Group #26110147 — subgroups

Subgroups — #26110147

Order 12032.

410 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 155 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	#20252469	C₂	1	1	yes	maximal, characteristic
2	#20244325	C₂	1	1	yes	maximal, characteristic
3	#20242140	C₂	1	2	yes	maximal
4	#20241226	C₂	1	2	yes	maximal
5	C₄×#101×C₄₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₄₇⋊C₈	—	2	2	no	—
7	Q₈×C₄₇⋊C₈	—	2	2	no	—
8	#15689176	—	2	2	no	—
9	#15689176	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	#15688878	—	2	2	no	—
13	#15688876	—	2	2	no	—
14	#15688874	—	2	2	no	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#101×C₄₇	C₄	1	1	yes	characteristic
17	C₂×#101×C₄₇	C₄	1	1	yes	characteristic
18	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#343	C₄	1	2	yes	—
20	C₂²×C₄₇⋊C₈	—	2	1	no	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
26	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄×C₄₇⋊C₈	—	2	4	no	—
29	C₄×C₄₇⋊C₈	—	2	2	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
34	C₄×Q₈×C₄₇	—	2	2	no	—
35	C₄×Q₈×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
38	C₂×C₄²×C₄₇	D₄	1	2	yes	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	#101×C₄₇	—	2	2	no	—
41	#101×C₄₇	C₈	1	4	yes	complemented
42	#97×C₄₇	—	2	2	no	—
43	C₄×C₈×C₄₇	—	2	2	no	—
44	C₂×Q₈×C₄₇	—	2	2	no	—
45	C₂×Q₈×C₄₇	—	2	2	no	—
46	C₂×Q₈×C₄₇	C₂×C₈	1	2	yes	—
47	C₂×Q₈×C₄₇	M₁₆	1	2	yes	—
48	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
53	M₁₆×C₄₇	—	2	2	no	—
54	M₁₆×C₄₇	—	2	2	no	—
55	M₁₆×C₄₇	—	2	2	no	—
56	M₁₆×C₄₇	C₂×C₈	1	4	yes	—
57	C₂×C₈×C₄₇	—	2	2	no	—
58	C₂×C₈×C₄₇	—	2	2	no	—
59	C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₄⋊C₄×C₄₇	—	2	4	no	—
61	C₄²×C₄₇	—	2	2	no	—
62	C₄²×C₄₇	—	2	2	no	—
63	C₄²×C₄₇	C₂×D₄	1	2	yes	—
64	C₄²×C₄₇	#41	1	2	yes	—
65	C₂×C₄₇⋊C₈	—	2	2	no	—
66	C₂×C₄₇⋊C₈	—	2	2	no	—
67	C₂×C₄₇⋊C₈	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	4	1	no	—
69	C₂×C₄₇⋊C₈	—	4	1	no	—
70	C₂×C₄₇⋊C₈	—	4	2	no	—
71	C₂×C₄₇⋊C₈	—	4	1	no	—
72	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
73	Q₈×C₄₇	—	2	4	no	—
74	Q₈×C₄₇	—	2	4	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	1	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	4	1	no	—
81	C₂×C₄×C₄₇	—	4	2	no	—
82	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	—
83	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
85	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
87	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#131	1	2	yes	—
90	C₈×C₄₇	—	2	4	no	—
91	C₈×C₄₇	—	4	2	no	—
92	C₄₇⋊C₈	—	4	2	no	—
93	C₄₇⋊C₈	—	4	2	no	—
94	C₄₇⋊C₈	—	4	2	no	—
95	C₄₇⋊C₈	—	8	1	no	—
96	#8836	—	47	1	no	maximal, Sylow
97	C₂²×C₄₇	—	2	1	no	—
98	C₂²×C₄₇	—	2	1	no	—
99	C₂²×C₄₇	#385	1	1	yes	characteristic
100	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
101	C₂²×C₄₇	#424	1	1	yes	characteristic
102	C₄×C₄₇	—	2	4	no	—
103	C₄×C₄₇	—	2	1	no	—
104	C₄×C₄₇	—	2	2	no	—
105	C₄×C₄₇	—	4	2	no	—
106	C₄×C₄₇	C₈×D₄	1	2	yes	—
107	C₄×C₄₇	#435	1	2	yes	—
108	C₄×C₄₇	#454	1	1	yes	characteristic
109	C₄×C₄₇	#456	1	1	yes	characteristic
110	#2982	—	47	1	no	—
111	#1984	—	47	1	no	—
112	C₄×#101	D₄₇	1	1	yes	characteristic
113	#1565	—	47	2	no	—
