Finite Group Databasebeta

Subgroups — #21461091

Order 7808.

204 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840782	C₂	1	1	yes	maximal, characteristic
2	#16840778	C₂	1	1	yes	maximal, characteristic
3	#16840608	C₂	1	2	yes	maximal
4	#16840607	C₂	1	2	yes	maximal
5	C₂×#14519767	C₂	1	1	yes	maximal, characteristic
6	#14519844	—	2	1	no	—
7	C₄⋊#92420	—	2	1	no	—
8	C₂²⋊#92420	C₂²	1	2	yes	—
9	C₂²⋊#92420	C₂²	1	2	yes	—
10	#14519832	—	2	1	no	—
11	C₄×#92420	—	2	1	no	—
12	#14519767	—	2	1	no	—
13	#14519767	—	2	1	no	—
14	#14519767	—	2	1	no	—
15	#14519767	—	2	1	no	—
16	C₂×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
17	C₂×#11758196	C₄	1	1	yes	characteristic
18	C₂×#11758196	C₄	1	1	yes	characteristic
19	C₂×#11758196	C₄	1	1	yes	characteristic
20	C₂×#11758196	C₂²	1	1	yes	characteristic
21	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
23	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
30	C₂×#92420	—	2	2	no	—
31	C₂×#92420	—	2	2	no	—
32	C₄⋊C₄×C₆₁	—	2	1	no	—
33	C₄⋊C₄×C₆₁	—	2	1	no	—
34	C₄⋊Dic₆₁	—	2	1	no	—
35	C₄⋊Dic₆₁	—	2	1	no	—
36	#11758196	—	2	1	no	—
37	#11758196	—	2	1	no	—
38	#11758196	—	2	1	no	—
39	#11758196	—	2	1	no	—
40	#11758196	—	2	1	no	—
41	#11758196	—	2	1	no	—
42	#11758196	—	2	1	no	—
43	#11758196	—	2	1	no	—
44	C₄×Dic₆₁	D₄	1	1	yes	characteristic
45	C₄×Dic₆₁	D₄	1	1	yes	characteristic
46	C₄×Dic₆₁	D₄	1	1	yes	characteristic
47	C₄×Dic₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₆₁	—	2	2	no	—
50	C₂×C₄×C₆₁	—	2	1	no	—
51	C₂×C₄×C₆₁	—	2	1	no	—
52	C₂×C₄×C₆₁	—	2	2	no	—
53	C₂×C₄×C₆₁	—	4	1	no	—
54	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₆₁	—	2	2	no	—
57	C₂×Dic₆₁	—	2	1	no	—
58	C₂×Dic₆₁	—	2	1	no	—
59	C₂×Dic₆₁	—	2	2	no	—
60	C₂×Dic₆₁	—	4	1	no	—
61	C₂×Dic₆₁	—	4	1	no	—
62	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
65	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
66	#92420	—	4	2	no	—
67	#92420	—	4	2	no	—
68	C₂²×C₆₁	—	2	1	no	—
69	C₂²×C₆₁	—	2	1	no	—
70	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₆₁	#131	1	2	yes	—
72	C₄×C₆₁	—	2	1	no	—
73	C₄×C₆₁	—	2	1	no	—
74	C₄×C₆₁	—	4	1	no	—
75	C₄×C₆₁	—	4	1	no	—
76	Dic₆₁	—	2	1	no	—
77	Dic₆₁	—	2	1	no	—
78	Dic₆₁	—	2	1	no	—
79	Dic₆₁	—	4	1	no	—
80	Dic₆₁	—	4	1	no	—
81	Dic₆₁	#101	1	2	yes	—
82	#1470	—	61	1	no	maximal, Sylow
83	C₂×C₆₁	—	2	2	no	—
84	C₂×C₆₁	#408	1	1	yes	characteristic
85	C₂×C₆₁	#410	1	1	yes	characteristic
86	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
87	C₂×#125	—	61	1	no	—
88	#432	—	61	1	no	—
89	#431	—	61	1	no	—
