Finite Group Databasebeta

← #30622246

Subgroups — #30622246

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840772C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic
4#21462345C211yesmaximal, characteristic, complemented
5#21461964C211yesmaximal, characteristic, complemented
6#21461922C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461807C211yesmaximal, characteristic
10#21461805C211yesmaximal, characteristic, complemented
11#21461783C211yesmaximal, characteristic, complemented
12#21461782C211yesmaximal, characteristic, complemented
13#106×#6923C211yesmaximal, characteristic, complemented
14C8×C22⋊#6923C211yesmaximal, characteristic, complemented
15#465×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20SD16×#6923—24no—
21#16840772—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519845C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840713C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840712—21no—
39#16840712—21no—
40#16840712—21no—
41#16840711—21no—
42#16840710—21no—
43C4⋊C4×#6923—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—
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72Q8×#6923—22no—
73Q8×#6923—41no—
74D4×#6923—22no—
75D4×#6923—41no—
76#14519856—22no—
77#14519856—22no—
78#14519856—41no—
79#14519856—41no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923D411yescharacteristic
93C2×C22⋊#6923D411yescharacteristic
94C2×C4×#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923C2311yescharacteristic
100C2×C4×#6923C2311yescharacteristic
101#14519846—22no—
102#14519846—22no—
103#14519845—22no—
104#14519845D414yescomplemented
105#14519840—22no—
106#14519840—41no—
107#14519839—22no—
108#14519839—41no—
109#14519834—21no—
110C22⋊#92420—21no—
111C8×#6923—22no—
112C8×#6923—22no—
113(C2×#6923)⋊C4—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—
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×D4×D61—21no—
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125C2×#11758190C2×C411yescharacteristic
126C2×#11758200C2×C411yescharacteristic
127C2×#11758201C2×C411yescharacteristic
128SD16×D61—22no—
129SD16×D61—22no—
130C22×#92418C2×C411yescharacteristic, complemented
131C2×C8×D61—22no—
132C2×C8×D61—22no—
133C2×C8×D61C2×C411yescharacteristic, complemented
134C2×C8×D61C2×C411yescharacteristic, complemented
135C2×C8×D61C2311yescharacteristic
136C2×C8×D61C2311yescharacteristic
137#14519757C2×C411yescharacteristic, complemented
138#14519756C2×C411yescharacteristic, complemented
139#14519755—21no—
140#14519754—21no—
141#14519753C2×C411yescharacteristic, complemented
142#14519752C2×C411yescharacteristic
143#14519751C2×C411yescharacteristic
144#14519750—21no—
145#14519749—21no—
146#14519748C2×C411yescharacteristic
147C4⋊C4×D61—21no—
148C4⋊C4×D61C2311yescharacteristic
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C22⋊C4×D61—21no—
152#14519709C2×C411yescharacteristic, complemented
153#14519708C2×C411yescharacteristic, complemented
154#14519708C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519701C2×C411yescharacteristic, complemented
157#14519700C2×C411yescharacteristic, complemented
158#14519699C2×C411yescharacteristic
159#14519698C2×C411yescharacteristic
160#14519697C2×C411yescharacteristic
161C2×SD16×C61C2×C411yescharacteristic
162C22×C8×C61C2×C411yescharacteristic, complemented
163C22⋊Q8×C61C2×C411yescharacteristic, complemented
164#121×C61C2×C411yescharacteristic
165#106×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic
168C23×D61—21no—
169C23×D61C2×D411yescharacteristic
170C22×#6923—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—42no—
175C22×#6923—42no—
176C22×#6923—81no—
177C22×#6923C2×D411yescharacteristic
178C22×#6923C2×D411yescharacteristic
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C22×Dic61#4111yescharacteristic
