Finite Group Databasebeta

← #482×#6923 #30617191

Subgroups — #482×#6923 #30617191

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×#6923C211yesmaximal, characteristic
2#117×#6923C211yesmaximal, characteristic, complemented
3#21461897C211yesmaximal, characteristic, complemented
4#21461896C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461882C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic
8#21461770C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#107×#6923C211yesmaximal, characteristic, complemented
11#106×#6923C211yesmaximal, characteristic, complemented
12#102×#6923C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14C22⋊C8×#6923C211yesmaximal, characteristic, complemented
15#482×D61C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4×#6923C2211yescharacteristic
20C2×#14519846C2211yescharacteristic
21C2×#14519845C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24D61⋊(C22⋊C8)C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27#16840714C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840710—21no—
31#16840704C2211yescharacteristic
32C4⋊C4×#6923C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C22⋊C4×#6923—21no—
40#16840698—21no—
41C42×#6923—21no—
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#121×D61C2211yescharacteristic
53#117×D61C2211yescharacteristic
54#16840089C411yescharacteristic, complemented
55#16840088C411yescharacteristic, complemented
56#16840087C411yescharacteristic, complemented
57#16840086C411yescharacteristic, complemented
58#16840085C411yescharacteristic, complemented
59#16840084C411yescharacteristic, complemented
60#16840083C411yescharacteristic, complemented
61#107×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65C22⋊C8×D61C2211yescharacteristic
66C61×#482C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923D411yescharacteristic
69C23×#6923D411yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71C2×D61⋊C8C2311yescharacteristic
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—44no—
75#14519856—22no—
76#14519856—22no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—22no—
89C2×C4×#6923—22no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—21no—
93C2×C4×#6923—21no—
94C2×C4×#6923—21no—
95C2×C4×#6923D411yescharacteristic
96C2×C4×#6923D411yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846—22no—
100#14519845—22no—
101#14519839—22no—
102#14519839—22no—
103#14519834—21no—
104C22⋊#92420—21no—
105C8×#6923—22no—
106C8×#6923—22no—
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—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114C2×D4×D61—21no—
115C2×D4×D61C2311yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C2×C8×D61C2311yescharacteristic
118C2×C8×D61C2311yescharacteristic
119#14519752C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519750—21no—
122#14519749—21no—
123#14519748C2×C411yescharacteristic
124#14519736C2×C411yescharacteristic, complemented
125#14519735C2×C411yescharacteristic, complemented
126#14519735C2×C411yescharacteristic, complemented
127#14519734—21no—
128#14519733—21no—
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C4⋊C4×D61C2311yescharacteristic
132C22⋊C4×D61—21no—
133C22⋊C4×D61—21no—
134C42×D61—21no—
135#14519711C2×C411yescharacteristic, complemented
136#14519710C2×C411yescharacteristic, complemented
137#14519710C2×C411yescharacteristic, complemented
138#14519709C2×C411yescharacteristic, complemented
139#14519708C2×C411yescharacteristic, complemented
140#14519708C2×C411yescharacteristic, complemented
141#14519699C2×C411yescharacteristic, complemented
142#14519699C2×C411yescharacteristic, complemented
143#14519698C2×C411yescharacteristic, complemented
144#14519698C2×C411yescharacteristic, complemented
145#14519697C2×C411yescharacteristic, complemented
146#14519697C2×C411yescharacteristic, complemented
147C22⋊#92418C2×C411yescharacteristic, complemented
148#14519689C2×C411yescharacteristic, complemented
149#14519689C2×C411yescharacteristic, complemented
150#121×C61C2×C411yescharacteristic
151#117×C61C2×C411yescharacteristic, complemented
