Finite Group Databasebeta

← #29695466

Subgroups — #29695466

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840414C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839759C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446740C211yesmaximal, characteristic, complemented
7#21446619C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic, complemented
9#21446132C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445757C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758222C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840414—24no—
20#16840414C418yescomplemented
21C2×#14519775C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519759—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61—21no—
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic
33#16839759—24no—
34#16839757—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839662—21no—
49#16839656—21no—
50#16839651—21no—
51#16839631C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54#16839613—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yes—
70C2×#11758222—22no—
71C2×#11758222—22no—
72C2×#11758222—22no—
73C2×#11758222—41no—
74C2×#11758222—41no—
75C2×#11758222C2×C414yes—
76C22×Dic122C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—22no—
88C2×C8×D61—22no—
89C2×C8×D61—41no—
90#14519775—22no—
91#14519775C2×C414yes—
92#14519762—28no—
93#14519759—28no—
94#14519757—22no—
95#14519757C2×C414yes—
96#14519750—28no—
97#14519739—22no—
98#14519739C2×C414yes—
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519736—22no—
102#14519736—41no—
103#14519735—22no—
104#14519735—41no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196D411yescharacteristic
113C4⋊C4×D61—28no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61D411yescharacteristic
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198D411yescharacteristic
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519706—22no—
126#14519702—22no—
127#14519702—22no—
128#14519701—22no—
129#14519701—41no—
130#14519700—41no—
131#14519700—41no—
132#14519699—22no—
133#14519699D414yescomplemented
134#14519697—22no—
135#14519697—22no—
136C22⋊#92418—22no—
137#14519689—22no—
138C8×Dic61—22no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22×C8×C61—22no—
144C22×C8×C61—22no—
145C22×C8×C61—41no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61C2×C414yes—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#103×C61—22no—
157#103×C61—41no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C23×D61—21no—
161C23×D61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D412yes—
179C22×C4×C61C2411yescharacteristic
180C2×C22⋊D61—24no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—22no—
183C2×C22⋊D61—42no—
184C2×C22⋊D61—42no—
185C2×C22⋊D61C22⋊C414yes—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61C2×D411yescharacteristic
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192#11758226—28no—
193#11758226—44no—
194#11758226—44no—
195#11758226—44no—
196#11758222—28no—
197#11758222—44no—
198#11758222—44no—
199#11758222—44no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—24no—
204C2×D244—42no—
205C2×D244—42no—
206C2×D244C22×C412yes—
207C2×D244C2×D412yes—
208C2×D244#4112yes—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—42no—
220C2×C4×D61—42no—
221C2×C4×D61—42no—
222C2×C4×D61C22×C412yes—
223C2×C4×D61C2×D412yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22×C412yes—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—44no—
236C2×C8×C61C2×D412yes—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C22×C412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—81no—
246C22⋊Dic61—42no—
247C22⋊Dic61C22⋊C414yes—
248#11758198—24no—
249#11758198—24no—
250#11758198—42no—
251#11758198—81no—
252#11758198C22⋊C414yes—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61C2×D412yes—
258#11758196—24no—
259#11758196—24no—
260#11758196—42no—
261#11758196—81no—
262#11758196C22⋊C414yes—
263C4×Dic61—42no—
264C4×Dic61—42no—
265C4×Dic61—42no—
266C4×Dic61C22×C412yes—
267C4×Dic61C2×D412yes—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C8×D61—44no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61C2×C22⋊C412yes—
282C23×C61C22×D411yescharacteristic
283C22×D61—22no—
284C22×D61—21no—
