Group #26126230 — subgroups

Subgroups — #26126230

Order 12032.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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×C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	#20245191	C₂	1	1	yes	maximal, characteristic
3	#20241368	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2162	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₉₄	C₄	1	1	yes	characteristic
6	C₈×Dic₉₄	—	2	1	no	—
7	C₈×Dic₉₄	—	2	1	no	—
8	C₈×Dic₉₄	C₄	1	2	yes	—
9	C₈×Dic₉₄	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₈	—	2	1	no	—
12	C₂×C₈×Dic₄₇	—	2	1	no	—
13	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	—
14	C₂²⋊(C₄₇⋊C₁₆)	—	2	1	no	—
15	#15688899	—	2	1	no	—
16	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×C₄⋊C₁₆	—	2	1	no	—
18	C₄₇×C₂²⋊C₁₆	—	2	1	no	—
19	C₄×C₁₆×C₄₇	C₂²	1	2	yes	—
20	C₂²×Dic₉₄	C₈	1	1	yes	characteristic
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₄×Dic₉₄	—	2	1	no	—
23	C₄×Dic₉₄	—	2	1	no	—
24	C₄×Dic₉₄	C₈	1	2	yes	—
25	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
26	C₂×C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
27	C₂×Dic₄₇⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₄₇	—	2	1	no	—
29	C₂×C₄₇⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
31	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
32	Dic₄₇⋊C₈	—	2	2	no	—
33	Dic₄₇⋊C₈	—	2	2	no	—
34	C₈×Dic₄₇	—	2	2	no	—
35	C₈×Dic₄₇	—	2	2	no	—
36	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₄₇	—	2	2	no	—
40	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
43	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	M₁₆	1	1	yes	characteristic
47	C₂²×Dic₄₇	—	2	1	no	—
48	C₂²×Dic₄₇	—	2	1	no	—
49	C₂×Dic₉₄	—	2	1	no	—
50	C₂×Dic₉₄	—	2	4	no	—
51	C₂×Dic₉₄	C₂×C₈	1	2	yes	—
52	C₂×C₈×C₄₇	—	2	2	no	—
53	C₂×C₈×C₄₇	—	4	1	no	—
54	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₄₇	C₂×C₈	1	1	yes	characteristic
60	C₄²×C₄₇	M₁₆	1	1	yes	characteristic
61	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₄⋊Dic₄₇	—	2	1	no	—
63	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
64	Dic₄₇⋊C₄	—	2	2	no	—
65	Dic₄₇⋊C₄	—	2	2	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	4	2	no	—
70	C₁₆×C₄₇	—	4	2	no	—
71	C₄₇⋊C₁₆	—	4	2	no	—
72	C₂³×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₄₇	—	2	4	no	—
84	C₂×Dic₄₇	—	2	2	no	—
85	C₂×Dic₄₇	—	2	2	no	—
86	C₂×Dic₄₇	—	4	2	no	—
87	Dic₉₄	—	2	4	no	—
88	Dic₉₄	—	2	2	no	—
89	Dic₉₄	M₃₂	1	4	yes	—
90	C₈×C₄₇	—	2	1	no	—
91	C₈×C₄₇	—	2	1	no	—
92	C₈×C₄₇	—	2	1	no	—
93	C₈×C₄₇	#137	1	2	yes	—
94	C₄₇⋊C₈	—	4	2	no	—
95	#11639	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	—	2	1	no	—
97	C₂²×C₄₇	—	2	1	no	—
98	C₂²×C₄₇	#350	1	2	yes	—
99	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
100	C₄×C₄₇	—	2	1	no	—
101	C₄×C₄₇	—	2	1	no	—
102	C₄×C₄₇	—	2	1	no	—
103	C₄×C₄₇	—	2	1	no	—
104	C₄×C₄₇	#419	1	1	yes	characteristic
105	C₄×C₄₇	#421	1	1	yes	characteristic
106	C₄×C₄₇	C₂×M₃₂	1	2	yes	—
107	Dic₄₇	—	2	4	no	—
108	Dic₄₇	—	4	2	no	—
109	C₂×C₈×Q₈	—	47	1	no	—
110	#2163	—	47	1	no	—
111	#2162	D₄₇	1	1	yes	characteristic
112	Q₈⋊C₁₆	—	47	4	no	—
113	C₂×C₄₇	—	2	2	no	—
114	C₂×C₄₇	#1479	1	1	yes	characteristic
115	C₂×C₄₇	#2112	1	1	yes	characteristic
116	C₂×C₄₇	C₂×#350	1	1	yes	characteristic
117	C₂×C₄×Q₈	—	47	1	no	—
118	C₈×Q₈	—	47	2	no	—