189Q8×D61—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193D4×D61—21no—
194D4×D61—21no—
195D4×D61—21no—
196D4×D61—21no—
197D4×D61—81no—
198D4×D61—81no—
199C2×D244—21no—
200C2×D244C22×C411yescharacteristic
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61C22×C411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61#4111yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122C22×C411yescharacteristic
214C22⋊#6923—22no—
215C22⋊#6923—22no—
216C22⋊#6923—42no—
217C22⋊#6923—42no—
218C22⋊#6923—42no—
219C22⋊#6923—42no—
220C22⋊#6923—81no—
221C2×#92420—21no—
222C2×#92420—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—21no—
226C4⋊#6923—21no—
227C4⋊#6923—21no—
228C4⋊#6923—21no—
229C4⋊#6923—42no—
230C4⋊#6923—42no—
231C4⋊#6923—81no—
232C4⋊#6923C2×D412yes—
233C4⋊#6923C2×D412yes—
234C4×#6923—21no—
235C4×#6923—21no—
236C4×#6923—21no—
237C4×#6923—21no—
238C4×#6923—42no—
239C4×#6923—42no—
240C4×#6923—42no—
241C4×#6923—42no—
242C4×#6923—81no—
243D61⋊C8—21no—
244D61⋊C8—21no—
245D61⋊C8—21no—
246D61⋊C8—21no—
247SD16×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C22×C411yescharacteristic
250C2×C8×C61C22×C411yescharacteristic
251C4⋊C4×C61—21no—
252C4⋊C4×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C22⋊Dic61—21no—
257C22⋊Dic61—21no—
258#11758201—22no—
259#11758200—22no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C411yescharacteristic
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271C2×#92418—22no—
272C2×#92418C22×C411yescharacteristic
273C2×#92418C22×C411yescharacteristic
274#11758190—22no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—22no—
278C8×D61—22no—
279C8×D61C2×D412yes—
280C8×D61#4112yes—
281C23×C61—21no—
282C23×C61C4×D411yescharacteristic
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61C4×D411yescharacteristic
297C22×D61C22×D411yescharacteristic
298C2×#6923—21no—
299C2×#6923—21no—
300C2×#6923—21no—
301C2×#6923—21no—
302C2×#6923—21no—
303C2×#6923—22no—
304C2×#6923—22no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—41no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—84no—
321C2×#6923#13512yes—
322C2×#6923#13512yes—
323Q8×C61—21no—
324Q8×C61—21no—
325D4×C61—21no—
326D4×C61—21no—
327D4×C61—81no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61C4×D411yescharacteristic
334C2×C4×C61C23×C411yescharacteristic
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—81no—
338C22⋊D61—81no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61C4×D411yescharacteristic
345C2×Dic61C2×#4111yescharacteristic
346D244—21no—
347D244—21no—
348D244—81no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61C22×D411yescharacteristic
362C4×D61C2×#4111yescharacteristic
363C4×D61H(5,𝔽2)11yescharacteristic
364C4×D612−1+411yescharacteristic
365Dic122—21no—
366Dic122—21no—
367Dic122—41no—
368Dic122—41no—
369#92420—41no—
370#92420—41no—
371C8×C61—21no—
372C8×C61C4×D412yes—
373#92418—21no—
374#92418C4×D412yes—
375#23023—611nomaximal, Sylow
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61C2×C4×D411yescharacteristic
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61—81no—
396C2×D61—81no—
397C2×D61D4211yescharacteristic
398C2×D61#54711yescharacteristic
399C2×D61C2×#13511yescharacteristic
400C2×D61C2×#13511yescharacteristic
401C2×D61#57711yescharacteristic
402C2×D61#57711yescharacteristic
403#6923—22no—
404#6923—22no—
405#6923—41no—
406#6923—42no—
407#6923—41no—
408#6923—42no—
409#6923—81no—
410#6923—81no—
411C4×C61—21no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C2×C4×D411yescharacteristic
416C4×C61#52011yescharacteristic
417Dic61—21no—
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421Dic61#54811yescharacteristic
422Dic61#55311yescharacteristic
423C2×#465—611no—
424C2×C4×SD16—611no—
