Finite Group Databasebeta

← #30617067

Subgroups — #30617067

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic, complemented
2C2×M16×#6923C211yesmaximal, characteristic, complemented
3C22⋊Q8×#6923C211yesmaximal, characteristic, complemented
4#121×#6923C211yesmaximal, characteristic
5#21461964C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461909C211yesmaximal, characteristic, complemented
8#21461908C211yesmaximal, characteristic, complemented
9#21461835C211yesmaximal, characteristic
10#21461834C211yesmaximal, characteristic, complemented
11#21461697C211yesmaximal, characteristic, complemented
12#21461634C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#21461590C211yesmaximal, characteristic, complemented
15#468×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923—21no—
19C2×D4×#6923C2211yescharacteristic
20C22×C4×#6923C2211yescharacteristic
21#16840801—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28M16×#6923—24no—
29C2×#14519831C2211yescharacteristic
30C2×#14519831C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840713C2211yescharacteristic
36#16840713C2211yescharacteristic
37#16840712—21no—
38#16840711—21no—
39#16840710—21no—
40#16840709—21no—
41#16840704C2211yescharacteristic
42#16840704C2211yescharacteristic
43C4⋊C4×#6923—21no—
44C4⋊C4×#6923C2211yescharacteristic
45C4⋊C4×#6923C2211yescharacteristic
46C22⋊C4×#6923—21no—
47C22⋊C4×#6923—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×M16×D61C2211yescharacteristic
56C22⋊Q8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16840011C411yescharacteristic, complemented
59#16840010C411yescharacteristic, complemented
60#16840009C411yescharacteristic, complemented
61#16840008C411yescharacteristic, complemented
62#16840007C411yescharacteristic, complemented
63#16840006C411yescharacteristic, complemented
64#16840005C411yescharacteristic, complemented
65#107×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#468C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923D411yescharacteristic
71C23×#6923D411yescharacteristic
72C2×#11758213—21no—
73D61⋊M16—22no—
74D61⋊M16—22no—
75C2×#11758217—21no—
76C2×D61⋊C8C2311yescharacteristic
77C2×D61⋊C8C2311yescharacteristic
78Q8×#6923—22no—
79Q8×#6923—22no—
80D4×#6923—22no—
81D4×#6923—22no—
82D4×#6923—44no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923C2311yescharacteristic
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C4×#6923—22no—
96C2×C4×#6923—22no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923D411yescharacteristic
101C2×C4×#6923D411yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519846—22no—
105#14519845—22no—
106#14519840—22no—
107#14519840—22no—
108#14519839—22no—
109#14519839—22no—
110#14519831—22no—
111#14519831D414yescomplemented
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)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
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—
131C2×#11758194C2×C411yescharacteristic, complemented
132C2×#11758189C2×C411yescharacteristic, complemented
133C2×#11758189C2×C411yescharacteristic, complemented
134M16×D61—22no—
135M16×D61—22no—
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#14519711C2×C411yescharacteristic, complemented
154#14519710C2×C411yescharacteristic, complemented
155#14519710C2×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
163C2×M16×C61C2×C411yescharacteristic, complemented
164C22⋊Q8×C61C2×C411yescharacteristic, complemented
165#121×C61C2×C411yescharacteristic
166#107×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61C2×D411yescharacteristic
171C22×#6923—22no—
172C22×#6923—22no—
173C22×#6923—22no—
174C22×#6923—22no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—41no—
180C22×#6923—41no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
