Group #38764546 — subgroups

Subgroups — C₂×D₄⋊C₈×C₁₉₉ #38764546

Order 25472.

344 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.

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

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₁₉₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄⋊C₈×C₁₉₉	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₄×C₁₉₉	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₁₉₉	—	2	1	no	—
7	C₂²×C₈×C₁₉₉	—	2	1	no	—
8	C₂²×C₈×C₁₉₉	—	2	1	no	—
9	C₄×D₄×C₁₉₉	—	2	1	no	—
10	C₄×D₄×C₁₉₉	—	2	1	no	—
11	C₄×D₄×C₁₉₉	C₄	1	2	yes	—
12	C₄×D₄×C₁₉₉	C₂²	1	2	yes	—
13	C₂×C₄⋊C₄×C₁₉₉	C₄	1	1	yes	characteristic
14	C₂×C₂²⋊C₄×C₁₉₉	—	2	1	no	—
15	C₂×C₄²×C₁₉₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₁₉₉	—	2	1	no	—
17	C₄⋊C₈×C₁₉₉	C₂²	1	2	yes	complemented
18	C₄×C₈×C₁₉₉	—	2	1	no	—
19	C₄×C₈×C₁₉₉	C₂²	1	2	yes	complemented
20	C₂⁴×C₁₉₉	—	2	1	no	—
21	C₂×D₄×C₁₉₉	—	2	1	no	—
22	C₂×D₄×C₁₉₉	—	2	2	no	—
23	C₂×D₄×C₁₉₉	C₈	1	4	yes	complemented
24	C₂×D₄×C₁₉₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₁₉₉	—	2	1	no	—
26	C₂²×C₄×C₁₉₉	—	2	2	no	—
27	C₂²×C₄×C₁₉₉	—	2	2	no	—
28	C₂²×C₄×C₁₉₉	—	4	2	no	—
29	C₂²×C₄×C₁₉₉	—	4	2	no	—
30	C₂²×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉₉	—	2	4	no	—
34	C₂×C₈×C₁₉₉	—	2	2	no	—
35	C₂×C₈×C₁₉₉	—	2	2	no	—
36	C₂×C₈×C₁₉₉	—	4	2	no	—
37	C₄⋊C₄×C₁₉₉	—	2	1	no	—
38	C₄⋊C₄×C₁₉₉	C₂×C₄	1	2	yes	—
39	C₂²⋊C₄×C₁₉₉	—	2	2	no	—
40	C₂²⋊C₄×C₁₉₉	—	2	2	no	—
41	C₄²×C₁₉₉	C₂×C₄	1	1	yes	characteristic
42	C₄²×C₁₉₉	D₄	1	1	yes	characteristic
43	C₄²×C₁₉₉	D₄	1	1	yes	characteristic
44	C₄²×C₁₉₉	C₂³	1	1	yes	characteristic
45	C₂³×C₁₉₉	—	2	4	no	—
46	C₂³×C₁₉₉	—	2	2	no	—
47	C₂³×C₁₉₉	—	4	2	no	—
48	C₂³×C₁₉₉	—	4	2	no	—
49	C₂³×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
50	D₄×C₁₉₉	—	2	4	no	—
51	D₄×C₁₉₉	—	2	2	no	—
52	D₄×C₁₉₉	C₂×C₈	1	4	yes	complemented
53	C₂×C₄×C₁₉₉	—	2	2	no	—
54	C₂×C₄×C₁₉₉	—	2	2	no	—
55	C₂×C₄×C₁₉₉	—	4	2	no	—
56	C₂×C₄×C₁₉₉	—	4	4	no	—
57	C₂×C₄×C₁₉₉	—	4	2	no	—
58	C₂×C₄×C₁₉₉	—	4	2	no	—
59	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉₉	C₂×C₈	1	2	yes	—
