Finite Group Databasebeta

← #29603231

Subgroups — #29603231

Order 15616.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic
2C2×#16839658C211yesmaximal, characteristic
3C2×#16839658C211yesmaximal, characteristic
4C2×#16839657C212yesmaximal
5C2×C4⋊C4×Dic61C211yesmaximal, characteristic
6#21444082C212yesmaximal
7#21444069C212yesmaximal
8#21444051C212yesmaximal
9#21444048C211yesmaximal, characteristic
10C4×#14519684C211yesmaximal, characteristic
11C2×C61×#384C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×#11758196C2212yes—
15C22×#11758196C2212yes—
16C22×#11758196C2212yes—
17C22×C4×Dic61C2211yescharacteristic
18C22×C4×Dic61C2212yes—
19C22×C4×Dic61C2211yescharacteristic
20#16839660C418yescomplemented
21#16839658—24no—
22#16839658—24no—
23#16839657—28no—
24C4⋊C4×Dic61—24no—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2212yes—
37C22×C4⋊C4×C61C2212yes—
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C61×#384—24no—
41C23×Dic61C2312yes—
42C23×Dic61C2311yescharacteristic
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2312yes—
46C23×Dic61C2311yescharacteristic
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61C2×C414yes—
50C2×C4⋊Dic61C2×C414yes—
51C2×C4⋊Dic61D414yes—
52C2×C4⋊Dic61Q814yes—
53C2×#11758196—24no—
54C2×#11758196—24no—
55C2×#11758196—24no—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—42no—
60C2×#11758196—42no—
61C2×#11758196C2×C418yes—
62C2×C4×Dic61—22no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—22no—
65C2×C4×Dic61—22no—
66C2×C4×Dic61—22no—
67C2×C4×Dic61—24no—
68C2×C4×Dic61—24no—
69C2×C4×Dic61—42no—
70C2×C4×Dic61Q814yes—
71#14519684—24no—
72#14519684—22no—
73#14519684—22no—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—42no—
78#14519684C2×C418yes—
79#14519684D414yes—
80#14519684Q814yes—
81C23×C4×C61C2312yes—
82C23×C4×C61C2312yes—
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—24no—
89C2×C4⋊C4×C61—24no—
90C2×C4⋊C4×C61—22no—
91C2×C4⋊C4×C61—24no—
92C2×C4⋊C4×C61—22no—
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—42no—
96C2×C4⋊C4×C61—42no—
97C2×C4⋊C4×C61D414yes—
98C2×C42×C61—22no—
99C2×C42×C61—22no—
100C2×C42×C61C2×C414yes—
101C24×C61C2411yescharacteristic
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61C22×C412yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C412yes—
126C22×C4×C61C2×D414yes—
127C22×C4×C61C2×D412yes—
128C22×C4×C61C2×D412yes—
129C22×C4×C61C2×D412yes—
130C22×C4×C61C2×Q812yes—
131C22×C4×C61C2×Q812yes—
132C22×C4×C61C2×Q812yes—
133C22×C4×C61#4112yes—
134C22×C4×C61#4112yes—
135C22×C4×C61#4112yes—
136C22×C4×C61#4112yes—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C22×C414yes—
170C22×Dic61C22×C414yes—
171C22×Dic61C2×D412yes—
172C22×Dic61C2×D414yes—
173C22×Dic61C2×D412yes—
174C22×Dic61C2×Q812yes—
175C22×Dic61C2×Q812yes—
176C22×Dic61C2×Q814yes—
177C22×Dic61C2×Q812yes—
178C22×Dic61C2×Q812yes—
179C4⋊C4×C61—28no—
180C4⋊C4×C61—48no—
181C4⋊C4×C61—48no—
182C4⋊C4×C61—44no—
183C42×C61—28no—
184C4⋊Dic61—28no—
185C4⋊Dic61C4⋊C4116yescomplemented
186#11758196—216no—
187#11758196—48no—
188#11758196—48no—
189C4×Dic61—28no—
190C4×Dic61—48no—
191C4×Dic61—44no—
192C23×C61C23×C411yescharacteristic
193C23×C61C22×D411yescharacteristic
194C23×C61C22×D411yescharacteristic
195C23×C61C22×D411yescharacteristic
196C23×C61C22×Q811yescharacteristic
197C23×C61C22×Q811yescharacteristic
