Finite Group Databasebeta

← #30622245

Subgroups — #30622245

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C22×#14519845C211yesmaximal, characteristic, complemented
3#21462344C211yesmaximal, characteristic
4#21462343C211yesmaximal, characteristic, complemented
5#21461964C211yesmaximal, characteristic, complemented
6#21461922C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461897C211yesmaximal, characteristic, complemented
9#21461806C211yesmaximal, characteristic
10#21461804C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461784C211yesmaximal, characteristic, complemented
13#106×#6923C211yesmaximal, characteristic, complemented
14C8×C22⋊#6923C211yesmaximal, characteristic, complemented
15#465×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923—21no—
18C2×D4×#6923C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21SD16×#6923—24no—
22C2×#14519845—24no—
23C2×#14519845C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519845C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31D61⋊(C22⋊C8)C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840714C2211yescharacteristic
36#16840713—21no—
37#16840713C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840712—21no—
40#16840711—21no—
41#16840710—21no—
42#16840709—21no—
43#16840709—21no—
44C4⋊C4×#6923C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C22×C8×D61C2211yescharacteristic
56C22⋊Q8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839994C411yescharacteristic, complemented
59#16839993C411yescharacteristic, complemented
60#16839992C411yescharacteristic, complemented
61#16839991C411yescharacteristic, complemented
62#16839990C411yescharacteristic, complemented
63#16839989C411yescharacteristic, complemented
64#16839988C411yescharacteristic, complemented
65#106×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#465C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8C2311yescharacteristic
73C2×D61⋊C8C2311yescharacteristic
74Q8×#6923—22no—
75Q8×#6923—41no—
76D4×#6923—22no—
77D4×#6923—41no—
78D4×#6923—44no—
79C2×C4⋊#6923—22no—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—41no—
87C2×C4⋊#6923—41no—
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923D411yescharacteristic
96C2×C22⋊#6923D411yescharacteristic
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519845—22no—
103#14519845—22no—
104#14519845—22no—
105#14519845D414yescomplemented
106#14519840—22no—
107#14519840—41no—
108#14519839—22no—
109#14519839—41no—
110#14519834—21no—
111C22⋊#92420—21no—
112C8×#6923—22no—
113C8×#6923—22no—
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—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4D411yescharacteristic
121(C2×#6923)⋊C4D411yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61C2311yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C2×#11758190C2×C411yescharacteristic, complemented
127C2×#11758200C2×C411yescharacteristic, complemented
128C2×#11758201C2×C411yescharacteristic, complemented
129SD16×D61—22no—
130SD16×D61—22no—
131C22×#92418C2×C411yescharacteristic, complemented
132C2×C8×D61—22no—
133C2×C8×D61—22no—
134C2×C8×D61C2×C411yescharacteristic, complemented
135C2×C8×D61C2×C411yescharacteristic, complemented
136C2×C8×D61C2311yescharacteristic
137C2×C8×D61C2311yescharacteristic
138#14519757C2×C411yescharacteristic, complemented
139#14519756C2×C411yescharacteristic, complemented
140#14519755—21no—
141#14519754—21no—
142#14519753C2×C411yescharacteristic, complemented
143#14519752C2×C411yescharacteristic
144#14519751C2×C411yescharacteristic
145#14519750—21no—
146#14519749—21no—
147#14519748C2×C411yescharacteristic
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C4⋊C4×D61C2311yescharacteristic
151C22⋊C4×D61—21no—
152C22⋊C4×D61—21no—
153#14519709C2×C411yescharacteristic, complemented
154#14519708C2×C411yescharacteristic, complemented
155#14519708C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519700C2×C411yescharacteristic, complemented
159#14519699C2×C411yescharacteristic, complemented
160#14519698C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic, complemented
163C22×C8×C61C2×C411yescharacteristic, complemented