63	C₂×C₄×C₁₉₉	M₁₆	1	2	yes	—
64	C₂×C₄×C₁₉₉	D₈	1	2	yes	—
65	C₂×C₄×C₁₉₉	SD₁₆	1	2	yes	—
66	C₂×C₄×C₁₉₉	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₉₉	C₂×D₄	1	1	yes	characteristic
69	C₈×C₁₉₉	—	2	4	no	—
70	C₈×C₁₉₉	—	4	2	no	—
71	C₂²×C₁₉₉	—	2	4	no	—
72	C₂²×C₁₉₉	—	4	8	no	—
73	C₂²×C₁₉₉	—	4	2	no	—
74	C₂²×C₁₉₉	—	4	2	no	—
75	C₂²×C₁₉₉	C₂²⋊C₈	1	2	yes	—
76	C₂²×C₁₉₉	#102	1	2	yes	—
77	C₂²×C₁₉₉	#104	1	2	yes	—
78	C₂²×C₁₉₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₄×C₁₉₉	—	2	1	no	—
80	C₄×C₁₉₉	—	2	1	no	—
81	C₄×C₁₉₉	—	4	2	no	—
82	C₄×C₁₉₉	C₂²⋊C₈	1	2	yes	—
83	C₄×C₁₉₉	#102	1	2	yes	—
84	C₄×C₁₉₉	C₂²×C₈	1	1	yes	characteristic
85	C₄×C₁₉₉	C₂×M₁₆	1	1	yes	characteristic
86	C₄×C₁₉₉	C₂×D₈	1	1	yes	characteristic
87	C₄×C₁₉₉	C₂×SD₁₆	1	1	yes	characteristic
88	C₂×C₁₉₉	—	4	4	no	—
89	C₂×C₁₉₉	D₄⋊C₈	1	4	yes	direct product factor
90	C₂×C₁₉₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₁₉₉	C₂×#102	1	1	yes	characteristic
92	C₂×C₁₉₉	C₂×#104	1	1	yes	characteristic
93	C₁₉₉	C₂×D₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×D₄⋊C₈	C₁₉₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂×C₄×D₄	C₂×C₁₉₉	1	1	yes	characteristic
96	C₂×C₄⋊C₈	C₂×C₁₉₉	1	1	yes	characteristic, complemented
97	C₂×C₄×C₈	C₂×C₁₉₉	1	1	yes	characteristic, complemented
98	D₄⋊C₈	C₂×C₁₉₉	1	4	yes	direct product factor
99	C₂²×D₄	C₄×C₁₉₉	1	1	yes	characteristic
100	C₂³×C₄	—	2	1	no	—
101	C₂²×C₈	—	2	1	no	—
102	C₂²×C₈	—	2	1	no	—
103	C₄×D₄	—	2	1	no	—
104	C₄×D₄	—	2	1	no	—
105	C₄×D₄	C₄×C₁₉₉	1	2	yes	—
106	C₄×D₄	C₂²×C₁₉₉	1	2	yes	—
107	C₂×C₄⋊C₄	C₄×C₁₉₉	1	1	yes	characteristic
108	C₂×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₄²	C₂²×C₁₉₉	1	1	yes	characteristic
110	C₄⋊C₈	—	2	1	no	—
111	C₄⋊C₈	C₂²×C₁₉₉	1	2	yes	complemented
112	C₄×C₈	—	2	1	no	—
113	C₄×C₈	C₂²×C₁₉₉	1	2	yes	complemented
114	C₂⁴	—	2	1	no	—
115	C₂×D₄	—	2	1	no	—
116	C₂×D₄	—	2	2	no	—
117	C₂×D₄	C₈×C₁₉₉	1	4	yes	complemented
118	C₂×D₄	C₂×C₄×C₁₉₉	1	2	yes	—
119	C₂²×C₄	—	2	1	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	—	2	2	no	—
