Finite Group Databasebeta

← #30621750

Subgroups — #30621750

Order 15616.

1182 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C22×#14519840C211yesmaximal, characteristic, complemented
3#21462344C211yesmaximal, characteristic
4Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461964C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461833C211yesmaximal, characteristic
9#21461815C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461769C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461554C211yesmaximal, characteristic, complemented
15#448×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923—21no—
20C2×D4×#6923C2211yescharacteristic
21C22×C4⋊#6923C2211yescharacteristic
22SD16×#6923—24no—
23C2×#14519845C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519840—24no—
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34(C2×#6923)⋊Q8—21no—
35(C2×#6923)⋊Q8—21no—
36(C2×#6923)⋊Q8C2211yescharacteristic
37(C2×#6923)⋊Q8C2211yescharacteristic
38#16840714C2211yescharacteristic
39#16840713C2211yescharacteristic
40#16840712—21no—
41#16840710—21no—
42#16840709—21no—
43#16840704—21no—
44#16840704C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C4×C22⋊#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C22×Q8×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839903C411yescharacteristic, complemented
59#16839902C411yescharacteristic, complemented
60#16839902C411yescharacteristic, complemented
61#16839901C411yescharacteristic, complemented
62#16839900C411yescharacteristic, complemented
63#16839899C411yescharacteristic, complemented
64#16839899C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#448C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8—22no—
72C2×D61⋊C8—21no—
73C2×D61⋊C8—41no—
74C2×D61⋊C8C2311yescharacteristic
75C2×D61⋊C8C2311yescharacteristic
76C22×#92420—21no—
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—41no—
80Q8×#6923—41no—
81D4×#6923—22no—
82D4×#6923—41no—
83D4×#6923—44no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—21no—
89C2×C4⋊#6923—41no—
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C4⋊#6923C2311yescharacteristic
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923D411yescharacteristic
99C2×C22⋊#6923D411yescharacteristic
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923—21no—
103C2×C4×#6923C2311yescharacteristic
104C2×C4×#6923C2311yescharacteristic
105#14519845—22no—
106#14519845—41no—
107#14519840—22no—
108#14519840—22no—
109#14519840—22no—
110#14519840D414yescomplemented
111#14519839—22no—
112#14519839—41no—
113C8×#6923—22no—
114C8×#6923—41no—
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)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C22×Dic122—21no—
125C22×Dic122C2×C411yescharacteristic, complemented
126C2×Q8×D61—21no—
127C2×Q8×D61—21no—
128C2×Q8×D61—22no—
129C2×Q8×D61—22no—
130C2×Q8×D61—41no—
131C2×Q8×D61—41no—
132C2×Q8×D61C2×C411yescharacteristic, complemented
133C2×Q8×D61C2×C411yescharacteristic, complemented
134C2×Q8×D61C2311yescharacteristic
135C2×Q8×D61C2311yescharacteristic
136C2×D4×D61—21no—
137C2×D4×D61C2311yescharacteristic
138C22×C4×D61—21no—
139C22×C4×D61C2311yescharacteristic
140C2×#11758190C2×C411yescharacteristic, complemented
141C2×#11758190C2×C411yescharacteristic, complemented
142C2×#11758200C2×C411yescharacteristic, complemented
143C2×#11758200C2×C411yescharacteristic, complemented
144C2×#11758201C2×C411yescharacteristic, complemented
145C2×#11758201C2×C411yescharacteristic, complemented
146SD16×D61—22no—
147SD16×D61—22no—
148SD16×D61—41no—
149SD16×D61—41no—
150C2×C8×D61C2311yescharacteristic
151C2×C8×D61C2311yescharacteristic
152#14519752C2×C411yescharacteristic
153#14519751C2×C411yescharacteristic
154#14519750—21no—
155#14519749—21no—
