Finite Group Databasebeta

← #30622392

Subgroups — #30622392

Order 15616.

1040 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×#16840789C211yesmaximal, characteristic, complemented
2C2×#16840780C211yesmaximal, characteristic, complemented
3#21461942C211yesmaximal, characteristic, complemented
4#21461942C211yesmaximal, characteristic, complemented
5#21461941C211yesmaximal, characteristic, complemented
6#21461918C211yesmaximal, characteristic, complemented
7#21461890C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461611C211yesmaximal, characteristic, complemented
12#21461553C211yesmaximal, characteristic, complemented
13C22⋊C4×#92420C211yesmaximal, characteristic, complemented
14C4×#14519834C211yesmaximal, characteristic, complemented
15#21448331C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18#16840789—24no—
19#16840780—24no—
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
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×#14519750C411yescharacteristic
47C2×#14519739C2211yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×C42×D61C2211yescharacteristic
51#16839662C411yescharacteristic
52#16839657C411yescharacteristic
53#16839653C411yescharacteristic
54#16839640C411yescharacteristic
55#16839638C411yescharacteristic
56#16839621C411yescharacteristic
57#16839613C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#388C411yescharacteristic
61C2×D61⋊C8—22no—
62C2×D61⋊C8—22no—
63C2×D61⋊C8—41no—
64C22×#92420—22no—
65C22×#92420—22no—
66C22×#92420—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—22no—
82#14519834—22no—
83#14519834—22no—
84#14519834—22no—
85#14519834—41no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420—41no—
89C4×#92420—22no—
90C4×#92420—22no—
91C4×#92420—22no—
92C4×#92420—22no—
93C4×#92420—41no—
94C4×#92420—41no—
95C22×D244C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C23×Dic61C2311yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2311yescharacteristic
103#14519750C818yescomplemented
104#14519739—41no—
105#14519739—41no—
106#14519737—22no—
107#14519737—22no—
108#14519737—41no—
109#14519737—41no—
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×#11758196C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×C4×Dic61C2×C411yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2311yescharacteristic
126C42×D61—22no—
127C42×D61—22no—
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131#14519684C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C42×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138#95×C61C2×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61C2×C814yes—
153C2×C22⋊D61C2×C814yescomplemented
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C2411yescharacteristic
166C2×D244—41no—
167C2×D244—41no—
168C2×D244C2×C814yescomplemented
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—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—41no—
186C2×C4×D61C2×C814yescomplemented
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—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—44no—
208C2×#92420C2×D412yes—
209C2×#92420C2×D412yes—
210C2×#92420#4112yes—
211C2×#92420#4112yes—
212D61⋊C8—44no—
213C4⋊C4×C61—41no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—41no—
216C22⋊C4×C61C2×C814yescomplemented
217C42×C61—22no—
218C22⋊Dic61—22no—
219#11758198—22no—
220#11758198—22no—
221#11758198—41no—
222#11758198—41no—
223#11758198—41no—
224#11758198C2×C814yescomplemented
225#11758196—22no—
226#11758196—22no—
227#11758196—41no—
228#11758196C2×C814yescomplemented
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×C61C22×C812yes—
245C23×C61C23×C411yescharacteristic
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61C22×C812yes—
259C22×D61C22×C812yes—
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—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×C61C4×D412yes—
276C2×C4×C61C22×C812yes—
277C2×C4×C61C22×C812yes—
278C22⋊D61—28no—
279C22⋊D61—44no—
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—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61C4×D412yes—
295C2×Dic61C22×C812yes—
296C2×Dic61C22×C812yes—
297C2×Dic61#13112yes—
298C2×Dic61#13112yes—
299C2×Dic61C22×D411yescharacteristic
300C2×Dic61C2×#4111yescharacteristic
301C2×Dic61C2×#4111yescharacteristic
302C2×Dic61C2×#4111yescharacteristic
303C2×Dic61H(5,𝔽2)11yescharacteristic
304C2×Dic61H(5,𝔽2)11yescharacteristic
305D244—44no—
306C4×D61—28no—
307C4×D61—44no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—41no—
311C4×D61—41no—
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#23083—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61C2×C4×D411yescharacteristic
333C22×C61C4×#4111yescharacteristic
334C22×C61#51811yescharacteristic
335C22×C61C23×C811yescharacteristic
336C22×C61C2×#13111yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61#56811yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—41no—
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—22no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61—41no—
359Dic61—22no—
360Dic61—22no—
361Dic61—41no—
362Dic61—41no—
363Dic61C8×D414yes—
364Dic61#54611yescharacteristic
365Dic61#55011yescharacteristic
366Dic61#55311yescharacteristic
367Dic61#55511yescharacteristic
