
505C2×D61—21no—
506C2×D61—21no—
507C2×D61—21no—
508C2×D61—21no—
509C2×D61—21no—
510C2×D61—21no—
511C2×D61—41no—
512C2×D61—41no—
513C2×D61—41no—
514C2×D61—41no—
515C2×D61—41no—
516C2×D61—41no—
517C2×D61—41no—
518C2×D61—41no—
519C2×D61—41no—
520C2×D61—41no—
521C2×D61—41no—
522C2×D61—81no—
523C2×D61—81no—
524C2×D61—81no—
525C2×D61—81no—
526C2×D61#54611yescharacteristic
527C2×D61#54711yescharacteristic
528C2×D61#57511yescharacteristic
529C2×D61#57511yescharacteristic
530C2×D61#57611yescharacteristic
531C2×D61#57711yescharacteristic
532#6923—42no—
533#6923—81no—
534#6923—81no—
535#6923—81no—
536C4×C61—21no—
537C4×C61—21no—
538C4×C61—21no—
539C4×C61—21no—
540C4×C61—41no—
541C4×C61—41no—
542C4×C61—41no—
543C4×C61C4×#4111yescharacteristic
544C4×C61#52011yescharacteristic
545Dic61—21no—
546Dic61—21no—
547Dic61—21no—
548Dic61—21no—
549Dic61—41no—
550Dic61—41no—
551Dic61—41no—
552Dic61#54611yescharacteristic
553Dic61#54711yescharacteristic
554C2×#555—611no—
555C2×#435—611no—
556#2352—611no—
557#1993—611no—
558#1988—611no—
559#1895—611no—
560#1893—611no—
561#1875—611no—
562#1874—611no—
563#1825—611no—
564#1825—611no—
565#1804—611no—
566#1762—611no—
567#1736—611no—
568#1735—611no—
569C2×C61—41no—
570C2×C61—41no—
571C2×C61—81no—
572C2×C61#233911yescharacteristic
573C2×C61#289611yescharacteristic
574C2×C61#289711yescharacteristic
575D61—41no—
576D61—41no—
577D61—81no—
578D61#331911yescharacteristic
579D61#332111yescharacteristic
580D61#334711yescharacteristic
581D61#334811yescharacteristic
582C22×M16—611no—
583C23×C8—611no—
584#555—611no—
585#555—611no—
586#555—611no—
587#555—611no—
588#555—611no—
589#555—611no—
590#555—611no—
591#555—1221no—
592#555—1221no—
593#555—1221no—
594#555—1221no—
595#555#692311yescharacteristic, complemented
596C2×C4⋊Q8—611no—
597C2×#124—1221no—
598C2×#124—1221no—
599C2×#121—611no—
600C2×#121—611no—
601C2×#121—1221no—
602C2×C4×D4—611no—
603C2×C4×D4—611no—
604C2×#117—611no—
605C2×#117—611no—
606C2×#117—611no—
607C2×#117—1221no—
608C22×C4⋊C4—611no—
609#435—1221no—
610#435—1221no—
611#435—1221no—
612#435—1221no—
613C2×C4⋊C8—611no—
614C2×#102—611no—
615C2×#102—611no—
616C2×#102—611no—
617C2×#102—611no—
618C2×C22⋊C8—611no—
619C2×C22⋊C8—611no—
620C2×#97—611no—
621#388—1221no—
622#387—1221no—
623#386—1221no—
624#382—611no—
625#380—611no—
626#380—611no—
627C4×C4⋊C4—611no—
628C4×C22⋊C4—1221no—
629#340—611no—
630#340—611no—
631#340—611no—
632#340—611no—
633#340—611no—
634#340—611no—
635#340—611no—
636#340—611no—
637#340—611no—
638#340—611no—
639#340—611no—
640#340—611no—
641C61#2249211yescharacteristic, complemented, Sylow
642C22×Q8—1221no—
643C22×D4—611no—
644C22×D4—611no—
645C22×D4—1221no—
646C22×D4—1221no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—1221no—
650C23×C4—1221no—
651C2×M16—1222no—
652C2×M16—1221no—
653C2×M16—1221no—
654C2×M16—2441no—
655C22×C8—611no—
656C22×C8—611no—
657C22×C8—611no—
658C22×C8—611no—
659C22×C8—1222no—
660C22×C8—1221no—
661C22×C8—1221no—
