Finite Group Databasebeta

← #30620105

Subgroups — #30620105

Order 15616.

1908 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840795C212yesmaximal, complemented
2C2×#16840734C211yesmaximal, characteristic, complemented
3C2×#16840733C211yesmaximal, characteristic, complemented
4#21461942C212yesmaximal, complemented
5#21461799C212yesmaximal, complemented
6#21461796C212yesmaximal, complemented
7#21461676C211yesmaximal, characteristic, complemented
8#21461642C211yesmaximal, characteristic, complemented
9#21461642C211yesmaximal, characteristic, complemented
10C4×#14519834C211yesmaximal, characteristic, complemented
11C2×C4×D4×D61C211yesmaximal, characteristic
12C22×#11758213C2212yescomplemented
13C22×#11758217C2212yescomplemented
14#16840795—28no—
15C2×#14519844C2212yescomplemented
16#16840734—24no—
17#16840733—24no—
18C2×#14519834C2211yescharacteristic
19C2×#14519834C2211yescharacteristic
20C2×#14519834C2211yescharacteristic
21C2×#14519834C2211yescharacteristic
22C2×#14519834C2212yescomplemented
23C2×#14519834C2212yescomplemented
24C2×#14519834C2212yescomplemented
25C2×C22⋊#92420C2212yescomplemented
26C2×C22⋊#92420C2212yescomplemented
27C2×C22⋊#92420C2212yescomplemented
28C2×C4×#92420C2212yescomplemented
29#16840628C2212yescomplemented
30#16840628C2212yescomplemented
31C22×D4×D61C411yescharacteristic
32C23×C4×D61C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34C2×C4×D244C411yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61C411yescharacteristic
38C2×C4×C22⋊D61C411yescharacteristic
39C2×#14519737C2211yescharacteristic
40C2×#14519737C2211yescharacteristic
41C4×D4×D61—28no—
42C2×C4⋊C4×D61C411yescharacteristic
43C2×C22⋊C4×D61C411yescharacteristic
44C2×C22⋊C4×D61C411yescharacteristic
45C2×C42×D61C2211yescharacteristic
46C2×C4×D4×C61C411yescharacteristic
47C2×#11758213—24no—
48C2×#11758213—24no—
49C2×#11758213—42no—
50C2×#11758217—24no—
51C2×#11758217—24no—
52C2×#11758217—42no—
53C22×#92420C2312yes—
54C22×#92420C2312yes—
55C22×#92420C2312yes—
56C22×#92420C2312yes—
57#14519844—24no—
58#14519834—22no—
59#14519834—22no—
60#14519834—24no—
61#14519834—22no—
62#14519834—24no—
63#14519834—42no—
64#14519834D414yescomplemented
65C22⋊#92420—24no—
66C22⋊#92420—24no—
67C22⋊#92420—42no—
68C4×#92420—24no—
69C24×D61C2×C411yescharacteristic
70C24×D61C2×C411yescharacteristic
71C22×D244C2×C411yescharacteristic
72C22×C22⋊D61C2×C411yescharacteristic
73C22×C22⋊D61C2×C411yescharacteristic
74C2×D4×D61—24no—
75C2×D4×D61—24no—
76C2×D4×D61—24no—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C22×C4×D61—24no—
80C22×C4×D61—24no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—22no—
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61C2×C411yescharacteristic
88C22×C4×D61C2×C411yescharacteristic
89C22×C4×D61C2×C411yescharacteristic
90C22×C4×D61C2×C411yescharacteristic
91C22×C4×D61C2×C411yescharacteristic
92C22×C4×D61C2×C411yescharacteristic
93C22×C4×D61C2311yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C4×D244—24no—
97D4×Dic61—24no—
98#14519739—24no—
99C4×C22⋊D61—24no—
100C4×C22⋊D61—24no—
101#14519737—24no—
102#14519737D418yes—
103C2×C4⋊Dic61C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C4⋊C4×D61—24no—
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2×C411yescharacteristic
112C2×#11758198C2×C411yescharacteristic
113C22⋊C4×D61—24no—
114C22⋊C4×D61—24no—
115C2×C4×Dic61C2×C411yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—24no—
119C22×D4×C61C2×C411yescharacteristic
120C23×C4×C61C2×C411yescharacteristic
121C23×C4×C61C2×C411yescharacteristic
122C4×D4×C61—24no—
123C2×C4⋊C4×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C42×C61C2×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C24×C61C22×C411yescharacteristic