156#14519748C2×C411yescharacteristic
157C4⋊C4×D61C2311yescharacteristic
158C22⋊C4×D61—21no—
159#14519702C2×C411yescharacteristic, complemented
160#14519702C2×C411yescharacteristic, complemented
161#14519701C2×C411yescharacteristic, complemented
162#14519701C2×C411yescharacteristic, complemented
163#14519700C2×C411yescharacteristic, complemented
164#14519700C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C22×Q8×C61C2×C411yescharacteristic, complemented
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C2×SD16×C61C2×C411yescharacteristic, complemented
171#121×C61C2×C411yescharacteristic
172#103×C61C2×C411yescharacteristic, complemented
173#103×C61C2×C411yescharacteristic, complemented
174C22⋊C8×C61C2×C411yescharacteristic, complemented
175C23×D61—21no—
176C23×D61C2×D411yescharacteristic
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—81no—
186C22×#6923—81no—
187C22×#6923C2×D411yescharacteristic
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—41no—
194C2×Q8×C61C22×C411yescharacteristic
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61C22×C411yescharacteristic
198C22×C4×C61—21no—
199C22×C4×C61C22×C411yescharacteristic
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C22×Dic61—21no—
204C22×Dic61#4111yescharacteristic
205Q8×D61—21no—
206Q8×D61—21no—
207Q8×D61—22no—
208Q8×D61—21no—
209Q8×D61—21no—
210Q8×D61—21no—
211Q8×D61—21no—
212Q8×D61—22no—
213Q8×D61—41no—
214Q8×D61—41no—
215Q8×D61—42no—
216Q8×D61—42no—
217Q8×D61—42no—
218Q8×D61—42no—
219Q8×D61C2×D412yes—
220Q8×D61#4112yes—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—21no—
225D4×D61—42no—
226D4×D61—42no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—42no—
239C2×C4×D61—42no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61#4111yescharacteristic
243C2×C4×D61C2411yescharacteristic
244C2×Dic122—21no—
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—41no—
251C2×Dic122—42no—
252C2×Dic122—42no—
253C2×Dic122C22×C411yescharacteristic
254C2×Dic122C22×C411yescharacteristic
255C22⋊#6923—22no—
256C22⋊#6923—42no—
257C22⋊#6923—42no—
258C22⋊#6923—42no—
259C22⋊#6923—81no—
260C22⋊#6923SD1614yescomplemented
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—42no—
264C4⋊#6923—21no—
265C4⋊#6923—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—42no—
272C4⋊#6923—42no—
273C4⋊#6923—42no—
274C4⋊#6923—42no—
275C4⋊#6923C2×D412yes—
276C4×#6923—21no—
277C4×#6923—21no—
278C4×#6923—21no—
279C4×#6923—21no—
280C4×#6923—42no—
281C4×#6923—42no—
282C4×#6923—42no—
283D61⋊C8—21no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8—42no—
287D61⋊C8C2×D412yes—
288SD16×C61—22no—
289SD16×C61—41no—
290C2×C8×C61C22×C411yescharacteristic
291C2×C8×C61C22×C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C22⋊C4×C61—21no—
294C22⋊Dic61—21no—
295#11758201—22no—
296#11758201—41no—
297#11758200—22no—
298#11758200—41no—
299#11758198—21no—
300#11758198—21no—
301C4⋊Dic61C22×C411yescharacteristic
302#11758196—21no—
303C2×#92418C22×C411yescharacteristic
304C2×#92418C22×C411yescharacteristic
305#11758190—22no—
306#11758190—41no—
307C8×D61—21no—
308C8×D61—21no—
309C8×D61—21no—
310C8×D61—21no—
311C23×C61—21no—
312C23×C61C4×D411yescharacteristic
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61C4×D411yescharacteristic
325C22×D61C2×SD1612yes—
326C22×D61#13512yes—
327C22×D61C22×D411yescharacteristic
328C2×#6923—21no—
329C2×#6923—21no—
330C2×#6923—21no—
331C2×#6923—21no—
332C2×#6923—21no—
333C2×#6923—22no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—21no—
338C2×#6923—21no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—84no—
351C2×#6923—84no—
352C2×#6923C2×SD1612yes—
353C2×#6923C2×SD1612yes—
354Q8×C61—21no—
355Q8×C61—21no—
356Q8×C61—21no—
357Q8×C61—42no—
358Q8×C61C4×D412yescomplemented
