Finite Group Databasebeta

← #478×#6923 #30617311

Subgroups — #478×#6923 #30617311

Order 15616.

948 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×#6923C211yesmaximal, characteristic, complemented
2C4×D4×#6923C211yesmaximal, characteristic
3#21461999C211yesmaximal, characteristic, complemented
4#21461932C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461784C211yesmaximal, characteristic
8#21461782C211yesmaximal, characteristic
9#21461689C211yesmaximal, characteristic
10#107×#6923C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12C4⋊C8×#6923C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic
14#102×#6923C211yesmaximal, characteristic
15#478×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C22×C4×#6923—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21D61⋊(C4⋊C8)C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×C8×#6923C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26#16840713C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840711—21no—
29#16840711—21no—
30#16840706C2211yescharacteristic
31C4⋊C4×#6923—21no—
32C4⋊C4×#6923—21no—
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4×C4⋊#6923C2211yescharacteristic
38C22⋊C4×#6923—21no—
39C22⋊C4×#6923—21no—
40C4×C22⋊#6923—21no—
41C42×#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#125×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840065C411yescharacteristic, complemented
55#16840064C411yescharacteristic, complemented
56#16840063C411yescharacteristic, complemented
57#16840062C411yescharacteristic, complemented
58#16840061C411yescharacteristic, complemented
59#16840060C411yescharacteristic, complemented
60#16840059C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#478C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923Q814yes—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—44no—
89C2×C4×#6923D411yescharacteristic
90C2×C4×#6923D411yescharacteristic
91C2×C4×#6923D411yescharacteristic
92C2×C4×#6923D411yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94C2×C4×#6923C2311yescharacteristic
95#14519846—22no—
96#14519845—22no—
97#14519844—21no—
98C4⋊#92420—21no—
99#14519839—22no—
100#14519839—22no—
101C8×#6923—22no—
102C8×#6923—22no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×C8×D61C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116#14519769C2×C411yescharacteristic, complemented
117#14519768C2×C411yescharacteristic, complemented
118#14519768C2×C411yescharacteristic, complemented
119#14519767—21no—
120#14519767—21no—
121C4×D244C2×C411yescharacteristic
122D4×Dic61C2×C411yescharacteristic
123#14519739C2×C411yescharacteristic
124C4×C22⋊D61—21no—
125#14519737—21no—
126C4⋊C4×D61—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C42×D61C2311yescharacteristic
133#14519711C2×C411yescharacteristic, complemented
134#14519710C2×C411yescharacteristic, complemented
135#14519710C2×C411yescharacteristic, complemented
136#14519709C2×C411yescharacteristic, complemented
137#14519708C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139C4⋊#92418C2×C411yescharacteristic, complemented
140#14519706C2×C411yescharacteristic, complemented
141#14519706C2×C411yescharacteristic, complemented
142#14519699C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519697C2×C411yescharacteristic
148#125×C61C2×C411yescharacteristic, complemented
149C4×D4×C61C2×C411yescharacteristic
150#107×C61C2×C411yescharacteristic, complemented
151#106×C61C2×C411yescharacteristic, complemented
152C4⋊C8×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155C23×D61—21no—
156C22×#6923—24no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—24no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—42no—
163C22×#6923—42no—
164C22×#6923—42no—
165C22×#6923—42no—
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C2×D4×C61C22×C411yescharacteristic
171C22×C4×C61—21no—
172C2×C22⋊D61—21no—
173C22×Dic61—21no—
174D4×D61—21no—
175D4×D61—21no—
176D4×D61C2×Q812yes—
177D4×D61#4112yes—
178C2×D244C22×C411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2411yescharacteristic
189C22⋊#6923—24no—
190C22⋊#6923—24no—
191C2×#92420—21no—
192C2×#92420—21no—
193C4⋊#6923—21no—
194C4⋊#6923—21no—
195C4⋊#6923—21no—
196C4⋊#6923—21no—
197C4⋊#6923—21no—
198C4⋊#6923—21no—
199C4⋊#6923—42no—
200C4⋊#6923—42no—
201C4⋊#6923C2×Q812yes—
202C4⋊#6923#4112yes—
203C4×#6923—22no—
204C4×#6923—22no—
205C4×#6923—22no—
206C4×#6923—21no—
207C4×#6923—21no—
208C4×#6923—41no—
209C4×#6923—42no—
210C4×#6923—42no—
211C4×#6923—42no—
212C4×#6923—42no—
213C4×#6923—42no—
214C4×#6923C2×Q812yes—
215C4×#6923#4112yes—
216D61⋊C8—21no—
217D61⋊C8—21no—
218D61⋊C8—21no—
219D61⋊C8—21no—
220C2×C8×C61C22×C411yescharacteristic
221C2×C8×C61C22×C411yescharacteristic
