Finite Group Databasebeta

← #29690428

Subgroups — #29690428

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839787C211yesmaximal, characteristic
2#21448427C211yesmaximal, characteristic
3#21448424C211yesmaximal, characteristic
4#21446590C211yesmaximal, characteristic, complemented
5#21446589C211yesmaximal, characteristic, complemented
6#21446587C211yesmaximal, characteristic, complemented
7#21446586C211yesmaximal, characteristic, complemented
8#21446580C211yesmaximal, characteristic, complemented
9#21446579C211yesmaximal, characteristic, complemented
10#21446579C211yesmaximal, characteristic, complemented
11#21445851C211yesmaximal, characteristic
12#21445849C211yesmaximal, characteristic
13#21445843C211yesmaximal, characteristic
14#21445841C211yesmaximal, characteristic
15C61×#1948C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25#16839787C418yescomplemented
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29#16839653—21no—
30#16839652—21no—
31#16839652—21no—
32#16839651—21no—
33#16839646—21no—
34#16839644—21no—
35#16839643—21no—
36#16839643—21no—
37#16839631C2211yescharacteristic
38#16839628C2211yescharacteristic
39#16839627C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×C4⋊Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#106×C61C2211yescharacteristic
54C2×#106×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C61×#384C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758189—41no—
62C2×#11758189—41no—
63C2×#11758189C2×C414yes—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C8×D61—41no—
67C2×C8×D61—41no—
68C2×C8×D61C2×C414yes—
69#14519734C2×C414yes—
70#14519734Q814yes—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196D411yescharacteristic
78C2×#11758196D411yescharacteristic
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198D411yescharacteristic
84C2×#11758198D411yescharacteristic
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89#14519711—41no—
90#14519710—41no—
91#14519709—41no—
92#14519708—41no—
93#14519708—41no—
94#14519708—41no—
95C4⋊#92418C2×C414yes—
96#14519706C2×C414yes—
97#14519706C2×C414yes—
98#14519684—21no—
99#14519684—21no—
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×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C42×C61—21no—
118C2×C42×C61C2311yescharacteristic
119#106×C61—41no—
120#106×C61—41no—
121C4⋊C8×C61C2×C414yes—
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×D61C22×C412yes—
143C2×C4×D61C2×Q812yes—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61C22×C412yes—
149C2×C8×C61C22×C412yes—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—81no—
159C4⋊C4×C61—81no—
160C42×C61—81no—
161C42×C61C22×C412yes—
162C42×C61C2×Q812yes—
163#11758198—81no—
164#11758198—81no—
165#11758198—81no—
166#11758198—81no—
167#11758198C4⋊C414yes—
168#11758198C4⋊C414yes—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177#11758196—81no—
178#11758196—81no—
179#11758196C4⋊C414yes—
180#11758196C4⋊C414yes—
181C4×Dic61—81no—
182C4×Dic61—81no—
183C4×Dic61—81no—
184C4×Dic61C22×C412yes—
185C4×Dic61C2×Q812yes—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418C22×C412yes—
191C2×#92418C22×C412yes—
192#11758189—44no—
193C8×D61—44no—
194C23×C61C22×D411yescharacteristic
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—21no—
201C22×D61C2×C4⋊C412yes—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
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×C61C2×C4⋊C412yes—
219C2×C4×C61C2×C4⋊C412yes—
220C2×C4×C61C23×C411yescharacteristic
221C2×C4×C61C22×Q811yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×C4×C612−1+411yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
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×Dic61C2×C4⋊C412yes—
245C2×Dic61C2×C4⋊C412yes—
246C2×Dic61C2×C4⋊C412yes—
247C4×D61—22no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C8×C61—22no—
252C8×C61—22no—
253#92418—22no—
254#92418—22no—
255#21967—611nomaximal, Sylow
256C22×C61C22×C4⋊C411yescharacteristic
257C22×C61#53711yescharacteristic
258C22×C61#53711yescharacteristic
259C22×C61#57711yescharacteristic
260C22×C61#57711yescharacteristic
261C22×C61#57711yescharacteristic
262C22×C61#57711yescharacteristic
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—22no—
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—41no—
270C4×C61—22no—
271C4×C61—22no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61#51811yescharacteristic
277C4×C61#51911yescharacteristic
278C4×C61#54411yescharacteristic
279C4×C61#54411yescharacteristic
280Dic61—22no—
281Dic61—22no—
282Dic61—22no—
283Dic61—81no—
284Dic61—81no—
285Dic61—81no—
286Dic61—81no—
287C2×#424—611no—
288#2314—611no—
289#2314—611no—
290#1949—611no—
291#1949—611no—
292#1949—611no—
293#1949—611no—
294#1948—611no—
295#1948—611no—
296#1948—611no—
297#1948D6111yescharacteristic, complemented
298#1809—611no—
299#1809—611no—
300#1807—611no—