122	C₂²×C₄	—	4	2	no	—
123	C₂²×C₄	—	4	2	no	—
124	C₂²×C₄	C₂×C₄×C₁₉₉	1	1	yes	characteristic
125	C₂²×C₄	D₄×C₁₉₉	1	1	yes	characteristic
126	C₂²×C₄	D₄×C₁₉₉	1	1	yes	characteristic
127	C₂×C₈	—	2	4	no	—
128	C₂×C₈	—	2	2	no	—
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	4	2	no	—
131	C₄⋊C₄	—	2	1	no	—
132	C₄⋊C₄	C₂×C₄×C₁₉₉	1	2	yes	—
133	C₂²⋊C₄	—	2	2	no	—
134	C₂²⋊C₄	—	2	2	no	—
135	C₄²	C₂×C₄×C₁₉₉	1	1	yes	characteristic
136	C₄²	D₄×C₁₉₉	1	1	yes	characteristic
137	C₄²	D₄×C₁₉₉	1	1	yes	characteristic
138	C₄²	C₂³×C₁₉₉	1	1	yes	characteristic
139	C₂³	—	2	4	no	—
140	C₂³	—	2	2	no	—
141	C₂³	—	4	2	no	—
142	C₂³	—	4	2	no	—
143	C₂³	C₂²⋊C₄×C₁₉₉	1	1	yes	characteristic
144	D₄	—	2	4	no	—
145	D₄	—	2	2	no	—
146	D₄	C₂×C₈×C₁₉₉	1	4	yes	complemented
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	4	4	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	C₂²⋊C₄×C₁₉₉	1	1	yes	characteristic
154	C₂×C₄	C₂²⋊C₄×C₁₉₉	1	1	yes	characteristic
155	C₂×C₄	C₂²⋊C₄×C₁₉₉	1	1	yes	characteristic
156	C₂×C₄	C₂×C₈×C₁₉₉	1	2	yes	—
157	C₂×C₄	M₁₆×C₁₉₉	1	2	yes	—
158	C₂×C₄	D₈×C₁₉₉	1	2	yes	—
159	C₂×C₄	SD₁₆×C₁₉₉	1	2	yes	—
160	C₂×C₄	C₂²×C₄×C₁₉₉	1	1	yes	characteristic
161	C₂×C₄	C₂×D₄×C₁₉₉	1	1	yes	characteristic
162	C₂×C₄	C₂×D₄×C₁₉₉	1	1	yes	characteristic
163	C₈	—	2	4	no	—
164	C₈	—	4	2	no	—
165	C₂²	—	2	4	no	—
166	C₂²	—	4	8	no	—
167	C₂²	—	4	2	no	—
168	C₂²	—	4	2	no	—
169	C₂²	C₂²⋊C₈×C₁₉₉	1	2	yes	—
170	C₂²	#102×C₁₉₉	1	2	yes	—
171	C₂²	#104×C₁₉₉	1	2	yes	—
172	C₂²	C₂×C₂²⋊C₄×C₁₉₉	1	1	yes	characteristic
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	4	2	no	—
176	C₄	C₂²⋊C₈×C₁₉₉	1	2	yes	—
177	C₄	#102×C₁₉₉	1	2	yes	—
178	C₄	C₂²×C₈×C₁₉₉	1	1	yes	characteristic
179	C₄	C₂×M₁₆×C₁₉₉	1	1	yes	characteristic
180	C₄	C₂×D₈×C₁₉₉	1	1	yes	characteristic
181	C₄	C₂×SD₁₆×C₁₉₉	1	1	yes	characteristic
182	C₂	—	4	4	no	—
183	C₂	D₄⋊C₈×C₁₉₉	1	4	yes	direct product factor
184	C₂	C₂×C₂²⋊C₈×C₁₉₉	1	1	yes	characteristic
185	C₂	C₂×#102×C₁₉₉	1	1	yes	characteristic
186	C₂	C₂×#104×C₁₉₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₄×C₁₉₉