359D4×C61—21no—
360D4×C61—21no—
361D4×C61—42no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—42no—
368C2×C4×C61C4×D411yescharacteristic
369C2×C4×C61C23×C411yescharacteristic
370C22⋊D61—42no—
371C22⋊D61—42no—
372C22⋊D61—41no—
373C22⋊D61—41no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—42no—
380C2×Dic61C4×D411yescharacteristic
381C2×Dic61C2×#4111yescharacteristic
382D244—21no—
383D244—21no—
384D244—42no—
385C4×D61—22no—
386C4×D61—21no—
387C4×D61—22no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—42no—
394C4×D61—42no—
395C4×D61—41no—
396C4×D61—41no—
397C4×D61—41no—
398C4×D61—41no—
399C4×D61C22×D411yescharacteristic
400C4×D61C2×#4111yescharacteristic
401C4×D61H(5,𝔽2)11yescharacteristic
402C4×D61H(5,𝔽2)11yescharacteristic
403Dic122—21no—
404Dic122—22no—
405Dic122—22no—
406Dic122—21no—
407Dic122—21no—
408Dic122—42no—
409Dic122—42no—
410Dic122—42no—
411Dic122—41no—
412Dic122—41no—
413Dic122C4×D412yescomplemented
414#92420—22no—
415#92420—41no—
416C8×C61—21no—
417C8×C61—21no—
418#92418—21no—
419#92418—21no—
420#22875—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61C4×SD1612yescomplemented
427C22×C61C2×C4×D411yescharacteristic
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—22no—
431C2×D61—22no—
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—81no—
438C2×D61—81no—
439C2×D61—81no—
440C2×D61—81no—
441C2×D61C4×SD1612yescomplemented
442C2×D61D4211yescharacteristic
443C2×D61#54611yescharacteristic
444C2×D61C22×SD1611yescharacteristic
445C2×D61C2×#13511yescharacteristic
446C2×D61#57711yescharacteristic
447C2×D61#57811yescharacteristic
448#6923—22no—
449#6923—22no—
450#6923—42no—
451#6923—41no—
452#6923—41no—
453#6923—81no—
454#6923—81no—
455#6923—81no—
456C4×C61—22no—
457C4×C61—21no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61C2×C4×D411yescharacteristic
461C4×C61#51811yescharacteristic
462Dic61—22no—
463Dic61—21no—
464Dic61—41no—
465Dic61—41no—
466Dic61#54611yescharacteristic
467Dic61#55111yescharacteristic
468C2×#448—611no—
469C2×C4×SD16—611no—
470C22×#103—611no—
471#2361—611no—
472Q8×C22⋊C4—611no—
473#1968—611no—
474#1933—611no—
475#1927—611no—
476#1893—611no—
477#1880—611no—
478#1877—611no—
479#1865—611no—
480#1853—611no—
481C4×#103—611no—
482C8×C22⋊C4—611no—
483C2×C61—22no—
484C2×C61—81no—
485C2×C61#235811yescharacteristic
486C2×C61C2×C4×SD1611yescharacteristic
487C2×C61#294711yescharacteristic
488D61—22no—
489D61—81no—
490D61D4×SD1611yescharacteristic
491D61#328511yescharacteristic
492D61#329811yescharacteristic
493D61#330111yescharacteristic
494C23×Q8—611no—
495C22×SD16—611no—
496C22×SD16—611no—
497C23×C8—611no—
498C2×#121—611no—
499C2×C4×Q8—611no—
500C2×C4×Q8—611no—
501C2×C4×D4—611no—
502C2×C4×D4—1221no—
503C22×C4⋊C4—611no—
504#448—611no—
505#448—611no—
506#448—611no—
507#448—611no—
508#448—611no—
509#448—611no—
510#448—611no—
511#448#692311yescharacteristic, complemented
512C4×SD16—1224no—
513C2×#106—611no—
514C2×#106—611no—
515C2×#103—611no—
516C2×#103—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103—611no—
520C2×#103—611no—
521C2×#103—1224no—
522C2×#102—611no—
523C2×#102—611no—
524C2×C22⋊C8—611no—
525C2×C4×C8—611no—
526C2×C4×C8—611no—
527#391—611no—
528#391—611no—
529#391—1221no—
530#391—1221no—
531#390—611no—
532#389—611no—
533#388—1221no—
534#386—1221no—
535#385—1221no—
536#380—611no—
537#380—1221no—
538C4×C4⋊C4—611no—
539C4×C22⋊C4—611no—
540C4×C22⋊C4—1221no—
541#340—611no—
542#340—611no—
543#340—611no—
544#340—611no—
545#336—611no—
546#336—611no—
547C61#2287511yescharacteristic, complemented, Sylow
548C22×Q8—611no—
549C22×Q8—611no—
550C22×Q8—611no—
551C22×Q8—611no—
552C22×Q8—611no—
553C22×Q8—1221no—
554C22×Q8—1221no—
555C22×Q8—1221no—
556C22×Q8—1222no—
557C22×Q8—1222no—
558C22×Q8—2441no—
559C22×Q8—2441no—
