Finite Group Databasebeta

← #30615500

Subgroups — #30615500

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2#21462472C211yesmaximal, characteristic, complemented
3#21462439C211yesmaximal, characteristic
4#21462300C211yesmaximal, characteristic, complemented
5#21461779C214yesmaximal, complemented
6#21461778C214yesmaximal, complemented
7C2×#16840641C211yesmaximal, characteristic, complemented
8#21461500C211yesmaximal, characteristic, complemented
9#421×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2211yescharacteristic
11#16840831—22no—
12#16840831—22no—
13#16840831—22no—
14#16840831C2214yes—
15C2×Q8×#6923—21no—
16C2×D4×#6923—22no—
17C2×D4×#6923—21no—
18C2×#14519856—21no—
19C2×#14519856C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21C22×C4⋊#6923—21no—
22C22×C4⋊#6923C2211yescharacteristic
23#16840773—21no—
24#16840773—21no—
25#16840773C2212yescomplemented
26#16840773C2212yescomplemented
27#16840772—22no—
28#16840755—21no—
29#16840754—21no—
30#16840753C2212yes—
31#16840753C2212yes—
32#16840752—22no—
33#16840713—22no—
34#16840709—22no—
35#16840708C2212yescomplemented
36#16840706C2212yescomplemented
37#16840641C2214yescomplemented
38#16840633C2214yescomplemented
39C2×#41×D61C2211yescharacteristic
40C2×M16×D61C2211yescharacteristic
41#117×D61C2211yescharacteristic
42#16839780C411yescharacteristic, complemented
43#16839779C411yescharacteristic, complemented
44#16839778C411yescharacteristic, complemented
45#16839777C414yescomplemented
46#104×D61C2214yes—
47C61×#421C411yescharacteristic, complemented
48C23×#6923—22no—
49C23×#6923D412yes—
50C2×#11758213—21no—
51D61⋊M16—21no—
52D61⋊M16—21no—
53D61⋊M16—21no—
54D61⋊M16C2312yes—
55C2×#11758217—21no—
56C2×D61⋊C8—21no—
57Q8×#6923—24no—
58Q8×#6923—24no—
59D4×#6923—28no—
60D4×#6923—24no—
61D4×#6923—28no—
62D4×#6923—24no—
63#14519856—24no—
64#14519856—21no—
65#14519856—21no—
66#14519856—24no—
67#14519856—21no—
68#14519856—21no—
69#14519856—21no—
70#14519856—21no—
71#14519856D412yes—
72#14519856C2312yes—
73C2×C4⋊#6923—22no—
74C2×C4⋊#6923—24no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—24no—
80C2×C4⋊#6923—24no—
81C2×C4⋊#6923D412yes—
82C2×C4⋊#6923D411yescharacteristic
83C2×C4⋊#6923D411yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2312yes—
87C2×C22⋊#6923—22no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C4×#6923—22no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93#14519846—22no—
94#14519846—22no—
95#14519845—22no—
96#14519845—22no—
97#14519840—22no—
98#14519840—22no—
99#14519839—22no—
100#14519839—22no—
101(C2×#6923)⋊C4—24no—
102C2×#11758226Q811yescharacteristic
103C2×#11758222—21no—
104C2×#11758222C2×C411yescharacteristic
105C2×#11758224—21no—
106C2×#11758224Q811yescharacteristic
107#41×D61—21no—
108#41×D61—21no—
109#41×D61—21no—
110#41×D61—21no—
111#41×D61C2×C412yes—
112#41×D61D412yes—
113#41×D61Q812yes—
114#41×D61C2312yes—
115C2×Q8×D61D411yescharacteristic
116C2×D4×D61—21no—
117C2×D4×D61D411yescharacteristic
118C22×C4×D61—21no—
119C22×C4×D61C2311yescharacteristic
120C2×#11758194C2×C411yescharacteristic, complemented
121C2×#11758189—21no—
122M16×D61—21no—
123M16×D61—21no—
124M16×D61C2×C412yescomplemented
125M16×D61C2312yes—
126C2×C8×D61—21no—
127#14519736C2×C411yescharacteristic, complemented
128#14519735—21no—
129#14519734C2×C412yescomplemented
130#14519733—21no—
131C4⋊C4×D61—21no—
132C22⋊C4×D61—21no—
133C42×D61C2312yes—
134#14519705C2×C414yescomplemented
135#14519704C2×C414yescomplemented
136#14519703C2×C414yescomplemented
137C2×#41×C61C2×C411yescharacteristic