119	C₈×Q₈	—	47	2	no	—
120	C₈×Q₈	—	94	1	no	—
121	C₈×Q₈	—	94	1	no	—
122	C₂×C₄⋊C₈	—	47	1	no	—
123	C₂×C₄⋊C₈	—	94	1	no	—
124	C₂×C₄×C₈	—	94	1	no	—
125	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
126	C₄⋊C₁₆	—	2	1	no	—
127	C₄⋊C₁₆	—	47	2	no	—
128	C₂²⋊C₁₆	—	2	1	no	—
129	C₂²⋊C₁₆	—	94	1	no	—
130	#346	—	94	1	no	—
131	C₄×C₁₆	C₂×D₄₇	1	2	yes	—
132	C₄₇	#11639	1	1	yes	characteristic, complemented, Sylow
133	C₂²×Q₈	—	47	1	no	—
134	C₂²×C₈	—	94	1	no	—
135	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
136	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
137	C₄×Q₈	—	47	2	no	—
138	C₄×Q₈	—	47	2	no	—
139	C₄×Q₈	—	94	1	no	—
140	C₄×Q₈	—	94	1	no	—
141	C₂×C₄⋊C₄	—	47	1	no	—
142	C₂×C₄⋊C₄	—	94	1	no	—
143	C₂×C₄²	—	94	1	no	—
144	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
145	C₂×C₁₆	—	2	2	no	—
146	C₂×C₁₆	—	94	2	no	—
147	C₄⋊C₈	—	47	2	no	—
148	C₄⋊C₈	—	94	2	no	—
149	C₄⋊C₈	—	94	2	no	—
150	C₄⋊C₈	—	94	1	no	—
151	C₄×C₈	—	94	2	no	—
152	C₄×C₈	—	94	2	no	—
153	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
154	C₄×C₈	D₁₈₈	1	1	yes	characteristic
155	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
156	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
157	C₂×Q₈	—	47	2	no	—
158	C₂×Q₈	—	94	4	no	—
159	C₂×Q₈	—	94	1	no	—
160	C₂²×C₄	—	94	1	no	—
161	C₂²×C₄	—	94	1	no	—
162	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
163	C₂²×C₄	#10625324	1	1	yes	characteristic
164	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	94	2	no	—
168	C₂×C₈	—	188	2	no	—
169	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
170	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
171	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
172	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
173	C₄⋊C₄	—	47	2	no	—
174	C₄⋊C₄	—	94	2	no	—
175	C₄⋊C₄	—	94	1	no	—
176	C₄⋊C₄	—	94	2	no	—
177	C₄²	—	94	2	no	—
178	C₄²	—	94	2	no	—
179	C₄²	C₈×D₄₇	1	1	yes	characteristic
180	C₄²	#10625324	1	1	yes	characteristic
181	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
182	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
183	C₁₆	—	4	2	no	—
184	C₁₆	—	188	2	no	—
185	C₂³	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
186	Q₈	—	47	4	no	—
187	Q₈	—	94	4	no	—
188	Q₈	—	94	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	94	4	no	—
194	C₂×C₄	—	94	2	no	—
195	C₂×C₄	—	94	2	no	—
196	C₂×C₄	—	188	2	no	—
197	C₂×C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
198	C₂×C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
199	C₂×C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
200	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
201	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
202	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
203	C₈	—	2	1	no	—
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	188	2	no	—
207	C₈	#13094057	1	2	yes	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	#15688906	1	2	yes	—
211	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	94	4	no	—
217	C₄	—	188	2	no	—
218	C₄	#15689133	1	1	yes	characteristic
219	C₄	#15689141	1	1	yes	characteristic
220	C₄	M₃₂×D₄₇	1	2	yes	—
221	C₂	—	2	2	no	—
222	C₂	#20241784	1	1	yes	characteristic
223	C₂	#20244998	1	1	yes	characteristic
224	C₂	C₂×#15688906	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₉₄

