Group #26132504 — subgroups

Subgroups — #26132504

Order 12032.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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×#15689075	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688904	C₂	1	2	yes	maximal
3	#20241469	C₂	1	2	yes	maximal, complemented
4	#20241468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10625324	C₄	1	1	yes	characteristic
7	C₂²×#10625324	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₄₇	C₄	1	1	yes	characteristic
9	C₂×#13093964	C₂²	1	2	yes	—
10	#15689075	—	2	4	no	—
11	C₂×#13093935	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15688904	—	2	4	no	—
15	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
16	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₇	—	2	1	no	—
18	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×#10625324	—	2	2	no	—
20	C₂×#10625324	—	2	2	no	—
21	C₂×#10625324	—	2	2	no	—
22	C₂×#10625324	—	2	1	no	—
23	C₂×#10625324	—	2	1	no	—
24	C₂×#10625324	—	2	2	no	—
25	C₂×#10625324	D₄	1	4	yes	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₄₇	—	2	1	no	—
29	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₄²×D₄₇	—	2	2	no	—
31	C₄²×D₄₇	C₈	1	4	yes	—
32	#13093964	—	2	2	no	—
33	#13093964	—	2	2	no	—
34	C₂×C₄₇⋊C₁₆	—	2	2	no	—
35	#13093935	—	2	2	no	—
36	C₈×Dic₄₇	—	2	2	no	—
37	C₈×Dic₄₇	—	2	2	no	—
38	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
41	M₃₂×C₄₇	—	2	2	no	—
42	M₃₂×C₄₇	—	2	2	no	—
43	C₂×C₁₆×C₄₇	—	2	2	no	—
44	#97×C₄₇	—	2	2	no	—
45	C₂³×D₄₇	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	—	2	1	no	—
47	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×Dic₄₇	—	2	1	no	—
49	C₂²×Dic₄₇	M₁₆	1	1	yes	characteristic
50	C₂×C₄×D₄₇	—	2	1	no	—
51	C₂×C₄×D₄₇	—	2	1	no	—
52	C₂×C₄×D₄₇	—	2	1	no	—
53	C₂×C₄×D₄₇	—	2	1	no	—
54	C₂×C₄×D₄₇	—	2	4	no	—
55	C₂×C₄×D₄₇	—	4	4	no	—
56	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
57	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
58	C₂×C₈×C₄₇	—	2	1	no	—
59	C₂×C₈×C₄₇	—	2	1	no	—
60	C₂×C₈×C₄₇	M₁₆	1	2	yes	—
61	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₄₇	#41	1	2	yes	—
63	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
64	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
65	C₄²×C₄₇	—	2	1	no	—
66	C₄²×C₄₇	C₂×C₈	1	2	yes	—
67	C₄×Dic₄₇	—	2	1	no	—
68	C₄×Dic₄₇	—	2	4	no	—
69	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
70	C₂×C₄₇⋊C₈	—	2	1	no	—
71	C₂×C₄₇⋊C₈	—	2	1	no	—
72	C₂×C₄₇⋊C₈	—	2	1	no	—
73	C₂×C₄₇⋊C₈	—	2	1	no	—
74	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
75	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
76	#10625324	—	2	8	no	—
77	#10625324	—	2	4	no	—
78	#10625324	—	2	4	no	—
79	C₁₆×C₄₇	—	4	2	no	—
80	C₄₇⋊C₁₆	—	4	2	no	—
81	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
82	C₂²×D₄₇	—	2	1	no	—
83	C₂²×D₄₇	—	2	1	no	—
84	C₂²×D₄₇	—	4	2	no	—
85	C₂²×D₄₇	C₂²⋊C₈	1	2	yes	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
91	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
94	C₂×Dic₄₇	—	2	4	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	—	2	1	no	—
97	C₂×Dic₄₇	—	2	1	no	—
98	C₂×Dic₄₇	C₂²⋊C₈	1	2	yes	—
99	C₄×D₄₇	—	2	2	no	—
100	C₄×D₄₇	—	2	2	no	—
101	C₄×D₄₇	—	2	2	no	—
102	C₄×D₄₇	—	2	2	no	—
103	C₄×D₄₇	—	4	8	no	—
104	C₈×C₄₇	—	2	2	no	—
105	C₈×C₄₇	#123	1	2	yes	—
106	C₈×C₄₇	#123	1	2	yes	—
107	C₄₇⋊C₈	—	2	2	no	—
108	C₄₇⋊C₈	—	2	2	no	—
109	#12849	—	47	1	no	maximal, Sylow
110	C₂²×C₄₇	—	2	2	no	—
111	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
112	C₂²×C₄₇	#432	1	1	yes	characteristic
113	C₂²×C₄₇	#432	1	1	yes	characteristic
114	C₂×D₄₇	—	2	2	no	—
115	C₂×D₄₇	—	4	2	no	—
116	C₂×D₄₇	—	4	2	no	—
117	C₂×D₄₇	—	4	2	no	—
118	C₄×C₄₇	—	4	2	no	—
119	C₄×C₄₇	#381	1	1	yes	characteristic
120	C₄×C₄₇	#407	1	1	yes	characteristic
121	C₄×C₄₇	#431	1	1	yes	characteristic
122	C₄×C₄₇	#431	1	1	yes	characteristic
123	Dic₄₇	—	2	4	no	—
124	Dic₄₇	—	2	2	no	—