138C2×M16×C61C2×C411yescharacteristic, complemented
139#117×C61C2×C411yescharacteristic, complemented
140#104×C61C2×C414yescomplemented
141C23×D61—21no—
142C23×D61C2×D411yescharacteristic
143C22×#6923—21no—
144C22×#6923—22no—
145C22×#6923—21no—
146C22×#6923—28no—
147C22×#6923—22no—
148C22×#6923—21no—
149C22×#6923—21no—
150C22×#6923—82no—
151C22×#6923—84no—
152C22×#6923C2×D414yes—
153#41×C61—21no—
154#41×C61—21no—
155#41×C61C4⋊C412yescomplemented
156#41×C61C22×C412yes—
157C2×Q8×C61C4⋊C411yescharacteristic, complemented
158C2×D4×C61—21no—
159C2×D4×C61C4⋊C411yescharacteristic, complemented
160C22×C4×C61—21no—
161C22×C4×C61C22×C411yescharacteristic
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—21no—
165C22×Dic61—21no—
166C22×Dic61#4111yescharacteristic
167#11758226—21no—
168#11758226—21no—
169#11758226C4⋊C412yescomplemented
170#11758226C2×Q812yes—
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61C4⋊C412yescomplemented
174Q8×D61C2×D412yes—
175#11758224—22no—
176#11758224—22no—
177#11758224—22no—
178#11758224—22no—
179#11758224—21no—
180#11758224—21no—
181#11758224C4⋊C412yescomplemented
182#11758224C2×Q812yes—
183D4×D61—22no—
184D4×D61—22no—
185D4×D61—22no—
186D4×D61—22no—
187D4×D61—21no—
188D4×D61—21no—
189D4×D61C4⋊C412yescomplemented
190D4×D61C2×D412yes—
191#11758222—21no—
192#11758222—21no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222C4⋊C412yescomplemented
198#11758222C22×C412yes—
199C2×D244—21no—
200C2×D244C4⋊C411yescharacteristic, complemented
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—22no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61C22×C411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×Q811yescharacteristic
216C2×C4×D61C2×Q811yescharacteristic
217C2×C4×D61#4111yescharacteristic
218C2×C4×D61#4111yescharacteristic
219C2×C4×D61#4111yescharacteristic
220C2×C4×D61C2411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122C4⋊C411yescharacteristic, complemented
223C22⋊#6923—28no—
224C22⋊#6923—22no—
225C22⋊#6923—22no—
226C22⋊#6923—41no—
227C22⋊#6923—41no—
228#11758217—22no—
229#11758217—41no—
230C2×#92420—41no—
231C4⋊#6923—28no—
232C4⋊#6923—22no—
233C4⋊#6923—21no—
234C4⋊#6923—22no—
235C4⋊#6923—21no—
236C4⋊#6923—22no—
237C4⋊#6923—22no—
238C4⋊#6923—21no—
239C4⋊#6923—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—84no—
243C4⋊#6923C2×D412yes—
244C4⋊#6923C2×D412yes—
245C4×#6923—28no—
246C4×#6923—22no—
247C4×#6923—22no—
248C4×#6923—41no—
249C4×#6923—41no—
250#11758213—22no—
251#11758213—41no—
252D61⋊C8—22no—
253D61⋊C8—41no—
254M16×C61—21no—
255M16×C61C22×C412yescomplemented
256C2×C8×C61—21no—
257C4⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C42×C61C22×C412yescomplemented
260C22⋊Dic61—21no—
261#11758198—22no—
262C4⋊Dic61—21no—
263#11758196—22no—
264C4×Dic61—22no—
265C4×Dic61C22×C412yescomplemented
266#11758194—21no—
267#11758194C22×C412yescomplemented
268C2×#92418—21no—
269#11758189—22no—
270#11758189—22no—
271C8×D61—22no—
272C8×D61—22no—
273C23×C61—21no—
274C23×C61C4×D411yescharacteristic
275C22×D61—21no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61C4×D411yescharacteristic
283C22×D61#12011yescharacteristic
284C22×D61#12011yescharacteristic
285C22×D61C22⋊Q811yescharacteristic
286C22×D61C22⋊Q811yescharacteristic
287C22×D61C22×D411yescharacteristic
288C2×#6923—22no—
289C2×#6923—24no—
290C2×#6923—22no—
291C2×#6923—42no—
292C2×#6923—44no—
293C2×#6923—42no—
294C2×#6923—44no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—82no—
300C2×#6923—88no—
301Q8×C61—21no—