152#107×C61C2×C411yescharacteristic, complemented
153#106×C61C2×C411yescharacteristic, complemented
154#102×C61C2×C411yescharacteristic, complemented
155#102×C61C2×C411yescharacteristic, complemented
156C22⋊C8×C61C2×C411yescharacteristic, complemented
157C23×D61—21no—
158C23×D61C2×D411yescharacteristic
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—22no—
162C22×#6923—22no—
163C22×#6923—22no—
164C22×#6923—22no—
165C22×#6923—22no—
166C22×#6923—21no—
167C22×#6923—21no—
168C22×#6923—41no—
169C22×#6923—42no—
170C22×#6923—42no—
171C22×#6923—42no—
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C22×#6923C2×D411yescharacteristic
175C22×#6923C2×D411yescharacteristic
176C2×D4×C61—21no—
177C2×D4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C2×C22⋊D61—21no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—21no—
182C22×Dic61#4111yescharacteristic
183D4×D61—21no—
184D4×D61—21no—
185D4×D61—21no—
186D4×D61—21no—
187D4×D61—42no—
188D4×D61—42no—
189C2×D244—21no—
190C2×D244C22×C411yescharacteristic
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61C22×C411yescharacteristic
199C2×C4×D61C2×D411yescharacteristic
200C2×C4×D61#4111yescharacteristic
201C2×C4×D61C2411yescharacteristic
202C22⋊#6923—24no—
203C22⋊#6923—42no—
204C22⋊#6923—42no—
205C22⋊#6923—42no—
206C22⋊#6923—42no—
207C2×#92420—21no—
208C2×#92420—21no—
209C4⋊#6923—21no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—42no—
216C4⋊#6923#4112yes—
217C4⋊#6923#4112yes—
218C4×#6923—24no—
219C4×#6923—22no—
220C4×#6923—22no—
221C4×#6923—21no—
222C4×#6923—21no—
223C4×#6923—42no—
224C4×#6923—42no—
225C4×#6923—42no—
226C4×#6923—42no—
227C4×#6923—42no—
228C4×#6923#4112yes—
229C4×#6923#4112yes—
230D61⋊C8—21no—
231D61⋊C8—21no—
232D61⋊C8—21no—
233D61⋊C8—21no—
234C2×C8×C61C22×C411yescharacteristic
235C2×C8×C61C22×C411yescharacteristic
236C4⋊C4×C61C22×C411yescharacteristic
237C4⋊C4×C61C22×C411yescharacteristic
238C4⋊C4×C61C22×C411yescharacteristic
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C42×C61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248C4⋊Dic61C22×C411yescharacteristic
249C4⋊Dic61C22×C411yescharacteristic
250C4⋊Dic61C22×C411yescharacteristic
251#11758196—21no—
252#11758196—21no—
253#11758196—21no—
254C4×Dic61—21no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C2×#92418C22×C411yescharacteristic
258C2×#92418C22×C411yescharacteristic
259C8×D61—21no—
260C8×D61—21no—
261C8×D61—21no—
262C8×D61—21no—
263C23×C61—21no—
264C23×C61C4×D411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61C4×D411yescharacteristic
279C22×D61C22×D411yescharacteristic
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—21no—
284C2×#6923—21no—
285C2×#6923—22no—
286C2×#6923—22no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—44no—
290C2×#6923—41no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923—41no—
294C2×#6923—44no—
295C2×#6923—41no—
296C2×#6923—41no—
297C2×#6923—41no—
298C2×#6923—41no—
299C2×#6923—41no—
300C2×#6923—41no—
301C2×#6923—84no—
302C2×#6923#12312yes—
303C2×#6923#12312yes—
304C2×#6923#13512yes—
305C2×#6923#13512yes—
306C2×#6923AGL(1,ℤ/8)12yes—
307D4×C61—21no—
308D4×C61—21no—
309D4×C61—42no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C22⋊D61—42no—
318C22⋊D61—42no—
319C22⋊D61—41no—
320C22⋊D61—41no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61C4×D411yescharacteristic
327C2×Dic61C2×#4111yescharacteristic
328D244—21no—
329D244—21no—
330D244—42no—
331C4×D61—21no—
332C4×D61—21no—
333C4×D61—21no—
334C4×D61—21no—
335C4×D61—21no—
336C4×D61—21no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61C2×#4111yescharacteristic
344C4×D61C2×#4111yescharacteristic
345C4×D61C2×#4111yescharacteristic
346C4×D61C2×#4111yescharacteristic
347#92420—41no—
348#92420—41no—
349C8×C61—21no—
350C8×C61—21no—
351#92418—21no—
352#92418—21no—
353C4×#482—611nomaximal, Sylow
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61C2×C4×D411yescharacteristic
361C2×D61—21no—
362C2×D61—21no—
363C2×D61—21no—
364C2×D61—41no—
365C2×D61—41no—
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—81no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61C2×#12311yescharacteristic
