Group #26115386 — subgroups

Subgroups — #26115386

Order 12032.

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

normal subgroups only

This group has 486 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	#20251766	C₂	1	1	yes	maximal, characteristic
2	#20243540	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688870	C₂	1	2	yes	maximal
4	C₂×#15688868	C₂	1	2	yes	maximal
5	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×#13094024	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
10	#15689029	—	2	2	no	—
11	#15689029	—	2	1	no	—
12	#15689029	—	2	1	no	—
13	#15688989	C₄	1	4	yes	—
14	#15688870	—	2	4	no	—
15	#15688868	—	2	4	no	—
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×#97×C₄₇	—	2	1	no	—
18	C₄³×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	—	2	1	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×Dic₉₄	—	2	1	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	#13094024	—	2	2	no	—
24	#13094024	—	2	2	no	—
25	#13094024	—	2	2	no	—
26	#13094024	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄⋊Dic₄₇	—	2	1	no	—
29	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	—	4	4	no	—
34	C₄₇⋊#95	—	2	4	no	—
35	C₄₇⋊#95	—	2	4	no	—
36	C₂²×C₈×C₄₇	—	2	2	no	—
37	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₇	D₄	1	2	yes	—
39	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄⋊C₈×C₄₇	D₄	1	4	yes	—
44	#97×C₄₇	—	4	2	no	—
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂²×Dic₄₇	—	2	2	no	—
52	C₂×Dic₉₄	—	4	2	no	—
53	C₂×Dic₉₄	—	4	1	no	—
54	C₂×Dic₉₄	—	4	1	no	—
55	C₂×Dic₉₄	—	4	2	no	—
56	C₂×Dic₉₄	—	4	1	no	—
57	C₂×Dic₉₄	—	4	2	no	—
58	C₂×Dic₉₄	—	4	1	no	—
59	C₂×Dic₉₄	—	4	2	no	—
60	C₂×C₈×C₄₇	—	2	4	no	—
61	C₂×C₈×C₄₇	—	4	2	no	—
62	C₂×C₈×C₄₇	—	4	2	no	—
63	C₄²×C₄₇	—	2	4	no	—
64	C₄²×C₄₇	—	2	2	no	—
65	C₄²×C₄₇	—	2	2	no	—
66	C₄²×C₄₇	—	2	1	no	—
67	C₄²×C₄₇	—	2	2	no	—
68	C₄²×C₄₇	—	2	1	no	—
69	C₄²×C₄₇	C₂×D₄	1	2	yes	—
70	C₄²×C₄₇	#41	1	2	yes	—
71	C₄⋊Dic₄₇	—	2	4	no	—
72	C₄⋊Dic₄₇	—	2	4	no	—
73	C₄⋊Dic₄₇	—	4	2	no	—
74	C₄⋊Dic₄₇	—	4	1	no	—
75	C₄⋊Dic₄₇	—	4	1	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	4	4	no	—
78	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	2	no	—
83	C₂×C₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	2	2	no	—
85	C₂×C₄×C₄₇	#101	1	4	yes	—
