Finite Group Databasebeta

← #30616747

Subgroups — #30616747

Order 15616.

1222 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462266C211yesmaximal, characteristic, complemented
2C4×#14519856C211yesmaximal, characteristic, complemented
3#21462010C212yesmaximal, complemented
4#21461960C212yesmaximal
5#21461843C212yesmaximal, complemented
6#21461842C212yesmaximal, complemented
7C4×#14519836C212yesmaximal, complemented
8C4×#14519835C212yesmaximal, complemented
9C2×#16840290C211yesmaximal, characteristic
10C2×#14519856C2212yes—
11C2×#14519836C2214yes—
12C2×#14519835C2214yes—
13#16840707—21no—
14#16840706—21no—
15#16840705C2212yes—
16#16840704C2212yes—
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923—21no—
19C4×C4⋊#6923—21no—
20C4×C22⋊#6923C2212yes—
21C4×C22⋊#6923C2212yes—
22C4×C22⋊#6923C2212yes—
23#16840698—21no—
24#16840698—21no—
25C42×#6923—21no—
26#16840640C2214yes—
27#16840640C2214yes—
28#16840290—21no—
29#16840290—21no—
30#16840290—21no—
31#16840290—21no—
32#16840290—21no—
33#16840290—21no—
34#16840290—21no—
35#16840290—21no—
36C2×#14519772C411yescharacteristic, complemented
37C2×#14519770C411yescharacteristic, complemented
38C2×#14519767C411yescharacteristic, complemented
39C2×#14519763C411yescharacteristic, complemented
40C2×#14519762C2211yescharacteristic
41C2×#14519759C2211yescharacteristic
42C2×#14519755C2211yescharacteristic
43C2×#14519750C2211yescharacteristic
44C2×C4×Dic122C411yescharacteristic, complemented
45C2×C4×D244C2211yescharacteristic
46C2×C4×C22⋊D61C411yescharacteristic, complemented
47C2×C4×C22⋊D61C2211yescharacteristic
48C2×#14519734C411yescharacteristic, complemented
49C2×C42×D61C2211yescharacteristic
50C2×#117×C61C411yescharacteristic, complemented
51#14519856—28no—
52C2×C4⋊#6923—22no—
53C2×C4⋊#6923—22no—
54C2×C22⋊#6923C2314yes—
55C2×C22⋊#6923C2314yes—
56C2×C4×#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—22no—
59C2×C4×#6923—22no—
60#14519836—28no—
61#14519835—28no—
62(C2×#6923)⋊C4—22no—
63(C2×#6923)⋊C4—22no—
64(C2×#6923)⋊C4—22no—
65(C2×#6923)⋊C4—22no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68C22×Dic122C2×C411yescharacteristic
69C22×D244C2311yescharacteristic
70C22×C22⋊D61C2×C411yescharacteristic
71C22×C22⋊D61C2311yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76#14519772—21no—
77#14519772—21no—
78#14519772—21no—
79#14519772—21no—
80#14519770—21no—
81#14519770—21no—
82#14519770—21no—
83#14519770—21no—
84#14519767—21no—
85#14519767—21no—
86#14519767—21no—
87#14519767—21no—
88#14519763—21no—
89#14519763—21no—
90#14519763—21no—
91#14519763—21no—
92#14519762—21no—
93#14519762—21no—
94#14519762—21no—
95#14519762—21no—
96#14519759—21no—
97#14519759—21no—
98#14519759—21no—
99#14519759—21no—
100#14519755—21no—
101#14519755—21no—
102#14519755—21no—
103#14519755—21no—
104#14519750—21no—
105#14519750—21no—
106#14519750—21no—
107#14519750—21no—
108C4×Dic122—21no—
109C4×Dic122—21no—
110C4×Dic122—21no—
111C4×Dic122—21no—
112C4×D244—21no—
113C4×D244—21no—
114C4×D244—21no—
115C4×D244—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124#14519734—21no—
125#14519734—21no—
126#14519734—21no—
127#14519734—21no—
128C2×C4⋊Dic61C2×C411yescharacteristic
129C2×C4⋊Dic61C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C2×#11758196C2×C411yescharacteristic
135C2×#11758196C2×C411yescharacteristic
136C2×C22⋊Dic61C2×C411yescharacteristic
137C2×C22⋊Dic61C2×C411yescharacteristic
138C2×#11758198C2×C411yescharacteristic
139C2×#11758198C2×C411yescharacteristic
140C2×#11758198C2×C411yescharacteristic
141C2×#11758198C2×C411yescharacteristic
142C2×#11758198C2311yescharacteristic
143C2×#11758198C2311yescharacteristic
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61C2×C411yescharacteristic
147C2×C4×Dic61C2×C411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C42×D61D411yescharacteristic
156C23×C4×C61C2×C411yescharacteristic
157#117×C61—21no—
158#117×C61—21no—
159#117×C61—21no—
160#117×C61—21no—
161C2×C4⋊C4×C61C2×C411yescharacteristic
162C2×C4⋊C4×C61C2×C411yescharacteristic
163C2×C22⋊C4×C61C2×C411yescharacteristic
164C2×C22⋊C4×C61C2×C411yescharacteristic
165C2×C42×C61C2×C411yescharacteristic
166C2×C42×C61C2×C411yescharacteristic
167C24×C61C22×C411yescharacteristic
168C23×D61C22×C411yescharacteristic
169C23×D61C2411yescharacteristic
170C22×#6923—24no—
171C22×#6923—24no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—42no—
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C22×C4×C61C22×C411yescharacteristic
180C22×C4×C61C22×C411yescharacteristic
181C2×C22⋊D61—21no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—24no—