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₁₉₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄×C₈×C₁₉₉

C₂

yes

maximal, characteristic, complemented

D₄⋊C₈×C₁₉₉

C₂

yes

maximal, direct product factor

C₂²×D₄×C₁₉₉

C₄

yes

characteristic

C₂³×C₄×C₁₉₉

—

C₂²×C₈×C₁₉₉

—

C₂²×C₈×C₁₉₉

—

C₄×D₄×C₁₉₉

—

C₄×D₄×C₁₉₉

—

C₄×D₄×C₁₉₉

C₄

yes

—

C₄×D₄×C₁₉₉

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉₉

C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉₉

—

C₂×C₄²×C₁₉₉

C₂²

yes

characteristic

C₄⋊C₈×C₁₉₉

—

C₄⋊C₈×C₁₉₉

C₂²

yes

complemented

C₄×C₈×C₁₉₉

—

C₄×C₈×C₁₉₉

C₂²

yes

complemented

C₂⁴×C₁₉₉

—

C₂×D₄×C₁₉₉

—

C₂×D₄×C₁₉₉

—

C₂×D₄×C₁₉₉

C₈

yes

complemented

C₂×D₄×C₁₉₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉₉

—

C₂²×C₄×C₁₉₉

—

C₂²×C₄×C₁₉₉

—

C₂²×C₄×C₁₉₉

—

C₂²×C₄×C₁₉₉

—

C₂²×C₄×C₁₉₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉₉

D₄

yes

characteristic

C₂²×C₄×C₁₉₉

D₄

yes

characteristic

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

—

C₂×C₈×C₁₉₉

—

C₄⋊C₄×C₁₉₉

—

C₄⋊C₄×C₁₉₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉₉

—

C₂²⋊C₄×C₁₉₉

—

C₄²×C₁₉₉

C₂×C₄

yes

characteristic

C₄²×C₁₉₉

D₄

yes

characteristic

C₄²×C₁₉₉

D₄

yes

characteristic

C₄²×C₁₉₉

C₂³

yes

characteristic

C₂³×C₁₉₉

—

C₂³×C₁₉₉

—

C₂³×C₁₉₉

—

C₂³×C₁₉₉

—

C₂³×C₁₉₉

C₂²⋊C₄

yes

characteristic

D₄×C₁₉₉

—

D₄×C₁₉₉

—

D₄×C₁₉₉

C₂×C₈

yes

complemented

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

—

C₂×C₄×C₁₉₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂×C₈

yes

—

C₂×C₄×C₁₉₉

M₁₆

yes

—

C₂×C₄×C₁₉₉

D₈

yes

—

C₂×C₄×C₁₉₉

SD₁₆

yes

—

C₂×C₄×C₁₉₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₉

C₂×D₄

yes

characteristic

C₈×C₁₉₉

—

C₈×C₁₉₉

—

C₂²×C₁₉₉

—

C₂²×C₁₉₉

—

C₂²×C₁₉₉

—

C₂²×C₁₉₉

—

C₂²×C₁₉₉

C₂²⋊C₈

yes

—

C₂²×C₁₉₉

#102

yes

—

C₂²×C₁₉₉

#104

yes

—

C₂²×C₁₉₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉₉

—

C₄×C₁₉₉

—

C₄×C₁₉₉

—

C₄×C₁₉₉

C₂²⋊C₈

yes

—

C₄×C₁₉₉

#102

yes

—

C₄×C₁₉₉

C₂²×C₈

yes

characteristic

C₄×C₁₉₉

C₂×M₁₆

yes

characteristic

C₄×C₁₉₉

C₂×D₈

yes

characteristic

C₄×C₁₉₉

C₂×SD₁₆

yes

characteristic

C₂×C₁₉₉

—

C₂×C₁₉₉

D₄⋊C₈

yes

direct product factor

C₂×C₁₉₉

C₂×C₂²⋊C₈

yes

C₂×C₁₉₉

yes

C₂×C₁₉₉

yes

C₁₉₉

C₂×D₄⋊C₈

yes

characteristic, direct product factor, Sylow

C₂×D₄⋊C₈

C₁₉₉

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄×D₄

C₂×C₁₉₉

yes

characteristic

C₂×C₄⋊C₈

C₂×C₁₉₉

yes

characteristic, complemented

C₂×C₄×C₈

C₂×C₁₉₉

yes

characteristic, complemented