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C4⋊C4×C61C22×C411yescharacteristic
227C22⋊C4×C61—21no—
228C42×C61C22×C411yescharacteristic
229C22⋊Dic61—21no—
230#11758198—21no—
231#11758198—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61C22×C411yescharacteristic
235C4⋊Dic61C22×C411yescharacteristic
236C4⋊Dic61C22×C411yescharacteristic
237#11758196—21no—
238#11758196—21no—
239#11758196—21no—
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244C4×Dic61C22×C411yescharacteristic
245C4×Dic61#4111yescharacteristic
246C4×Dic61#4111yescharacteristic
247C2×#92418C22×C411yescharacteristic
248C2×#92418C22×C411yescharacteristic
249C8×D61—21no—
250C8×D61—21no—
251C8×D61—21no—
252C8×D61—21no—
253C23×C61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61C22×D411yescharacteristic
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—22no—
267C2×#6923—21no—
268C2×#6923—22no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—48no—
272C2×#6923—41no—
273C2×#6923—41no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—48no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923C22⋊Q812yes—
284C2×#6923C22⋊Q812yes—
285C2×#6923#13512yes—
286C2×#6923#13512yes—
287C2×#6923AGL(1,ℤ/8)12yes—
288D4×C61—21no—
289D4×C61C4×Q812yes—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—42no—
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C23×C411yescharacteristic
297C22⋊D61—22no—
298C22⋊D61—22no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—42no—
303C2×Dic61C4×D411yescharacteristic
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306D244—21no—
307D244C4×Q812yes—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—42no—
313C4×D61—42no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61C22×Q811yescharacteristic
321C4×D61C2×#4111yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61C2×#4111yescharacteristic
324#92420—41no—
325#92420—41no—
326C8×C61—21no—
327C8×C61—21no—
328#92418—21no—
329#92418—21no—
330C4×#478—611nomaximal, Sylow
331C22×C61—22no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61C2×C4×D411yescharacteristic
335C2×D61—22no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61C2×C22⋊Q811yescharacteristic
343C2×D61#52511yescharacteristic
344C2×D61C2×#13511yescharacteristic
345C2×D61C2×#13511yescharacteristic
346C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
347C2×D61#57511yescharacteristic
348#6923—22no—
349#6923—22no—
350#6923—42no—
351#6923—41no—
352#6923—42no—
353#6923—81no—
354#6923—81no—
355#6923#47814yesdirect product factor
356C4×C61—21no—
357C4×C61—21no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61C2×C4×Q811yescharacteristic
362C4×C61C4×#4111yescharacteristic
363Dic61—21no—
364Dic61—21no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61#52911yescharacteristic
369Dic61#53311yescharacteristic
370C2×#478—611no—
371C4×#125—611no—
372C42×D4—611no—
373#1989—611no—
374#1949—611no—
375#1921—611no—
376#1919—611no—
377#1864—611no—
378#1862—611no—
379#1804—611no—
380C4×#107—611no—
381C4×#106—611no—
382C4×C4⋊C8—611no—
383C4×#102—611no—
384C4×#102—611no—
385C2×C61—42no—
386C2×C61C4×C22⋊Q811yescharacteristic
387C2×C61C4×#13511yescharacteristic
388C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
389D61—42no—
390D61C2×#47811yescharacteristic
391D61#307611yescharacteristic
392D61#310211yescharacteristic
393D61#310511yescharacteristic
394C2×#125—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C22×C42—1221no—
399#478—611no—
400#478—611no—
401#478—611no—
402#478—611no—
403#478—611no—
404#478—611no—
405#478—611no—
406#478#692311yescharacteristic, direct product factor
407C2×#107—611no—
408C2×#107—611no—
409C2×#106—611no—
410C2×#106—611no—
411C2×C4⋊C8—611no—
412C2×C4⋊C8—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×C4×C8—611no—
418C2×C4×C8—611no—
419#389—611no—
420#389—611no—
421#387—1221no—
422#387—1221no—
423#382—611no—
424C4×C4⋊C4—611no—
425C4×C4⋊C4—611no—
426C4×C4⋊C4—611no—
427C4×C4⋊C4—611no—
428C4×C4⋊C4—611no—
429C4×C4⋊C4—1221no—
430C4×C4⋊C4—1221no—
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C4×C22⋊C4—1221no—
434C43—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#336—611no—
444#336—611no—
445C61C4×#47811yescharacteristic, complemented, Sylow
446C22×D4—611no—
447C23×C4—1221no—
448C23×C4—1221no—
449C23×C4—1221no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454#125—611no—
455#125—611no—
456#125—611no—
457#125—1221no—
458#125—1221no—
459#125C2×#692311yescharacteristic, complemented
460C4×D4—614no—
461C4×D4—611no—
462C4×D4—611no—
463C4×D4—611no—
464C4×D4—1221no—
465C4×D4—1221no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4C2×#692311yescharacteristic
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42—2444no—
497#107—611no—
498#107—611no—
499#107—611no—
