Group #26115023 — subgroups

Subgroups — #26115023

Order 12032.

294 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 109 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	#20243525	C₂	1	1	yes	maximal, characteristic
2	#20243257	C₂	1	1	yes	maximal, characteristic
3	#20242164	C₂	1	1	yes	maximal, characteristic
4	#20242159	C₂	1	1	yes	maximal, characteristic
5	#20242134	C₂	1	1	yes	maximal, characteristic
6	#20241291	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1303	C₂	1	1	yes	maximal, characteristic
8	#15689176	C₂²	1	1	yes	characteristic
9	#15689147	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13093935	—	2	1	no	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15688887	—	2	1	no	—
14	#15688887	—	2	1	no	—
15	#15688878	—	2	1	no	—
16	#15688875	—	2	2	no	—
17	#15688875	C₄	1	2	yes	complemented
18	#15688874	—	2	2	no	—
19	#15688873	C₄	1	2	yes	complemented
20	C₄₇×#431	C₂²	1	1	yes	characteristic
21	C₄₇×#423	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#10625329	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	—	2	1	no	—
25	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
27	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
29	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
30	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
33	#13093935	—	4	2	no	—
34	C₄×C₄₇⋊C₈	—	2	1	no	—
35	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₄₇⋊C₈	Q₈	1	1	yes	characteristic
38	C₄×C₄₇⋊C₈	Q₈	1	1	yes	characteristic
39	C₂×M₁₆×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₂×C₄²×C₄₇	—	2	1	no	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	1	no	—
44	C₄⋊C₈×C₄₇	—	2	1	no	—
45	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₂²⋊C₈×C₄₇	—	2	1	no	—
47	C₄×C₈×C₄₇	—	2	1	no	—
48	#95×C₄₇	Q₈	1	2	yes	—
49	C₂²×C₄×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
53	M₁₆×C₄₇	—	4	1	no	—
54	M₁₆×C₄₇	—	4	1	no	—
55	C₂×C₈×C₄₇	—	2	2	no	—
56	C₂×C₈×C₄₇	—	4	1	no	—
57	C₄⋊C₄×C₄₇	—	4	2	no	—
58	C₄²×C₄₇	—	4	1	no	—
59	C₄²×C₄₇	—	4	1	no	—
60	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₄₇	#41	1	1	yes	characteristic
64	#10625329	—	4	1	no	—
65	#10625329	—	4	1	no	—
66	C₂×C₄₇⋊C₈	—	2	1	no	—
67	C₂×C₄₇⋊C₈	—	2	1	no	—
68	C₂×C₄₇⋊C₈	—	2	1	no	—
69	C₂×C₄₇⋊C₈	—	2	1	no	—
70	C₂×C₄₇⋊C₈	—	2	2	no	—
71	C₂×C₄₇⋊C₈	—	2	2	no	—
72	C₂×C₄₇⋊C₈	—	4	1	no	—
73	C₂×C₄₇⋊C₈	—	4	1	no	—
74	C₂×C₄₇⋊C₈	—	4	1	no	—
