Finite Group Databasebeta

← #29603739

Subgroups — #29603739

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic
2C2×#16839660C211yesmaximal, characteristic
3C2×#16839660C211yesmaximal, characteristic
4C2×C4×C4⋊Dic61C211yesmaximal, characteristic
5#21444082C212yesmaximal
6#21444070C212yesmaximal
7#21444051C212yesmaximal
8#21444049C211yesmaximal, characteristic
9#21444049C211yesmaximal, characteristic
10#21444047C212yesmaximal
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×#11758196C2212yes—
19C22×C4×Dic61C2212yes—
20#16839660—24no—
21#16839660—24no—
22#16839660C418yescomplemented
23C4×C4⋊Dic61—24no—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C42×C61C2211yescharacteristic
35C22×C42×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C4×C4⋊C4×C61—24no—
38C2×#95×C61C2211yescharacteristic
39C2×#95×C61C2211yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C2×C4⋊Dic61—22no—
45C2×C4⋊Dic61—22no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61—22no—
49C2×C4⋊Dic61—22no—
50C2×C4⋊Dic61—22no—
51C2×C4⋊Dic61C2×C414yes—
52C2×C4⋊Dic61C2×C414yes—
53C2×C4⋊Dic61D414yes—
54C2×C4⋊Dic61Q814yes—
55C2×C4⋊Dic61Q814yes—
56C2×#11758196—24no—
57C2×#11758196—24no—
58C2×#11758196—24no—
59C2×#11758196—42no—
60C2×#11758196—42no—
61C2×#11758196—42no—
62C2×#11758196—42no—
63C2×#11758196—42no—
64C2×#11758196C2×C418yes—
65C2×C4×Dic61—24no—
66C2×C4×Dic61—24no—
67C2×C4×Dic61—42no—
68#14519684—24no—
69#14519684—24no—
70#14519684—24no—
71#14519684—24no—
72#14519684—42no—
73#14519684—42no—
74#14519684—42no—
75#14519684C2×C418yes—
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C23×C4×C61C2311yescharacteristic
83C2×C4⋊C4×C61—22no—
84C2×C4⋊C4×C61—22no—
85C2×C4⋊C4×C61—22no—
86C2×C4⋊C4×C61—22no—
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61Q814yes—
89C2×C42×C61—22no—
90C2×C42×C61—22no—
91C2×C42×C61—22no—
92C2×C42×C61—22no—
93C2×C42×C61—22no—
94C2×C42×C61—22no—
95C2×C42×C61—22no—
96C2×C42×C61C2×C414yes—
97C2×C42×C61D414yes—
98#95×C61—22no—
99#95×C61—22no—
100C24×C61C2411yescharacteristic
101C22×C4×C61—21no—
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—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61C22×C412yes—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C22×C412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×D412yes—
138C22×C4×C61C2×D412yes—
139C22×C4×C61C2×D412yes—
140C22×C4×C61C2×Q812yes—
141C22×C4×C61C2×Q812yes—
142C22×C4×C61C2×Q812yes—
143C22×C4×C61C2×Q812yes—
144C22×C4×C61C2×Q812yes—
145C22×C4×C61#4112yes—
146C22×C4×C61#4112yes—
147C22×C4×C61#4112yes—
148C22×C4×C61#4112yes—
149C22×C4×C61#4112yes—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—22no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61C22×C414yes—
174C22×Dic61C22×C414yes—
175C22×Dic61C2×D414yes—
176C22×Dic61C2×Q814yes—
177C22×Dic61C2×Q814yes—
178C4⋊C4×C61—28no—
179C4⋊C4×C61—28no—
180C42×C61—28no—
181C42×C61—28no—
182C42×C61—44no—
183C4⋊Dic61—28no—
184C4⋊Dic61—28no—
185C4⋊Dic61—44no—
186C4⋊Dic61C4⋊C4116yescomplemented
187#11758196—48no—
188#11758196—48no—
189#11758196—48no—
190C4×Dic61—48no—
191C23×C61C23×C411yescharacteristic
192C23×C61C22×D411yescharacteristic
193C23×C61C22×D411yescharacteristic
