Subgroups — C₄×#20258607 #37565714

Order 24256.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20258607	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₁₅₁₆	C₂	1	3	yes	maximal, complemented
4	#27131293	C₂	1	3	yes	maximal, complemented
5	#27131289	C₂	1	3	yes	maximal, complemented
6	C₄²×D₃₇₉	C₂	1	3	yes	maximal, complemented
7	C₄×Q₈×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#20258607	C₄	1	8	yes	direct product factor
9	C₂×D₁₅₁₆	C₂²	1	3	yes	—
10	C₂×C₄×D₃₇₉	C₂²	1	3	yes	—
11	C₂×C₄×D₃₇₉	C₂²	1	3	yes	—
12	C₂×C₄×D₃₇₉	C₂²	1	3	yes	—
13	C₄⋊Dic₃₇₉	C₂²	1	3	yes	—
14	(C₂×D₃₇₉)⋊C₄	C₂²	1	6	yes	—
15	C₄×Dic₃₇₉	C₂²	1	1	yes	characteristic
16	C₄×Dic₃₇₉	C₂²	1	3	yes	—
17	C₄×Dic₃₇₉	C₂²	1	3	yes	—
18	C₂×Q₈×C₃₇₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₃₇₉	C₂²	1	3	yes	—
20	C₄²×C₃₇₉	C₂²	1	3	yes	—
21	C₂²×D₃₇₉	C₂³	1	3	yes	—
22	D₁₅₁₆	C₂×C₄	1	12	yes	complemented
23	C₂×Dic₃₇₉	C₂³	1	3	yes	—
24	C₂×Dic₃₇₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₇₉	C₂³	1	1	yes	characteristic
26	C₄×D₃₇₉	—	2	6	no	—
27	C₄×D₃₇₉	—	2	6	no	—
28	C₄×D₃₇₉	C₂×C₄	1	12	yes	complemented
29	Q₈×C₃₇₉	C₂×C₄	1	4	yes	complemented
30	C₂×C₄×C₃₇₉	C₂³	1	3	yes	—
31	C₂×C₄×C₃₇₉	C₂³	1	3	yes	—
32	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
33	C₂²×C₃₇₉	C₂⁴	1	1	yes	characteristic
34	C₂×D₃₇₉	—	2	3	no	—
35	C₂×D₃₇₉	—	2	3	no	—
36	C₂×D₃₇₉	C₂²×C₄	1	6	yes	—
37	C₄×C₃₇₉	—	2	3	no	—
38	C₄×C₃₇₉	C₂²×C₄	1	6	yes	—
39	C₄×C₃₇₉	#41	1	2	yes	complemented
40	Dic₃₇₉	—	2	3	no	—
41	Dic₃₇₉	C₂²×C₄	1	2	yes	—
42	Dic₃₇₉	#41	1	2	yes	complemented
43	C₂×C₃₇₉	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₃₇₉	C₂×#41	1	1	yes	characteristic
45	C₂×C₃₇₉	C₂×#41	1	1	yes	characteristic
46	D₃₇₉	—	2	6	no	—
47	C₃₇₉	C₄×#41	1	1	yes	characteristic, complemented, Sylow
48	C₄×#41	—	379	1	no	maximal, Sylow
49	C₂×#41	—	379	1	no	—
50	C₄×Q₈	—	379	1	no	—
51	C₄×Q₈	D₃₇₉	1	1	yes	characteristic, complemented
52	C₄×D₄	—	379	3	no	—
53	C₄×D₄	—	379	3	no	—
54	#117	—	379	3	no	—
55	C₂×C₄²	—	379	3	no	—
56	#41	—	379	8	no	—
57	C₂×Q₈	C₂×D₃₇₉	1	1	yes	characteristic
58	C₂×D₄	—	379	3	no	—
59	C₂²×C₄	—	379	3	no	—
60	C₂²×C₄	—	379	3	no	—
61	C₂²×C₄	—	379	3	no	—
62	C₄⋊C₄	—	379	3	no	—
63	C₄⋊C₄	C₂×D₃₇₉	1	3	yes	—
64	C₂²⋊C₄	—	379	6	no	—
65	C₄²	—	379	3	no	—
66	C₄²	—	379	3	no	—
67	C₄²	—	379	1	no	—
68	C₄²	C₂×D₃₇₉	1	3	yes	—
69	C₂³	—	379	3	no	—
70	Q₈	C₄×D₃₇₉	1	4	yes	complemented
71	D₄	—	379	12	no	—
72	C₂×C₄	—	379	1	no	—
73	C₂×C₄	—	379	1	no	—
74	C₂×C₄	—	379	12	no	—
75	C₂×C₄	—	379	3	no	—
76	C₂×C₄	—	758	6	no	—
77	C₂×C₄	—	758	6	no	—
78	C₂×C₄	C₂²×D₃₇₉	1	3	yes	—
79	C₂×C₄	C₂²×D₃₇₉	1	3	yes	—
80	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
81	C₂²	—	379	6	no	—
82	C₂²	—	758	3	no	—
83	C₂²	—	758	3	no	—
84	C₂²	C₂³×D₃₇₉	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	379	2	no	—
87	C₄	—	379	2	no	—
88	C₄	—	758	3	no	—
89	C₄	C₂×C₄×D₃₇₉	1	6	yes	—
90	C₄	#20258607	1	2	yes	direct product factor
91	C₂	—	758	6	no	—
92	C₂	C₂²×C₄×D₃₇₉	1	1	yes	characteristic
93	C₂	#41×D₃₇₉	1	1	yes	characteristic
94	C₂	C₂×#20258607	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₇₉
commutator	C₂×C₃₇₉	C₂³×C₄
Frattini	C₂²	C₂³×D₃₇₉
Fitting	C₄×Q₈×C₃₇₉	C₂
socle, cosocle	C₂²×C₃₇₉	C₂⁴
prime radical	C₂×#20258607	C₂
hypercenter	C₄×Q₈	D₃₇₉
hypocenter	C₃₇₉	C₄×#41
LCS	G ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₃₇₉	C₂	semidirect
3. C₄×D₁₅₁₆	C₂	semidirect
4. #27131293	C₂	semidirect
5. #27131289	C₂	semidirect
6. C₄²×D₃₇₉	C₂	semidirect
7. C₄×Q₈×C₃₇₉	C₂	semidirect
8. #20258607	C₄	direct (N × H)
22. D₁₅₁₆	C₂×C₄	semidirect
28. C₄×D₃₇₉	C₂×C₄	semidirect
29. Q₈×C₃₇₉	C₂×C₄	semidirect
39. C₄×C₃₇₉	#41	semidirect
42. Dic₃₇₉	#41	semidirect
47. C₃₇₉	C₄×#41	semidirect
51. C₄×Q₈	D₃₇₉	semidirect
70. Q₈	C₄×D₃₇₉	semidirect
90. C₄	#20258607	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20258607	2
Q₈×Dic₃₇₉	2
C₄×D₁₅₁₆	2
#27131293	2
#27131289	2
C₄²×D₃₇₉	2
C₄×Q₈×C₃₇₉	2
C₄×#41	379

Subgroups — C4×#20258607 #37565714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#20258607 #37565714