129C23×D61—22no—
130C23×D61—22no—
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—41no—
140C23×D61—41no—
141C23×D61—41no—
142C23×D61—41no—
143C23×D61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—41no—
154C22×C4×C61—41no—
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61C22⋊C414yes—
165C2×C22⋊D61M1614yescomplemented
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C2×D414yes—
178C22×Dic61C2411yescharacteristic
179D4×D61—232no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—21no—
201C2×C4×D61—22no—
202C2×C4×D61—21no—
203C2×C4×D61—22no—
204C2×C4×D61—48no—
205C2×C4×D61—48no—
206C2×C4×D61—48no—
207C2×C4×D61—48no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
212C2×C4×D61—41no—
213C2×C4×D61M1614yescomplemented
214C2×C4×D61C2×D414yes—
215C2×C4×D61C2×D412yes—
216C2×C4×D61#4112yes—
217#11758217—48no—
218C2×#92420—22no—
219C2×#92420—22no—
220C2×#92420—22no—
221C2×#92420—22no—
222C2×#92420—22no—
223C2×#92420—22no—
224C2×#92420—22no—
225C2×#92420—22no—
226C2×#92420—22no—
227C2×#92420—22no—
228C2×#92420—22no—
229C2×#92420C2×D414yescomplemented
230#11758213—48no—
231C4⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61C22⋊C414yes—
234C42×C61—22no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198C22⋊C414yes—
241C4⋊Dic61—22no—
242#11758196—22no—
243#11758196C22⋊C414yes—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61C2×D414yes—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61C2×C22⋊C412yes—
260C23×C61C2×M1612yes—
261C23×C61C23×C411yescharacteristic
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—28no—
267C22×D61—28no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—44no—
281C22×D61—44no—
282C22×D61—44no—
283C22×D61—44no—
284C22×D61—44no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61—44no—
291C22×D61—44no—
292C22×D61C2×C22⋊C412yes—
293C22×D61C4×D412yes—
294C22×D61C2×M1612yes—
295C22×D61C2×M1612yes—
296C22×D61#13112yes—
297D4×C61—28no—
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×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61C2×C22⋊C412yes—
312C2×C4×C61C2×C22⋊C412yes—
313C2×C4×C61C4×D412yes—
314C2×C4×C61C2×M1612yes—
315C22⋊D61—28no—
316C22⋊D61—28no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—24no—
320C2×Dic61—24no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61C2×C22⋊C412yes—
330C2×Dic61C2×C22⋊C412yes—
331C2×Dic61C2×M1612yes—
332C2×Dic61C2×M1612yes—
333C2×Dic61C22×D411yescharacteristic
334C2×Dic61C22×D412yes—
335C2×Dic61C2×#4111yescharacteristic
336C2×Dic61H(5,𝔽2)12yes—
337D244—28no—
338C4×D61—24no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—24no—
342C4×D61—28no—
343C4×D61—44no—
344C4×D61—44no—
345C4×D61—44no—
346C4×D61—44no—
347C4×D61—44no—
348C4×D61—42no—
349C4×D61—42no—
350#92420—24no—
351#92420—42no—
352#92420—42no—
353#92420—42no—
354#22401—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61C22×C22⋊C411yescharacteristic
370C22×C61C2×C4×D411yescharacteristic
371C22×C61#51811yescharacteristic
372C22×C61C22×M1611yescharacteristic
373C22×C61C22×M1611yescharacteristic
374C22×C61C2×#13111yescharacteristic
375C22×C61#56811yescharacteristic
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—22no—
379C2×D61—22no—
380C2×D61—22no—
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—416no—
389C2×D61—416no—
390C2×D61—41no—
391C2×D61—41no—
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61#43614yescomplemented
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61—41no—
404Dic61—22no—
405Dic61—41no—
406Dic61—41no—
407Dic61#40714yescomplemented
408Dic61D4212yes—
409Dic61#54612yes—
410C22×C4×D4—611no—
411C2×#436—612no—
412C2×#407—611no—
413C2×#407—611no—
414#1954—612no—
415#1870—612no—
