Subgroups — #11919403

Order 1152.

249 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#376⋊C₉	C₂	1	3	yes	maximal
2	C₃×#2276	C₃	1	1	yes	maximal, characteristic
3	Q₈×C₂²⋊C₉	—	4	1	no	maximal
4	#95⋊C₉	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄×Q₈	—	3	1	no	—
6	C₃×C₄×C₄⋊C₄	—	3	3	no	—
7	C₃×#376	C₂×C₃	1	3	yes	—
8	C₄×C₂²⋊C₉	—	4	3	no	—
9	#2276	C₉	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₃×Q₈	A₄	1	1	yes	characteristic
11	C₃×C₄×Q₈	—	3	6	no	—
12	C₃×C₄×Q₈	—	3	2	no	—
13	C₂×C₃×C₄⋊C₄	—	3	3	no	—
14	C₂×C₃×C₄²	—	3	3	no	—
15	C₂×C₃×C₄²	—	3	2	no	—
16	C₃×#95	—	3	3	no	—
17	C₃×#95	C₂²×C₃	1	1	yes	characteristic
18	C₂×C₂²⋊C₉	—	4	1	no	—
19	Q₈×C₉	—	16	1	no	—
20	C₂×C₄×Q₈	—	3	1	no	—
21	C₄×C₄⋊C₄	—	3	3	no	—
22	#376	C₂×C₉	1	3	yes	—
23	C₂×C₃×Q₈	—	3	3	no	—
24	C₂×C₃×Q₈	—	3	1	no	—
25	C₂²×C₃×C₄	—	3	1	no	—
26	C₂²×C₃×C₄	—	3	3	no	—
27	C₂²×C₃×C₄	C₂×A₄	1	3	yes	—
28	C₃×C₄⋊C₄	—	3	6	no	—
29	C₃×C₄⋊C₄	—	3	6	no	—
30	C₃×C₄²	—	3	6	no	—
31	C₃×C₄²	—	3	6	no	—
32	C₃×C₄²	—	12	2	no	—
33	C₂²⋊C₉	—	4	1	no	—
34	C₄×C₉	—	16	3	no	—
35	C₂²×Q₈	C₂²⋊C₉	1	1	yes	characteristic
36	C₄×Q₈	—	3	6	no	—
37	C₄×Q₈	—	3	2	no	—
38	C₂×C₄⋊C₄	—	3	3	no	—
39	C₂×C₄²	—	3	3	no	—
40	C₂×C₄²	—	3	2	no	—
41	#95	—	3	3	no	—
42	#95	C₂²×C₉	1	1	yes	characteristic
43	C₂³×C₃	C₂²×A₄	1	1	yes	characteristic
44	C₃×Q₈	—	3	2	no	—
45	C₃×Q₈	—	3	3	no	—
46	C₃×Q₈	C₄²⋊C₃	1	1	yes	characteristic
47	C₂×C₃×C₄	—	3	3	no	—
48	C₂×C₃×C₄	—	3	3	no	—
49	C₂×C₃×C₄	—	3	2	no	—
50	C₂×C₃×C₄	—	3	6	no	—
51	C₂×C₃×C₄	—	6	2	no	—
52	C₂×C₃×C₄	—	6	3	no	—
53	C₂×C₃×C₄	—	6	3	no	—
54	C₂×C₉	—	16	1	no	—
55	C₂×Q₈	—	3	3	no	—
56	C₂×Q₈	—	3	1	no	—
57	C₂²×C₄	—	3	1	no	—
58	C₂²×C₄	—	3	3	no	—
59	C₂²×C₄	C₂×C₂²⋊C₉	1	3	yes	—
60	C₄⋊C₄	—	3	6	no	—
61	C₄⋊C₄	—	3	6	no	—
62	C₄²	—	3	6	no	—
63	C₄²	—	3	6	no	—
64	C₄²	—	12	2	no	—
65	C₂²×C₃	—	3	1	no	—
66	C₂²×C₃	—	3	1	no	—
67	C₂²×C₃	#994	1	1	yes	characteristic
68	C₃×C₄	—	3	3	no	—
69	C₃×C₄	—	6	6	no	—
70	C₃×C₄	—	6	2	no	—
71	C₃×C₄	C₂×C₄²⋊C₃	1	3	yes	—
72	C₉	—	16	1	no	Sylow
73	C₂³	C₂²×C₂²⋊C₉	1	1	yes	characteristic
74	Q₈	—	3	2	no	—
75	Q₈	—	3	3	no	—
76	Q₈	C₄²⋊C₉	1	1	yes	characteristic
77	C₂×C₄	—	3	3	no	—
78	C₂×C₄	—	3	3	no	—
79	C₂×C₄	—	3	2	no	—
80	C₂×C₄	—	3	6	no	—
81	C₂×C₄	—	6	2	no	—
82	C₂×C₄	—	6	3	no	—
83	C₂×C₄	—	6	3	no	—
84	C₂×C₃	—	3	1	no	—
85	C₂×C₃	—	3	1	no	—
86	C₂×C₃	C₂²×C₄²⋊C₃	1	1	yes	characteristic
87	C₂²	—	3	1	no	—
88	C₂²	—	3	1	no	—
89	C₂²	#63700	1	1	yes	characteristic
90	C₄	—	3	3	no	—
91	C₄	—	6	6	no	—
92	C₄	—	6	2	no	—
93	C₄	C₂×C₄²⋊C₉	1	3	yes	—
94	C₃	#73166	1	1	yes	characteristic
95	C₂	—	3	1	no	—
96	C₂	—	3	1	no	—
97	C₂	C₂²×C₄²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×C₄²⋊C₃
commutator, hypocenter	#95	C₂²×C₉
Frattini, socle, prime radical	C₂³×C₃	C₂²×A₄
Fitting	C₃×#2276	C₃
cosocle	C₃×#95	C₂²×C₃
hypercenter	C₃×Q₈	C₄²⋊C₃
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
9. #2276	C₉	semidirect

Maximal subgroups

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

subgroup	index
#376⋊C₉	2
C₃×#2276	3
Q₈×C₂²⋊C₉	4