Finite Group Databasebeta

← #30615501

Subgroups — #30615501

Order 15616.

1394 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462799C211yesmaximal, characteristic
2C2×#16840773C211yesmaximal, characteristic, complemented
3C2×#16840753C211yesmaximal, characteristic
4#21462300C211yesmaximal, characteristic, complemented
5#21461779C214yesmaximal, complemented
6#21461778C214yesmaximal, complemented
7#21461523C211yesmaximal, characteristic, complemented
8#21461500C211yesmaximal, characteristic, complemented
9#421×D61C211yesmaximal, characteristic
10C2×D61⋊M16C2211yescharacteristic
11#16840831—21no—
12#16840831—21no—
13#16840831C2212yes—
14#16840831C2212yes—
15#16840830—21no—
16#16840829—22no—
17#16840829—21no—
18#41×#6923—22no—
19#41×#6923—22no—
20C2×#14519856—22no—
21C2×#14519856C2211yescharacteristic
22C2×#14519856C2211yescharacteristic
23C22×C4⋊#6923C2211yescharacteristic
24#16840773—22no—
25#16840773C2214yescomplemented
26C2×#14519846—21no—
27C2×#14519845—21no—
28#16840753—22no—
29#16840753C2214yes—
30C2×#14519840—21no—
31C2×#14519839—21no—
32#16840713—22no—
33#16840709—22no—
34#16840708C2212yescomplemented
35#16840706C2212yescomplemented
36#16840641C2212yescomplemented
37#16840641C2212yescomplemented
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—21no—
49C2×#11758213—21no—
50D61⋊M16—21no—
51D61⋊M16—21no—
52D61⋊M16—21no—
53D61⋊M16C2312yes—
54C2×#11758217—21no—
55C2×D61⋊C8—21no—
56Q8×#6923—22no—
57Q8×#6923—22no—
58Q8×#6923—22no—
59Q8×#6923—22no—
60D4×#6923—24no—
61D4×#6923—24no—
62D4×#6923—22no—
63D4×#6923—22no—
64D4×#6923—24no—
65D4×#6923—24no—
66D4×#6923—22no—
67D4×#6923—22no—
68#14519856—24no—
69#14519856—24no—
70#14519856—21no—
71#14519856—21no—
72#14519856—21no—
73#14519856—21no—
74#14519856—21no—
75#14519856—21no—
76#14519856—22no—
77#14519856—22no—
78#14519856D412yes—
79#14519856C2312yes—
80C2×C4⋊#6923—22no—
81C2×C4⋊#6923—22no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923—24no—
88C2×C4⋊#6923D411yescharacteristic
89C2×C4⋊#6923D411yescharacteristic
90C2×C4⋊#6923C2312yes—
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C22⋊#6923—24no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923D412yes—
96C2×C4×#6923—24no—
97C2×C4×#6923—21no—
98C2×C4×#6923D412yes—
99#14519846—24no—
100#14519845—24no—
101#14519840—24no—
102#14519839—24no—
103(C2×#6923)⋊C4—24no—
104C2×#11758226Q811yescharacteristic
105C2×#11758222—21no—
106C2×#11758222C2×C411yescharacteristic
107C2×#11758224—21no—
108C2×#11758224Q811yescharacteristic
109#41×D61—21no—
110#41×D61—21no—
111#41×D61—21no—
112#41×D61—21no—
113#41×D61C2×C412yes—
114#41×D61D412yes—
115#41×D61Q812yes—
116#41×D61C2312yes—
117C2×Q8×D61D411yescharacteristic
118C2×D4×D61—21no—
119C2×D4×D61D411yescharacteristic
120C22×C4×D61—21no—
121C22×C4×D61C2311yescharacteristic
122C2×#11758194C2×C411yescharacteristic, complemented
123C2×#11758189—21no—
124M16×D61—21no—
125M16×D61—21no—
126M16×D61C2×C412yescomplemented
127M16×D61C2312yes—
128C2×C8×D61—21no—
129#14519736C2×C411yescharacteristic, complemented
130#14519735—21no—
131#14519734C2×C412yescomplemented
132#14519733—21no—
133C4⋊C4×D61—21no—
134C22⋊C4×D61—21no—
135C42×D61C2312yes—
136#14519705C2×C414yescomplemented
137#14519704C2×C414yescomplemented
138#14519703C2×C414yescomplemented
139C2×#41×C61C2×C411yescharacteristic
140C2×M16×C61C2×C411yescharacteristic, complemented
141#117×C61C2×C411yescharacteristic, complemented
142#104×C61C2×C414yescomplemented
143C23×D61—21no—