285C22×D61—22no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61C2×C22⋊C412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—41no—
300Q8×C61—41no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61C2×C22⋊C412yes—
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C2×#4111yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C2×C4×C61H(5,𝔽2)11yescharacteristic
326C22⋊D61—28no—
327C22⋊D61—48no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61C2×C22⋊C412yes—
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61C2×C22⋊C412yes—
344C2×Dic61#13512yes—
345C2×Dic61#13512yes—
346D244—22no—
347D244—22no—
348D244—22no—
349D244—48no—
350D244C4×D414yes—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—48no—
356C4×D61—48no—
357C4×D61—48no—
358Dic122—22no—
359Dic122—22no—
360Dic122—41no—
361Dic122—41no—
362C8×C61—22no—
363C8×C61—41no—
364#92418—41no—
365#92418—41no—
366#22417—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61D4211yescharacteristic
376C22×C61#54611yescharacteristic
377C22×C61C2×#13511yescharacteristic
378C22×C61C2×#13511yescharacteristic
379C22×C61#57711yescharacteristic
380C22×C61#57811yescharacteristic
381C2×D61—22no—
382C2×D61—24no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—41no—
388C2×D61—42no—
389C2×D61—41no—
390C2×D61—42no—
391C2×D61—41no—
392C2×D61—42no—
393C2×D61—41no—
394C2×D61—42no—
395C4×C61—22no—
396C4×C61—42no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61—81no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#51811yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404Dic61—22no—
405Dic61—22no—
406Dic61—42no—
407Dic61—42no—
408Dic61—81no—
409Dic61#41614yescomplemented
410C2×#547—611no—
411C2×C8×D4—611no—
412C2×#416—611no—
413C2×#416—611no—
414#2354—611no—
415#1981—611no—
416#1956—611no—
417#1892—611no—
418#1892D6111yescharacteristic, complemented
419#1873—611no—
420#1873—611no—
421#1802—611no—
422#1788—611no—
423#1788—611no—
424C4×#102—611no—
425C2×C61—42no—
426C2×C61D4×C22⋊C411yescharacteristic
427C2×C61C2×#41611yescharacteristic
428C2×C61#289811yescharacteristic
429C2×C61#328311yescharacteristic
430C2×C61#328411yescharacteristic
431C2×C61#330211yescharacteristic
432C2×C61#330311yescharacteristic
433D61—42no—
434D61—44no—
435C22×#41—611no—
436C22×#41—611no—
437C23×C8—611no—
438C23×C8C2×D6111yescharacteristic
439#547—618no—
440#547—1224no—
441C2×C4⋊Q8—611no—
442C2×#123—1221no—
443C2×#123—1221no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8C2×D6111yescharacteristic
446C2×#121—1221no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×#117—611no—
450C2×#117—611no—
451C22×C4⋊C4—1221no—
452C8×D4—1224no—
453C2×C4⋊C8—611no—
454#416—1224no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C4×C8—611no—
471#390—1221no—
472#388—1221no—
473#388—1221no—
474#384—611no—
475#380—611no—
476#380C2×D6111yescharacteristic
477C4×C4⋊C4—611no—
478C4×C4⋊C4—1221no—
479#340—611no—
480#340—611no—
481#340C2×D6111yescharacteristic
482#340C2×D6111yescharacteristic
483C61#2241711yescharacteristic, complemented, Sylow
484C2×#41—614no—
485C2×#41—614no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—1222no—
490C2×#41—1222no—
491C2×#41—1222no—
492C2×#41—2441no—
493C2×#41—2441no—
494C2×#41—2441no—
495C2×#41—2441no—
496C22×Q8—611no—
497C22×Q8C22×D6111yescharacteristic
498C22×D4—611no—
499C22×D4—611no—
500C22×D4—1221no—
501C22×D4—1221no—
502C23×C4—611no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4C22×D6111yescharacteristic
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—1222no—
513C22×C8—1222no—
514C22×C8—2441no—
515C22×C8C22×D6111yescharacteristic
516C22×C8C22×D6111yescharacteristic
517C4⋊Q8—614no—
518C4⋊Q8—1222no—
519#123—1228no—
520#123—1228no—
521C22⋊Q8—22no—
522C22⋊Q8—614no—
523C22⋊Q8—1222no—
524C22⋊Q8C4×D6114yes—
525#121—1228no—
526C4×D4—614no—
527C4×D4—614no—
528C4×D4—614no—
529C4×D4—1222no—
530#117—1222no—
531#117—1222no—
532#117—2441no—
533#117—2441no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1228no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C42—611no—
557C2×C42—1221no—
558C2×C42—1221no—
559C2×C42—1221no—
560C4⋊C8—1222no—
561#103—22no—
562#103—41no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—2441no—
567#103—2441no—
568#103—2441no—
569#102—614no—
570#102—1222no—
571#102—1222no—
572#102—1222no—
573C22⋊C8—1222no—
574C22⋊C8—1222no—
575C4×C8—1222no—
576#95—21no—
