Subgroups — C₄×Q₈×D₃₇₉ #37565707

Order 24256.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₃₇₉	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₇₅₈	C₂	1	3	yes	maximal, complemented
4	#27131296	C₂	1	3	yes	maximal, complemented
5	C₄⋊C₄×D₃₇₉	C₂	1	3	yes	maximal
6	C₄²×D₃₇₉	C₂	1	3	yes	maximal
7	C₄×Q₈×C₃₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₇₅₈	C₂²	1	3	yes	—
9	Q₈×D₃₇₉	C₄	1	8	yes	direct product factor
10	C₂×C₄×D₃₇₉	C₂²	1	3	yes	—
11	C₂×C₄×D₃₇₉	C₂²	1	3	yes	—
12	C₂×C₄×D₃₇₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₃₇₉	C₂²	1	3	yes	—
14	Dic₃₇₉⋊C₄	C₂²	1	6	yes	—
15	C₄×Dic₃₇₉	C₂²	1	3	yes	—
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	1	yes	characteristic
22	Dic₇₅₈	C₂×C₄	1	12	yes	complemented
23	C₂×Dic₃₇₉	C₂³	1	3	yes	—
24	C₂×Dic₃₇₉	C₂³	1	3	yes	—
25	C₂×Dic₃₇₉	C₂³	1	1	yes	characteristic
26	C₄×D₃₇₉	—	2	6	no	—
27	C₄×D₃₇₉	C₂×C₄	1	12	yes	—
28	C₄×D₃₇₉	Q₈	1	4	yes	direct product factor
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	C₂²×C₄	1	2	yes	—
35	C₂×D₃₇₉	C₂×Q₈	1	2	yes	—
36	C₂×D₃₇₉	#41	1	2	yes	—
37	C₄×C₃₇₉	—	2	3	no	—
38	C₄×C₃₇₉	C₂²×C₄	1	6	yes	—
39	C₄×C₃₇₉	C₂×Q₈	1	2	yes	complemented
40	Dic₃₇₉	—	2	3	no	—
41	Dic₃₇₉	C₂²×C₄	1	6	yes	—
42	Dic₃₇₉	C₂×Q₈	1	2	yes	complemented
43	C₂×C₃₇₉	C₂³×C₄	1	1	yes	characteristic
44	C₂×C₃₇₉	C₂²×Q₈	1	1	yes	characteristic
45	C₂×C₃₇₉	C₂×#41	1	1	yes	characteristic
46	D₃₇₉	C₄×Q₈	1	4	yes	direct product factor
47	C₃₇₉	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄×Q₈	—	379	1	no	maximal, Sylow
49	C₂²×Q₈	—	379	1	no	—
50	C₄×Q₈	—	379	1	no	—
51	C₄×Q₈	—	379	3	no	—
52	C₄×Q₈	—	379	3	no	—
53	C₄×Q₈	D₃₇₉	1	1	yes	characteristic, direct product factor
54	C₂×C₄⋊C₄	—	379	3	no	—
55	C₂×C₄²	—	379	3	no	—
56	C₂×Q₈	—	379	8	no	—
57	C₂×Q₈	—	379	3	no	—
58	C₂×Q₈	C₂×D₃₇₉	1	1	yes	characteristic
59	C₂²×C₄	—	379	3	no	—
60	C₂²×C₄	—	379	1	no	—
61	C₂²×C₄	—	379	3	no	—
62	C₄⋊C₄	—	379	6	no	—
63	C₄⋊C₄	—	379	3	no	—
64	C₄⋊C₄	C₂×D₃₇₉	1	3	yes	—
65	C₄²	—	379	3	no	—
66	C₄²	—	379	3	no	—
67	C₄²	—	379	3	no	—
68	C₄²	C₂×D₃₇₉	1	3	yes	—
69	C₂³	—	379	1	no	—
70	Q₈	—	379	12	no	—
71	Q₈	C₄×D₃₇₉	1	4	yes	direct product factor
72	C₂×C₄	—	379	1	no	—
73	C₂×C₄	—	379	3	no	—
74	C₂×C₄	—	379	12	no	—
75	C₂×C₄	—	379	4	no	—
76	C₂×C₄	—	379	3	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	2	no	—
82	C₂²	—	379	2	no	—
83	C₂²	—	379	2	no	—
84	C₂²	C₂³×D₃₇₉	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	379	6	no	—
87	C₄	—	379	2	no	—
88	C₄	—	758	3	no	—
89	C₄	C₂×C₄×D₃₇₉	1	6	yes	—
90	C₄	Q₈×D₃₇₉	1	2	yes	direct product factor
91	C₂	—	379	4	no	—
92	C₂	C₂²×C₄×D₃₇₉	1	1	yes	characteristic
93	C₂	C₂×Q₈×D₃₇₉	1	1	yes	characteristic
94	C₂	#41×D₃₇₉	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	C₂²×D₃₇₉	C₂³
hypercenter	C₄×Q₈	D₃₇₉
hypocenter	C₃₇₉	C₂×C₄×Q₈
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×Dic₇₅₈	C₂	semidirect
4. #27131296	C₂	semidirect
7. C₄×Q₈×C₃₇₉	C₂	semidirect
9. Q₈×D₃₇₉	C₄	direct (N × H)
22. Dic₇₅₈	C₂×C₄	semidirect
28. C₄×D₃₇₉	Q₈	direct (N × H)
29. Q₈×C₃₇₉	C₂×C₄	semidirect
39. C₄×C₃₇₉	C₂×Q₈	semidirect
42. Dic₃₇₉	C₂×Q₈	semidirect
46. D₃₇₉	C₄×Q₈	direct (N × H)
47. C₃₇₉	C₂×C₄×Q₈	semidirect
53. C₄×Q₈	D₃₇₉	direct (N × H)
71. Q₈	C₄×D₃₇₉	direct (N × H)
90. C₄	Q₈×D₃₇₉	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×Q₈×D₃₇₉	2
Q₈×Dic₃₇₉	2
C₄×Dic₇₅₈	2
#27131296	2
C₄⋊C₄×D₃₇₉	2
C₄²×D₃₇₉	2
C₄×Q₈×C₃₇₉	2
C₂×C₄×Q₈	379

Subgroups — C4×Q8×D379 #37565707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×D₃₇₉ #37565707