144C23×D61C2×D411yescharacteristic
145C22×#6923—24no—
146C22×#6923—24no—
147C22×#6923—21no—
148C22×#6923—21no—
149C22×#6923—22no—
150C22×#6923—41no—
151C22×#6923—41no—
152C22×#6923—82no—
153C22×#6923C2×D412yes—
154C22×#6923C2×D412yes—
155#41×C61—21no—
156#41×C61—21no—
157#41×C61C4⋊C412yescomplemented
158#41×C61C22×C412yes—
159C2×Q8×C61C4⋊C411yescharacteristic, complemented
160C2×D4×C61—21no—
161C2×D4×C61C4⋊C411yescharacteristic, complemented
162C22×C4×C61—21no—
163C22×C4×C61C22×C411yescharacteristic
164C2×C22⋊D61—21no—
165C2×C22⋊D61—21no—
166C2×C22⋊D61—21no—
167C22×Dic61—21no—
168C22×Dic61#4111yescharacteristic
169#11758226—21no—
170#11758226—21no—
171#11758226C4⋊C412yescomplemented
172#11758226C2×Q812yes—
173Q8×D61—21no—
174Q8×D61—21no—
175Q8×D61C4⋊C412yescomplemented
176Q8×D61C2×D412yes—
177#11758224—22no—
178#11758224—22no—
179#11758224—22no—
180#11758224—22no—
181#11758224—21no—
182#11758224—21no—
183#11758224C4⋊C412yescomplemented
184#11758224C2×Q812yes—
185D4×D61—22no—
186D4×D61—22no—
187D4×D61—22no—
188D4×D61—22no—
189D4×D61—21no—
190D4×D61—21no—
191D4×D61C4⋊C412yescomplemented
192D4×D61C2×D412yes—
193#11758222—21no—
194#11758222—21no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—22no—
199#11758222C4⋊C412yescomplemented
200#11758222C22×C412yes—
201C2×D244—21no—
202C2×D244C4⋊C411yescharacteristic, complemented
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—22no—
211C2×C4×D61C22×C411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×Q811yescharacteristic
218C2×C4×D61C2×Q811yescharacteristic
219C2×C4×D61#4111yescharacteristic
220C2×C4×D61#4111yescharacteristic
221C2×C4×D61#4111yescharacteristic
222C2×C4×D61C2411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122C4⋊C411yescharacteristic, complemented
225C22⋊#6923—24no—
226C22⋊#6923—24no—
227C22⋊#6923—22no—
228C22⋊#6923—22no—
229C22⋊#6923—22no—
230C22⋊#6923—22no—
231#11758217—22no—
232#11758217—41no—
233C2×#92420—41no—
234C4⋊#6923—24no—
235C4⋊#6923—24no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923—21no—
239C4⋊#6923—21no—
240C4⋊#6923—21no—
241C4⋊#6923—21no—
242C4⋊#6923—22no—
243C4⋊#6923—22no—
244C4⋊#6923—41no—
245C4⋊#6923—41no—
246C4⋊#6923—84no—
247C4⋊#6923C2×D412yes—
248C4⋊#6923C2×D412yes—
249C4×#6923—24no—
250C4×#6923—24no—
251C4×#6923—22no—
252C4×#6923—22no—
253C4×#6923—22no—
254C4×#6923—22no—
255#11758213—22no—
256#11758213—41no—
257D61⋊C8—22no—
258D61⋊C8—41no—
259M16×C61—21no—
260M16×C61C22×C412yes—
261C2×C8×C61—21no—
262C4⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C42×C61C22×C412yes—
265C22⋊Dic61—21no—
266#11758198—22no—
267C4⋊Dic61—21no—
268#11758196—22no—
269C4×Dic61—22no—
270C4×Dic61C22×C412yes—
271#11758194—21no—
272#11758194C22×C412yes—
273C2×#92418—21no—
274#11758189—22no—
275#11758189—22no—
276C8×D61—22no—
277C8×D61—22no—
278C23×C61—21no—
279C23×C61C4×D411yescharacteristic
280C22×D61—21no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—81no—
286C22×D61—81no—
287C22×D61C4×D411yescharacteristic
288C22×D61#12011yescharacteristic
289C22×D61#12011yescharacteristic
290C22×D61C22⋊Q811yescharacteristic
291C22×D61C22⋊Q811yescharacteristic
292C22×D61C22×D411yescharacteristic
293C2×#6923—22no—
294C2×#6923—22no—
295C2×#6923—22no—
296C2×#6923—22no—
297C2×#6923—42no—
298C2×#6923—42no—
299C2×#6923—44no—
300C2×#6923—42no—
301C2×#6923—81no—
302C2×#6923—81no—
303C2×#6923—84no—
304C2×#6923—84no—
305C2×#6923—82no—
306C2×#6923—82no—
307Q8×C61—21no—