164C22⋊Q8×C61C2×C411yescharacteristic, complemented
165#121×C61C2×C411yescharacteristic
166#106×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61C2×D411yescharacteristic
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—42no—
180C22×#6923—42no—
181C22×#6923—81no—
182C22×#6923—81no—
183C22×#6923—81no—
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188C2×Q8×C61C22×C411yescharacteristic
189C2×D4×C61—21no—
190C2×D4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C22×Dic61#4111yescharacteristic
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61—21no—
199Q8×D61—21no—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—42no—
205D4×D61—42no—
206C2×D244—21no—
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61#4111yescharacteristic
218C2×C4×D61C2411yescharacteristic
219C2×Dic122—21no—
220C2×Dic122C22×C411yescharacteristic
221C22⋊#6923—22no—
222C22⋊#6923—42no—
223C22⋊#6923—42no—
224C22⋊#6923—81no—
225C22⋊#6923SD1614yescomplemented
226C2×#92420—21no—
227C2×#92420—21no—
228C4⋊#6923—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—42no—
235C4⋊#6923—42no—
236C4⋊#6923—42no—
237C4⋊#6923—42no—
238C4⋊#6923—81no—
239C4⋊#6923C2×D412yes—
240C4⋊#6923C2×D412yes—
241C4×#6923—21no—
242C4×#6923—21no—
243C4×#6923—21no—
244C4×#6923—21no—
245C4×#6923—42no—
246C4×#6923—42no—
247C4×#6923—81no—
248D61⋊C8—21no—
249D61⋊C8—21no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252SD16×C61—22no—
253C2×C8×C61—22no—
254C2×C8×C61C22×C411yescharacteristic
255C2×C8×C61C22×C411yescharacteristic
256C4⋊C4×C61—21no—
257C4⋊C4×C61C22×C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263#11758201—22no—
264#11758200—22no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C22×C411yescharacteristic
271C4⋊Dic61C22×C411yescharacteristic
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276C2×#92418—22no—
277C2×#92418C22×C411yescharacteristic
278C2×#92418C22×C411yescharacteristic
279#11758190—22no—
280C8×D61—21no—
281C8×D61—21no—
282C8×D61—22no—
283C8×D61—22no—
284C8×D61C2×D412yes—
285C8×D61#4112yes—
286C23×C61—21no—
287C23×C61C4×D411yescharacteristic
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61C4×D411yescharacteristic
300C22×D61C2×SD1612yes—
301C22×D61#13512yes—
302C22×D61C22×D411yescharacteristic
303C2×#6923—21no—
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—22no—
309C2×#6923—22no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—21no—
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—84no—
328C2×#6923C2×SD1612yes—
329C2×#6923C2×SD1612yes—
330Q8×C61—21no—
331Q8×C61—21no—
332D4×C61—21no—
333D4×C61—21no—
334D4×C61—42no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C23×C411yescharacteristic
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—41no—
345C22⋊D61—41no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61C4×D411yescharacteristic
352C2×Dic61C2×#4111yescharacteristic
353D244—21no—
354D244—21no—
355D244—42no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61C22×D411yescharacteristic
369C4×D61C2×#4111yescharacteristic
370C4×D61H(5,𝔽2)11yescharacteristic
371C4×D612−1+411yescharacteristic
372Dic122—21no—
373Dic122—21no—
374Dic122—41no—
375Dic122—41no—
376#92420—41no—
377#92420—41no—
378C8×C61—21no—
379C8×C61C4×D412yescomplemented
380#92418—21no—
381#92418C4×D412yescomplemented
382#23022—611nomaximal, Sylow
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61C4×SD1612yescomplemented
389C22×C61C2×C4×D411yescharacteristic
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—22no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61C4×SD1612yescomplemented
404C2×D61D4211yescharacteristic
405C2×D61#54711yescharacteristic
406C2×D61C22×SD1611yescharacteristic
407C2×D61C2×#13511yescharacteristic
408C2×D61#57711yescharacteristic
409C2×D61#57711yescharacteristic
410#6923—22no—
411#6923—22no—
412#6923—41no—
413#6923—42no—
414#6923—41no—
415#6923—42no—
416#6923—81no—
417#6923—81no—
418C4×C61—21no—
419C4×C61—41no—
420C4×C61—41no—
421C4×C61—41no—
422C4×C61C2×C4×D411yescharacteristic
423C4×C61#52011yescharacteristic
424Dic61—21no—
425Dic61—41no—
426Dic61—41no—
427Dic61—41no—
428Dic61#54811yescharacteristic
429Dic61#55311yescharacteristic
