Group #26115178 — subgroups

Subgroups — #26115178

Order 12032.

482 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 147 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×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#20244323	C₂	1	2	yes	maximal
3	C₂×#15688853	C₂	1	2	yes	maximal
4	C₂×#15688845	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#334	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₈₈	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
8	C₄×Dic₁₈₈	—	2	2	no	—
9	C₄×Dic₁₈₈	—	2	2	no	—
10	C₂×#13093958	C₄	1	1	yes	characteristic
11	C₂×#13093949	C₄	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15688877	—	2	4	no	—
15	#15688853	—	2	4	no	—
16	#15688845	—	2	2	no	—
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#334	—	2	2	no	—
20	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
21	C₂×Dic₁₈₈	—	2	4	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
25	C₄×Dic₉₄	—	2	2	no	—
26	C₄×Dic₉₄	—	2	2	no	—
27	C₄×Dic₉₄	—	2	2	no	—
28	C₄×Dic₉₄	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
30	C₂×Dic₄₇⋊C₄	—	2	2	no	—
31	C₂×C₄×Dic₄₇	—	2	2	no	—
32	#13093958	—	2	2	no	—
33	#13093949	—	2	4	no	—
34	C₄×C₄₇⋊C₈	—	2	1	no	—
35	C₄×C₄₇⋊C₈	—	2	1	no	—
36	C₄×C₄₇⋊C₈	—	2	1	no	—
37	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
38	C₂²×C₈×C₄₇	—	2	2	no	—
39	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₄×C₈×C₄₇	D₄	1	2	yes	—
45	C₄×C₈×C₄₇	D₄	1	2	yes	—
46	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
49	C₂²×Dic₄₇	—	2	2	no	—
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₂×Dic₉₄	—	2	2	no	—
53	C₂×Dic₉₄	—	2	2	no	—
54	C₂×Dic₉₄	—	2	2	no	—
55	C₂×Dic₉₄	—	2	2	no	—
56	C₂×Dic₉₄	M₁₆	1	4	yes	—
57	C₂×C₈×C₄₇	—	2	2	no	—
58	C₂×C₈×C₄₇	—	2	2	no	—
59	C₂×C₈×C₄₇	—	4	2	no	—
60	C₂×C₈×C₄₇	—	4	4	no	—
61	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₄₇	#41	1	1	yes	characteristic
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	2	2	no	—
69	Dic₄₇⋊C₄	—	4	2	no	—
70	Dic₄₇⋊C₄	—	4	2	no	—
71	C₄×Dic₄₇	—	4	2	no	—
72	C₄×Dic₄₇	—	4	2	no	—
73	C₂×C₄₇⋊C₈	—	2	4	no	—
74	C₂×C₄₇⋊C₈	—	2	2	no	—
75	C₂×C₄₇⋊C₈	—	2	2	no	—
76	C₂×C₄₇⋊C₈	—	2	4	no	—
77	Dic₁₈₈	—	2	8	no	—
78	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
83	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₄₇	#131	1	2	yes	—
88	C₂×C₄×C₄₇	#137	1	4	yes	—
89	C₂×Dic₄₇	—	2	4	no	—
90	C₂×Dic₄₇	—	4	2	no	—
91	C₂×Dic₄₇	—	4	2	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	4	no	—
94	Dic₉₄	—	2	4	no	—
95	Dic₉₄	—	2	4	no	—
96	Dic₉₄	—	4	2	no	—
97	Dic₉₄	—	4	2	no	—
98	C₈×C₄₇	—	2	2	no	—
99	C₈×C₄₇	—	2	2	no	—
100	C₈×C₄₇	—	8	2	no	—
101	C₄₇⋊C₈	—	2	4	no	—
102	C₄₇⋊C₈	—	4	2	no	—
103	#9664	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	#390	1	1	yes	characteristic
105	C₂²×C₄₇	#435	1	2	yes	—
106	C₂²×C₄₇	#441	1	2	yes	—
107	C₂²×C₄₇	#443	1	2	yes	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	#407	1	1	yes	characteristic
111	C₄×C₄₇	#408	1	1	yes	characteristic
112	C₄×C₄₇	#435	1	2	yes	—
113	C₄×C₄₇	#470	1	2	yes	—
114	C₄×C₄₇	#497	1	2	yes	—
115	Dic₄₇	—	4	4	no	—
116	Dic₄₇	—	8	2	no	—
117	C₂×C₄×Q₁₆	—	47	1	no	—
118	#1984	—	47	2	no	—
119	C₂×#334	D₄₇	1	1	yes	characteristic
120	C₂×Q₈⋊C₈	—	47	2	no	—
121	C₂×#322	—	47	1	no	—
122	C₂×C₄₇	#1587	1	4	yes	—
123	C₂×C₄₇	#1955	1	1	yes	characteristic
124	C₂×C₄₇	#1971	1	1	yes	characteristic
125	C₂×C₄₇	#1974	1	1	yes	characteristic
126	C₂²×Q₁₆	—	47	1	no	—