114	#1278	—	47	2	no	—
115	C₂×C₄₇	—	2	1	no	—
116	C₂×C₄₇	—	2	1	no	—
117	C₂×C₄₇	#1850	1	1	yes	characteristic
118	C₂×C₄₇	#1857	1	1	yes	characteristic
119	C₂×C₄₇	#1858	1	1	yes	characteristic
120	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
121	C₈×Q₈	—	94	2	no	—
122	C₈×Q₈	—	94	2	no	—
123	#431	—	47	2	no	—
124	#431	—	94	2	no	—
125	C₂×C₄⋊C₈	—	47	1	no	—
126	C₂×#101	Dic₄₇	1	1	yes	characteristic
127	C₂×#101	Dic₄₇	1	1	yes	characteristic
128	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
129	C₂×C₄×C₈	—	47	1	no	—
130	#343	Dic₄₇	1	2	yes	—
131	#336	—	94	2	no	—
132	#335	—	94	2	no	—
133	#334	—	94	2	no	—
134	C₄₇	#8836	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
136	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
137	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
138	C₂²×C₈	—	94	1	no	—
139	C₂²×C₈	—	94	1	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
143	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
144	C₂×C₄²	D₁₈₈	1	2	yes	—
145	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
146	C₄⋊C₈	—	47	2	no	—
147	C₄⋊C₈	—	47	2	no	—
148	C₄⋊C₈	—	94	2	no	—
149	C₄⋊C₈	—	94	2	no	—
150	C₄⋊C₈	—	94	2	no	—
151	#101	—	2	2	no	—
152	#101	C₄₇⋊C₈	1	4	yes	complemented
153	C₂²⋊C₈	—	94	2	no	—
154	#97	—	2	2	no	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	94	4	no	—
157	C₄×C₈	—	94	2	no	—
158	C₄×C₈	—	94	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₂×C₄₇⋊C₈	1	2	yes	—
162	C₂×Q₈	#10625329	1	2	yes	—
163	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
164	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
165	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
167	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
168	M₁₆	—	2	2	no	—
169	M₁₆	—	2	2	no	—
170	M₁₆	—	2	2	no	—
171	M₁₆	C₂×C₄₇⋊C₈	1	4	yes	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	94	2	no	—
175	C₂×C₈	—	94	2	no	—
176	C₂×C₈	—	94	2	no	—
177	C₂×C₈	—	188	2	no	—
178	C₂×C₈	—	188	1	no	—
179	C₂×C₈	—	188	1	no	—
180	C₂×C₈	—	188	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	D₄×D₄₇	1	2	yes	—
186	C₄²	#10625352	1	2	yes	—
187	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₄⋊(C₄₇⋊C₈)	1	4	yes	—
198	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
199	C₂×C₄	#13093994	1	1	yes	characteristic
200	C₂×C₄	#13094001	1	2	yes	—
201	C₂×C₄	#13094008	1	1	yes	characteristic
202	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
203	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
204	C₂×C₄	#13094031	1	2	yes	—
205	C₈	—	2	4	no	—
206	C₈	—	4	2	no	—
207	C₈	—	376	1	no	—
208	C₈	—	188	2	no	—
209	C₈	—	188	2	no	—
210	C₈	—	188	2	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#15688998	1	1	yes	characteristic
214	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
215	C₂²	#15689150	1	1	yes	characteristic
216	C₄	—	2	4	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	2	no	—
220	C₄	D₄×C₄₇⋊C₈	1	2	yes	—
221	C₄	#15689195	1	2	yes	—
222	C₄	#15689298	1	1	yes	characteristic
223	C₄	#15689308	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	#20243568	1	1	yes	characteristic
227	C₂	#20243605	1	1	yes	characteristic
228	C₂	#20243610	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252469

