Finite Group Databasebeta

← #30621727

Subgroups — #30621727

Order 15616.

1164 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840796C211yesmaximal, characteristic, complemented
2C2×#16840795C211yesmaximal, characteristic, complemented
3C2×#16840736C211yesmaximal, characteristic, complemented
4C2×#16840735C211yesmaximal, characteristic, complemented
5#21461942C211yesmaximal, characteristic, complemented
6#21461889C211yesmaximal, characteristic, complemented
7#21461888C211yesmaximal, characteristic, complemented
8#21461797C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461767C211yesmaximal, characteristic, complemented
12#21461766C211yesmaximal, characteristic, complemented
13#21461553C211yesmaximal, characteristic, complemented
14C22⋊C4×#92420C211yesmaximal, characteristic, complemented
15#21449033C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20C23×#92420C2211yescharacteristic
21#16840796—24no—
22#16840795—24no—
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2211yescharacteristic
25C2×C4⋊#92420C2211yescharacteristic
26#16840736—24no—
27#16840735—24no—
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40C2×C4×#92420C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C22×#11758224C2211yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52#16839682C411yescharacteristic
53#16839677C411yescharacteristic
54#16839677C411yescharacteristic
55#16839675C411yescharacteristic
56#16839671C411yescharacteristic
57#16839671C411yescharacteristic
58#16839670C411yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#394C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—41no—
68C2×#11758213—41no—
69C2×#11758217—22no—
70C2×#11758217—22no—
71C2×#11758217—41no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—22no—
74C2×D61⋊C8—41no—
75C22×#92420—22no—
76C22×#92420—22no—
77C22×#92420—41no—
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85C22×#92420C2311yescharacteristic
86#14519844—22no—
87#14519844—41no—
88C4⋊#92420—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—41no—
93#14519834D414yescomplemented
94C22⋊#92420—22no—
95C22⋊#92420—22no—
96C22⋊#92420—22no—
97C22⋊#92420—22no—
98C22⋊#92420—22no—
99C22⋊#92420D414yescomplemented
100C4×#92420—22no—
101C4×#92420—22no—
102C4×#92420—41no—
103C2×#11758224—22no—
104C2×#11758224—22no—
105C2×#11758224—22no—
106C2×#11758224—22no—
107C2×#11758224—41no—
108C2×#11758224—41no—
109C22×Dic122C2×C411yescharacteristic
110C22×D244C2×C411yescharacteristic
111C22×C22⋊D61C2×C411yescharacteristic
112C22×C22⋊D61C2×C411yescharacteristic
113C22×C22⋊D61C2×C411yescharacteristic
114C22×C22⋊D61C2×C411yescharacteristic
115C23×Dic61C2311yescharacteristic
116C23×Dic61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119#14519739—22no—
120#14519739—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—41no—
124#14519737—41no—
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×C22⋊Dic61C2×C411yescharacteristic
128C2×C22⋊Dic61C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143C22×D4×C61C2×C411yescharacteristic
144C2×C4⋊C4×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150C24×C61C22×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C2×D4×C61—22no—
155C2×D4×C61—22no—
156C2×D4×C61—41no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C2×C22⋊D61—41no—
173C2×C22⋊D61—41no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C2×D412yes—
190C22×Dic61#4112yes—
191C22×Dic61C2411yescharacteristic
192#11758224—44no—
193#11758224—44no—
194#11758224—44no—
195#11758224—44no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—41no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61C2×D412yes—
210C2×C4×D61#4112yes—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—41no—
214#11758217—44no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—21no—
231C2×#92420—21no—
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—44no—
236C2×#92420C2×D412yes—
237C2×#92420C2×D412yes—
238C2×#92420C2×D412yes—
239C2×#92420C2×D412yes—
240#11758213—44no—
241#11758213—44no—
242D61⋊C8—44no—
243C4⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—41no—
248C22⋊Dic61—22no—
