Group #26115071 — subgroups

Subgroups — #26115071

Order 12032.

698 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 167 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	C₄×#13094021	C₂	1	1	yes	maximal, characteristic
2	#20243134	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15688850	C₂	1	4	yes	maximal, complemented
4	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#13094021	C₄	1	1	yes	characteristic
6	C₂×C₄×D₁₈₈	—	2	2	no	—
7	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	#15689025	—	2	2	no	—
10	#15689025	C₄	1	2	yes	—
11	#15688993	C₄	1	1	yes	characteristic
12	#15688878	—	2	2	no	—
13	#15688850	—	2	8	no	—
14	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
15	C₄³×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#336	—	2	2	no	—
17	C₂²×D₁₈₈	—	2	2	no	—
18	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
19	C₂²×C₄×D₄₇	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	#13094021	—	2	2	no	—
22	#13094021	C₈	1	4	yes	complemented
23	C₄×D₁₈₈	—	2	4	no	—
24	C₄×D₁₈₈	—	2	4	no	—
25	C₄×D₁₈₈	—	4	8	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
28	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
29	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
32	C₂²×C₈×C₄₇	—	2	2	no	—
33	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₄₇	D₄	1	2	yes	—
36	C₂×C₄²×C₄₇	D₄	1	2	yes	—
37	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
38	C₄⋊C₈×C₄₇	—	2	4	no	—
39	C₂³×D₄₇	—	2	2	no	—
40	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₄₇	—	2	2	no	—
46	C₂×D₁₈₈	—	2	4	no	—
47	C₂×D₁₈₈	—	2	4	no	—
48	C₂×D₁₈₈	—	2	8	no	—
49	C₂×D₁₈₈	—	2	2	no	—
50	C₂×D₁₈₈	—	4	4	no	—
51	C₂×D₁₈₈	—	4	4	no	—
52	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
53	C₂×C₄×D₄₇	—	4	2	no	—
54	C₂×C₄×D₄₇	—	4	2	no	—
55	C₂×C₄×D₄₇	—	4	8	no	—
56	C₂×C₈×C₄₇	—	4	2	no	—
57	C₂×C₈×C₄₇	—	4	4	no	—
58	C₄²×C₄₇	—	2	2	no	—
59	C₄²×C₄₇	—	2	4	no	—
60	C₄²×C₄₇	—	4	2	no	—
61	C₄²×C₄₇	C₂×C₈	1	2	yes	—
62	C₄²×C₄₇	M₁₆	1	2	yes	—
63	C₄²×C₄₇	C₂×D₄	1	2	yes	—
64	C₄²×C₄₇	#41	1	2	yes	—
65	(C₂×D₄₇)⋊C₄	—	4	8	no	—
66	(C₂×D₄₇)⋊C₄	—	4	4	no	—
67	C₄⋊Dic₄₇	—	2	4	no	—
68	C₄⋊Dic₄₇	—	4	4	no	—
69	C₂×C₄₇⋊C₈	—	2	4	no	—
70	C₂×C₄₇⋊C₈	—	4	4	no	—
71	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×D₄₇	—	2	4	no	—
73	C₂²×D₄₇	—	4	2	no	—
74	C₂²×D₄₇	—	4	2	no	—
75	C₂²×D₄₇	—	4	4	no	—
76	C₂²×D₄₇	—	4	4	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
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	C₂²⋊C₈	1	4	yes	—
84	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₄₇	#121	1	2	yes	—
86	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#131	1	2	yes	—
91	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	4	no	—
94	D₁₈₈	—	2	8	no	—
95	D₁₈₈	—	4	16	no	—
96	D₁₈₈	—	4	4	no	—
97	C₄×D₄₇	—	8	4	no	—
98	C₄×D₄₇	—	8	4	no	—
99	C₈×C₄₇	—	8	2	no	—
100	C₄₇⋊C₈	—	4	4	no	—
101	#9642	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	#390	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
104	C₂²×C₄₇	#408	1	1	yes	characteristic
105	C₂²×C₄₇	#418	1	2	yes	—
106	C₂²×C₄₇	#421	1	2	yes	—
107	C₂×D₄₇	—	4	4	no	—
108	C₂×D₄₇	—	4	8	no	—
109	C₂×D₄₇	—	8	2	no	—
110	C₂×D₄₇	—	8	2	no	—
111	C₂×D₄₇	—	8	4	no	—
112	C₄×C₄₇	—	2	2	no	—
113	C₄×C₄₇	—	2	4	no	—
114	C₄×C₄₇	—	4	2	no	—
115	C₄×C₄₇	C₈×D₄	1	2	yes	—
116	C₄×C₄₇	#436	1	2	yes	—
117	C₄×C₄₇	#490	1	2	yes	—
118	C₄×C₄₇	#496	1	2	yes	—
119	Dic₄₇	—	8	2	no	—
120	C₄×#127	—	47	1	no	—
121	#1831	D₄₇	1	1	yes	characteristic, complemented
122	#1744	—	47	1	no	—
123	C₂×D₄⋊C₈	—	47	4	no	—
124	C₂×C₄₇	#1478	1	2	yes	—
125	C₂×C₄₇	#1496	1	2	yes	—