125	C₂×C₄×M₁₆	—	47	1	no	—
126	C₂×#349	—	47	2	no	—
127	#1376	—	47	2	no	—
128	#1375	—	47	1	no	—
129	#1375	D₄₇	1	1	yes	characteristic, complemented
130	C₂×C₄₇	—	2	1	no	—
131	C₂×C₄₇	—	2	1	no	—
132	C₂×C₄₇	#1817	1	1	yes	characteristic
133	C₂×C₄₇	#2165	1	2	yes	—
134	D₄₇	—	4	2	no	—
135	C₂²×M₁₆	—	47	1	no	—
136	C₂²×M₁₆	—	47	1	no	—
137	C₂²×C₄²	—	47	1	no	—
138	C₂×M₃₂	—	47	2	no	—
139	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
140	C₄×M₁₆	—	94	4	no	—
141	C₂×#97	—	47	1	no	—
142	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
143	C₂×C₄×C₈	—	47	1	no	—
144	C₂×C₄×C₈	—	47	1	no	—
145	#349	—	94	4	no	—
146	C₄₇	#12849	1	1	yes	characteristic, complemented, Sylow
147	C₂³×C₄	—	47	1	no	—
148	C₂³×C₄	—	94	1	no	—
149	C₂×M₁₆	—	47	4	no	—
150	C₂×M₁₆	—	94	2	no	—
151	C₂×M₁₆	—	94	2	no	—
152	C₂×M₁₆	—	94	2	no	—
153	C₂×M₁₆	—	94	2	no	—
154	C₂×M₁₆	—	94	1	no	—
155	C₂×M₁₆	—	94	1	no	—
156	C₂²×C₈	—	47	1	no	—
157	C₂²×C₈	—	47	1	no	—
158	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
159	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
160	C₂×C₄²	—	47	1	no	—
161	C₂×C₄²	—	47	4	no	—
162	C₂×C₄²	—	94	2	no	—
163	C₂×C₄²	—	94	1	no	—
164	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
165	M₃₂	—	2	2	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	94	2	no	—
168	M₃₂	—	94	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	94	2	no	—
171	#97	—	2	2	no	—
172	#97	—	94	2	no	—
173	C₄×C₈	—	94	2	no	—
174	C₄×C₈	—	94	2	no	—
175	C₂⁴	—	47	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	47	1	no	—
178	C₂²×C₄	—	47	2	no	—
179	C₂²×C₄	—	47	2	no	—
180	C₂²×C₄	—	94	4	no	—
181	C₂²×C₄	—	94	1	no	—
182	C₂²×C₄	—	94	1	no	—
183	C₂²×C₄	—	94	1	no	—
184	C₂²×C₄	—	94	1	no	—
185	C₂²×C₄	—	94	1	no	—
186	C₂²×C₄	—	188	4	no	—
187	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
188	M₁₆	—	94	8	no	—
189	M₁₆	—	94	4	no	—
190	M₁₆	—	94	4	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	47	2	no	—
194	C₂×C₈	—	47	2	no	—
195	C₂×C₈	—	94	1	no	—
196	C₂×C₈	—	94	1	no	—
197	C₂×C₈	—	94	1	no	—
198	C₂×C₈	—	94	1	no	—
199	C₂×C₈	#10625324	1	2	yes	—
200	C₂×C₈	#10625350	1	2	yes	—
201	C₂×C₈	D₄×D₄₇	1	2	yes	—
202	C₂×C₈	#10625352	1	1	yes	characteristic
203	C₂×C₈	#10625354	1	1	yes	characteristic
204	C₄²	—	2	1	no	—
205	C₄²	—	47	2	no	—
206	C₄²	—	94	4	no	—
207	C₄²	—	94	1	no	—
208	C₄²	C₈×D₄₇	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₁₆	—	188	2	no	—
211	C₂³	—	47	2	no	—
212	C₂³	—	94	1	no	—
213	C₂³	—	94	1	no	—
214	C₂³	—	188	2	no	—
215	C₂³	M₁₆×D₄₇	1	1	yes	characteristic
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	47	2	no	—
219	C₂×C₄	—	94	4	no	—
220	C₂×C₄	—	94	2	no	—
221	C₂×C₄	—	94	1	no	—
222	C₂×C₄	—	94	1	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	94	2	no	—
225	C₂×C₄	—	94	2	no	—
226	C₂×C₄	—	94	2	no	—
227	C₂×C₄	—	188	8	no	—
228	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
229	C₂×C₄	#13093981	1	1	yes	characteristic
230	C₂×C₄	#13093982	1	1	yes	characteristic
231	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
232	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
233	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
234	C₈	—	2	2	no	—
235	C₈	—	94	2	no	—
236	C₈	—	94	2	no	—
237	C₈	#13094006	1	2	yes	—
238	C₈	#13094009	1	2	yes	—
239	C₂²	—	2	2	no	—
240	C₂²	—	94	2	no	—
241	C₂²	—	188	2	no	—
242	C₂²	—	188	2	no	—
243	C₂²	—	188	2	no	—
244	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
245	C₂²	#15689178	1	1	yes	characteristic
246	C₂²	#15689179	1	1	yes	characteristic
247	C₄	—	4	2	no	—
248	C₄	—	94	4	no	—
249	C₄	—	94	2	no	—
250	C₄	#15688985	1	1	yes	characteristic
251	C₄	#15689085	1	1	yes	characteristic
252	C₄	#15689174	1	1	yes	characteristic
253	C₄	#15689175	1	1	yes	characteristic
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	—	188	2	no	—
257	C₂	#20243455	1	1	yes	characteristic
258	C₂	#20245198	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689075

