Finite Group Databasebeta

← #30619616

Subgroups — #30619616

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#21461943C211yesmaximal, characteristic, complemented
2#21461940C211yesmaximal, characteristic, complemented
3#21461889C211yesmaximal, characteristic, complemented
4#21461888C211yesmaximal, characteristic, complemented
5#21461876C211yesmaximal, characteristic, complemented
6#21461875C211yesmaximal, characteristic, complemented
7#21461796C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461792C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461710C211yesmaximal, characteristic, complemented
12#21461561C211yesmaximal, characteristic, complemented
13C22⋊C4×#92420C211yesmaximal, characteristic, complemented
14C4×C22⋊#92420C211yesmaximal, characteristic, complemented
15#121×Dic61C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×C22⋊#92420C2211yescharacteristic
21C2×C22⋊#92420C2211yescharacteristic
22C2×C22⋊#92420C2211yescharacteristic
23C2×C22⋊#92420C2211yescharacteristic
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×D4×Dic61C2211yescharacteristic
45C2×D4×Dic61C2211yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C22×C4×Dic61C2211yescharacteristic
48#16839665C411yescharacteristic
49#16839661C411yescharacteristic
50#16839655C411yescharacteristic
51#16839655C411yescharacteristic
52#16839642C411yescharacteristic
53#16839642C411yescharacteristic
54#16839622C411yescharacteristic
55C4⋊C4×Dic61C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C2×#121×C61C411yescharacteristic
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—
75C22⋊#92420—22no—
76C22⋊#92420—22no—
77C22⋊#92420—22no—
78C22⋊#92420—22no—
79C22⋊#92420—41no—
80C22⋊#92420—41no—
81C22⋊#92420—41no—
82C22⋊#92420—41no—
83C22⋊#92420—41no—
84C22⋊#92420—41no—
85#14519832—41no—
86C4×#92420—41no—
87C4×#92420—41no—
88C4×#92420—41no—
89C23×Dic61C2×C411yescharacteristic
90C23×Dic61C2311yescharacteristic
91C23×Dic61C2311yescharacteristic
92C23×Dic61C2311yescharacteristic
93D4×Dic61—41no—
94D4×Dic61—41no—
95D4×Dic61—41no—
96D4×Dic61—41no—
97D4×Dic61—41no—
98D4×Dic61—41no—
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×C4⋊Dic61C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×C22⋊Dic61C2×C411yescharacteristic
105C2×C22⋊Dic61C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C4×Dic61—41no—
112C2×C4×Dic61—41no—
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125C22×D4×C61C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127C22×D4×C61C2×C411yescharacteristic
128C23×C4×C61C2×C411yescharacteristic
129#121×C61—24no—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C24×C61C22×C411yescharacteristic
134C24×C61C22×C411yescharacteristic
135C24×C61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—41no—
143C2×D4×C61—41no—
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×Dic61—22no—
153C22×Dic61—22no—
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×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—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C2411yescharacteristic
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×C61M1614yescomplemented
210C22⋊Dic61—22no—
211C22⋊Dic61—22no—
212C22⋊Dic61—41no—
213C22⋊Dic61—41no—
214C22⋊Dic61—41no—
215C22⋊Dic61—41no—
216C22⋊Dic61—41no—
217C22⋊Dic61—41no—
218C4⋊Dic61—22no—
219C4⋊Dic61—41no—
220C4⋊Dic61—41no—
221C4⋊Dic61—41no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—41no—
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×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61C2×M1612yes—
252C23×C61#13112yes—
253C23×C61C23×C411yescharacteristic
254D4×C61—44no—
255D4×C61—44no—
256D4×C61—44no—
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—44no—
267C2×C4×C61C2×M1612yes—
268C2×C4×C61C2×M1612yes—
269C2×C4×C61#13112yes—
270C2×Dic61—21no—
271C2×Dic61—21no—
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—21no—
289C2×Dic61—21no—
290C2×Dic61—44no—
291C2×Dic61—41no—
292C2×Dic61—41no—
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—41no—
302C2×Dic61—41no—
303C2×Dic61#13112yes—
304C2×Dic61C2×#4111yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306C2×Dic61H(5,𝔽2)11yescharacteristic
307C2×Dic61H(5,𝔽2)11yescharacteristic
308C2×Dic61H(5,𝔽2)11yescharacteristic
309C2×Dic61H(5,𝔽2)11yescharacteristic
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—22no—
