Finite Group Databasebeta

← #29695462

Subgroups — #29695462

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×#16840418C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#16839755C211yesmaximal, characteristic, complemented
4C22×#14519702C211yesmaximal, characteristic, complemented
5#21448750C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446629C211yesmaximal, characteristic, complemented
8#21446241C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445833C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445753C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840418—24no—
20#16840418C418yescomplemented
21C2×#14519764C2211yescharacteristic
22C2×#14519763—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519754—21no—
25C2×#14519749—21no—
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61—21no—
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C8×C22⋊D61—24no—
32C2×#14519706C2211yescharacteristic
33#16839755—24no—
34C2×#14519702—24no—
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839654—21no—
49#16839649—21no—
50#16839639—21no—
51#16839627C2211yescharacteristic
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic
54C22⋊C4×Dic61—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C23×C8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—41no—
68C2×#11758224—41no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122—22no—
71C22×Dic122—22no—
72C22×Dic122—21no—
73C22×Dic122—22no—
74C22×Dic122—41no—
75C22×Dic122—41no—
76C22×Dic122C2×C414yes—
77C22×Dic122C2311yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C2×C8×D61—22no—
88C2×C8×D61—22no—
89C2×C8×D61—41no—
90#14519764—22no—
91#14519764C2×C414yescomplemented
92#14519763—28no—
93#14519757—22no—
94#14519757C2×C414yescomplemented
95#14519754—28no—
96#14519749—28no—
97#14519742—22no—
98#14519742C2×C414yescomplemented
99D4×Dic61—28no—
100C4×C22⋊D61C2×C414yes—
101C4×C22⋊D61D414yes—
102#14519735—22no—
103#14519735—41no—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—22no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61—41no—
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519702—22no—
125#14519702—22no—
126#14519702—22no—
127#14519702D414yescomplemented
128#14519700—22no—
129#14519700—22no—
130#14519700—41no—
131#14519700—41no—
132#14519698—22no—
133#14519698—41no—
134C22⋊#92418—22no—
135#14519689—22no—
136C8×Dic61—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61—22no—
145C22×C8×C61—22no—
146C22×C8×C61—41no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#121×C61—22no—
150#121×C61C2×C414yes—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162C2×D4×C61—24no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61C22×C412yes—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D412yes—
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—22no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61C22⋊C414yes—
188C22×Dic61—21no—
189C22×Dic61—24no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—24no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—81no—
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204#11758224—28no—
205#11758224—44no—
206#11758224—44no—
207#11758224—44no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61C22×C412yes—
213C2×C4×D61C2×D412yes—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—28no—
222C2×Dic122—24no—
223C2×Dic122—21no—
224C2×Dic122—44no—
225C2×Dic122—44no—
226C2×Dic122—44no—
227C2×Dic122—42no—
228C2×Dic122—42no—
229C2×Dic122C22×C412yes—
230C2×Dic122C22×C412yes—
231C2×Dic122C2×D412yes—
232C2×Dic122#4112yes—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—44no—
239C2×C8×C61C2×D412yes—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C22×C412yes—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—42no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61C22⋊C414yes—
251#11758198—24no—
252#11758198—42no—
253#11758198—81no—
254#11758198C22⋊C414yes—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—42no—
260C4⋊Dic61C2×D412yes—
261#11758196—24no—
262#11758196C22⋊C414yes—
263C4×Dic61—24no—
264C4×Dic61—42no—
265C4×Dic61—81no—
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—22no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61C2×C22⋊C412yes—
287C23×C61#13512yes—
