Subgroups — #398×C₄₉₉ #44542628

Order 31936.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₄₉₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₄₉₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×C₄₉₉	C₂	1	2	yes	maximal
4	#95×C₄₉₉	C₂	1	2	yes	maximal
5	#95×C₄₉₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₉₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₄₉₉	C₂²	1	2	yes	—
8	C₂²×C₄×C₄₉₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₄₉₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₄₉₉	C₂²	1	2	yes	—
11	C₄⋊C₄×C₄₉₉	—	2	2	no	—
12	C₄⋊C₄×C₄₉₉	—	2	4	no	—
13	C₄⋊C₄×C₄₉₉	—	2	2	no	—
14	C₂³×C₄₉₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₄₉₉	—	2	1	no	—
16	C₂×C₄×C₄₉₉	—	2	2	no	—
17	C₂×C₄×C₄₉₉	—	2	1	no	—
18	C₂×C₄×C₄₉₉	—	2	2	no	—
19	C₂×C₄×C₄₉₉	—	2	2	no	—
20	C₂×C₄×C₄₉₉	—	2	2	no	—
21	C₂×C₄×C₄₉₉	—	2	2	no	—
22	C₂×C₄×C₄₉₉	—	2	1	no	—
23	C₂×C₄×C₄₉₉	—	2	2	no	—
24	C₂×C₄×C₄₉₉	—	2	2	no	—
25	C₂×C₄×C₄₉₉	D₄	1	2	yes	—
26	C₂×C₄×C₄₉₉	D₄	1	2	yes	—
27	C₂×C₄×C₄₉₉	Q₈	1	4	yes	—
28	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄₉₉	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₄₉₉	C₂×Q₈	1	2	yes	—
31	C₂²×C₄₉₉	#41	1	1	yes	characteristic
32	C₂²×C₄₉₉	#41	1	2	yes	—
33	C₄×C₄₉₉	—	2	2	no	—
34	C₄×C₄₉₉	—	2	4	no	—
35	C₄×C₄₉₉	—	2	2	no	—
36	C₄×C₄₉₉	—	4	2	no	—
37	C₄×C₄₉₉	—	4	1	no	—
38	C₂×C₄₉₉	#121	1	1	yes	characteristic
39	C₂×C₄₉₉	C₂²⋊Q₈	1	2	yes	—
40	C₂×C₄₉₉	#123	1	1	yes	characteristic
41	C₂×C₄₉₉	#125	1	2	yes	—
42	C₂×C₄₉₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₄₉₉	#398	1	1	yes	characteristic, direct product factor, Sylow
44	#398	C₄₉₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₄⋊C₄	C₂×C₄₉₉	1	1	yes	characteristic
46	C₂×C₄⋊C₄	C₂×C₄₉₉	1	1	yes	characteristic
47	C₂×C₄⋊C₄	C₂×C₄₉₉	1	2	yes	—
48	#95	C₂×C₄₉₉	1	2	yes	—
49	#95	C₂×C₄₉₉	1	1	yes	characteristic
50	C₂²×C₄	C₂²×C₄₉₉	1	1	yes	characteristic
51	C₂²×C₄	C₂²×C₄₉₉	1	2	yes	—
52	C₂²×C₄	C₂²×C₄₉₉	1	1	yes	characteristic
53	C₂²×C₄	C₂²×C₄₉₉	1	1	yes	characteristic
54	C₂²×C₄	C₂²×C₄₉₉	1	2	yes	—
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	—	2	4	no	—
57	C₄⋊C₄	—	2	2	no	—
58	C₂³	C₂³×C₄₉₉	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	D₄×C₄₉₉	1	2	yes	—
70	C₂×C₄	D₄×C₄₉₉	1	2	yes	—
71	C₂×C₄	Q₈×C₄₉₉	1	4	yes	—
72	C₂²	C₂×D₄×C₄₉₉	1	1	yes	characteristic
73	C₂²	C₂×D₄×C₄₉₉	1	1	yes	characteristic
74	C₂²	C₂×Q₈×C₄₉₉	1	2	yes	—
75	C₂²	#41×C₄₉₉	1	1	yes	characteristic
76	C₂²	#41×C₄₉₉	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	2	4	no	—
79	C₄	—	2	2	no	—
80	C₄	—	4	2	no	—
81	C₄	—	4	1	no	—
82	C₂	#121×C₄₉₉	1	1	yes	characteristic
83	C₂	C₂²⋊Q₈×C₄₉₉	1	2	yes	—
84	C₂	#123×C₄₉₉	1	1	yes	characteristic
85	C₂	#125×C₄₉₉	1	2	yes	—
86	C₂	C₄⋊Q₈×C₄₉₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₉₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₄₉₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₉₉ ◁ G

Complements

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

N	H ≅ G/N	type
43. C₄₉₉	#398	direct (N × H)
44. #398	C₄₉₉	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×C₄⋊C₄×C₄₉₉	2
#95×C₄₉₉	2
#398	499

Subgroups — #398×C499 #44542628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #398×C₄₉₉ #44542628