75	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
79	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	4	1	no	—
82	C₂×C₄×C₄₇	—	4	2	no	—
83	C₂×C₄×C₄₇	—	4	2	no	—
84	C₂×C₄×C₄₇	—	4	2	no	—
85	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
88	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
90	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
92	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
93	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
95	C₈×C₄₇	—	4	2	no	—
96	C₈×C₄₇	—	8	1	no	—
97	C₄₇⋊C₈	—	2	1	no	—
98	C₄₇⋊C₈	—	2	1	no	—
99	C₄₇⋊C₈	—	2	1	no	—
100	C₄₇⋊C₈	—	2	1	no	—
101	C₄₇⋊C₈	—	4	2	no	—
102	C₄₇⋊C₈	—	4	2	no	—
103	C₄₇⋊C₈	—	8	1	no	—
104	#9632	—	47	1	no	maximal, Sylow
105	C₂²×C₄₇	—	2	1	no	—
106	C₂²×C₄₇	—	2	1	no	—
107	C₂²×C₄₇	#389	1	1	yes	characteristic
108	C₂²×C₄₇	#478	1	1	yes	characteristic
109	C₂²×C₄₇	#479	1	1	yes	characteristic
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	2	1	no	—
112	C₄×C₄₇	—	2	1	no	—
113	C₄×C₄₇	—	8	2	no	—
114	C₄×C₄₇	#427	1	1	yes	characteristic
115	C₄×C₄₇	#428	1	1	yes	characteristic
116	C₄×C₄₇	#444	1	2	yes	—
117	C₄×C₄₇	#463	1	1	yes	characteristic
118	C₄×C₄₇	#464	1	1	yes	characteristic
119	#1837	—	47	1	no	—
120	#1770	—	47	1	no	—
121	#1571	—	47	1	no	—
122	#1570	—	47	1	no	—
123	#1564	—	47	1	no	—
124	#1303	—	47	1	no	—
125	#1303	D₄₇	1	1	yes	characteristic
126	C₂×C₄₇	—	2	1	no	—
127	C₂×C₄₇	—	2	1	no	—
128	C₂×C₄₇	#1946	1	1	yes	characteristic
129	C₂×C₄₇	#1949	1	1	yes	characteristic
130	C₂×C₄₇	#1953	1	1	yes	characteristic
131	#431	—	47	1	no	—
132	#431	C₂×D₄₇	1	1	yes	characteristic
133	#423	—	47	1	no	—
134	#423	C₂×D₄₇	1	1	yes	characteristic
135	C₂×C₄⋊C₈	—	47	1	no	—
136	C₂×#97	—	94	1	no	—
137	C₂×C₄×C₈	—	47	1	no	—
138	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
139	#341	—	94	1	no	—
140	#341	—	94	1	no	—
141	#336	—	94	1	no	—
142	#335	—	47	2	no	—
143	#335	—	94	2	no	—
144	#334	—	47	2	no	—
145	#334	—	94	2	no	—
146	C₄₇	#9632	1	1	yes	characteristic, complemented, Sylow
147	C₂×M₁₆	—	2	1	no	—
148	C₂×M₁₆	—	94	1	no	—
149	C₂²×C₈	—	47	1	no	—
150	C₂²×C₈	—	47	1	no	—
151	C₂²×C₈	—	94	1	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄²	—	2	1	no	—
154	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
155	C₄⋊C₈	—	2	1	no	—
156	C₄⋊C₈	—	2	1	no	—
157	C₄⋊C₈	—	47	2	no	—
158	C₄⋊C₈	—	47	2	no	—
159	C₄⋊C₈	—	94	1	no	—
160	C₄⋊C₈	—	94	1	no	—
161	C₄⋊C₈	—	94	1	no	—
