Finite Group Databasebeta

← #29714567

Subgroups — #29714567

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840044C211yesmaximal, characteristic, complemented
2C2×#16839981C211yesmaximal, characteristic, complemented
3#21448501C211yesmaximal, characteristic, complemented
4#21447012C211yesmaximal, characteristic, complemented
5#21447005C211yesmaximal, characteristic
6#21446827C211yesmaximal, characteristic, complemented
7#21446822C211yesmaximal, characteristic
8#21446768C211yesmaximal, characteristic, complemented
9#21446752C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446087C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445803C211yesmaximal, characteristic, complemented
15C2×C61×#542C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16840044—24no—
21#16839981—24no—
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839657—21no—
39#16839656—21no—
40#16839650—21no—
41#16839643—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C61×#542—24no—
51C61×#542—24no—
52C2×C4⋊Q8×C61C2211yescharacteristic
53C2×#126×C61—21no—
54C2×#124×C61—21no—
55C2×#124×C61C2211yescharacteristic
56C2×#123×C61—21no—
57C2×C22⋊Q8×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic
61C2×C4×D4×C61C2211yescharacteristic
62C2×#117×C61C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—41no—
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519756—22no—
75#14519756—22no—
76C4×Dic122—22no—
77C4×Dic122—22no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88#14519708—22no—
89#14519708—22no—
90C4⋊#92418—22no—
91C4⋊#92418—22no—
92#14519701—22no—
93#14519701—22no—
94#14519701—41no—
95#14519700—22no—
96#14519700—22no—
97#14519698—22no—
98#14519698—22no—
99#14519698—41no—
100C22⋊#92418—41no—
101C22⋊#92418—41no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61D414yes—
115#126×C61—28no—
116#124×C61—28no—
117#124×C61—22no—
118#124×C61D414yes—
119#123×C61—28no—
120C22⋊Q8×C61—28no—
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125C4×Q8×C61—22no—
126C4×Q8×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129#117×C61—22no—
130#117×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C2×Q8×C61—24no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—81no—
157C2×Q8×C61—81no—
158C2×Q8×C61C2×D412yes—
159C2×D4×C61—24no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—81no—
166C2×D4×C61—81no—
167C2×D4×C61C2×D412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—24no—
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×C61—81no—
179C22×C4×C61—81no—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122#4112yes—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61C2×D412yes—
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—24no—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—24no—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—24no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C42×C61—24no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61C2×D412yes—
216C42×C61C2×D412yes—
217C22⋊Dic61—24no—
218C22⋊Dic61—81no—
219#11758202—44no—
220#11758200—44no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61#4112yes—
227#11758196—24no—
228#11758196—42no—
229#11758196—81no—
230C4×Dic61—42no—
231C4×Dic61—81no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C22×D411yescharacteristic
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—84no—
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—84no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—22no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
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—84no—
296C2×C4×C61#12012yes—
297C2×C4×C61#12012yes—
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×C4×C612−1+411yescharacteristic
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316Dic122—22no—
317Dic122—22no—
318Dic122—41no—
319Dic122—41no—
320#92418—41no—
321#92418—41no—
322#92418—41no—
323#92418—41no—
324#24169—611nomaximal, Sylow
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—42no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—42no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C2×#12011yescharacteristic
340C22×C61#52511yescharacteristic
341C22×C61#53711yescharacteristic
342C22×C61#57711yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57811yescharacteristic
346C4×C61—22no—
347C4×C61—22no—
348C4×C61—41no—
349C4×C61—42no—
350C4×C61—41no—
351C4×C61—42no—
352C4×C61—42no—
353C4×C61—41no—
354C4×C61#54611yescharacteristic
355C4×C61#54711yescharacteristic
356C4×C61#54811yescharacteristic
357C4×C61#55011yescharacteristic
358Dic61—42no—
359Dic61—42no—
360Dic61—81no—
361Dic61—81no—
362C2×#542D6111yescharacteristic
363C2×#475—611no—
364C2×#464—611no—
365#2323—611no—
366#2035—611no—
367#2034—611no—
368#2001—611no—
369#2000—611no—
370#1987—611no—
371#1983—611no—
372#1878—611no—
373#1877—611no—
374#1865—611no—
375#1864—611no—
376#1798—611no—
377C2×C61—81no—
378C2×C61—82no—
379C2×C61#240711yescharacteristic
380C2×C61#300911yescharacteristic
381C2×C61#301311yescharacteristic
382C2×C61#312111yescharacteristic
383C2×C61#312511yescharacteristic
384C2×C61#325811yescharacteristic
385C2×C61#326311yescharacteristic
386C22×Q16—611no—
387C22×SD16—611no—