662C22×C8—2441no—
663C4⋊Q8—611no—
664C4⋊Q8—611no—
665C4⋊Q8—611no—
666C4⋊Q8—1221no—
667C4⋊Q8—1221no—
668C4⋊Q8C2×#692311yescharacteristic, complemented
669#124—21no—
670#124—21no—
671#124—1221no—
672#124—1221no—
673#124—1221no—
674#124—1221no—
675#124—1221no—
676#124—1221no—
677#124—1221no—
678#124—1221no—
679#124—1221no—
680#124—1221no—
681#124—1221no—
682#124—1221no—
683#124—1221no—
684#124—1221no—
685#121—21no—
686#121—611no—
687#121—611no—
688#121—611no—
689#121—611no—
690#121—611no—
691#121—611no—
692#121—1221no—
693#121—1221no—
694#121—1221no—
695#121—1221no—
696#121—1221no—
697#121—1221no—
698#121—1221no—
699#121—1221no—
700#121—1221no—
701#121—1221no—
702#121—1221no—
703#121C2×#692311yescharacteristic
704#121C2×#692311yescharacteristic, complemented
705C4×D4—611no—
706C4×D4—611no—
707C4×D4—611no—
708C4×D4—611no—
709C4×D4—611no—
710C4×D4—611no—
711C4×D4—611no—
712C4×D4—611no—
713C4×D4—611no—
714C4×D4—611no—
715C4×D4—1221no—
716C4×D4—1221no—
717C4×D4C2×#692311yescharacteristic
718C4×D4C2×#692311yescharacteristic, complemented
719#117—21no—
720#117—611no—
721#117—611no—
722#117—611no—
723#117—611no—
724#117—611no—
725#117—611no—
726#117—1221no—
727#117—1221no—
728#117—1221no—
729#117—1221no—
730#117—1221no—
731#117—1221no—
732#117—1221no—
733#117—1221no—
734#117—1221no—
735#117—1221no—
736#117—1221no—
737#117—1222no—
738#117—2441no—
739#117C2×#692311yescharacteristic
740#117C2×#692311yescharacteristic, complemented
741C2×C4⋊C4—611no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—611no—
747C2×C4⋊C4—611no—
748C2×C4⋊C4—611no—
749C2×C4⋊C4—1221no—
750C2×C4⋊C4—1222no—
751C2×C4⋊C4—1221no—
752C2×C4⋊C4—2441no—
753C2×C22⋊C4—611no—
754C2×C22⋊C4—611no—
755C2×C22⋊C4—1221no—
756C2×C22⋊C4—1221no—
757C2×C22⋊C4—1221no—
758C2×C22⋊C4—1221no—
759C2×C22⋊C4—1221no—
760C2×C22⋊C4—1221no—
761C2×C22⋊C4—1221no—
762C2×C22⋊C4—1221no—
763C2×C42—611no—
764C2×C42—1221no—
765C2×C42—1221no—
766C2×C42—1221no—
767C2×C42—1221no—
768C4⋊C8—1221no—
769C4⋊C8—1221no—
770#102—1222no—
771#102—1222no—
772#102—2441no—
773#102—2441no—
774C22⋊C8—1221no—
775C22⋊C8—1221no—
776C22⋊C8—1221no—
777C22⋊C8—1221no—
778#97—1221no—
779#97—1221no—
780#95—1221no—
781#95—1221no—
782#95—1221no—
783#95—1221no—
784#95—1221no—
785C24—611no—
786C24—611no—
787C24—1221no—
788C2×Q8—21no—
789C2×Q8—1221no—
790C2×Q8—1221no—
791C2×Q8—1221no—
792C2×Q8—4881no—
793C2×Q8—4881no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—611no—
797C2×D4—611no—
798C2×D4—611no—
799C2×D4—611no—
800C2×D4—1221no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—1221no—
807C2×D4—1221no—
808C2×D4—1221no—
809C2×D4—1221no—
810C2×D4—1221no—
811C2×D4—4881no—
812C2×D4—4881no—
813C2×D4—4881no—
814C2×D4—4881no—
815C2×D4—2441no—
816C2×D4—2441no—
817C2×D4C22⋊#692311yescharacteristic
818C2×D4C22×#692311yescharacteristic
819C22×C4—21no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—4881no—
850C22×C4—2442no—
851C22×C4—2442no—
852C22×C4—2442no—
853C22×C4—2442no—
