Finite Group Databasebeta

← #29841001

Subgroups — #29841001

Order 15616.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840243C211yesmaximal, characteristic
2#21448755C214yesmaximal, complemented
3#21448744C214yesmaximal, complemented
4#21448711C212yesmaximal, complemented
5#21448703C212yesmaximal, complemented
6#21448695C212yesmaximal, complemented
7#21448687C212yesmaximal, complemented
8#21448466C212yesmaximal, complemented
9#21448458C212yesmaximal, complemented
10#21448437C211yesmaximal, characteristic, complemented
11#21448412C211yesmaximal, characteristic
12#21448309C211yesmaximal, characteristic
13#21448290C212yesmaximal, complemented
14#21448277C212yesmaximal, complemented
15#21448176C211yesmaximal, characteristic, complemented
16C4×#14519736C211yesmaximal, characteristic, complemented
17C2×C61×#389C211yesmaximal, characteristic, complemented
18C22×#11758222C2211yescharacteristic
19#16840243C4116yescomplemented
20C2×#14519742C2212yes—
21C2×#14519739C2212yes—
22C2×C4×C22⋊D61C2214yes—
23C2×#14519736C2211yescharacteristic
24C2×#14519736C2211yescharacteristic
25C2×#14519736C2211yescharacteristic
26C2×#14519735C2214yes—
27C2×#14519735C2212yes—
28C2×C4⋊C4×D61C2212yes—
29#16839668C2211yescharacteristic
30#16839668C2211yescharacteristic
31#16839667C2212yes—
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839663C2212yes—
35#16839661C2212yes—
36#16839661C2212yes—
37#16839661C2212yes—
38#16839661C2212yes—
39#16839654C2214yes—
40#16839654C2214yes—
41#16839652C2214yes—
42#16839652C2214yes—
43#16839649C2214yes—
44#16839649C2214yes—
45#16839643C2214yes—
46#16839643C2214yes—
47#16839641C2212yes—
48#16839641C2214yes—
49#16839641C2212yes—
50#16839629C2214yes—
51#16839627C2214yes—
52#16839624C2214yes—
53#16839622C2214yes—
54#16839619C2212yes—
55#16839619C2214yes—
56#16839619C2212yes—
57C4⋊C4×Dic61C2214yes—
58C4⋊C4×Dic61C2212yes—
59C4⋊C4×Dic61C2212yes—
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2212yes—
62C4×C4⋊Dic61C2211yescharacteristic
63C4×C4⋊Dic61C2211yescharacteristic
64C4×C4⋊Dic61C2211yescharacteristic
65C4×C4⋊Dic61C2211yescharacteristic
66C4×#11758198C2212yes—
67C4×#11758198C2212yes—
68C4×C22⋊Dic61C2212yes—
69C4×C22⋊Dic61C2214yes—
70C4×C22⋊Dic61C2212yes—
71#16839609C2214yes—
72#16839608C2212yes—
73#16839607C2214yes—
74C42×Dic61C2212yes—
75C22×C4⋊C4×C61C2211yescharacteristic
76C22×C4⋊C4×C61C2212yes—
77C22×C4⋊C4×C61C2211yescharacteristic
78C22×C42×C61C2211yescharacteristic
79C61×#389C2212yes—
80C61×#389C2212yes—
81C61×#389C2212yes—
82C61×#389C2212yes—
83C2×#95×C61C2212yes—
84C2×#11758222—24no—
85C2×#11758222—24no—
86C2×#11758222C2×C418yes—
87C22×Dic122C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61C2312yes—
90C22×C4×D61C2312yes—
91C22×C4×D61C2314yes—
92#14519742C2×C4116yescomplemented
93#14519739C2×C4116yescomplemented
94C4×C22⋊D61C2×C4132yes—
95#14519736—24no—
96#14519736—24no—
97#14519736C2×C418yes—
98#14519735—48no—
99#14519735C2×C4116yescomplemented
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2314yes—
105C2×C4⋊Dic61C2314yes—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×#11758196C2314yes—
109C4⋊C4×D61C2×C4116yescomplemented