86	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₄₇	#121	1	2	yes	—
88	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#135	1	2	yes	—
91	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
94	C₂×C₄×C₄₇	#137	1	2	yes	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	C₂×Dic₄₇	—	4	2	no	—
99	C₂×Dic₄₇	—	4	4	no	—
100	Dic₉₄	—	8	2	no	—
101	Dic₉₄	—	8	2	no	—
102	Dic₉₄	—	8	2	no	—
103	Dic₉₄	—	8	1	no	—
104	Dic₉₄	—	8	1	no	—
105	C₈×C₄₇	—	4	4	no	—
106	C₄₇⋊C₈	—	8	2	no	—
107	#9708	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	#390	1	1	yes	characteristic
109	C₂²×C₄₇	C₂×#101	1	2	yes	—
110	C₂²×C₄₇	#416	1	1	yes	characteristic
111	C₂²×C₄₇	#417	1	1	yes	characteristic
112	C₂²×C₄₇	#417	1	2	yes	—
113	C₄×C₄₇	—	2	4	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	4	2	no	—
116	C₄×C₄₇	#463	1	2	yes	—
117	C₄×C₄₇	#464	1	2	yes	—
118	C₄×C₄₇	#489	1	2	yes	—
119	C₄×C₄₇	#496	1	1	yes	characteristic
120	C₄×C₄₇	#497	1	1	yes	characteristic
121	Dic₄₇	—	8	2	no	—
122	Dic₄₇	—	8	2	no	—
123	#2862	—	47	1	no	—
124	#1842	—	47	1	no	—
125	#1767	D₄₇	1	1	yes	characteristic
126	C₂×#332	—	47	2	no	—
127	C₂×#332	—	47	2	no	—
128	C₂×C₄₇	#1552	1	2	yes	—
129	C₂×C₄₇	#1561	1	2	yes	—
130	C₂×C₄₇	#1959	1	1	yes	characteristic
131	C₂×C₄₇	#1966	1	1	yes	characteristic
132	C₂×C₄₇	#1983	1	1	yes	characteristic
133	C₂×C₄⋊Q₈	—	47	1	no	—
134	C₂×C₄⋊Q₈	—	47	1	no	—
135	C₂×C₄⋊C₈	—	47	2	no	—
136	C₂×C₄⋊C₈	—	94	2	no	—
137	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
138	C₂×#97	—	2	1	no	—
139	#391	—	94	2	no	—
140	#391	—	94	1	no	—
141	#391	—	94	1	no	—
142	#382	—	47	4	no	—
143	C₄³	C₂×D₄₇	1	1	yes	characteristic
144	#336	—	2	1	no	—
145	#332	—	94	4	no	—
146	#332	—	94	4	no	—
147	C₄₇	#9708	1	1	yes	characteristic, complemented, Sylow
148	C₂²×Q₈	—	94	1	no	—
149	C₂²×Q₈	—	94	1	no	—
150	C₂²×C₈	—	2	2	no	—
151	C₂²×C₈	—	94	2	no	—
152	C₄⋊Q₈	—	94	2	no	—
153	C₄⋊Q₈	—	94	2	no	—
154	C₄⋊Q₈	—	94	2	no	—
155	C₄⋊Q₈	—	94	2	no	—
156	C₂×C₄⋊C₄	—	47	2	no	—
157	C₂×C₄⋊C₄	—	47	2	no	—
158	C₂×C₄⋊C₄	—	94	1	no	—
159	C₂×C₄⋊C₄	—	94	1	no	—
160	C₂×C₄²	C₄×D₄₇	1	2	yes	—
161	C₂×C₄²	D₁₈₈	1	2	yes	—
162	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
163	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
164	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	94	2	no	—
167	C₄⋊C₈	—	94	2	no	—
168	C₄⋊C₈	—	188	4	no	—