854C22×C4C22×#692311yescharacteristic
855C22×C4C22×#692311yescharacteristic
856M16—2442no—
857M16—2442no—
858C2×C8—612no—
859C2×C8—1221no—
860C2×C8—1221no—
861C2×C8—1221no—
862C2×C8—1221no—
863C2×C8—1221no—
864C2×C8—1221no—
865C2×C8—1221no—
866C2×C8—1221no—
867C2×C8—1221no—
868C2×C8—1221no—
869C2×C8—1221no—
870C2×C8—2442no—
871C2×C8—2442no—
872C4⋊C4—21no—
873C4⋊C4—611no—
874C4⋊C4—611no—
875C4⋊C4—611no—
876C4⋊C4—612no—
877C4⋊C4—611no—
878C4⋊C4—611no—
879C4⋊C4—611no—
880C4⋊C4—1221no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4—1221no—
885C4⋊C4—1221no—
886C4⋊C4—1221no—
887C4⋊C4—1221no—
888C4⋊C4—1221no—
889C4⋊C4—1221no—
890C4⋊C4—1221no—
891C4⋊C4—1221no—
892C4⋊C4—1221no—
893C4⋊C4—2442no—
894C4⋊C4C22⋊#692311yescharacteristic
895C4⋊C4C22×#692311yescharacteristic
896C4⋊C4C22×#692311yescharacteristic
897C4⋊C4C22×#692311yescharacteristic
898C22⋊C4—21no—
899C22⋊C4—21no—
900C22⋊C4—21no—
901C22⋊C4—21no—
902C22⋊C4—21no—
903C22⋊C4—611no—
904C22⋊C4—611no—
905C22⋊C4—611no—
906C22⋊C4—611no—
907C22⋊C4—611no—
908C22⋊C4—611no—
909C22⋊C4—1221no—
910C22⋊C4—1221no—
911C22⋊C4—1221no—
912C22⋊C4—1221no—
913C22⋊C4—1221no—
914C22⋊C4—1221no—
915C22⋊C4—1221no—
916C22⋊C4—1221no—
917C22⋊C4—1221no—
918C22⋊C4—1221no—
919C22⋊C4—1221no—
920C22⋊C4—1221no—
921C22⋊C4—1221no—
922C22⋊C4—1221no—
923C22⋊C4—1221no—
924C22⋊C4—4881no—
925C22⋊C4—2442no—
926C22⋊C4—2442no—
927C22⋊C4C22⋊#692311yescharacteristic
928C22⋊C4C22⋊#692311yescharacteristic
929C42—21no—
930C42—21no—
931C42—611no—
932C42—611no—
933C42—611no—
934C42—1221no—
935C42—1221no—
936C42—1221no—
937C42—1221no—
938C42—1221no—
939C42—1221no—
940C42—4881no—
941C42—2442no—
942C42C22×#692311yescharacteristic
943C23—21no—
944C23—611no—
945C23—611no—
946C23—611no—
947C23—1221no—
948C23—1221no—
949C23—1221no—
950C23—1221no—
951C23—1221no—
952C23—1221no—
953C23—1221no—
954C23—1221no—
955C23—1221no—
956C23—1221no—
957C23—1221no—
958C23—1221no—
959C23—1221no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23C2×C22⋊#692311yescharacteristic
967C23C2×C22⋊#692311yescharacteristic
968Q8—81no—
969Q8—4881no—
970Q8—4881no—
971Q8—4881no—
972D4—21no—
973D4—21no—
974D4—41no—
975D4—81no—
976D4—81no—
977D4—1221no—
978D4—1221no—
979D4—4881no—
980D4—4881no—
981D4—4881no—
982D4—4881no—
983D4—4881no—
984D4—4881no—
985D4—2441no—
986D4—2441no—
987D4—2441no—
988D4—2441no—
989D4—2441no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—42no—
998C2×C4—611no—
999C2×C4—611no—
1000C2×C4—611no—
1001C2×C4—611no—
1002C2×C4—611no—
1003C2×C4—611no—
1004C2×C4—611no—
1005C2×C4—611no—
1006C2×C4—611no—
1007C2×C4—1221no—
1008C2×C4—1221no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
1024C2×C4—1221no—
1025C2×C4—1221no—
1026C2×C4—1221no—
1027C2×C4—1222no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—1221no—
1031C2×C4—4884no—
1032C2×C4—2442no—
1033C2×C4—2442no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2442no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4C2×C22⋊#692311yescharacteristic
