Finite Group Databasebeta

← #30617024

Subgroups — #30617024

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic
2C2×SD16×#6923C211yesmaximal, characteristic
3#21462310C211yesmaximal, characteristic, complemented
4#21462258C211yesmaximal, characteristic
5#21461985C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461898C211yesmaximal, characteristic, complemented
9#21461812C211yesmaximal, characteristic
10#21461812C211yesmaximal, characteristic
11#21461689C211yesmaximal, characteristic
12#21461608C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#103×#6923C211yesmaximal, characteristic, complemented
15#461×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840801—24no—
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840711—21no—
36#16840711—21no—
37#16840711—21no—
38#16840711—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C22⋊C4×#6923—21no—
44C22⋊C4×#6923—21no—
45C4×C22⋊#6923—21no—
46#16840698C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C4⋊Q8×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839968C411yescharacteristic, complemented
59#16839967C411yescharacteristic, complemented
60#16839966C411yescharacteristic, complemented
61#16839966C411yescharacteristic, complemented
62#16839965C411yescharacteristic, complemented
63#16839965C411yescharacteristic, complemented
64#16839964C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67#103×D61C2211yescharacteristic
68C61×#461C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—22no—
76Q8×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923D414yes—
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×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923C2311yescharacteristic
95C2×C4×#6923C2311yescharacteristic
96#14519846—22no—
97#14519845—22no—
98#14519844—21no—
99C4⋊#92420—21no—
100#14519840—22no—
101#14519840—22no—
102#14519840—22no—
103#14519840—22no—
104#14519839—22no—
105#14519839—22no—
106#14519831—22no—
107C8×#6923—22no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×Q8×D61C2311yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61—21no—
125C2×#11758190C2×C411yescharacteristic
126C2×#11758190C2×C411yescharacteristic
127C2×#11758200C2×C411yescharacteristic
128C2×#11758200C2×C411yescharacteristic
129C2×#11758201C2×C411yescharacteristic
130C2×#11758201C2×C411yescharacteristic
131SD16×D61—22no—
132SD16×D61—22no—
133SD16×D61—22no—
134SD16×D61—22no—
135C2×C8×D61C2311yescharacteristic
136C2×C8×D61C2311yescharacteristic
137#14519777C2×C411yescharacteristic, complemented
138#14519776—21no—
139#14519776—21no—
140#14519775C2×C411yescharacteristic, complemented
141#14519775C2×C411yescharacteristic, complemented
142C4×D244C2×C411yescharacteristic
143D4×Dic61C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145C4×C22⋊D61—21no—
146#14519737—21no—
147C4⋊C4×D61—21no—
148C4⋊C4×D61—21no—
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519702C2×C411yescharacteristic, complemented
156#14519702C2×C411yescharacteristic, complemented
157#14519701C2×C411yescharacteristic, complemented
158#14519701C2×C411yescharacteristic, complemented
159#14519700C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161C2×SD16×C61C2×C411yescharacteristic
162C2×SD16×C61C2×C411yescharacteristic
163C4⋊Q8×C61C2×C411yescharacteristic, complemented
164C4×D4×C61C2×C411yescharacteristic
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#103×C61C2×C411yescharacteristic, complemented
167#103×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C22×#6923—21no—
170C22×#6923—21no—
171C22×#6923—24no—
172C22×#6923—24no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—81no—
176C22×#6923—81no—
177C22×#6923—81no—
178C22×#6923—81no—
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C2×Q8×C61C22×C411yescharacteristic