376C2×D61#52511yescharacteristic
377C2×D61C2×#13511yescharacteristic
378C2×D61C2×#13511yescharacteristic
379C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
380C2×D61#57511yescharacteristic
381#6923—22no—
382#6923—22no—
383#6923—41no—
384#6923—42no—
385#6923—42no—
386#6923—81no—
387#6923—81no—
388#6923#48214yesdirect product factor
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61C4×#4111yescharacteristic
394C4×C61C4×#4111yescharacteristic
395Dic61—21no—
396Dic61—41no—
397Dic61—41no—
398Dic61—41no—
399Dic61#52911yescharacteristic
400Dic61#52911yescharacteristic
401C2×#482—611no—
402C4×#121—611no—
403C4×#117—611no—
404#1926—611no—
405#1925—611no—
406#1921—611no—
407#1920—611no—
408#1875—611no—
409#1854—611no—
410#1825—611no—
411C4×#107—611no—
412C4×#106—611no—
413C4×#102—611no—
414C4×#102—611no—
415C4×C22⋊C8—611no—
416C2×C61—41no—
417C2×C61—81no—
418C2×C61C4×#12311yescharacteristic
419C2×C61C4×#13511yescharacteristic
420C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
421D61—41no—
422D61—81no—
423D61C2×#48211yescharacteristic
424D61#309111yescharacteristic
425D61#310211yescharacteristic
426D61#310611yescharacteristic
427C2×#121—611no—
428C2×C4×D4—611no—
429C2×C4×D4—1221no—
430C2×#117—611no—
431C2×#117—611no—
432C22×C42—611no—
433#482—611no—
434#482—611no—
435#482—611no—
436#482—611no—
437#482—611no—
438#482—611no—
439#482—611no—
440#482#692311yescharacteristic, direct product factor
441C2×#107—611no—
442C2×#107—611no—
443C2×#106—611no—
444C2×#106—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453#390—611no—
454#389—611no—
455#388—1221no—
456#386—1221no—
457#380—611no—
458C4×C4⋊C4—611no—
459C4×C4⋊C4—611no—
460C4×C4⋊C4—611no—
461C4×C4⋊C4—611no—
462C4×C4⋊C4—611no—
463C4×C22⋊C4—1221no—
464C4×C22⋊C4—1221no—
465C4×C22⋊C4—1221no—
466#376—1221no—
467C43—1221no—
468#340—611no—
469#340—611no—
470#340—611no—
471#340—611no—
472#340—611no—
473#340—611no—
474#340—611no—
475#340—611no—
476#336—611no—
477#336—611no—
478C61C4×#48211yescharacteristic, complemented, Sylow
479C22×D4—611no—
480C22×D4—1221no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—1221no—
485C22×C8—611no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489#121—611no—
490#121—611no—
491#121—611no—
492#121—1221no—
493#121—1221no—
494#121C2×#692311yescharacteristic
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—2444no—
498#117—611no—
499#117—611no—
500#117—611no—
501#117—1221no—
502#117—1221no—
503#117—1222no—
504#117—1222no—
505#117C2×#692311yescharacteristic, complemented
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—1221no—
526C2×C42—1222no—
527C2×C42—1222no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532C2×C42—1221no—
533C2×C42—1221no—
534#107—611no—
535#107—611no—
536#107—611no—
537#107—1222no—
538#107C2×#692311yescharacteristic, complemented
539#106—611no—
540#106—611no—
541#106—611no—
542#106—1222no—
543#106C2×#692311yescharacteristic, complemented
544#102—611no—
545#102—611no—
546#102—611no—
547#102—611no—
548#102—611no—
549#102—611no—
550#102—1222no—
551#102—1222no—
552#102C2×#692311yescharacteristic, complemented
553#102C2×#692311yescharacteristic, complemented
554C22⋊C8—611no—
555C22⋊C8—611no—
556C22⋊C8—611no—
557C22⋊C8—1221no—
558C22⋊C8—1221no—
559C22⋊C8C2×#692311yescharacteristic, complemented
560C4×C8—1222no—
561C4×C8—1222no—
562#95—1221no—
563#95—1221no—
564#95—1221no—
565#95—1221no—
566#95—1221no—
567#95—1221no—
568#95—1221no—
569C24—611no—
570C24—1221no—
571C2×D4—21no—
572C2×D4—611no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—1221no—
580C2×D4—1221no—
581C2×D4—2442no—
582C2×D4—2442no—
583C2×D4C22×#692311yescharacteristic
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2441no—
613C22×C4C22×#692311yescharacteristic
614C2×C8—611no—
615C2×C8—611no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8C22×#692311yescharacteristic
627C2×C8C22×#692311yescharacteristic
628C4⋊C4—612no—
629C4⋊C4—612no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—611no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—1221no—