194C23×C61C22×Q811yescharacteristic
195C23×C61C22×Q811yescharacteristic
196C23×C61C22×Q811yescharacteristic
197C23×C61C2×#4111yescharacteristic
198C23×C61C2×#4111yescharacteristic
199C23×C61C2×#4111yescharacteristic
200C23×C61C2×#4111yescharacteristic
201C23×C61C2×#4111yescharacteristic
202C23×C61H(5,𝔽2)11yescharacteristic
203C23×C61H(5,𝔽2)11yescharacteristic
204C23×C61H(5,𝔽2)11yescharacteristic
205C23×C612−1+411yescharacteristic
206C2×C4×C61—22no—
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—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61C2×C4⋊C414yes—
247C2×C4×C61C4×D414yes—
248C2×C4×C61C4×Q814yes—
249C2×C4×C61C4×Q814yes—
250C2×C4×C61#12114yes—
251C2×C4×C61C22⋊Q814yes—
252C2×C4×C61C22⋊Q814yes—
253C2×C4×C61#12514yes—
254C2×C4×C61C4⋊Q814yes—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—24no—
261C2×Dic61—24no—
262C2×Dic61—24no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—24no—
267C2×Dic61—42no—
268C2×Dic61—42no—
269C2×Dic61—42no—
270C2×Dic61—42no—
271C2×Dic61—42no—
272C2×Dic61—42no—
273C2×Dic61—42no—
274C2×Dic61—42no—
275C2×Dic61—42no—
276C2×Dic61—42no—
277C2×Dic61—42no—
278C2×Dic61—42no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61C2×C4⋊C418yes—
283#14045—611nomaximal, Sylow
284C22×C61C22×C4⋊C411yescharacteristic
285C22×C61C2×C4×D411yescharacteristic
286C22×C61C2×C4×Q811yescharacteristic
287C22×C61C2×C4×Q811yescharacteristic
288C22×C61C4×#4111yescharacteristic
289C22×C61#51811yescharacteristic
290C22×C61#52011yescharacteristic
291C22×C61C2×#12111yescharacteristic
292C22×C61C2×C22⋊Q811yescharacteristic
293C22×C61C2×C22⋊Q811yescharacteristic
294C22×C61#52511yescharacteristic
295C22×C61C2×#12511yescharacteristic
296C22×C61#52911yescharacteristic
297C22×C61C2×C4⋊Q811yescharacteristic
298C22×C61#53311yescharacteristic
299C22×C61#53511yescharacteristic
300C22×C61#53711yescharacteristic
301C22×C61#54011yescharacteristic
302C22×C61#54211yescharacteristic
303C22×C61#54611yescharacteristic
304C22×C61#54611yescharacteristic
305C22×C61D4×Q811yescharacteristic
306C22×C61#55011yescharacteristic
307C22×C61#55211yescharacteristic
308C22×C61#55311yescharacteristic
309C22×C61#55411yescharacteristic
310C22×C61#55411yescharacteristic
311C22×C61#55411yescharacteristic
312C22×C61#55411yescharacteristic
313C22×C61#55411yescharacteristic
314C22×C61#55511yescharacteristic
315C22×C61#55711yescharacteristic
316C22×C61#55711yescharacteristic
317C22×C61Q8211yescharacteristic
318C22×C61Q8211yescharacteristic
319C4×C61—24no—
320C4×C61—24no—
321C4×C61—42no—
322C4×C61—42no—
323C4×C61—42no—
324C4×C61—42no—
325C4×C61#38918yes—
326Dic61—28no—
327Dic61—44no—
328Dic61—44no—
329Dic61—82no—
330C2×#389—611no—
331C2×#389—611no—
332C2×#389—611no—
333C2×C4×C4⋊C4—611no—
334C2×C4×C4⋊C4D6111yescharacteristic
335#1444—612no—
336#1441—612no—
337#1436—612no—
338C4⋊#95—611no—
339C4⋊#95—611no—
340C4⋊#95—612no—
341C2×C61C2×#38911yescharacteristic
342C2×C61C4×C22⋊Q811yescharacteristic
343C2×C61#232411yescharacteristic
344C2×C61#234911yescharacteristic
345C2×C61Q8×C4⋊C411yescharacteristic
346C2×C61#236911yescharacteristic
347C2×C61#237011yescharacteristic
348C2×C61#241411yescharacteristic
349C2×C61#241711yescharacteristic