184C2×Q8×C61C22×C411yescharacteristic
185C2×D4×C61C22×C411yescharacteristic
186C22×C4×C61—21no—
187C2×C22⋊D61—21no—
188C22×Dic61—21no—
189Q8×D61—21no—
190Q8×D61—21no—
191Q8×D61—21no—
192Q8×D61—21no—
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—21no—
196Q8×D61—21no—
197D4×D61—21no—
198D4×D61—21no—
199D4×D61C2×D412yes—
200D4×D61#4112yes—
201C2×D244C22×C411yescharacteristic
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2411yescharacteristic
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C411yescharacteristic
215C2×Dic122C22×C411yescharacteristic
216C22⋊#6923—24no—
217C22⋊#6923—24no—
218C2×#92420—21no—
219C2×#92420—21no—
220C4⋊#6923—21no—
221C4⋊#6923—21no—
222C4⋊#6923—21no—
223C4⋊#6923—21no—
224C4⋊#6923—21no—
225C4⋊#6923—21no—
226C4⋊#6923—42no—
227C4⋊#6923—42no—
228C4⋊#6923C2×D412yes—
229C4⋊#6923#4112yes—
230C4×#6923—21no—
231C4×#6923—21no—
232C4×#6923—42no—
233C4×#6923—42no—
234C4×#6923—81no—
235C4×#6923—81no—
236C4×#6923—81no—
237C4×#6923C2×D412yes—
238C4×#6923#4112yes—
239D61⋊C8—21no—
240D61⋊C8—21no—
241D61⋊C8—21no—
242D61⋊C8—21no—
243SD16×C61—22no—
244SD16×C61—22no—
245C2×C8×C61C22×C411yescharacteristic
246C2×C8×C61C22×C411yescharacteristic
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C42×C61C22×C411yescharacteristic
252C22⋊Dic61—21no—
253#11758201—22no—
254#11758201—22no—
255#11758200—22no—
256#11758200—22no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61C22×C411yescharacteristic
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267C4×Dic61C22×C411yescharacteristic
268C4×Dic61#4111yescharacteristic
269C4×Dic61#4111yescharacteristic
270C2×#92418C22×C411yescharacteristic
271C2×#92418C22×C411yescharacteristic
272#11758190—22no—
273#11758190—22no—
274C8×D61—21no—
275C8×D61—21no—
276C8×D61—21no—
277C8×D61—21no—
278C23×C61—21no—
279C22×D61—21no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61C22×D411yescharacteristic
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—22no—
292C2×#6923—21no—
293C2×#6923—21no—
294C2×#6923—22no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—21no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—84no—
310C2×#6923—84no—
311C2×#6923#12112yes—
312C2×#6923#12112yes—
313Q8×C61—21no—
314Q8×C61—21no—
315Q8×C61—21no—
316Q8×C61—21no—
317D4×C61—21no—
318D4×C61C4×D412yes—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—81no—
323C2×C4×C61C4×D411yescharacteristic
324C2×C4×C61C4×D411yescharacteristic
325C2×C4×C61C23×C411yescharacteristic
326C22⋊D61—22no—
327C22⋊D61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—81no—
332C2×Dic61C4×D411yescharacteristic
333C2×Dic61C4×D411yescharacteristic
334C2×Dic61C2×#4111yescharacteristic
335D244—21no—
336D244C4×D412yes—
337C4×D61—21no—
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—81no—
348C4×D61—81no—
349C4×D61C22×D411yescharacteristic
350C4×D61C2×#4111yescharacteristic
351C4×D61C2×#4111yescharacteristic
352C4×D61C2×#4111yescharacteristic
353Dic122—21no—
354Dic122—21no—
355Dic122—21no—
356Dic122—21no—
357Dic122—41no—
358Dic122—41no—
359Dic122—41no—
360Dic122—41no—
361#92420—41no—
362#92420—41no—
363C8×C61—21no—
364C8×C61—21no—
365#92418—21no—
366#92418—21no—
367#21514—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61C2×C4×D411yescharacteristic
372C2×D61—22no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61C2×#12111yescharacteristic
380C2×D61#52511yescharacteristic
381C2×D61#57711yescharacteristic
382C2×D61#57711yescharacteristic
383C2×D61#57711yescharacteristic
384C2×D61#57811yescharacteristic
385#6923—22no—
386#6923—22no—
387#6923—41no—
388#6923—41no—
389#6923—42no—
390#6923—42no—
391#6923—81no—
392#6923—81no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61C2×C4×D411yescharacteristic
