Finite Group Databasebeta

← #30619617

Subgroups — #30619617

Order 15616.

884 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461944C211yesmaximal, characteristic, complemented
2#21461942C211yesmaximal, characteristic, complemented
3#21461889C211yesmaximal, characteristic, complemented
4#21461888C211yesmaximal, characteristic, complemented
5#21461879C211yesmaximal, characteristic, complemented
6#21461872C211yesmaximal, characteristic, complemented
7#21461798C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461794C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461711C211yesmaximal, characteristic, complemented
12#21461561C211yesmaximal, characteristic, complemented
13C22⋊C4×#92420C211yesmaximal, characteristic, complemented
14C4×#14519834C211yesmaximal, characteristic, complemented
15#21448335C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×#14519834C2211yescharacteristic
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32C2×C4×#92420C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519748C411yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839660C411yescharacteristic
50#16839656C411yescharacteristic
51#16839656C411yescharacteristic
52#16839638C411yescharacteristic
53#16839638C411yescharacteristic
54#16839619C411yescharacteristic
55C4⋊C4×Dic61C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C61×#390C411yescharacteristic
59C2×#11758217—22no—
60C2×#11758217—41no—
61C2×#11758217—41no—
62C22×#92420—22no—
63C22×#92420—41no—
64C22×#92420—41no—
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73#14519844—41no—
74C4⋊#92420—41no—
75#14519834—22no—
76#14519834—22no—
77#14519834—41no—
78#14519834—41no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C22⋊#92420—41no—
82C22⋊#92420—41no—
83C22⋊#92420—41no—
84C22⋊#92420—41no—
85#14519832—41no—
86C4×#92420—41no—
87C4×#92420—41no—
88C4×#92420—41no—
89C22×C22⋊D61C2×C411yescharacteristic
90C22×C22⋊D61C2×C411yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93C22×C4×D61C2×C411yescharacteristic
94C22×C4×D61C2×C411yescharacteristic
95C22×C4×D61C2311yescharacteristic
96#14519748—24no—
97D4×Dic61—41no—
98D4×Dic61—41no—
99#14519737—41no—
100#14519737—41no—
101#14519737—41no—
102#14519737—41no—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×C4⋊Dic61C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—41no—
119C42×D61—41no—
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C42×C61C2×C411yescharacteristic
133C24×C61C22×C411yescharacteristic
134C24×C61C22×C411yescharacteristic
135C23×D61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—41no—
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—22no—
145C2×C22⋊D61—22no—
146C2×C22⋊D61—22no—
147C2×C22⋊D61—22no—
148C2×C22⋊D61—41no—
149C2×C22⋊D61—41no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C2411yescharacteristic
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181#11758217—44no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—21no—
187C2×#92420—21no—
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—44no—
205C2×#92420#4112yes—
206C2×#92420#4112yes—
207C4⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—41no—
211C22⋊C4×C61—41no—
212C42×C61—41no—
213C22⋊Dic61—22no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61M1614yescomplemented
217#11758198—41no—
218#11758198—41no—
219C4⋊Dic61—22no—
220C4⋊Dic61—41no—
221#11758196—41no—
222#11758196—41no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—41no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C2×M1612yes—
246C23×C61C23×C411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61#13112yes—