416#1870—612no—
417#1797—611no—
418#1779—611no—
419#1779—611no—
420C4×C22⋊C8—611no—
421C2×C61—42no—
422C2×C61—42no—
423C2×C61D4×C22⋊C411yescharacteristic
424C2×C61C2×#40711yescharacteristic
425C2×C61#288011yescharacteristic
426C2×C61C2×#43611yescharacteristic
427C2×C61D4×M1611yescharacteristic
428C2×C61#297411yescharacteristic
429C2×C61#297511yescharacteristic
430D61—24no—
431D61—42no—
432D61—42no—
433C23×D4—611no—
434C24×C4—611no—
435C24×C4—611no—
436C22×M16—612no—
437C22×M16—612no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×C4×D4—611no—
442C2×C4×D4—611no—
443C2×C4×D4—611no—
444C2×C4×D4—611no—
445C2×C4×D4—1228no—
446C2×C4×D4#692311yescharacteristic
447C22×C4⋊C4—611no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C42—611no—
451#436—1228no—
452C2×C4⋊C8—612no—
453#407—1224no—
454#407—1224no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×C22⋊C8—612no—
459C2×C22⋊C8—612no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—612no—
462C2×C22⋊C8—612no—
463C2×C22⋊C8—612no—
464C2×C22⋊C8—612no—
465C2×C4×C8—612no—
466#336—612no—
467#336—612no—
468C61#2240111yescharacteristic, complemented, Sylow
469C25—611no—
470C25—611no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—611no—
474C22×D4—1224no—
475C22×D4—1224no—
476C22×D4—1224no—
477C22×D4C2×#692311yescharacteristic
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—1224no—
490C23×C4—1224no—
491C23×C4—1222no—
492C23×C4—1222no—
493C23×C4—1222no—
494C23×C4—1222no—
495C23×C4—2442no—
496C23×C4—2442no—
497C23×C4C2×#692311yescharacteristic
498C23×C4C2×#692311yescharacteristic
499C2×M16—1224no—
500C2×M16—1224no—
501C2×M16—1224no—
502C2×M16—1224no—
503C2×M16—2442no—
504C2×M16—2442no—
505C22×C8—612no—
506C22×C8—612no—
507C22×C8—612no—
508C22×C8—612no—
509C4×D4—24no—
510C4×D4—618no—
511C4×D4—1224no—
512C4×D4—1224no—
513C4×D4—1224no—
514C4×D4—1224no—
515C4×D4—1224no—
516C4×D4—1224no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4C2×#692311yescharacteristic
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4C2×#692311yescharacteristic
531C2×C22⋊C4C2×#692311yescharacteristic
532C2×C42—611no—
533C2×C42—611no—
534C2×C42—611no—
535C2×C42—1224no—
536C2×C42C2×#692311yescharacteristic
537C4⋊C8—1224no—
538C22⋊C8—614no—
539C22⋊C8—1224no—
540C22⋊C8—1224no—
541C22⋊C8—1224no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1224no—
546C22⋊C8—2442no—
547C22⋊C8—2442no—
548C4×C8—1224no—
549C24—611no—
550C24—611no—
551C24—611no—
552C24—1222no—
553C24—1222no—
554C24—1222no—
555C24—1222no—
556C24—1222no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24—2441no—
563C24—2441no—
564C24—2441no—
565C24—2441no—
566C24C22×#692311yescharacteristic
567C24C22×#692311yescharacteristic
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—614no—
572C2×D4—614no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—12232no—
580C2×D4—1222no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—614no—
590C22×C4—611no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—614no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1221no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1221no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1221no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—2441no—
626C22×C4—2441no—
627C22×C4—2441no—
628C22×C4—2441no—
629C22×C4—2441no—
630C22×C4—2448no—
631C22×C4—2448no—
632C22×C4—2448no—
633C22×C4—2448no—
634C22×C4C22×#692311yescharacteristic
635C22×C4C22×#692311yescharacteristic
636C22×C4C22×#692311yescharacteristic
637C22×C4C22×#692311yescharacteristic
638C22×C4C22×#692311yescharacteristic
639M16—2448no—
640M16—2448no—
641C2×C8—614no—
642C2×C8—1222no—
643C2×C8—1222no—
644C2×C8—1222no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8—1222no—
