Subgroups — #38763374

Order 25408.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27163153	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#13097544)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#27163071	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13097544	—	2	1	no	—
5	C₂×#15691794	—	2	1	no	—
6	C₂×D₁₅₈₈	—	2	1	no	—
7	C₂×D₁₅₈₈	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₃₉₇	C₂²	1	1	yes	characteristic
9	#20263708	—	2	1	no	—
10	C₄⋊C₄×C₃₉₇	C₄	1	1	yes	characteristic, complemented
11	C₂×#13097544	—	2	2	no	—
12	C₂×#13097544	—	4	1	no	—
13	C₂×#13097544	—	4	1	no	—
14	#15691794	—	4	1	no	—
15	C₂²×D₃₉₇	—	2	1	no	—
16	C₂²×D₃₉₇	D₄	1	1	yes	characteristic
17	D₁₅₈₈	—	4	1	no	—
18	D₁₅₈₈	—	4	1	no	—
19	D₁₅₈₈	—	4	1	no	—
20	C₂×Dic₃₉₇	D₄	1	1	yes	characteristic
21	C₄×D₃₉₇	—	4	1	no	—
22	C₂×C₄×C₃₉₇	—	2	1	no	—
23	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₃₉₇	—	2	1	no	—
26	C₂×D₃₉₇	—	2	1	no	—
27	C₂×D₃₉₇	—	4	1	no	—
28	C₂×D₃₉₇	—	4	1	no	—
29	C₂×D₃₉₇	—	4	1	no	—
30	C₂×D₃₉₇	D₈	1	1	yes	characteristic
31	C₂×D₃₉₇	SD₁₆	1	1	yes	characteristic
32	#13097544	—	4	2	no	—
33	C₄×C₃₉₇	—	2	1	no	—
34	C₄×C₃₉₇	—	4	1	no	—
35	Dic₃₉₇	—	2	1	no	—
36	C₂×C₃₉₇	#99	1	1	yes	characteristic
37	C₂×C₃₉₇	#102	1	1	yes	characteristic
38	C₂×C₃₉₇	#104	1	1	yes	characteristic
39	D₃₉₇	—	2	1	no	—
40	D₃₉₇	—	2	1	no	—
41	D₃₉₇	—	8	1	no	—
42	C₃₉₇	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	397	1	no	maximal, Sylow
44	#121	—	397	1	no	—
45	C₂²⋊C₈	—	397	1	no	—
46	#95	—	397	1	no	—
47	C₂×D₄	—	794	1	no	—
48	C₂×D₄	—	397	1	no	—
49	C₂²×C₄	—	794	1	no	—
50	C₂²×C₄	—	397	1	no	—
51	C₂×C₈	—	794	1	no	—
52	C₄⋊C₄	#13097544	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	794	1	no	—
54	C₂³	—	794	1	no	—
55	C₂³	—	397	1	no	—
56	D₄	—	1588	1	no	—
57	D₄	—	1588	1	no	—
58	D₄	—	1588	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	794	2	no	—
61	C₂×C₄	—	1588	1	no	—
62	C₂×C₄	—	1588	1	no	—
63	C₂×C₄	—	1588	1	no	—
64	C₂×C₄	—	397	1	no	—
65	C₂×C₄	C₂×#13097544	1	1	yes	characteristic
66	C₈	—	1588	1	no	—
67	C₂²	—	794	1	no	—
68	C₂²	—	794	1	no	—
69	C₂²	—	1588	1	no	—
70	C₂²	—	1588	1	no	—
71	C₂²	—	1588	1	no	—
72	C₂²	—	397	1	no	—
73	C₂²	—	397	1	no	—
74	C₂²	C₂²⋊#13097544	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	794	1	no	—
78	C₄	—	1588	2	no	—
79	C₂	—	794	1	no	—
80	C₂	—	794	1	no	—
81	C₂	—	3176	1	no	—
82	C₂	#27163155	1	1	yes	characteristic
83	C₂	#27163158	1	1	yes	characteristic
84	C₂	#27163161	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13097544
commutator	C₂×C₄×C₃₉₇	C₂×C₄
Frattini	C₂×C₄	C₂×#13097544
Fitting	C₄⋊C₄×C₃₉₇	C₄
socle	C₂²×C₃₉₇	C₂²⋊C₄
prime radical	#27163071	C₂
cosocle	C₂×C₄×D₃₉₇	C₂²
hypercenter	C₄⋊C₄	#13097544
hypocenter	C₃₉₇	#327
LCS	G ▷ C₂×C₄×C₃₉₇ ▷ C₂²×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #27163153	C₂	semidirect
2. (C₂×#13097544)⋊C₄	C₂	semidirect
7. C₂×D₁₅₈₈	C₄	semidirect
10. C₄⋊C₄×C₃₉₇	C₄	semidirect
42. C₃₉₇	#327	semidirect
52. C₄⋊C₄	#13097544	semidirect

Maximal subgroups

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

subgroup	index
#27163153	2
(C₂×#13097544)⋊C₄	2
#27163071	2
#327	397