560C22×Q8C2×#692311yescharacteristic, complemented
561C22×D4—611no—
562C22×D4—1221no—
563C23×C4—611no—
564C23×C4—1221no—
565C23×C4—1221no—
566C23×C4—1221no—
567C2×SD16—611no—
568C2×SD16—611no—
569C2×SD16—611no—
570C2×SD16—611no—
571C2×SD16—611no—
572C2×SD16—611no—
573C2×SD16—1222no—
574C2×SD16—1222no—
575C2×SD16—2441no—
576C2×SD16—2441no—
577C2×SD16C2×#692311yescharacteristic, complemented
578C2×SD16C2×#692311yescharacteristic, complemented
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—1222no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—2441no—
587#121—611no—
588#121—611no—
589#121—611no—
590#121—1221no—
591#121—1221no—
592#121C2×#692311yescharacteristic
593C4×Q8—1222no—
594C4×Q8—1222no—
595C4×Q8—2441no—
596C4×Q8—2441no—
597C4×D4—1222no—
598C4×D4—2441no—
599C4×D4—2444no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1222no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—2441no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—1221no—
621C2×C42—1221no—
622C2×C42—1221no—
623#106—1222no—
624#106—2441no—
625#103—614no—
626#103—611no—
627#103—611no—
628#103—611no—
629#103—611no—
630#103—611no—
631#103—611no—
632#103—1222no—
633#103—1222no—
634#103—1222no—
635#103C2×#692311yescharacteristic, complemented
636#103C2×#692311yescharacteristic, complemented
637#102—1222no—
638#102—2441no—
639C22⋊C8—611no—
640C22⋊C8—611no—
641C22⋊C8—611no—
642C22⋊C8C2×#692311yescharacteristic, complemented
643C4×C8—1222no—
644C4×C8—2441no—
645#95—611no—
646#95—611no—
647#95—1221no—
648#95—1221no—
649#95—1221no—
650#95—1221no—
651#95—1221no—
652#95—1221no—
653#95—1221no—
654C24—611no—
655C24—1221no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—41no—
659C2×Q8—612no—
660C2×Q8—612no—
661C2×Q8—611no—
662C2×Q8—611no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1222no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1221no—
674C2×Q8—1221no—
675C2×Q8—1222no—
676C2×Q8—1222no—
677C2×Q8—2441no—
678C2×Q8—2442no—
679C2×Q8—2442no—
680C2×Q8—2442no—
681C2×Q8—2442no—
682C2×Q8—2441no—
683C2×Q8—2441no—
684C2×Q8—2442no—
685C2×Q8—2442no—
686C2×Q8C22×#692311yescharacteristic
687C2×Q8C22×#692311yescharacteristic
688C2×D4—21no—
689C2×D4—611no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4C22×#692311yescharacteristic
701C22×C4—21no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—611no—
707C22×C4—611no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—2442no—
728C22×C4—2442no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4—2442no—
733C22×C4C22×#692311yescharacteristic
734SD16—22no—
735SD16—41no—
736SD16—1222no—
737SD16—1222no—
738SD16—1222no—
739SD16—2441no—
740SD16—2441no—
741SD16—2441no—
742C2×C8—612no—
743C2×C8—611no—
744C2×C8—611no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—2442no—
755C2×C8—2442no—
756C2×C8C22×#692311yescharacteristic
757C2×C8C22×#692311yescharacteristic
758C4⋊C4—612no—
759C4⋊C4—611no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—2442no—
769C4⋊C4—2442no—
770C4⋊C4—2442no—
771C4⋊C4—2442no—
772C4⋊C4C22×#692311yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—614no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1222no—
778C22⋊C4—1221no—
779C22⋊C4—4881no—
780C22⋊C4—2442no—
781C22⋊C4—2442no—
782C22⋊C4—2442no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—1221no—
787C42—2442no—
788C42—2442no—
789C42—2442no—
790C23—21no—
791C23—611no—
792C23—612no—
793C23—612no—
794C23—611no—
795C23—1221no—
796C23—1221no—
797C23—1221no—
798C23—1221no—
799C23—1221no—
800C23—2441no—
801C23—2441no—
802C23—2441no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23D4×#692311yescharacteristic
807Q8—21no—
808Q8—21no—
809Q8—21no—
810Q8—42no—
811Q8—612no—
812Q8—1222no—
813Q8—1222no—
814Q8—1221no—
815Q8—1221no—
