Finite Group Databasebeta

← #29695453

Subgroups — #29695453

Order 15616.

1498 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840424C211yesmaximal, characteristic
2C2×#16839827C211yesmaximal, characteristic, complemented
3C2×#16839757C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5#21448745C211yesmaximal, characteristic, complemented
6#21446749C211yesmaximal, characteristic, complemented
7#21446628C211yesmaximal, characteristic, complemented
8#21446246C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21446130C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14C4×#14519701C211yesmaximal, characteristic, complemented
15C61×#1805C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840424—24no—
21#16840424C418yescomplemented
22C2×#14519765—21no—
23C2×#14519765C2211yescharacteristic
24C2×#14519757—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519752—21no—
27C2×#14519752C2211yescharacteristic
28C2×C4×D244—21no—
29C2×C4×D244C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839827—24no—
33#16839757—24no—
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40#103×D61—24no—
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48#16839651—21no—
49#16839645—21no—
50#16839640—21no—
51#16839619C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4×C4⋊Dic61C2211yescharacteristic
54#16839609—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#382C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yescomplemented
70C22×Dic122—21no—
71C22×Dic122C2311yescharacteristic
72C2×Q8×D61—22no—
73C2×Q8×D61—22no—
74C2×Q8×D61—22no—
75C2×Q8×D61—41no—
76C2×Q8×D61—41no—
77C2×Q8×D61C2×C414yes—
78C22×D244—21no—
79C22×D244—21no—
80C22×D244D411yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94C2×C8×D61—41no—
95#14519765—22no—
96#14519765—28no—
97#14519765C2×C414yescomplemented
98#14519757—22no—
99#14519757—28no—
100#14519757C2×C414yescomplemented
101#14519752—28no—
102#14519752—22no—
103#14519752C2×C414yes—
104C4×D244—28no—
105C4×D244C2×C414yes—
106C4×D244D414yes—
107#14519735—22no—
108#14519735—41no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61D411yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61—41no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×#11758198D411yescharacteristic
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127#14519702—22no—
128#14519702—41no—
129#14519701—22no—
130#14519701D414yescomplemented
131#14519700—22no—
132#14519700—41no—
133#14519699—22no—
134#14519699—41no—
135#14519697—22no—
136#14519697—41no—
137#14519689—22no—
138#14519689—22no—
139C4×#92418—22no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×Q8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C4×Q8×C61—22no—
147C4×Q8×C61C2×C414yescomplemented
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C4⋊C8×C61—22no—
155#103×C61—22no—
156#103×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159C23×D61—21no—
160C23×D61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61C22×C412yes—
166C2×Q8×C61C2×D412yes—
167C2×Q8×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2411yescharacteristic
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758226—28no—
181#11758226—44no—
182#11758226—44no—
183#11758226—44no—
184Q8×D61—28no—
185Q8×D61—44no—
186Q8×D61—44no—
187Q8×D61—44no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—21no—
191C2×D244—21no—
192C2×D244—21no—
193C2×D244—21no—
194C2×D244—24no—
195C2×D244—24no—
196C2×D244—21no—
197C2×D244—42no—
198C2×D244—42no—
199C2×D244—42no—
200C2×D244—42no—
201C2×D244C22⋊C414yes—
202C2×D244C22×C412yes—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—42no—
217C2×C4×D61—42no—
218C2×C4×D61—42no—
219C2×C4×D61—81no—
220C2×C4×D61C22×C412yes—
221C2×C4×D61C22×C412yes—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2×D412yes—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—24no—
230C2×Dic122—42no—
231C2×Dic122—42no—
232C2×Dic122C22×C412yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C22×C412yes—
246C42×C61—24no—
247C42×C61C22×C412yes—
248C42×C61C2×D412yes—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253#11758198—42no—
254#11758198—42no—
255#11758198—81no—
256#11758198C22⋊C414yes—
257#11758198C22⋊C414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22⋊C414yes—
263C4⋊Dic61C2×D412yes—
264#11758196—42no—
265C4×Dic61—42no—
266C4×Dic61—81no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418C2×D412yes—
273C8×D61—44no—
274C8×D61—44no—
