Subgroups — #38767006

Order 25472.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27164408	C₂	1	1	yes	maximal, characteristic
2	#27163815	C₂	1	1	yes	maximal, characteristic, complemented
3	#354×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15691873	—	2	1	no	—
5	C₂×#15691871	—	2	1	no	—
6	#20263952	C₄	1	1	yes	characteristic, complemented
7	#20263874	—	2	1	no	—
8	#20263866	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₉₉	C₂²	1	1	yes	characteristic
10	#99×C₁₉₉	—	2	1	no	—
11	C₂×D₇₉₆	—	2	1	no	—
12	C₂×D₇₉₆	—	4	1	no	—
13	#15691873	—	4	2	no	—
14	#15691871	—	4	2	no	—
15	#15691870	—	4	1	no	—
16	C₂×C₁₉₉⋊C₈	—	2	1	no	—
17	C₂×Q₈×C₁₉₉	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₉₉	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×C₁₉₉	—	4	1	no	—
20	C₂²⋊C₄×C₁₉₉	—	4	1	no	—
21	C₄²×C₁₉₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₉₉	—	4	1	no	—
23	D₇₉₆	—	4	1	no	—
24	D₇₉₆	—	4	1	no	—
25	D₇₉₆	—	8	2	no	—
26	C₁₉₉⋊C₈	—	2	2	no	—
27	C₁₉₉⋊C₈	—	8	1	no	—
28	C₂³×C₁₉₉	—	2	1	no	—
29	Q₈×C₁₉₉	—	4	1	no	—
30	D₄×C₁₉₉	—	4	1	no	—
31	C₂×C₄×C₁₉₉	—	2	1	no	—
32	C₂×C₄×C₁₉₉	—	2	1	no	—
33	C₂×C₄×C₁₉₉	—	8	1	no	—
34	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₁₉₉	—	4	1	no	—
36	C₂²×C₁₉₉	—	8	1	no	—
37	C₂²×C₁₉₉	#99	1	1	yes	characteristic
38	C₂×D₁₉₉	—	8	2	no	—
39	C₂×D₁₉₉	—	8	1	no	—
40	C₄×C₁₉₉	—	2	1	no	—
41	C₄×C₁₉₉	—	4	1	no	—
42	C₄×C₁₉₉	—	4	1	no	—
43	C₄×C₁₉₉	—	16	1	no	—
44	C₂×C₁₉₉	—	2	1	no	—
45	C₂×C₁₉₉	—	8	1	no	—
46	C₂×C₁₉₉	#353	1	1	yes	characteristic
47	D₁₉₉	—	16	1	no	—
48	C₁₉₉	#1406	1	1	yes	characteristic, complemented, Sylow
49	#1406	—	199	1	no	maximal, Sylow
50	#496	—	199	1	no	—
51	#355	—	199	1	no	—
52	#354	D₁₉₉	1	1	yes	characteristic, complemented
53	C₂×SD₁₆	—	398	1	no	—
54	C₂×D₈	—	398	1	no	—
55	#127	—	199	1	no	—
56	#124	C₂×D₁₉₉	1	1	yes	characteristic
57	#101	—	398	1	no	—
58	#99	—	2	1	no	—
59	#97	—	199	1	no	—
60	C₂×Q₈	D₇₉₆	1	1	yes	characteristic
61	C₂×D₄	—	796	1	no	—
62	C₂×D₄	—	398	1	no	—
63	C₂×D₄	C₂²⋊D₁₉₉	1	1	yes	characteristic
64	SD₁₆	—	796	2	no	—
65	D₈	—	796	2	no	—
66	M₁₆	—	796	1	no	—
67	C₂×C₈	—	398	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₁₉₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	796	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	796	1	no	—
76	D₄	—	796	1	no	—
77	D₄	—	1592	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	(C₂×D₁₉₉)⋊C₄	1	1	yes	characteristic
82	C₈	—	1592	1	no	—
83	C₈	—	398	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	1592	2	no	—
87	C₂²	—	1592	1	no	—
88	C₂²	#20263869	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	3184	1	no	—
96	C₂	#27163810	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27163810
commutator	C₄²×C₁₉₉	C₂×C₄
Frattini	#124	C₂×D₁₉₉
Fitting	#354×C₁₉₉	C₂
socle	C₂×C₁₉₉	#353
prime radical	#27164408	C₂
cosocle	#124×C₁₉₉	C₂²
hypercenter	#354	D₁₉₉
hypocenter	C₁₉₉	#1406
LCS	G ▷ C₄²×C₁₉₉ ▷ C₂×C₄×C₁₉₉ ▷ C₂²×C₁₉₉ ▷ C₂×C₁₉₉ ▷ C₁₉₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #27163815	C₂	semidirect
3. #354×C₁₉₉	C₂	semidirect
6. #20263952	C₄	semidirect
8. #20263866	C₄	semidirect
48. C₁₉₉	#1406	semidirect
52. #354	D₁₉₉	semidirect

Maximal subgroups

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

subgroup	index
#27164408	2
#27163815	2
#354×C₁₉₉	2
#1406	199