288C23×C61#13512yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61C2×C22⋊C412yes—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—48no—
300D4×C61—41no—
301D4×C61—41no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
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×C61C2×C22⋊C412yes—
318C2×C4×C61C23×C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C2×C4×C61H(5,𝔽2)11yescharacteristic
324C22⋊D61—28no—
325C22⋊D61—48no—
326C2×Dic61—22no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—48no—
338C2×Dic61—48no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61—41no—
345C2×Dic61—41no—
346C2×Dic61—84no—
347C2×Dic61C2×C22⋊C412yes—
348C2×Dic61C2×C22⋊C412yes—
349C2×Dic61C2×C22⋊C412yes—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—48no—
360Dic122—41no—
361Dic122—41no—
362Dic122C4×D414yes—
363C8×C61—22no—
364C8×C61—41no—
365#92418—41no—
366#92418—41no—
367#22416—611nomaximal, Sylow
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61#41614yescomplemented
382C22×C61C22×C22⋊C411yescharacteristic
383C22×C61D4211yescharacteristic
384C22×C61#54611yescharacteristic
385C22×C61C2×#13511yescharacteristic
386C22×C61C2×#13511yescharacteristic
387C22×C61#57711yescharacteristic
388C22×C61#57811yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—42no—
398C4×C61—81no—
399C4×C61—81no—
400C4×C61C2×C4×D411yescharacteristic
401C4×C61#51811yescharacteristic
402C4×C61D4211yescharacteristic
403C4×C61#54611yescharacteristic
404Dic61—24no—
405Dic61—22no—
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#1893D6111yescharacteristic, complemented
419#1892—611no—
420#1874—611no—
421#1873—611no—
422#1805—611no—
423#1788—611no—
424#1787—611no—
425C4×#103—611no—
426C2×C61—24no—
427C2×C61—82no—
428C2×C61D4×C22⋊C411yescharacteristic
429C2×C61C2×#41611yescharacteristic
430C2×C61#289811yescharacteristic
431C2×C61#328211yescharacteristic
432C2×C61#328511yescharacteristic
433C2×C61#330011yescharacteristic
434C2×C61#330111yescharacteristic
435D61—42no—
436C22×#41—611no—
437C23×Q8—611no—
438C23×C8—611no—
439C23×C8C2×D6111yescharacteristic
440#548—618no—
441#548—1224no—
442C2×#124—611no—
443C2×#124—1221no—
444C2×C22⋊Q8—611no—
445C2×C22⋊Q8—1221no—
446C2×#121—1221no—
447C2×#121C2×D6111yescharacteristic
448C2×C4×Q8—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×#117—611no—
452C22×C4⋊C4—611no—
453C8×D4—1224no—
454C2×C4⋊C8—611no—
455#416—1224no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—1224no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×#102C2×D6111yescharacteristic
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C4×C8—611no—
472#388—1221no—
473#387—1221no—
474#386—1221no—
475#382—611no—
476#380—611no—
477#380C2×D6111yescharacteristic
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—611no—
494C22×Q8—1222no—
495C22×Q8—1222no—
496C22×Q8—1221no—
497C22×Q8—1222no—
498C22×Q8—2441no—
499C22×Q8—2441no—
500C22×D4—21no—
501C22×D4—611no—
502C22×D4—1221no—
503C22×D4C22×D6111yescharacteristic
504C23×C4—611no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4C22×D6111yescharacteristic
509C22×C8—22no—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—2441no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519#124—614no—
520#124—1222no—
521#124—1228no—
522C22⋊Q8—614no—
523C22⋊Q8—1228no—
524C22⋊Q8—1222no—
525#121—22no—
526#121—1228no—
527#121C4×D6114yes—
528C4×Q8—614no—
529C4×Q8—1222no—
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—1228no—
533#117—1222no—
534#117—2441no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1221no—
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—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C42—611no—
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42—1221no—
559C4⋊C8—1222no—
560#103—614no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—1222no—
565#103—1222no—
566#103—2441no—
567#103—2441no—
568#102—22no—
569#102—41no—
570#102—1222no—
571#102—2441no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C4×C8—1222no—
575#95—21no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—21no—
581C24—611no—
582C24D4×D6111yescharacteristic
583#41—1228no—
584#41—2444no—
585#41—2444no—
586#41—2444no—
587C2×Q8—612no—
588C2×Q8—612no—
589C2×Q8—612no—
590C2×Q8—612no—
