Finite Group Databasebeta

← #29695513

Subgroups — #29695513

Order 15616.

1478 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×#16840416C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5#21448751C211yesmaximal, characteristic, complemented
6#21446742C211yesmaximal, characteristic, complemented
7#21446639C211yesmaximal, characteristic, complemented
8#21446251C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21445829C211yesmaximal, characteristic, complemented
13#21445756C211yesmaximal, characteristic, complemented
14#21445756C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840416—24no—
21#16840416C418yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519761—21no—
24C2×#14519761—21no—
25C2×#14519757C2211yescharacteristic
26C2×#14519757C2211yescharacteristic
27C2×#14519751—21no—
28C2×C4×D244C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C22×C4⋊Dic61—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839835—24no—
33C2×C4⋊#92418C2211yescharacteristic
34#16839760—24no—
35#16839755—24no—
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519698C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C2×#14519689C2211yescharacteristic
48#16839653—21no—
49#16839647—21no—
50#16839640—21no—
51#16839628C2211yescharacteristic
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4×#11758198—21no—
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—41no—
71C2×#11758224—41no—
72C2×#11758224—41no—
73C2×#11758224—41no—
74C2×#11758224C2×C414yes—
75C2×#11758224C2×C414yescomplemented
76C22×Dic122C2311yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244D411yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758189—22no—
87C2×#11758189—22no—
88C2×#11758189—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94#14519777—22no—
95#14519777C2×C414yescomplemented
96#14519761—28no—
97#14519761—28no—
98#14519757—22no—
99#14519757—22no—
100#14519757C2×C414yes—
101#14519757C2×C414yescomplemented
102#14519751—28no—
103C4×D244C2×C414yes—
104C4×D244D414yes—
105#14519735—22no—
106#14519735—41no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61—21no—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61—28no—
112C2×C4⋊Dic61D411yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198D411yescharacteristic
124C2×#11758198D411yescharacteristic
125C2×C4×Dic61—21no—
126C4⋊#92418—22no—
127#14519702—22no—
128#14519702—22no—
129#14519702—41no—
130#14519702—41no—
131#14519700—22no—
132#14519700—22no—
133#14519700—41no—
134#14519700—41no—
135#14519698—22no—
136#14519698—22no—
137#14519689—22no—
138#14519689—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C4×D4×C61—22no—
148C4×D4×C61C2×C414yescomplemented
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C42×C61—21no—
154C2×C42×C61C2311yescharacteristic
155#102×C61—22no—
156#102×C61D414yescomplemented
157#97×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C23×D61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C2×D412yes—
167C2×D4×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—42no—
173C22×C4×C61—42no—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2411yescharacteristic
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C2×C22⋊D61—42no—
182C2×C22⋊D61—42no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—24no—
186C22×Dic61—24no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195#11758224—28no—
196#11758224—28no—
197#11758224—44no—
198#11758224—44no—
199#11758224—44no—
200#11758224—44no—
201#11758224—44no—
202#11758224—44no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244C22⋊C414yes—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—42no—
215C2×C4×D61—42no—
216C2×C4×D61—81no—
217C2×C4×D61C22×C412yes—
218C2×C4×D61C22×C412yes—
219C2×C4×D61C2×D412yes—
220C2×C4×D61C2×D412yes—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122C22×C412yes—
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×C61C2×D412yes—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C22×C412yes—
244C4⋊C4×C61C2×D412yes—
245C22⋊C4×C61—24no—
246C42×C61—81no—
247C42×C61C22×C412yes—
248C42×C61C2×D412yes—
249#11758198—24no—
250#11758198—24no—
251#11758198—42no—
252#11758198—42no—
253#11758198—81no—
254#11758198C22⋊C414yes—
255#11758198C22⋊C414yes—
256C4⋊Dic61—24no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22⋊C414yes—
