Group #26113878 — subgroups

Subgroups — #26113878

Order 12032.

504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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	#20252455	C₂	1	1	yes	maximal, characteristic
2	#20242123	C₂	1	1	yes	maximal, characteristic
3	#20242073	C₂	1	2	yes	maximal, complemented
4	#20241278	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3152	C₂	1	1	yes	maximal, characteristic
6	#15689201	—	2	2	no	—
7	D₄×C₄₇⋊C₈	—	2	2	no	—
8	#15689176	C₂²	1	2	yes	—
9	#15689147	C₂²	1	2	yes	—
10	#15689090	—	2	2	no	—
11	#15688872	—	2	1	no	—
12	#15688869	—	2	2	no	—
13	#15688869	—	2	2	no	—
14	#15688867	—	2	1	no	—
15	C₂×#137×C₄₇	—	2	2	no	—
16	C₄₇×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#497	C₄	1	4	yes	—
19	C₄₇×#494	—	2	1	no	—
20	C₄₇×#492	—	2	1	no	—
21	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
28	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
29	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄×C₄₇⋊C₈	—	2	2	no	—
32	C₂×#41×C₄₇	D₄	1	2	yes	—
33	C₂²×Q₈×C₄₇	—	2	1	no	—
34	#137×C₄₇	—	4	4	no	—
35	#137×C₄₇	—	4	4	no	—
36	C₂×Q₁₆×C₄₇	—	2	4	no	—
37	C₂×SD₁₆×C₄₇	—	2	4	no	—
38	C₂×M₁₆×C₄₇	—	2	1	no	—
39	C₄⋊Q₈×C₄₇	—	2	2	no	—
40	C₄⋊Q₈×C₄₇	—	2	1	no	—
41	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
43	#127×C₄₇	D₄	1	1	yes	characteristic
44	#124×C₄₇	C₂×C₄	1	2	yes	—
45	#121×C₄₇	—	2	2	no	—
46	C₄×D₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
49	#97×C₄₇	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₄₇	—	2	1	no	—
51	#41×C₄₇	—	4	2	no	—
52	#41×C₄₇	—	4	2	no	—
53	C₂×Q₈×C₄₇	—	2	2	no	—
54	C₂×Q₈×C₄₇	—	4	2	no	—
55	C₂×Q₈×C₄₇	—	4	2	no	—
56	C₂×Q₈×C₄₇	—	4	1	no	—
57	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
58	C₂×D₄×C₄₇	—	2	2	no	—
59	C₂×D₄×C₄₇	—	2	2	no	—
60	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	4	1	no	—
63	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	#41	1	2	yes	—
65	Q₁₆×C₄₇	—	4	8	no	—
66	SD₁₆×C₄₇	—	4	8	no	—
67	M₁₆×C₄₇	—	2	2	no	—
68	M₁₆×C₄₇	—	2	2	no	—
69	C₂×C₈×C₄₇	—	2	2	no	—
70	C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₄⋊C₄×C₄₇	—	2	4	no	—
72	C₄⋊C₄×C₄₇	—	4	2	no	—
73	C₂²⋊C₄×C₄₇	—	2	4	no	—
74	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₄₇	C₂×D₄	1	2	yes	—
77	#10625329	—	8	2	no	—
78	#10625329	—	8	2	no	—
79	C₂×C₄₇⋊C₈	—	2	2	no	—
80	C₂×C₄₇⋊C₈	—	2	2	no	—
81	C₂×C₄₇⋊C₈	—	4	2	no	—
82	C₂×C₄₇⋊C₈	—	8	2	no	—
83	C₂³×C₄₇	—	2	2	no	—
84	C₂³×C₄₇	#123	1	1	yes	characteristic
85	Q₈×C₄₇	—	4	2	no	—
86	Q₈×C₄₇	—	4	4	no	—
87	Q₈×C₄₇	—	8	1	no	—
88	Q₈×C₄₇	—	8	1	no	—
89	D₄×C₄₇	—	4	2	no	—
90	D₄×C₄₇	—	4	2	no	—
91	D₄×C₄₇	—	4	2	no	—
92	D₄×C₄₇	—	8	2	no	—
93	C₂×C₄×C₄₇	—	2	1	no	—
94	C₂×C₄×C₄₇	—	2	1	no	—
95	C₂×C₄×C₄₇	—	2	2	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	4	2	no	—
99	C₂×C₄×C₄₇	—	4	2	no	—
100	C₂×C₄×C₄₇	—	4	2	no	—
101	C₂×C₄×C₄₇	—	8	2	no	—
102	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
104	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
105	C₂×C₄×C₄₇	#121	1	2	yes	—
106	C₈×C₄₇	—	2	4	no	—
107	C₄₇⋊C₈	—	4	2	no	—
108	C₄₇⋊C₈	—	4	2	no	—
109	C₄₇⋊C₈	—	8	2	no	—
110	#9435	—	47	1	no	maximal, Sylow
111	C₂²×C₄₇	—	2	1	no	—
112	C₂²×C₄₇	—	2	2	no	—
113	C₂²×C₄₇	—	4	2	no	—
114	C₂²×C₄₇	—	4	4	no	—
115	C₂²×C₄₇	#386	1	1	yes	characteristic
116	C₄×C₄₇	—	2	1	no	—
117	C₄×C₄₇	—	2	2	no	—
118	C₄×C₄₇	—	4	2	no	—
119	C₄×C₄₇	—	8	2	no	—
120	C₄×C₄₇	#453	1	1	yes	characteristic
121	C₄×C₄₇	#453	1	1	yes	characteristic
122	C₄×C₄₇	#471	1	2	yes	—
