Group #26110152 — subgroups

Subgroups — #26110152

Order 12032.

454 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20252429	C₂	1	1	yes	maximal, characteristic
2	#20244183	C₂	1	1	yes	maximal, characteristic
3	#20242140	C₂	1	2	yes	maximal, complemented
4	#20241226	C₂	1	2	yes	maximal, complemented
5	C₄×#100×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#15689201	—	2	2	no	—
7	#15689201	—	2	2	no	—
8	#15689176	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
10	#15689087	—	2	2	no	—
11	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15688876	—	2	2	no	—
14	#15688874	—	2	2	no	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#100×C₄₇	C₄	1	2	yes	—
17	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#343	C₄	1	1	yes	characteristic
19	C₄₇×#343	C₄	1	1	yes	characteristic
20	C₂×#10625329	—	2	2	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
26	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
28	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
29	C₂²⋊(C₄₇⋊C₈)	—	4	4	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	D₄	1	2	yes	—
34	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
35	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
36	C₄×D₄×C₄₇	—	2	2	no	—
37	C₄×D₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₄₇	Q₈	1	2	yes	—
40	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
41	#100×C₄₇	—	2	4	no	—
42	#97×C₄₇	—	2	2	no	—
43	C₄×C₈×C₄₇	—	2	2	no	—
44	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
45	C₂×D₄×C₄₇	—	2	2	no	—
46	C₂×D₄×C₄₇	—	2	2	no	—
47	C₂×D₄×C₄₇	—	2	1	no	—
48	C₂×D₄×C₄₇	—	2	1	no	—
49	C₂²×C₄×C₄₇	—	2	2	no	—
50	C₂²×C₄×C₄₇	—	2	2	no	—
51	C₂²×C₄×C₄₇	—	4	2	no	—
52	C₂²×C₄×C₄₇	—	4	2	no	—
53	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
57	M₁₆×C₄₇	—	2	2	no	—
58	M₁₆×C₄₇	—	2	2	no	—
59	M₁₆×C₄₇	—	2	2	no	—
60	M₁₆×C₄₇	M₁₆	1	4	yes	complemented
61	C₂×C₈×C₄₇	—	2	2	no	—
62	C₂×C₈×C₄₇	—	2	2	no	—
63	C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂²⋊C₄×C₄₇	—	2	4	no	—
65	C₄²×C₄₇	C₂×D₄	1	2	yes	—
66	C₄²×C₄₇	#41	1	2	yes	—
67	#10625329	—	8	2	no	—
68	#10625329	—	8	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	2	2	no	—
71	C₂×C₄₇⋊C₈	—	2	2	no	—
72	C₂×C₄₇⋊C₈	—	4	1	no	—
73	C₂×C₄₇⋊C₈	—	4	1	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂×C₄₇⋊C₈	—	4	1	no	—
76	C₂³×C₄₇	—	2	2	no	—
77	C₂³×C₄₇	—	2	2	no	—
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	—	4	2	no	—
80	C₂³×C₄₇	—	4	2	no	—
81	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
82	D₄×C₄₇	—	4	2	no	—
83	D₄×C₄₇	—	4	2	no	—
84	C₂×C₄×C₄₇	—	2	1	no	—
85	C₂×C₄×C₄₇	—	2	1	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	4	1	no	—
88	C₂×C₄×C₄₇	—	4	2	no	—
89	C₂×C₄×C₄₇	—	4	2	no	—
90	C₂×C₄×C₄₇	—	4	2	no	—
91	C₂×C₄×C₄₇	—	8	2	no	—
92	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
94	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
95	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
96	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
99	C₈×C₄₇	—	2	4	no	—
100	C₈×C₄₇	—	4	2	no	—
101	C₄₇⋊C₈	—	4	2	no	—
102	C₄₇⋊C₈	—	4	2	no	—
103	C₄₇⋊C₈	—	4	2	no	—
104	C₄₇⋊C₈	—	8	1	no	—
105	#8837	—	47	1	no	maximal, Sylow
106	C₂²×C₄₇	—	2	1	no	—
107	C₂²×C₄₇	—	2	1	no	—
108	C₂²×C₄₇	—	4	4	no	—
109	C₂²×C₄₇	—	4	2	no	—
110	C₂²×C₄₇	—	4	2	no	—
111	C₂²×C₄₇	—	4	2	no	—
112	C₂²×C₄₇	—	8	2	no	—
113	C₂²×C₄₇	#385	1	1	yes	characteristic
114	C₂²×C₄₇	#423	1	1	yes	characteristic
115	C₂²×C₄₇	#424	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	#435	1	2	yes	—
120	C₄×C₄₇	#436	1	2	yes	—
121	C₄×C₄₇	#453	1	1	yes	characteristic
122	C₄×C₄₇	#455	1	1	yes	characteristic
123	#2975	—	47	1	no	—