254D4×C61—44no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
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#13112yes—
269C2×C4×C61#13112yes—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
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—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61C2×M1612yes—
297C2×Dic61C2×M1612yes—
298C2×Dic61C2×#4111yescharacteristic
299C2×Dic61C2×#4111yescharacteristic
300C2×Dic61H(5,𝔽2)11yescharacteristic
301C2×Dic61H(5,𝔽2)11yescharacteristic
302C2×Dic61H(5,𝔽2)11yescharacteristic
303C2×Dic61H(5,𝔽2)11yescharacteristic
304C4×D61—44no—
305C4×D61—44no—
306C4×D61—41no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—41no—
310#92420—22no—
311#92420—22no—
312#92420—41no—
313#92420—41no—
314#92420—41no—
315#92420—41no—
316#92420—41no—
317#92420—41no—
318#22333—611nomaximal, Sylow
319C22×C61—22no—
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C4×#4111yescharacteristic
334C22×C61#51811yescharacteristic
335C22×C61#51811yescharacteristic
336C22×C61C22×M1611yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61C2×#13111yescharacteristic
339C22×C61C2×#13111yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—41no—
352Dic61—22no—
353Dic61—22no—
354Dic61—41no—
355Dic61—41no—
356Dic61—41no—
357Dic61—41no—
358Dic61#53811yescharacteristic
359Dic61#53811yescharacteristic
360Dic61#54011yescharacteristic
361Dic61#54011yescharacteristic
362C4×#121—611no—
363#1955—611no—
364#1954—611no—
365#1923—611no—
366#1923—611no—
367#1917—611no—
368#1916—611no—
369#1870—611no—
370#1870—611no—
371#1869—611no—
372#1869—611no—
373#1817—611no—
374#1753—611no—
375C8×C22⋊C4—611no—
376C4×C22⋊C8—611no—
377C2×C61—42no—
378C2×C61—81no—
379C2×C61#233311yescharacteristic
380C2×C61#296511yescharacteristic
381C2×C61#296611yescharacteristic
382C2×C61#297411yescharacteristic
383C2×C61#297411yescharacteristic
384C2×C61#297711yescharacteristic
385C2×C61#297911yescharacteristic
386D61—42no—
387C22×M16—611no—
388C23×C8—611no—
389C2×#121—611no—
390C2×C4×D4—611no—
391C2×C4×D4—611no—
392C2×C4×D4—611no—
393C22×C42—611no—
394C2×C4⋊C8—611no—
395C2×C4⋊C8—611no—
396C2×C22⋊C8—611no—
397C2×C22⋊C8—611no—
398C2×C22⋊C8—611no—
399C2×C22⋊C8—611no—
400C2×C22⋊C8—611no—
401C2×C22⋊C8—611no—
402C2×C22⋊C8—611no—
403C2×C22⋊C8—611no—
404C2×C22⋊C8—611no—
405C2×C22⋊C8—611no—
406C2×#97—611no—
407C2×C4×C8—611no—
408C2×C4×C8—611no—
409C2×C4×C8—611no—
410#390#692311yescharacteristic
411#389—611no—
412#388—611no—
413#388—611no—
414#386—611no—
415#386—611no—
416#380—611no—
417C4×C4⋊C4—611no—
418C4×C22⋊C4—611no—
419C4×C22⋊C4—611no—
420#336—611no—
421#336—611no—
422#336—611no—
423#336—611no—
424#336—611no—
425#336—611no—
426#336—611no—
427#336—611no—
428#336—611no—
429#336—611no—
430C61#2233311yescharacteristic, complemented, Sylow
431C22×D4—611no—
432C22×D4—611no—
433C22×D4C2×#692311yescharacteristic
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C2×M16—1222no—
440C2×M16—2441no—
441C2×M16—2441no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—1222no—
451C22×C8—2441no—
452C22×C8—2441no—
453#121—1224no—
454C4×D4—2441no—
455C4×D4—2441no—
456C4×D4—2441no—
457C4×D4—2441no—
458C4×D4—2441no—
459C4×D4—2441no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4C2×#692311yescharacteristic
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4C2×#692311yescharacteristic
472C2×C22⋊C4C2×#692311yescharacteristic
473C2×C22⋊C4C2×#692311yescharacteristic
474C2×C22⋊C4C2×#692311yescharacteristic
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—2441no—
481C2×C42—2441no—
482C2×C42C2×#692311yescharacteristic
483C4⋊C8—2441no—
484C4⋊C8—2441no—