430C2×#465—611no—
431C2×C4×SD16—611no—
432C22×#106—611no—
433#2361—611no—
434#2360—611no—
435#1968—611no—
436#1941—611no—
437#1927—611no—
438#1926—611no—
439#1874—611no—
440#1872—611no—
441#1865—611no—
442#1864—611no—
443C4×#106—611no—
444C8×C22⋊C4—611no—
445C2×C61—22no—
446C2×C61—81no—
447C2×C61#236111yescharacteristic
448C2×C61C2×C4×SD1611yescharacteristic
449C2×C61#295211yescharacteristic
450D61—22no—
451D61—81no—
452D61D4×SD1611yescharacteristic
453D61#328211yescharacteristic
454D61#333511yescharacteristic
455D61#333711yescharacteristic
456C22×SD16—611no—
457C23×C8—611no—
458C2×C22⋊Q8—611no—
459C2×#121—611no—
460C2×C4×Q8—611no—
461C2×C4×D4—611no—
462C2×C4×D4—1221no—
463C22×C4⋊C4—611no—
464C22×C4⋊C4—611no—
465#465—611no—
466#465—611no—
467#465—611no—
468#465—611no—
469#465—611no—
470#465—611no—
471#465—611no—
472#465#692311yescharacteristic, complemented
473C4×SD16—1224no—
474C2×#106—611no—
475C2×#106—611no—
476C2×#106—611no—
477C2×#106—611no—
478C2×#106—611no—
479C2×#106—1224no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×C22⋊C8—611no—
487C2×C4×C8—611no—
488C2×C4×C8—611no—
489#391—611no—
490#390—611no—
491#389—611no—
492#389—611no—
493#389—1221no—
494#388—1221no—
495#387—1221no—
496#386—1221no—
497#385—1221no—
498#385—1221no—
499C4×C4⋊C4—611no—
500C4×C4⋊C4—611no—
501C4×C22⋊C4—611no—
502C4×C22⋊C4—1221no—
503#340—611no—
504#340—611no—
505#340—611no—
506#340—611no—
507#336—611no—
508#336—611no—
509C61#2302211yescharacteristic, complemented, Sylow
510C22×Q8—611no—
511C22×D4—611no—
512C22×D4—1221no—
513C23×C4—611no—
514C23×C4—1221no—
515C23×C4—1221no—
516C23×C4—1221no—
517C2×SD16—611no—
518C2×SD16—611no—
519C2×SD16—611no—
520C2×SD16—1222no—
521C2×SD16—1222no—
522C2×SD16C2×#692311yescharacteristic, complemented
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—1222no—
532C22×C8C2×#692311yescharacteristic, complemented
533C22⋊Q8—611no—
534C22⋊Q8—611no—
535C22⋊Q8—611no—
536C22⋊Q8—1221no—
537C22⋊Q8—1221no—
538C22⋊Q8C2×#692311yescharacteristic, complemented
539#121—611no—
540#121—611no—
541#121—611no—
542#121—1221no—
543#121—1221no—
544#121C2×#692311yescharacteristic
545C4×Q8—1222no—
546C4×Q8—2441no—
547C4×D4—1222no—
548C4×D4—2441no—
549C4×D4—2444no—
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—1221no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—2441no—
565C2×C4⋊C4—2441no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—1221no—
576C2×C42—1221no—
577C2×C42—1221no—
578#106—614no—
579#106—611no—
580#106—611no—
581#106—611no—
582#106—1222no—
583#106—1222no—
584#106—1222no—
585#106C2×#692311yescharacteristic, complemented
586#103—611no—
587#103—611no—
588#103—611no—
589#103—1222no—
590#103—2441no—
591#103C2×#692311yescharacteristic, complemented
592#102—611no—
593#102—611no—
594#102—611no—
595#102—1222no—
596#102—2441no—
597#102C2×#692311yescharacteristic, complemented
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C4×C8—1222no—
601C4×C8—1222no—
602#95—611no—
603#95—611no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609#95—1221no—
610C24—611no—
611C24—1221no—
612C2×Q8—611no—
613C2×Q8—1221no—
614C2×Q8—1221no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8C22×#692311yescharacteristic
619C2×D4—21no—
620C2×D4—611no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—2442no—
630C2×D4—2442no—
631C2×D4C22×#692311yescharacteristic
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—4881no—
653C22×C4—4881no—
654C22×C4—4881no—
655C22×C4—2442no—
656C22×C4—2442no—
657C22×C4—2442no—
658C22×C4—2442no—
659C22×C4—2442no—
660C22×C4—2442no—
661C22×C4C22×#692311yescharacteristic
662SD16—22no—
663SD16—1222no—
664SD16—1222no—
665SD16—1222no—
666C2×C8—22no—
667C2×C8—611no—
668C2×C8—612no—
669C2×C8—612no—
670C2×C8—611no—
671C2×C8—1222no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1222no—
675C2×C8—1222no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8C22×#692311yescharacteristic
683C2×C8C22×#692311yescharacteristic
684C4⋊C4—21no—
685C4⋊C4—612no—
686C4⋊C4—612no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—4881no—
701C4⋊C4—2442no—
702C4⋊C4—2442no—
703C4⋊C4—2442no—
704C4⋊C4—2442no—
705C4⋊C4C22×#692311yescharacteristic