651C2×C8—1222no—
652C2×C8—1222no—
653C4⋊C4—22no—
654C4⋊C4—614no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C22⋊C4—22no—
658C22⋊C4—614no—
659C22⋊C4—1222no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C22⋊C4—1222no—
663C22⋊C4—1222no—
664C22⋊C4C22⋊#692314yes—
665C42—22no—
666C42—614no—
667C42—1222no—
668C42—1222no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—612no—
682C23—612no—
683C23—612no—
684C23—612no—
685C23—612no—
686C23—1228no—
687C23—1228no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23—1221no—
703C23—1221no—
704C23—2444no—
705C23—2444no—
706C23—2444no—
707C23—2444no—
708C23—2444no—
709C23—2444no—
710C23—2444no—
711C23—2444no—
712C23—2444no—
713C23—2444no—
714C23—2444no—
715C23—2444no—
716C23C2×C22⋊#692312yes—
717C23D61⋊M1612yes—
718C23C23×#692311yescharacteristic
719D4—28no—
720D4—1228no—
721D4—1228no—
722D4—1228no—
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—44no—
735C2×C4—44no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—1224no—
748C2×C4—1228no—
749C2×C4—1224no—
750C2×C4—1224no—
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—2444no—
760C2×C4—2444no—
761C2×C4—2444no—
762C2×C4—2444no—
763C2×C4—2442no—
764C2×C4—2442no—
765C2×C4—2444no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4C2×C22⋊#692312yes—
769C2×C4C2×C22⋊#692312yes—
770C2×C4D4×#692312yes—
771C2×C4D61⋊M1612yes—
772C8—1224no—
773C8—2442no—
774C8—2442no—
775C8—2442no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—614no—
791C22—1222no—
792C22—1222no—
793C22—1222no—
794C22—1222no—
795C22—1222no—
796C22—1222no—
797C22—1222no—
798C22—1222no—
799C22—1222no—
800C22—1222no—
801C22—1222no—
802C22—1222no—
803C22—24416no—
804C22—24416no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22—2441no—
812C22—2441no—
813C22C22×C22⋊#692311yescharacteristic
814C22C2×D4×#692311yescharacteristic
815C22#1684082911yescharacteristic
816C22C2×D61⋊M1611yescharacteristic
817C22C2×D61⋊M1611yescharacteristic
818C22D61⋊#13111yescharacteristic
819C22#1684084111yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—41no—
825C4—612no—
826C4—612no—
827C4—614no—
828C4—1222no—
829C4—2441no—
830C4—2441no—
831C2—42no—
832C2—42no—
833C2—1224no—
834C2—2442no—
835C2—2442no—
836C2D4×C22⋊#692311yescharacteristic
837C2D61⋊#40711yescharacteristic
838C2#2146240911yescharacteristic
839C2D61⋊#43611yescharacteristic
840C2#2146255811yescharacteristic
841C2#2146267611yescharacteristic
842C2#2146268211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C4×D4×C61C4
prime radicalC22×D4×D61C4
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#22401
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840795C2semidirect
2. C2×#16840734C2semidirect
3. C2×#16840733C2semidirect
4. #21461942C2semidirect
5. #21461799C2semidirect
6. #21461796C2semidirect
7. #21461676C2semidirect
8. #21461642C2semidirect
9. #21461642C2semidirect
10. C4×#14519834C2semidirect
12. C22×#11758213C22semidirect
13. C22×#11758217C22semidirect
15. C2×#14519844C22semidirect
22. C2×#14519834C22semidirect
23. C2×#14519834C22semidirect
24. C2×#14519834C22semidirect
25. C2×C22⋊#92420C22semidirect
26. C2×C22⋊#92420C22semidirect
27. C2×C22⋊#92420C22semidirect
28. C2×C4×#92420C22semidirect
29. #16840628C22semidirect
30. #16840628C22semidirect
64. #14519834D4semidirect
165. C2×C22⋊D61M16semidirect
213. C2×C4×D61M16semidirect
229. C2×#92420C2×D4semidirect
398. C2×D61#436semidirect
407. Dic61#407semidirect
468. C61#22401semidirect

Maximal subgroups

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

subgroupindex
C2×#168407952
C2×#168407342
C2×#168407332
#214619422
#214617992
#214617962
#214616762
#214616422
C4×#145198342
C2×C4×D4×D612
#2240161