Finite Group Databasebeta

← #29690591

Subgroups — #29690591

Order 15616.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839818C211yesmaximal, characteristic
2#21448225C211yesmaximal, characteristic
3#21448215C211yesmaximal, characteristic
4#21446589C211yesmaximal, characteristic, complemented
5#21446587C211yesmaximal, characteristic, complemented
6#21446585C211yesmaximal, characteristic, complemented
7#21446021C211yesmaximal, characteristic
8#21446019C211yesmaximal, characteristic
9#21446017C211yesmaximal, characteristic
10#21446015C211yesmaximal, characteristic
11#21445986C211yesmaximal, characteristic, complemented
12#21445984C211yesmaximal, characteristic, complemented
13#21445951C211yesmaximal, characteristic, complemented
14#21445951C211yesmaximal, characteristic, complemented
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×#14519735C2211yescharacteristic
17C2×#14519735C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19#16839818C418yescomplemented
20C2×#14519711C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519687C2211yescharacteristic
30C2×#14519687C2211yescharacteristic
31#16839631C2211yescharacteristic
32#16839631C2211yescharacteristic
33#16839629—21no—
34#16839628C2211yescharacteristic
35#16839627C2211yescharacteristic
36#16839627C2211yescharacteristic
37#16839624—21no—
38#16839621—21no—
39#16839621—21no—
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43#16839613—21no—
44#16839613—21no—
45C4×#11758198—21no—
46#16839608—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519735—41no—
66#14519735—41no—
67#14519735—41no—
68#14519735—41no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87C42×D61C2×C414yes—
88C42×D61Q814yes—
89#14519711—41no—
90#14519710—41no—
91#14519710—41no—
92#14519709—41no—
93#14519708—41no—
94#14519708—41no—
95C4⋊#92418C2×C414yes—
96#14519689C2×C414yes—
97#14519689C2×C414yes—
98#14519687C2×C414yes—
99#14519687C2×C414yes—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117#107×C61—41no—
118#106×C61—41no—
119C4⋊C8×C61C2×C414yes—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—41no—
143C2×C4×D61—41no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61C4⋊C414yes—
147C2×C4×D61C4⋊C414yes—
148C2×C4×D61C22×C412yes—
149C2×C4×D61C2×Q812yes—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61C22×C412yes—
155C2×C8×C61C22×C412yes—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C42×C61—42no—
165C42×C61C22×C412yes—
166C42×C61C2×Q812yes—
167#11758198—42no—
168#11758198—42no—
169#11758198—42no—
170#11758198—42no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179#11758196—42no—
180#11758196—42no—
181#11758196—42no—
182#11758196—42no—
183C4×Dic61—42no—
184C4×Dic61—42no—
185C4×Dic61—42no—
186C4×Dic61C4⋊C414yes—
187C4×Dic61C4⋊C414yes—
188C4×Dic61C22×C412yes—
189C4×Dic61C2×Q812yes—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418C22×C412yes—
195C2×#92418C22×C412yes—
196C23×C61C22×D411yescharacteristic
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61—21no—
202C22×D61—21no—
203C22×D61C2×C4⋊C412yes—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61C2×C4⋊C412yes—
221C2×C4×C61C2×C4⋊C412yes—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×Q811yescharacteristic
224C2×C4×C61H(5,𝔽2)11yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C612−1+411yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61C2×C4⋊C412yes—
247C2×Dic61C2×C4⋊C412yes—
248C2×Dic61C2×C4⋊C412yes—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—22no—
253C4×D61—44no—
254C4×D61—44no—
255C8×C61—22no—
256C8×C61—22no—
257#92418—22no—
258#92418—22no—
259#21989—611nomaximal, Sylow
260C22×C61C22×C4⋊C411yescharacteristic
261C22×C61#53511yescharacteristic
262C22×C61#53611yescharacteristic
263C22×C61#57511yescharacteristic
264C22×C61#57511yescharacteristic
265C22×C61#57511yescharacteristic
266C22×C61#57511yescharacteristic
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—41no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C4×C61—22no—
275C4×C61—22no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61—81no—
280C4×C61#52011yescharacteristic
281C4×C61#52011yescharacteristic
282C4×C61#54411yescharacteristic
283C4×C61#54411yescharacteristic
284Dic61—22no—
285Dic61—22no—
286Dic61—22no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290Dic61—81no—
291C2×#432—611no—
292#2285—611no—
293#2283—611no—
294#1949—611no—
295#1949—611no—
296#1949—611no—
297#1949D6111yescharacteristic, complemented
298#1854—611no—
299#1854—611no—
300#1854—611no—
301#1854—611no—
302#1847—611no—
303#1847—611no—
304#1836—611no—
305#1836—611no—
306C2×C61#231711yescharacteristic