126	C₂×C₄₇	#1954	1	1	yes	characteristic
127	C₂×C₄₇	#1961	1	1	yes	characteristic
128	C₂×C₄₇	#1963	1	1	yes	characteristic
129	D₄₇	—	8	4	no	—
130	C₂×#127	—	47	1	no	—
131	C₂×C₄×D₄	—	47	2	no	—
132	C₂×C₄×D₄	—	94	2	no	—
133	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
134	C₂×C₄×C₈	—	47	2	no	—
135	#390	—	47	2	no	—
136	#390	—	94	2	no	—
137	#384	—	47	1	no	—
138	C₄³	C₂×D₄₇	1	1	yes	characteristic
139	#336	—	2	2	no	—
140	#336	—	94	2	no	—
141	D₄⋊C₈	—	94	8	no	—
142	C₄₇	#9642	1	1	yes	characteristic, complemented, Sylow
143	C₂²×D₄	—	47	2	no	—
144	C₂²×D₄	—	94	2	no	—
145	C₂³×C₄	—	94	2	no	—
146	C₂²×C₈	—	2	2	no	—
147	C₂²×C₈	—	94	2	no	—
148	#127	—	47	4	no	—
149	#127	—	94	2	no	—
150	C₄×D₄	—	94	4	no	—
151	C₄×D₄	—	94	4	no	—
152	C₄×D₄	—	188	8	no	—
153	C₂×C₄⋊C₄	—	47	2	no	—
154	C₂×C₄⋊C₄	—	94	2	no	—
155	C₂×C₂²⋊C₄	—	94	4	no	—
156	C₂×C₂²⋊C₄	—	94	2	no	—
157	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
158	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
159	C₂×C₄²	D₁₈₈	1	2	yes	—
160	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
161	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
162	C₄⋊C₈	—	2	4	no	—
163	C₄×C₈	—	47	4	no	—
164	C₄×C₈	—	94	2	no	—
165	C₂⁴	—	94	2	no	—
166	C₂×D₄	—	47	4	no	—
167	C₂×D₄	—	94	8	no	—
168	C₂×D₄	—	94	4	no	—
169	C₂×D₄	—	94	2	no	—
170	C₂×D₄	—	94	4	no	—
171	C₂×D₄	—	188	4	no	—
172	C₂×D₄	—	188	4	no	—
173	C₂²×C₄	—	94	2	no	—
174	C₂²×C₄	—	188	2	no	—
175	C₂²×C₄	—	188	2	no	—
176	C₂²×C₄	—	188	8	no	—
177	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
178	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
179	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
180	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	4	4	no	—
184	C₂×C₈	—	94	4	no	—
185	C₂×C₈	—	188	4	no	—
186	C₄⋊C₄	—	94	4	no	—
187	C₄⋊C₄	—	188	4	no	—
188	C₂²⋊C₄	—	188	8	no	—
189	C₂²⋊C₄	—	188	4	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	2	4	no	—
192	C₄²	—	4	2	no	—
193	C₄²	C₈×D₄₇	1	2	yes	—
194	C₄²	#10625324	1	2	yes	—
195	C₄²	D₄×D₄₇	1	2	yes	—
196	C₄²	#10625354	1	2	yes	—
197	C₂³	—	94	4	no	—
198	C₂³	—	188	2	no	—
199	C₂³	—	188	2	no	—
200	C₂³	—	188	4	no	—
201	C₂³	—	188	4	no	—
202	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
203	D₄	—	94	8	no	—
204	D₄	—	188	16	no	—
205	D₄	—	188	4	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	376	4	no	—
213	C₂×C₄	—	376	4	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	—	188	4	no	—
216	C₂×C₄	(C₂×D₄₇)⋊C₈	1	4	yes	—
217	C₂×C₄	#13093986	1	2	yes	—
218	C₂×C₄	#13093999	1	2	yes	—
219	C₂×C₄	#13094013	1	1	yes	characteristic
220	C₂×C₄	#13094020	1	1	yes	characteristic
221	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
222	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
223	C₂×C₄	#13094032	1	2	yes	—
224	C₂×C₄	#13094049	1	4	yes	—
225	C₈	—	8	2	no	—
226	C₈	—	188	4	no	—
227	C₂²	—	376	4	no	—
228	C₂²	—	376	2	no	—
229	C₂²	—	376	2	no	—
230	C₂²	—	188	8	no	—
231	C₂²	—	188	4	no	—
232	C₂²	#15689024	1	1	yes	characteristic
233	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
234	C₂²	#15689091	1	1	yes	characteristic
235	C₂²	#15689127	1	2	yes	—
236	C₂²	#15689139	1	2	yes	—
237	C₄	—	2	4	no	—
238	C₄	—	2	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	376	2	no	—
241	C₄	#15689188	1	2	yes	—
242	C₄	#15689200	1	2	yes	—
243	C₄	#15689489	1	2	yes	—
244	C₄	#15689513	1	2	yes	—
245	C₂	—	376	4	no	—
246	C₂	#20241778	1	2	yes	—
247	C₂	#20241856	1	2	yes	—
248	C₂	#20244181	1	1	yes	characteristic
249	C₂	#20244211	1	1	yes	characteristic
250	C₂	#20244219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13094021