110C2×C22⋊Dic61C2312yes—
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×#11758198C2312yes—
114C2×#11758198C2312yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2312yes—
118C2×#11758198C2312yes—
119C2×#11758198C2314yes—
120C2×C4×Dic61C2312yes—
121C2×C4×Dic61C2312yes—
122C2×C4×Dic61C2312yes—
123C2×C4×Dic61C2312yes—
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2312yes—
126C2×C4×Dic61C2312yes—
127C2×C4×Dic61C2314yes—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2312yes—
130#14519684C2312yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2312yes—
134#14519684C2312yes—
135#14519684C2312yes—
136#14519684C2312yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2312yes—
143#14519684C2314yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2312yes—
147C23×C4×C61C2312yes—
148C23×C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61—24no—
150C2×C4⋊C4×C61—44no—
151C2×C4⋊C4×C61C2×C418yes—
152C2×C4⋊C4×C61C2314yes—
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2314yes—
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2312yes—
158C2×C42×C61—24no—
159C2×C42×C61C2311yescharacteristic
160C2×C42×C61C2311yescharacteristic
161C2×C42×C61C2311yescharacteristic
162C2×C42×C61C2311yescharacteristic
163#95×C61C2314yes—
164#95×C61C2314yes—
165C24×C61C2411yescharacteristic
166C23×D61C2412yes—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—24no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—42no—
173C22×C4×C61—41no—
174C22×C4×C61—41no—
175C22×C4×C61—42no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61C22×C418yes—
179C22×C4×C61C22×C414yes—
180C22×C4×C61#4114yes—
181C22×C4×C61#4114yes—
182C22×C4×C61C2411yescharacteristic
183C22×C4×C61C2414yes—
184C22×C4×C61C2411yescharacteristic
185C22×C4×C61C2414yes—
186C22×C4×C61C2411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61C22×C418yes—
193C22×Dic61C2412yes—
194C22×Dic61C2412yes—
195C22×Dic61C2412yes—
196C22×Dic61C2412yes—
197C22×Dic61C2412yes—
198C22×Dic61C2412yes—
199C22×Dic61C2412yes—
200#11758222—232no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244C22×C414yes—
204C2×C4×D61—24no—
205C2×C4×D61—24no—
206C2×C4×D61—44no—
207C2×C4×D61—44no—
208C2×C4×D61C22×C418yes—
209C2×C4×D61C22×C4116yes—
210C2×Dic122—22no—
211C2×Dic122—22no—
212C2×Dic122C22×C414yes—
213C4⋊C4×C61—24no—
214C4⋊C4×C61—24no—
215C4⋊C4×C61—28no—
216C4⋊C4×C61—44no—
217C4⋊C4×C61C22×C418yes—
218C4⋊C4×C61C22×C418yes—
219C42×C61—22no—
220C42×C61—22no—
221C42×C61—22no—
222C42×C61—22no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225C22⋊Dic61C22×C418yes—
226#11758198—24no—
227#11758198—24no—
228#11758198—42no—
229#11758198—44no—
230#11758198—42no—
231#11758198—44no—
232#11758198C22×C4116yes—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61—22no—
236C4⋊Dic61—22no—
237C4⋊Dic61—44no—
238C4⋊Dic61—44no—
239C4⋊Dic61C22×C414yes—
240C4⋊Dic61C22×C414yes—
241#11758196C22×C4116yes—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—44no—
247C4×Dic61—42no—
248C4×Dic61—42no—
249C4×Dic61—44no—
250C4×Dic61C22×C4116yes—
251C4×Dic61C22×C418yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61C23×C412yes—
257C23×C61C2×#4112yes—
