Finite Group Databasebeta

← #29680773

Subgroups — #29680773

Order 15616.

1462 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2C2×#16839801C211yesmaximal, characteristic, complemented
3C2×#106×D61C211yesmaximal, characteristic, complemented
4C2×#16839727C211yesmaximal, characteristic
5#21448408C211yesmaximal, characteristic
6#21446021C211yesmaximal, characteristic, complemented
7#21446020C211yesmaximal, characteristic, complemented
8#21446017C211yesmaximal, characteristic, complemented
9#21446016C211yesmaximal, characteristic, complemented
10#21446013C211yesmaximal, characteristic, complemented
11#21446012C211yesmaximal, characteristic, complemented
12#21446010C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1853C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840243—24no—
20#16840243—24no—
21C2×#14519742—21no—
22C2×#14519739—21no—
23C2×C4×C22⋊D61—21no—
24C2×C4×C22⋊D61—21no—
25C2×#14519736C2211yescharacteristic
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839801—24no—
33C2×#14519711C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519709C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519708C2211yescharacteristic
38C2×#14519708C2211yescharacteristic
39#106×D61—24no—
40#16839727C418yescomplemented
41C2×C22⋊#92418C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44#16839666—21no—
45#16839662—21no—
46#16839640—21no—
47#16839638—21no—
48#16839622C2211yescharacteristic
49#16839619C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222C2×C414yes—
69C2×#11758222Q814yes—
70C22×Dic122D411yescharacteristic
71C22×D244D411yescharacteristic
72C22×C22⋊D61D411yescharacteristic
73C22×C22⋊D61D411yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61C2×C414yescomplemented
87#14519742—28no—
88#14519739—28no—
89C4×C22⋊D61—28no—
90C4×C22⋊D61—28no—
91#14519736—22no—
92#14519736—22no—
93#14519735—22no—
94#14519735—22no—
95#14519735—22no—
96#14519735—22no—
97#14519735—22no—
98#14519735D414yes—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C4⋊C4×D61D414yes—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519711—22no—
124#14519710—22no—
125#14519709—22no—
126#14519708—22no—
127#14519708—22no—
128#14519708—22no—
129C22⋊#92418C2×C414yescomplemented
130#14519689C2×C414yescomplemented
131#14519689C2×C414yescomplemented
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C23×C4×C61—21no—
136C23×C4×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#106×C61—22no—
148#106×C61—22no—
149C22⋊C8×C61C2×C414yescomplemented
150#95×C61—21no—
151C24×C61C2×D411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—24no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—81no—
164C22×C4×C61—81no—
165C22×C4×C61C22×C412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×Q812yes—
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61C4⋊C414yes—
174C2×C22⋊D61C4⋊C414yes—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181#11758222—28no—
182#11758222—28no—
183#11758222—28no—
184#11758222—28no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244C4⋊C414yes—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—42no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×C4×D61—81no—
199C2×C4×D61—81no—
200C2×C4×D61—81no—
201C2×C4×D61C22×C412yes—
202C2×C4×D61C22×C412yes—
203C2×C4×D61C2×D412yes—
204C2×C4×D61C2×D412yes—
205C2×C4×D61C2×Q812yes—
206C2×C4×D61C2×Q812yes—
207C2×C4×D61#4112yes—
208C2×C4×D61#4112yes—
209C2×Dic122—22no—
210C2×Dic122—22no—
211C2×Dic122C4⋊C414yes—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61C22×C412yes—
217C2×C8×C61C22×C412yes—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61C2×D412yes—
226C4⋊C4×C61C2×D412yes—
227C22⋊C4×C61—81no—
228C22⋊Dic61—24no—
229C22⋊Dic61—81no—
230#11758198—24no—
231#11758198—24no—
232#11758198—42no—
233#11758198—81no—
234#11758198—81no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61C2×D412yes—
242C4⋊Dic61C2×D412yes—
243#11758196—24no—
244#11758196—24no—
245#11758196—42no—
246C4×Dic61—24no—
247C4×Dic61—24no—
248C4×Dic61—24no—
249C4×Dic61—42no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418C22×C412yes—
255C2×#92418C22×C412yes—