350C2×C61#245111yescharacteristic
351C2×C61#245411yescharacteristic
352C2×C61#250711yescharacteristic
353C2×C61#250811yescharacteristic
354C2×C61#256711yescharacteristic
355C2×C61#258411yescharacteristic
356C22×C4⋊C4—611no—
357C22×C4⋊C4—611no—
358C22×C4⋊C4—611no—
359C22×C4⋊C4—612no—
360C22×C4⋊C4—611no—
361C22×C4⋊C4—612no—
362C22×C4⋊C4—612no—
363C22×C4⋊C4C2×D6111yescharacteristic
364C22×C4⋊C4C2×D6111yescharacteristic
365C22×C42—612no—
366C22×C42C2×D6111yescharacteristic
367C22×C42C2×D6111yescharacteristic
368C22×C42C2×D6111yescharacteristic
369#389—618no—
370#389—1224no—
371#389—1224no—
372C4×C4⋊C4—24no—
373C4×C4⋊C4—1224no—
374C2×#95—612no—
375C2×#95—612no—
376C2×#95—612no—
377C2×#95—612no—
378C2×#95—612no—
379C2×#95—612no—
380C2×#95—612no—
381C2×#95—612no—
382C2×#95C2×D6111yescharacteristic
383C2×#95C2×D6111yescharacteristic
384C61#1404511yescharacteristic, complemented, Sylow
385C23×C4—612no—
386C23×C4—612no—
387C23×C4—612no—
388C23×C4—612no—
389C23×C4C22×D6111yescharacteristic
390C23×C4C22×D6111yescharacteristic
391C23×C4C22×D6111yescharacteristic
392C23×C4C22×D6111yescharacteristic
393C23×C4C22×D6111yescharacteristic
394C23×C4C22×D6111yescharacteristic
395C23×C4C22×D6111yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—614no—
402C2×C4⋊C4—614no—
403C2×C4⋊C4—614no—
404C2×C4⋊C4—614no—
405C2×C4⋊C4—614no—
406C2×C4⋊C4—618no—
407C2×C4⋊C4—1222no—
408C2×C4⋊C4—1222no—
409C2×C4⋊C4—1222no—
410C2×C4⋊C4—1222no—
411C2×C4⋊C4—1224no—
412C2×C4⋊C4—1224no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1222no—
415C2×C4⋊C4—1224no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—2442no—
418C2×C4⋊C4—2442no—
419C2×C4⋊C4—2442no—
420C2×C4⋊C4—2442no—
421C2×C4⋊C4—2442no—
422C2×C4⋊C4Dic12214yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—1224no—
431C2×C42—1224no—
432C2×C42—2442no—
433C2×C42C4×D6114yes—
434C2×C42C22⋊D6114yes—
435#95—22no—
436#95—22no—
437#95—618no—
438#95—1224no—
439#95—1224no—
440#95—1224no—
441#95—1224no—
442#95—2442no—
443#95—2442no—
444#95—2442no—
445C24C23×D6111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
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—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—614no—
479C22×C4—614no—
480C22×C4—614no—
481C22×C4—614no—
482C22×C4—614no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1222no—
505C22×C4—1222no—
506C22×C4C2×Dic12212yes—
507C22×C4C2×Dic12212yes—
508C22×C4C2×Dic12212yes—
509C22×C4C2×C4×D6112yes—
510C22×C4C2×C4×D6112yes—
511C22×C4C2×C4×D6112yes—
512C22×C4#1175822212yes—
513C22×C4#1175822212yes—
514C22×C4#1175822212yes—
515C22×C4#1175822212yes—
516C22×C4D4×D6112yes—
517C22×C4#1175822412yes—
518C22×C4Q8×D6112yes—
519C22×C4Q8×D6112yes—
520C22×C4C2×C22⋊D6112yes—
521C22×C4C2×C22⋊D6112yes—
522C22×C4C2×C22⋊D6112yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—6116no—
526C4⋊C4—1228no—
527C4⋊C4—1228no—
528C4⋊C4—2448no—
529C4⋊C4—2448no—
530C4⋊C4—2448no—
531C4⋊C4—2444no—
532C42—28no—
533C42—28no—
534C42—44no—
535C42—2448no—
536C23C22×C4×D6111yescharacteristic
537C23C2×D4×D6111yescharacteristic
538C23C22×C22⋊D6111yescharacteristic
539C23C2×Q8×D6111yescharacteristic
540C23C2×Q8×D6111yescharacteristic
541C23C22×Dic12211yescharacteristic