123	C₄×C₄₇	#473	1	2	yes	—
124	#3152	D₄₇	1	1	yes	characteristic
125	#2979	—	47	1	no	—
126	#1560	—	47	1	no	—
127	#1549	—	47	2	no	—
128	#1299	—	47	2	no	—
129	C₂×C₄₇	—	4	1	no	—
130	C₂×C₄₇	—	8	2	no	—
131	C₂×C₄₇	#1887	1	1	yes	characteristic
132	C₂×C₄₇	#1908	1	2	yes	—
133	C₂×#137	—	2	2	no	—
134	#532	C₂×D₄₇	1	1	yes	characteristic
135	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
136	#497	Dic₄₇	1	4	yes	—
137	#494	—	2	1	no	—
138	#492	—	2	1	no	—
139	#436	—	94	2	no	—
140	C₈×D₄	—	94	2	no	—
141	#431	—	47	2	no	—
142	#423	—	47	2	no	—
143	#408	—	94	2	no	—
144	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
145	#333	—	94	1	no	—
146	#332	—	94	2	no	—
147	#332	—	94	2	no	—
148	#331	—	94	1	no	—
149	C₄₇	#9435	1	1	yes	characteristic, complemented, Sylow
150	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
151	C₂²×Q₈	—	2	1	no	—
152	#137	—	4	4	no	—
153	#137	—	4	4	no	—
154	C₂×Q₁₆	—	2	4	no	—
155	C₂×SD₁₆	—	2	4	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	94	2	no	—
158	C₂×M₁₆	—	94	2	no	—
159	C₂²×C₈	—	94	2	no	—
160	C₄⋊Q₈	—	2	2	no	—
161	C₄⋊Q₈	—	2	1	no	—
162	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
163	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
164	#127	C₂²⋊D₄₇	1	1	yes	characteristic
165	#124	C₂×Dic₄₇	1	2	yes	—
166	#121	—	2	2	no	—
167	C₄×D₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	2	2	no	—
169	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
170	C₄⋊C₈	—	47	2	no	—
171	C₄⋊C₈	—	47	2	no	—
172	C₄⋊C₈	—	94	2	no	—
173	C₄⋊C₈	—	94	2	no	—
174	C₂²⋊C₈	—	94	4	no	—
175	C₂²⋊C₈	—	94	2	no	—
176	#97	C₂×Dic₄₇	1	2	yes	—
177	C₄×C₈	—	2	1	no	—
178	C₄×C₈	—	94	2	no	—
179	#41	—	4	2	no	—
180	#41	—	4	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
189	C₂²×C₄	—	2	2	no	—
190	C₂²×C₄	—	4	1	no	—
191	C₂²×C₄	#10625352	1	2	yes	—
192	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
193	Q₁₆	—	4	8	no	—
194	SD₁₆	—	4	8	no	—
195	M₁₆	—	2	2	no	—
196	M₁₆	—	2	2	no	—
197	M₁₆	—	376	2	no	—
198	M₁₆	—	376	2	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	94	2	no	—
201	C₂×C₈	—	94	2	no	—
202	C₂×C₈	—	376	2	no	—
203	C₂×C₈	—	188	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	2	4	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	2	4	no	—
208	C₄²	D₄×D₄₇	1	2	yes	—
209	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
210	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
211	C₂³	—	2	2	no	—
212	C₂³	#13094005	1	1	yes	characteristic
213	Q₈	—	4	2	no	—
214	Q₈	—	4	4	no	—
215	Q₈	—	8	1	no	—
216	Q₈	—	8	1	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	4	2	no	—
220	D₄	—	8	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	8	2	no	—
230	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
231	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
232	C₂×C₄	#13093992	1	1	yes	characteristic
233	C₂×C₄	#13093996	1	2	yes	—
234	C₈	—	2	4	no	—
235	C₈	—	376	2	no	—
236	C₈	—	188	2	no	—
237	C₈	—	188	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	4	2	no	—
241	C₂²	—	4	4	no	—
242	C₂²	#15689003	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	2	no	—
245	C₄	—	4	2	no	—
246	C₄	—	8	2	no	—
247	C₄	#15689290	1	1	yes	characteristic
248	C₄	#15689290	1	1	yes	characteristic
249	C₄	#15689388	1	2	yes	—
250	C₄	#15689396	1	2	yes	—
251	C₂	—	4	1	no	—
252	C₂	—	8	2	no	—
253	C₂	#20243787	1	1	yes	characteristic
254	C₂	#20243905	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20252455