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—42no—
222C22⋊#6923—42no—
223C22⋊#6923—42no—
224C22⋊#6923—42no—
225C22⋊#6923—42no—
226#11758217—24no—
227C2×#92420—21no—
228C2×#92420—21no—
229C4⋊#6923—21no—
230C4⋊#6923—21no—
231C4⋊#6923—21no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—21no—
236C4⋊#6923—21no—
237C4⋊#6923—42no—
238C4⋊#6923—42no—
239C4⋊#6923—42no—
240C4×#6923—22no—
241C4×#6923—22no—
242C4×#6923—21no—
243C4×#6923—21no—
244C4×#6923—42no—
245C4×#6923—42no—
246C4×#6923—42no—
247C4×#6923C2×D412yes—
248C4×#6923#4112yes—
249#11758213—24no—
250D61⋊C8—21no—
251D61⋊C8—21no—
252D61⋊C8C2×D412yes—
253D61⋊C8#4112yes—
254SD16×C61—22no—
255M16×C61—22no—
256C2×C8×C61C22×C411yescharacteristic
257C2×C8×C61C22×C411yescharacteristic
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22×C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758201—22no—
266#11758200—22no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61C22×C411yescharacteristic
273C4⋊Dic61C22×C411yescharacteristic
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758194—22no—
279C2×#92418C22×C411yescharacteristic
280C2×#92418C22×C411yescharacteristic
281#11758190—22no—
282#11758189—22no—
283#11758189—22no—
284C8×D61—21no—
285C8×D61—21no—
286C8×D61C2×D412yes—
287C8×D61#4112yes—
288C23×C61—21no—
289C23×C61C4×D411yescharacteristic
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C4×D411yescharacteristic
304C22×D61C22×D411yescharacteristic
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—21no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—44no—
314C2×#6923—44no—
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—41no—
326C2×#6923—41no—
327C2×#6923—84no—
328C2×#6923#12112yes—
329C2×#6923#12112yes—
330C2×#6923AGL(1,ℤ/8)12yes—
331C2×#6923#13712yes—
332Q8×C61—21no—
333Q8×C61—21no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—42no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61C4×D411yescharacteristic
343C2×C4×C61C23×C411yescharacteristic
344C22⋊D61—42no—
345C22⋊D61—42no—
346C22⋊D61—41no—
347C22⋊D61—41no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61C4×D411yescharacteristic
354C2×Dic61C2×#4111yescharacteristic
355D244—21no—
356D244—21no—
357D244—42no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61C22×D411yescharacteristic
371C4×D61C2×#4111yescharacteristic
372C4×D61C2×#4111yescharacteristic
373C4×D61C2×#4111yescharacteristic
374Dic122—21no—
375Dic122—21no—
376Dic122—41no—
377Dic122—41no—
378#92420—22no—
379#92420—22no—
380C8×C61—21no—
381C8×C61C4×D412yescomplemented
382#92418—21no—
383#92418C4×D412yescomplemented
384#21540—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61C2×C4×D411yescharacteristic
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—81no—
406C2×D61C2×#12111yescharacteristic
407C2×D61#53211yescharacteristic
408C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
409C2×D61C2×#13711yescharacteristic
410C2×D61#57511yescharacteristic
411C2×D61#57511yescharacteristic
412#6923—22no—
413#6923—22no—
414#6923—22no—
415#6923—22no—
416#6923—81no—
417#6923—81no—
418#6923—81no—
419#6923—81no—
420C4×C61—21no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61C4×#4111yescharacteristic
426Dic61—21no—
427Dic61—41no—
428Dic61—41no—
429Dic61—41no—
430Dic61#52511yescharacteristic
431Dic61#52911yescharacteristic
432C2×#468—611no—
433C2×#440—611no—
434C2×C4×M16—611no—
435C4×C22⋊Q8—611no—
436C4×#121—611no—
437#1968—611no—
438#1942—611no—
439#1934—611no—
440#1933—611no—
441#1895—611no—
442#1894—611no—
443#1809—611no—
444#1776—611no—
445#1763—611no—
446#1762—611no—
447C2×C61—41no—
448C2×C61—81no—
449C2×C61C4×#12111yescharacteristic
450C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C61C4×#13711yescharacteristic
452D61—41no—
453D61—81no—
454D61#305511yescharacteristic
455D61#305611yescharacteristic