162	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
163	C₂²⋊C₈	—	2	1	no	—
164	C₂²⋊C₈	—	94	1	no	—
165	#97	—	188	2	no	—
166	C₄×C₈	—	2	1	no	—
167	C₄×C₈	—	47	1	no	—
168	C₄×C₈	—	47	1	no	—
169	C₄×C₈	—	47	1	no	—
170	C₄×C₈	—	47	1	no	—
171	C₄×C₈	—	94	1	no	—
172	#95	Dic₉₄	1	2	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
175	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
176	C₂²×C₄	#10625352	1	1	yes	characteristic
177	M₁₆	—	4	1	no	—
178	M₁₆	—	4	1	no	—
179	M₁₆	—	188	1	no	—
180	M₁₆	—	188	1	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	47	1	no	—
184	C₂×C₈	—	47	1	no	—
185	C₂×C₈	—	47	1	no	—
186	C₂×C₈	—	47	1	no	—
187	C₂×C₈	—	94	1	no	—
188	C₂×C₈	—	94	1	no	—
189	C₂×C₈	—	94	1	no	—
190	C₂×C₈	—	94	1	no	—
191	C₂×C₈	—	94	2	no	—
192	C₂×C₈	—	94	2	no	—
193	C₂×C₈	—	188	1	no	—
194	C₂×C₈	—	188	1	no	—
195	C₂×C₈	—	188	1	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄²	—	4	1	no	—
198	C₄²	—	4	1	no	—
199	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
200	C₄²	#10625350	1	1	yes	characteristic
201	C₄²	D₄×D₄₇	1	1	yes	characteristic
202	C₄²	Q₈×D₄₇	1	1	yes	characteristic
203	C₂³	#13094001	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
210	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
211	C₂×C₄	C₄×Dic₉₄	1	1	yes	characteristic
212	C₂×C₄	#13093997	1	1	yes	characteristic
213	C₂×C₄	#13094014	1	1	yes	characteristic
214	C₂×C₄	#13094023	1	1	yes	characteristic
215	C₂×C₄	#13094045	1	1	yes	characteristic
216	C₂×C₄	#13094045	1	1	yes	characteristic
217	C₂×C₄	#13094048	1	1	yes	characteristic
218	C₂×C₄	#13094056	1	1	yes	characteristic
219	C₈	—	4	2	no	—
220	C₈	—	8	1	no	—
221	C₈	—	94	1	no	—
222	C₈	—	94	1	no	—
223	C₈	—	94	1	no	—
224	C₈	—	94	1	no	—
225	C₈	—	376	1	no	—
226	C₈	—	188	2	no	—
227	C₈	—	188	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#15689020	1	1	yes	characteristic
231	C₂²	#15689425	1	1	yes	characteristic
232	C₂²	#15689428	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	2	1	no	—
236	C₄	—	8	2	no	—
237	C₄	#15689158	1	1	yes	characteristic
238	C₄	#15689164	1	1	yes	characteristic
239	C₄	#15689242	1	2	yes	—
240	C₄	#15689337	1	1	yes	characteristic
241	C₄	#15689348	1	1	yes	characteristic
242	C₂	—	2	1	no	—
243	C₂	—	2	1	no	—
244	C₂	#20244140	1	1	yes	characteristic
245	C₂	#20244155	1	1	yes	characteristic
246	C₂	#20244177	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20243525