388#542—24no—
389#542—24no—
390C2×C4⋊Q8C2×D6111yescharacteristic
391C2×#126—21no—
392C2×#124—21no—
393C2×#124C2×D6111yescharacteristic
394C2×#123—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8C2×D6111yescharacteristic
398C2×#121C2×D6111yescharacteristic
399C2×C4×Q8—611no—
400C2×C4×Q8C2×D6111yescharacteristic
401C2×C4×D4C2×D6111yescharacteristic
402C2×#117C2×D6111yescharacteristic
403#475—1224no—
404#464—1224no—
405C2×#106—611no—
406C2×#106—611no—
407C2×C4⋊C8—611no—
408C2×C4⋊C8—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419#391—611no—
420#389—611no—
421#389—1221no—
422#388—1221no—
423#388—1221no—
424#387—1221no—
425#380—611no—
426C4×C4⋊C4—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#336—611no—
432#336—611no—
433C61#2416911yescharacteristic, complemented, Sylow
434C22×Q8—21no—
435C22×Q8—611no—
436C22×Q8C22×D6111yescharacteristic
437C22×D4—21no—
438C22×D4C22×D6111yescharacteristic
439C23×C4—21no—
440C23×C4C22×D6111yescharacteristic
441C2×Q16—1222no—
442C2×Q16—1222no—
443C2×Q16—2441no—
444C2×SD16—1222no—
445C2×SD16—1222no—
446C2×SD16—2441no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451C4⋊Q8—22no—
452C4⋊Q8C22⋊D6114yes—
453#126—28no—
454#124—28no—
455#124—22no—
456#124C22⋊D6114yes—
457#123—28no—
458C22⋊Q8—28no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—1222no—
462C22⋊Q8—1222no—
463#121—22no—
464#121—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×Q8—1222no—
468C4×Q8—1222no—
469C4×D4—22no—
470C4×D4—22no—
471#117—22no—
472#117—22no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22⋊D6111yescharacteristic
483C2×C4⋊C4C22⋊D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4C22⋊D6111yescharacteristic
494C2×C22⋊C4C22⋊D6111yescharacteristic
495C2×C42—21no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42C22×D6111yescharacteristic
499C2×C42C22×D6111yescharacteristic
500#106—1222no—
501#106—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504#103—1222no—
505#103—1222no—
506#103—1222no—
507#103—1222no—
508#103—2441no—
509#102—1222no—
510#102—1222no—
511#102—2441no—
512C22⋊C8—2441no—
513C22⋊C8—2441no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519C24—21no—
520C24C2×C22⋊D6111yescharacteristic
521C2×Q8—21no—
522C2×Q8—24no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—81no—
528C2×Q8—81no—
529C2×Q8—612no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8C2×C22⋊D6112yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4C2×C22⋊D6112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4C2×C22⋊D6111yescharacteristic
562C22×C4C2×C22⋊D6111yescharacteristic
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C23×D6111yescharacteristic
567Q16—2444no—
568SD16—2444no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—612no—
589C4⋊C4—1224no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—4881no—
596C4⋊C4—2442no—
597C4⋊C4C2×C22⋊D6112yes—
598C4⋊C4C2×C22⋊D6112yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—1224no—
607C22⋊C4—4881no—
608C42—24no—
609C42—21no—
610C42—21no—
611C42—4881no—
612C42—2442no—
613C42C2×C22⋊D6112yes—
614C42C2×C22⋊D6112yes—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23C22×C22⋊D6111yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—84no—
635Q8—1222no—
636Q8—1222no—
637Q8—2441no—
638Q8—2441no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—41no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4#1451974612yes—
684C2×C4#1451974612yes—
685C2×C4C22×C22⋊D6111yescharacteristic
686C2×C4C22×C22⋊D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4#1451982311yescharacteristic
690C2×C4#1451982411yescharacteristic
691C8—2441no—
692C8—2441no—
693C8—2441no—
694C8—2441no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×#1451974611yescharacteristic
710C22#1684026911yescharacteristic
711C22#1684034011yescharacteristic
712C22#1684057011yescharacteristic
713C22#1684057311yescharacteristic
714C22#1684057311yescharacteristic
715C22#1684057711yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—4881no—
725C4—4881no—
726C4—2442no—
727C4—2442no—
728C4#1684040011yescharacteristic
729C4#1684041111yescharacteristic
730C4#1684041911yescharacteristic
731C4#1684043111yescharacteristic
732C2—81no—
733C2—82no—
734C2#2144915811yescharacteristic
735C2#2145509611yescharacteristic
736C2#2145513411yescharacteristic
737C2#2145604211yescharacteristic
738C2#2145609011yescharacteristic
739C2#2145724511yescharacteristic
740C2#2145728411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
hypercenterC2×#542D61
hypocenterC61#24169
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840044C2semidirect
2. C2×#16839981C2semidirect
3. #21448501C2semidirect
4. #21447012C2semidirect
6. #21446827C2semidirect
8. #21446768C2semidirect
9. #21446752C2semidirect
10. #21446160C2semidirect
11. #21446153C2semidirect
12. #21446087C2semidirect
13. #21446080C2semidirect
14. #21445803C2semidirect
433. C61#24169semidirect

Maximal subgroups

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

subgroupindex
C2×#168400442
C2×#168399812
#214485012
#214470122
#214470052
#214468272
#214468222
#214467682
#214467522
#214461602
#214461532
#214460872
#214460802
#214458032
C2×C61×#5422
#2416961