308Q8×C61C2×C4⋊C412yes—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—21no—
312D4×C61C2×C4⋊C412yes—
313C2×C4×C61—21no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61C2×C4⋊C411yescharacteristic
318C2×C4×C61C2×C4⋊C411yescharacteristic
319C2×C4×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C22⋊D61—22no—
324C22⋊D61—22no—
325C22⋊D61—22no—
326C22⋊D61—22no—
327C22⋊D61—22no—
328C22⋊D61—22no—
329C2×Dic61—21no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61C4×D411yescharacteristic
334C2×Dic61C22⋊Q811yescharacteristic
335C2×Dic61C22⋊Q811yescharacteristic
336C2×Dic61#12311yescharacteristic
337C2×Dic61#12311yescharacteristic
338C2×Dic61C2×#4111yescharacteristic
339D244—22no—
340D244—22no—
341D244—21no—
342D244C2×C4⋊C412yes—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—42no—
350C4×D61—42no—
351C4×D61C2×C4⋊C411yescharacteristic
352C4×D61C2×C4⋊C411yescharacteristic
353C4×D61C4×D411yescharacteristic
354C4×D61C4×D411yescharacteristic
355C4×D61#12011yescharacteristic
356C4×D61#12011yescharacteristic
357C4×D61C22⋊Q811yescharacteristic
358C4×D61C22⋊Q811yescharacteristic
359C4×D61C22⋊Q811yescharacteristic
360C4×D61C22⋊Q811yescharacteristic
361C4×D61#12311yescharacteristic
362C4×D61#12311yescharacteristic
363C4×D61C22×D411yescharacteristic
364C4×D61C22×D411yescharacteristic
365C4×D61C22×Q811yescharacteristic
366C4×D61C2×#4111yescharacteristic
367Dic122—21no—
368Dic122—22no—
369Dic122—22no—
370Dic122C2×C4⋊C412yes—
371#92420—42no—
372C8×C61—22no—
373#92418—22no—
374#20865—611nomaximal, Sylow
375C22×C61—22no—
376C22×C61—41no—
377C22×C61—81no—
378C22×C61#38511yescharacteristic
379C22×C61#38511yescharacteristic
380C22×C61C2×C4×D411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—22no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—82no—
394C2×D61—81no—
395C2×D61#38511yescharacteristic
396C2×D61#38511yescharacteristic
397C2×D61C2×#12011yescharacteristic
398C2×D61C2×C22⋊Q811yescharacteristic
399#6923—42no—
400#6923—42no—
401#6923—42no—
402#6923—42no—
403#6923—82no—
404C4×C61—22no—
405C4×C61—42no—
406C4×C61#38511yescharacteristic
407C4×C61#38511yescharacteristic
408C4×C61C22×C4⋊C411yescharacteristic
409C4×C61C2×C4×D411yescharacteristic
410Dic61—22no—
411Dic61—42no—
412Dic61#38511yescharacteristic
413Dic61#38511yescharacteristic
414Dic61C2×C22⋊Q811yescharacteristic
415Dic61C2×#12311yescharacteristic
416#3428—611no—
417C2×#428—611no—
418C2×#421—611no—
419C2×#417—611no—
420#2317—611no—
421#1860—614no—
422#1859—614no—
423#1742—611no—
424#1733—611no—
425C2×C61—21no—
426C2×C61—21no—
427C2×C61—21no—
428C2×C61—42no—
429C2×C61C2×#38511yescharacteristic
430D61—21no—
431D61—21no—
432D61—21no—
433D61—42no—
434D61#302111yescharacteristic
435D61#302211yescharacteristic
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439#520—612no—
440#520—612no—
441#520—1221no—
442#520—1221no—
443#519—1221no—
444#518—1222no—
445#518—1221no—
446C4×#41—1222no—
447C4×#41—1222no—
448C2×#117—611no—
449C2×#117—611no—
450C2×#117—611no—
451C2×#117—1222no—
452C22×C4⋊C4—611no—
453#428—614no—
454#428—1222no—
455C2×#107—1221no—
456C2×#106—1221no—
457#421—611no—
458#421—611no—
459#421—611no—
460#421—614no—
461#421#692311yescharacteristic, complemented
462C2×#104—614no—
463#417—614no—
464#417—1222no—
465C2×#103—1221no—
466C2×#102—1221no—
467#389—1222no—
468#385—1222no—
469#384—612no—
470#382—612no—
471#343—612no—
472#343—612no—
473#339—614no—
474C61#2086511yescharacteristic, complemented, Sylow
475C2×#41—612no—
476C2×#41—612no—