169	C₄⋊C₈	D₁₈₈	1	4	yes	—
170	#97	—	4	2	no	—
171	#95	—	94	4	no	—
172	#95	—	94	4	no	—
173	C₂×Q₈	—	188	2	no	—
174	C₂×Q₈	—	188	1	no	—
175	C₂×Q₈	—	188	1	no	—
176	C₂×Q₈	—	188	2	no	—
177	C₂×Q₈	—	188	1	no	—
178	C₂×Q₈	—	188	2	no	—
179	C₂×Q₈	—	188	1	no	—
180	C₂×Q₈	—	188	2	no	—
181	C₂²×C₄	—	94	2	no	—
182	C₂²×C₄	—	94	2	no	—
183	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
184	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
185	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
186	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	188	2	no	—
192	C₂×C₈	—	188	4	no	—
193	C₄⋊C₄	—	94	4	no	—
194	C₄⋊C₄	—	94	4	no	—
195	C₄⋊C₄	—	188	2	no	—
196	C₄⋊C₄	—	188	1	no	—
197	C₄⋊C₄	—	188	1	no	—
198	C₄²	—	2	4	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	1	no	—
201	C₄²	—	2	2	no	—
202	C₄²	—	2	1	no	—
203	C₄²	—	2	2	no	—
204	C₄²	C₂×D₁₈₈	1	2	yes	—
205	C₄²	#10625350	1	2	yes	—
206	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
207	Q₈	—	376	2	no	—
208	Q₈	—	376	1	no	—
209	Q₈	—	376	1	no	—
210	Q₈	—	376	2	no	—
211	Q₈	—	376	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	188	2	no	—
219	C₂×C₄	—	188	2	no	—
220	C₂×C₄	—	188	2	no	—
221	C₂×C₄	—	188	2	no	—
222	C₂×C₄	—	188	4	no	—
223	C₂×C₄	#13093942	1	4	yes	—
224	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
225	C₂×C₄	#13093998	1	2	yes	—
226	C₂×C₄	#13094012	1	1	yes	characteristic
227	C₂×C₄	#13094021	1	1	yes	characteristic
228	C₂×C₄	#13094044	1	2	yes	—
229	C₂×C₄	#13094050	1	1	yes	characteristic
230	C₂×C₄	#13094052	1	2	yes	—
231	C₂×C₄	#13094055	1	1	yes	characteristic
232	C₂×C₄	#13094057	1	2	yes	—
233	C₈	—	4	4	no	—
234	C₈	—	376	2	no	—
235	C₂²	#15689025	1	1	yes	characteristic
236	C₂²	C₂×#13093942	1	2	yes	—
237	C₂²	#15689117	1	1	yes	characteristic
238	C₂²	#15689122	1	1	yes	characteristic
239	C₂²	#15689125	1	2	yes	—
240	C₄	—	2	2	no	—
241	C₄	—	2	4	no	—
242	C₄	—	4	2	no	—
243	C₄	—	376	2	no	—
244	C₄	—	376	2	no	—
245	C₄	#15689338	1	2	yes	—
246	C₄	#15689345	1	2	yes	—
247	C₄	#15689483	1	2	yes	—
248	C₄	#15689512	1	1	yes	characteristic
249	C₄	#15689517	1	1	yes	characteristic
250	C₂	#20242089	1	2	yes	—
251	C₂	#20242125	1	2	yes	—
252	C₂	#20244204	1	1	yes	characteristic
253	C₂	#20244232	1	1	yes	characteristic
254	C₂	#20244320	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20251766