198C23×C61C22×Q811yescharacteristic
199C23×C61C2×#4111yescharacteristic
200C23×C61C2×#4111yescharacteristic
201C23×C61C2×#4111yescharacteristic
202C23×C61C2×#4111yescharacteristic
203C23×C61H(5,𝔽2)11yescharacteristic
204C23×C61H(5,𝔽2)11yescharacteristic
205C23×C612−1+411yescharacteristic
206C23×C612−1+411yescharacteristic
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61C2×C4⋊C414yes—
234C2×C4×C61C4×D414yes—
235C2×C4×C61C4×D414yes—
236C2×C4×C61C4×Q814yes—
237C2×C4×C61C4×Q814yes—
238C2×C4×C61#12114yes—
239C2×C4×C61C22⋊Q814yes—
240C2×C4×C61#12514yes—
241C2×C4×C61C4⋊Q814yes—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—24no—
248C2×Dic61—24no—
249C2×Dic61—22no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—24no—
253C2×Dic61—22no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—22no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—22no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—42no—
271C2×Dic61—41no—
272C2×Dic61—42no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—42no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—42no—
281C2×Dic61—41no—
282C2×Dic61C2×C4⋊C418yes—
283C2×Dic61C4⋊Q814yes—
284#14005—611nomaximal, Sylow
285C22×C61C22×C4⋊C411yescharacteristic
286C22×C61C2×C4×D411yescharacteristic
287C22×C61C2×C4×D411yescharacteristic
288C22×C61C2×C4×Q811yescharacteristic
289C22×C61C2×C4×Q811yescharacteristic
290C22×C61#52011yescharacteristic
291C22×C61#52011yescharacteristic
292C22×C61C2×#12111yescharacteristic
293C22×C61C2×C22⋊Q811yescharacteristic
294C22×C61C2×#12511yescharacteristic
295C22×C61C2×C4⋊Q811yescharacteristic
296C22×C61C2×C4⋊Q811yescharacteristic
297C22×C61#53211yescharacteristic
298C22×C61#53311yescharacteristic
299C22×C61#53311yescharacteristic
300C22×C61#54011yescharacteristic
301C22×C61#54111yescharacteristic
302C22×C61#54411yescharacteristic
303C22×C61#54411yescharacteristic
304C22×C61D4211yescharacteristic
305C22×C61D4211yescharacteristic
306C22×C61#54611yescharacteristic
307C22×C61#54711yescharacteristic
308C22×C61#54711yescharacteristic
309C22×C61#54811yescharacteristic
310C22×C61D4×Q811yescharacteristic
311C22×C61D4×Q811yescharacteristic
312C22×C61D4×Q811yescharacteristic
313C22×C61#55011yescharacteristic
314C22×C61#55211yescharacteristic
315C22×C61#55311yescharacteristic
316C22×C61#55411yescharacteristic
317C22×C61#55411yescharacteristic
318C22×C61#55711yescharacteristic
319C22×C61Q8211yescharacteristic
320C4×C61—24no—
321C4×C61—24no—
322C4×C61—44no—
323C4×C61—82no—
324C4×C61#38918yescomplemented
325Dic61—28no—
326Dic61—24no—
327Dic61—44no—
328Dic61—42no—
329Dic61—42no—
330Dic61—42no—
331C2×#389—611no—
332C2×#389—612no—
333C2×#389—611no—
334C2×#389—611no—
335C2×#384D6111yescharacteristic
336C2×C4×C4⋊C4—611no—
337#1444—612no—
338#1441—612no—
339#1436—612no—
340C4⋊#95—611no—
341C4×#95—611no—
342C2×C61C2×#38911yescharacteristic
343C2×C61C4×C4⋊Q811yescharacteristic
344C2×C61#233011yescharacteristic
345C2×C61D4×C4⋊C411yescharacteristic
346C2×C61Q8×C4⋊C411yescharacteristic
347C2×C61#236011yescharacteristic
348C2×C61#236111yescharacteristic
349C2×C61#242811yescharacteristic
350C2×C61#242911yescharacteristic
351C2×C61#244011yescharacteristic
352C2×C61#244111yescharacteristic
353C2×C61#250611yescharacteristic
354C2×C61#250711yescharacteristic
355C2×C61#255011yescharacteristic
