Finite Group Databasebeta

← #30622511

Subgroups — #30622511

Order 15616.

1014 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840793C211yesmaximal, characteristic, complemented
2C2×#16840789C211yesmaximal, characteristic, complemented
3#21461895C211yesmaximal, characteristic, complemented
4#21461892C211yesmaximal, characteristic, complemented
5#21461878C211yesmaximal, characteristic, complemented
6#21461874C211yesmaximal, characteristic, complemented
7#21461798C211yesmaximal, characteristic, complemented
8#21461794C211yesmaximal, characteristic, complemented
9#21461793C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461561C211yesmaximal, characteristic, complemented
12#21461557C211yesmaximal, characteristic, complemented
13#21461545C211yesmaximal, characteristic, complemented
14C2×#16840628C211yesmaximal, characteristic, complemented
15#21448329C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C23×#92420C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840793—24no—
21#16840789—24no—
22C2×#14519844C2211yescharacteristic
23C2×#14519844C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
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×#11758217—22no—
62C2×#11758217—22no—
63C2×#11758217—41no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—41no—
67C22×#92420—22no—
68C22×#92420—22no—
69C22×#92420—22no—
70C22×#92420—22no—
71C22×#92420—41no—
72C22×#92420—41no—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82#14519844—22no—
83#14519834—22no—
84#14519834—22no—
85#14519834—41no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420—22no—
89C22⋊#92420—41no—
90C22⋊#92420D414yescomplemented
91#14519832—22no—
92#14519832—41no—
93#14519832—41no—
94C4×#92420—22no—
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C23×Dic61C2×C411yescharacteristic
98C23×Dic61C2311yescharacteristic
99C23×Dic61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101#14519749—24no—
102D4×Dic61—22no—
103D4×Dic61—22no—
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—41no—
121C2×C4×Dic61—41no—
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—22no—
145C22×C4×C61—22no—
146C22×C4×C61—41no—
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—41no—
158C2×C22⋊D61M1614yescomplemented
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—41no—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C2×D412yes—
179C22×Dic61#4112yes—
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×#92420—44no—
209C2×#92420—44no—
210C2×#92420C2×D412yes—
211C2×#92420C2×D412yes—
212C2×#92420#4112yes—
213C2×#92420#4112yes—
214D61⋊C8—44no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—41no—
217C22⋊C4×C61—41no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221#11758198—22no—
222#11758198—22no—
223#11758198—41no—
224#11758198—41no—
225C4⋊Dic61—22no—
226#11758196—22no—
227#11758196—22no—
228#11758196—22no—
229#11758196—41no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—41no—
239C4×Dic61—41no—
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×C61C4×D412yes—
252C23×C61C2×M1612yes—
253C23×C61#13112yes—
254C23×C61C23×C411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61C2×M1612yes—
262D4×C61—44no—
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—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—44no—
279C22⋊D61—28no—
280C22⋊D61—44no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—44no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61C4×D412yes—
306C2×Dic61C2×M1612yes—
307C2×Dic61#13112yes—
308C2×Dic61C22×D411yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61H(5,𝔽2)11yescharacteristic
313C2×Dic61H(5,𝔽2)11yescharacteristic
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318#92420—22no—
319#92420—22no—
320#92420—22no—
321#92420—22no—
322#92420—41no—
323#92420—41no—
324#92420—41no—
325#92420—41no—
326#23117—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61#43514yes—
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C4×#4111yescharacteristic
343C22×C61#51811yescharacteristic
344C22×C61C22×M1611yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61C2×#13111yescharacteristic
347C22×C61#56811yescharacteristic
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C4×C61—41no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—41no—
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—41no—
364Dic61—41no—
365Dic61—41no—
366Dic61#54611yescharacteristic
367Dic61#54611yescharacteristic
368Dic61#55311yescharacteristic
369Dic61#55311yescharacteristic
370C2×#435—611no—
371C2×C8×D4—611no—
372C4×#121—611no—
373#1924—611no—
374#1924—611no—
375#1917—611no—
376#1916—611no—
377#1870—611no—
378#1869—611no—
379#1869—611no—
380#1869—611no—
381#1753—611no—
382#1752—611no—
383#1749—611no—
384C2×#336—611no—
385C2×C61—24no—
386C2×C61—81no—
387C2×C61#236411yescharacteristic
388C2×C61C2×#43511yescharacteristic
389C2×C61#293511yescharacteristic
390C2×C61#296611yescharacteristic
391C2×C61#297011yescharacteristic