C₂

yes

maximal, characteristic

#20245191

C₂

yes

maximal, characteristic

#20241368

C₂

yes

maximal, complemented

C₄₇×#2162

C₂

yes

maximal, characteristic

C₂×C₄×Dic₉₄

C₄

yes

characteristic

C₈×Dic₉₄

—

C₈×Dic₉₄

—

C₈×Dic₉₄

C₄

yes

—

C₈×Dic₉₄

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₄

yes

characteristic

C₂×Dic₄₇⋊C₈

—

C₂×C₈×Dic₄₇

—

C₄⋊(C₄₇⋊C₁₆)

C₂²

yes

—

C₂²⋊(C₄₇⋊C₁₆)

—

#15688899

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×C₄⋊C₁₆

—

C₄₇×C₂²⋊C₁₆

—

C₄×C₁₆×C₄₇

C₂²

yes

—

C₂²×Dic₉₄

C₈

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₈

yes

—

C₄×Dic₉₄

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₇

C₈

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄₇⋊C₁₆

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

D₄

yes

characteristic

C₄×C₈×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

M₁₆

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂×C₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂²⋊C₄

yes

characteristic

C₄²×C₄₇

C₂×C₈

yes

characteristic

C₄²×C₄₇

M₁₆

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×C₈

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

M₃₂

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#137

yes

—

C₄₇⋊C₈

—

#11639

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#350

yes

—

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

#419

yes

characteristic

105

C₄×C₄₇

#421

yes

characteristic

106

C₄×C₄₇

C₂×M₃₂

yes

—

107

Dic₄₇

—

108

Dic₄₇

—

109

C₂×C₈×Q₈

—

110

#2163

—

111

#2162

D₄₇

yes

characteristic

112

Q₈⋊C₁₆

—

113

C₂×C₄₇

—

114

C₂×C₄₇

#1479

yes

characteristic

115

C₂×C₄₇

#2112

yes

characteristic

116

C₂×C₄₇

C₂×#350

yes

characteristic

117

C₂×C₄×Q₈

—

118

C₈×Q₈

—

119

C₈×Q₈

—

120

C₈×Q₈

—

121

C₈×Q₈

—

122

C₂×C₄⋊C₈

—

123

C₂×C₄⋊C₈

—

124

C₂×C₄×C₈

—

125

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

126

C₄⋊C₁₆

—

127

C₄⋊C₁₆

—

128

C₂²⋊C₁₆

—

129

C₂²⋊C₁₆

—

130

#346

—

131

C₄×C₁₆

C₂×D₄₇

yes

—

132

C₄₇

#11639

yes

characteristic, complemented, Sylow

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

D₁₈₈

yes

characteristic

136

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

C₂×C₄²

C₄×D₄₇

yes

characteristic

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄×C₈

—

152

C₄×C₈

—

153

C₄×C₈

C₄×D₄₇

yes

characteristic

154

C₄×C₈

D₁₈₈

yes

characteristic

155

C₄×C₈

C₂²⋊D₄₇

yes

characteristic

156

C₄×C₈

C₂²×D₄₇

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₈×D₄₇

yes

characteristic

163

C₂²×C₄

#10625324

yes

characteristic

164

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

188

—

169

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

170

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

171

C₂×C₈

C₂×D₁₈₈

yes

characteristic

172

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄²

—

178

C₄²

—

179

C₄²

C₈×D₄₇

yes

characteristic

180

C₄²

#10625324

yes

characteristic

181

C₄²

(C₂×D₄₇)⋊C₄

yes

characteristic

182

C₄²

C₂×C₄×D₄₇

yes

characteristic

183

C₁₆

—

184

C₁₆

—

188

—

185

C₂³

(C₂×D₄₇)⋊C₈

yes

characteristic

186

Q₈

—

187

Q₈

—

188

Q₈

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

188

—

197

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

characteristic

198

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

characteristic

199

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

characteristic

200

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

201

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

202

C₂×C₄

C₂×#10625324

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

188

—

207

C₈

#13094057

yes

—

208

C₂²

—

209

C₂²

—

210

C₂²

#15688906

yes

—

211

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

188

—

218

C₄

#15689133

yes

characteristic

219

C₄

#15689141

yes

characteristic

220

C₄

M₃₂×D₄₇

yes

—

221

C₂

—

222

C₂

#20241784

yes

characteristic

223

C₂

#20244998

yes

characteristic

224

C₂

C₂×#15688906

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₇
Fitting	C₄₇×#2162	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	C₂³×C₄₇	C₂²⋊C₈
cosocle	C₄×C₈×C₄₇	C₂³
hypercenter	#2162	D₄₇
hypocenter	C₄₇	#11639
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₈

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₄₇

Fitting

C₄₇×#2162

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₈

prime radical

C₂³×C₄₇

C₂²⋊C₈

cosocle

C₄×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
3. #20241368	C₂	semidirect
132. C₄₇	#11639	semidirect

H ≅ G/N

type

3. #20241368

C₂

semidirect

132. C₄₇

#11639

semidirect

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

subgroup	index
C₂×C₈×Dic₉₄	2
#20245191	2
#20241368	2
C₄₇×#2162	2
#11639	47

subgroup

index

C₂×C₈×Dic₉₄

#20245191

#20241368

C₄₇×#2162

#11639

Subgroups — #26126230

Conjugacy classes of subgroups

Complements

Maximal subgroups