Group #26107231 — subgroups

Subgroups — #26107231

Order 12032.

684 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 183 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	#20243241	C₂	1	2	yes	maximal, complemented
2	C₂×#15688867	C₂	1	2	yes	maximal
3	#20241271	C₂	1	2	yes	maximal, complemented
4	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
6	C₂×#13093935	—	2	2	no	—
7	#15688878	—	2	2	no	—
8	#15688867	C₄	1	8	yes	complemented
9	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₄₇	—	2	2	no	—
11	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
12	C₄₇×#390	—	2	2	no	—
13	C₄₇×#390	C₄	1	2	yes	—
14	C₄₇×#384	C₂²	1	1	yes	characteristic
15	C₄³×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄₇⋊C₈	—	2	4	no	—
17	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
18	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
19	#13093935	—	4	4	no	—
20	C₂²×D₄×C₄₇	—	2	2	no	—
21	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₄₇	—	2	2	no	—
23	#127×C₄₇	—	2	2	no	—
24	#127×C₄₇	C₂×C₄	1	4	yes	—
25	C₄×D₄×C₄₇	—	4	8	no	—
26	C₄×D₄×C₄₇	—	4	4	no	—
27	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
28	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
30	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
31	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₇	D₄	1	2	yes	—
34	C₂×C₄²×C₄₇	D₄	1	2	yes	—
35	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
36	C₂⁴×C₄₇	—	2	2	no	—
37	C₂×D₄×C₄₇	—	2	2	no	—
38	C₂×D₄×C₄₇	—	2	8	no	—
39	C₂×D₄×C₄₇	—	4	2	no	—
40	C₂×D₄×C₄₇	—	4	2	no	—
41	C₂×D₄×C₄₇	—	4	4	no	—
42	C₂×D₄×C₄₇	—	4	2	no	—
43	C₂×D₄×C₄₇	—	4	2	no	—
44	C₂×D₄×C₄₇	C₄²	1	4	yes	—
45	C₂²×C₄×C₄₇	—	2	2	no	—
46	C₂²×C₄×C₄₇	—	4	8	no	—
47	C₂²×C₄×C₄₇	—	4	4	no	—
48	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
53	C₄⋊C₄×C₄₇	—	4	2	no	—
54	C₄⋊C₄×C₄₇	—	4	4	no	—
55	C₂²⋊C₄×C₄₇	—	4	4	no	—
56	C₂²⋊C₄×C₄₇	—	4	8	no	—
57	C₄²×C₄₇	—	2	2	no	—
58	C₄²×C₄₇	—	2	4	no	—
59	C₄²×C₄₇	—	2	2	no	—
60	C₄²×C₄₇	—	2	2	no	—
61	C₄²×C₄₇	—	4	1	no	—
62	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
63	C₄²×C₄₇	#41	1	2	yes	—
64	C₂×C₄₇⋊C₈	—	2	8	no	—
65	C₂×C₄₇⋊C₈	—	4	4	no	—
66	C₂×C₄₇⋊C₈	—	4	4	no	—
67	C₂³×C₄₇	—	2	4	no	—
68	C₂³×C₄₇	—	4	2	no	—
69	C₂³×C₄₇	—	4	2	no	—
70	C₂³×C₄₇	—	4	4	no	—
71	C₂³×C₄₇	—	4	4	no	—
72	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	D₄×C₄₇	—	4	4	no	—
74	D₄×C₄₇	—	4	4	no	—
75	D₄×C₄₇	—	4	8	no	—
76	D₄×C₄₇	—	4	8	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	—	2	1	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	—	4	2	no	—
86	C₂×C₄×C₄₇	—	4	4	no	—
87	C₂×C₄×C₄₇	—	8	8	no	—
88	C₂×C₄×C₄₇	#100	1	2	yes	—
89	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
92	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
93	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
94	C₂×C₄×C₄₇	#137	1	2	yes	—
95	C₄₇⋊C₈	—	4	8	no	—
96	#8231	—	47	1	no	maximal, Sylow
97	C₂²×C₄₇	—	4	4	no	—
98	C₂²×C₄₇	—	4	8	no	—
99	C₂²×C₄₇	—	8	2	no	—
100	C₂²×C₄₇	—	8	4	no	—
101	C₂²×C₄₇	—	8	2	no	—
102	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
104	C₂²×C₄₇	#413	1	1	yes	characteristic
105	C₂²×C₄₇	#417	1	2	yes	—
106	C₂²×C₄₇	#418	1	2	yes	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	2	1	no	—
110	C₄×C₄₇	—	4	2	no	—
111	C₄×C₄₇	—	4	1	no	—
112	C₄×C₄₇	—	8	2	no	—
113	C₄×C₄₇	#440	1	4	yes	—
114	C₄×C₄₇	#442	1	4	yes	—
115	C₄×#127	D₄₇	1	1	yes	characteristic
116	#1767	—	47	2	no	—
117	C₂×#331	—	47	2	no	—