C₂

yes

maximal, characteristic

#20243540

C₂

yes

maximal, characteristic

C₂×#15688870

C₂

yes

maximal

C₂×#15688868

C₂

yes

maximal

C₄₇×#1767

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×C₄⋊(C₄₇⋊C₈)

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

C₄

yes

—

#15688870

—

#15688868

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×#97×C₄₇

—

C₄³×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×Dic₉₄

—

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

—

—

—

—

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

D₄

yes

—

#97×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#101

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

characteristic

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

100

Dic₉₄

—

101

Dic₉₄

—

102

Dic₉₄

—

103

Dic₉₄

—

104

Dic₉₄

—

105

C₈×C₄₇

—

106

C₄₇⋊C₈

—

107

#9708

—

maximal, Sylow

108

C₂²×C₄₇

#390

yes

characteristic

109

C₂²×C₄₇

C₂×#101

yes

—

110

C₂²×C₄₇

#416

yes

characteristic

111

C₂²×C₄₇

#417

yes

characteristic

112

C₂²×C₄₇

#417

yes

—

113

C₄×C₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

#463

yes

—

117

C₄×C₄₇

#464

yes

—

118

C₄×C₄₇

#489

yes

—

119

C₄×C₄₇

#496

yes

characteristic

120

C₄×C₄₇

#497

yes

characteristic

121

Dic₄₇

—

122

Dic₄₇

—

123

#2862

—

124

#1842

—

125

#1767

D₄₇

yes

characteristic

126

C₂×#332

—

127

C₂×#332

—

128

C₂×C₄₇

#1552

yes

—

129

C₂×C₄₇

#1561

yes

—

130

C₂×C₄₇

#1959

yes

characteristic

131

C₂×C₄₇

#1966

yes

characteristic

132

C₂×C₄₇

#1983

yes

characteristic

133

C₂×C₄⋊Q₈

—

134

C₂×C₄⋊Q₈

—

135

C₂×C₄⋊C₈

—

136

C₂×C₄⋊C₈

—

137

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

138

C₂×#97

—

139

#391

—

140

#391

—

141

#391

—

142

#382

—

143

C₄³

C₂×D₄₇

yes

characteristic

144

#336

—

145

#332

—

146

#332

—

147

C₄₇

#9708

yes

characteristic, complemented, Sylow

148

C₂²×Q₈

—

149

C₂²×Q₈

—

150

C₂²×C₈

—

151

C₂²×C₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

C₄⋊Q₈

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄²

C₄×D₄₇

yes

—

161

C₂×C₄²

D₁₈₈

yes

—

162

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

163

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

164

C₂×C₄²

C₂²×D₄₇

yes

characteristic

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₄⋊C₈

—

188

—

169

C₄⋊C₈

D₁₈₈

yes

—

170

#97

—

171

#95

—

172

#95

—

173

C₂×Q₈

—

188

—

174

C₂×Q₈

—

188

—

175

C₂×Q₈

—

188

—

176

C₂×Q₈

—

188

—

177

C₂×Q₈

—

188

—

178

C₂×Q₈

—

188

—

179

C₂×Q₈

—

188

—

180

C₂×Q₈

—

188

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

184

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

185

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

186

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

187

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

188

—

192

C₂×C₈

—

188

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

188

—

196

C₄⋊C₄

—

188

—

197

C₄⋊C₄

—

188

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

C₂×D₁₈₈

yes

—

205

C₄²

#10625350

yes

—

206

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

207

Q₈

—

376

—

208

Q₈

—

376

—

209

Q₈

—

376

—

210

Q₈

—

376

—

211

Q₈

—

376

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

188

—

219

C₂×C₄

—

188

—

220

C₂×C₄

—

188

—

221

C₂×C₄

—

188

—

222

C₂×C₄

—

188

—

223

C₂×C₄

#13093942

yes

—

224

C₂×C₄

C₄×D₁₈₈

yes

—

225

C₂×C₄

#13093998

yes

—

226

C₂×C₄

#13094012

yes

characteristic

227

C₂×C₄

#13094021

yes

characteristic

228

C₂×C₄

#13094044

yes

—

229

C₂×C₄

#13094050

yes

characteristic

230

C₂×C₄

#13094052

yes

—

231

C₂×C₄

#13094055

yes

characteristic

232

C₂×C₄

#13094057

yes

—

233

C₈

—

234

C₈

—

376

—

235

C₂²

#15689025

yes

characteristic

236

C₂²

C₂×#13093942

yes

—

237

C₂²

#15689117

yes

characteristic

238

C₂²

#15689122

yes

characteristic

239

C₂²

#15689125

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

376

—

244

C₄

—

376

—

245

C₄

#15689338

yes

—

246

C₄

#15689345

yes

—

247

C₄

#15689483

yes

—

248

C₄

#15689512

yes

characteristic

249

C₄

#15689517

yes

characteristic

250

C₂

#20242089

yes

—

251

C₂

#20242125

yes

—

252

C₂

#20244204

yes

characteristic

253

C₂

#20244232

yes

characteristic

254

C₂

#20244320

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1767	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1767	D₄₇
hypocenter	C₄₇	#9708
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂³

C₂×(C₂×D₄₇)⋊C₄

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1767

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
147. C₄₇	#9708	semidirect

H ≅ G/N

type

147. C₄₇

#9708

semidirect

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

subgroup	index
#20251766	2
#20243540	2
C₂×#15688870	2
C₂×#15688868	2
C₄₇×#1767	2
#9708	47

subgroup

index

C₄₇×#1767

Subgroups — #26115386

Conjugacy classes of subgroups

Complements

Maximal subgroups