392C2×C61#297411yescharacteristic
393C2×C61#297611yescharacteristic
394D61—42no—
395C22×M16—611no—
396C23×C8—611no—
397C23×C8—611no—
398C23×C8—611no—
399C2×#121—611no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403C22×C42—611no—
404#435—1224no—
405C8×D4—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊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×#97—611no—
419C2×C4×C8—611no—
420#390—611no—
421#389—611no—
422#388—611no—
423#388—611no—
424#386—611no—
425#386#692311yescharacteristic
426#380—611no—
427C4×C4⋊C4—611no—
428C4×C22⋊C4—611no—
429C4×C22⋊C4—611no—
430#336—611no—
431#336—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440C61#2311711yescharacteristic, complemented, Sylow
441C22×D4—611no—
442C22×D4—611no—
443C22×D4C2×#692311yescharacteristic
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4C2×#692311yescharacteristic
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—2441no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—1222no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—1222no—
464C22×C8—1222no—
465C22×C8—1222no—
466C22×C8—2441no—
467C22×C8—2441no—
468C22×C8—2441no—
469#121—1224no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2441no—
475C4×D4—2441no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4C2×#692311yescharacteristic
489C2×C22⋊C4C2×#692311yescharacteristic
490C2×C22⋊C4C2×#692311yescharacteristic
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—2441no—
498C2×C42—2441no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C22⋊C8—614no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—2441no—
508C22⋊C8—2441no—
509#97—1222no—
510#97—2441no—
511#97—2441no—
512C4×C8—1222no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95C2×#692311yescharacteristic
518#95C2×#692311yescharacteristic
519C24—611no—
520C24C22×#692311yescharacteristic
521C24C22×#692311yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—614no—
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—2441no—
531C22×C4—22no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—611no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
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—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—2441no—
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565C22×C4C22×#692311yescharacteristic
566C22×C4C22×#692311yescharacteristic
567M16—2444no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—612no—
571C2×C8—612no—
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—
591C2×C8—1221no—
592C2×C8—2444no—
593C2×C8—2444no—
594C2×C8—2444no—
595C4⋊C4—1222no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—2441no—
609C22⋊C4—2441no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—2441no—
619C42—2441no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—612no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23D4×#692312yes—
639C23D61⋊M1612yes—
640C23#1451986412yes—
641C23C23×#692311yescharacteristic
642D4—44no—
643D4—1228no—
644D4—2444no—
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—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—44no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2444no—
698C8—1222no—
699C8—1222no—
700C8—1222no—
701C8—1222no—
702C8—2441no—
703C8—2441no—
704C8—2441no—
705C8—2441no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22#1684079414yes—
727C22C2×D4×#692311yescharacteristic
728C22#41×#692311yescharacteristic
729C22#1684082911yescharacteristic
730C22C2×D61⋊M1611yescharacteristic
731C22C2×#1451986411yescharacteristic
732C22D61⋊#13111yescharacteristic
733C22#1684084011yescharacteristic
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—611no—
740C4—611no—
741C4—611no—
742C4—611no—
743C4—1222no—
744C4—1222no—
745C4—1222no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C2—24no—
750C2—81no—
751C2—2442no—
752C2#2146234711yescharacteristic
753C2C2×#1684079411yescharacteristic
754C2#2146256311yescharacteristic
755C2#2146263411yescharacteristic
756C2#2146265911yescharacteristic
757C2#2146267611yescharacteristic
758C2#2146268511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC2×#14519749C4
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#23117
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840793C2semidirect
2. C2×#16840789C2semidirect
3. #21461895C2semidirect
4. #21461892C2semidirect
5. #21461878C2semidirect
6. #21461874C2semidirect
7. #21461798C2semidirect
8. #21461794C2semidirect
9. #21461793C2semidirect
10. #21461792C2semidirect
11. #21461561C2semidirect
12. #21461557C2semidirect
13. #21461545C2semidirect
14. C2×#16840628C2semidirect
90. C22⋊#92420D4semidirect
158. C2×C22⋊D61M16semidirect
440. C61#23117semidirect

Maximal subgroups

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

subgroupindex
C2×#168407932
C2×#168407892
#214618952
#214618922
#214618782
#214618742
#214617982
#214617942
#214617932
#214617922
#214615612
#214615572
#214615452
C2×#168406282
#214483292
#2311761