C₂

yes

maximal, characteristic

C₂×#15688904

C₂

yes

maximal

#20241469

C₂

yes

maximal, complemented

#20241468

C₂

yes

maximal, characteristic, complemented

C₄₇×#1375

C₂

yes

maximal, characteristic, complemented

C₂²×#10625324

C₄

yes

characteristic

C₂²×#10625324

C₂²

yes

characteristic

C₂×C₄²×D₄₇

C₄

yes

characteristic

C₂×#13093964

C₂²

yes

—

#15689075

—

C₂×#13093935

C₄

yes

characteristic

C₂×C₈×Dic₄₇

C₄

yes

characteristic

C₂×C₈×Dic₄₇

C₂²

yes

characteristic

#15688904

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂×#97×C₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

—

C₂²×C₄×D₄₇

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄²×D₄₇

—

C₄²×D₄₇

C₈

yes

—

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093935

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

#97×C₄₇

—

C₂³×D₄₇

M₁₆

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

M₁₆

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂²⋊C₄

yes

—

C₂×C₄×D₄₇

C₂×C₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

M₁₆

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

#41

yes

—

C₂×C₈×C₄₇

yes

C₂×C₈×C₄₇

yes

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₈

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

M₁₆

yes

—

#10625324

—

#10625324

—

#10625324

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂²⋊C₈

yes

—

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×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₈

