Group #26109205 — subgroups

Subgroups — #26109205

Order 12032.

486 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 121 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	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
2	#20243377	C₂	1	2	yes	maximal
3	#20242146	C₂	1	2	yes	maximal, complemented
4	#20241263	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1292	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₇	C₄	1	2	yes	—
7	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
8	#15689188	—	2	2	no	—
9	#15689188	—	2	2	no	—
10	#15689147	C₂²	1	2	yes	—
11	C₂×#13093940	—	2	2	no	—
12	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15688891	—	2	2	no	—
15	#15688875	—	2	2	no	—
16	#15688875	—	2	2	no	—
17	C₄₇×#423	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
21	C₂×#10625329	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₄₇	—	2	2	no	—
25	C₂×C₈×D₄₇	—	2	2	no	—
26	C₂×C₈×D₄₇	—	4	4	no	—
27	C₄×D₁₈₈	—	2	2	no	—
28	C₄×D₁₈₈	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
30	C₂×(C₂×D₄₇)⋊C₄	Q₈	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	#13093940	—	4	4	no	—
34	(C₂×D₄₇)⋊C₈	—	2	4	no	—
35	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
36	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₇	—	2	2	no	—
41	C₄⋊C₈×C₄₇	—	2	2	no	—
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₂³×D₄₇	C₄⋊C₄	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
47	C₂²×Dic₄₇	C₄⋊C₄	1	2	yes	—
48	C₂×D₁₈₈	—	2	2	no	—
49	C₂×D₁₈₈	—	2	2	no	—
50	C₂×D₁₈₈	D₈	1	2	yes	—
51	C₂×D₁₈₈	Q₁₆	1	2	yes	—
52	C₂×C₄×D₄₇	—	2	2	no	—
53	C₂×C₄×D₄₇	—	2	2	no	—
54	C₂×C₄×D₄₇	—	4	2	no	—
55	C₂×C₄×D₄₇	—	4	2	no	—
56	M₁₆×C₄₇	—	4	2	no	—
57	M₁₆×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	2	2	no	—
59	C₂×C₈×C₄₇	—	4	2	no	—
60	C₂×C₈×C₄₇	—	4	2	no	—
61	C₄²×C₄₇	C₂×D₄	1	2	yes	—
62	C₄²×C₄₇	#41	1	2	yes	—
63	(C₂×D₄₇)⋊C₄	—	2	4	no	—
64	C₄⋊Dic₄₇	—	2	2	no	—
65	#10625329	—	4	2	no	—
66	#10625329	—	4	2	no	—
67	C₂×C₄₇⋊C₈	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	4	1	no	—
69	C₂×C₄₇⋊C₈	—	4	2	no	—
70	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
71	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
73	C₈×D₄₇	—	4	4	no	—
74	C₈×D₄₇	—	4	4	no	—
75	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×D₄₇	—	2	2	no	—
77	C₂²×D₄₇	—	2	2	no	—
78	C₂²×D₄₇	—	4	2	no	—
79	C₂²×D₄₇	—	4	2	no	—
