Subgroups — #34061026

Order 19072.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011985	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14558739	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#14558739	C₂	1	4	yes	maximal, complemented
4	#23749581	C₂	1	1	yes	maximal, characteristic
5	#18011985	—	2	2	no	—
6	C₂×#14558739	—	2	2	no	—
7	C₂×#14558739	C₂²	1	2	yes	—
8	C₂×#14558739	C₂²	1	2	yes	—
9	C₂×#14558720	C₄	1	1	yes	characteristic
10	C₂²×#11924746	C₂²	1	1	yes	characteristic
11	#18011822	C₄	1	2	yes	—
12	C₄×#11924746	C₂²	1	2	yes	—
13	#117×C₁₄₉	C₄	1	1	yes	characteristic
14	#14558739	—	2	2	no	—
15	#14558739	—	2	2	no	—
16	#14558720	—	2	2	no	—
17	C₂×#11924746	C₂×C₄	1	2	yes	—
18	C₂×#11924746	C₂×C₄	1	1	yes	characteristic
19	C₂×#11924746	D₄	1	2	yes	—
20	C₂×#11924746	Q₈	1	2	yes	—
21	C₂×#11924746	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₄₉	C₈	1	2	yes	—
24	C₂²⋊C₄×C₁₄₉	C₈	1	2	yes	—
25	C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
26	#11924746	—	2	2	no	—
27	#11924746	C₄⋊C₄	1	2	yes	—
28	#11924746	C₂×D₄	1	1	yes	characteristic
29	#11924746	C₂×Q₈	1	1	yes	characteristic
30	C₂³×C₁₄₉	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₁₄₉	C₂×C₈	1	4	yes	—
33	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₄₉	M₁₆	1	2	yes	—
35	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₁₄₉	—	2	2	no	—
37	C₂²×C₁₄₉	C₄⋊C₈	1	2	yes	—
38	C₂²×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₄₉	—	2	4	no	—
40	C₄×C₁₄₉	C₄⋊C₈	1	2	yes	—
41	C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
43	C₂×C₁₄₉	—	2	2	no	—
44	C₂×C₁₄₉	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂×C₁₄₉	#504	1	2	yes	—
46	C₁₄₉	#2151	1	1	yes	characteristic, complemented, Sylow
47	#2151	—	149	1	no	maximal, Sylow
48	C₂×M₃₂	—	149	1	no	—
49	C₂²×C₁₆	—	149	1	no	—
50	#405	—	149	1	no	—
51	C₄⋊C₁₆	—	149	4	no	—
52	C₂×M₁₆	—	149	1	no	—
53	C₂²×C₈	—	149	1	no	—
54	#117	#10597010	1	1	yes	characteristic
55	M₃₂	—	298	2	no	—
56	C₂×C₁₆	—	298	2	no	—
57	C₂×C₁₆	—	149	2	no	—
58	C₂×C₁₆	—	149	2	no	—
59	#97	—	149	2	no	—
60	C₄×C₈	—	149	2	no	—
61	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
62	M₁₆	—	298	2	no	—
63	C₂×C₈	—	149	2	no	—
64	C₂×C₈	—	149	2	no	—
65	C₂×C₈	—	149	2	no	—
66	C₂×C₈	—	149	1	no	—
67	C₂×C₈	—	149	1	no	—
68	C₄⋊C₄	#11924753	1	2	yes	—
69	C₂²⋊C₄	#11924753	1	2	yes	—
70	C₄²	C₂×#10597010	1	2	yes	—
71	C₁₆	—	298	2	no	—
72	C₁₆	—	298	2	no	—
73	C₂³	C₂×#11924753	1	1	yes	characteristic
74	C₂×C₄	C₄⋊#10597010	1	2	yes	—
75	C₂×C₄	C₂×#11924753	1	4	yes	—
76	C₂×C₄	C₂×#11924753	1	1	yes	characteristic
77	C₂×C₄	#14558746	1	2	yes	—
78	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
79	C₈	—	298	2	no	—
80	C₈	—	149	2	no	—
81	C₈	—	149	1	no	—
82	C₈	—	149	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#11924753	1	2	yes	—
85	C₂²	C₂²×#11924753	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#11924753	1	2	yes	—
88	C₄	C₂×C₄⋊#10597010	1	1	yes	characteristic
89	C₄	C₂×#14558746	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#11924753	1	1	yes	characteristic
92	C₂	#23750683	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10597010
commutator, socle	C₂²×C₁₄₉	C₂²×C₈
Fitting	#117×C₁₄₉	C₄
prime radical	C₂³×C₁₄₉	C₂×C₈
cosocle	C₂×#11924746	C₂³
hypercenter	#117	#10597010
hypocenter	C₁₄₉	#2151
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#14558739	C₂	semidirect
46. C₁₄₉	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011985	2
C₂²×#14558739	2
C₄⋊#14558739	2
#23749581	2
#2151	149