127	C₂×C₄×Q₈	—	47	2	no	—
128	C₄×Q₁₆	—	94	2	no	—
129	C₄×Q₁₆	—	94	2	no	—
130	C₂×#107	—	47	1	no	—
131	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
132	C₂×#103	—	47	2	no	—
133	C₂×C₄×C₈	—	47	1	no	—
134	C₂×C₄×C₈	—	47	1	no	—
135	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
136	#336	—	94	4	no	—
137	#334	—	2	2	no	—
138	Q₈⋊C₈	—	94	4	no	—
139	#322	—	94	2	no	—
140	C₄₇	#9664	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	2	no	—
142	C₂×Q₁₆	—	94	4	no	—
143	C₂×Q₁₆	—	94	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	47	2	no	—
146	C₂²×C₈	—	94	1	no	—
147	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
148	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
149	C₄×Q₈	—	94	2	no	—
150	C₄×Q₈	—	94	2	no	—
151	C₄×Q₈	—	94	2	no	—
152	C₄×Q₈	—	94	2	no	—
153	C₂×C₄⋊C₄	—	47	2	no	—
154	C₂×C₄⋊C₄	—	94	2	no	—
155	C₂×C₄²	—	94	2	no	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	#107	—	94	2	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	#103	—	94	4	no	—
161	C₄×C₈	—	47	2	no	—
162	C₄×C₈	—	94	1	no	—
163	C₄×C₈	—	94	1	no	—
164	C₄×C₈	—	94	1	no	—
165	C₄×C₈	D₁₈₈	1	2	yes	—
166	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
167	C₂×Q₈	—	47	4	no	—
168	C₂×Q₈	—	94	2	no	—
169	C₂×Q₈	—	94	2	no	—
170	C₂×Q₈	—	94	2	no	—
171	C₂×Q₈	—	94	2	no	—
172	C₂×Q₈	—	94	2	no	—
173	C₂²×C₄	—	94	2	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
177	C₂²×C₄	#10625354	1	1	yes	characteristic
178	Q₁₆	—	94	8	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	4	no	—
183	C₂×C₈	—	94	4	no	—
184	C₂×C₈	—	94	2	no	—
185	C₂×C₈	—	94	2	no	—
186	C₂×C₈	—	94	4	no	—
187	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
188	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
189	C₄⋊C₄	—	94	2	no	—
190	C₄⋊C₄	—	94	2	no	—
191	C₄⋊C₄	—	188	2	no	—
192	C₄⋊C₄	—	188	2	no	—
193	C₄²	—	188	2	no	—
194	C₄²	—	188	2	no	—
195	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
196	C₄²	D₄×D₄₇	1	1	yes	characteristic
197	C₄²	#10625354	1	1	yes	characteristic
198	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
199	C₂³	#13093986	1	1	yes	characteristic
200	Q₈	—	94	4	no	—
201	Q₈	—	94	4	no	—
202	Q₈	—	188	2	no	—
203	Q₈	—	188	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	94	4	no	—
206	C₂×C₄	—	188	4	no	—
207	C₂×C₄	—	188	2	no	—
208	C₂×C₄	—	188	2	no	—
209	C₂×C₄	—	188	2	no	—
210	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	#13093986	1	1	yes	characteristic
212	C₂×C₄	#13093999	1	1	yes	characteristic
213	C₂×C₄	#13093999	1	1	yes	characteristic
214	C₂×C₄	#13094013	1	1	yes	characteristic
215	C₂×C₄	#13094020	1	1	yes	characteristic
216	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
217	C₂×C₄	#13094030	1	2	yes	—
218	C₂×C₄	#13094053	1	4	yes	—
219	C₈	—	2	2	no	—
220	C₈	—	2	2	no	—
221	C₈	—	8	2	no	—
222	C₈	—	94	4	no	—
223	C₈	—	188	2	no	—
224	C₂²	#15689024	1	1	yes	characteristic
225	C₂²	#15689193	1	2	yes	—
226	C₂²	#15689229	1	2	yes	—
227	C₂²	#15689239	1	2	yes	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	376	2	no	—
231	C₄	—	188	4	no	—
232	C₄	#15689086	1	1	yes	characteristic
233	C₄	#15689089	1	1	yes	characteristic
234	C₄	#15689193	1	2	yes	—
235	C₄	#15689382	1	2	yes	—
236	C₄	#15689514	1	2	yes	—
237	C₂	#20242258	1	4	yes	—
238	C₂	#20244185	1	1	yes	characteristic
239	C₂	#20244257	1	1	yes	characteristic
240	C₂	#20244274	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#20244323