249C22⋊Dic61—22no—
250#11758198—22no—
251#11758198—22no—
252#11758198—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—41no—
256#11758196—22no—
257#11758196—41no—
258C4×Dic61—21no—
259C4×Dic61—21no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—21no—
263C4×Dic61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61C4×D412yes—
278C23×C61C23×C411yescharacteristic
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61C4×D412yes—
293D4×C61—44no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61C4×D412yes—
308C2×C4×C61#13112yes—
309C22⋊D61—44no—
310C22⋊D61—44no—
311C22⋊D61—44no—
312C22⋊D61—44no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61C4×D412yes—
334C2×Dic61#13112yes—
335C2×Dic61#13112yes—
336C2×Dic61C22×D411yescharacteristic
337C2×Dic61C22×D411yescharacteristic
338C2×Dic61C2×#4111yescharacteristic
339C2×Dic61C2×#4111yescharacteristic
340C2×Dic61H(5,𝔽2)11yescharacteristic
341C2×Dic61H(5,𝔽2)11yescharacteristic
342D244—44no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351Dic122—44no—
352#92420—22no—
353#92420—22no—
354#92420—22no—
355#92420—22no—
356#92420—41no—
357#92420—41no—
358#92420—41no—
359#92420—41no—
360#22853—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61C2×C4×D411yescharacteristic
376C22×C61C2×C4×D411yescharacteristic
377C22×C61#51811yescharacteristic
378C22×C61C2×#13111yescharacteristic
379C22×C61C2×#13111yescharacteristic
380C22×C61C2×#13111yescharacteristic
381C22×C61#56811yescharacteristic
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—41no—
401Dic61—22no—
402Dic61—22no—
403Dic61—22no—
404Dic61—41no—
405Dic61—41no—
406Dic61D4211yescharacteristic
407Dic61#54611yescharacteristic
408Dic61#54611yescharacteristic
409Dic61#55111yescharacteristic
410C2×#436—611no—
411C2×#436—611no—
412C2×#408—611no—
413C2×#408—611no—
414#2388—611no—
415#1954—611no—
416#1923—611no—
417#1923—611no—
418#1870—611no—
419#1869—611no—
420#1869—611no—
421#1851—611no—
422#1851—611no—
423C8×C22⋊C4—611no—
424C8×C22⋊C4—611no—
425C2×C61—42no—
426C2×C61—81no—
427C2×C61#235811yescharacteristic
428C2×C61#293111yescharacteristic
429C2×C61#293111yescharacteristic
430C2×C61#293311yescharacteristic
431C2×C61#293311yescharacteristic
432C2×C61#297611yescharacteristic
433C2×C61#297911yescharacteristic
434D61—42no—
435D61—81no—
436C22×#41—611no—
437C22×M16—611no—
438C22×M16—611no—
439C22×M16—611no—
440C23×C8—611no—
441C23×C8—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445#436—1224no—
446#436—1224no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450#408—1224no—
451#408—1224no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8—611no—
463C2×C4×C8—611no—
464C2×C4×C8—611no—
465C2×C4×C8—611no—
466#395—611no—
467#394—611no—
468#394—611no—
469#394#692311yescharacteristic
470#393—611no—
471#392—611no—
472#392—611no—
473#392—611no—
474C4×C22⋊C4—611no—
475C4×C22⋊C4—611no—
476C4×C22⋊C4—611no—
477#336—611no—
478#336—611no—
479#336—611no—
480#336—611no—
481#336—611no—
482#336—611no—
483C61#2285311yescharacteristic, complemented, Sylow
484C2×#41—1222no—
485C2×#41—1222no—
486C2×#41—1222no—
487C2×#41—1222no—
488C2×#41—2441no—
489C2×#41—2441no—
490C22×Q8—611no—
491C22×D4—611no—
492C22×D4—611no—
493C22×D4—611no—
494C22×D4—611no—
495C22×D4—611no—
496C22×D4C2×#692311yescharacteristic
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C2×M16—1222no—
502C2×M16—1222no—
503C2×M16—1222no—
504C2×M16—1222no—
505C2×M16—1222no—
506C2×M16—1222no—
507C2×M16—2441no—
508C2×M16—2441no—
509C2×M16—2441no—
510C22×C8—611no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8—611no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—1222no—
519C22×C8—1222no—
520C22×C8—1222no—
521C22×C8—1222no—
522C22×C8—2441no—
523C22×C8—2441no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—2441no—
529C4×D4—2441no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4C2×#692311yescharacteristic
533C2×C22⋊C4—611no—
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—611no—
538C2×C22⋊C4—611no—
539C2×C22⋊C4—611no—
540C2×C22⋊C4—611no—
541C2×C22⋊C4C2×#692311yescharacteristic
542C2×C22⋊C4C2×#692311yescharacteristic
543C2×C22⋊C4C2×#692311yescharacteristic