80	C₂²×D₄₇	#107	1	4	yes	—
81	C₂×C₄×C₄₇	—	2	1	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	4	1	no	—
84	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#121	1	2	yes	—
87	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#135	1	2	yes	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	D₁₈₈	—	2	4	no	—
94	D₁₈₈	—	2	4	no	—
95	C₄×D₄₇	—	4	4	no	—
96	C₄×D₄₇	—	4	2	no	—
97	C₄×D₄₇	—	4	2	no	—
98	C₈×C₄₇	—	4	2	no	—
99	C₈×C₄₇	—	8	2	no	—
100	C₄₇⋊C₈	—	2	1	no	—
101	C₄₇⋊C₈	—	2	2	no	—
102	C₄₇⋊C₈	—	8	2	no	—
103	C₄₇⋊C₈	#100	1	2	yes	complemented
104	#8616	—	47	1	no	maximal, Sylow
105	C₂²×C₄₇	—	2	1	no	—
106	C₂²×C₄₇	—	2	1	no	—
107	C₂²×C₄₇	#380	1	1	yes	characteristic
108	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
109	C₂²×C₄₇	#427	1	1	yes	characteristic
110	C₂×D₄₇	—	2	4	no	—
111	C₂×D₄₇	—	4	4	no	—
112	C₂×D₄₇	—	4	2	no	—
113	C₂×D₄₇	—	4	2	no	—
114	C₂×D₄₇	—	4	4	no	—
115	C₄×C₄₇	—	2	1	no	—
116	C₄×C₄₇	—	2	2	no	—
117	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
118	C₄×C₄₇	#413	1	1	yes	characteristic
119	C₄×C₄₇	#466	1	2	yes	—
120	C₄×C₄₇	#467	1	2	yes	—
121	Dic₄₇	—	4	2	no	—
122	C₂×C₈×D₄	—	47	1	no	—
123	#1800	—	47	2	no	—
124	#1567	—	47	2	no	—
125	#1292	—	47	1	no	—
126	#1292	D₄₇	1	1	yes	characteristic, complemented
127	C₂×C₄₇	—	2	1	no	—
128	C₂×C₄₇	—	2	1	no	—
129	C₂×C₄₇	#1800	1	1	yes	characteristic
130	C₂×C₄₇	#1808	1	1	yes	characteristic
131	C₂×C₄₇	#1813	1	1	yes	characteristic
132	D₄₇	—	4	4	no	—
133	C₂³×C₈	—	47	2	no	—
134	C₂×C₄×D₄	—	47	1	no	—
135	C₈×D₄	—	94	2	no	—
136	C₈×D₄	—	94	2	no	—
137	#423	—	47	2	no	—
138	#423	C₂×D₄₇	1	2	yes	—
139	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
140	C₂×#100	—	94	2	no	—
141	C₂×C₂²⋊C₈	—	47	2	no	—
142	C₂×C₄×C₈	—	47	1	no	—
143	#343	—	94	2	no	—
144	#335	—	94	2	no	—
145	#335	—	94	2	no	—
146	C₄₇	#8616	1	1	yes	characteristic, complemented, Sylow
147	C₂²×D₄	—	47	1	no	—
148	C₂³×C₄	—	47	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	94	2	no	—
151	C₂²×C₈	—	47	1	no	—
152	C₂²×C₈	—	47	1	no	—
153	C₂²×C₈	—	94	2	no	—
154	C₂²×C₈	—	94	2	no	—
155	C₂²×C₈	—	188	4	no	—
156	C₂²×C₈	C₄×D₄₇	1	2	yes	—
157	C₄×D₄	—	94	2	no	—
158	C₄×D₄	—	94	2	no	—
159	C₂×C₄⋊C₄	—	47	1	no	—
160	C₂×C₂²⋊C₄	—	47	2	no	—
161	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
162	C₄⋊C₈	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	94	2	no	—
166	C₄⋊C₈	—	94	2	no	—
167	#100	—	188	4	no	—