258C23×C61C2×#4112yes—
259C23×C61C2511yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61C23×C414yes—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—24no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—24no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—24no—
276C2×C4×C61—24no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—24no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—48no—
283C2×C4×C61—44no—
284C2×C4×C61—44no—
285C2×C4×C61—84no—
286C2×C4×C61#117116yescomplemented
287C2×C4×C61C23×C418yes—
288C2×C4×C61C23×C412yes—
289C2×C4×C61C23×C412yes—
290C2×C4×C61C2×#4112yes—
291C2×C4×C61C2×#4112yes—
292C2×C4×C61C2×#4112yes—
293C2×C4×C61C2×#4112yes—
294C2×C4×C61H(5,𝔽2)12yes—
295C2×C4×C612−1+412yes—
296C22⋊D61—216no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61C23×C414yes—
316C2×Dic61C23×C414yes—
317C2×Dic61C23×C414yes—
318D244—28no—
319C4×D61—216no—
320C4×D61—416no—
321Dic122—28no—
322#34253—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61C2×#11714yes—
330C22×C61C24×C411yescharacteristic
331C22×C61C22×#4111yescharacteristic
332C22×C61C22×#4111yescharacteristic
333C22×C61C2×H(5,𝔽2)11yescharacteristic
334C22×C61C2×2−1+411yescharacteristic
335C22×C61#58511yescharacteristic
336C22×C61#58511yescharacteristic
337C2×D61—24no—
338C2×D61—24no—
339C2×D61—24no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C4×C61—28no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—41no—
348C4×C61—44no—
349C4×C61—41no—
350C4×C61C2×#11714yes—
351C4×C61C2×#11714yes—
352Dic61—24no—
353Dic61—24no—
354Dic61—24no—
355Dic61—42no—
356Dic61—42no—
357Dic61—42no—
358Dic61—42no—
359C2×#520—611no—
360#2353—614no—
361#2352—614no—
362#2347—612no—
363#2346—612no—
364#2345—612no—
365#2344—612no—
366#2320—612no—
367#2319—612no—
368#2316—611no—
369#2311—611no—
370#2297—611no—
371#2295—612no—
372#2293—612no—
373C2×#389D6111yescharacteristic, complemented
374#2274—611no—
375C4×#117—611no—
376C2×C61—24no—
377C2×C61C22×#11711yescharacteristic
378C2×C61C4×H(5,𝔽2)11yescharacteristic
379C2×C61C4×2−1+411yescharacteristic
380C2×C61#349411yescharacteristic
381C2×C61#349511yescharacteristic
382C2×C61#351111yescharacteristic
383C2×C61#351211yescharacteristic
384D61—44no—
385C22×#41—611no—
386#520—6116no—
387C2×C4×Q8—612no—
388C2×C4×D4—614no—
389C2×C4×D4—612no—
390C2×#117—611no—
391C2×#117—611no—
392C2×#117—611no—
393C2×#117—612no—
394C2×#117—614no—
395C22×C4⋊C4—612no—
396C22×C4⋊C4C2×D6111yescharacteristic
397C22×C4⋊C4C2×D6112yes—
398C22×C4⋊C4C2×D6111yescharacteristic
399C22×C42C2×D6111yescharacteristic
400#391—612no—
401#391—611no—
402#391—611no—
403#390—612no—
404#390—611no—
405#390—611no—
406#389—612no—
407#389—612no—
408#389—612no—
409#389—612no—
410#389C2×D6112yes—
411#389C2×D6112yes—
412#389C2×D6112yes—
413#389C2×D6112yes—
414#388—614no—
415#388—614no—
416#388—614no—
417#388—614no—
418#387—614no—
419#387—614no—
420#387—614no—
421#387—614no—
422#386—614no—
423#386—612no—
424#386—612no—
425#383—614no—
426#382—614no—
427#381—614no—
428#380—614no—
429#380—612no—
430#380—612no—
431#380—614no—
432C4×C4⋊C4—612no—
433C4×C4⋊C4—612no—
434C4×C4⋊C4—612no—
435C4×C4⋊C4—612no—