544C2×C22⋊C4C2×#692311yescharacteristic
545C2×C42—611no—
546C2×C42—611no—
547C2×C42—611no—
548C4⋊C8—1222no—
549C4⋊C8—1222no—
550C4⋊C8—2441no—
551C22⋊C8—614no—
552C22⋊C8—614no—
553C22⋊C8—1222no—
554C22⋊C8—1222no—
555C22⋊C8—1222no—
556C22⋊C8—1222no—
557C22⋊C8—1222no—
558C22⋊C8—1222no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—2441no—
562C4×C8—1222no—
563C4×C8—1222no—
564C4×C8—2441no—
565#95—611no—
566#95—611no—
567#95—611no—
568#95—611no—
569#95—611no—
570#95C2×#692311yescharacteristic
571C24—611no—
572C24—611no—
573C24C22×#692311yescharacteristic
574C24C22×#692311yescharacteristic
575#41—2444no—
576#41—2444no—
577#41—2444no—
578#41—2444no—
579C2×Q8—1222no—
580C2×Q8—1222no—
581C2×Q8—2441no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—41no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C22×C4—611no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4C22×#692311yescharacteristic
631C22×C4C22×#692311yescharacteristic
632C22×C4C22×#692311yescharacteristic
633C22×C4C22×#692311yescharacteristic
634C22×C4C22×#692311yescharacteristic
635M16—2444no—
636M16—2444no—
637M16—2444no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—612no—
641C2×C8—612no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—1221no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—2444no—
663C2×C8—2444no—
664C4⋊C4—22no—
665C4⋊C4—1222no—
666C4⋊C4—2441no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—41no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1222no—
677C22⋊C4—1222no—
678C22⋊C4—2441no—
679C42—1221no—
680C42—1221no—
681C42—1221no—
682C42—1221no—
683C42—1221no—
684C42—1221no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—612no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—1221no—
705C23—1221no—
706C23—1221no—
707C23—1221no—
708C23—1221no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23D4×#692312yes—
713C23C23×#692311yescharacteristic
714Q8—2444no—
715D4—44no—
716D4—2444no—
717D4—2444no—
718D4—2444no—
719D4—2444no—
720D4—2444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—611no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1221no—
752C2×C4—1221no—
753C2×C4—1221no—
754C2×C4—1221no—
755C2×C4—1221no—
756C2×C4—1221no—
757C2×C4—1221no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4D4×#692312yes—
772C2×C4#1451986412yes—
773C8—1222no—
774C8—1222no—
775C8—1222no—
776C8—1222no—
777C8—2441no—
778C8—2441no—
779C8—2441no—
780C8—2441no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22C2×D4×#692311yescharacteristic
810C22C2×D4×#692311yescharacteristic
811C22#1684082911yescharacteristic
812C22C2×#1451986411yescharacteristic
813C22D61⋊#13111yescharacteristic
814C22D61⋊#13111yescharacteristic
815C22#1684084111yescharacteristic
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—611no—
822C4—611no—
823C4—611no—
824C4—611no—
825C4—1222no—
826C4—1222no—
827C4—1222no—
828C4—2441no—
829C4—2441no—
830C2—42no—
831C2—81no—
832C2—4881no—
833C2—2442no—
834C2#2146234111yescharacteristic
835C2#2146254211yescharacteristic
836C2#2146254311yescharacteristic
837C2#2146254911yescharacteristic
838C2#2146255311yescharacteristic
839C2#2146268711yescharacteristic
840C2#2146269911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#394C4
prime radical#21449033C2
cosocleC22×Dic61C24
hypercenter#394#6923
hypocenterC61#22853
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#16840796C2semidirect
2. C2×#16840795C2semidirect
3. C2×#16840736C2semidirect
4. C2×#16840735C2semidirect
5. #21461942C2semidirect
6. #21461889C2semidirect
7. #21461888C2semidirect
8. #21461797C2semidirect
9. #21461795C2semidirect
10. #21461794C2semidirect
11. #21461767C2semidirect
12. #21461766C2semidirect
13. #21461553C2semidirect
14. C22⋊C4×#92420C2semidirect
93. #14519834D4semidirect
99. C22⋊#92420D4semidirect
483. C61#22853semidirect

Maximal subgroups

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

subgroupindex
C2×#168407962
C2×#168407952
C2×#168407362
C2×#168407352
#214619422
#214618892
#214618882
#214617972
#214617952
#214617942
#214617672
#214617662
#214615532
C22⋊C4×#924202
#214490332
#2285361