168	C₂²⋊C₈	—	94	4	no	—
169	C₄×C₈	—	47	2	no	—
170	C₄×C₈	—	47	2	no	—
171	C₂⁴	—	47	2	no	—
172	C₂×D₄	—	47	2	no	—
173	C₂×D₄	—	47	2	no	—
174	C₂×D₄	—	94	2	no	—
175	C₂×D₄	—	94	2	no	—
176	C₂²×C₄	—	47	2	no	—
177	C₂²×C₄	—	94	2	no	—
178	C₂²×C₄	—	94	2	no	—
179	C₂²×C₄	—	188	2	no	—
180	C₂²×C₄	—	188	2	no	—
181	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
182	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
183	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
184	M₁₆	—	4	2	no	—
185	M₁₆	—	4	2	no	—
186	M₁₆	—	188	2	no	—
187	M₁₆	—	188	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	47	1	no	—
192	C₂×C₈	—	47	2	no	—
193	C₂×C₈	—	47	1	no	—
194	C₂×C₈	—	94	2	no	—
195	C₂×C₈	—	188	4	no	—
196	C₂×C₈	—	188	4	no	—
197	C₂×C₈	—	188	1	no	—
198	C₂×C₈	—	188	2	no	—
199	C₄⋊C₄	—	94	2	no	—
200	C₂²⋊C₄	—	94	4	no	—
201	C₄²	#10625350	1	2	yes	—
202	C₄²	D₄×D₄₇	1	2	yes	—
203	C₂³	—	47	4	no	—
204	C₂³	—	94	2	no	—
205	C₂³	—	94	2	no	—
206	C₂³	—	188	2	no	—
207	C₂³	—	188	2	no	—
208	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
209	D₄	—	94	4	no	—
210	D₄	—	94	4	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	94	2	no	—
215	C₂×C₄	—	188	4	no	—
216	C₂×C₄	—	188	2	no	—
217	C₂×C₄	—	188	2	no	—
218	C₂×C₄	—	188	2	no	—
219	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
220	C₂×C₄	#13093981	1	1	yes	characteristic
221	C₂×C₄	#13093997	1	2	yes	—
222	C₂×C₄	#13094002	1	2	yes	—
223	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
224	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
225	C₂×C₄	#13094045	1	2	yes	—
226	C₈	—	4	2	no	—
227	C₈	—	8	2	no	—
228	C₈	—	47	2	no	—
229	C₈	—	94	1	no	—
230	C₈	—	94	2	no	—
231	C₈	—	376	2	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	1	no	—
234	C₂²	—	94	4	no	—
235	C₂²	—	188	4	no	—
236	C₂²	—	188	4	no	—
237	C₂²	—	188	2	no	—
238	C₂²	—	188	2	no	—
239	C₂²	#15688982	1	1	yes	characteristic
240	C₂²	#107×D₄₇	1	1	yes	characteristic
241	C₂²	#15689158	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	2	no	—
244	C₄	—	188	2	no	—
245	C₄	#100×D₄₇	1	1	yes	characteristic
246	C₄	#15689106	1	1	yes	characteristic
247	C₄	#15689358	1	2	yes	—
248	C₄	#15689363	1	2	yes	—
249	C₂	—	2	1	no	—
250	C₂	—	2	1	no	—
251	C₂	—	188	4	no	—
252	C₂	#20243379	1	1	yes	characteristic
253	C₂	#20243416	1	1	yes	characteristic
254	C₂	#20243437	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689188