436C4×C4⋊C4—614no—
437C4×C4⋊C4—611no—
438C4×C4⋊C4—611no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441C4×C22⋊C4—612no—
442C4×C22⋊C4—614no—
443C4×C22⋊C4—612no—
444C4×C22⋊C4—612no—
445C4×C22⋊C4—612no—
446C4×C22⋊C4—614no—
447#376—612no—
448#376—614no—
449C2×#95C2×D6112yes—
450C43—612no—
451C61#3425311yescharacteristic, complemented, Sylow
452C2×#41—618no—
453C2×#41—1224no—
454C2×#41—1224no—
455C22×Q8—611no—
456C22×D4—612no—
457C22×D4—611no—
458C23×C4—612no—
459C23×C4—614no—
460C23×C4C22×D6111yescharacteristic
461C23×C4C22×D6111yescharacteristic
462C23×C4C22×D6112yes—
463C23×C4C22×D6112yes—
464C23×C4C22×D6111yescharacteristic
465C4×Q8—6116no—
466C4×D4—6132no—
467C4×D4—6116no—
468#117—618no—
469#117—6116no—
470#117—1224no—
471#117—1224no—
472#117—2448no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—44no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—6116no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4C4×D6118yes—
486C2×C4⋊C4C22×D6114yes—
487C2×C4⋊C4C22×D6112yes—
488C2×C4⋊C4C22×D6112yes—
489C2×C4⋊C4C22×D6114yes—
490C2×C4⋊C4C22×D6112yes—
491C2×C4⋊C4C22×D6112yes—
492C2×C22⋊C4—612no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—612no—
495C2×C22⋊C4—612no—
496C2×C22⋊C4—612no—
497C2×C22⋊C4—612no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—612no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—612no—
502C2×C42—24no—
503C2×C42—612no—
504C2×C42—614no—
505C2×C42—612no—
506C2×C42—612no—
507C2×C42—612no—
508C2×C42—612no—
509C2×C42—614no—
510C2×C42—612no—
511C2×C42—612no—
512C2×C42—614no—
513C2×C42C22×D6111yescharacteristic
514C2×C42C22×D6111yescharacteristic
515C2×C42C22×D6111yescharacteristic
516C2×C42C22×D6111yescharacteristic
517#95—612no—
518#95—612no—
519#95—612no—
520#95—612no—
521#95—612no—
522#95—614no—
523#95—614no—
524#95—614no—
525#95—614no—
526#95—612no—
527#95—614no—
528#95—612no—
529#95—612no—
530#95—614no—
531#95C22×D6114yes—
532#95C22×D6114yes—
533C24—612no—
534C24C23×D6111yescharacteristic
535#41—12232no—
536C2×Q8—614no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×D4—618no—
540C2×D4—614no—
541C2×D4—1224no—
542C2×D4—1224no—
543C2×D4—1222no—
544C2×D4—1222no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—618no—
560C22×C4—6116no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—2444no—
568C22×C4—2444no—
569C22×C4C2×C4×D6118yes—
570C22×C4C2×C4×D6114yes—
571C22×C4#1175822414yes—
572C22×C4#1175822614yes—
573C22×C4C23×D6111yescharacteristic
574C22×C4C23×D6111yescharacteristic
575C22×C4C23×D6114yes—
576C22×C4C23×D6114yes—
577C22×C4C23×D6111yescharacteristic
578C22×C4C23×D6111yescharacteristic
579C22×C4C23×D6111yescharacteristic
580C22×C4C23×D6111yescharacteristic
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—28no—
584C4⋊C4—44no—
585C4⋊C4—614no—
586C4⋊C4—6116no—
587C4⋊C4—614no—
588C4⋊C4—1222no—
589C4⋊C4—1222no—
590C4⋊C4—1222no—
591C4⋊C4—1222no—
592C4⋊C4—2444no—
593C4⋊C4—2444no—
594C4⋊C4C2×C4×D6118yes—
595C4⋊C4C2×C4×D6118yes—
596C22⋊C4—618no—
597C22⋊C4—6116no—
598C22⋊C4—1224no—
599C22⋊C4—1224no—
600C22⋊C4—1224no—
601C22⋊C4—1224no—
602C22⋊C4—2444no—
603C22⋊C4—2444no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—6116no—