323C22×C61—22no—
324C22×C61—22no—
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×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C4×#4111yescharacteristic
341C22×C61#51811yescharacteristic
342C22×C61#51811yescharacteristic
343C22×C61C22×M1611yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61C2×#13111yescharacteristic
347C4×C61—22no—
348C4×C61—22no—
349C4×C61—22no—
350C4×C61—41no—
351Dic61—22no—
352Dic61—41no—
353Dic61—41no—
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—42no—
379C2×C61—81no—
380C2×C61#233311yescharacteristic
381C2×C61#296511yescharacteristic
382C2×C61#296611yescharacteristic
383C2×C61#297411yescharacteristic
384C2×C61#297411yescharacteristic
385C2×C61#297711yescharacteristic
386C2×C61#297911yescharacteristic
387C22×M16—611no—
388C23×C8—611no—
389C2×#121#692311yescharacteristic
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—611no—
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×D4C2×#692311yescharacteristic
432C22×D4C2×#692311yescharacteristic
433C22×D4C2×#692311yescharacteristic
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4C2×#692311yescharacteristic
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—24no—
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⋊C4—611no—
472C2×C22⋊C4—611no—
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—611no—
481C2×C42—2441no—
482C2×C42—2441no—
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—
505C24C22×#692311yescharacteristic
506C24C22×#692311yescharacteristic
507C24C22×#692311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
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—1221no—
545C22×C4—1221no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—2441no—
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—1222no—
586C22⋊C4—1222no—
587C22⋊C4—2441no—
588C22⋊C4—2441no—
589C22⋊C4—2441no—
590C22⋊C4—2441no—
591C22⋊C4—2441no—
592C22⋊C4—2441no—
593C22⋊C4#1175821714yescomplemented
594C42—1221no—
595C42—1221no—
596C42—1221no—
597C42—1221no—
598C42—1221no—
599C42—1221no—
600C42—1221no—
601C42—1221no—
602C42—2441no—
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—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×#1175821712yes—
624C23#1451986412yes—
625C23C23×#692311yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
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—44no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—612no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
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—2441no—
667C2×C4—2441no—
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—2444no—
679C2×C4C2×#1175821712yes—
680C2×C4C2×#1175821712yes—
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—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22#41×#692311yescharacteristic
712C22#1684082911yescharacteristic
713C22#1684082911yescharacteristic
714C22C22×#1175821711yescharacteristic
715C22C2×#1451986411yescharacteristic
716C22C2×#1451986411yescharacteristic
717C22D61⋊#13111yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—611no—
723C4—611no—
724C4—611no—
725C4—611no—
726C4—1222no—
727C4—2441no—
728C4—2441no—
729C4—2441no—
730C4—2441no—
731C4—2441no—
732C4—2441no—
733C2—42no—
734C2—42no—
735C2—81no—
736C2#2146231611yescharacteristic
737C2#2146262811yescharacteristic
738C2#2146263211yescharacteristic
739C2#2146267511yescharacteristic
740C2#2146267511yescharacteristic
741C2#2146269211yescharacteristic
742C2#2146269911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
Fitting, prime radicalC2×#121×C61C4
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#22333
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461943C2semidirect
2. #21461940C2semidirect
3. #21461889C2semidirect
4. #21461888C2semidirect
5. #21461876C2semidirect
6. #21461875C2semidirect
7. #21461796C2semidirect
8. #21461796C2semidirect
9. #21461792C2semidirect
10. #21461792C2semidirect
11. #21461710C2semidirect
12. #21461561C2semidirect
13. C22⋊C4×#92420C2semidirect
14. C4×C22⋊#92420C2semidirect
209. C22⋊C4×C61M16semidirect
430. C61#22333semidirect
593. C22⋊C4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214619432
#214619402
#214618892
#214618882
#214618762
#214618752
#214617962
#214617922
#214617102
#214615612
C22⋊C4×#924202
C4×C22⋊#924202
#121×Dic612
#2233361