C₂

yes

maximal, characteristic

#20243377

C₂

yes

maximal

#20242146

C₂

yes

maximal, complemented

#20241263

C₂

yes

maximal, characteristic, complemented

C₄₇×#1292

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₇

C₄

yes

—

C₂×C₄×D₁₈₈

C₂²

yes

—

—

C₂²

yes

—

C₂×#13093940

—

C₂×(C₂×D₄₇)⋊C₈

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₄₇×#423

C₂²

yes

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂²×D₁₈₈

D₄

yes

characteristic

C₂²×C₄×D₄₇

C₂×C₄

yes

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₂×C₄⋊Dic₄₇

D₄

yes

characteristic

C₂×(C₂×D₄₇)⋊C₄

Q₈

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093940

—

(C₂×D₄₇)⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₂³×D₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂²×Dic₄₇

C₄⋊C₄

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

D₈

yes

—

C₂×D₁₈₈

Q₁₆

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₄₇

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

#107

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

yes

104

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

#380

yes

characteristic

108

C₂²×C₄₇

C₂×#107

yes

characteristic

109

C₂²×C₄₇

#427

yes

characteristic

110

C₂×D₄₇

—

111

C₂×D₄₇

—

112

C₂×D₄₇

—

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

C₂×#100

yes

characteristic

118

C₄×C₄₇

#413

yes

characteristic

119

C₄×C₄₇

#466

yes

—

120

C₄×C₄₇

#467

yes

—

121

Dic₄₇

—

122

C₂×C₈×D₄

—

123

#1800

—

124

#1567

—

125

#1292

—

126

#1292

D₄₇

yes

characteristic, complemented

127

C₂×C₄₇

—

128

C₂×C₄₇

—

129

C₂×C₄₇

#1800

yes

characteristic

130

C₂×C₄₇

#1808

yes

characteristic

131

C₂×C₄₇

#1813

yes

characteristic

132

D₄₇

—

133

C₂³×C₈

—

134

C₂×C₄×D₄

—

135

C₈×D₄

—

136

C₈×D₄

—

137

#423

—

138

#423

C₂×D₄₇

yes

—

139

C₂×C₄⋊C₈

C₂×D₄₇

yes

characteristic

140

C₂×#100

—

141

C₂×C₂²⋊C₈

—

142

C₂×C₄×C₈

—

143

#343

—

144

#335

—

145

#335

—

146

C₄₇

#8616

yes

characteristic, complemented, Sylow

147

C₂²×D₄

—

148

C₂³×C₄

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂²×C₈

—

152

C₂²×C₈

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

188

—

156

C₂²×C₈

C₄×D₄₇

yes

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₂²⋊C₄

—

161

C₂×C₄²

C₂²×D₄₇

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

#100

—

188

—

168

C₂²⋊C₈

—

169

C₄×C₈

—

170

C₄×C₈

—

171

C₂⁴

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

188

—

180

C₂²×C₄

—

188

—

181

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

182

C₂²×C₄

D₄×D₄₇

yes

characteristic

183

C₂²×C₄

Q₈×D₄₇

yes

characteristic

184

M₁₆

—

185

M₁₆

—

186

M₁₆

—

188

—

187

M₁₆

—

188

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

188

—

196

C₂×C₈

—

188

—

197

C₂×C₈

—

188

—

198

C₂×C₈

—

188

—

199

C₄⋊C₄

—

200

C₂²⋊C₄

—

201

C₄²

#10625350

yes

—

202

C₄²

D₄×D₄₇

yes

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

188

—

207

C₂³

—

188

—

208

C₂³

C₄⋊C₄×D₄₇

yes

characteristic

209

D₄

—

210

D₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

188

—

216

C₂×C₄

—

188

—

217

C₂×C₄

—

188

—

218

C₂×C₄

—

188

—

219

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

220

C₂×C₄

#13093981

yes

characteristic

221

C₂×C₄

#13093997

yes

—

222

C₂×C₄

#13094002

yes

—

223

C₂×C₄

D₈×D₄₇

yes

characteristic

224

C₂×C₄

Q₁₆×D₄₇

yes

characteristic

225

C₂×C₄

#13094045

yes

—

226

C₈

—

227

C₈

—

228

C₈

—

229

C₈

—

230

C₈

—

231

C₈

—

376

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

188

—

236

C₂²

—

188

—

237

C₂²

—

188

—

238

C₂²

—

188

—

239

C₂²

#15688982

yes

characteristic

240

C₂²

#107×D₄₇

yes

characteristic

241

C₂²

#15689158

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

188

—

245

C₄

#100×D₄₇

yes

characteristic

246

C₄

#15689106

yes

characteristic

247

C₄

#15689358

yes

—

248

C₄

#15689363

yes

—

249

C₂

—

250

C₂

—

251

C₂

—

188

—

252

C₂

#20243379

yes

characteristic

253

C₂

#20243416

yes

characteristic

254

C₂

#20243437

yes

characteristic

	subgroup	G/H
center	C₂²	#15688982
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1292	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1292	D₄₇
hypocenter	C₄₇	#8616
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

subgroup

G/H

center

C₂²

#15688982

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1292

C₂

socle

C₂²×C₄₇

#380

prime radical

C₂²×D₁₈₈

D₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

N	H ≅ G/N	type
3. #20242146	C₂	semidirect
4. #20241263	C₂	semidirect
5. C₄₇×#1292	C₂	semidirect
103. C₄₇⋊C₈	#100	semidirect
126. #1292	D₄₇	semidirect
146. C₄₇	#8616	semidirect

H ≅ G/N

type

3. #20242146

C₂

semidirect

4. #20241263

C₂

semidirect

5. C₄₇×#1292

C₂

semidirect

103. C₄₇⋊C₈

#100

semidirect

126. #1292

D₄₇

semidirect

146. C₄₇

#8616

semidirect

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

subgroup	index
C₂×#15689188	2
#20243377	2
#20242146	2
#20241263	2
C₄₇×#1292	2
#8616	47

subgroup

index

C₄₇×#1292

Subgroups — #26109205

Conjugacy classes of subgroups

Complements

Maximal subgroups