Subgroups — (C₂×#15667734)⋊C₄ #36378878

Order 22592.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667734	C₂	1	2	yes	maximal
2	C₂×C₄×#13083443	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667734	—	2	2	no	—
4	C₂×#15667734	—	2	2	no	—
5	C₂×#15667734	C₄	1	4	yes	complemented
6	C₂²×#13083443	C₄	1	1	yes	characteristic
7	C₂²×#13083443	C₂²	1	1	yes	characteristic
8	C₄×#13083443	—	2	2	no	—
9	C₂×C₄×D₃₅₃	C₄	1	1	yes	characteristic
10	#15667734	—	2	4	no	—
11	C₂×#13083443	—	2	1	no	—
12	C₂×#13083443	—	2	1	no	—
13	C₂×#13083443	C₈	1	2	yes	complemented
14	C₂×#13083443	C₂×C₄	1	2	yes	—
15	C₂×#13083443	D₄	1	1	yes	characteristic
16	C₂×#13083443	D₄	1	2	yes	—
17	C₂×#13083443	Q₈	1	1	yes	characteristic
18	C₂²×D₃₅₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃₅₃	C₈	1	1	yes	characteristic, complemented
20	C₄×D₃₅₃	—	2	1	no	—
21	C₄×D₃₅₃	—	2	1	no	—
22	C₂×C₄×C₃₅₃	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₃₅₃	C₂×C₈	1	1	yes	characteristic
24	C₂×D₃₅₃	C₄²	1	1	yes	characteristic
25	C₂×D₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×D₃₅₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂×D₃₅₃	C₂×C₈	1	1	yes	characteristic
28	C₂×D₃₅₃	M₁₆	1	1	yes	characteristic
29	C₂×D₃₅₃	M₁₆	1	1	yes	characteristic
30	#13083443	—	2	2	no	—
31	#13083443	C₂²⋊C₄	1	2	yes	—
32	#13083443	C₄⋊C₄	1	2	yes	—
33	C₄×C₃₅₃	—	2	1	no	—
34	Dic₃₅₃	—	2	1	no	—
35	C₂×C₃₅₃	C₄×C₈	1	1	yes	characteristic
36	C₂×C₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×C₃₅₃	C₄⋊C₈	1	1	yes	characteristic
38	D₃₅₃	#95	1	1	yes	characteristic
39	D₃₅₃	#97	1	1	yes	characteristic
40	D₃₅₃	C₂²⋊C₈	1	1	yes	characteristic
41	D₃₅₃	C₄⋊C₈	1	1	yes	characteristic
42	C₃₅₃	#336	1	1	yes	characteristic, complemented, Sylow
43	#336	—	353	1	no	maximal, Sylow
44	C₂²×C₈	—	353	2	no	—
45	C₂×C₄²	—	353	1	no	—
46	C₂²×C₄	—	353	1	no	—
47	C₂²×C₄	—	353	1	no	—
48	C₂²×C₄	—	353	1	no	—
49	C₂×C₈	—	353	4	no	—
50	C₂×C₈	—	706	2	no	—
51	C₂×C₈	—	706	2	no	—
52	C₄²	—	706	2	no	—
53	C₂³	—	353	1	no	—
54	C₂×C₄	—	353	2	no	—
55	C₂×C₄	—	353	2	no	—
56	C₂×C₄	—	353	1	no	—
57	C₂×C₄	—	353	1	no	—
58	C₂×C₄	—	353	2	no	—
59	C₂×C₄	—	353	1	no	—
60	C₂×C₄	—	706	1	no	—
61	C₂×C₄	—	706	1	no	—
62	C₂×C₄	—	706	1	no	—
63	C₂×C₄	—	706	1	no	—
64	C₂×C₄	#15667734	1	1	yes	characteristic, complemented
65	C₈	—	706	4	no	—
66	C₂²	—	353	1	no	—
67	C₂²	—	353	1	no	—
68	C₂²	—	353	1	no	—
69	C₂²	—	353	1	no	—
70	C₂²	—	353	1	no	—
71	C₂²	—	353	1	no	—
72	C₂²	C₂×#15667734	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	353	2	no	—
75	C₄	—	353	2	no	—
76	C₄	—	706	2	no	—
77	C₄	—	706	1	no	—
78	C₂	—	353	1	no	—
79	C₂	—	353	1	no	—
80	C₂	—	353	1	no	—
81	C₂	—	353	1	no	—
82	C₂	C₄×#15667734	1	1	yes	characteristic
83	C₂	C₂²⋊#15667734	1	1	yes	characteristic
84	C₂	C₄⋊#15667734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#15667734
commutator	C₂×C₃₅₃	C₄×C₈
Fitting	C₂×C₄×C₃₅₃	C₈
socle	C₂²×C₃₅₃	C₂×C₈
prime radical	C₂²×D₃₅₃	C₂×C₄
cosocle	C₂²×#13083443	C₂²
hypercenter	C₂×C₄	#15667734
hypocenter	C₃₅₃	#336
LCS	G ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#15667734	C₄	semidirect
13. C₂×#13083443	C₈	semidirect
19. C₂×Dic₃₅₃	C₈	semidirect
22. C₂×C₄×C₃₅₃	C₈	semidirect
42. C₃₅₃	#336	semidirect
64. C₂×C₄	#15667734	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15667734	2
C₂×C₄×#13083443	2
#336	353

Subgroups — (C2×#15667734)⋊C4 #36378878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#15667734)⋊C₄ #36378878