D₄⋊C₈

C₂×C₁₉₉

yes

direct product factor

C₂²×D₄

C₄×C₁₉₉

yes

characteristic

100

C₂³×C₄

—

101

C₂²×C₈

—

102

C₂²×C₈

—

103

C₄×D₄

—

104

C₄×D₄

—

105

C₄×D₄

C₄×C₁₉₉

yes

—

106

C₄×D₄

C₂²×C₁₉₉

yes

—

107

C₂×C₄⋊C₄

C₄×C₁₉₉

yes

characteristic

108

C₂×C₂²⋊C₄

—

109

C₂×C₄²

C₂²×C₁₉₉

yes

characteristic

110

C₄⋊C₈

—

111

C₄⋊C₈

C₂²×C₁₉₉

yes

complemented

112

C₄×C₈

—

113

C₄×C₈

C₂²×C₁₉₉

yes

complemented

114

C₂⁴

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

C₈×C₁₉₉

yes

complemented

118

C₂×D₄

C₂×C₄×C₁₉₉

yes

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

C₂×C₄×C₁₉₉

yes

characteristic

125

C₂²×C₄

D₄×C₁₉₉

yes

characteristic

126

C₂²×C₄

D₄×C₁₉₉

yes

characteristic

127

C₂×C₈

—

128

C₂×C₈

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₄⋊C₄

—

132

C₄⋊C₄

C₂×C₄×C₁₉₉

yes

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

C₂×C₄×C₁₉₉

yes

characteristic

136

C₄²

D₄×C₁₉₉

yes

characteristic

137

C₄²

D₄×C₁₉₉

yes

characteristic

138

C₄²

C₂³×C₁₉₉

yes

characteristic

139

C₂³

—

140

C₂³

—

141

C₂³

—

142

C₂³

—

143

C₂³

C₂²⋊C₄×C₁₉₉

yes

characteristic

144

D₄

—

145

D₄

—

146

D₄

C₂×C₈×C₁₉₉

yes

complemented

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

C₂²⋊C₄×C₁₉₉

yes

characteristic

154

C₂×C₄

C₂²⋊C₄×C₁₉₉

yes

characteristic

155

C₂×C₄

C₂²⋊C₄×C₁₉₉

yes

characteristic

156

C₂×C₄

C₂×C₈×C₁₉₉

yes

—

157

C₂×C₄

M₁₆×C₁₉₉

yes

—

158

C₂×C₄

D₈×C₁₉₉

yes

—

159

C₂×C₄

SD₁₆×C₁₉₉

yes

—

160

C₂×C₄

C₂²×C₄×C₁₉₉

yes

characteristic

161

C₂×C₄

C₂×D₄×C₁₉₉

yes

characteristic

162

C₂×C₄

C₂×D₄×C₁₉₉

yes

characteristic

163

C₈

—

164

C₈

—

165

C₂²

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

C₂²⋊C₈×C₁₉₉

yes

—

170

C₂²

#102×C₁₉₉

yes

—

171

C₂²

#104×C₁₉₉

yes

—

172

C₂²

C₂×C₂²⋊C₄×C₁₉₉

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

C₂²⋊C₈×C₁₉₉

yes

—

177

C₄

#102×C₁₉₉

yes

—

178

C₄

C₂²×C₈×C₁₉₉

yes

characteristic

179

C₄

C₂×M₁₆×C₁₉₉

yes

characteristic

180

C₄

C₂×D₈×C₁₉₉

yes

characteristic

181

C₄

C₂×SD₁₆×C₁₉₉

yes

characteristic

182

C₂

—

183

C₂

D₄⋊C₈×C₁₉₉

yes

direct product factor

184

C₂

C₂×C₂²⋊C₈×C₁₉₉

yes

characteristic

185

C₂

C₂×#102×C₁₉₉

yes

characteristic

186

C₂

C₂×#104×C₁₉₉

yes

characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉₉	D₄
commutator	C₄	C₂²×C₈×C₁₉₉
Frattini, cosocle	C₄²	C₂³×C₁₉₉
socle	C₂³×C₁₉₉	C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉₉	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉₉ ◁ C₂×C₄²×C₁₉₉ ◁ G

