Finite Group Databasebeta

← #30622425

Subgroups — #30622425

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840795C211yesmaximal, characteristic, complemented
2C2×#16840782C211yesmaximal, characteristic, complemented
3#21461942C211yesmaximal, characteristic, complemented
4#21461942C211yesmaximal, characteristic, complemented
5#21461940C211yesmaximal, characteristic, complemented
6#21461918C211yesmaximal, characteristic, complemented
7#21461894C211yesmaximal, characteristic, complemented
8#21461892C211yesmaximal, characteristic, complemented
9#21461797C211yesmaximal, characteristic, complemented
10#21461796C211yesmaximal, characteristic, complemented
11#21461611C211yesmaximal, characteristic, complemented
12#21461561C211yesmaximal, characteristic, complemented
13#21461560C211yesmaximal, characteristic, complemented
14C4×C22⋊#92420C211yesmaximal, characteristic, complemented
15#21448329C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18#16840795—24no—
19#16840782—24no—
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36C2×C4×#92420C2211yescharacteristic
37C2×C4×#92420C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519749C411yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C22×C4×Dic61C2211yescharacteristic
51#16839662C411yescharacteristic
52#16839659C411yescharacteristic
53#16839654C411yescharacteristic
54#16839650C411yescharacteristic
55#16839641C411yescharacteristic
56#16839620C411yescharacteristic
57#16839613C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#386C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—22no—
63C2×#11758213—41no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—41no—
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75#14519844—22no—
76#14519844—41no—
77#14519844D414yescomplemented
78C4⋊#92420—41no—
79#14519834—22no—
80#14519834—22no—
81#14519834—41no—
82C22⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—22no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420—41no—
89#14519832—22no—
90#14519832—22no—
91C4×#92420—22no—
92C4×#92420—22no—
93C4×#92420—41no—
94C4×#92420—41no—
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C23×Dic61C2×C411yescharacteristic
98C23×Dic61C2311yescharacteristic
99C23×Dic61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101#14519749—24no—
102D4×Dic61—41no—
103D4×Dic61—41no—
104#14519737—22no—
105#14519737—22no—
106#14519737—41no—
107#14519737—41no—
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61C2×C411yescharacteristic
123C2×C4×Dic61C2×C411yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2311yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132C22×D4×C61C2×C411yescharacteristic
133C23×C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138#95×C61C2×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—41no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—41no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—41no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C2411yescharacteristic
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187#11758217—44no—
188C2×#92420—21no—
189C2×#92420—21no—
190C2×#92420—21no—
191C2×#92420—21no—
192C2×#92420—21no—
193C2×#92420—21no—
194C2×#92420—21no—
195C2×#92420—21no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—21no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420C2×D412yes—
209C2×#92420C2×D412yes—
210C2×#92420#4112yes—
211C2×#92420#4112yes—
212#11758213—44no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—41no—
215C22⋊C4×C61—41no—
216C22⋊Dic61—22no—
217C22⋊Dic61—41no—
218C22⋊Dic61—41no—
219#11758198—22no—
220#11758198—22no—
221#11758198—41no—
222#11758198—41no—
223C4⋊Dic61—41no—
224#11758196—22no—
225#11758196—22no—
226#11758196—41no—
227#11758196M1614yescomplemented
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61C2×D412yes—
237C4×Dic61#4112yes—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61#13112yes—
252C23×C61C23×C411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260D4×C61—44no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—44no—
275C2×C4×C61C4×D412yes—
276C2×C4×C61C2×M1612yes—
277C22⋊D61—44no—
278C22⋊D61—44no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—44no—
302C2×Dic61C4×D412yes—
303C2×Dic61C2×M1612yes—
304C2×Dic61C2×M1612yes—
305C2×Dic61#13112yes—
306C2×Dic61C22×D411yescharacteristic
307C2×Dic61C2×#4111yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61H(5,𝔽2)11yescharacteristic
311C2×Dic61H(5,𝔽2)11yescharacteristic
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316#92420—22no—
317#92420—22no—
318#92420—22no—
319#92420—22no—
320#92420—41no—
321#92420—41no—
322#92420—41no—
323#92420—41no—
324#23088—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61C2×C4×D411yescharacteristic
340C22×C61C4×#4111yescharacteristic
341C22×C61#51811yescharacteristic
342C22×C61C22×M1611yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61#56811yescharacteristic
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358Dic61—22no—
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—41no—
363Dic61#43614yes—
364Dic61#54611yescharacteristic
365Dic61#55011yescharacteristic
366Dic61#55311yescharacteristic
367Dic61#55511yescharacteristic
368C2×#436—611no—
369C2×#432—611no—
370C4×#121—611no—
371#1954—611no—
372#1954—611no—
373#1954—611no—
374#1939—611no—
375#1924—611no—
376#1924—611no—
377#1870—611no—
378#1870—611no—
