Subgroups — #382×C₁₇₉ #26037953

Order 11456.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₁₇₉	C₂	1	2	yes	maximal
2	C₂×C₄²×C₁₇₉	C₂	1	1	yes	maximal, characteristic
3	#95×C₁₇₉	C₂	1	4	yes	maximal
4	C₂²×C₄×C₁₇₉	C₂²	1	4	yes	—
5	C₂²×C₄×C₁₇₉	C₂²	1	2	yes	—
6	C₂²×C₄×C₁₇₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₇₉	—	2	4	no	—
8	C₄²×C₁₇₉	C₄	1	4	yes	complemented
9	C₂³×C₁₇₉	C₂³	1	1	yes	characteristic
10	C₂×C₄×C₁₇₉	—	2	4	no	—
11	C₂×C₄×C₁₇₉	—	2	4	no	—
12	C₂×C₄×C₁₇₉	—	2	8	no	—
13	C₂×C₄×C₁₇₉	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₁₇₉	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₁₇₉	D₄	1	2	yes	—
16	C₂×C₄×C₁₇₉	Q₈	1	2	yes	—
17	C₂²×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₁₇₉	C₂×D₄	1	1	yes	characteristic
19	C₂²×C₁₇₉	C₂×Q₈	1	1	yes	characteristic
20	C₂²×C₁₇₉	#41	1	4	yes	—
21	C₄×C₁₇₉	—	2	4	no	—
22	C₄×C₁₇₉	—	4	4	no	—
23	C₄×C₁₇₉	C₄⋊C₄	1	4	yes	—
24	C₂×C₁₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₁₇₉	#117	1	2	yes	—
26	C₂×C₁₇₉	#124	1	2	yes	—
27	C₂×C₁₇₉	#125	1	2	yes	—
28	C₁₇₉	#382	1	1	yes	characteristic, direct product factor, Sylow
29	#382	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂×C₄⋊C₄	C₂×C₁₇₉	1	2	yes	—
31	C₂×C₄²	C₂×C₁₇₉	1	1	yes	characteristic
32	#95	C₂×C₁₇₉	1	4	yes	—
33	C₂²×C₄	C₂²×C₁₇₉	1	4	yes	—
34	C₂²×C₄	C₂²×C₁₇₉	1	2	yes	—
35	C₂²×C₄	C₂²×C₁₇₉	1	1	yes	characteristic
36	C₄⋊C₄	—	2	4	no	—
37	C₄²	C₄×C₁₇₉	1	4	yes	complemented
38	C₂³	C₂³×C₁₇₉	1	1	yes	characteristic
39	C₂×C₄	—	2	4	no	—
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	2	8	no	—
42	C₂×C₄	C₂×C₄×C₁₇₉	1	4	yes	—
43	C₂×C₄	C₂×C₄×C₁₇₉	1	2	yes	—
44	C₂×C₄	D₄×C₁₇₉	1	2	yes	—
45	C₂×C₄	Q₈×C₁₇₉	1	2	yes	—
46	C₂²	C₂²×C₄×C₁₇₉	1	1	yes	characteristic
47	C₂²	C₂×D₄×C₁₇₉	1	1	yes	characteristic
48	C₂²	C₂×Q₈×C₁₇₉	1	1	yes	characteristic
49	C₂²	#41×C₁₇₉	1	4	yes	—
50	C₄	—	2	4	no	—
51	C₄	—	4	4	no	—
52	C₄	C₄⋊C₄×C₁₇₉	1	4	yes	—
53	C₂	C₂×C₄⋊C₄×C₁₇₉	1	1	yes	characteristic
54	C₂	#117×C₁₇₉	1	2	yes	—
55	C₂	#124×C₁₇₉	1	2	yes	—
56	C₂	#125×C₁₇₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇₉	C₂³
commutator	C₂²	C₂²×C₄×C₁₇₉
Frattini, cosocle	C₂³	C₂³×C₁₇₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₄²×C₁₇₉	C₄	semidirect
28. C₁₇₉	#382	direct (N × H)
29. #382	C₁₇₉	direct (N × H)
37. C₄²	C₄×C₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₁₇₉	2
C₂×C₄²×C₁₇₉	2
#95×C₁₇₉	2
#382	179

Subgroups — #382×C179 #26037953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #382×C₁₇₉ #26037953