591C2×Q8—1228no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1224no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—2442no—
602C2×Q8—2442no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8—2444no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—614no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1224no—
618C2×D4—2442no—
619C2×D4—2442no—
620C2×D4C2×C4×D6112yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—1224no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—4881no—
644C22×C4—2442no—
645C22×C4—2442no—
646C22×C4—2442no—
647C22×C4—2442no—
648C22×C4—2442no—
649C22×C4—2442no—
650C22×C4C2×C4×D6112yes—
651C22×C4D4×D6112yes—
652C22×C4D4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—44no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—2444no—
667C2×C8D4×D6112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—614no—
674C4⋊C4—612no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—2442no—
681C4⋊C4C2×C4×D6112yes—
682C22⋊C4—24no—
683C22⋊C4—42no—
684C22⋊C4—614no—
685C22⋊C4—614no—
686C22⋊C4—1224no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—4881no—
690C22⋊C4—2442no—
691C42—612no—
692C42—612no—
693C42—1224no—
694C42—4881no—
695C42—2442no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—612no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23C22⋊C4×D6112yes—
715C23#1451979612yes—
716C23#1451979812yes—
717C23C2×D4×D6111yescharacteristic
718Q8—614no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—1222no—
723Q8—1222no—
724Q8—2448no—
725Q8—2441no—
726Q8—2441no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—1228no—
733D4—2448no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
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—612no—
750C2×C4—612no—
751C2×C4—612no—
752C2×C4—1222no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1222no—
759C2×C4—1221no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—4884no—
768C2×C4—2448no—
769C2×C4—2448no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4C22⋊C4×D6112yes—
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C2×C4#41×D6111yescharacteristic
782C2×C4#1451982211yescharacteristic
783C2×C4#1451982311yescharacteristic
784C8—22no—
785C8—41no—
786C8—2441no—
787C8—2441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—1222no—
802C22—1222no—
803C22—1222no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22#1683975514yescomplemented
809C22C2×C22⋊C4×D6111yescharacteristic
810C22#1684039611yescharacteristic
811C22#1684040111yescharacteristic
812C22C2×#1451979611yescharacteristic
813C22C2×#1451979811yescharacteristic
814C22#1684056911yescharacteristic
815C22#1684057611yescharacteristic
816C4—22no—
817C4—42no—
818C4—81no—
819C4—81no—
820C4—1222no—
821C4—1222no—
822C4—1224no—
823C4—1222no—
824C4—4881no—
825C4—2442no—
826C4—2442no—
827C4C4×D4×D6111yescharacteristic
828C4#1684023411yescharacteristic
829C4#1684039411yescharacteristic
830C4#1684040411yescharacteristic
831C2—24no—
832C2—82no—
833C2—2442no—
834C2#2144863711yescharacteristic
835C2C2×#1683975511yescharacteristic
836C2#2145434811yescharacteristic
837C2#2145752311yescharacteristic
838C2#2145755711yescharacteristic
839C2#2145771211yescharacteristic
840C2#2145772711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840418C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#22416
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D61C2semidirect
3. C2×#16839755C2semidirect
4. C22×#14519702C2semidirect
5. #21448750C2semidirect
6. #21446750C2semidirect
7. #21446629C2semidirect
8. #21446241C2semidirect
9. #21446137C2semidirect
10. #21446130C2semidirect
11. #21445833C2semidirect
12. #21445756C2semidirect
13. #21445753C2semidirect
14. #21445638C2semidirect
15. C61×#1893C2semidirect
20. #16840418C4semidirect
69. C2×#11758224C2×C4semidirect
91. #14519764C2×C4semidirect
94. #14519757C2×C4semidirect
98. #14519742C2×C4semidirect
127. #14519702D4semidirect
381. C22×C61#416semidirect
418. #1893D61semidirect
484. C61#22416semidirect
808. C22#16839755semidirect

Maximal subgroups

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

subgroupindex
C2×#168404182
C2×C8×C22⋊D612
C2×#168397552
C22×#145197022
#214487502
#214467502
#214466292
#214462412
#214461372
#214461302
#214458332
#214457562
#214457532
#214456382
C61×#18932
#2241661