subgroup

G/H

center

C₂²×C₄×C₁₉₉

D₄

commutator

C₄

C₂²×C₈×C₁₉₉

Frattini, cosocle

C₄²

C₂³×C₁₉₉

socle

C₂³×C₁₉₉

C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉₉

C₄

LCS

G ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₄×C₁₉₉ ◁ C₂×C₄²×C₁₉₉ ◁ G

N	H ≅ G/N	type
2. C₂×C₄⋊C₈×C₁₉₉	C₂	semidirect
3. C₂×C₄×C₈×C₁₉₉	C₂	semidirect
4. D₄⋊C₈×C₁₉₉	C₂	direct (N × H)
17. C₄⋊C₈×C₁₉₉	C₂²	semidirect
19. C₄×C₈×C₁₉₉	C₂²	semidirect
23. C₂×D₄×C₁₉₉	C₈	semidirect
52. D₄×C₁₉₉	C₂×C₈	semidirect
89. C₂×C₁₉₉	D₄⋊C₈	direct (N × H)
93. C₁₉₉	C₂×D₄⋊C₈	direct (N × H)
94. C₂×D₄⋊C₈	C₁₉₉	direct (N × H)
96. C₂×C₄⋊C₈	C₂×C₁₉₉	semidirect
97. C₂×C₄×C₈	C₂×C₁₉₉	semidirect
98. D₄⋊C₈	C₂×C₁₉₉	direct (N × H)
111. C₄⋊C₈	C₂²×C₁₉₉	semidirect
113. C₄×C₈	C₂²×C₁₉₉	semidirect
117. C₂×D₄	C₈×C₁₉₉	semidirect
146. D₄	C₂×C₈×C₁₉₉	semidirect
183. C₂	D₄⋊C₈×C₁₉₉	direct (N × H)

H ≅ G/N

type

2. C₂×C₄⋊C₈×C₁₉₉

C₂

semidirect

3. C₂×C₄×C₈×C₁₉₉

C₂

semidirect

4. D₄⋊C₈×C₁₉₉

C₂

direct (N × H)

17. C₄⋊C₈×C₁₉₉

C₂²

semidirect

19. C₄×C₈×C₁₉₉

C₂²

semidirect

23. C₂×D₄×C₁₉₉

C₈

semidirect

52. D₄×C₁₉₉

C₂×C₈

semidirect

89. C₂×C₁₉₉

D₄⋊C₈

direct (N × H)

93. C₁₉₉

C₂×D₄⋊C₈

direct (N × H)

94. C₂×D₄⋊C₈

C₁₉₉

direct (N × H)

96. C₂×C₄⋊C₈

C₂×C₁₉₉

semidirect

97. C₂×C₄×C₈

C₂×C₁₉₉

semidirect

98. D₄⋊C₈

C₂×C₁₉₉

direct (N × H)

111. C₄⋊C₈

C₂²×C₁₉₉

semidirect

113. C₄×C₈

C₂²×C₁₉₉

semidirect

117. C₂×D₄

C₈×C₁₉₉

semidirect

146. D₄

C₂×C₈×C₁₉₉

semidirect

183. C₂

D₄⋊C₈×C₁₉₉

direct (N × H)

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

subgroup	index
C₂×C₄×D₄×C₁₉₉	2
C₂×C₄⋊C₈×C₁₉₉	2
C₂×C₄×C₈×C₁₉₉	2
D₄⋊C₈×C₁₉₉	2
C₂×D₄⋊C₈	199

subgroup

index

C₂×C₄×D₄×C₁₉₉

C₂×C₄⋊C₈×C₁₉₉

C₂×C₄×C₈×C₁₉₉

D₄⋊C₈×C₁₉₉

C₂×D₄⋊C₈

199

Subgroups — C₂×D₄⋊C₈×C₁₉₉ #38764546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×D4⋊C8×C199 #38764546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄⋊C₈×C₁₉₉ #38764546