302Q8×C61C2×C4⋊C412yes—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61—21no—
306D4×C61C2×C4⋊C412yes—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61C2×C4⋊C411yescharacteristic
312C2×C4×C61C2×C4⋊C411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C22⋊D61—22no—
318C22⋊D61—22no—
319C22⋊D61—22no—
320C22⋊D61—22no—
321C22⋊D61—22no—
322C22⋊D61—22no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61C4×D411yescharacteristic
328C2×Dic61C22⋊Q811yescharacteristic
329C2×Dic61C22⋊Q811yescharacteristic
330C2×Dic61#12311yescharacteristic
331C2×Dic61#12311yescharacteristic
332C2×Dic61C2×#4111yescharacteristic
333D244—22no—
334D244—22no—
335D244—21no—
336D244C2×C4⋊C412yes—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61C2×C4⋊C411yescharacteristic
346C4×D61C2×C4⋊C411yescharacteristic
347C4×D61C4×D411yescharacteristic
348C4×D61C4×D411yescharacteristic
349C4×D61#12011yescharacteristic
350C4×D61#12011yescharacteristic
351C4×D61C22⋊Q811yescharacteristic
352C4×D61C22⋊Q811yescharacteristic
353C4×D61C22⋊Q811yescharacteristic
354C4×D61C22⋊Q811yescharacteristic
355C4×D61#12311yescharacteristic
356C4×D61#12311yescharacteristic
357C4×D61C22×D411yescharacteristic
358C4×D61C22×D411yescharacteristic
359C4×D61C22×Q811yescharacteristic
360C4×D61C2×#4111yescharacteristic
361Dic122—21no—
362Dic122—22no—
363Dic122—22no—
364Dic122C2×C4⋊C412yes—
365#92420—42no—
366C8×C61—22no—
367#92418—22no—
368#20864—611nomaximal, Sylow
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61#38511yescharacteristic
373C22×C61#38511yescharacteristic
374C22×C61C2×C4×D411yescharacteristic
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—22no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—44no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61#38511yescharacteristic
390C2×D61#38511yescharacteristic
391C2×D61C2×#12011yescharacteristic
392C2×D61C2×C22⋊Q811yescharacteristic
393#6923—44no—
394#6923—42no—
395#6923—42no—
396#6923—81no—
397#6923—81no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61#38511yescharacteristic
401C4×C61#38511yescharacteristic
402C4×C61C22×C4⋊C411yescharacteristic
403C4×C61C2×C4×D411yescharacteristic
404Dic61—22no—
405Dic61—42no—
406Dic61#38511yescharacteristic
407Dic61#38511yescharacteristic
408Dic61C2×C22⋊Q811yescharacteristic
409Dic61C2×#12311yescharacteristic
410C2×#520—611no—
411#2911—611no—
412C2×#421—611no—
413#2896—611no—
414#2317—611no—
415#1860—614no—
416#1859—614no—
417C2×#343—611no—
418#1733—611no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—42no—
423C2×C61C2×#38511yescharacteristic
424D61—21no—
425D61—21no—
426D61—21no—
427D61—42no—
428D61#301911yescharacteristic
429D61#302011yescharacteristic
430C22×#41—611no—
431C22×M16—611no—
432C22×M16—611no—
433#520—614no—
434#520—1222no—
435#520—1222no—
436#520—1222no—
437C2×C4×Q8—1221no—
438C2×C4×D4—1222no—
439C2×C4×D4—1221no—
440C2×#117—611no—
441C2×#117—611no—
442C2×#117—611no—
443C2×#117—1221no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—1221no—
446#428—612no—
447#428—612no—
448#428—1221no—
449#428—1221no—
450#427—1222no—
451#421—611no—
452#421—611no—
453#421—611no—
454#421—614no—
455#421#692311yescharacteristic, complemented
456C2×#104—614no—
457#419—1221no—
458#418—1221no—
459#417—612no—
460#417—612no—
461#416—1222no—
462#389—1222no—
463#385—1222no—
464#384—612no—
465#382—612no—
466#343—614no—
467#339—614no—
468C61#2086411yescharacteristic, complemented, Sylow
469C2×#41—612no—
470C2×#41—612no—
471C2×#41—612no—
472C2×#41—612no—
473C2×#41—611no—
474C2×#41—611no—