542C23C2×#1175822411yescharacteristic
543C23C2×#1175822211yescharacteristic
544C23C2×#1175822211yescharacteristic
545C23C2×#1175822211yescharacteristic
546C23C2×#1175822211yescharacteristic
547C23#1451982311yescharacteristic
548C23#1451982311yescharacteristic
549C23#1451982311yescharacteristic
550C23#1451982411yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
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—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—618no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1224no—
598C2×C4—1224no—
599C2×C4—1224no—
600C2×C4—1224no—
601C2×C4—1224no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2442no—
617C2×C4—2442no—
618C2×C4—2442no—
619C2×C4C4⋊C4×D6114yes—
620C2×C4C4×C22⋊D6114yes—
621C2×C4#1451974214yes—
622C2×C4C4×Dic12214yes—
623C2×C4#1451974914yes—
624C2×C4#1451975514yes—
625C2×C4#1451975614yes—
626C2×C4#1451976714yes—
627C2×C4#1451977514yes—
628C22C2×C4⋊C4×D6111yescharacteristic
629C22C2×C4×C22⋊D6111yescharacteristic
630C22C2×#1451974211yescharacteristic
631C22C2×C4×Dic12211yescharacteristic
632C22C4×#1175822211yescharacteristic
633C22#1684023611yescharacteristic
634C22#1684024211yescharacteristic
635C22C2×#1451974911yescharacteristic
636C22C2×#1451975511yescharacteristic
637C22C2×#1451975611yescharacteristic
638C22#1684027311yescharacteristic
639C22C2×#1451976711yescharacteristic
640C22#1684029611yescharacteristic
641C22C2×#1451977511yescharacteristic
642C22#1684031911yescharacteristic
643C22#1684032611yescharacteristic
644C22#1684034011yescharacteristic
645C22#1684036711yescharacteristic
646C22#1684038311yescharacteristic
647C22#1684040811yescharacteristic
648C22#1684040811yescharacteristic
649C22D4×Dic12211yescharacteristic
650C22#1684043311yescharacteristic
651C22#1684045211yescharacteristic
652C22#1684045811yescharacteristic
653C22#1684046911yescharacteristic
654C22#1684047211yescharacteristic
655C22#1684047211yescharacteristic
656C22#1684047211yescharacteristic
657C22#1684047211yescharacteristic
658C22#1684047711yescharacteristic
659C22#1684049011yescharacteristic
660C22#1684049011yescharacteristic
661C22Q8×Dic12211yescharacteristic
662C22Q8×Dic12211yescharacteristic
663C4—24no—
664C4—24no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—1228no—
670C4—4882no—
671C4—2444no—
672C4—2444no—
673C4#1683965718yes—
674C2C2×#1683965711yescharacteristic
675C2C4×#1451975611yescharacteristic
676C2#2144851211yescharacteristic
677C2#2144873011yescharacteristic
678C2C4⋊C4×Dic12211yescharacteristic
679C2#2144890811yescharacteristic
680C2#2144891311yescharacteristic
681C2#2144923711yescharacteristic
682C2#2144927011yescharacteristic
683C2#2144965811yescharacteristic
684C2#2144969111yescharacteristic
685C2#2145034611yescharacteristic
686C2#2145035711yescharacteristic
687C2#2145102411yescharacteristic
688C2#2145120711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#14045
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #16839660C4semidirect
186. C4⋊Dic61C4⋊C4semidirect
384. C61#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
C2×C4×C4⋊Dic612
#214440822
#214440702
#214440512
#214440492
#214440472
C2×C4×C4⋊C4×C612
#1404561