256#11758189—28no—
257C8×D61—28no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61C2×C4⋊C412yes—
265C23×C61C22×D411yescharacteristic
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61C2×C4⋊C412yes—
277C22×D61C2×C4⋊C412yes—
278C22×D61#12012yes—
279C22×D61#12312yes—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—84no—
299C2×C4×C61C2×C4⋊C412yes—
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×Q811yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C22⋊D61—28no—
307C22⋊D61—28no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61C2×C4⋊C412yes—
323C2×Dic61C2×C4⋊C412yes—
324C2×Dic61#12012yes—
325C2×Dic61#12312yes—
326D244—28no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—84no—
332C4×D61—84no—
333C4×D61—84no—
334C4×D61C4×D414yes—
335C4×D61C4×D414yes—
336C4×D61C22⋊Q814yes—
337C4×D61C22⋊Q814yes—
338Dic122—28no—
339C8×C61—22no—
340C8×C61—22no—
341#92418—22no—
342#92418—22no—
343#20848—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61C22×C4⋊C411yescharacteristic
352C22×C61C2×#12011yescharacteristic
353C22×C61C2×#12311yescharacteristic
354C22×C61#57711yescharacteristic
355C22×C61#57711yescharacteristic
356C22×C61#57711yescharacteristic
357C22×C61#57711yescharacteristic
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61#38514yes—
372C4×C61—22no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—81no—
376C4×C61—81no—
377C4×C61C2×C4×D411yescharacteristic
378C4×C61C2×C4×D411yescharacteristic
379C4×C61C2×C22⋊Q811yescharacteristic
380C4×C61C2×C22⋊Q811yescharacteristic
381Dic61—22no—
382Dic61—42no—
383Dic61—42no—
384Dic61—81no—
385Dic61—81no—
386Dic61#38514yes—
387C2×#520—611no—
388C2×#428—611no—
389C22×#106—611no—
390C2×#408—611no—
391#2311—611no—
392#1854—611no—
393#1854—611no—
394#1854—611no—
395#1854—611no—
396#1853—611no—
397#1853—611no—
398#1853—611no—
399#1853D6111yescharacteristic, complemented
400#1736—611no—
401#1735—611no—
402C2×C61—42no—
403C2×C61C2×#38511yescharacteristic
404C2×C61#291211yescharacteristic
405C2×C61#291211yescharacteristic
406C2×C61#300911yescharacteristic
407C2×C61#301011yescharacteristic
408C2×C61#309911yescharacteristic
409C2×C61#309911yescharacteristic
410D61—24no—
411D61—42no—
412C22×#41—611no—
413C22×M16—611no—
414C23×C8—611no—
415#520—1224no—
416#520—1224no—
417C2×C4×Q8—1221no—
418C2×C4×D4—1221no—
419C2×C4×D4—1221no—
420C2×C4×D4—1221no—
421C2×#117—611no—
422C2×#117—611no—
423C2×#117—611no—
424C2×#117—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429#428—1224no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×#106—611no—
435C2×#106—611no—
436C2×#106—1224no—
437C2×#106C2×D6111yescharacteristic
438C2×#106C2×D6111yescharacteristic
439#408—618no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8C2×D6111yescharacteristic
444#391—1221no—
445#390—1221no—
446#386—1221no—
447#386—1221no—
448#380—611no—
449#380—611no—
450#380—611no—
451#380C2×D6111yescharacteristic
452#340—611no—
453#340—611no—
454#340—611no—
455#340—611no—
456#340—611no—
457#340—611no—
458#340C2×D6111yescharacteristic
459#340C2×D6111yescharacteristic
460C61#2084811yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—614no—
463C2×#41—1222no—
464C2×#41—1222no—
465C2×#41—1222no—
466C2×#41—1222no—
467C22×Q8—611no—
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—611no—
471C23×C4—21no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4C22×D6111yescharacteristic
478C2×M16—614no—
479C2×M16—1222no—
480C2×M16—1222no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—614no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8C22×D6111yescharacteristic
487C22×C8C22×D6111yescharacteristic
488C4×Q8—1228no—
489C4×D4—1228no—
490C4×D4—1228no—
491C4×D4—1228no—
492#117—614no—
493#117—1222no—
494#117—1222no—
495#117—1222no—
496#117—1222no—
497#117—1222no—
498#117—1222no—
499#117—1222no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—1222no—
509C2×C4⋊C4—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1222no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C22×D6111yescharacteristic
517C2×C4⋊C4C22×D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42—1221no—