456D61#318211yescharacteristic
457D61#318311yescharacteristic
458C22×SD16—611no—
459C22×M16—611no—
460C22×M16—611no—
461C2×C22⋊Q8—611no—
462C2×#121—611no—
463C2×C4×Q8—611no—
464C2×C4×D4—611no—
465C2×C4×D4—1221no—
466C22×C42—611no—
467#468—611no—
468#468—611no—
469#468—611no—
470#468—611no—
471#468—611no—
472#468—611no—
473#468—611no—
474#468#692311yescharacteristic, complemented
475#440—1224no—
476C2×#107—611no—
477C2×#107—611no—
478C2×#106—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C4×M16—1224no—
486C2×#97—611no—
487C2×#97—611no—
488C2×C4×C8—611no—
489C2×C4×C8—611no—
490#391—611no—
491#390—611no—
492#389—611no—
493#389—611no—
494#388—1221no—
495#387—1221no—
496#386—1221no—
497#385—1221no—
498#380—611no—
499#380—611no—
500C4×C4⋊C4—611no—
501C4×C4⋊C4—611no—
502C4×C4⋊C4—1221no—
503C4×C22⋊C4—1221no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#340—611no—
510#340—611no—
511C61#2154011yescharacteristic, complemented, Sylow
512C22×Q8—611no—
513C22×D4—611no—
514C22×D4—1221no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—1221no—
519C2×SD16—611no—
520C2×SD16—611no—
521C2×SD16—611no—
522C2×SD16—1222no—
523C2×SD16—1222no—
524C2×SD16C2×#692311yescharacteristic, complemented
525C2×M16—611no—
526C2×M16—611no—
527C2×M16—611no—
528C2×M16—1222no—
529C2×M16—1222no—
530C2×M16—1222no—
531C2×M16—1222no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16C2×#692311yescharacteristic, complemented
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—611no—
538C22×C8—611no—
539C22⋊Q8—611no—
540C22⋊Q8—611no—
541C22⋊Q8—611no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8C2×#692311yescharacteristic, complemented
545#121—611no—
546#121—611no—
547#121—611no—
548#121—1221no—
549#121—1221no—
550#121C2×#692311yescharacteristic
551C4×Q8—1222no—
552C4×Q8—1222no—
553C4×D4—1222no—
554C4×D4—1222no—
555C4×D4—2444no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
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—611no—
576C2×C42—611no—
577C2×C42—1222no—
578C2×C42—1222no—
579C2×C42—1221no—
580C2×C42—1221no—
581C2×C42—1221no—
582#107—611no—
583#107—611no—
584#107—611no—
585#107—1222no—
586#107C2×#692311yescharacteristic, complemented
587#106—1222no—
588#103—611no—
589#103—611no—
590#103—611no—
591#103—1222no—
592#103—1222no—
593#103C2×#692311yescharacteristic, complemented
594#102—611no—
595#102—611no—
596#102—611no—
597#102—1222no—
598#102—1222no—
599#102C2×#692311yescharacteristic, complemented
600#97—614no—
601#97—1222no—
602C4×C8—1222no—
603C4×C8—1222no—
604#95—1221no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608#95—1221no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—611no—
613C24—1221no—
614C2×Q8—611no—
615C2×Q8—1221no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8C22×#692311yescharacteristic
621C2×D4—21no—
622C2×D4—611no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—2442no—
632C2×D4—2442no—
633C2×D4C22×#692311yescharacteristic
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—2442no—
659C22×C4—2441no—
660C22×C4—2441no—
661C22×C4—2442no—
662C22×C4—2442no—
663C22×C4C22×#692311yescharacteristic
664SD16—22no—
665SD16—1222no—
666SD16—1222no—
667SD16—1222no—
668M16—22no—
669M16—1222no—
670M16—1222no—
671M16—1224no—
672M16—1224no—
673M16—1222no—
674C2×C8—611no—
675C2×C8—612no—
676C2×C8—612no—
677C2×C8—612no—
678C2×C8—612no—
679C2×C8—611no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8C22×#692311yescharacteristic
687C2×C8C22×#692311yescharacteristic
688C4⋊C4—21no—
689C4⋊C4—611no—
690C4⋊C4—611no—
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—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—2442no—
705C4⋊C4—2442no—
706C4⋊C4—2442no—
707C4⋊C4C22×#692311yescharacteristic
708C4⋊C4C22×#692311yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C22⋊C4—2442no—
