Subgroups — #34059613

Order 19072.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14558739	C₂	1	2	yes	maximal, complemented
2	#23749592	C₂	1	1	yes	maximal, characteristic
3	C₂×#14558739	—	2	2	no	—
4	C₂×#14558720	C₄	1	1	yes	characteristic
5	C₂²×#11924746	C₂²	1	1	yes	characteristic
6	C₂²⋊#11924746	—	2	2	no	—
7	C₂×#41×C₁₄₉	C₄	1	1	yes	characteristic
8	#14558739	—	4	2	no	—
9	#14558720	—	4	1	no	—
10	C₂×#11924746	—	2	1	no	—
11	C₂×#11924746	—	4	1	no	—
12	C₂×#11924746	D₄	1	2	yes	—
13	#41×C₁₄₉	—	4	1	no	—
14	#41×C₁₄₉	—	4	1	no	—
15	C₂×Q₈×C₁₄₉	C₈	1	1	yes	characteristic
16	C₂×D₄×C₁₄₉	—	2	1	no	—
17	C₂×D₄×C₁₄₉	C₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₄₉	—	2	1	no	—
19	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	#11924746	—	2	2	no	—
21	#11924746	—	4	1	no	—
22	C₂³×C₁₄₉	—	2	1	no	—
23	C₂³×C₁₄₉	M₁₆	1	1	yes	characteristic
24	Q₈×C₁₄₉	—	4	1	no	—
25	D₄×C₁₄₉	—	4	1	no	—
26	D₄×C₁₄₉	—	4	2	no	—
27	C₂×C₄×C₁₄₉	—	2	1	no	—
28	C₂×C₄×C₁₄₉	—	2	1	no	—
29	C₂×C₄×C₁₄₉	—	2	1	no	—
30	C₂×C₄×C₁₄₉	—	4	1	no	—
31	C₂×C₄×C₁₄₉	—	4	1	no	—
32	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
34	C₂²×C₁₄₉	—	2	1	no	—
35	C₂²×C₁₄₉	—	2	2	no	—
36	C₂²×C₁₄₉	—	4	1	no	—
37	C₂²×C₁₄₉	—	4	2	no	—
38	C₂²×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₁₄₉	—	2	1	no	—
40	C₄×C₁₄₉	—	4	1	no	—
41	C₄×C₁₄₉	#99	1	1	yes	characteristic
42	C₄×C₁₄₉	#100	1	1	yes	characteristic
43	C₂×C₁₄₉	—	4	1	no	—
44	C₂×C₁₄₉	—	8	1	no	—
45	C₂×C₁₄₉	#323	1	1	yes	characteristic
46	C₂×C₁₄₉	#350	1	2	yes	—
47	C₁₄₉	#1315	1	1	yes	characteristic, complemented, Sylow
48	#1315	—	149	1	no	maximal, Sylow
49	#408	—	149	1	no	—
50	C₂²⋊C₁₆	—	149	2	no	—
51	C₂×#41	#10597010	1	1	yes	characteristic
52	C₂×M₁₆	—	149	1	no	—
53	C₂²×C₈	—	149	1	no	—
54	C₂×C₁₆	—	298	2	no	—
55	C₂²⋊C₈	—	298	2	no	—
56	#41	—	4	1	no	—
57	#41	—	4	1	no	—
58	C₂×Q₈	#11924753	1	1	yes	characteristic
59	C₂×D₄	—	2	1	no	—
60	C₂×D₄	#11924753	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
63	M₁₆	—	596	1	no	—
64	C₂×C₈	—	298	1	no	—
65	C₂×C₈	—	596	1	no	—
66	C₂×C₈	—	149	2	no	—
67	C₁₆	—	596	2	no	—
68	C₂³	—	2	1	no	—
69	C₂³	#14558745	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	D₄	—	4	1	no	—
72	D₄	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
79	C₂×C₄	C₂×#11924753	1	1	yes	characteristic
80	C₈	—	298	2	no	—
81	C₈	—	596	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	2	no	—
86	C₂²	C₂²⋊#11924753	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	#18011969	1	1	yes	characteristic
90	C₄	#18011971	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	8	1	no	—
93	C₂	#23750468	1	1	yes	characteristic
94	C₂	#23750523	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10597010
commutator	C₂×C₄×C₁₄₉	C₂×C₈
Frattini	C₂²×C₄	C₂×#10597010
Fitting, prime radical	C₂×#41×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²⋊C₈
cosocle	C₂²×#11924746	C₂²
hypercenter	C₂×#41	#10597010
hypocenter	C₁₄₉	#1315
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#14558739	C₂	semidirect
47. C₁₄₉	#1315	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#14558739	2
#23749592	2
#1315	149