477C2×#41—612no—
478C2×#41—612no—
479C2×#41—611no—
480C2×#41—611no—
481C2×#41—611no—
482C2×#41—1221no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1221no—
488C2×#41C2×#692311yescharacteristic
489C22×Q8—611no—
490C22×D4—611no—
491C22×D4—1221no—
492C23×C4—611no—
493C23×C4—1221no—
494C23×C4—1221no—
495C2×M16—611no—
496C2×M16—612no—
497C2×M16—612no—
498C2×M16—612no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16C2×#692311yescharacteristic, complemented
508C22×C8—1221no—
509C22×C8—1221no—
510C4×Q8—1222no—
511C4×Q8—1222no—
512C4×Q8—1222no—
513C4×Q8—1222no—
514C4×D4—1224no—
515C4×D4—1224no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1224no—
521C4×D4—1224no—
522#117—611no—
523#117—612no—
524#117—612no—
525#117—612no—
526#117—1221no—
527#117—1221no—
528#117—1222no—
529#117—1222no—
530#117—1221no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535#117—1221no—
536#117—1224no—
537#117—1224no—
538#117C2×#692311yescharacteristic, complemented
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—612no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1222no—
546C2×C4⋊C4—1222no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1224no—
552C2×C4⋊C4—1221no—
553C2×C22⋊C4—612no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1224no—
557C2×C42—612no—
558C2×C42—612no—
559C2×C42—1221no—
560C2×C42—1224no—
561#107—1224no—
562#106—1224no—
563#104—614no—
564#104—614no—
565#104—614no—
566#104C2×#692314yescomplemented
567#103—1224no—
568#102—1224no—
569#95—1224no—
570C24—611no—
571C24—1221no—
572#41—21no—
573#41—21no—
574#41—612no—
575#41—612no—
576#41—612no—
577#41—612no—
578#41—612no—
579#41—612no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584#41—1222no—
585#41—1222no—
586#41—1222no—
587#41—1222no—
588#41—1221no—
589#41—1221no—
590#41—1221no—
591#41—1221no—
592#41—1221no—
593#41—1221no—
594#41C4⋊#692312yescomplemented
595#41C22×#692312yes—
596C2×Q8—612no—
597C2×Q8—612no—
598C2×Q8—611no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8C4⋊#692311yescharacteristic, complemented
603C2×D4—21no—
604C2×D4—612no—
605C2×D4—612no—
606C2×D4—611no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4C4⋊#692311yescharacteristic, complemented
618C22×C4—21no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
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—612no—
633C22×C4—612no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1221no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1221no—
640C22×C4—1222no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1224no—
646C22×C4—1224no—
647C22×C4—1222no—
648C22×C4—4882no—
649C22×C4—2441no—
650C22×C4—2441no—
651C22×C4C22×#692311yescharacteristic
652M16—21no—
653M16—612no—
654M16—1222no—
655M16—1222no—
656M16—1221no—
657M16—1222no—
658M16—1222no—
659M16—2441no—
660M16—2441no—
661M16C22×#692312yes—
662C2×C8—21no—
663C2×C8—1222no—
664C2×C8—1222no—
665C2×C8—1221no—
666C2×C8—1222no—
667C2×C8—2441no—
668C2×C8—2441no—
669C4⋊C4—21no—
670C4⋊C4—612no—
671C4⋊C4—612no—
672C4⋊C4—1222no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4—4884no—
685C4⋊C4—2441no—
686C4⋊C4—2441no—
687C22⋊C4—21no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1221no—
696C42—612no—
697C42—1222no—
698C42—1222no—
699C42—1222no—
700C42—1222no—
701C42—1222no—
702C42—1224no—
703C42—1224no—
704C42C22×#692312yes—
705C23—21no—
706C23—611no—
707C23—611no—
708C23—611no—
709C23—611no—
710C23—611no—
711C23—611no—
712C23—1222no—
713C23—1222no—
714C23—1221no—