90	#324	—	61	2	no	—
91	#324	—	61	2	no	—
92	C₆₁	#1470	1	1	yes	characteristic, complemented, Sylow
93	#125	—	122	1	no	—
94	#125	—	122	1	no	—
95	#125	—	122	1	no	—
96	#125	—	122	1	no	—
97	C₂×C₄⋊C₄	—	61	1	no	—
98	C₂×C₄⋊C₄	—	61	1	no	—
99	C₂×C₄⋊C₄	—	61	1	no	—
100	C₂×C₄⋊C₄	—	61	1	no	—
101	C₂×C₄⋊C₄	—	61	1	no	—
102	C₂×C₄⋊C₄	#6923	1	1	yes	characteristic
103	C₂×C₄²	—	61	1	no	—
104	C₄⋊C₈	—	122	1	no	—
105	C₄⋊C₈	—	122	1	no	—
106	C₂²⋊C₈	—	61	2	no	—
107	C₂²⋊C₈	—	61	2	no	—
108	#97	—	122	1	no	—
109	C₄×C₈	—	122	1	no	—
110	C₂²×C₄	—	61	1	no	—
111	C₂²×C₄	—	61	1	no	—
112	C₂²×C₄	—	61	1	no	—
113	C₂²×C₄	—	61	1	no	—
114	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
115	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
116	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
117	C₂×C₈	—	122	2	no	—
118	C₂×C₈	—	122	2	no	—
119	C₄⋊C₄	—	2	1	no	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	122	1	no	—
122	C₄⋊C₄	—	122	1	no	—
123	C₄⋊C₄	—	122	1	no	—
124	C₄⋊C₄	—	122	1	no	—
125	C₄⋊C₄	—	122	1	no	—
126	C₄⋊C₄	—	122	1	no	—
127	C₄⋊C₄	—	122	1	no	—
128	C₄⋊C₄	—	122	1	no	—
129	C₄⋊C₄	—	122	1	no	—
130	C₄⋊C₄	—	122	1	no	—
131	C₄²	—	61	1	no	—
132	C₄²	—	61	1	no	—
133	C₄²	—	61	1	no	—
134	C₄²	—	61	1	no	—
135	C₂³	C₂²×#6923	1	1	yes	characteristic
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	2	1	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	4	1	no	—
141	C₂×C₄	—	61	1	no	—
142	C₂×C₄	—	61	1	no	—
143	C₂×C₄	—	61	1	no	—
144	C₂×C₄	—	61	1	no	—
145	C₂×C₄	—	122	2	no	—
146	C₂×C₄	—	122	1	no	—
147	C₂×C₄	—	122	1	no	—
148	C₂×C₄	—	122	2	no	—
149	C₂×C₄	—	244	1	no	—
150	C₂×C₄	—	244	1	no	—
151	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
152	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
153	C₈	—	244	2	no	—
154	C₈	—	244	2	no	—
155	C₂²	—	2	1	no	—
156	C₂²	—	2	1	no	—
157	C₂²	C₂×C₂²⋊#6923	1	1	yes	characteristic
158	C₂²	#14519864	1	2	yes	—
159	C₄	—	2	1	no	—
160	C₄	—	2	1	no	—
161	C₄	—	4	1	no	—
162	C₄	—	4	1	no	—
163	C₄	—	61	2	no	—
164	C₄	—	122	1	no	—
165	C₄	—	122	1	no	—
166	C₄	—	122	1	no	—
167	C₄	—	244	1	no	—
168	C₄	—	244	1	no	—
169	C₂	—	2	2	no	—
170	C₂	#16840735	1	1	yes	characteristic
171	C₂	#16840741	1	1	yes	characteristic
172	C₂	D₆₁⋊#101	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#6923
commutator	C₂³×C₆₁	C₂²×C₄
Frattini	C₂³	C₂²×#6923
Fitting	C₂×C₄⋊C₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#6923
hypocenter	C₆₁	#1470
LCS	G ▷ C₂³×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
92. C₆₁	#1470	semidirect