379C8×C4⋊C4—611no—
380#1753—611no—
381#1753—611no—
382C4×C22⋊C8—611no—
383C2×C61—42no—
384C2×C61—81no—
385C2×C61#236311yescharacteristic
386C2×C61C2×#43611yescharacteristic
387C2×C61#293311yescharacteristic
388C2×C61#296611yescharacteristic
389C2×C61#297111yescharacteristic
390C2×C61#297411yescharacteristic
391C2×C61#298111yescharacteristic
392D61—81no—
393C22×M16—611no—
394C22×M16—611no—
395C2×#121—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C22×C42—611no—
400#436—1224no—
401#432—1224no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C22⋊C8—611no—
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×#97—611no—
417C2×#97—611no—
418C2×C4×C8—611no—
419C2×C4×C8—611no—
420C2×C4×C8—611no—
421C2×C4×C8—611no—
422#390—611no—
423#389—611no—
424#388—611no—
425#388—611no—
426#386—611no—
427#386#692311yescharacteristic
428#380—611no—
429C4×C4⋊C4—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438C61#2308811yescharacteristic, complemented, Sylow
439C22×D4—611no—
440C22×D4—611no—
441C22×D4C2×#692311yescharacteristic
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4C2×#692311yescharacteristic
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—2441no—
452C2×M16—2441no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461#121—1224no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—2441no—
465C4×D4—2441no—
466C4×D4—2441no—
467C4×D4—2441no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C22⋊C4—611no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4C2×#692311yescharacteristic
481C2×C22⋊C4C2×#692311yescharacteristic
482C2×C22⋊C4C2×#692311yescharacteristic
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—1222no—
490C2×C42—1222no—
491C4⋊C8—614no—
492C4⋊C8—1222no—
493C4⋊C8—2441no—
494C4⋊C8—2441no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497C22⋊C8—1222no—
498C22⋊C8—1222no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—2441no—
504C22⋊C8—2441no—
505#97—1222no—
506#97—1222no—
507C4×C8—1222no—
508C4×C8—1222no—
509C4×C8—2441no—
510C4×C8—2441no—
511#95—611no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95C2×#692311yescharacteristic
516#95C2×#692311yescharacteristic
517C24—611no—
518C24C22×#692311yescharacteristic
519C24C22×#692311yescharacteristic
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—1222no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—2441no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—41no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1222no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1222no—
558C22×C4—1221no—
559C22×C4—1222no—
560C22×C4C22×#692311yescharacteristic
561C22×C4C22×#692311yescharacteristic
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565M16—2444no—
566M16—2444no—
567C2×C8—612no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—612no—
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—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C4⋊C4—614no—
592C4⋊C4—1222no—
593C4⋊C4—1222no—
594C4⋊C4—2441no—
595C4⋊C4—2441no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—2441no—
603C22⋊C4—2441no—
604C22⋊C4—2441no—
605C22⋊C4—2441no—
606C42—612no—
607C42—612no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1222no—
614C42—1221no—
615C42—1222no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23#1451986412yes—
637C23C23×#692311yescharacteristic
638D4—44no—
639D4—2444no—
640D4—2444no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—44no—
655C2×C4—612no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—612no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2444no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4D4×#692312yes—
693C2×C4D61⋊M1612yes—
694C8—1222no—
695C8—1222no—
696C8—1222no—
697C8—1222no—
698C8—2441no—
699C8—2441no—
700C8—2441no—
701C8—2441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22C2×D4×#692311yescharacteristic
724C22#41×#692311yescharacteristic
725C22#1684082911yescharacteristic
726C22C2×D61⋊M1611yescharacteristic
727C22C2×#1451986411yescharacteristic
728C22D61⋊#13111yescharacteristic
729C22#1684084011yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—614no—
736C4—611no—
737C4—611no—
738C4—611no—
739C4—611no—
740C4—1222no—
741C4—2441no—
742C4—2441no—
743C4—2441no—
744C4—2441no—
745C2—42no—
746C2—81no—
747C2—4881no—
748C2#2146234611yescharacteristic
749C2D61⋊#43611yescharacteristic
750C2#2146255111yescharacteristic
751C2#2146263411yescharacteristic
752C2#2146266411yescharacteristic
753C2#2146267811yescharacteristic
754C2#2146270711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC2×#14519749C4
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#23088
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840795C2semidirect
2. C2×#16840782C2semidirect
3. #21461942C2semidirect
4. #21461942C2semidirect
5. #21461940C2semidirect
6. #21461918C2semidirect
7. #21461894C2semidirect
8. #21461892C2semidirect
9. #21461797C2semidirect
10. #21461796C2semidirect
11. #21461611C2semidirect
12. #21461561C2semidirect
13. #21461560C2semidirect
14. C4×C22⋊#92420C2semidirect
77. #14519844D4semidirect
227. #11758196M16semidirect
438. C61#23088semidirect

Maximal subgroups

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

subgroupindex
C2×#168407952
C2×#168407822
#214619422
#214619402
#214619182
#214618942
#214618922
#214617972
#214617962
#214616112
#214615612
#214615602
C4×C22⋊#924202
#214483292
#2308861