1053C2×C4C2×C22⋊#692311yescharacteristic
1054C2×C4C2×C22⋊#692311yescharacteristic
1055C2×C4C2×C22⋊#692311yescharacteristic
1056C2×C4C23×#692311yescharacteristic
1057C8—1222no—
1058C8—2441no—
1059C8—2441no—
1060C8—2441no—
1061C22—21no—
1062C22—21no—
1063C22—21no—
1064C22—21no—
1065C22—21no—
1066C22—21no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—611no—
1071C22—611no—
1072C22—611no—
1073C22—611no—
1074C22—611no—
1075C22—611no—
1076C22—1221no—
1077C22—1221no—
1078C22—1221no—
1079C22—1221no—
1080C22—1221no—
1081C22—1221no—
1082C22—4881no—
1083C22—4881no—
1084C22—4881no—
1085C22—4881no—
1086C22—2441no—
1087C22—2441no—
1088C22—2441no—
1089C22—2441no—
1090C22—2441no—
1091C22—2441no—
1092C22—2441no—
1093C22—2441no—
1094C22—2441no—
1095C22—2441no—
1096C22—2441no—
1097C22C22×C22⋊#692311yescharacteristic
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—611no—
1106C4—611no—
1107C4—1221no—
1108C4—1221no—
1109C4—1221no—
1110C4—1221no—
1111C4—4881no—
1112C4—4881no—
1113C4—4881no—
1114C4—2442no—
1115C4—2441no—
1116C4—2441no—
1117C4—2441no—
1118C4#41×#692311yescharacteristic
1119C4#1684083111yescharacteristic
1120C2—41no—
1121C2—41no—
1122C2—81no—
1123C2—611no—
1124C2—611no—
1125C2—611no—
1126C2—611no—
1127C2—4881no—
1128C2—2441no—
1129C2—2441no—
1130C2#2146232211yescharacteristic
1131C2#2146243911yescharacteristic
1132C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#555C4
socleC22×C61C22×C22⋊C4
prime radical#555×D61C2
cosocleC2×C4×D61C24
hypercenter#555#6923
hypocenterC61#22492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. D61⋊#435C2semidirect
2. #21462335C2semidirect
3. #21462003C2semidirect
4. #21461998C2semidirect
5. #21461835C2semidirect
6. #21461833C2semidirect
7. #21461807C2semidirect
8. #21461806C2semidirect
9. #21461724C2semidirect
10. #21461724C2semidirect
11. #21461689C2semidirect
12. #21461589C2semidirect
13. #21461508C2semidirect
14. #21461504C2semidirect
52. #16840478C4semidirect
53. #16840477C4semidirect
54. #16840477C4semidirect
56. #16840476C4semidirect
57. #16840476C4semidirect
59. #16840475C4semidirect
60. #16840475C4semidirect
74. C61×#555C4semidirect
127. #14519777C2×C4semidirect
129. #14519776C2×C4semidirect
130. #14519776C2×C4semidirect
148. #14519752C2×C4semidirect
151. #14519751C2×C4semidirect
162. #14519748C2×C4semidirect
164. C4×D244C2×C4semidirect
165. D4×Dic61C2×C4semidirect
167. #14519739C2×C4semidirect
177. #14519736C2×C4semidirect
182. #14519735C2×C4semidirect
183. #14519735C2×C4semidirect
207. C4⋊Q8×C61C2×C4semidirect
212. #121×C61C2×C4semidirect
214. C4×D4×C61C2×C4semidirect
217. #117×C61C2×C4semidirect
595. #555#6923semidirect
641. C61#22492semidirect
668. C4⋊Q8C2×#6923semidirect
704. #121C2×#6923semidirect
718. C4×D4C2×#6923semidirect
740. #117C2×#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
#214618352
#214618332
#214618072
#214618062
#214617242
#214616892
#214615892
#214615082
#214615042
#555×D612
#2249261