124	#1954	—	47	1	no	—
125	C₄×#100	D₄₇	1	1	yes	characteristic
126	#1565	—	47	2	no	—
127	#1278	—	47	2	no	—
128	C₂×C₄₇	—	2	1	no	—
129	C₂×C₄₇	—	2	1	no	—
130	C₂×C₄₇	—	8	2	no	—
131	C₂×C₄₇	#1851	1	1	yes	characteristic
132	C₂×C₄₇	#1856	1	1	yes	characteristic
133	C₂×C₄₇	#1858	1	1	yes	characteristic
134	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
135	#436	—	94	2	no	—
136	#436	—	94	2	no	—
137	#431	—	47	2	no	—
138	C₂×C₄⋊C₈	—	47	1	no	—
139	C₂×#100	Dic₄₇	1	2	yes	—
140	#407	—	94	2	no	—
141	C₂×C₂²⋊C₈	—	94	2	no	—
142	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
143	C₂×C₄×C₈	—	47	1	no	—
144	#343	Dic₄₇	1	1	yes	characteristic
145	#343	Dic₄₇	1	1	yes	characteristic
146	#335	—	94	2	no	—
147	#334	—	94	2	no	—
148	C₄₇	#8837	1	1	yes	characteristic, complemented, Sylow
149	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
150	C₂³×C₄	D₁₈₈	1	2	yes	—
151	C₂×M₁₆	—	94	2	no	—
152	C₂×M₁₆	—	94	2	no	—
153	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
154	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
155	C₂²×C₈	—	94	1	no	—
156	C₂²×C₈	—	94	1	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	Dic₉₄	1	2	yes	—
161	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
162	C₄⋊C₈	—	47	2	no	—
163	C₄⋊C₈	—	47	2	no	—
164	C₄⋊C₈	—	94	2	no	—
165	#100	—	2	4	no	—
166	C₂²⋊C₈	—	94	4	no	—
167	C₂²⋊C₈	—	94	2	no	—
168	C₂²⋊C₈	—	188	4	no	—
169	#97	—	2	2	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	94	2	no	—
172	C₄×C₈	—	94	2	no	—
173	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	1	no	—
177	C₂×D₄	—	2	1	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
183	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
184	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
185	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
186	M₁₆	—	2	2	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	2	2	no	—
189	M₁₆	—	376	2	no	—
190	M₁₆	—	376	2	no	—
191	M₁₆	#10625329	1	4	yes	complemented
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	2	no	—
194	C₂×C₈	—	94	2	no	—
195	C₂×C₈	—	94	2	no	—
196	C₂×C₈	—	94	2	no	—
197	C₂×C₈	—	188	2	no	—
198	C₂×C₈	—	188	1	no	—
199	C₂×C₈	—	188	1	no	—
200	C₂×C₈	—	188	1	no	—
201	C₄⋊C₄	—	2	2	no	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	D₄×D₄₇	1	2	yes	—
204	C₄²	#10625352	1	2	yes	—
205	C₂³	—	2	2	no	—
206	C₂³	—	2	2	no	—
207	C₂³	—	2	2	no	—
208	C₂³	—	4	2	no	—
209	C₂³	—	4	2	no	—
210	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
211	D₄	—	4	2	no	—
212	D₄	—	4	2	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
222	C₂×C₄	#13093994	1	1	yes	characteristic
223	C₂×C₄	#13094001	1	2	yes	—
224	C₂×C₄	#13094008	1	1	yes	characteristic
225	C₂×C₄	C₂×#10625329	1	2	yes	—
226	C₂×C₄	#13094031	1	1	yes	characteristic
227	C₂×C₄	#13094031	1	1	yes	characteristic
228	C₈	—	2	4	no	—
229	C₈	—	4	2	no	—
230	C₈	—	376	1	no	—
231	C₈	—	188	2	no	—
232	C₈	—	188	2	no	—
233	C₈	—	188	2	no	—
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	4	4	no	—
237	C₂²	—	4	2	no	—
238	C₂²	—	4	2	no	—
239	C₂²	—	4	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	#15688998	1	1	yes	characteristic
242	C₂²	#15689147	1	1	yes	characteristic
243	C₂²	#15689150	1	1	yes	characteristic
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	—	4	2	no	—
247	C₄	#15689195	1	2	yes	—
248	C₄	#15689201	1	2	yes	—
249	C₄	#15689293	1	1	yes	characteristic
250	C₄	#15689303	1	1	yes	characteristic
251	C₂	—	2	1	no	—
252	C₂	—	2	1	no	—
253	C₂	—	8	2	no	—
254	C₂	#20243573	1	1	yes	characteristic
255	C₂	#20243600	1	1	yes	characteristic
256	C₂	#20243610	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252429