C₂

yes

maximal, characteristic

#20242123

C₂

yes

maximal, characteristic

#20242073

C₂

yes

maximal, complemented

#20241278

C₂

yes

maximal, complemented

C₄₇×#3152

C₂

yes

maximal, characteristic

#15689201

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

—

—

—

—

—

C₂×#137×C₄₇

—

C₄₇×#532

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₄₇×#497

C₄

yes

—

C₄₇×#494

—

C₄₇×#492

—

C₄×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂×#41×C₄₇

D₄

yes

—

C₂²×Q₈×C₄₇

—

#137×C₄₇

—

#137×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×M₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

D₄

yes

characteristic

#127×C₄₇

D₄

yes

characteristic

#124×C₄₇

C₂×C₄

yes

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

#123

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

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

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

103

C₂×C₄×C₄₇

C₄×D₄

yes

—

104

C₂×C₄×C₄₇

#120

yes

characteristic

105

C₂×C₄×C₄₇

#121

yes

—

106

C₈×C₄₇

—

107

C₄₇⋊C₈

—

108

C₄₇⋊C₈

—

109

C₄₇⋊C₈

—

110

#9435

—

maximal, Sylow

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

#386

yes

characteristic

116

C₄×C₄₇

—

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

#453

yes

characteristic

121

C₄×C₄₇

#453

yes

characteristic

122

C₄×C₄₇

#471

yes

—

123

C₄×C₄₇

#473

yes

—

124

#3152

D₄₇

yes

characteristic

125

#2979

—

126

#1560

—

127

#1549

—

128

#1299

—

129

C₂×C₄₇

—

130

C₂×C₄₇

—

131

C₂×C₄₇

#1887

yes

characteristic

132

C₂×C₄₇

#1908

yes

—

133

C₂×#137

—

134

#532

C₂×D₄₇

yes

characteristic

135

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

136

#497

Dic₄₇

yes

—

137

#494

—

138

#492

—

139

#436

—

140

C₈×D₄

—

141

#431

—

142

#423

—

143

#408

—

144

C₄×M₁₆

C₂×D₄₇

yes

characteristic

145

#333

—

146

#332

—

147

#332

—

148

#331

—

149

C₄₇

#9435

yes

characteristic, complemented, Sylow

150

C₂×#41

C₂²⋊D₄₇

yes

—

151

C₂²×Q₈

—

152

#137

—

153

#137

—

154

C₂×Q₁₆

—

155

C₂×SD₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

C₂×Dic₄₇

yes

—

163

C₄⋊Q₈

C₂²⋊D₄₇

yes

characteristic

164

#127

C₂²⋊D₄₇

yes

characteristic

165

#124

C₂×Dic₄₇

yes

—

166

#121

—

167

C₄×D₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄²

C₂²×D₄₇

yes

characteristic

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

C₂²⋊C₈

—

175

C₂²⋊C₈

—

176

#97

C₂×Dic₄₇

yes

—

177

C₄×C₈

—

178

C₄×C₈

—

179

#41

—

180

#41

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

C₂²⋊Dic₄₇

yes

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

#10625352

yes

—

192

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

193

Q₁₆

—

194

SD₁₆

—

195

M₁₆

—

196

M₁₆

—

197

M₁₆

—

376

—

198

M₁₆

—

376

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

376

—

203

C₂×C₈

—

188

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₄²

D₄×D₄₇

yes

—

209

C₄²

C₂²×Dic₄₇

yes

characteristic

210

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

211

C₂³

—

212

C₂³

#13094005

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

231

C₂×C₄

D₄×Dic₄₇

yes

—

232

C₂×C₄

#13093992

yes

characteristic

233

C₂×C₄

#13093996

yes

—

234

C₈

—

235

C₈

—

376

—

236

C₈

—

188

—

237

C₈

—

188

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

#15689003

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#15689290

yes

characteristic

248

C₄

#15689290

yes

characteristic

249

C₄

#15689388

yes

—

250

C₄

#15689396

yes

—

251

C₂

—

252

C₂

—

253

C₂

#20243787

yes

characteristic

254

C₂

#20243905

yes

—

	subgroup	G/H
center	C₂²	#15689003
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#3152	C₂
socle	C₂²×C₄₇	#386
prime radical	C₄₇×#532	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#3152	D₄₇
hypocenter	C₄₇	#9435
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

subgroup

G/H

center

C₂²

#15689003

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#3152

C₂

socle

C₂²×C₄₇

#386

prime radical

C₄₇×#532

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

N	H ≅ G/N	type
3. #20242073	C₂	semidirect
4. #20241278	C₂	semidirect
149. C₄₇	#9435	semidirect

H ≅ G/N

type

3. #20242073

C₂

semidirect

4. #20241278

C₂

semidirect

149. C₄₇

#9435

semidirect

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

subgroup	index
#20252455	2
#20242123	2
#20242073	2
#20241278	2
C₄₇×#3152	2
#9435	47

subgroup

index

C₄₇×#3152

Subgroups — #26113878

Conjugacy classes of subgroups

Complements

Maximal subgroups