Subgroups — D₈×#13097544 #38763558

Order 25408.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#13097544	C₂	1	2	yes	maximal, complemented
2	#27163165	C₂	1	1	yes	maximal, characteristic, complemented
3	#27163158	C₂	1	2	yes	maximal, complemented
4	C₈×#13097544	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13097544	—	2	2	no	—
7	D₃₉₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊#13097544	C₂²	1	2	yes	—
9	C₂²⋊#13097544	—	2	2	no	—
10	C₄×#13097544	C₂²	1	1	yes	characteristic
11	D₄×D₃₉₇	C₂²	1	2	yes	—
12	D₃₁₇₆	C₄	1	1	yes	characteristic, complemented
13	#20263716	C₄	1	2	yes	complemented
14	C₈×D₃₉₇	C₂²	1	1	yes	characteristic
15	D₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
16	C₂×#13097544	—	2	2	no	—
17	C₂×#13097544	—	4	4	no	—
18	C₂×#13097544	D₄	1	1	yes	characteristic
19	C₂×#13097544	D₄	1	1	yes	characteristic
20	#15691794	—	2	1	no	—
21	C₂²×D₃₉₇	—	2	2	no	—
22	D₁₅₈₈	C₂×C₄	1	2	yes	complemented
23	C₂²⋊D₃₉₇	—	2	2	no	—
24	C₄×D₃₉₇	C₂³	1	1	yes	characteristic
25	#15691787	C₂×C₄	1	1	yes	characteristic, complemented
26	D₄×C₃₉₇	C₂×C₄	1	2	yes	complemented
27	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic, complemented
28	C₂²×C₃₉₇	—	2	2	no	—
29	C₂×D₃₉₇	—	2	2	no	—
30	C₂×D₃₉₇	—	4	2	no	—
31	C₂×D₃₉₇	—	4	2	no	—
32	C₂×D₃₉₇	C₂×D₄	1	1	yes	characteristic
33	#13097544	—	2	1	no	—
34	#13097544	—	4	2	no	—
35	#13097544	D₈	1	2	yes	direct product factor
36	C₄×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
37	Dic₃₉₇	#41	1	1	yes	characteristic
38	C₂×C₃₉₇	—	4	2	no	—
39	C₂×C₃₉₇	C₄×D₄	1	1	yes	characteristic
40	D₃₉₇	—	4	2	no	—
41	D₃₉₇	C₂×D₈	1	1	yes	characteristic
42	D₃₉₇	#135	1	1	yes	characteristic
43	C₃₉₇	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₄×D₈	—	397	1	no	maximal, Sylow
45	C₂×D₈	—	397	1	no	—
46	C₄×D₄	—	397	2	no	—
47	#107	—	397	1	no	—
48	#102	—	397	2	no	—
49	C₄×C₈	—	397	1	no	—
50	C₂×D₄	—	397	2	no	—
51	C₂²×C₄	—	794	2	no	—
52	D₈	—	397	2	no	—
53	D₈	—	397	1	no	—
54	D₈	#13097544	1	1	yes	characteristic, direct product factor
55	C₂×C₈	—	397	1	no	—
56	C₂×C₈	—	397	1	no	—
57	C₄⋊C₄	—	397	2	no	—
58	C₂²⋊C₄	—	794	2	no	—
59	C₄²	—	397	1	no	—
60	C₂³	—	794	2	no	—
61	D₄	—	794	2	no	—
62	D₄	—	397	2	no	—
63	D₄	C₂×#13097544	1	2	yes	complemented
64	C₂×C₄	—	794	2	no	—
65	C₂×C₄	—	1588	4	no	—
66	C₂×C₄	—	397	1	no	—
67	C₂×C₄	—	397	1	no	—
68	C₂×C₄	—	397	1	no	—
69	C₈	—	794	1	no	—
70	C₈	—	397	1	no	—
71	C₈	C₂×#13097544	1	1	yes	characteristic, complemented
72	C₂²	—	2	2	no	—
73	C₂²	—	794	2	no	—
74	C₂²	—	1588	2	no	—
75	C₂²	—	1588	2	no	—
76	C₂²	—	397	1	no	—
77	C₄	—	794	1	no	—
78	C₄	—	1588	2	no	—
79	C₄	—	397	2	no	—
80	C₄	—	397	1	no	—
81	C₄	C₂²×#13097544	1	1	yes	characteristic
82	C₂	—	4	2	no	—
83	C₂	—	1588	2	no	—
84	C₂	—	397	1	no	—
85	C₂	—	397	1	no	—
86	C₂	D₄×#13097544	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#13097544
commutator	C₄×C₃₉₇	C₂²×C₄
Frattini	C₄	C₂²×#13097544
Fitting	D₈×C₃₉₇	C₄
socle	C₂×C₃₉₇	C₄×D₄
prime radical	D₈×D₃₉₇	C₂
cosocle	C₄×D₃₉₇	C₂³
hypercenter	D₈	#13097544
hypocenter	C₃₉₇	C₄×D₈
LCS	G ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#13097544	C₂	semidirect
2. #27163165	C₂	semidirect
3. #27163158	C₂	semidirect
4. C₈×#13097544	C₂	semidirect
12. D₃₁₇₆	C₄	semidirect
13. #20263716	C₄	semidirect
15. D₈×C₃₉₇	C₄	semidirect
22. D₁₅₈₈	C₂×C₄	semidirect
25. #15691787	C₂×C₄	semidirect
26. D₄×C₃₉₇	C₂×C₄	semidirect
27. C₈×C₃₉₇	C₂×C₄	semidirect
35. #13097544	D₈	direct (N × H)
43. C₃₉₇	C₄×D₈	semidirect
54. D₈	#13097544	direct (N × H)
63. D₄	C₂×#13097544	semidirect
71. C₈	C₂×#13097544	semidirect

Maximal subgroups

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

subgroup	index
D₄×#13097544	2
#27163165	2
#27163158	2
C₈×#13097544	2
D₈×D₃₉₇	2
C₄×D₈	397

Subgroups — D8×#13097544 #38763558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#13097544 #38763558