Finite Group Databasebeta

← #30620480

Subgroups — #30620480

Order 15616.

1172 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462328C212yesmaximal, complemented
2#21461960C212yesmaximal, complemented
3#21461960C212yesmaximal, complemented
4#21461959C212yesmaximal, complemented
5#21461682C211yesmaximal, characteristic, complemented
6#21461681C211yesmaximal, characteristic, complemented
7#21461680C211yesmaximal, characteristic, complemented
8#21461566C211yesmaximal, characteristic, complemented
9C4×#14519836C211yesmaximal, characteristic, complemented
10#21461564C211yesmaximal, characteristic, complemented
11C2×#16840463C211yesmaximal, characteristic
12C2×#14519836C2212yes—
13C2×#14519836C2212yes—
14C2×#14519836C2212yes—
15C2×#14519836C2212yes—
16C2×#14519835C2212yes—
17C2×#14519835C2212yes—
18#16840713—22no—
19#16840711—22no—
20#16840711—22no—
21#16840704C2212yes—
22#16840704C2212yes—
23#16840704C2212yes—
24C4⋊C4×#6923—22no—
25C4×C22⋊#6923C2212yes—
26C4×C22⋊#6923C2212yes—
27C4×C22⋊#6923C2212yes—
28#16840640C2211yescharacteristic
29#16840640C2211yescharacteristic
30#16840640C2211yescharacteristic
31#16840640C2211yescharacteristic
32#16840463—22no—
33#16840463—22no—
34#16840463—22no—
35#16840463—22no—
36C2×#14519772C411yescharacteristic, complemented
37C2×#14519767C411yescharacteristic, complemented
38C2×#14519762C411yescharacteristic, complemented
39C2×#14519761C411yescharacteristic, complemented
40C2×#14519752C2211yescharacteristic
41C2×#14519750C411yescharacteristic, complemented
42C2×#14519750C2211yescharacteristic
43C2×#14519750C2211yescharacteristic
44C2×C4×D244C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519737C411yescharacteristic, complemented
47C2×#14519737C2211yescharacteristic
48C2×#14519734C411yescharacteristic, complemented
49C2×C4⋊C4×D61C2211yescharacteristic
50C2×#126×C61C411yescharacteristic, complemented
51C2×C4⋊#6923—22no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923C2312yes—
55C2×C22⋊#6923C2312yes—
56C2×C22⋊#6923C2312yes—
57C2×C22⋊#6923C2312yes—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60C2×C4×#6923—22no—
61#14519836—24no—
62#14519836—24no—
63#14519836—42no—
64#14519836—42no—
65#14519835—24no—
66#14519835—42no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—22no—
72(C2×#6923)⋊C4—22no—
73C22×D244C2×C411yescharacteristic
74C22×D244C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2311yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85#14519772—22no—
86#14519772—22no—
87#14519767—22no—
88#14519767—22no—
89#14519762—22no—
90#14519762—22no—
91#14519761—22no—
92#14519761—22no—
93#14519752—22no—
94#14519752—22no—
95#14519750—22no—
96#14519750—22no—
97#14519750—22no—
98#14519750—22no—
99#14519750—22no—
100#14519750—22no—
101C4×D244—22no—
102C4×D244—22no—
103#14519739—22no—
104#14519739—22no—
105#14519737—22no—
106#14519737—22no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519734—21no—
112#14519734—21no—
113#14519734—21no—
114#14519734—21no—
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C4⋊C4×D61D412yes—
123C4⋊C4×D61D412yes—
124C4⋊C4×D61D412yes—
125C4⋊C4×D61D412yes—
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2311yescharacteristic
133C2×C4×Dic61C2×C411yescharacteristic
134C2×C4×Dic61C2×C411yescharacteristic
135#126×C61—22no—
136#126×C61—22no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C2411yescharacteristic
148C22×#6923—22no—
149C22×#6923—22no—
150C22×#6923—22no—
151C22×#6923—22no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—21no—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—42no—
166C2×C22⋊D61—81no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—81no—
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—22no—
184C2×D244—81no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×C4×D61C2×D412yes—
195C2×C4×D61C2×D412yes—
196C2×C4×D61C2×D412yes—
197C2×C4×D61C2×D412yes—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C22⋊#6923—22no—
201C22⋊#6923—22no—
202C22⋊#6923—22no—
203C22⋊#6923—22no—
204C22⋊#6923—22no—
205C22⋊#6923—22no—
206C22⋊#6923—22no—
207C22⋊#6923#4114yes—
208C4⋊#6923—44no—
209C4⋊#6923—82no—
210C4⋊#6923—82no—
211C4×#6923—44no—
212C4×#6923—82no—
213C4×#6923—82no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61C22⋊C412yes—
217C4⋊C4×C61C22⋊C412yes—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C42×C61—21no—
223C42×C61—21no—
224#11758198—22no—
225#11758198—21no—
226#11758198—21no—
227#11758198—22no—
228#11758198—22no—
229#11758198—21no—
230#11758198—21no—
231#11758198—21no—
232#11758198—21no—
233#11758198—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61C22⋊C412yes—