356C2×C61#255111yescharacteristic
357C22×C4⋊C4—611no—
358C22×C4⋊C4—612no—
359C22×C4⋊C4—611no—
360C22×C4⋊C4—612no—
361C22×C4⋊C4—612no—
362C22×C4⋊C4C2×D6111yescharacteristic
363C22×C4⋊C4C2×D6112yes—
364C22×C4⋊C4C2×D6112yes—
365C22×C4⋊C4C2×D6111yescharacteristic
366C22×C42—611no—
367C22×C42—611no—
368C22×C42—612no—
369C22×C42C2×D6111yescharacteristic
370#389—618no—
371#389—1228no—
372#389—1224no—
373#389—1224no—
374#384—24no—
375C4×C4⋊C4—1224no—
376C2×#95—611no—
377C2×#95—611no—
378C2×#95—612no—
379C2×#95—611no—
380C2×#95—611no—
381C2×#95—612no—
382C2×#95—612no—
383C2×#95—612no—
384C2×#95—612no—
385C2×#95—612no—
386C61#1400511yescharacteristic, complemented, Sylow
387C23×C4—612no—
388C23×C4—611no—
389C23×C4—611no—
390C23×C4—612no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4C22×D6112yes—
394C23×C4C22×D6112yes—
395C23×C4C22×D6111yescharacteristic
396C23×C4C22×D6111yescharacteristic
397C23×C4C22×D6111yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—614no—
410C2×C4⋊C4—614no—
411C2×C4⋊C4—614no—
412C2×C4⋊C4—618no—
413C2×C4⋊C4—614no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1224no—
416C2×C4⋊C4—1224no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1224no—
419C2×C4⋊C4—1224no—
420C2×C4⋊C4—1224no—
421C2×C4⋊C4—1224no—
422C2×C4⋊C4—2442no—
423C2×C4⋊C4—2442no—
424C2×C4⋊C4C22⋊D6114yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—614no—
428C2×C42—1222no—
429C2×C42—1222no—
430C2×C42—1224no—
431C2×C42—1224no—
432C2×C42—1222no—
433C2×C42—1222no—
434C2×C42—1222no—
435C2×C42—2442no—
436C2×C42C4×D6114yes—
437#95—618no—
438#95—614no—
439#95—614no—
440#95—1224no—
441#95—1224no—
442#95—1224no—
443#95—1222no—
444#95—1222no—
445#95—1224no—
446#95—2442no—
447C24C23×D6111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—614no—
470C22×C4—612no—
471C22×C4—614no—
472C22×C4—612no—
473C22×C4—612no—
474C22×C4—614no—
475C22×C4—614no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—1221no—
480C22×C4—1222no—
481C22×C4—1221no—
482C22×C4—1222no—
483C22×C4—1221no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1222no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1222no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1222no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1222no—
503C22×C4—1221no—
504C22×C4—1222no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1222no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4C2×C4×D6112yes—
512C22×C4C2×C4×D6112yes—
513C22×C4C2×C4×D6112yes—
514C22×C4#1175822212yes—
515C22×C4D4×D6112yes—
516C22×C4D4×D6112yes—
517C22×C4#1175822412yes—
518C22×C4#1175822412yes—
519C22×C4Q8×D6112yes—
520C22×C4Q8×D6112yes—
521C22×C4Q8×D6112yes—
522C22×C4#1175822612yes—
523C22×C4C2×C22⋊D6114yes—
524C22×C4C2×C22⋊D6112yes—
525C4⋊C4—28no—
526C4⋊C4—48no—
527C4⋊C4—48no—
528C4⋊C4—44no—
529C4⋊C4—6116no—
530C4⋊C4—1228no—
531C4⋊C4—12216no—
532C4⋊C4—2448no—
533C4⋊C4—2448no—
534C42—28no—
535C42—1228no—
536C42—2448no—
537C42—2444no—
538C23C22×C4×D6111yescharacteristic
539C23C2×D4×D6111yescharacteristic
540C23C2×D4×D6111yescharacteristic
541C23C22×C22⋊D6111yescharacteristic
542C23C2×Q8×D6111yescharacteristic
543C23C2×Q8×D6111yescharacteristic
544C23C2×Q8×D6111yescharacteristic
545C23C2×#1175822411yescharacteristic
546C23C2×#1175822411yescharacteristic
547C23C2×#1175822211yescharacteristic
548C23C2×#1175822611yescharacteristic