532#107—1222no—
533#107—1222no—
534#106—22no—
535#106—22no—
536#106—1222no—
537#106—1222no—
538#106—1222no—
539#106—1222no—
540C22⋊C8—614no—
541C22⋊C8—614no—
542C22⋊C8—614no—
543C22⋊C8C4×D6114yescomplemented
544#95—21no—
545#95—1221no—
546#95—1221no—
547#95—1221no—
548C24—611no—
549C24—611no—
550C24D4×D6111yescharacteristic
551#41—1228no—
552#41—1228no—
553#41—1228no—
554#41—1228no—
555C2×Q8—614no—
556C2×Q8—1222no—
557C2×Q8—1222no—
558C2×D4—614no—
559C2×D4—614no—
560C2×D4—614no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—611no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1224no—
589C22×C4—1224no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—4881no—
599C22×C4—4881no—
600C22×C4—4881no—
601C22×C4—4881no—
602C22×C4—4881no—
603C22×C4—4881no—
604C22×C4—2442no—
605C22×C4C2×C4×D6112yes—
606C22×C4D4×D6111yescharacteristic
607C22×C4Q8×D6112yes—
608C22×C4C23×D6111yescharacteristic
609M16—1228no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1228no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8C2×C4×D6112yes—
622C2×C8C2×C4×D6112yes—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—612no—
631C4⋊C4—612no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—2442no—
641C4⋊C4D4×D6112yes—
642C4⋊C4D4×D6112yes—
643C22⋊C4—81no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—4881no—
648C22⋊C4—4881no—
649C22⋊C4—4881no—
650C22⋊C4—2442no—
651C42—1224no—
652C42—1224no—
653C42—1224no—
654C42—2442no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—612no—
662C23—612no—
663C23—612no—
664C23—612no—
665C23—1221no—
666C23—1221no—
667C23—1221no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23C4⋊C4×D6112yes—
676C23C2×D4×D6111yescharacteristic
677Q8—1228no—
678D4—1228no—
679D4—1228no—
680D4—1228no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—614no—
704C2×C4—614no—
705C2×C4—614no—
706C2×C4—614no—
707C2×C4—612no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—4884no—
717C2×C4—4884no—
718C2×C4—4884no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4C4⋊C4×D6112yes—
730C2×C4C22×C4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×Q8×D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C8—22no—
737C8—22no—
738C8—1222no—
739C8—1222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—614no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22C2×C4⋊C4×D6111yescharacteristic
762C22#120×D6111yescharacteristic
763C22#123×D6111yescharacteristic
764C22#1684056811yescharacteristic
765C22#1684056811yescharacteristic
766C22#1684057111yescharacteristic
767C22#1684057211yescharacteristic
768C4—22no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—614no—
774C4—1222no—
775C4—4881no—
776C4—4881no—
777C4—2442no—
778C4—2442no—
779C4C4×D4×D6111yescharacteristic
780C4C4×D4×D6111yescharacteristic
781C4C22⋊Q8×D6111yescharacteristic
782C4C22⋊Q8×D6111yescharacteristic
783C2—42no—
784C2—1224no—
785C2—2442no—
786C2#385×D6111yescharacteristic
787C2#2145441011yescharacteristic
788C2#2145441311yescharacteristic
789C2#2145509111yescharacteristic
790C2#2145510011yescharacteristic
791C2#2145580311yescharacteristic
792C2#2145580911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1853C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1853D61
hypocenterC61#20848
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#16839801C2semidirect
3. C2×#106×D61C2semidirect
6. #21446021C2semidirect
7. #21446020C2semidirect
8. #21446017C2semidirect
9. #21446016C2semidirect
10. #21446013C2semidirect
11. #21446012C2semidirect
12. #21446010C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1853C2semidirect
40. #16839727C4semidirect
81. C2×#11758189C2×C4semidirect
86. C2×C8×D61C2×C4semidirect
129. C22⋊#92418C2×C4semidirect
130. #14519689C2×C4semidirect
131. #14519689C2×C4semidirect
149. C22⋊C8×C61C2×C4semidirect
399. #1853D61semidirect
460. C61#20848semidirect
543. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402432
C2×#168398012
C2×#106×D612
C2×#168397272
#214484082
#214460212
#214460202
#214460172
#214460162
#214460132
#214460122
#214460102
#214455372
#214455342
C61×#18532
#2084861