C₂

yes

maximal, characteristic

#20244325

C₂

yes

maximal, characteristic

#20242140

C₂

yes

maximal

#20241226

C₂

yes

maximal

C₄×#101×C₄₇

C₂

yes

maximal, characteristic

Q₈×C₄₇⋊C₈

—

Q₈×C₄₇⋊C₈

—

#15689176

—

#15689176

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₂×#101×C₄₇

C₄

yes

characteristic

C₂×#101×C₄₇

C₄

yes

characteristic

C₄×M₁₆×C₄₇

C₂²

yes

—

C₄₇×#343

C₄

yes

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₄₇

Q₈

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#101×C₄₇

—

#101×C₄₇

C₈

yes

complemented

#97×C₄₇

—

C₄×C₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₈

yes

—

C₂×Q₈×C₄₇

M₁₆

yes

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₈

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

#131

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

#8836

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#385

yes

characteristic

100

C₂²×C₄₇

C₂×C₄⋊C₈

yes

characteristic

101

C₂²×C₄₇

#424

yes

characteristic

102

C₄×C₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

—

106

C₄×C₄₇

C₈×D₄

yes

—

107

C₄×C₄₇

#435

yes

—

108

C₄×C₄₇

#454

yes

characteristic

109

C₄×C₄₇

#456

yes

characteristic

110

#2982

—

111

#1984

—

112

C₄×#101

D₄₇

yes

characteristic

113

#1565

—

114

#1278

—

115

C₂×C₄₇

—

116

C₂×C₄₇

—

117

C₂×C₄₇

#1850

yes

characteristic

118

C₂×C₄₇

#1857

yes

characteristic

119

C₂×C₄₇

#1858

yes

characteristic

120

C₂×C₄×Q₈

C₂×D₄₇

yes

characteristic

121

C₈×Q₈

—

122

C₈×Q₈

—

123

#431

—

124

#431

—

125

C₂×C₄⋊C₈

—

126

C₂×#101

Dic₄₇

yes

characteristic

127

C₂×#101

Dic₄₇

yes

characteristic

128

C₄×M₁₆

C₂×D₄₇

yes

—

129

C₂×C₄×C₈

—

130

#343

Dic₄₇

yes

—

131

#336

—

132

#335

—

133

#334

—

134

C₄₇

#8836

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

C₂×Dic₄₇

yes

characteristic

136

C₂×M₁₆

C₂×Dic₄₇

yes

—

137

C₂×M₁₆

C₂×Dic₄₇

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₂×C₄⋊C₄

Dic₉₄

yes

—

143

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

characteristic

144

C₂×C₄²

D₁₈₈

yes

—

145

C₂×C₄²

C₂²×D₄₇

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#101

—

152

#101

C₄₇⋊C₈

yes

complemented

153

C₂²⋊C₈

—

154

#97

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₂×C₄₇⋊C₈

yes

—

162

C₂×Q₈

#10625329

yes

—

163

C₂²×C₄

C₄⋊Dic₄₇

yes

—

164

C₂²×C₄

C₄⋊Dic₄₇

yes

—

165

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

166

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

167

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

M₁₆

C₂×C₄₇⋊C₈

yes

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

188

—

178

C₂×C₈

—

188

—

179

C₂×C₈

—

188

—

180

C₂×C₈

—

188

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

D₄×D₄₇

yes

—

186

C₄²

#10625352

yes

—

187

C₂³

C₂×C₄⋊Dic₄₇

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₄⋊(C₄₇⋊C₈)

yes

—

198

C₂×C₄

D₄×Dic₄₇

yes

—

199

C₂×C₄

#13093994

yes

characteristic

200

C₂×C₄

#13094001

yes

—

201

C₂×C₄

#13094008

yes

characteristic

202

C₂×C₄

C₂²×C₄₇⋊C₈

yes

characteristic

203

C₂×C₄

C₂×#10625329

yes

characteristic

204

C₂×C₄

#13094031

yes

—

205

C₈

—

206

C₈

—

207

C₈

—

376

—

208

C₈

—

188

—

209

C₈

—

188

—

210

C₈

—

188

—

211

C₂²

—

212

C₂²

—

213

C₂²

#15688998

yes

characteristic

214

C₂²

C₂×C₄⋊(C₄₇⋊C₈)

yes

characteristic

215

C₂²

#15689150

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

D₄×C₄₇⋊C₈

yes

—

221

C₄

#15689195

yes

—

222

C₄

#15689298

yes

characteristic

223

C₄

#15689308

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#20243568

yes

characteristic

227

C₂

#20243605

yes

characteristic

228

C₂

#20243610

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#101×C₄₇	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂³×C₄₇	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#101	D₄₇
hypocenter	C₄₇	#8836
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

subgroup

G/H

center

C₂×C₄

#13093994

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×#101×C₄₇

C₂

socle

C₂²×C₄₇

#385

prime radical

C₂³×C₄₇

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

N	H ≅ G/N	type
41. #101×C₄₇	C₈	semidirect
134. C₄₇	#8836	semidirect
152. #101	C₄₇⋊C₈	semidirect

H ≅ G/N

type

41. #101×C₄₇

C₈

semidirect

134. C₄₇

#8836

semidirect

152. #101

C₄₇⋊C₈

semidirect

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

subgroup	index
#20252469	2
#20244325	2
#20242140	2
#20241226	2
C₄×#101×C₄₇	2
#8836	47

subgroup

index

C₄×#101×C₄₇

Subgroups — #26110147

Conjugacy classes of subgroups

Complements

Maximal subgroups