275C23×C61C22×D411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—22no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—41no—
290C22×D61—41no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61C2×C22⋊C412yes—
294C22×D61C2×C22⋊C412yes—
295C22×D61#13512yes—
296C22×D61#13512yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61C4×D414yes—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
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×C61C2×C22⋊C412yes—
318C2×C4×C61C2×C22⋊C412yes—
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C2×#4111yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C2×C4×C61H(5,𝔽2)11yescharacteristic
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61C2×C22⋊C412yes—
339C2×Dic61C2×C22⋊C412yes—
340D244—28no—
341D244—22no—
342D244—22no—
343D244—48no—
344D244—48no—
345D244—41no—
346D244—41no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—48no—
356C4×D61—48no—
357C4×D61—84no—
358Dic122—22no—
359Dic122—22no—
360Dic122—48no—
361Dic122—41no—
362Dic122—41no—
363C8×C61—41no—
364C8×C61—41no—
365#92418—22no—
366#92418—41no—
367#22416—611nomaximal, Sylow
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61C2×#13511yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C22×C61#57711yescharacteristic
374C22×C61#57811yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—81no—
392C2×D61—81no—
393C2×D61—81no—
394C2×D61—81no—
395C2×D61#41614yescomplemented
396C4×C61—24no—
397C4×C61—22no—
398C4×C61—22no—
399C4×C61—42no—
400C4×C61—81no—
401C4×C61—81no—
402C4×C61C2×C4×D411yescharacteristic
403C4×C61#51811yescharacteristic
404C4×C61D4211yescharacteristic
405C4×C61#54611yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—81no—
411C2×#548—611no—
412C2×C8×D4—611no—
413C2×#416—611no—
414C22×#103—611no—
415#2352—611no—
416#1983—611no—
417#1958—611no—
418#1893—611no—
419#1892—611no—
420#1874—611no—
421#1873—611no—
422#1805D6111yescharacteristic, complemented
423#1788—611no—
424#1787—611no—
425C4×#103—611no—
426C2×C61D4×C22⋊C411yescharacteristic
427C2×C61C2×#41611yescharacteristic
428C2×C61#289811yescharacteristic
429C2×C61#328211yescharacteristic
430C2×C61#328511yescharacteristic
431C2×C61#330011yescharacteristic
432C2×C61#330111yescharacteristic
433D61—24no—
434D61—42no—
435D61—82no—
436C22×#41—611no—
437C23×Q8—611no—
438C23×C8—611no—
439C23×C8—611no—
440#548—618no—
441#548—1224no—
442C2×#124—611no—
443C2×#124—1221no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8—1221no—
446C2×#121—611no—
447C2×#121—1221no—
448C2×C4×Q8C2×D6111yescharacteristic
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×#117—611no—
452C22×C4⋊C4—611no—
453C8×D4—1224no—
454C2×C4⋊C8C2×D6111yescharacteristic
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—1224no—
463C2×#103C2×D6111yescharacteristic
464C2×#103C2×D6111yescharacteristic
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C4×C8—611no—
472#388—1221no—
473#387—1221no—
474#386—1221no—
475#382C2×D6111yescharacteristic
476#380—611no—
477#380—611no—
478C4×C4⋊C4—611no—
479C4×C22⋊C4—1221no—
480#340—611no—
481#340—611no—
482#340C2×D6111yescharacteristic
483#340C2×D6111yescharacteristic
484C61#2241611yescharacteristic, complemented, Sylow
485C2×#41—614no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—2441no—
490C2×#41—2441no—
491C22×Q8—614no—
492C22×Q8—611no—
493C22×Q8—1221no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1222no—
497C22×Q8—2441no—
498C22×Q8—2441no—
499C22×Q8C22×D6111yescharacteristic
500C22×D4—611no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4—1221no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C22×C8—611no—
510C22×C8—611no—
511C22×C8—1222no—
512C22×C8—1222no—
513C22×C8—1222no—
514C22×C8—1222no—
515C22×C8—2441no—
516C22×C8—2441no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519#124—614no—
520#124—1228no—
521#124—1222no—
522C22⋊Q8—614no—
523C22⋊Q8—1228no—
524C22⋊Q8—1222no—
525#121—614no—
526#121—1222no—
527#121—1228no—
528C4×Q8—22no—
529C4×Q8C4×D6114yescomplemented
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—1228no—
533#117—1222no—
534#117—2441no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1222no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—2441no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—21no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559C4⋊C8—22no—
560#103—22no—
561#103—22no—
562#103—614no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—2441no—
567#103—2441no—
568#102—1222no—
569#102—1222no—
570#102—2441no—