118	#1296	—	47	2	no	—
119	C₂×C₄₇	—	8	4	no	—
120	C₂×C₄₇	#1555	1	1	yes	characteristic
121	C₂×C₄₇	#1557	1	2	yes	—
122	C₂×C₄₇	#1560	1	1	yes	characteristic
123	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
124	C₂×C₄₇	#1762	1	2	yes	—
125	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
126	C₂×C₄×D₄	—	2	2	no	—
127	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
128	C₂×C₄⋊C₈	—	47	4	no	—
129	C₂×#97	—	94	2	no	—
130	#390	—	2	2	no	—
131	#390	Dic₄₇	1	2	yes	—
132	#384	C₂×D₄₇	1	1	yes	characteristic
133	C₄³	C₂×D₄₇	1	1	yes	characteristic
134	#336	—	94	2	no	—
135	#331	—	47	8	no	—
136	C₄₇	#8231	1	1	yes	characteristic, complemented, Sylow
137	C₂²×D₄	—	2	2	no	—
138	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
139	C₂³×C₄	—	2	2	no	—
140	C₂²×C₈	—	94	4	no	—
141	#127	—	2	2	no	—
142	#127	C₄×D₄₇	1	4	yes	—
143	C₄×D₄	—	4	8	no	—
144	C₄×D₄	—	4	4	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
147	C₂×C₂²⋊C₄	—	2	4	no	—
148	C₂×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
150	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
153	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
154	C₄⋊C₈	—	47	8	no	—
155	C₄⋊C₈	—	94	4	no	—
156	#97	—	188	4	no	—
157	C₂⁴	—	2	2	no	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	2	8	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	4	2	no	—
162	C₂×D₄	—	4	2	no	—
163	C₂×D₄	—	4	4	no	—
164	C₂×D₄	—	4	2	no	—
165	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	4	8	no	—
168	C₂²×C₄	—	4	4	no	—
169	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
170	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
171	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
172	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
174	C₂×C₈	—	94	8	no	—
175	C₂×C₈	—	188	4	no	—
176	C₂×C₈	—	188	4	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	4	no	—
179	C₂²⋊C₄	—	4	4	no	—
180	C₂²⋊C₄	—	4	8	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	2	4	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	4	1	no	—
186	C₄²	C₂×C₄×D₄₇	1	2	yes	—
187	C₄²	#10625350	1	2	yes	—
188	C₂³	—	2	4	no	—
189	C₂³	—	4	2	no	—
190	C₂³	—	4	2	no	—
191	C₂³	—	4	4	no	—
192	C₂³	—	4	4	no	—
193	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
194	D₄	—	4	4	no	—
195	D₄	—	4	4	no	—
196	D₄	—	4	8	no	—
197	D₄	—	4	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	8	8	no	—
209	C₂×C₄	#13093941	1	2	yes	—
210	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
211	C₂×C₄	#13093983	1	1	yes	characteristic
212	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
213	C₂×C₄	#13094049	1	2	yes	—
214	C₂×C₄	#13094050	1	4	yes	—
215	C₂×C₄	#13094054	1	2	yes	—
216	C₈	—	188	8	no	—
217	C₂²	—	4	8	no	—
218	C₂²	—	4	4	no	—
219	C₂²	—	8	2	no	—
220	C₂²	—	8	4	no	—
221	C₂²	—	8	2	no	—
222	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
223	C₂²	C₂×#13093941	1	1	yes	characteristic
224	C₂²	#15689107	1	1	yes	characteristic
225	C₂²	#15689124	1	2	yes	—
226	C₂²	#15689128	1	2	yes	—
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	4	2	no	—
231	C₄	—	4	1	no	—
232	C₄	—	8	2	no	—
233	C₄	#15689223	1	4	yes	—
234	C₄	#15689233	1	4	yes	—
235	C₂	—	8	4	no	—
236	C₂	#20242102	1	1	yes	characteristic
237	C₂	#20242110	1	2	yes	—
238	C₂	#20242123	1	1	yes	characteristic
239	C₂	C₄×#13093941	1	1	yes	characteristic
240	C₂	#20243213	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20243241

