Finite Group Databasebeta

← #29738244

Subgroups — #29738244

Order 15616.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450834C211yesmaximal, characteristic, complemented
2#21448768C211yesmaximal, characteristic
3#21447189C211yesmaximal, characteristic
4#21447189C211yesmaximal, characteristic
5#21446963C211yesmaximal, characteristic
6#21446953C211yesmaximal, characteristic
7#21446773C211yesmaximal, characteristic, complemented
8#21446769C211yesmaximal, characteristic, complemented
9#21446582C211yesmaximal, characteristic, complemented
10#21446542C211yesmaximal, characteristic, complemented
11#21446407C211yesmaximal, characteristic, complemented
12#21446400C211yesmaximal, characteristic, complemented
13#21445953C211yesmaximal, characteristic, complemented
14#21445829C211yesmaximal, characteristic
15C61×#1762C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519736—21no—
19C2×#14519708C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26#16839694—21no—
27#16839683—21no—
28#16839668—21no—
29#16839665C2211yescharacteristic
30#16839665C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660—21no—
34#16839655—21no—
35#16839655—21no—
36#16839632C2211yescharacteristic
37#16839628C2211yescharacteristic
38#16839622—21no—
39C4⋊C4×Dic61C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519776—22no—
63#14519776—41no—
64#14519768—22no—
65#14519768—41no—
66#14519736—44no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61D411yescharacteristic
73C2×C4⋊Dic61D411yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519708—22no—
89#14519708—22no—
90C4⋊#92418—22no—
91#14519706—41no—
92#14519706—41no—
93#14519698—41no—
94#14519698—41no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684D411yescharacteristic
102#14519684D411yescharacteristic
103C22×D4×C61C2311yescharacteristic
104C23×C4×C61—21no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C4×D4×C61—22no—
108C4×D4×C61Q814yescomplemented
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61C2311yescharacteristic
115#102×C61—22no—
116#102×C61—22no—
117#97×C61—22no—
118#95×C61—21no—
119C24×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61C2×Q812yes—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—24no—
130C22×C4×C61—42no—
131C22×C4×C61—42no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C2×Dic122—42no—
144C2×Dic122—42no—
145C2×Dic122—81no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61C2×Q812yes—
156C4⋊C4×C61#4112yes—
157C4⋊C4×C61#4112yes—
158C22⋊C4×C61—24no—
159C42×C61—81no—
160C42×C61C2×Q812yes—
161C42×C61#4112yes—
162C22⋊Dic61—42no—
163C22⋊Dic61—42no—
164C22⋊Dic61—81no—
165C22⋊Dic61—81no—
166C4⋊Dic61—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—41no—
176C4⋊Dic61—42no—
177C4⋊Dic61—42no—
178C4⋊Dic61—42no—
179C4⋊Dic61—81no—
180C4⋊Dic61—81no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—42no—
188C4×Dic61—42no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C23×C61—22no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61C22×D411yescharacteristic
203D4×C61—22no—
204D4×C61—22no—
205D4×C61—41no—
206D4×C61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—48no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61C22⋊Q812yes—
222C2×C4×C61C22⋊Q812yes—
223C2×C4×C61C22×Q811yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×C4×C612−1+411yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61AGL(1,ℤ/8)12yes—
253Dic122—84no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—41no—
257#92418—41no—
258#26032—611nomaximal, Sylow
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61C2×C22⋊Q811yescharacteristic
267C22×C61#54611yescharacteristic
268C22×C61#54811yescharacteristic
269C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C61#57511yescharacteristic
271C22×C61#57711yescharacteristic
272C22×C61#57711yescharacteristic
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—42no—
276C4×C61—42no—
277C4×C61—42no—
278C4×C61#53311yescharacteristic
279C4×C61#54411yescharacteristic
280C4×C61#55511yescharacteristic
281C4×C61#55611yescharacteristic
282Dic61—22no—
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290#2550—611no—
291#2354—611no—
292#2065—611no—
293#2065—611no—
294#2025—611no—
295#2023—611no—
296#1989—611no—
297#1988—611no—
298#1948—611no—
299#1940—611no—
300#1920—611no—
301#1919—611no—
302#1836—611no—
303#1804—611no—
304#1762D6111yescharacteristic
305C2×C61—82no—
306C2×C61#243911yescharacteristic
307C2×C61#307711yescharacteristic
308C2×C61#308411yescharacteristic
309C2×C61#330611yescharacteristic
310C2×C61#332111yescharacteristic