485C22⋊C8—1222no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489C22⋊C8—2441no—
490C22⋊C8—2441no—
491C22⋊C8—2441no—
492C22⋊C8—2441no—
493C22⋊C8—2441no—
494C22⋊C8—2441no—
495#97—2441no—
496C4×C8—2441no—
497C4×C8—2441no—
498C4×C8—2441no—
499#95—611no—
500#95—611no—
501#95—611no—
502#95—611no—
503#95—611no—
504#95—611no—
505C24—611no—
506C24C22×#692311yescharacteristic
507C24C22×#692311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—1222no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—2441no—
516C2×D4—2441no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—2441no—
547C22×C4—2441no—
548C22×C4C22×#692311yescharacteristic
549C22×C4C22×#692311yescharacteristic
550C22×C4C22×#692311yescharacteristic
551C22×C4C22×#692311yescharacteristic
552C22×C4C22×#692311yescharacteristic
553M16—2444no—
554C2×C8—612no—
555C2×C8—612no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
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—2444no—
579C4⋊C4—22no—
580C4⋊C4—1222no—
581C4⋊C4—2441no—
582C4⋊C4—2441no—
583C4⋊C4—2441no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—614no—
589C22⋊C4—1222no—
590C22⋊C4—2441no—
591C22⋊C4—2441no—
592C22⋊C4—2441no—
593C22⋊C4—2441no—
594C42—41no—
595C42—1221no—
596C42—1221no—
597C42—1221no—
598C42—1221no—
599C42—1221no—
600C42—1221no—
601C42—1221no—
602C42—1221no—
603C42—2441no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—612no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23D61⋊M1612yes—
625C23C23×#692311yescharacteristic
626D4—44no—
627D4—2444no—
628D4—2444no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—611no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1221no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—2444no—
667C2×C4—2444no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4#1451986412yes—
681C2×C4#1451986412yes—
682C8—1222no—
683C8—1222no—
684C8—2441no—
685C8—2441no—
686C8—2441no—
687C8—2441no—
688C8—2441no—
689C8—2441no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—1222no—
705C22—1222no—
706C22—1222no—
707C22—2441no—
708C22—2441no—
709C22—2441no—
710C22—2441no—
711C22#41×#692311yescharacteristic
712C22#1684082911yescharacteristic
713C22#1684082911yescharacteristic
714C22C2×D61⋊M1611yescharacteristic
715C22C2×#1451986411yescharacteristic
716C22C2×#1451986411yescharacteristic
717C22D61⋊#13111yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—611no—
724C4—611no—
725C4—611no—
726C4—611no—
727C4—1222no—
728C4—1222no—
729C4—2441no—
730C4—2441no—
731C4—2441no—
732C4—2441no—
733C2—42no—
734C2—81no—
735C2—2442no—
736C2#2146231611yescharacteristic
737C2#2146262911yescharacteristic
738C2#2146263311yescharacteristic
739C2#2146267611yescharacteristic
740C2#2146267811yescharacteristic
741C2#2146269211yescharacteristic
742C2#2146270011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC2×#14519748C4
cosocleC22×Dic61C24
hypercenter#390#6923
hypocenterC61#22333
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461944C2semidirect
2. #21461942C2semidirect
3. #21461889C2semidirect
4. #21461888C2semidirect
5. #21461879C2semidirect
6. #21461872C2semidirect
7. #21461798C2semidirect
8. #21461796C2semidirect
9. #21461794C2semidirect
10. #21461792C2semidirect
11. #21461711C2semidirect
12. #21461561C2semidirect
13. C22⋊C4×#92420C2semidirect
14. C4×#14519834C2semidirect
216. C22⋊Dic61M16semidirect
430. C61#22333semidirect

Maximal subgroups

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

subgroupindex
#214619442
#214619422
#214618892
#214618882
#214618792
#214618722
#214617982
#214617962
#214617942
#214617922
#214617112
#214615612
C22⋊C4×#924202
C4×#145198342
#214483352
#2233361