184C2×C22⋊D61—21no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—42no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—24no—
196C2×C4×D61—24no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2×D411yescharacteristic
205C2×C4×D61C2×D411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61C2×D411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—42no—
217C22⋊#6923—24no—
218C22⋊#6923—24no—
219C22⋊#6923—24no—
220C22⋊#6923#4118yes—
221C4⋊#6923—28no—
222C4⋊#6923—44no—
223C4×#6923—28no—
224C4×#6923—44no—
225C4×#6923—44no—
226C4×#6923—44no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61C22⋊C411yescharacteristic
238C42×C61C22⋊C411yescharacteristic
239C42×C61C22⋊C411yescharacteristic
240C42×C61C22⋊C411yescharacteristic
241C22⋊Dic61—21no—
242C22⋊Dic61—21no—
243C22⋊Dic61—21no—
244C22⋊Dic61—21no—
245#11758198—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261#11758196—21no—
262#11758196—21no—
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61C22⋊C411yescharacteristic
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22⋊C411yescharacteristic
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61C23×C411yescharacteristic
292C22×D61—21no—
293C22×D61—22no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61C22×D411yescharacteristic
299C22×D61C22×D411yescharacteristic
300C22×D61C2×#4114yes—
301C2×#6923—28no—
302C2×#6923—44no—
303C2×#6923—44no—
304C2×#6923—44no—
305C2×#6923—44no—
306C2×#6923—44no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—41no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C2×C22⋊C411yescharacteristic
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343D244—42no—
344D244—42no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—42no—
358C4×D61—42no—
359Dic122—42no—
360Dic122—42no—
361#21421—611nomaximal, Sylow
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—82no—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61C4×#4112yes—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—44no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—82no—
379C2×D61#52512yes—
380C2×D61#53212yes—
381#6923—48no—
382#6923—84no—
383C4×C61—21no—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61#41012yes—
392Dic61—21no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—21no—
397Dic61—41no—
398Dic61—41no—
399Dic61—41no—
400Dic61#41012yes—
401C2×#529—611no—
402#2283—611no—
403C4×#117—611no—
404#1996—612no—
405#1964—612no—
406#1899—612no—
407#1899—612no—
408C4×#99—612no—
409C4×#99—612no—
410C2×C61—22no—
411C2×C61—81no—
412C2×C61#229711yescharacteristic
413C2×C61C2×#41011yescharacteristic
414C2×C61C2×#41011yescharacteristic
415D61—22no—
416D61—22no—
417D61—81no—
418#529—1221no—
419#529—1221no—
420#529—1221no—
421#529—1221no—
422#529—1221no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426C2×#126—611no—
427C2×#126—611no—
428C2×#125—611no—
429C2×#124—611no—
430C2×#123—611no—
431C2×#123—611no—
432C2×C22⋊Q8—611no—
433C2×#121—611no—
434C2×C4×Q8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×#117—611no—
439C2×#117—612no—
440C2×#117#692311yescharacteristic, complemented
441C22×C42—611no—
442C2×#99—614no—
443C2×#99—614no—
444#383—1221no—
445#382—1221no—
446#381—612no—
447#380—612no—
448C4×C4⋊C4—1221no—
449C4×C4⋊C4—1221no—
450C4×C4⋊C4—1221no—
451C4×C22⋊C4—612no—
452C4×C22⋊C4—612no—
453C4×C22⋊C4—612no—
454#376—1221no—
455#376—1221no—
456C43—1221no—
457#342—614no—
458#342—614no—
459C61#2142111yescharacteristic, complemented, Sylow
460C22×Q8—611no—
461C22×D4—611no—
462C22×D4—611no—
463C22×D4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4C2×#692311yescharacteristic
469#126—1221no—
470#126—1221no—
471#126—1221no—
472#126—1221no—
473#126—1221no—
474#126—1221no—
475#126—1221no—
476#126—1221no—
477#125—1221no—
478#125—1221no—
479#125—1221no—
480#125—1221no—
481#124—1221no—
482#124—1221no—
483#124—1221no—
484#124—1221no—
485#123—1221no—
486#123—1221no—
487#123—1221no—
488#123—1221no—
489#123—1221no—
490#123—1221no—
491#123—1221no—
492#123—1221no—
493C22⋊Q8—1221no—
494C22⋊Q8—1221no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497#121—1221no—
498#121—1221no—
499#121—1221no—
500#121—1221no—
501C4×Q8—1221no—
502C4×Q8—1221no—
503C4×Q8—1221no—
504C4×Q8—1221no—
505C4×D4—1221no—
506C4×D4—1221no—
507C4×D4—1221no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1221no—
513C4×D4—1221no—
514C4×D4—1221no—
515C4×D4—1221no—
516C4×D4—1221no—
517#117—21no—
518#117—21no—
519#117—21no—
520#117—21no—
521#117—1228no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—611no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4C2×#692311yescharacteristic
537C2×C4⋊C4C2×#692311yescharacteristic