311C2×C61#336811yescharacteristic
312C2×C61#337611yescharacteristic
313C2×C4⋊Q8—611no—
314C2×#125—611no—
315C2×C4×D4C2×D6111yescharacteristic
316C2×#117—1221no—
317C2×#106—611no—
318C2×#106—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8—611no—
321C2×C4⋊C8—611no—
322C2×#102—611no—
323C2×#102—611no—
324C2×#102C2×D6111yescharacteristic
325C2×#102C2×D6111yescharacteristic
326C2×#97C2×D6111yescharacteristic
327#398—1221no—
328#395—1221no—
329#391—1221no—
330#390—611no—
331#390—611no—
332#389—611no—
333#389—611no—
334#389—1221no—
335#388—1221no—
336#388—1221no—
337#384—611no—
338#382—611no—
339#380—1221no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4C2×D6111yescharacteristic
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340C2×D6111yescharacteristic
353#340C2×D6111yescharacteristic
354#336—611no—
355#336—611no—
356C61#2603211yescharacteristic, complemented, Sylow
357C22×Q8—1221no—
358C22×D4C22×D6111yescharacteristic
359C23×C4—21no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8C22×D6111yescharacteristic
363C22×C8C22×D6111yescharacteristic
364C4⋊Q8—1222no—
365C4⋊Q8—2441no—
366#125—1222no—
367#125—2441no—
368C4×D4—22no—
369C4×D4Dic12214yescomplemented
370#117—2444no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C42—21no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—1221no—
396C2×C42—1221no—
397C2×C42C22×D6111yescharacteristic
398#106—1222no—
399#106—1222no—
400C4⋊C8—1222no—
401C4⋊C8—2441no—
402C4⋊C8—2441no—
403#102—22no—
404#102—22no—
405#102—2441no—
406#102—2441no—
407#97—22no—
408#95—21no—
409#95—611no—
410#95—611no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417C24—21no—
418C2×Q8—4881no—
419C2×Q8—2442no—
420C2×Q8—2442no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×Dic12212yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4D4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443C22×C4C23×D6111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—1222no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—4881no—
469C4⋊C4—4881no—
470C4⋊C4—2441no—
471C4⋊C4—2442no—
472C4⋊C4—2442no—
473C4⋊C4—2442no—
474C4⋊C4—2442no—
475C4⋊C4—2442no—
476C4⋊C4C2×Dic12212yes—
477C4⋊C4#1175822212yes—
478C4⋊C4#1175822212yes—
479C22⋊C4—24no—
480C22⋊C4—4881no—
481C22⋊C4—4881no—
482C22⋊C4—2442no—
483C22⋊C4—2442no—
484C42—81no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42—2442no—
490C42—2442no—
491C42C2×Dic12212yes—
492C42#1175822412yes—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C2×D4×D6111yescharacteristic
501Q8—4884no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—612no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4#1451975412yes—
545C2×C4#1451975412yes—
546C2×C4C22×Dic12211yescharacteristic
547C2×C4C2×#1175822411yescharacteristic
548C2×C4C2×#1175822211yescharacteristic
549C2×C4C2×#1175822211yescharacteristic
550C2×C4#1451982311yescharacteristic
551C2×C4#1451982411yescharacteristic
552C8—41no—
553C8—41no—
554C8—2441no—
555C8—2441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×#1451975411yescharacteristic
564C22#1684040811yescharacteristic
565C22#1684042111yescharacteristic
566C22AGL(1,ℤ/8)×D6111yescharacteristic
567C22#1684055811yescharacteristic
568C22#1684057111yescharacteristic
569C22#1684057211yescharacteristic
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—1222no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4—4881no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4#1684031911yescharacteristic
584C4#1684039011yescharacteristic
585C4#1684047711yescharacteristic
586C4#1684048211yescharacteristic
587C2—82no—
588C2#2144951011yescharacteristic
589C2#2145561311yescharacteristic
590C2#2145568511yescharacteristic
591C2#2145778511yescharacteristic
592C2#2145801011yescharacteristic
593C2#2145854911yescharacteristic
594C2#2145864711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1762C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#1762D61
hypocenterC61#26032
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. #21450834C2semidirect
7. #21446773C2semidirect
8. #21446769C2semidirect
9. #21446582C2semidirect
10. #21446542C2semidirect
11. #21446407C2semidirect
12. #21446400C2semidirect
13. #21445953C2semidirect
108. C4×D4×C61Q8semidirect
356. C61#26032semidirect
369. C4×D4Dic122semidirect

Maximal subgroups

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

subgroupindex
#214508342
#214487682
#214471892
#214469632
#214469532
#214467732
#214467692
#214465822
#214465422
#214464072
#214464002
#214459532
#214458292
C61×#17622
#2603261