C₂

yes

maximal, characteristic

#20244183

C₂

yes

maximal, characteristic

#20242140

C₂

yes

maximal, complemented

#20241226

C₂

yes

maximal, complemented

C₄×#100×C₄₇

C₂

yes

maximal, characteristic

#15689201

—

#15689201

—

#15689176

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

#15689087

—

C₂×C₂²⋊(C₄₇⋊C₈)

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688876

—

#15688874

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₂×#100×C₄₇

C₄

yes

—

C₄×M₁₆×C₄₇

C₂²

yes

—

C₄₇×#343

C₄

yes

characteristic

C₄₇×#343

C₄

yes

characteristic

C₂×#10625329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₂²×D₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

Q₈

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#100×C₄₇

—

#97×C₄₇

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

C₄⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

M₁₆

yes

complemented

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

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

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

#123

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₈×C₄₇

—

100

C₈×C₄₇

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

—

104

C₄₇⋊C₈

—

105

#8837

—

maximal, Sylow

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

#385

yes

characteristic

114

C₂²×C₄₇

#423

yes

characteristic

115

C₂²×C₄₇

#424

yes

characteristic

116

C₄×C₄₇

—

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

#435

yes

—

120

C₄×C₄₇

#436

yes

—

121

C₄×C₄₇

#453

yes

characteristic

122

C₄×C₄₇

#455

yes

characteristic

123

#2975

—

124

#1954

—

125

C₄×#100

D₄₇

yes

characteristic

126

#1565

—

127

#1278

—

128

C₂×C₄₇

—

129

C₂×C₄₇

—

130

C₂×C₄₇

—

131

C₂×C₄₇

#1851

yes

characteristic

132

C₂×C₄₇

#1856

yes

characteristic

133

C₂×C₄₇

#1858

yes

characteristic

134

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

135

#436

—

136

#436

—

137

#431

—

138

C₂×C₄⋊C₈

—

139

C₂×#100

Dic₄₇

yes

—

140

#407

—

141

C₂×C₂²⋊C₈

—

142

C₄×M₁₆

C₂×D₄₇

yes

—

143

C₂×C₄×C₈

—

144

#343

Dic₄₇

yes

characteristic

145

#343

Dic₄₇

yes

characteristic

146

#335

—

147

#334

—

148

C₄₇

#8837

yes

characteristic, complemented, Sylow

149

C₂²×D₄

C₂×Dic₄₇

yes

characteristic

150

C₂³×C₄

D₁₈₈

yes

—

151

C₂×M₁₆

—

152

C₂×M₁₆

—

153

C₂×M₁₆

C₂×Dic₄₇

yes

—

154

C₂×M₁₆

C₂×Dic₄₇

yes

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

characteristic

160

C₂×C₂²⋊C₄

Dic₉₄

yes

—

161

C₂×C₄²

C₂²×D₄₇

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#100

—

166

C₂²⋊C₈

—

167

C₂²⋊C₈

—

168

C₂²⋊C₈

—

188

—

169

#97

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₄×C₈

—

173

C₂⁴

C₄⋊Dic₄₇

yes

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₄⋊Dic₄₇

yes

—

183

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

184

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

185

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

M₁₆

—

376

—

190

M₁₆

—

376

—

191

M₁₆

#10625329

yes

complemented

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

188

—

198

C₂×C₈

—

188

—

199

C₂×C₈

—

188

—

200

C₂×C₈

—

188

—

201

C₄⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

D₄×D₄₇

yes

—

204

C₄²

#10625352

yes

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×C₄⋊Dic₄₇

yes

characteristic

211

D₄

—

212

D₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

D₄×Dic₄₇

yes

—

222

C₂×C₄

#13093994

yes

characteristic

223

C₂×C₄

#13094001

yes

—

224

C₂×C₄

#13094008

yes

characteristic

225

C₂×C₄

C₂×#10625329

yes

—

226

C₂×C₄

#13094031

yes

characteristic

227

C₂×C₄

#13094031

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

376

—

231

C₈

—

188

—

232

C₈

—

188

—

233

C₈

—

188

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

#15688998

yes

characteristic

242

C₂²

#15689147

yes

characteristic

243

C₂²

#15689150

yes

characteristic

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

#15689195

yes

—

248

C₄

#15689201

yes

—

249

C₄

#15689293

yes

characteristic

250

C₄

#15689303

yes

characteristic

251

C₂

—

252

C₂

—

253

C₂

—

254

C₂

#20243573

yes

characteristic

255

C₂

#20243600

yes

characteristic

256

C₂

#20243610

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×#100×C₄₇	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×#100	D₄₇
hypocenter	C₄₇	#8837
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

subgroup

G/H

center

C₂×C₄

#13093994

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×#100×C₄₇

C₂

socle

C₂²×C₄₇

#385

prime radical

C₂²×D₄×C₄₇

C₂×C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#100

N	H ≅ G/N	type
3. #20242140	C₂	semidirect
4. #20241226	C₂	semidirect
60. M₁₆×C₄₇	M₁₆	semidirect
148. C₄₇	#8837	semidirect
191. M₁₆	#10625329	semidirect

H ≅ G/N

type

3. #20242140

C₂

semidirect

4. #20241226

C₂

semidirect

60. M₁₆×C₄₇

M₁₆

semidirect

148. C₄₇

#8837

semidirect

191. M₁₆

#10625329

semidirect

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

subgroup	index
#20252429	2
#20244183	2
#20242140	2
#20241226	2
C₄×#100×C₄₇	2
#8837	47

subgroup

index

C₄×#100×C₄₇

Subgroups — #26110152

Conjugacy classes of subgroups

Complements

Maximal subgroups