706C4⋊C4C22×#692311yescharacteristic
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—614no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1222no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—4881no—
718C22⋊C4—2442no—
719C22⋊C4—2442no—
720C42—1221no—
721C42—1221no—
722C42—1221no—
723C42—1221no—
724C42—4881no—
725C42—2442no—
726C42—2442no—
727C23—21no—
728C23—611no—
729C23—612no—
730C23—612no—
731C23—611no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23D4×#692311yescharacteristic
744Q8—21no—
745Q8—21no—
746Q8—1221no—
747Q8—1221no—
748Q8—2441no—
749Q8—2441no—
750D4—21no—
751D4—21no—
752D4—42no—
753D4—1221no—
754D4—1221no—
755D4—2442no—
756D4—2441no—
757D4—2441no—
758D4—2442no—
759D4—2442no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—611no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
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—1222no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—4884no—
797C2×C4—4884no—
798C2×C4—4884no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4D4×#692311yescharacteristic
816C2×C4C23×#692311yescharacteristic
817C8—21no—
818C8—612no—
819C8—1221no—
820C8—2441no—
821C8—2441no—
822C8D4×#692312yescomplemented
823C22—21no—
824C22—21no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—611no—
829C22—611no—
830C22—611no—
831C22—611no—
832C22—611no—
833C22—611no—
834C22—612no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22—1221no—
840C22—1221no—
841C22—4881no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—2441no—
846C22—2441no—
847C22—2441no—
848C22SD16×#692312yescomplemented
849C22C2×D4×#692311yescharacteristic
850C4—21no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—611no—
855C4—611no—
856C4—1222no—
857C4—1222no—
858C4—1221no—
859C4—4881no—
860C4—4881no—
861C4—2441no—
862C4—2441no—
863C4—2442no—
864C4—2442no—
865C4—2441no—
866C4—2441no—
867C4—2441no—
868C4C2×D4×#692311yescharacteristic
869C4#1684083111yescharacteristic
870C2—22no—
871C2—81no—
872C2—611no—
873C2—611no—
874C2—611no—
875C2—611no—
876C2—1222no—
877C2—4881no—
878C2#2146234411yescharacteristic
879C2C2×SD16×#692311yescharacteristic
880C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#465C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#465#6923
hypocenterC61#23022
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
2. C22×#14519845C2semidirect
4. #21462343C2semidirect
5. #21461964C2semidirect
6. #21461922C2semidirect
7. #21461898C2semidirect
8. #21461897C2semidirect
10. #21461804C2semidirect
11. #21461785C2semidirect
12. #21461784C2semidirect
13. #106×#6923C2semidirect
14. C8×C22⋊#6923C2semidirect
58. #16839994C4semidirect
59. #16839993C4semidirect
60. #16839992C4semidirect
61. #16839991C4semidirect
62. #16839990C4semidirect
63. #16839989C4semidirect
64. #16839988C4semidirect
68. C61×#465C4semidirect
105. #14519845D4semidirect
126. C2×#11758190C2×C4semidirect
127. C2×#11758200C2×C4semidirect
128. C2×#11758201C2×C4semidirect
131. C22×#92418C2×C4semidirect
134. C2×C8×D61C2×C4semidirect
135. C2×C8×D61C2×C4semidirect
138. #14519757C2×C4semidirect
139. #14519756C2×C4semidirect
142. #14519753C2×C4semidirect
153. #14519709C2×C4semidirect
154. #14519708C2×C4semidirect
155. #14519708C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519700C2×C4semidirect
159. #14519699C2×C4semidirect
160. #14519698C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
163. C22×C8×C61C2×C4semidirect
164. C22⋊Q8×C61C2×C4semidirect
166. #106×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
225. C22⋊#6923SD16semidirect
379. C8×C61C4×D4semidirect
381. #92418C4×D4semidirect
388. C22×C61C4×SD16semidirect
403. C2×D61C4×SD16semidirect
472. #465#6923semidirect
509. C61#23022semidirect
522. C2×SD16C2×#6923semidirect
532. C22×C8C2×#6923semidirect
538. C22⋊Q8C2×#6923semidirect
585. #106C2×#6923semidirect
591. #103C2×#6923semidirect
597. #102C2×#6923semidirect
822. C8D4×#6923semidirect
848. C22SD16×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C22×#145198452
#214623442
#214623432
#214619642
#214619222
#214618982
#214618972
#214618062
#214618042
#214617852
#214617842
#106×#69232
C8×C22⋊#69232
#465×D612
#2302261