425C2×#427—611no—
426#2363—611no—
427#2362—611no—
428#1968—611no—
429#1941—611no—
430#1928—611no—
431#1925—611no—
432#1875—611no—
433#1873—611no—
434#1863—611no—
435#1862—611no—
436C4×#106—611no—
437C8×C22⋊C4—611no—
438C2×C61—41no—
439C2×C61—81no—
440C2×C61#236111yescharacteristic
441C2×C61C4×#13511yescharacteristic
442C2×C61#294911yescharacteristic
443D61—41no—
444D61—81no—
445D61#328211yescharacteristic
446D61#328411yescharacteristic
447D61#333711yescharacteristic
448D61#334011yescharacteristic
449C22×SD16—611no—
450C23×C8—611no—
451C2×C22⋊Q8—611no—
452C2×#121—611no—
453C2×C4×Q8—611no—
454C2×C4×D4—611no—
455C2×#117—611no—
456C2×#117—611no—
457#465—611no—
458#465—611no—
459#465—611no—
460#465—611no—
461#465—611no—
462#465—611no—
463#465—611no—
464#465#692311yescharacteristic, complemented
465C4×SD16—1224no—
466#427—1224no—
467C2×#107—611no—
468C2×#107—611no—
469C2×#106—611no—
470C2×#106—611no—
471C2×#106—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×C22⋊C8—611no—
479C2×C4×C8—611no—
480C2×C4×C8—611no—
481#391—611no—
482#390—611no—
483#390—1221no—
484#389—611no—
485#389—611no—
486#388—1221no—
487#388—1221no—
488#388—1221no—
489#387—1221no—
490#386—1221no—
491C4×C4⋊C4—611no—
492C4×C4⋊C4—611no—
493C4×C4⋊C4—1221no—
494C4×C22⋊C4—611no—
495C4×C22⋊C4—1221no—
496#340—611no—
497#340—611no—
498#340—611no—
499#340—611no—
500#336—611no—
501#336—611no—
502C61#2302311yescharacteristic, complemented, Sylow
503C22×Q8—611no—
504C22×D4—611no—
505C22×D4—1221no—
506C23×C4—611no—
507C23×C4—1221no—
508C2×SD16—611no—
509C2×SD16—611no—
510C2×SD16—611no—
511C2×SD16—1222no—
512C2×SD16—1222no—
513C2×SD16C2×#692311yescharacteristic
514C22×C8—611no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—611no—
520C22×C8—611no—
521C22×C8—1222no—
522C22×C8—1222no—
523C22×C8C2×#692311yescharacteristic, complemented
524C22⋊Q8—611no—
525C22⋊Q8—611no—
526C22⋊Q8—611no—
527C22⋊Q8—1221no—
528C22⋊Q8—1221no—
529C22⋊Q8C2×#692311yescharacteristic, complemented
530#121—611no—
531#121—611no—
532#121—611no—
533#121—1221no—
534#121—1221no—
535#121C2×#692311yescharacteristic
536C4×Q8—1222no—
537C4×Q8—2441no—
538C4×D4—1222no—
539C4×D4—2441no—
540#117—1222no—
541#117—1222no—
542#117—2441no—
543#117—2441no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—611no—
547C2×C4⋊C4—611no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—1221no—
566C2×C42—1221no—
567C2×C42—1221no—
568C2×C42—1221no—
569C2×C42—1221no—
570#107—1222no—
571#107—1222no—
572#106—614no—
573#106—611no—
574#106—611no—
575#106—611no—
576#106—1222no—
577#106C2×#692311yescharacteristic, complemented
578#103—611no—
579#103—611no—
580#103—611no—
581#103—1222no—
582#103—2441no—
583#103C2×#692311yescharacteristic, complemented
584#102—611no—
585#102—611no—
586#102—611no—
587#102—1222no—
588#102—2441no—
589#102C2×#692311yescharacteristic
590C22⋊C8—1221no—
591C22⋊C8—1221no—
592C4×C8—1222no—
593C4×C8—1222no—
594#95—611no—
595#95—611no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602C24—611no—
603C24—1221no—
604C2×Q8—611no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8—1221no—
608C2×Q8—1221no—
609C2×Q8—1221no—
610C2×Q8C22×#692311yescharacteristic
611C2×D4—21no—
612C2×D4—611no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C2×D4—4881no—
622C2×D4—4881no—
623C2×D4C22×#692311yescharacteristic
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—4881no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4C22×#692311yescharacteristic
648SD16—22no—
649SD16—1222no—
650SD16—1222no—
651SD16—1222no—
652C2×C8—22no—
653C2×C8—611no—
654C2×C8—612no—
655C2×C8—612no—
656C2×C8—611no—
657C2×C8—1222no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1222no—
661C2×C8—1222no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8C22×#692311yescharacteristic