642C4⋊C4—2442no—
643C4⋊C4C22×#692311yescharacteristic
644C4⋊C4C22×#692311yescharacteristic
645C4⋊C4C22×#692311yescharacteristic
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—1221no—
649C22⋊C4—1221no—
650C22⋊C4—1221no—
651C22⋊C4—1221no—
652C22⋊C4—1224no—
653C22⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—2442no—
656C22⋊C4—2442no—
657C22⋊C4—2442no—
658C22⋊C4—2442no—
659C42—21no—
660C42—612no—
661C42—612no—
662C42—1221no—
663C42—1221no—
664C42—1222no—
665C42—1221no—
666C42—1221no—
667C42—1222no—
668C42—1224no—
669C42—1221no—
670C42—2442no—
671C42—2442no—
672C42—2442no—
673C42—2442no—
674C42—2442no—
675C23—21no—
676C23—611no—
677C23—611no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23D4×#692311yescharacteristic
692D4—21no—
693D4—21no—
694D4—42no—
695D4—1221no—
696D4—1221no—
697D4—2442no—
698D4—2441no—
699D4—2441no—
700D4—2442no—
701D4—2442no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—612no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—611no—
715C2×C4—612no—
716C2×C4—612no—
717C2×C4—611no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—4884no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2444no—
746C2×C4—2444no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4D4×#692311yescharacteristic
758C2×C4C23×#692311yescharacteristic
759C8—21no—
760C8—21no—
761C8—1221no—
762C8—1221no—
763C8—2441no—
764C8—2441no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—611no—
772C22—611no—
773C22—611no—
774C22—611no—
775C22—611no—
776C22—611no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—4881no—
781C22—4881no—
782C22—4881no—
783C22—4881no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22C2×D4×#692311yescharacteristic
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—614no—
797C4—611no—
798C4—611no—
799C4—1222no—
800C4—1222no—
801C4—1221no—
802C4—4881no—
803C4—4881no—
804C4—2441no—
805C4—2442no—
806C4—2442no—
807C4—2441no—
808C4—2441no—
809C4—2441no—
810C4#41×#692311yescharacteristic
811C4#41×#692311yescharacteristic
812C2—41no—
813C2—81no—
814C2—611no—
815C2—611no—
816C2—611no—
817C2—611no—
818C2—4881no—
819C2—2441no—
820C2#123×#692311yescharacteristic
821C2#135×#692311yescharacteristic
822C2AGL(1,ℤ/8)×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#482C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#482#6923
hypocenterC61C4×#482
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×#6923C2semidirect
3. #21461897C2semidirect
4. #21461896C2semidirect
5. #21461883C2semidirect
6. #21461882C2semidirect
8. #21461770C2semidirect
9. #21461724C2semidirect
10. #107×#6923C2semidirect
11. #106×#6923C2semidirect
12. #102×#6923C2semidirect
13. #102×#6923C2semidirect
14. C22⋊C8×#6923C2semidirect
54. #16840089C4semidirect
55. #16840088C4semidirect
56. #16840087C4semidirect
57. #16840086C4semidirect
58. #16840085C4semidirect
59. #16840084C4semidirect
60. #16840083C4semidirect
66. C61×#482C4semidirect
124. #14519736C2×C4semidirect
125. #14519735C2×C4semidirect
126. #14519735C2×C4semidirect
135. #14519711C2×C4semidirect
136. #14519710C2×C4semidirect
137. #14519710C2×C4semidirect
138. #14519709C2×C4semidirect
139. #14519708C2×C4semidirect
140. #14519708C2×C4semidirect
141. #14519699C2×C4semidirect
142. #14519699C2×C4semidirect
143. #14519698C2×C4semidirect
144. #14519698C2×C4semidirect
145. #14519697C2×C4semidirect
146. #14519697C2×C4semidirect
147. C22⋊#92418C2×C4semidirect
148. #14519689C2×C4semidirect
149. #14519689C2×C4semidirect
151. #117×C61C2×C4semidirect
152. #107×C61C2×C4semidirect
153. #106×C61C2×C4semidirect
154. #102×C61C2×C4semidirect
155. #102×C61C2×C4semidirect
156. C22⋊C8×C61C2×C4semidirect
388. #6923#482direct (N × H)
440. #482#6923direct (N × H)
478. C61C4×#482semidirect
505. #117C2×#6923semidirect
538. #107C2×#6923semidirect
543. #106C2×#6923semidirect
552. #102C2×#6923semidirect
553. #102C2×#6923semidirect
559. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#121×#69232
#117×#69232
#214618972
#214618962
#214618832
#214618822
#214618072
#214617702
#214617242
#107×#69232
#106×#69232
#102×#69232
C22⋊C8×#69232
#482×D612
C4×#48261