577#95—1221no—
578#95—1221no—
579C24—611no—
580C24—1221no—
581C24D4×D6111yescharacteristic
582#41—1228no—
583#41—1228no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587#41—2444no—
588#41—2444no—
589#41—2444no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—612no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8C2×C4×D6112yes—
602C2×D4—614no—
603C2×D4—612no—
604C2×D4—612no—
605C2×D4—612no—
606C2×D4—1224no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1224no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—2442no—
614C2×D4—2442no—
615C2×D4—2442no—
616C2×D4—2442no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1224no—
639C22×C4—1221no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4—2442no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4C2×C4×D6112yes—
647C22×C4D4×D6112yes—
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—44no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8D4×D6112yes—
664C4⋊C4—21no—
665C4⋊C4—24no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—614no—
671C4⋊C4—612no—
672C4⋊C4—1224no—
673C4⋊C4—1224no—
674C4⋊C4—1224no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—4881no—
679C4⋊C4—2442no—
680C4⋊C4C2×C4×D6112yes—
681C22⋊C4—24no—
682C22⋊C4—81no—
683C22⋊C4—614no—
684C22⋊C4—614no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—4881no—
688C22⋊C4—2442no—
689C22⋊C4—2442no—
690C42—612no—
691C42—612no—
692C42—2442no—
693C42—2442no—
694C42—2442no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—612no—
702C23—1222no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1222no—
709C23—1221no—
710C23—1222no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23C22⋊C4×D6112yes—
716C23C2×D4×D6111yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721Q8—1222no—
722Q8—1222no—
723Q8—2441no—
724Q8—2441no—
725D4—614no—
726D4—1228no—
727D4—1222no—
728D4—1222no—
729D4—1222no—
730D4—2448no—
731D4—2448no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—612no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—2448no—
766C2×C4—2448no—
767C2×C4—2448no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22⋊C4×D6112yes—
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4#41×D6111yescharacteristic
780C2×C4#1451982211yescharacteristic
781C2×C4#1451982311yescharacteristic
782C8—22no—
783C8—41no—
784C8—2441no—
785C8—2441no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—1222no—
794C22—1222no—
795C22—1224no—
796C22—1222no—
797C22—2442no—
798C22—2441no—
799C22—2442no—
800C22—2441no—
801C22—2442no—
802C22—2441no—
803C22—2442no—
804C22—2441no—
805C22—2442no—
806C22—2442no—
807C22C2×C22⋊C4×D6111yescharacteristic
808C22#1684039611yescharacteristic
809C22#1684040111yescharacteristic
810C22#135×D6111yescharacteristic
811C22#135×D6111yescharacteristic
812C22#1684056811yescharacteristic
813C22#1684057511yescharacteristic
814C4—22no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—614no—
820C4—1222no—
821C4—1222no—
822C4—4881no—
823C4—2442no—
824C4—2442no—
825C4C4×D4×D6111yescharacteristic
826C4#1684023411yescharacteristic
827C4#1684039411yescharacteristic
828C4#1684040411yescharacteristic
829C2—42no—
830C2—2442no—
831C2—2444no—
832C2#2144863711yescharacteristic
833C2#416×D6111yescharacteristic
834C2#2145434711yescharacteristic
835C2#2145753811yescharacteristic
836C2#2145754611yescharacteristic
837C2#2145773111yescharacteristic
838C2#2145774211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC2×#16840414C2
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#22417
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. C2×#16839759C2semidirect
4. C2×#16839757C2semidirect
5. #21448763C2semidirect
6. #21446740C2semidirect
7. #21446619C2semidirect
8. #21446241C2semidirect
9. #21446132C2semidirect
10. #21446130C2semidirect
11. #21445818C2semidirect
12. #21445758C2semidirect
13. #21445757C2semidirect
14. #21445633C2semidirect
15. C61×#1892C2semidirect
20. #16840414C4semidirect
133. #14519699D4semidirect
409. Dic61#416semidirect
418. #1892D61semidirect
483. C61#22417semidirect

Maximal subgroups

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

subgroupindex
C2×#168404142
C2×C8×C22⋊D612
C2×#168397592
C2×#168397572
#214487632
#214467402
#214466192
#214462412
#214461322
#214461302
#214458182
#214457582
#214457572
#214456332
C61×#18922
#2241761