307C2×C61#291111yescharacteristic
308C2×C61#291111yescharacteristic
309C2×C61#321911yescharacteristic
310C2×C61#321911yescharacteristic
311C2×C61#324011yescharacteristic
312C2×C61#324011yescharacteristic
313D61—42no—
314C2×#117—611no—
315C2×#117—611no—
316C22×C42—611no—
317#432—618no—
318C2×#107—611no—
319C2×#107—611no—
320C2×#107—611no—
321C2×#107C2×D6111yescharacteristic
322C2×#106—611no—
323C2×#106—611no—
324C2×#106—611no—
325C2×#106C2×D6111yescharacteristic
326C2×C4⋊C8—611no—
327C2×C4⋊C8C2×D6111yescharacteristic
328C2×C22⋊C8—611no—
329C2×C22⋊C8—611no—
330C2×#97—611no—
331C2×#97—611no—
332#384—611no—
333#384—611no—
334#383—1221no—
335#382—611no—
336#382—611no—
337#382—611no—
338#382C2×D6111yescharacteristic
339#381—1221no—
340#380—611no—
341#380—611no—
342#380—1221no—
343#380—1221no—
344C4×C4⋊C4—611no—
345C4×C4⋊C4—1221no—
346C4×C4⋊C4—1221no—
347C4×C4⋊C4C2×D6111yescharacteristic
348C4×C22⋊C4—1221no—
349#376—1221no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340C2×D6111yescharacteristic
357#340C2×D6111yescharacteristic
358C61#2198911yescharacteristic, complemented, Sylow
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8C22×D6111yescharacteristic
365C22×C8C22×D6111yescharacteristic
366#117—2441no—
367#117—2441no—
368#117—2441no—
369#117—2441no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C42—21no—
387C2×C42—611no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—614no—
391C2×C42—614no—
392C2×C42—1221no—
393C2×C42—1221no—
394C2×C42—1221no—
395C2×C42C22×D6111yescharacteristic
396#107—41no—
397#107—2441no—
398#107—2441no—
399#107—2441no—
400#106—41no—
401#106—2441no—
402#106—2441no—
403#106—2441no—
404C4⋊C8—614no—
405C4⋊C8C4×D6114yes—
406C22⋊C8—614no—
407C22⋊C8—614no—
408#97—614no—
409#97—614no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421#95—1221no—
422C24—611no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—614no—
433C22×C4—614no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4—2441no—
446C22×C4D4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4C23×D6111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—612no—
454C2×C8—612no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C4×D6112yes—
460C2×C8C2×C4×D6112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C22⋊C4—2442no—
482C22⋊C4—2442no—
483C22⋊C4—2442no—
484C22⋊C4—2442no—
485C42—42no—
486C42—612no—
487C42—612no—
488C42—614no—
489C42—614no—
490C42—2442no—
491C42—2442no—
492C42—2442no—
493C42C2×C4×D6112yes—
494C42Q8×D6112yes—
495C23—612no—
496C23—1221no—
497C23—1221no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23C2×D4×D6111yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—2444no—
533C2×C4—2444no—
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—2441no—
545C2×C4—2441no—
546C2×C4C4⋊C4×D6112yes—
547C2×C4C4⋊C4×D6112yes—
548C2×C4C22×C4×D6111yescharacteristic
549C2×C4C2×Q8×D6111yescharacteristic
550C2×C4#1451982211yescharacteristic
551C2×C4#1451982311yescharacteristic
552C2×C4#1451982411yescharacteristic
553C2×C4#1451982511yescharacteristic
554C8—22no—
555C8—22no—
556C8—1222no—
557C8—1222no—
558C22—1222no—
559C22—1222no—
560C22—1222no—
561C22—2441no—
562C22—2441no—
563C22—2441no—
564C22—2441no—
565C22C2×C4⋊C4×D6111yescharacteristic
566C22#1684032811yescharacteristic
567C22#1684033511yescharacteristic
568C22#1684055811yescharacteristic
569C22#1684055911yescharacteristic
570C22#1684055911yescharacteristic
571C22#1684056111yescharacteristic
572C4—22no—
573C4—22no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—1222no—
579C4—1222no—
580C4—1222no—
581C4—4881no—
582C4—4881no—
583C4—4881no—
584C4—4881no—
585C4#1684024111yescharacteristic
586C4#1684024411yescharacteristic
587C4#1684038911yescharacteristic
588C4#1684039211yescharacteristic
589C2—2442no—
590C2#2144844111yescharacteristic
591C2#2145440611yescharacteristic
592C2#2145440711yescharacteristic
593C2#2145685511yescharacteristic
594C2#2145686111yescharacteristic
595C2#2145705811yescharacteristic
596C2#2145706411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1949D61
hypocenterC61#21989
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #21446589C2semidirect
5. #21446587C2semidirect
6. #21446585C2semidirect
11. #21445986C2semidirect
12. #21445984C2semidirect
13. #21445951C2semidirect
14. #21445951C2semidirect
15. C61×#1949C2semidirect
19. #16839818C4semidirect
297. #1949D61semidirect
358. C61#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#168398182
#214482252
#214482152
#214465892
#214465872
#214465852
#214460212
#214460192
#214460172
#214460152
#214459862
#214459842
#214459512
C61×#19492
#2198961