538C2×C22⋊C4—614no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4—611no—
542C2×C22⋊C4—611no—
543C2×C22⋊C4—611no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4C2×#692311yescharacteristic
549C2×C22⋊C4C2×#692311yescharacteristic
550C2×C42—611no—
551C2×C42—611no—
552C2×C42—611no—
553C2×C42—611no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—1222no—
563C2×C42—1222no—
564C2×C42—1222no—
565C2×C42—1222no—
566C2×C42C2×#692311yescharacteristic
567C2×C42C2×#692311yescharacteristic
568#99—1228no—
569#99—1228no—
570#95—1222no—
571#95—1222no—
572#95—1222no—
573#95—1222no—
574#95—1222no—
575#95—1222no—
576C24—611no—
577C24—611no—
578C24C22×#692311yescharacteristic
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—2442no—
582C2×D4—1224no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1224no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—2442no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1224no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4C22×#692311yescharacteristic
621C22×C4C22×#692311yescharacteristic
622C22×C4C22×#692311yescharacteristic
623C22×C4C22×#692311yescharacteristic
624C22×C4C22×#692311yescharacteristic
625C22×C4C22×#692311yescharacteristic
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
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—1228no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—2444no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—618no—
653C22⋊C4—1221no—
654C22⋊C4—1221no—
655C22⋊C4—1221no—
656C22⋊C4—1221no—
657C22⋊C4—1221no—
658C22⋊C4—1221no—
659C22⋊C4—1221no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1224no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C42—21no—
673C42—21no—
674C42—611no—
675C42—611no—
676C42—611no—
677C42—611no—
678C42—611no—
679C42—611no—
680C42—611no—
681C42—611no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—1228no—
687C42—1221no—
688C42—1221no—
689C42—2444no—
690C42—2444no—
691C42—2444no—
692C42C22⋊#692311yescharacteristic
693C42C22⋊#692311yescharacteristic
694C42C22⋊#692311yescharacteristic
695C42C22⋊#692311yescharacteristic
696C23—21no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—611no—
701C23—611no—
702C23—614no—
703C23—1222no—
704C23—1221no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23C23×#692311yescharacteristic
710Q8—2442no—
711Q8—2442no—
712D4—2442no—
713D4—2442no—
714D4—2442no—
715D4—2442no—
716D4—2442no—
717D4—2442no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—611no—
730C2×C4—611no—
731C2×C4—611no—
732C2×C4—611no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1228no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2442no—
755C2×C4—2441no—
756C2×C4—2444no—
757C2×C4—2444no—
758C2×C4—2444no—
759C2×C4—2444no—
760C2×C4—2444no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4C2×C22⋊#692311yescharacteristic
765C2×C4C2×C22⋊#692311yescharacteristic
766C2×C4C2×C22⋊#692311yescharacteristic
767C2×C4C2×C22⋊#692311yescharacteristic
768C2×C4C2×C22⋊#692311yescharacteristic
769C2×C4C2×C22⋊#692311yescharacteristic
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—82no—
776C22—612no—
777C22—612no—
778C22—1221no—
779C22—1221no—
780C22—1221no—
781C22—1221no—
782C22—4882no—
783C22—2444no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22C22×C22⋊#692311yescharacteristic
788C22#41×#692312yes—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—21no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—612no—
798C4—1221no—
799C4—1221no—
800C4—1221no—
801C4—1221no—
802C4—1221no—
803C4—4884no—
804C4—2448no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C4#1684074112yes—
809C2—22no—
810C2—81no—
811C2—1222no—
812C2—1222no—
813C2—4881no—
814C2#2146228011yescharacteristic
815C2C2×#1684074111yescharacteristic
816C2D61⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519750C22
cosocleC23×D61C24
hypercenterC2×#117#6923
hypocenterC61#21421
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462266C2semidirect
2. C4×#14519856C2semidirect
3. #21462010C2semidirect
5. #21461843C2semidirect
6. #21461842C2semidirect
7. C4×#14519836C2semidirect
8. C4×#14519835C2semidirect
36. C2×#14519772C4semidirect
37. C2×#14519770C4semidirect
38. C2×#14519767C4semidirect
39. C2×#14519763C4semidirect
44. C2×C4×Dic122C4semidirect
46. C2×C4×C22⋊D61C4semidirect
48. C2×#14519734C4semidirect
50. C2×#117×C61C4semidirect
440. C2×#117#6923semidirect
459. C61#21421semidirect

Maximal subgroups

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

subgroupindex
#214622662
C4×#145198562
#214620102
#214619602
#214618432
#214618422
C4×#145198362
C4×#145198352
C2×#168402902
#2142161