475C2×#41—611no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41—1221no—
480C2×#41—1221no—
481C2×#41—1221no—
482C2×#41C2×#692311yescharacteristic
483C22×Q8—611no—
484C22×D4—611no—
485C22×D4—1221no—
486C23×C4—611no—
487C23×C4—612no—
488C23×C4—1221no—
489C23×C4—1222no—
490C2×M16—611no—
491C2×M16—612no—
492C2×M16—612no—
493C2×M16—612no—
494C2×M16—1221no—
495C2×M16—1221no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16C2×#692311yescharacteristic, complemented
503C22×C8—1221no—
504C22×C8—1221no—
505C4×Q8—1224no—
506C4×Q8—1224no—
507C4×D4—1228no—
508C4×D4—1224no—
509C4×D4—1224no—
510C4×D4—1228no—
511#117—611no—
512#117—612no—
513#117—612no—
514#117—612no—
515#117—1221no—
516#117—1221no—
517#117—1224no—
518#117—1221no—
519#117—1221no—
520#117—1224no—
521#117—1221no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117C2×#692311yescharacteristic, complemented
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—612no—
529C2×C4⋊C4—612no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1224no—
540C2×C4⋊C4—1224no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1222no—
544C2×C22⋊C4—1221no—
545C2×C42—612no—
546C2×C42—1221no—
547C2×C42—1222no—
548C2×C42—1221no—
549#107—1222no—
550#107—1222no—
551#106—1222no—
552#106—1222no—
553#104—614no—
554#104—614no—
555#104—614no—
556#104C2×#692314yescomplemented
557#103—1222no—
558#103—1222no—
559#102—1222no—
560#102—1222no—
561#95—1224no—
562C24—611no—
563C24—1221no—
564#41—21no—
565#41—21no—
566#41—612no—
567#41—612no—
568#41—612no—
569#41—612no—
570#41—612no—
571#41—612no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—1221no—
581#41—1221no—
582#41—1221no—
583#41—1221no—
584#41—1221no—
585#41—1221no—
586#41C4⋊#692312yescomplemented
587#41C22×#692312yes—
588C2×Q8—612no—
589C2×Q8—612no—
590C2×Q8—611no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8C4⋊#692311yescharacteristic, complemented
595C2×D4—21no—
596C2×D4—612no—
597C2×D4—612no—
598C2×D4—611no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4C4⋊#692311yescharacteristic, complemented
610C22×C4—21no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—614no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1221no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1221no—
631C22×C4—1222no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1222no—
635C22×C4—1228no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1222no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—4884no—
642C22×C4—4882no—
643C22×C4C22×#692311yescharacteristic
644M16—21no—
645M16—612no—
646M16—1222no—
647M16—1222no—
648M16—1221no—
649M16—1222no—
650M16—1222no—
651M16—2441no—
652M16—2441no—
653M16C22×#692312yescomplemented
654C2×C8—21no—
655C2×C8—1222no—
656C2×C8—1222no—
657C2×C8—1221no—
658C2×C8—1222no—
659C2×C8—2441no—
660C2×C8—2441no—
661C4⋊C4—21no—
662C4⋊C4—612no—
663C4⋊C4—612no—
664C4⋊C4—1222no—
665C4⋊C4—1221no—
666C4⋊C4—1222no—
667C4⋊C4—1222no—
668C4⋊C4—1222no—
669C4⋊C4—1222no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1228no—
676C4⋊C4—1221no—
677C4⋊C4—4884no—
678C22⋊C4—21no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—1228no—
683C22⋊C4—1221no—
684C22⋊C4—2441no—
685C22⋊C4—2441no—
686C42—612no—
687C42—1222no—
688C42—1222no—
689C42—1222no—
690C42—1228no—
691C42—2441no—
692C42—2441no—
693C42C22×#692312yescomplemented
694C23—21no—
695C23—611no—
696C23—611no—
697C23—611no—
698C23—611no—
699C23—611no—
700C23—611no—
701C23—1222no—
702C23—1222no—
703C23—1221no—
704C23—2441no—
705C23—2441no—
706C23—2442no—
707C23—2442no—