399C4×C61C4×#4111yescharacteristic
400Dic61—21no—
401Dic61—21no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61#52911yescharacteristic
406Dic61#53211yescharacteristic
407C2×#461—611no—
408C2×#440—611no—
409C2×C4×SD16—611no—
410#2327—611no—
411#2275—611no—
412#1981—611no—
413#1949—611no—
414#1928—611no—
415#1927—611no—
416#1877—611no—
417#1877—611no—
418#1804—611no—
419#1768—611no—
420#1763—611no—
421C4×#103—611no—
422C2×C61—42no—
423C2×C61C4×#12111yescharacteristic
424C2×C61#294711yescharacteristic
425C2×C61#294911yescharacteristic
426D61—42no—
427D61#304211yescharacteristic
428D61#304611yescharacteristic
429D61#312011yescharacteristic
430D61#312311yescharacteristic
431C22×SD16—611no—
432C22×SD16—611no—
433C2×C4⋊Q8—611no—
434C2×C4×Q8—611no—
435C2×C4×Q8—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439#461—611no—
440#461—611no—
441#461—611no—
442#461—611no—
443#461—611no—
444#461—611no—
445#461—611no—
446#461#692311yescharacteristic, complemented
447#440—1224no—
448C4×SD16—1224no—
449C2×#107—611no—
450C2×#106—611no—
451C2×C4⋊C8—611no—
452C2×C4⋊C8—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#97—611no—
462C2×C4×C8—611no—
463#391—611no—
464#391—611no—
465#387—1221no—
466#387—1221no—
467#387—1221no—
468#387—1221no—
469#382—611no—
470C4×C4⋊C4—611no—
471C4×C4⋊C4—611no—
472C4×C4⋊C4—611no—
473C4×C22⋊C4—1221no—
474C4×C22⋊C4—1221no—
475C4×C22⋊C4—1221no—
476#376—611no—
477C2×#95—1221no—
478#340—611no—
479#340—611no—
480#340—611no—
481#340—611no—
482#336—611no—
483#336—611no—
484C61#2151411yescharacteristic, complemented, Sylow
485C22×Q8—611no—
486C22×Q8—611no—
487C22×D4—611no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C2×SD16—611no—
492C2×SD16—611no—
493C2×SD16—611no—
494C2×SD16—611no—
495C2×SD16—611no—
496C2×SD16—611no—
497C2×SD16—1222no—
498C2×SD16—1222no—
499C2×SD16—1222no—
500C2×SD16—1222no—
501C2×SD16C2×#692311yescharacteristic
502C2×SD16C2×#692311yescharacteristic
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—611no—
506C22×C8—611no—
507C4⋊Q8—611no—
508C4⋊Q8—611no—
509C4⋊Q8—611no—
510C4⋊Q8—1221no—
511C4⋊Q8—1221no—
512C4⋊Q8C2×#692311yescharacteristic, complemented
513C4×Q8—1222no—
514C4×Q8—1222no—
515C4×Q8—1222no—
516C4×Q8—1222no—
517C4×D4—614no—
518C4×D4—611no—
519C4×D4—611no—
520C4×D4—611no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1222no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4C2×#692311yescharacteristic
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547#107—1222no—
548#106—1222no—
549C4⋊C8—611no—
550C4⋊C8—611no—
551C4⋊C8—611no—
552C4⋊C8—1221no—
553C4⋊C8—1221no—
554C4⋊C8C2×#692311yescharacteristic, complemented
555#103—611no—
556#103—611no—
557#103—611no—
558#103—611no—
559#103—611no—
560#103—611no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103C2×#692311yescharacteristic, complemented
566#103C2×#692311yescharacteristic, complemented
567#102—1222no—
568#102—1222no—
569#97—1222no—
570C4×C8—1222no—
571#95—611no—
572#95—611no—
573#95—611no—
574#95—611no—
575#95—1221no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583#95—1221no—
584C24—1221no—
585C2×Q8—611no—
586C2×Q8—611no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1221no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8C22×#692311yescharacteristic
598C2×Q8C22×#692311yescharacteristic
599C2×D4—612no—
600C2×D4—612no—
601C2×D4—611no—
602C2×D4—1221no—
603C2×D4—1221no—
604C2×D4—1221no—
605C2×D4C22×#692311yescharacteristic
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1224no—
620C22×C4—1224no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—4881no—
627C22×C4—4881no—
628C22×C4—4881no—
629C22×C4—4881no—
630C22×C4—4881no—
631C22×C4—4881no—
632SD16—22no—
633SD16—22no—
634SD16—1222no—
635SD16—1222no—
636SD16—1222no—