236C4⋊Dic61C22⋊C412yes—
237#11758196—22no—
238#11758196—21no—
239#11758196—21no—
240#11758196—22no—
241#11758196C22⋊C411yescharacteristic
242#11758196C22⋊C411yescharacteristic
243#11758196C22⋊C411yescharacteristic
244#11758196C22⋊C411yescharacteristic
245#11758196C22⋊C412yes—
246#11758196C22⋊C412yes—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61C23×C411yescharacteristic
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61C22×D412yes—
270C22×D61C2×#4112yes—
271C22×D61H(5,𝔽2)11yescharacteristic
272C22×D612−1+411yescharacteristic
273C2×#6923—24no—
274C2×#6923—42no—
275C2×#6923—42no—
276C2×#6923—42no—
277C2×#6923—42no—
278C2×#6923—42no—
279C2×#6923—42no—
280C2×#6923—42no—
281C2×#6923—42no—
282C2×#6923—42no—
283C2×#6923—42no—
284C2×#6923—42no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C2×C22⋊C412yes—
300C22⋊D61—42no—
301C22⋊D61—42no—
302C22⋊D61—42no—
303C22⋊D61—42no—
304C22⋊D61—82no—
305C2×Dic61—22no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—81no—
314C2×Dic61—81no—
315C2×Dic61C2×C22⋊C411yescharacteristic
316C2×Dic61C2×C22⋊C411yescharacteristic
317C2×Dic61C2×C22⋊C411yescharacteristic
318C2×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C411yescharacteristic
320D244—42no—
321D244—42no—
322D244—42no—
323D244—42no—
324D244—82no—
325C4×D61—24no—
326C4×D61—42no—
327C4×D61—42no—
328C4×D61—42no—
329C4×D61—42no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—42no—
333C4×D61—81no—
334C4×D61—81no—
335#22535—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61C22×C22⋊C411yescharacteristic
344C22×C61C4×#4111yescharacteristic
345C22×C61#52011yescharacteristic
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—42no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—81no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61#54812yes—
362C2×D61#55012yes—
363#6923—44no—
364#6923—82no—
365#6923—82no—
366#6923—82no—
367C4×C61—22no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—22no—
371C4×C61—41no—
372C4×C61—41no—
373C4×C61—41no—
374Dic61—21no—
375Dic61—21no—
376Dic61—21no—
377Dic61—22no—
378Dic61—41no—
379Dic61—41no—
380Dic61#41012yes—
381C2×#553—611no—
382#2345—612no—
383#1964—612no—
384#1964—612no—
385#1964—612no—
386#1799—611no—
387#1799—611no—
388#1799—611no—
389C4×#99—611no—
390C4×#99—611no—
391C4×#99—611no—
392C2×C61—21no—
393C2×C61—21no—
394C2×C61—81no—
395C2×C61#234111yescharacteristic
396C2×C61C2×#41011yescharacteristic
397C2×C61#288311yescharacteristic
398D61—22no—
399D61—22no—
400D61—81no—
401D61—81no—
402#553—1222no—
403#553—1222no—
404#553—1222no—
405#553—1222no—
406C2×#126—611no—
407C2×#126#692311yescharacteristic, complemented
408C2×#125—611no—
409C2×#123—611no—
410C2×#123—611no—
411C2×#121—611no—
412C2×#121—611no—
413C2×#121—611no—
414C2×#121—611no—
415C2×C4×D4—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×C4×D4—611no—
419C2×#117—611no—
420C22×C4⋊C4—611no—
421C2×#99—612no—
422C2×#99—612no—
423C2×#99—612no—
424C2×#99—612no—
425C2×#99—612no—
426C2×#99—612no—
427#389—1222no—
428#387—1222no—
429#387—1222no—
430#380—612no—
431#380—612no—
432#380—612no—
433C4×C4⋊C4—1222no—
434C4×C22⋊C4—612no—
435C4×C22⋊C4—612no—
436C4×C22⋊C4—612no—
437#342—611no—
438#342—611no—
439#342—611no—
440#342—611no—
441C61#2253511yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C22×D4—611no—
446C22×D4—611no—
447C22×D4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454#126—22no—
455#126—22no—
456#126—1222no—
457#126—1222no—
458#125—1222no—
459#125—1222no—
460#123—1222no—
461#123—1222no—
462#123—1222no—
463#123—1222no—
464#121—1222no—
465#121—1222no—
466#121—1222no—
467#121—1222no—
468#121—1222no—
469#121—1222no—
470#121—1222no—
471#121—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—1221no—
475C4×D4—1221no—
476C4×D4—1221no—
477C4×D4—1221no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482#117—1221no—
483#117—1221no—
484#117—1221no—
485#117—1221no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—612no—
490C2×C4⋊C4—612no—
491C2×C4⋊C4—612no—
492C2×C4⋊C4—612no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—1222no—
498C2×C4⋊C4—1222no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4C2×#692311yescharacteristic
501C2×C4⋊C4C2×#692311yescharacteristic
502C2×C4⋊C4C2×#692311yescharacteristic
503C2×C22⋊C4—612no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—611no—
507C2×C22⋊C4—611no—
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—612no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—612no—
514C2×C22⋊C4C2×#692311yescharacteristic
515C2×C22⋊C4C2×#692311yescharacteristic
516C2×C22⋊C4C2×#692311yescharacteristic
517C2×C42—611no—
518C2×C42—611no—
519C2×C42—1222no—