C₂

yes

maximal, characteristic

#20243257

C₂

yes

maximal, characteristic

#20242164

C₂

yes

maximal, characteristic

#20242159

C₂

yes

maximal, characteristic

#20242134

C₂

yes

maximal, characteristic

#20241291

C₂

yes

maximal, characteristic

C₄₇×#1303

C₂

yes

maximal, characteristic

#15689176

C₂²

yes

characteristic

#15689147

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×#13093935

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

—

C₄

yes

complemented

#15688874

—

#15688873

C₄

yes

complemented

C₄₇×#431

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

D₄

yes

characteristic

C₂²×C₄₇⋊C₈

D₄

yes

characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₄₇⋊C₈

Q₈

yes

characteristic

C₄×C₄₇⋊C₈

Q₈

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

#95×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×Q₈

yes

C₄²×C₄₇

yes

—

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂³×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

C₂×C₄×C₄₇

C₄×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₄⋊Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

100

C₄₇⋊C₈

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

—

104

#9632

—

maximal, Sylow

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

#389

yes

characteristic

108

C₂²×C₄₇

#478

yes

characteristic

109

C₂²×C₄₇

#479

yes

characteristic

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

#427

yes

characteristic

115

C₄×C₄₇

#428

yes

characteristic

116

C₄×C₄₇

#444

yes

—

117

C₄×C₄₇

#463

yes

characteristic

118

C₄×C₄₇

#464

yes

characteristic

119

#1837

—

120

#1770

—

121

#1571

—

122

#1570

—

123

#1564

—

124

#1303

—

125

#1303

D₄₇

yes

characteristic

126

C₂×C₄₇

—

127

C₂×C₄₇

—

128

C₂×C₄₇

#1946

yes

characteristic

129

C₂×C₄₇

#1949

yes

characteristic

130

C₂×C₄₇

#1953

yes

characteristic

131

#431

—

132

#431

C₂×D₄₇

yes

characteristic

133

#423

—

134

#423

C₂×D₄₇

yes

characteristic

135

C₂×C₄⋊C₈

—

136

C₂×#97

—

137

C₂×C₄×C₈

—

138

C₄×C₄⋊C₄

C₂×D₄₇

yes

characteristic

139

#341

—

140

#341

—

141

#336

—

142

#335

—

143

#335

—

144

#334

—

145

#334

—

146

C₄₇

#9632

yes

characteristic, complemented, Sylow

147

C₂×M₁₆

—

148

C₂×M₁₆

—

149

C₂²×C₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₄₇

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

—

162

C₄⋊C₈

C₄×D₄₇

yes

—

163

C₂²⋊C₈

—

164

C₂²⋊C₈

—

165

#97

—

188

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₄×C₈

—

172

#95

Dic₉₄

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

175

C₂²×C₄

D₄×D₄₇

yes

characteristic

176

C₂²×C₄

#10625352

yes

characteristic

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

188

—

180

M₁₆

—

188

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

188

—

194

C₂×C₈

—

188

—

195

C₂×C₈

—

188

—

196

C₄⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

C₂×C₄×D₄₇

yes

characteristic

200

C₄²

#10625350

yes

characteristic

201

C₄²

D₄×D₄₇

yes

characteristic

202

C₄²

Q₈×D₄₇

yes

characteristic

203

C₂³

#13094001

yes

characteristic

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₄⋊C₄×D₄₇

yes

characteristic

210

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

characteristic

211

C₂×C₄

C₄×Dic₉₄

yes

characteristic

212

C₂×C₄

#13093997

yes

characteristic

213

C₂×C₄

#13094014

yes

characteristic

214

C₂×C₄

#13094023

yes

characteristic

215

C₂×C₄

#13094045

yes

characteristic

216

C₂×C₄

#13094045

yes

characteristic

217

C₂×C₄

#13094048

yes

characteristic

218

C₂×C₄

#13094056

yes

characteristic

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

376

—

226

C₈

—

188

—

227

C₈

—

188

—

228

C₂²

—

229

C₂²

—

230

C₂²

#15689020

yes

characteristic

231

C₂²

#15689425

yes

characteristic

232

C₂²

#15689428

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#15689158

yes

characteristic

238

C₄

#15689164

yes

characteristic

239

C₄

#15689242

yes

—

240

C₄

#15689337

yes

characteristic

241

C₄

#15689348

yes

characteristic

242

C₂

—

243

C₂

—

244

C₂

#20244140

yes

characteristic

245

C₂

#20244155

yes

characteristic

246

C₂

#20244177

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093997
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1303	C₂
socle	C₂²×C₄₇	#389
prime radical	C₂³×C₄₇	C₂²⋊Q₈
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1303	D₄₇
hypocenter	C₄₇	#9632
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#13093997

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1303

C₂

socle

C₂²×C₄₇

#389

prime radical

C₂³×C₄₇

C₂²⋊Q₈

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
17. #15688875	C₄	semidirect
19. #15688873	C₄	semidirect
146. C₄₇	#9632	semidirect

H ≅ G/N

type

17. #15688875

C₄

semidirect

19. #15688873

C₄

semidirect

146. C₄₇

#9632

semidirect

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

subgroup	index
#20243525	2
#20243257	2
#20242164	2
#20242159	2
#20242134	2
#20241291	2
C₄₇×#1303	2
#9632	47

subgroup

index

C₄₇×#1303

Subgroups — #26115023

Conjugacy classes of subgroups

Complements

Maximal subgroups