265#11758196—42no—
266C4×Dic61—42no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273#11758189—44no—
274C8×D61—44no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61C22×D411yescharacteristic
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61C2×C22⋊C412yes—
296C22×D61C2×C22⋊C412yes—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61C4×D414yes—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—48no—
308C2×C4×C61—41no—
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×C61C2×C22⋊C412yes—
316C2×C4×C61C2×C22⋊C412yes—
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61—48no—
324C22⋊D61—48no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—48no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61C2×C22⋊C412yes—
344C2×Dic61C2×C22⋊C412yes—
345D244—44no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—84no—
355Dic122—22no—
356Dic122—22no—
357Dic122—22no—
358Dic122—22no—
359Dic122—41no—
360Dic122—41no—
361Dic122—41no—
362Dic122—41no—
363C8×C61—22no—
364C8×C61—41no—
365#92418—41no—
366#92418—41no—
367#22420—611nomaximal, Sylow
368C22×C61—24no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61C22×C22⋊C411yescharacteristic
376C22×C61D4211yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57711yescharacteristic
381C22×C61#57811yescharacteristic
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—81no—
401C4×C61C2×C4×D411yescharacteristic
402C4×C61#51811yescharacteristic
403C4×C61D4211yescharacteristic
404C4×C61#54611yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—42no—
408Dic61—42no—
409Dic61—81no—
410Dic61—81no—
411C2×#547—611no—
412C2×#435—611no—
413C2×#417—611no—
414C2×#416—611no—
415#2352—611no—
416#1981—611no—
417#1960—611no—
418#1894—611no—
419#1892—611no—
420#1873—611no—
421#1872—611no—
422#1804—611no—
423#1788—611no—
424#1788—611no—
425#1762D6111yescharacteristic, complemented
426C2×C61—44no—
427C2×C61D4×C22⋊C411yescharacteristic
428C2×C61#289611yescharacteristic
429C2×C61#289811yescharacteristic
430C2×C61#326711yescharacteristic
431C2×C61#326911yescharacteristic
432C2×C61#330711yescharacteristic
433C2×C61#331511yescharacteristic
434D61—42no—
435D61—42no—
436C22×#41—611no—
437C22×#41—611no—
438C22×M16—611no—
439C23×C8—611no—
440#547—618no—
441#547—1224no—
442C2×C4⋊Q8—611no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×C22⋊Q8—611no—
446C2×C22⋊Q8—611no—
447C2×#121—1221no—
448C2×C4×D4—611no—
449C2×C4×D4C2×D6111yescharacteristic
450C2×#117—611no—
451C22×C4⋊C4—611no—
452C22×C4⋊C4—1221no—
453#435—1224no—
454C2×C4⋊C8—611no—
455#417—1224no—
456#416—1224no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#103—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×#102C2×D6111yescharacteristic
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×#97C2×D6111yescharacteristic
472#388—1221no—
473#387—1221no—
474#386—1221no—
475#382—611no—
476#380—611no—
477#380—611no—
478C4×C4⋊C4C2×D6111yescharacteristic
479C4×C22⋊C4—1221no—
480#340—611no—
481#340—611no—
482#340C2×D6111yescharacteristic
483#340C2×D6111yescharacteristic
484C61#2242011yescharacteristic, complemented, Sylow
485C2×#41—614no—
486C2×#41—614no—
487C2×#41—1222no—
488C2×#41—1222no—
489C2×#41—1222no—
490C2×#41—1222no—
491C2×#41—1222no—
492C2×#41—1222no—
493C2×#41—2441no—
494C2×#41—2441no—
495C2×#41—2441no—
496C2×#41—2441no—
497C22×Q8—611no—
498C22×Q8—611no—
499C22×D4—611no—
500C22×D4—1221no—
501C22×D4—1221no—
502C22×D4C22×D6111yescharacteristic
503C23×C4—21no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1221no—
507C23×C4—1221no—
508C23×C4—1221no—
509C2×M16—1222no—
510C2×M16—1222no—
511C2×M16—2441no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—1222no—
515C22×C8—1222no—
516C22×C8—2441no—
517C22×C8C22×D6111yescharacteristic
518C22×C8C22×D6111yescharacteristic
519C4⋊Q8—614no—
520C4⋊Q8—1222no—
521#123—1228no—
522#123—1228no—
523C22⋊Q8—614no—
524C22⋊Q8—614no—
525C22⋊Q8—1222no—
526C22⋊Q8—1222no—
527#121—1228no—
528C4×D4—22no—
529C4×D4—614no—
530C4×D4—614no—
531C4×D4C4×D6114yescomplemented
532#117—1222no—
533#117—2441no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1228no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1222no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—2441no—
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