669C2×C8C22×#692311yescharacteristic
670C4⋊C4—21no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—611no—
674C4⋊C4—611no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—4881no—
687C4⋊C4—2442no—
688C4⋊C4—2442no—
689C4⋊C4C22×#692311yescharacteristic
690C4⋊C4C22×#692311yescharacteristic
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—4881no—
702C22⋊C4—2442no—
703C22⋊C4—2442no—
704C22⋊C4—2442no—
705C22⋊C4—2442no—
706C42—1221no—
707C42—1221no—
708C42—1221no—
709C42—1221no—
710C42—4881no—
711C42—2442no—
712C42—2442no—
713C42—2442no—
714C42—2442no—
715C23—21no—
716C23—611no—
717C23—611no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—2441no—
726C23—2441no—
727C23—2441no—
728C23—2441no—
729C23—2441no—
730C23—2441no—
731C23D4×#692311yescharacteristic
732Q8—21no—
733Q8—21no—
734Q8—1221no—
735Q8—1221no—
736Q8—2441no—
737Q8—2441no—
738D4—21no—
739D4—21no—
740D4—81no—
741D4—1221no—
742D4—1221no—
743D4—4881no—
744D4—4881no—
745D4—4881no—
746D4—2441no—
747D4—2441no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—612no—
759C2×C4—612no—
760C2×C4—611no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1221no—
766C2×C4—1221no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—4884no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4D4×#692311yescharacteristic
802C2×C4C23×#692311yescharacteristic
803C8—21no—
804C8—612no—
805C8—1221no—
806C8—2441no—
807C8—2441no—
808C8D4×#692312yes—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—611no—
816C22—611no—
817C22—611no—
818C22—611no—
819C22—611no—
820C22—611no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—4881no—
825C22—4881no—
826C22—4881no—
827C22—4881no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C2×D4×#692311yescharacteristic
836C4—21no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—611no—
841C4—611no—
842C4—1222no—
843C4—1222no—
844C4—1221no—
845C4—4881no—
846C4—4881no—
847C4—2441no—
848C4—2441no—
849C4—2442no—
850C4—2442no—
851C4—2441no—
852C4—2441no—
853C4—2441no—
854C4C2×D4×#692311yescharacteristic
855C4#1684083111yescharacteristic
856C2—41no—
857C2—81no—
858C2—611no—
859C2—611no—
860C2—611no—
861C2—611no—
862C2—4881no—
863C2—2441no—
864C2#2146234411yescharacteristic
865C2#135×#692311yescharacteristic
866C2#2146257911yescharacteristic
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#23023
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. C2×#16840772C2semidirect
4. #21462345C2semidirect
5. #21461964C2semidirect
6. #21461922C2semidirect
7. #21461899C2semidirect
8. #21461896C2semidirect
10. #21461805C2semidirect
11. #21461783C2semidirect
12. #21461782C2semidirect
13. #106×#6923C2semidirect
14. C8×C22⋊#6923C2semidirect
58. #16839994C4semidirect
59. #16839993C4semidirect
60. #16839992C4semidirect
61. #16839991C4semidirect
62. #16839990C4semidirect
63. #16839989C4semidirect
64. #16839988C4semidirect
68. C61×#465C4semidirect
104. #14519845D4semidirect
130. C22×#92418C2×C4semidirect
133. C2×C8×D61C2×C4semidirect
134. C2×C8×D61C2×C4semidirect
137. #14519757C2×C4semidirect
138. #14519756C2×C4semidirect
141. #14519753C2×C4semidirect
152. #14519709C2×C4semidirect
153. #14519708C2×C4semidirect
154. #14519708C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519701C2×C4semidirect
157. #14519700C2×C4semidirect
162. C22×C8×C61C2×C4semidirect
163. C22⋊Q8×C61C2×C4semidirect
165. #106×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
464. #465#6923semidirect
502. C61#23023semidirect
523. C22×C8C2×#6923semidirect
529. C22⋊Q8C2×#6923semidirect
577. #106C2×#6923semidirect
583. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407722
#214623462
#214623452
#214619642
#214619222
#214618992
#214618962
#214618072
#214618052
#214617832
#214617822
#106×#69232
C8×C22⋊#69232
#465×D612
#2302361