611C42—618no—
612C42—1224no—
613C42—1224no—
614C42—1224no—
615C42—1224no—
616C42—2442no—
617C42—2442no—
618C42—2444no—
619C42—2444no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—614no—
625C23—1222no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23C22×C4×D6112yes—
632C23C2×#1175822412yes—
633C23C2×#1175822612yes—
634C23C24×D6111yescharacteristic
635Q8—1228no—
636D4—12216no—
637D4—1228no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—24no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—24no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—48no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—84no—
657C2×C4—614no—
658C2×C4—614no—
659C2×C4—614no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—12216no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—24416no—
680C2×C4#14519735116yescomplemented
681C2×C4C22×C4×D6118yes—
682C2×C4C22×C4×D6112yes—
683C2×C4C22×C4×D6112yes—
684C2×C4C2×#1175822412yes—
685C2×C4C2×#1175822412yes—
686C2×C4C2×#1175822612yes—
687C2×C4C2×#1175822612yes—
688C2×C4#1451982212yes—
689C2×C4#1451982512yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—1224no—
697C22—1224no—
698C22—1224no—
699C22—2442no—
700C22—2442no—
701C22—2442no—
702C22—2442no—
703C22C2×#1451973514yes—
704C22C23×C4×D6111yescharacteristic
705C22C22×#1175822411yescharacteristic
706C22C22×#1175822611yescharacteristic
707C22C2×#1451982211yescharacteristic
708C22C2×#1451982511yescharacteristic
709C22#1684059811yescharacteristic
710C22#1684059811yescharacteristic
711C4—28no—
712C4—22no—
713C4—22no—
714C4—41no—
715C4—44no—
716C4—41no—
717C4—1224no—
718C4—1224no—
719C4—1224no—
720C4—2442no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4C2×#1451973514yes—
725C4C2×#1451973514yes—
726C2—24no—
727C2—2444no—
728C2C22×#1451973511yescharacteristic
729C2C4×#1451982211yescharacteristic
730C2C4×#1451982511yescharacteristic
731C2#2145954811yescharacteristic
732C2#2145956511yescharacteristic
733C2#2145973211yescharacteristic
734C2#2145974311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC2×C61×#389C2
socle, cosocleC23×C61C25
prime radicalC22×#11758222C22
hypercenterC2×#389D61
hypocenterC61#34253
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #21448755C2semidirect
3. #21448744C2semidirect
4. #21448711C2semidirect
5. #21448703C2semidirect
6. #21448695C2semidirect
7. #21448687C2semidirect
8. #21448466C2semidirect
9. #21448458C2semidirect
10. #21448437C2semidirect
13. #21448290C2semidirect
14. #21448277C2semidirect
15. #21448176C2semidirect
16. C4×#14519736C2semidirect
17. C2×C61×#389C2semidirect
19. #16840243C4semidirect
92. #14519742C2×C4semidirect
93. #14519739C2×C4semidirect
99. #14519735C2×C4semidirect
109. C4⋊C4×D61C2×C4semidirect
286. C2×C4×C61#117semidirect
373. C2×#389D61semidirect
451. C61#34253semidirect
680. C2×C4#14519735semidirect

Maximal subgroups

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

subgroupindex
C2×#168402432
#214487552
#214487442
#214487112
#214487032
#214486952
#214486872
#214484662
#214484582
#214484372
#214484122
#214483092
#214482902
#214482772
#214481762
C4×#145197362
C2×C61×#3892
#3425361