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—21no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559C4⋊C8—1222no—
560#103—1222no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—2441no—
565#103—2441no—
566#103—2441no—
567#103—2441no—
568#102—22no—
569#102—1222no—
570#102—1222no—
571#102D24414yescomplemented
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574#97—22no—
575#95—21no—
576#95—1221no—
577#95—1221no—
578#95—1221no—
579#95—1221no—
580C24—21no—
581C24—611no—
582C24—611no—
583#41—1228no—
584#41—1228no—
585#41—2444no—
586#41—2444no—
587#41—2444no—
588#41—2444no—
589#41—2444no—
590#41—2444no—
591C2×Q8—612no—
592C2×Q8—612no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1221no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—614no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—2441no—
610C2×D4—2441no—
611C2×D4—2442no—
612C2×D4—2442no—
613C2×D4—2442no—
614C2×D4—2442no—
615C2×D4C2×C4×D6112yes—
616C2×D4C2×D24412yes—
617C2×D4#1175822212yes—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—21no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—612no—
627C22×C4—612no—
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—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
654M16—2444no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—2444no—
667C2×C8C2×D24412yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—614no—
673C4⋊C4—1224no—
674C4⋊C4—1224no—
675C4⋊C4—1224no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—2442no—
682C4⋊C4C2×C4×D6112yes—
683C4⋊C4C2×D24412yes—
684C22⋊C4—24no—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—4881no—
690C22⋊C4—2442no—
691C22⋊C4—2442no—
692C42—81no—
693C42—2442no—
694C42C2×C4×D6112yes—
695C42D4×D6112yes—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—612no—
704C23—612no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23C2×D4×D6111yescharacteristic
718Q8—1222no—
719Q8—1222no—
720Q8—1222no—
721Q8—1222no—
722Q8—2441no—
723Q8—2441no—
724Q8—2441no—
725Q8—2441no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—2444no—
730D4—2448no—
731D4—2448no—
732D4C4×D24414yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—48no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—4884no—
764C2×C4—2448no—
765C2×C4—2448no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
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×C4C22×D24411yescharacteristic
781C2×C4C2×#1175822211yescharacteristic
782C2×C4#1451982311yescharacteristic
783C2×C4#1451982311yescharacteristic
784C8—22no—
785C8—41no—
786C8—2441no—
787C8—2441no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×C22⋊C4×D6111yescharacteristic
810C22D4×D24411yescharacteristic
811C22#1684040811yescharacteristic
812C22#1684055811yescharacteristic
813C22#1684055811yescharacteristic
814C22#1684057211yescharacteristic
815C22#1684057811yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—81no—
821C4—1222no—
822C4—1222no—
823C4—4881no—
824C4—4881no—
825C4—2442no—
826C4—2442no—
827C4C2×C4×D24411yescharacteristic
828C4#1684023611yescharacteristic
829C4D4×D24411yescharacteristic
830C4#1684040811yescharacteristic
831C2—44no—
832C2—2442no—
833C2—2442no—
834C2C22⋊C4×D24411yescharacteristic
835C2#2145433311yescharacteristic
836C2#2145435011yescharacteristic
837C2#2145734611yescharacteristic
838C2#2145737611yescharacteristic
839C2#2145780011yescharacteristic
840C2#2145792011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC2×#16840416C2
cosocleC22×C4×C61C24
hypercenter#1762D61
hypocenterC61#22420
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839755C2semidirect
5. #21448751C2semidirect
6. #21446742C2semidirect
7. #21446639C2semidirect
8. #21446251C2semidirect
9. #21446241C2semidirect
10. #21446130C2semidirect
11. #21446125C2semidirect
12. #21445829C2semidirect
13. #21445756C2semidirect
14. #21445756C2semidirect
15. C61×#1762C2semidirect
21. #16840416C4semidirect
75. C2×#11758224C2×C4semidirect
95. #14519777C2×C4semidirect
101. #14519757C2×C4semidirect
148. C4×D4×C61C2×C4semidirect
156. #102×C61D4semidirect
425. #1762D61semidirect
484. C61#22420semidirect
531. C4×D4C4×D61semidirect
571. #102D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168404162
C2×#168398352
C2×#168397602
C2×#168397552
#214487512
#214467422
#214466392
#214462512
#214462412
#214461302
#214461252
#214458292
#214457562
C61×#17622
#2242061