549C23#1451982211yescharacteristic
550C23#1451982211yescharacteristic
551C23#1451982511yescharacteristic
552C23#1451982511yescharacteristic
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—618no—
580C2×C4—614no—
581C2×C4—1222no—
582C2×C4—1224no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1224no—
589C2×C4—1222no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1222no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—2441no—
606C2×C4—2442no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2442no—
612C2×C4—2441no—
613C2×C4—2442no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2442no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4C4⋊C4×D6114yes—
622C2×C4C4×C22⋊D6114yes—
623C2×C4#1451973914yes—
624C2×C4#1451974214yes—
625C2×C4#1451974214yes—
626C2×C4#1451974914yes—
627C2×C4#1451975514yes—
628C2×C4#1451976714yes—
629C2×C4#1451977514yes—
630C22C2×C4⋊C4×D6111yescharacteristic
631C22C2×C4×C22⋊D6111yescharacteristic
632C22C2×#1451973911yescharacteristic
633C22C2×#1451974211yescharacteristic
634C22C2×#1451974211yescharacteristic
635C22#1684024311yescharacteristic
636C22#1684024311yescharacteristic
637C22C2×#1451974911yescharacteristic
638C22C2×#1451975511yescharacteristic
639C22C2×#1451976711yescharacteristic
640C22C4⋊Q8×D6111yescharacteristic
641C22C2×#1451977511yescharacteristic
642C22#1684031011yescharacteristic
643C22#1684031711yescharacteristic
644C22#1684031711yescharacteristic
645C22#1684036611yescharacteristic
646C22#1684037311yescharacteristic
647C22#1684038911yescharacteristic
648C22#1684038911yescharacteristic
649C22D4×C22⋊D6111yescharacteristic
650C22#1684039711yescharacteristic
651C22#1684040611yescharacteristic
652C22#1684041311yescharacteristic
653C22#1684041511yescharacteristic
654C22#1684042311yescharacteristic
655C22Q8×C22⋊D6111yescharacteristic
656C22#1684042711yescharacteristic
657C22#1684042711yescharacteristic
658C22#1684043211yescharacteristic
659C22#1684044711yescharacteristic
660C22#1684046011yescharacteristic
661C22#1684046711yescharacteristic
662C22#1684047311yescharacteristic
663C22#1684048711yescharacteristic
664C22#1684049211yescharacteristic
665C4—24no—
666C4—24no—
667C4—44no—
668C4—82no—
669C4—1228no—
670C4—1224no—
671C4—2442no—
672C4—2444no—
673C4—2442no—
674C4—2442no—
675C4#1683965718yescomplemented
676C2C2×#1683965711yescharacteristic
677C2#2144838611yescharacteristic
678C2#2144855811yescharacteristic
679C2#2144871911yescharacteristic
680C2#2144873111yescharacteristic
681C2#2144882411yescharacteristic
682C2#2144883511yescharacteristic
683C2#2144941011yescharacteristic
684C2#2144942111yescharacteristic
685C2#2144952411yescharacteristic
686C2#2144953511yescharacteristic
687C2#2145033111yescharacteristic
688C2#2145034211yescharacteristic
689C2#2145083611yescharacteristic
690C2#2145084611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#384C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#384D61
hypocenterC61#14005
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
20. #16839660C4semidirect
185. C4⋊Dic61C4⋊C4semidirect
324. C4×C61#389semidirect
386. C61#14005semidirect
675. C4#16839657semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
C2×#168396582
C2×#168396572
C2×C4⋊C4×Dic612
#214440822
#214440692
#214440512
#214440482
C4×#145196842
C2×C61×#3842
#1400561