368C2×C8×D4—611no—
369C2×#431—611no—
370C4×#121—611no—
371#1954—611no—
372#1954—611no—
373#1954—611no—
374#1939—611no—
375#1923—611no—
376#1923—611no—
377#1869—611no—
378#1869—611no—
379C8×C4⋊C4—611no—
380C8×C22⋊C4—611no—
381C8×C22⋊C4—611no—
382C4×C22⋊C8—611no—
383C2×C61—42no—
384C2×C61#236311yescharacteristic
385C2×C61C2×C8×D411yescharacteristic
386C2×C61#293311yescharacteristic
387C2×C61C8×#4111yescharacteristic
388C2×C61#296911yescharacteristic
389C2×C61#297211yescharacteristic
390C2×C61#297911yescharacteristic
391D61—42no—
392D61—42no—
393C23×C8—611no—
394C23×C8—611no—
395C2×#121—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C22×C42—611no—
400C8×D4—1224no—
401#431—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×C4×C8—611no—
417C2×C4×C8—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#692311yescharacteristic
426#386—611no—
427#386—611no—
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#2308311yescharacteristic, complemented, Sylow
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—1222no—
456C22×C8—1222no—
457C22×C8—1222no—
458C22×C8—1222no—
459C22×C8—2441no—
460C22×C8—2441no—
461#121—618no—
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⋊C4C2×#692311yescharacteristic
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—1222no—
489C2×C42—1222no—
490C2×C42C2×#692311yescharacteristic
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—
505C4×C8—1222no—
506C4×C8—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—
518C24—611no—
519C24C22×#692311yescharacteristic
520C2×D4—614no—
521C2×D4—614no—
522C2×D4—614no—
523C2×D4—1222no—
524C2×D4—1222no—
525C2×D4—2441no—
526C2×D4—2441no—
527C2×D4—2441no—
528C2×D4—2441no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—614no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—1222no—
537C22×C4—1222no—
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—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1222no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1222no—
558C22×C4—2441no—
559C22×C4C22×#692311yescharacteristic
560C22×C4C22×#692311yescharacteristic
561C22×C4C22×#692311yescharacteristic
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565C2×C8—612no—
566C2×C8—612no—
567C2×C8—612no—
568C2×C8—612no—
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—
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—2444no—
590C2×C8—2444no—
591C4⋊C4—41no—
592C4⋊C4—614no—
593C4⋊C4—1222no—
594C4⋊C4—1222no—
595C4⋊C4—2441no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—614no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—1222no—
602C22⋊C4—2441no—
603C22⋊C4—2441no—
604C22⋊C4—2441no—
605C22⋊C4D61⋊C814yescomplemented
606C42—22no—
607C42—612no—
608C42—612no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1222no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—612no—
623C23—612no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23C2×D61⋊C812yes—
637C23C23×#692311yescharacteristic
638D4—1228no—
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—21no—
655C2×C4—21no—
656C2×C4—612no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—612no—
664C2×C4—612no—
665C2×C4—612no—
666C2×C4—612no—
667C2×C4—1228no—
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—2444no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4D4×#692312yes—
692C2×C4C2×D61⋊C812yes—
693C2×C4C2×D61⋊C812yes—
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—1222no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22C2×D4×#692311yescharacteristic
724C22#41×#692311yescharacteristic
725C22#1684082911yescharacteristic
726C22C22×D61⋊C811yescharacteristic
727C22D61⋊#13111yescharacteristic
728C22D61⋊#13111yescharacteristic
729C22#1684084111yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—611no—
737C4—611no—
738C4—611no—
739C4—611no—
740C4—614no—
741C4—1222no—
742C4—1222no—
743C4—2441no—
744C4—2441no—
745C2—42no—
746C2—2442no—
747C2—2442no—
748C2#2146234611yescharacteristic
749C2D4×D61⋊C811yescharacteristic
750C2#2146255311yescharacteristic
751C2#2146262311yescharacteristic
752C2#2146265411yescharacteristic
753C2#2146266711yescharacteristic
754C2#2146270111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C23×C8
FittingC61×#388C4
socleC23×C61C23×C4
prime radicalC2×#14519750C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61#23083
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840789C2semidirect
2. C2×#16840780C2semidirect
3. #21461942C2semidirect
4. #21461942C2semidirect
5. #21461941C2semidirect
6. #21461918C2semidirect
7. #21461890C2semidirect
8. #21461888C2semidirect
9. #21461795C2semidirect
10. #21461794C2semidirect
11. #21461611C2semidirect
12. #21461553C2semidirect
13. C22⋊C4×#92420C2semidirect
14. C4×#14519834C2semidirect
77. #14519844D4semidirect
103. #14519750C8semidirect
153. C2×C22⋊D61C2×C8semidirect
168. C2×D244C2×C8semidirect
186. C2×C4×D61C2×C8semidirect
216. C22⋊C4×C61C2×C8semidirect
224. #11758198C2×C8semidirect
228. #11758196C2×C8semidirect
438. C61#23083semidirect
605. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#168407892
C2×#168407802
#214619422
#214619412
#214619182
#214618902
#214618882
#214617952
#214617942
#214616112
#214615532
C22⋊C4×#924202
C4×#145198342
#214483312
#2308361