C₂

yes

maximal, complemented

C₂×#15688867

C₂

yes

maximal

#20241271

C₂

yes

maximal, complemented

C₄×#127×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093935

—

#15688878

—

#15688867

C₄

yes

complemented

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄×C₄₇

—

C₂×C₄×D₄×C₄₇

C₄

yes

—

C₄₇×#390

—

C₄₇×#390

C₄

yes

—

C₄₇×#384

C₂²

yes

characteristic

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

complemented

#13093935

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×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

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₄²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

#41

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×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

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#100

yes

—

C₂×C₄×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₄₇⋊C₈

—

#8231

—

maximal, Sylow

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

—

101

C₂²×C₄₇

—

102

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

103

C₂²×C₄₇

C₂×#100

yes

characteristic

104

C₂²×C₄₇

#413

yes

characteristic

105

C₂²×C₄₇

#417

yes

—

106

C₂²×C₄₇

#418

yes

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

—

113

C₄×C₄₇

#440

yes

—

114

C₄×C₄₇

#442

yes

—

115

C₄×#127

D₄₇

yes

characteristic

116

#1767

—

117

C₂×#331

—

118

#1296

—

119

C₂×C₄₇

—

120

C₂×C₄₇

#1555

yes

characteristic

121

C₂×C₄₇

#1557

yes

—

122

C₂×C₄₇

#1560

yes

characteristic

123

C₂×C₄₇

C₄×#100

yes

characteristic

124

C₂×C₄₇

#1762

yes

—

125

C₂×#127

C₂×D₄₇

yes

characteristic

126

C₂×C₄×D₄

—

127

C₂×C₄×D₄

Dic₄₇

yes

—

128

C₂×C₄⋊C₈

—

129

C₂×#97

—

130

#390

—

131

#390

Dic₄₇

yes

—

132

#384

C₂×D₄₇

yes

characteristic

133

C₄³

C₂×D₄₇

yes

characteristic

134

#336

—

135

#331

—

136

C₄₇

#8231

yes

characteristic, complemented, Sylow

137

C₂²×D₄

—

138

C₂²×D₄

C₂×Dic₄₇

yes

—

139

C₂³×C₄

—

140

C₂²×C₈

—

141

#127

—

142

#127

C₄×D₄₇

yes

—

143

C₄×D₄

—

144

C₄×D₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

147

C₂×C₂²⋊C₄

—

148

C₂×C₂²⋊C₄

—

149

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

150

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

151

C₂×C₄²

C₂²⋊D₄₇

yes

—

152

C₂×C₄²

C₂²⋊D₄₇

yes

—

153

C₂×C₄²

C₂²×D₄₇

yes

characteristic

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

#97

—

188

—

157

C₂⁴

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

—

164

C₂×D₄

—

165

C₂×D₄

C₄×Dic₄₇

yes

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

170

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

171

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

172

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

173

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

174

C₂×C₈

—

175

C₂×C₈

—

188

—

176

C₂×C₈

—

188

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₂²⋊C₄

—

180

C₂²⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

C₂×C₄×D₄₇

yes

—

187

C₄²

#10625350

yes

—

188

C₂³

—

189

C₂³

—

190

C₂³

—

191

C₂³

—

192

C₂³

—

193

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

194

D₄

—

195

D₄

—

196

D₄

—

197

D₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

#13093941

yes

—

210

C₂×C₄

C₂×C₄×Dic₄₇

yes

characteristic

211

C₂×C₄

#13093983

yes

characteristic

212

C₂×C₄

C₄×C₂²⋊D₄₇

yes

—

213

C₂×C₄

#13094049

yes

—

214

C₂×C₄

#13094050

yes

—

215

C₂×C₄

#13094054

yes

—

216

C₈

—

188

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

C₄×C₂²⋊Dic₄₇

yes

characteristic

223

C₂²

C₂×#13093941

yes

characteristic

224

C₂²

#15689107

yes

characteristic

225

C₂²

#15689124

yes

—

226

C₂²

#15689128

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

#15689223

yes

—

234

C₄

#15689233

yes

—

235

C₂

—

236

C₂

#20242102

yes

characteristic

237

C₂

#20242110

yes

—

238

C₂

#20242123

yes

characteristic

239

C₂

C₄×#13093941

yes

characteristic

240

C₂

#20243213

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#127	D₄₇
hypocenter	C₄₇	#8231
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×#127×C₄₇

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

N	H ≅ G/N	type
1. #20243241	C₂	semidirect
3. #20241271	C₂	semidirect
8. #15688867	C₄	semidirect
18. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
136. C₄₇	#8231	semidirect

H ≅ G/N

type

1. #20243241

C₂

semidirect

3. #20241271

C₂

semidirect

8. #15688867

C₄

semidirect

18. C₄⋊(C₄₇⋊C₈)

C₂×C₄

semidirect

136. C₄₇

#8231

semidirect

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

subgroup	index
#20243241	2
C₂×#15688867	2
#20241271	2
C₄×#127×C₄₇	2
#8231	47

subgroup

index

C₄×#127×C₄₇

Subgroups — #26107231

Conjugacy classes of subgroups

Complements

Maximal subgroups