637SD16—1222no—
638SD16—1222no—
639SD16—1222no—
640C2×C8—611no—
641C2×C8—611no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8C22×#692311yescharacteristic
653C2×C8C22×#692311yescharacteristic
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—611no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—2442no—
673C4⋊C4—2442no—
674C4⋊C4C22×#692311yescharacteristic
675C22⋊C4—21no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1221no—
681C42—612no—
682C42—612no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—1221no—
687C42—1221no—
688C42—4881no—
689C42—4881no—
690C42—4881no—
691C42—2442no—
692C42—2442no—
693C42C22×#692311yescharacteristic
694C23—21no—
695C23—611no—
696C23—1222no—
697C23—1222no—
698C23—1221no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—1221no—
708Q8—1221no—
709Q8—1221no—
710Q8—1221no—
711Q8—2441no—
712Q8—2441no—
713Q8—2441no—
714Q8—2441no—
715D4—21no—
716D4—612no—
717D4—1222no—
718D4—1222no—
719D4—1221no—
720D4D4×#692312yes—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—81no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—611no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—612no—
731C2×C4—612no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1221no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—4881no—
754C2×C4—4881no—
755C2×C4—4881no—
756C2×C4—4884no—
757C2×C4—4884no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4D4×#692311yescharacteristic
775C2×C4D4×#692311yescharacteristic
776C2×C4C23×#692311yescharacteristic
777C8—21no—
778C8—21no—
779C8—1221no—
780C8—1221no—
781C8—2441no—
782C8—2441no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—611no—
787C22—611no—
788C22—611no—
789C22—611no—
790C22—611no—
791C22—611no—
792C22—1222no—
793C22—2442no—
794C22—2442no—
795C22—2442no—
796C22—2442no—
797C22—2441no—
798C22—2441no—
799C22C2×D4×#692311yescharacteristic
800C4—21no—
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—611no—
806C4—611no—
807C4—1222no—
808C4—1222no—
809C4—1221no—
810C4—1221no—
811C4—4881no—
812C4—4881no—
813C4—2441no—
814C4—2441no—
815C4—2442no—
816C4—2442no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4C2×D4×#692311yescharacteristic
821C4#41×#692311yescharacteristic
822C2—42no—
823C2—611no—
824C2—611no—
825C2—611no—
826C2—611no—
827C2—2442no—
828C2#121×#692311yescharacteristic
829C2#2146257711yescharacteristic
830C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#461C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#461#6923
hypocenterC61#21514
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
3. #21462310C2semidirect
5. #21461985C2semidirect
6. #21461932C2semidirect
7. #21461899C2semidirect
8. #21461898C2semidirect
12. #21461608C2semidirect
13. #21461592C2semidirect
14. #103×#6923C2semidirect
58. #16839968C4semidirect
59. #16839967C4semidirect
60. #16839966C4semidirect
61. #16839966C4semidirect
62. #16839965C4semidirect
63. #16839965C4semidirect
64. #16839964C4semidirect
68. C61×#461C4semidirect
137. #14519777C2×C4semidirect
140. #14519775C2×C4semidirect
141. #14519775C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519702C2×C4semidirect
156. #14519702C2×C4semidirect
157. #14519701C2×C4semidirect
158. #14519701C2×C4semidirect
159. #14519700C2×C4semidirect
160. #14519700C2×C4semidirect
163. C4⋊Q8×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #103×C61C2×C4semidirect
167. #103×C61C2×C4semidirect
446. #461#6923semidirect
484. C61#21514semidirect
512. C4⋊Q8C2×#6923semidirect
554. C4⋊C8C2×#6923semidirect
565. #103C2×#6923semidirect
566. #103C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×SD16×#69232
#214623102
#214622582
#214619852
#214619322
#214618992
#214618982
#214618122
#214616892
#214616082
#214615922
#103×#69232
#461×D612
#2151461