500#107—1222no—
501#107C2×#692311yescharacteristic, complemented
502#106—611no—
503#106—611no—
504#106—611no—
505#106—1222no—
506#106C2×#692311yescharacteristic, complemented
507C4⋊C8—611no—
508C4⋊C8—611no—
509C4⋊C8—611no—
510C4⋊C8—1221no—
511C4⋊C8—1221no—
512C4⋊C8C2×#692311yescharacteristic, complemented
513#102—611no—
514#102—611no—
515#102—611no—
516#102—611no—
517#102—611no—
518#102—611no—
519#102—1222no—
520#102—1222no—
521#102C2×#692311yescharacteristic
522#102C2×#692311yescharacteristic
523C4×C8—1222no—
524C4×C8—1222no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534C24—1221no—
535C2×D4—612no—
536C2×D4—612no—
537C2×D4—611no—
538C2×D4—1221no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4C22×#692311yescharacteristic
542C22×C4—21no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1224no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1224no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C2×C8—611no—
569C2×C8—611no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8C22×#692311yescharacteristic
581C2×C8C22×#692311yescharacteristic
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—612no—
585C4⋊C4—612no—
586C4⋊C4—611no—
587C4⋊C4—611no—
588C4⋊C4—611no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—2442no—
605C4⋊C4—2442no—
606C4⋊C4C22×#692311yescharacteristic
607C4⋊C4C22×#692311yescharacteristic
608C4⋊C4C22×#692311yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—1221no—
611C22⋊C4—1221no—
612C22⋊C4—1224no—
613C22⋊C4—1224no—
614C22⋊C4—1221no—
615C42—612no—
616C42—612no—
617C42—611no—
618C42—611no—
619C42—611no—
620C42—1222no—
621C42—1221no—
622C42—1221no—
623C42—1222no—
624C42—1222no—
625C42—2442no—
626C42—2442no—
627C42—2442no—
628C42—2441no—
629C42—2442no—
630C42—2442no—
631C42C22×#692311yescharacteristic
632C23—21no—
633C23—611no—
634C23—1222no—
635C23—1222no—
636C23—1221no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641D4—21no—
642D4—612no—
643D4—1222no—
644D4—1222no—
645D4—1221no—
646D4Q8×#692312yes—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—42no—
651C2×C4—612no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—612no—
660C2×C4—612no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2448no—
688C2×C4—2442no—
689C2×C4—2448no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4D4×#692311yescharacteristic
701C2×C4D4×#692311yescharacteristic
702C2×C4C23×#692311yescharacteristic
703C8—21no—
704C8—21no—
705C8—1221no—
706C8—1221no—
707C8—2441no—
708C8—2441no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—611no—
713C22—611no—
714C22—611no—
715C22—611no—
716C22—611no—
717C22—611no—
718C22—1222no—
719C22—2442no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22—2441no—
724C22—2441no—
725C22C2×D4×#692311yescharacteristic
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—614no—
732C4—611no—
733C4—611no—
734C4—1222no—
735C4—1222no—
736C4—1221no—
737C4—1221no—
738C4—4881no—
739C4—4881no—
740C4—2441no—
741C4—2442no—
742C4—2442no—
743C4—2441no—
744C4—2441no—
745C4—2441no—
746C4C2×Q8×#692311yescharacteristic
747C4#41×#692311yescharacteristic
748C2—42no—
749C2—611no—
750C2—611no—
751C2—611no—
752C2—611no—
753C2—2442no—
754C2C22⋊Q8×#692311yescharacteristic
755C2#135×#692311yescharacteristic
756C2AGL(1,ℤ/8)×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#478C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#478#6923
hypocenterC61C4×#478
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×#6923C2semidirect
3. #21461999C2semidirect
4. #21461932C2semidirect
5. #21461883C2semidirect
6. #21461881C2semidirect
10. #107×#6923C2semidirect
11. #106×#6923C2semidirect
12. C4⋊C8×#6923C2semidirect
54. #16840065C4semidirect
55. #16840064C4semidirect
56. #16840063C4semidirect
57. #16840062C4semidirect
58. #16840061C4semidirect
59. #16840060C4semidirect
60. #16840059C4semidirect
66. C61×#478C4semidirect
116. #14519769C2×C4semidirect
117. #14519768C2×C4semidirect
118. #14519768C2×C4semidirect
133. #14519711C2×C4semidirect
134. #14519710C2×C4semidirect
135. #14519710C2×C4semidirect
136. #14519709C2×C4semidirect
137. #14519708C2×C4semidirect
138. #14519708C2×C4semidirect
139. C4⋊#92418C2×C4semidirect
140. #14519706C2×C4semidirect
141. #14519706C2×C4semidirect
148. #125×C61C2×C4semidirect
150. #107×C61C2×C4semidirect
151. #106×C61C2×C4semidirect
152. C4⋊C8×C61C2×C4semidirect
355. #6923#478direct (N × H)
406. #478#6923direct (N × H)
445. C61C4×#478semidirect
459. #125C2×#6923semidirect
501. #107C2×#6923semidirect
506. #106C2×#6923semidirect
512. C4⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#125×#69232
C4×D4×#69232
#214619992
#214619322
#214618832
#214618812
#214617842
#214617822
#214616892
#107×#69232
#106×#69232
C4⋊C8×#69232
#102×#69232
#478×D612
C4×#47861