520C2×C42—1222no—
521C2×C42—1222no—
522C2×C42C2×#692311yescharacteristic
523#99—1224no—
524#99—1224no—
525#99—1224no—
526#99—2442no—
527#99—2442no—
528#99—2442no—
529#95—1222no—
530#95—1222no—
531#95—1222no—
532#95—1222no—
533#95—1222no—
534#95—1222no—
535C24—611no—
536C24—611no—
537C24—611no—
538C24C22×#692311yescharacteristic
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1222no—
544C2×D4—1222no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1222no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1222no—
551C2×D4—1221no—
552C2×D4—1222no—
553C2×D4—1221no—
554C2×D4—1222no—
555C2×D4—4881no—
556C2×D4—4881no—
557C2×D4—2442no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—612no—
566C22×C4—612no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—4881no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4C22×#692311yescharacteristic
586C22×C4C22×#692311yescharacteristic
587C22×C4C22×#692311yescharacteristic
588C22×C4C22×#692311yescharacteristic
589C22×C4C22×#692311yescharacteristic
590C22×C4C22×#692311yescharacteristic
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—611no—
594C4⋊C4—611no—
595C4⋊C4—611no—
596C4⋊C4—611no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—612no—
600C4⋊C4—612no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1222no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—4882no—
607C4⋊C4—4882no—
608C4⋊C4—2444no—
609C4⋊C4C22⋊#692312yes—
610C4⋊C4C22⋊#692312yes—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—614no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—1222no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1222no—
622C22⋊C4—1222no—
623C22⋊C4—1221no—
624C22⋊C4—1221no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—1222no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C42—21no—
634C42—21no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—4882no—
640C42—4882no—
641C42—2444no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—41no—
646C23—41no—
647C23—612no—
648C23—612no—
649C23—611no—
650C23—611no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663C23C23×#692311yescharacteristic
664D4—4882no—
665D4—4882no—
666D4—2442no—
667D4—2442no—
668D4—2442no—
669D4—2442no—
670D4—2442no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—611no—
686C2×C4—611no—
687C2×C4—611no—
688C2×C4—611no—
689C2×C4—612no—
690C2×C4—1224no—
691C2×C4—1222no—
692C2×C4—1224no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—4881no—
698C2×C4—4881no—
699C2×C4—4881no—
700C2×C4—4881no—
701C2×C4—2442no—
702C2×C4—2442no—
703C2×C4—2442no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4—2441no—
722C2×C4C2×C22⋊#692311yescharacteristic
723C2×C4C2×C22⋊#692311yescharacteristic
724C2×C4C2×C22⋊#692312yes—
725C2×C4C2×C22⋊#692312yes—
726C22—21no—
727C22—21no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—81no—
732C22—81no—
733C22—612no—
734C22—612no—
735C22—1222no—
736C22—1222no—
737C22—4881no—
738C22—4881no—
739C22—4881no—
740C22—4881no—
741C22—2442no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22—2441no—
746C22—2441no—
747C22—2441no—
748C22—2441no—
749C22—2441no—
750C22C22×C22⋊#692311yescharacteristic
751C22#41×#692311yescharacteristic
752C22#1684083111yescharacteristic
753C4—22no—
754C4—21no—
755C4—21no—
756C4—22no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—612no—
761C4—1221no—
762C4—1221no—
763C4—1221no—
764C4—1222no—
765C4—4882no—
766C4—4882no—
767C4—4882no—
768C4—2444no—
769C4—2441no—
770C4—2441no—
771C2—21no—
772C2—21no—
773C2—81no—
774C2—1222no—
775C2—1222no—
776C2—4881no—
777C2—4881no—
778C2#2146232411yescharacteristic
779C2D61⋊#41011yescharacteristic
780C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#126×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840463C2
cosocleC23×D61C24
hypercenterC2×#126#6923
hypocenterC61#22535
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #21462328C2semidirect
2. #21461960C2semidirect
3. #21461960C2semidirect
4. #21461959C2semidirect
5. #21461682C2semidirect
6. #21461681C2semidirect
7. #21461680C2semidirect
8. #21461566C2semidirect
9. C4×#14519836C2semidirect
10. #21461564C2semidirect
36. C2×#14519772C4semidirect
37. C2×#14519767C4semidirect
38. C2×#14519762C4semidirect
39. C2×#14519761C4semidirect
41. C2×#14519750C4semidirect
46. C2×#14519737C4semidirect
48. C2×#14519734C4semidirect
50. C2×#126×C61C4semidirect
407. C2×#126#6923semidirect
441. C61#22535semidirect

Maximal subgroups

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

subgroupindex
#214623282
#214619602
#214619592
#214616822
#214616812
#214616802
#214615662
C4×#145198362
#214615642
C2×#168404632
#2253561