571#102—2441no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C4×C8—1222no—
575#95—21no—
576#95—21no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—611no—
581C24—611no—
582C24—1221no—
583#41—1228no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—612no—
591C2×Q8—1224no—
592C2×Q8—1221no—
593C2×Q8—1228no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—2442no—
599C2×Q8—2442no—
600C2×Q8—2444no—
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8C2×C4×D6112yes—
604C2×Q8D4×D6112yes—
605C2×Q8#1175822612yes—
606C2×D4—612no—
607C2×D4—614no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4—2442no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4—2442no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—612no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—1224no—
632C22×C4—1224no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—4881no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4—2442no—
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—612no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—2444no—
667C2×C8—2444no—
668C4⋊C4—21no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—614no—
675C4⋊C4—612no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—2442no—
681C4⋊C4C2×C4×D6112yes—
682C22⋊C4—614no—
683C22⋊C4—614no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—4881no—
689C22⋊C4—2442no—
690C22⋊C4—2442no—
691C42—24no—
692C42—4881no—
693C42—2442no—
694C42C2×C4×D6112yes—
695C42D4×D6112yes—
696C23—612no—
697C23—612no—
698C23—612no—
699C23—612no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1222no—
711C23—2441no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23—2441no—
716C23—2441no—
717C23C2×D4×D6111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—1222no—
722Q8—1222no—
723Q8—2448no—
724Q8—2441no—
725Q8—2441no—
726Q8#1451973914yes—
727D4—1228no—
728D4—1222no—
729D4—1222no—
730D4—2448no—
731D4—2448no—
732D4—2441no—
733D4—2441no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
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—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—4884no—
767C2×C4—2448no—
768C2×C4—2448no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4C22⋊C4×D6112yes—
777C2×C4C22⋊C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4C2×#1175822611yescharacteristic
782C2×C4#1451982311yescharacteristic
783C2×C4#1451982311yescharacteristic
784C8—41no—
785C8—41no—
786C8—1222no—
787C8—2441no—
788C22—614no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—4881no—
799C22—4881no—
800C22—4881no—
801C22—4881no—
802C22—2442no—
803C22—2442no—
804C22—2442no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×C22⋊C4×D6111yescharacteristic
810C22#1684039611yescharacteristic
811C22#1684040311yescharacteristic
812C22#135×D6111yescharacteristic
813C22#135×D6111yescharacteristic
814C22#1684057111yescharacteristic
815C22#1684057811yescharacteristic
816C4—22no—
817C4—24no—
818C4—22no—
819C4—42no—
820C4—81no—
821C4—81no—
822C4—1222no—
823C4—1222no—
824C4—4881no—
825C4—2442no—
826C4—2442no—
827C4C2×#1451973911yescharacteristic
828C4#1684023611yescharacteristic
829C4#1684039611yescharacteristic
830C4#1684040311yescharacteristic
831C2—1224no—
832C2—4882no—
833C2—2442no—
834C2#2144863911yescharacteristic
835C2#416×D6111yescharacteristic
836C2#2145435111yescharacteristic
837C2#2145752111yescharacteristic
838C2#2145755511yescharacteristic
839C2#2145770311yescharacteristic
840C2#2145771811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1805C2
socleC23×C61C22×D4
prime radicalC2×#16840424C2
cosocleC22×C4×C61C24
hypercenter#1805D61
hypocenterC61#22416
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#16839827C2semidirect
3. C2×#16839757C2semidirect
4. C2×#103×D61C2semidirect
5. #21448745C2semidirect
6. #21446749C2semidirect
7. #21446628C2semidirect
8. #21446246C2semidirect
9. #21446241C2semidirect
10. #21446135C2semidirect
11. #21446130C2semidirect
12. #21445758C2semidirect
13. #21445752C2semidirect
14. C4×#14519701C2semidirect
15. C61×#1805C2semidirect
21. #16840424C4semidirect
69. C2×#11758226C2×C4semidirect
97. #14519765C2×C4semidirect
100. #14519757C2×C4semidirect
130. #14519701D4semidirect
147. C4×Q8×C61C2×C4semidirect
395. C2×D61#416semidirect
422. #1805D61semidirect
484. C61#22416semidirect
529. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404242
C2×#168398272
C2×#168397572
C2×#103×D612
#214487452
#214467492
#214466282
#214462462
#214462412
#214461352
#214461302
#214457582
#214457522
C4×#145197012
C61×#18052
#2241661