C₂

yes

maximal, characteristic

#20243134

C₂

yes

maximal, characteristic, complemented

C₂×#15688850

C₂

yes

maximal, complemented

C₄₇×#1831

C₂

yes

maximal, characteristic, complemented

C₂×#13094021

C₄

yes

characteristic

C₂×C₄×D₁₈₈

—

C₂×C₄×D₁₈₈

C₂²

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

#15689025

—

#15689025

C₄

yes

—

#15688993

C₄

yes

characteristic

#15688878

—

#15688850

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄³×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×D₁₈₈

—

C₂²×D₁₈₈

C₂×C₄

yes

—

C₂²×C₄×D₄₇

—

C₂²×C₄₇⋊C₈

—

#13094021

—

#13094021

C₈

yes

complemented

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

complemented

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂³×D₄₇

—

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

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₈

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₈

yes

—

C₄²×C₄₇

M₁₆

yes

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

#9642

—

maximal, Sylow

102

C₂²×C₄₇

#390

yes

characteristic

103

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

104

C₂²×C₄₇

#408

yes

characteristic

105

C₂²×C₄₇

#418

yes

—

106

C₂²×C₄₇

#421

yes

—

107

C₂×D₄₇

—

108

C₂×D₄₇

—

109

C₂×D₄₇

—

110

C₂×D₄₇

—

111

C₂×D₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

C₈×D₄

yes

—

116

C₄×C₄₇

#436

yes

—

117

C₄×C₄₇

#490

yes

—

118

C₄×C₄₇

#496

yes

—

119

Dic₄₇

—

120

C₄×#127

—

121

#1831

D₄₇

yes

characteristic, complemented

122

#1744

—

123

C₂×D₄⋊C₈

—

124

C₂×C₄₇

#1478

yes

—

125

C₂×C₄₇

#1496

yes

—

126

C₂×C₄₇

#1954

yes

characteristic

127

C₂×C₄₇

#1961

yes

characteristic

128

C₂×C₄₇

#1963

yes

characteristic

129

D₄₇

—

130

C₂×#127

—

131

C₂×C₄×D₄

—

132

C₂×C₄×D₄

—

133

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

134

C₂×C₄×C₈

—

135

#390

—

136

#390

—

137

#384

—

138

C₄³

C₂×D₄₇

yes

characteristic

139

#336

—

140

#336

—

141

D₄⋊C₈

—

142

C₄₇

#9642

yes

characteristic, complemented, Sylow

143

C₂²×D₄

—

144

C₂²×D₄

—

145

C₂³×C₄

—

146

C₂²×C₈

—

147

C₂²×C₈

—

148

#127

—

149

#127

—

150

C₄×D₄

—

151

C₄×D₄

—

152

C₄×D₄

—

188

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₂²⋊C₄

—

156

C₂×C₂²⋊C₄

—

157

C₂×C₄²

C₄×D₄₇

yes

characteristic

158

C₂×C₄²

C₄×D₄₇

yes

characteristic

159

C₂×C₄²

D₁₈₈

yes

—

160

C₂×C₄²

C₂²⋊D₄₇

yes

—

161

C₂×C₄²

C₂²×D₄₇

yes

characteristic

162

C₄⋊C₈

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₂⁴

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

188

—

172

C₂×D₄

—

188

—

173

C₂²×C₄

—

174

C₂²×C₄

—

188

—

175

C₂²×C₄

—

188

—

176

C₂²×C₄

—

188

—

177

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

178

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