708C23D4×#692311yescharacteristic
709Q8—21no—
710Q8—612no—
711Q8—1222no—
712Q8—1222no—
713Q8—1221no—
714Q8C2×C4⋊#692312yes—
715D4—22no—
716D4—22no—
717D4—21no—
718D4—612no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—1222no—
725D4—1222no—
726D4—1222no—
727D4—1221no—
728D4C2×C4⋊#692312yes—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—611no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1221no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1224no—
767C2×C4—1222no—
768C2×C4—4882no—
769C2×C4—4888no—
770C2×C4—2442no—
771C2×C4—2442no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2444no—
779C2×C4—2444no—
780C2×C4C2×C4⋊#692311yescharacteristic
781C2×C4C2×C4⋊#692311yescharacteristic
782C2×C4D4×#692311yescharacteristic
783C2×C4D4×#692311yescharacteristic
784C2×C4D4×#692311yescharacteristic
785C2×C4C23×#692311yescharacteristic
786C8—22no—
787C8—1222no—
788C8—2442no—
789C22—22no—
790C22—41no—
791C22—42no—
792C22—611no—
793C22—611no—
794C22—611no—
795C22—611no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—1222no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2444no—
810C22#1684070911yescharacteristic
811C22#1684070911yescharacteristic
812C22C2×D4×#692311yescharacteristic
813C4—22no—
814C4—42no—
815C4—611no—
816C4—611no—
817C4—611no—
818C4—611no—
819C4—1222no—
820C4—4881no—
821C4—4881no—
822C4—2442no—
823C4—2442no—
824C4—2444no—
825C4—2442no—
826C4#1684070911yescharacteristic
827C4#1684070911yescharacteristic
828C4C22×C4⋊#692311yescharacteristic
829C4C2×D4×#692311yescharacteristic
830C2—21no—
831C2—21no—
832C2—21no—
833C2—42no—
834C2—611no—
835C2—611no—
836C2—1221no—
837C2—1221no—
838C2—1221no—
839C2—2442no—
840C2C2×#1684070911yescharacteristic
subgroupG/H
centerC2C2×#16840709
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#421C4
socleC2×C61C2×#385
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#421#6923
hypocenterC61#20864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #21462472C2semidirect
4. #21462300C2semidirect
5. #21461779C2semidirect
6. #21461778C2semidirect
7. C2×#16840641C2semidirect
8. #21461500C2semidirect
25. #16840773C22semidirect
26. #16840773C22semidirect
35. #16840708C22semidirect
36. #16840706C22semidirect
37. #16840641C22semidirect
38. #16840633C22semidirect
42. #16839780C4semidirect
43. #16839779C4semidirect
44. #16839778C4semidirect
45. #16839777C4semidirect
47. C61×#421C4semidirect
120. C2×#11758194C2×C4semidirect
124. M16×D61C2×C4semidirect
127. #14519736C2×C4semidirect
129. #14519734C2×C4semidirect
134. #14519705C2×C4semidirect
135. #14519704C2×C4semidirect
136. #14519703C2×C4semidirect
138. C2×M16×C61C2×C4semidirect
139. #117×C61C2×C4semidirect
140. #104×C61C2×C4semidirect
155. #41×C61C4⋊C4semidirect
157. C2×Q8×C61C4⋊C4semidirect
159. C2×D4×C61C4⋊C4semidirect
169. #11758226C4⋊C4semidirect
173. Q8×D61C4⋊C4semidirect
181. #11758224C4⋊C4semidirect
189. D4×D61C4⋊C4semidirect
197. #11758222C4⋊C4semidirect
200. C2×D244C4⋊C4semidirect
222. C2×Dic122C4⋊C4semidirect
255. M16×C61C22×C4semidirect
259. C42×C61C22×C4semidirect
265. C4×Dic61C22×C4semidirect
267. #11758194C22×C4semidirect
455. #421#6923semidirect
468. C61#20864semidirect
502. C2×M16C2×#6923semidirect
525. #117C2×#6923semidirect
556. #104C2×#6923semidirect
586. #41C4⋊#6923semidirect
594. C2×Q8C4⋊#6923semidirect
609. C2×D4C4⋊#6923semidirect
653. M16C22×#6923semidirect
693. C42C22×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
#214624722
#214624392
#214623002
#214617792
#214617782
C2×#168406412
#214615002
#421×D612
#2086461