301#1807—611no—
302C2×C61#231611yescharacteristic
303C2×C61#291211yescharacteristic
304C2×C61#291211yescharacteristic
305C2×C61#326011yescharacteristic
306C2×C61#326011yescharacteristic
307C2×C61#326311yescharacteristic
308C2×C61#326311yescharacteristic
309D61—42no—
310C22×M16—611no—
311C23×C8—611no—
312C2×#117—611no—
313C2×#107—611no—
314C2×#107—611no—
315C2×#106—611no—
316C2×#106—611no—
317C2×#106—611no—
318C2×#106—611no—
319C2×#106C2×D6111yescharacteristic
320C2×#106C2×D6111yescharacteristic
321#424—618no—
322C2×C4⋊C8—611no—
323C2×C4⋊C8—611no—
324C2×C4⋊C8—611no—
325C2×C4⋊C8C2×D6111yescharacteristic
326#388—1221no—
327#388—1221no—
328#388—1221no—
329#388—1221no—
330#387—1221no—
331#387—1221no—
332#387—1221no—
333#387—1221no—
334#384—611no—
335#384C2×D6111yescharacteristic
336#382—611no—
337#382—611no—
338#380—611no—
339#380—611no—
340#380—611no—
341#380—611no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4—611no—
344C4×C4⋊C4—611no—
345C4×C4⋊C4C2×D6111yescharacteristic
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340C2×D6111yescharacteristic
353#340C2×D6111yescharacteristic
354C61#2196711yescharacteristic, complemented, Sylow
355C23×C4—611no—
356C2×M16—614no—
357C2×M16—2441no—
358C2×M16—2441no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—614no—
362C22×C8—2441no—
363C22×C8—2441no—
364C22×C8C22×D6111yescharacteristic
365C22×C8C22×D6111yescharacteristic
366#117—614no—
367#117—614no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
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—611no—
383C2×C22⋊C4—611no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C42—21no—
389C2×C42—611no—
390C2×C42—1221no—
391C2×C42—1221no—
392C2×C42—1221no—
393C2×C42C22×D6111yescharacteristic
394#107—2441no—
395#107—2441no—
396#106—41no—
397#106—41no—
398#106—2441no—
399#106—2441no—
400#106—2441no—
401#106—2441no—
402C4⋊C8—614no—
403C4⋊C8—614no—
404C4⋊C8—614no—
405C4⋊C8C4×D6114yes—
406#95—21no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418C24—611no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4D4×D6111yescharacteristic
437C22×C4D4×D6111yescharacteristic
438C22×C4C23×D6111yescharacteristic
439M16—2444no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—612no—
445C2×C8—612no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—2444no—
451C2×C8C2×C4×D6112yes—
452C2×C8C2×C4×D6112yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—614no—
464C4⋊C4—614no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—4881no—
474C4⋊C4—4881no—
475C22⋊C4—614no—
476C22⋊C4—614no—
477C22⋊C4—4881no—
478C22⋊C4—4881no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C42—81no—
482C42—612no—
483C42—612no—
484C42—4881no—
485C42—4881no—
486C42—4881no—
487C42C2×C4×D6112yes—
488C42Q8×D6112yes—
489C23—612no—
490C23—1221no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1221no—
496C23C2×D4×D6111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4C4⋊C4×D6112yes—
539C2×C4C4⋊C4×D6112yes—
540C2×C4C22×C4×D6111yescharacteristic
541C2×C4C2×Q8×D6111yescharacteristic
542C2×C4#1451982211yescharacteristic
543C2×C4#1451982311yescharacteristic
544C2×C4#1451982411yescharacteristic
545C2×C4#1451982511yescharacteristic
546C8—22no—
547C8—22no—
548C8—1222no—
549C8—1222no—
550C22—1222no—
551C22—1222no—
552C22—1222no—
553C22—2441no—
554C22—2441no—
555C22—2441no—
556C22—2441no—
557C22C2×C4⋊C4×D6111yescharacteristic
558C22#1684034111yescharacteristic
559C22#1684034211yescharacteristic
560C22#1684056811yescharacteristic
561C22#1684056811yescharacteristic
562C22#1684057111yescharacteristic
563C22#1684057211yescharacteristic
564C4—22no—
565C4—22no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—1222no—
571C4—1222no—
572C4—1222no—
573C4—4881no—
574C4—4881no—
575C4—4881no—
576C4—4881no—
577C4#1684023411yescharacteristic
578C4#1684023811yescharacteristic
579C4#1684038911yescharacteristic
580C4#1684039211yescharacteristic
581C2—2442no—
582C2#2144843411yescharacteristic
583C2#2145441011yescharacteristic
584C2#2145441311yescharacteristic
585C2#2145726211yescharacteristic
586C2#2145726311yescharacteristic
587C2#2145728811yescharacteristic
588C2#2145729111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1948C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1948D61
hypocenterC61#21967
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. #21446590C2semidirect
5. #21446589C2semidirect
6. #21446587C2semidirect
7. #21446586C2semidirect
8. #21446580C2semidirect
9. #21446579C2semidirect
10. #21446579C2semidirect
15. C61×#1948C2semidirect
25. #16839787C4semidirect
297. #1948D61semidirect
354. C61#21967semidirect

Maximal subgroups

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

subgroupindex
C2×#168397872
#214484272
#214484242
#214465902
#214465892
#214465872
#214465862
#214465802
#214465792
#214458512
#214458492
#214458432
#214458412
C61×#19482
#2196761