Subgroups — #34059643

Order 19072.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14558739	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750513	C₂	1	1	yes	maximal, characteristic, complemented
3	#23749703	C₂	1	1	yes	maximal, characteristic
4	C₂×#14558739	—	2	1	no	—
5	C₂×#14558739	—	2	1	no	—
6	C₂×#14558720	—	2	1	no	—
7	C₄⋊#11924746	C₄	1	1	yes	characteristic
8	C₂²⋊#11924746	—	2	1	no	—
9	C₄×#11924746	C₂²	1	1	yes	characteristic
10	C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
11	#14558739	—	2	2	no	—
12	#14558739	—	4	1	no	—
13	#14558720	—	4	1	no	—
14	#14558720	—	4	1	no	—
15	C₂×#11924746	—	2	1	no	—
16	C₂×#11924746	D₄	1	1	yes	characteristic
17	C₂×#11924746	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₄₉	C₈	1	1	yes	characteristic
19	C₂²×C₄×C₁₄₉	—	2	1	no	—
20	C₄⋊C₄×C₁₄₉	C₈	1	1	yes	characteristic
21	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
22	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
23	#11924746	—	2	1	no	—
24	#11924746	—	4	1	no	—
25	#11924746	D₈	1	1	yes	characteristic
26	#11924746	SD₁₆	1	1	yes	characteristic
27	C₂³×C₁₄₉	—	2	1	no	—
28	D₄×C₁₄₉	—	4	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	C₂×C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
35	C₂²×C₁₄₉	—	4	1	no	—
36	C₂²×C₁₄₉	—	4	1	no	—
37	C₂²×C₁₄₉	—	4	1	no	—
38	C₂²×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₁₄₉	—	2	1	no	—
40	C₄×C₁₄₉	—	2	1	no	—
41	C₄×C₁₄₉	—	4	1	no	—
42	C₄×C₁₄₉	#102	1	1	yes	characteristic
43	C₄×C₁₄₉	#104	1	1	yes	characteristic
44	C₂×C₁₄₉	—	8	1	no	—
45	C₂×C₁₄₉	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₁₄₉	#349	1	1	yes	characteristic
47	C₂×C₁₄₉	#350	1	1	yes	characteristic
48	C₁₄₉	#1330	1	1	yes	characteristic, complemented, Sylow
49	#1330	—	149	1	no	maximal, Sylow
50	#436	—	149	1	no	—
51	C₄⋊C₁₆	—	149	1	no	—
52	#346	—	149	1	no	—
53	C₂×M₁₆	—	298	1	no	—
54	C₄×D₄	#10597010	1	1	yes	characteristic
55	C₂×C₁₆	—	298	1	no	—
56	C₂×C₁₆	—	298	1	no	—
57	C₄⋊C₈	—	149	1	no	—
58	C₂²⋊C₈	—	298	1	no	—
59	C₄×C₈	—	149	1	no	—
60	C₂×D₄	#11924753	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	M₁₆	—	596	1	no	—
63	M₁₆	—	596	1	no	—
64	C₂×C₈	—	298	1	no	—
65	C₂×C₈	—	149	1	no	—
66	C₂×C₈	—	149	1	no	—
67	C₄⋊C₄	#11924753	1	1	yes	characteristic
68	C₂²⋊C₄	—	2	1	no	—
69	C₄²	C₂×#10597010	1	1	yes	characteristic
70	C₁₆	—	298	2	no	—
71	C₁₆	—	596	1	no	—
72	C₂³	—	2	1	no	—
73	D₄	—	4	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
78	C₂×C₄	C₂×#11924753	1	1	yes	characteristic
79	C₂×C₄	#14558745	1	1	yes	characteristic
80	C₈	—	298	1	no	—
81	C₈	—	596	1	no	—
82	C₈	—	149	1	no	—
83	C₈	—	149	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	C₂²⋊#11924753	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	#18011973	1	1	yes	characteristic
92	C₄	#18011975	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	D₄⋊#11924753	1	1	yes	characteristic
95	C₂	#23750521	1	1	yes	characteristic
96	C₂	#23750523	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10597010
commutator	C₂×C₄×C₁₄₉	C₂×C₈
Frattini	C₄²	C₂×#10597010
Fitting	C₄×D₄×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²⋊C₈
prime radical	C₂×D₄×C₁₄₉	C₈
cosocle	C₄×#11924746	C₂²
hypercenter	C₄×D₄	#10597010
hypocenter	C₁₄₉	#1330
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#14558739	C₂	semidirect
2. #23750513	C₂	semidirect
48. C₁₄₉	#1330	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14558739	2
#23750513	2
#23749703	2
#1330	149