179

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

180

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

181

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

188

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

—

188

C₂²⋊C₄

—

188

—

189

C₂²⋊C₄

—

188

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

C₈×D₄₇

yes

—

194

C₄²

#10625324

yes

—

195

C₄²

D₄×D₄₇

yes

—

196

C₄²

#10625354

yes

—

197

C₂³

—

198

C₂³

—

188

—

199

C₂³

—

188

—

200

C₂³

—

188

—

201

C₂³

—

188

—

202

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

203

D₄

—

204

D₄

—

188

—

205

D₄

—

188

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

376

—

213

C₂×C₄

—

376

—

214

C₂×C₄

—

188

—

215

C₂×C₄

—

188

—

216

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

217

C₂×C₄

#13093986

yes

—

218

C₂×C₄

#13093999

yes

—

219

C₂×C₄

#13094013

yes

characteristic

220

C₂×C₄

#13094020

yes

characteristic

221

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

222

C₂×C₄

C₂×#10625324

yes

characteristic

223

C₂×C₄

#13094032

yes

—

224

C₂×C₄

#13094049

yes

—

225

C₈

—

226

C₈

—

188

—

227

C₂²

—

376

—

228

C₂²

—

376

—

229

C₂²

—

376

—

230

C₂²

—

188

—

231

C₂²

—

188

—

232

C₂²

#15689024

yes

characteristic

233

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

234

C₂²

#15689091

yes

characteristic

235

C₂²

#15689127

yes

—

236

C₂²

#15689139

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

376

—

241

C₄

#15689188

yes

—

242

C₄

#15689200

yes

—

243

C₄

#15689489

yes

—

244

C₄

#15689513

yes

—

245

C₂

—

376

—

246

C₂

#20241778

yes

—

247

C₂

#20241856

yes

—

248

C₂

#20244181

yes

characteristic

249

C₂

#20244211

yes

characteristic

250

C₂

#20244219

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1831	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#13094021	C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#9642
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1831

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂×#13094021

C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

N	H ≅ G/N	type
2. #20243134	C₂	semidirect
3. C₂×#15688850	C₂	semidirect
4. C₄₇×#1831	C₂	semidirect
22. #13094021	C₈	semidirect
31. C₄×C₄₇⋊C₈	D₄	semidirect
121. #1831	D₄₇	semidirect
142. C₄₇	#9642	semidirect

H ≅ G/N

type

2. #20243134

C₂

semidirect

3. C₂×#15688850

C₂

semidirect

4. C₄₇×#1831

C₂

semidirect

22. #13094021

C₈

semidirect

31. C₄×C₄₇⋊C₈

D₄

semidirect

121. #1831

D₄₇

semidirect

142. C₄₇

#9642

semidirect

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

subgroup	index
C₄×#13094021	2
#20243134	2
C₂×#15688850	2
C₄₇×#1831	2
#9642	47

subgroup

index

C₄₇×#1831

Subgroups — #26115071

Conjugacy classes of subgroups

Complements

Maximal subgroups