yes

—

C₄×D₄₇

—

100

C₄×D₄₇

—

101

C₄×D₄₇

—

102

C₄×D₄₇

—

103

C₄×D₄₇

—

104

C₈×C₄₇

—

105

C₈×C₄₇

#123

yes

—

106

C₈×C₄₇

#123

yes

—

107

C₄₇⋊C₈

—

108

C₄₇⋊C₈

—

109

#12849

—

maximal, Sylow

110

C₂²×C₄₇

—

111

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

112

C₂²×C₄₇

#432

yes

characteristic

113

C₂²×C₄₇

#432

yes

characteristic

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

—

117

C₂×D₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

#381

yes

characteristic

120

C₄×C₄₇

#407

yes

characteristic

121

C₄×C₄₇

#431

yes

characteristic

122

C₄×C₄₇

#431

yes

characteristic

123

Dic₄₇

—

124

Dic₄₇

—

125

C₂×C₄×M₁₆

—

126

C₂×#349

—

127

#1376

—

128

#1375

—

129

#1375

D₄₇

yes

characteristic, complemented

130

C₂×C₄₇

—

131

C₂×C₄₇

—

132

C₂×C₄₇

#1817

yes

characteristic

133

C₂×C₄₇

#2165

yes

—

134

D₄₇

—

135

C₂²×M₁₆

—

136

C₂²×M₁₆

—

137

C₂²×C₄²

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₄₇

yes

—

140

C₄×M₁₆

—

141

C₂×#97

—

142

C₂×#97

C₂×D₄₇

yes

characteristic

143

C₂×C₄×C₈

—

144

C₂×C₄×C₈

—

145

#349

—

146

C₄₇

#12849

yes

characteristic, complemented, Sylow

147

C₂³×C₄

—

148

C₂³×C₄

—

149

C₂×M₁₆

—

150

C₂×M₁₆

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

C₄×D₄₇

yes

characteristic

159

C₂²×C₈

C₂²×D₄₇

yes

characteristic

160

C₂×C₄²

—

161

C₂×C₄²

—

162

C₂×C₄²

—

163

C₂×C₄²

—

164

C₂×C₄²

C₄×D₄₇

yes

characteristic

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

M₃₂

—

169

C₂×C₁₆

—

170

C₂×C₁₆

—

171

#97

—

172

#97

—

173

C₄×C₈

—

174

C₄×C₈

—

175

C₂⁴

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

188

—

187

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

188

M₁₆

—

189

M₁₆

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

#10625324

yes

—

200

C₂×C₈

#10625350

yes

—

201

C₂×C₈

D₄×D₄₇

yes

—

202

C₂×C₈

#10625352

yes

characteristic

203

C₂×C₈

#10625354

yes

characteristic

204

C₄²

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

C₈×D₄₇

yes

—

209

C₁₆

—

210

C₁₆

—

188

—

211

C₂³

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

188

—

215

C₂³

M₁₆×D₄₇

yes

characteristic

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

188

—

228

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

229

C₂×C₄

#13093981

yes

characteristic

230

C₂×C₄

#13093982

yes

characteristic

231

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

232

C₂×C₄

M₁₆×D₄₇

yes

characteristic

233

C₂×C₄

C₂×#10625324

yes

characteristic

234

C₈

—

235

C₈

—

236

C₈

—

237

C₈

#13094006

yes

—

238

C₈

#13094009

yes

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

188

—

242

C₂²

—

188

—

243

C₂²

—

188

—

244

C₂²

C₂²⋊C₈×D₄₇

yes

characteristic

245

C₂²

#15689178

yes

characteristic

246

C₂²

#15689179

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

#15688985

yes

characteristic

251

C₄

#15689085

yes

characteristic

252

C₄

#15689174

yes

characteristic

253

C₄

#15689175

yes

characteristic

254

C₂

—

255

C₂

—

256

C₂

—

188

—

257

C₂

#20243455

yes

characteristic

258

C₂

#20245198

yes

—

	subgroup	G/H
center	C₂×C₄	#13093981
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1375	C₂
socle	C₂²×C₄₇	#432
prime radical	C₂³×D₄₇	M₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1375	D₄₇
hypocenter	C₄₇	#12849
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1375

subgroup

G/H

center

C₂×C₄

#13093981

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1375

C₂

socle

C₂²×C₄₇

#432

prime radical

C₂³×D₄₇

M₁₆

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1375

N	H ≅ G/N	type
3. #20241469	C₂	semidirect
4. #20241468	C₂	semidirect
5. C₄₇×#1375	C₂	semidirect
129. #1375	D₄₇	semidirect
146. C₄₇	#12849	semidirect

H ≅ G/N

type

3. #20241469

C₂

semidirect

4. #20241468

C₂

semidirect

5. C₄₇×#1375

C₂

semidirect

129. #1375

D₄₇

semidirect

146. C₄₇

#12849

semidirect

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

subgroup	index
C₂×#15689075	2
C₂×#15688904	2
#20241469	2
#20241468	2
C₄₇×#1375	2
#12849	47

subgroup

index

C₄₇×#1375

Subgroups — #26132504

Conjugacy classes of subgroups

Complements

Maximal subgroups