816Q8—1221no—
817Q8—2442no—
818Q8—2442no—
819Q8—2441no—
820Q8—2441no—
821Q8—2442no—
822Q8D4×#692312yescomplemented
823D4—21no—
824D4—21no—
825D4—42no—
826D4—1221no—
827D4—1221no—
828D4—2442no—
829D4—2441no—
830D4—2441no—
831D4—2442no—
832D4—2442no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—42no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—612no—
845C2×C4—612no—
846C2×C4—611no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—4884no—
872C2×C4—4884no—
873C2×C4—2442no—
874C2×C4—2442no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2442no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4D4×#692311yescharacteristic
892C2×C4C23×#692311yescharacteristic
893C8—21no—
894C8—21no—
895C8—1222no—
896C8—1221no—
897C8—1221no—
898C8—2441no—
899C22—21no—
900C22—21no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—611no—
905C22—611no—
906C22—611no—
907C22—611no—
908C22—611no—
909C22—611no—
910C22—612no—
911C22—1222no—
912C22—1222no—
913C22—1222no—
914C22—1222no—
915C22—1221no—
916C22—1221no—
917C22—4881no—
918C22—4881no—
919C22—4881no—
920C22—4881no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22SD16×#692312yescomplemented
925C22C2×D4×#692311yescharacteristic
926C4—21no—
927C4—22no—
928C4—41no—
929C4—41no—
930C4—611no—
931C4—611no—
932C4—1222no—
933C4—1222no—
934C4—1221no—
935C4—1222no—
936C4—4881no—
937C4—4881no—
938C4—4881no—
939C4—2441no—
940C4—2441no—
941C4—2442no—
942C4—2441no—
943C4—2441no—
944C4C2×D4×#692311yescharacteristic
945C4#1684082911yescharacteristic
946C2—22no—
947C2—81no—
948C2—611no—
949C2—611no—
950C2—611no—
951C2—611no—
952C2—1222no—
953C2—4881no—
954C2#2146234111yescharacteristic
955C2C2×SD16×#692311yescharacteristic
956C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#448C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#448#6923
hypocenterC61#22875
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
2. C22×#14519840C2semidirect
4. Q8×C22⋊#6923C2semidirect
5. #21461964C2semidirect
6. #21461908C2semidirect
7. #21461898C2semidirect
9. #21461815C2semidirect
10. #21461812C2semidirect
11. #21461785C2semidirect
12. #21461769C2semidirect
13. #103×#6923C2semidirect
14. #21461554C2semidirect
58. #16839903C4semidirect
59. #16839902C4semidirect
60. #16839902C4semidirect
61. #16839901C4semidirect
62. #16839900C4semidirect
63. #16839899C4semidirect
64. #16839899C4semidirect
68. C61×#448C4semidirect
110. #14519840D4semidirect
125. C22×Dic122C2×C4semidirect
132. C2×Q8×D61C2×C4semidirect
133. C2×Q8×D61C2×C4semidirect
140. C2×#11758190C2×C4semidirect
141. C2×#11758190C2×C4semidirect
142. C2×#11758200C2×C4semidirect
143. C2×#11758200C2×C4semidirect
144. C2×#11758201C2×C4semidirect
145. C2×#11758201C2×C4semidirect
159. #14519702C2×C4semidirect
160. #14519702C2×C4semidirect
161. #14519701C2×C4semidirect
162. #14519701C2×C4semidirect
163. #14519700C2×C4semidirect
164. #14519700C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
168. C22×Q8×C61C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C2×SD16×C61C2×C4semidirect
172. #103×C61C2×C4semidirect
173. #103×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
260. C22⋊#6923SD16semidirect
358. Q8×C61C4×D4semidirect
413. Dic122C4×D4semidirect
426. C22×C61C4×SD16semidirect
441. C2×D61C4×SD16semidirect
511. #448#6923semidirect
547. C61#22875semidirect
560. C22×Q8C2×#6923semidirect
577. C2×SD16C2×#6923semidirect
578. C2×SD16C2×#6923semidirect
635. #103C2×#6923semidirect
636. #103C2×#6923semidirect
642. C22⋊C8C2×#6923semidirect
822. Q8D4×#6923semidirect
924. 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×#145198402
#214623442
Q8×C22⋊#69232
#214619642
#214619082
#214618982
#214618332
#214618152
#214618122
#214617852
#214617692
#103×#69232
#214615542
#448×D612
#2287561