C₂

yes

maximal

C₂×#15688853

C₂

yes

maximal

C₂×#15688845

C₂

yes

maximal, characteristic

C₂×C₄₇×#334

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

C₄

yes

characteristic

C₂×C₄×Dic₉₄

C₂²

yes

—

C₄×Dic₁₈₈

—

C₄×Dic₁₈₈

—

C₂×#13093958

C₄

yes

characteristic

C₂×#13093949

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#334

—

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

D₄

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

#13093958

—

#13093949

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

M₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

#41

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

C₂³×C₄₇

C₄×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

#9664

—

maximal, Sylow

104

C₂²×C₄₇

#390

yes

characteristic

105

C₂²×C₄₇

#435

yes

—

106

C₂²×C₄₇

#441

yes

—

107

C₂²×C₄₇

#443

yes

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#407

yes

characteristic

111

C₄×C₄₇

#408

yes

characteristic

112

C₄×C₄₇

#435

yes

—

113

C₄×C₄₇

#470

yes

—

114

C₄×C₄₇

#497

yes

—

115

Dic₄₇

—

116

Dic₄₇

—

117

C₂×C₄×Q₁₆

—

118

#1984

—

119

C₂×#334

D₄₇

yes

characteristic

120

C₂×Q₈⋊C₈

—

121

C₂×#322

—

122

C₂×C₄₇

#1587

yes

—

123

C₂×C₄₇

#1955

yes

characteristic

124

C₂×C₄₇

#1971

yes

characteristic

125

C₂×C₄₇

#1974

yes

characteristic

126

C₂²×Q₁₆

—

127

C₂×C₄×Q₈

—

128

C₄×Q₁₆

—

129

C₄×Q₁₆

—

130

C₂×#107

—

131

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

132

C₂×#103

—

133

C₂×C₄×C₈

—

134

C₂×C₄×C₈

—

135

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

136

#336

—

137

#334

—

138

Q₈⋊C₈

—

139

#322

—

140

C₄₇

#9664

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₂²×C₈

C₄×D₄₇

yes

characteristic

148

C₂²×C₈

C₄×D₄₇

yes

characteristic

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄²

—

156

C₂×C₄²

C₂²×D₄₇

yes

characteristic

157

#107

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

C₄×C₈

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

D₁₈₈

yes

—

166

C₄×C₈

C₂²⋊D₄₇

yes

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

176

C₂²×C₄

D₄×D₄₇

yes

characteristic

177

C₂²×C₄

#10625354

yes

characteristic

178

Q₁₆

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

188

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

188

—

192

C₄⋊C₄

—

188

—

193

C₄²

—

188

—

194

C₄²

—

188

—

195

C₄²

C₂×D₁₈₈

yes

characteristic

196

C₄²

D₄×D₄₇

yes

characteristic

197

C₄²

#10625354

yes

characteristic

198

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

199

C₂³

#13093986

yes

characteristic

200

Q₈

—

201

Q₈

—

202

Q₈

—

188

—

203

Q₈

—

188

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

188

—

207

C₂×C₄

—

188

—

208

C₂×C₄

—

188

—

209

C₂×C₄

—

188

—

210

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

211

C₂×C₄

#13093986

yes

characteristic

212

C₂×C₄

#13093999

yes

characteristic

213

C₂×C₄

#13093999

yes

characteristic

214

C₂×C₄

#13094013

yes

characteristic

215

C₂×C₄

#13094020

yes

characteristic

216

C₂×C₄

M₁₆×D₄₇

yes

—

217

C₂×C₄

#13094030

yes

—

218

C₂×C₄

#13094053

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

188

—

224

C₂²

#15689024

yes

characteristic

225

C₂²

#15689193

yes

—

226

C₂²

#15689229

yes

—

227

C₂²

#15689239

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

376

—

231

C₄

—

188

—

232

C₄

#15689086

yes

characteristic

233

C₄

#15689089

yes

characteristic

234

C₄

#15689193

yes

—

235

C₄

#15689382

yes

—

236

C₄

#15689514

yes

—

237

C₂

#20242258

yes

—

238

C₂

#20244185

yes

characteristic

239

C₂

#20244257

yes

characteristic

240

C₂

#20244274

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#334	C₂
socle, prime radical	C₂³×C₄₇	C₄×D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#334	D₄₇
hypocenter	C₄₇	#9664
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

subgroup

G/H

center

C₂²×C₄

D₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#334

C₂

socle, prime radical

C₂³×C₄₇

C₄×D₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

N	H ≅ G/N	type
140. C₄₇	#9664	semidirect

H ≅ G/N

type

140. C₄₇

#9664

semidirect

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

subgroup	index
C₂×C₄×Dic₁₈₈	2
#20244323	2
C₂×#15688853	2
C₂×#15688845	2
C₂×C₄₇×#334	2
#9664	47

subgroup

index

C₂×C₄×Dic₁₈₈

C₂×C₄₇×#334

Subgroups — #26115178

Conjugacy classes of subgroups

Complements

Maximal subgroups