715C23—4881no—
716C23—4881no—
717C23—2441no—
718C23—2441no—
719C23D4×#692311yescharacteristic
720Q8—21no—
721Q8—612no—
722Q8—1222no—
723Q8—1222no—
724Q8—1221no—
725Q8C2×C4⋊#692312yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—612no—
730D4—1222no—
731D4—1222no—
732D4—1222no—
733D4—1222no—
734D4—1222no—
735D4—1222no—
736D4—1222no—
737D4—1222no—
738D4—1221no—
739D4C2×C4⋊#692312yes—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
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—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1221no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—4882no—
781C2×C4—4882no—
782C2×C4—4881no—
783C2×C4—4881no—
784C2×C4—4884no—
785C2×C4—4884no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2444no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4C2×C4⋊#692311yescharacteristic
793C2×C4C2×C4⋊#692311yescharacteristic
794C2×C4D4×#692311yescharacteristic
795C2×C4D4×#692311yescharacteristic
796C2×C4D4×#692311yescharacteristic
797C2×C4C23×#692311yescharacteristic
798C8—22no—
799C8—1222no—
800C8—2442no—
801C22—22no—
802C22—41no—
803C22—81no—
804C22—611no—
805C22—611no—
806C22—611no—
807C22—611no—
808C22—1221no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—1221no—
814C22—1222no—
815C22—4881no—
816C22—4882no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2442no—
821C22—2442no—
822C22#1684070911yescharacteristic
823C22#1684070911yescharacteristic
824C22C2×D4×#692311yescharacteristic
825C4—22no—
826C4—42no—
827C4—611no—
828C4—611no—
829C4—611no—
830C4—611no—
831C4—1222no—
832C4—4882no—
833C4—2442no—
834C4—2442no—
835C4—2442no—
836C4—2442no—
837C4—2442no—
838C4#1684070911yescharacteristic
839C4#1684070911yescharacteristic
840C4C22×C4⋊#692311yescharacteristic
841C4C2×D4×#692311yescharacteristic
842C2—21no—
843C2—21no—
844C2—21no—
845C2—42no—
846C2—611no—
847C2—611no—
848C2—1221no—
849C2—1221no—
850C2—1221no—
851C2—2442no—
852C2C2×#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#20865
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. C2×#16840773C2semidirect
4. #21462300C2semidirect
5. #21461779C2semidirect
6. #21461778C2semidirect
7. #21461523C2semidirect
8. #21461500C2semidirect
25. #16840773C22semidirect
34. #16840708C22semidirect
35. #16840706C22semidirect
36. #16840641C22semidirect
37. #16840641C22semidirect
38. #16840633C22semidirect
42. #16839780C4semidirect
43. #16839779C4semidirect
44. #16839778C4semidirect
45. #16839777C4semidirect
47. C61×#421C4semidirect
122. C2×#11758194C2×C4semidirect
126. M16×D61C2×C4semidirect
129. #14519736C2×C4semidirect
131. #14519734C2×C4semidirect
136. #14519705C2×C4semidirect
137. #14519704C2×C4semidirect
138. #14519703C2×C4semidirect
140. C2×M16×C61C2×C4semidirect
141. #117×C61C2×C4semidirect
142. #104×C61C2×C4semidirect
157. #41×C61C4⋊C4semidirect
159. C2×Q8×C61C4⋊C4semidirect
161. C2×D4×C61C4⋊C4semidirect
171. #11758226C4⋊C4semidirect
175. Q8×D61C4⋊C4semidirect
183. #11758224C4⋊C4semidirect
191. D4×D61C4⋊C4semidirect
199. #11758222C4⋊C4semidirect
202. C2×D244C4⋊C4semidirect
224. C2×Dic122C4⋊C4semidirect
461. #421#6923semidirect
474. C61#20865semidirect
507. C2×M16C2×#6923semidirect
538. #117C2×#6923semidirect
566. #104C2×#6923semidirect
594. #41C4⋊#6923semidirect
602. C2×Q8C4⋊#6923semidirect
617. C2×D4C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
#214627992
C2×#168407732
C2×#168407532
#214623002
#214617792
#214617782
#214615232
#214615002
#421×D612
#2086561