720C22⋊C4—2442no—
721C22⋊C4—2442no—
722C42—612no—
723C42—612no—
724C42—1221no—
725C42—1221no—
726C42—1222no—
727C42—1222no—
728C42—2442no—
729C42—2442no—
730C42—2442no—
731C23—21no—
732C23—611no—
733C23—611no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23D4×#692311yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—1221no—
751Q8—1221no—
752Q8—2441no—
753Q8—2441no—
754D4—21no—
755D4—21no—
756D4—42no—
757D4—1221no—
758D4—1221no—
759D4—2442no—
760D4—2441no—
761D4—2441no—
762D4—2442no—
763D4—2442no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—612no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—611no—
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—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—4884no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2444no—
806C2×C4—2444no—
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×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4D4×#692311yescharacteristic
820C2×C4C23×#692311yescharacteristic
821C8—21no—
822C8—612no—
823C8—1222no—
824C8—1222no—
825C8—1221no—
826C8D4×#692312yescomplemented
827C22—21no—
828C22—21no—
829C22—21no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—611no—
834C22—611no—
835C22—611no—
836C22—611no—
837C22—611no—
838C22—611no—
839C22—1221no—
840C22—1221no—
841C22—1221no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—4881no—
846C22—2441no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22C2×D4×#692311yescharacteristic
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—611no—
859C4—611no—
860C4—1222no—
861C4—1222no—
862C4—1222no—
863C4—1222no—
864C4—1221no—
865C4—4881no—
866C4—4881no—
867C4—4881no—
868C4—4881no—
869C4—2441no—
870C4—2441no—
871C4—2441no—
872C4C2×D4×#692311yescharacteristic
873C4#41×#692311yescharacteristic
874C2—41no—
875C2—81no—
876C2—611no—
877C2—611no—
878C2—611no—
879C2—611no—
880C2—4881no—
881C2—2441no—
882C2#121×#692311yescharacteristic
883C2AGL(1,ℤ/8)×#692311yescharacteristic
884C2#137×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#468C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#468#6923
hypocenterC61#21540
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#16840801C2semidirect
2. C2×M16×#6923C2semidirect
3. C22⋊Q8×#6923C2semidirect
5. #21461964C2semidirect
6. #21461923C2semidirect
7. #21461909C2semidirect
8. #21461908C2semidirect
10. #21461834C2semidirect
11. #21461697C2semidirect
12. #21461634C2semidirect
13. #21461592C2semidirect
14. #21461590C2semidirect
58. #16840011C4semidirect
59. #16840010C4semidirect
60. #16840009C4semidirect
61. #16840008C4semidirect
62. #16840007C4semidirect
63. #16840006C4semidirect
64. #16840005C4semidirect
68. C61×#468C4semidirect
111. #14519831D4semidirect
126. C2×#11758190C2×C4semidirect
127. C2×#11758200C2×C4semidirect
128. C2×#11758201C2×C4semidirect
131. C2×#11758194C2×C4semidirect
132. C2×#11758189C2×C4semidirect
133. C2×#11758189C2×C4semidirect
138. #14519757C2×C4semidirect
139. #14519756C2×C4semidirect
142. #14519753C2×C4semidirect
153. #14519711C2×C4semidirect
154. #14519710C2×C4semidirect
155. #14519710C2×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. C2×M16×C61C2×C4semidirect
164. C22⋊Q8×C61C2×C4semidirect
166. #107×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
381. C8×C61C4×D4semidirect
383. #92418C4×D4semidirect
474. #468#6923semidirect
511. C61#21540semidirect
524. C2×SD16C2×#6923semidirect
534. C2×M16C2×#6923semidirect
544. C22⋊Q8C2×#6923semidirect
586. #107C2×#6923semidirect
593. #103C2×#6923semidirect
599. #102C2×#6923semidirect
826. C8D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×M16×#69232
C22⋊Q8×#69232
#121×#69232
#214619642
#214619232
#214619092
#214619082
#214618352
#214618342
#214616972
#214616342
#214615922
#214615902
#468×D612
#2154061