Group #26106923 — subgroups

Subgroups — #26106923

Order 12032.

486 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 167 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	#20245865	C₂	1	1	yes	maximal, characteristic
2	#20243134	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688853	C₂	1	2	yes	maximal
4	#20241227	C₂	1	2	yes	maximal
5	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
8	#15689029	C₄	1	2	yes	—
9	#15689021	C₄	1	2	yes	—
10	#15689007	—	2	2	no	—
11	C₄×Dic₄₇⋊C₄	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	#15688969	—	2	1	no	—
14	#15688878	—	2	2	no	—
15	#15688853	C₄	1	8	yes	complemented
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×#97×C₄₇	—	2	1	no	—
18	C₄³×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#336	—	2	1	no	—
20	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₄×Dic₉₄	—	2	2	no	—
23	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
24	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₄	—	2	1	no	—
27	C₂×Dic₄₇⋊C₄	—	2	2	no	—
28	C₂×C₄×Dic₄₇	—	2	1	no	—
29	C₂×C₄×Dic₄₇	—	2	1	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
32	C₄₇⋊#95	—	2	2	no	—
33	C₄₇⋊#95	—	2	2	no	—
34	C₄₇⋊#95	—	2	2	no	—
35	C₄₇⋊#95	—	2	1	no	—
36	C₂²×C₈×C₄₇	—	2	2	no	—
37	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₄₇	D₄	1	2	yes	—
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
44	#97×C₄₇	—	4	2	no	—
45	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₄₇	—	2	1	no	—
51	C₂²×Dic₄₇	—	2	1	no	—
52	C₂²×Dic₄₇	—	2	2	no	—
53	C₂×Dic₉₄	—	2	4	no	—
54	C₂×Dic₉₄	—	2	1	no	—
55	C₂×Dic₉₄	C₄²	1	2	yes	—
56	C₂×C₈×C₄₇	—	2	4	no	—
57	C₂×C₈×C₄₇	—	4	2	no	—
58	C₂×C₈×C₄₇	—	4	2	no	—
59	C₄²×C₄₇	—	2	4	no	—
60	C₄²×C₄₇	—	2	1	no	—
61	C₄²×C₄₇	—	2	1	no	—
62	C₄²×C₄₇	—	2	2	no	—
63	C₄²×C₄₇	—	4	2	no	—
64	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
65	C₄²×C₄₇	#41	1	2	yes	—
66	C₄⋊Dic₄₇	—	2	1	no	—
67	C₄⋊Dic₄₇	—	2	4	no	—
68	C₄⋊Dic₄₇	C₄²	1	2	yes	—
69	Dic₄₇⋊C₄	—	2	4	no	—
70	Dic₄₇⋊C₄	—	4	4	no	—
71	C₄×Dic₄₇	—	2	4	no	—
72	C₄×Dic₄₇	—	4	1	no	—
73	C₄×Dic₄₇	—	4	1	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂×C₄₇⋊C₈	—	4	4	no	—
76	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	2	2	no	—
80	C₂×C₄×C₄₇	—	2	2	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	C₂×C₄²	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₄₇	#131	1	4	yes	—
89	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#137	1	2	yes	—
91	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	2	no	—
96	C₂×Dic₄₇	—	4	2	no	—
97	C₂×Dic₄₇	—	4	2	no	—
98	C₂×Dic₄₇	—	4	2	no	—
99	Dic₉₄	—	2	4	no	—
100	Dic₉₄	—	4	2	no	—
101	C₈×C₄₇	—	4	4	no	—
102	C₄₇⋊C₈	—	4	4	no	—
103	#8178	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄₇	#408	1	2	yes	—
106	C₂²×C₄₇	#417	1	1	yes	characteristic
107	C₂²×C₄₇	#419	1	1	yes	characteristic
108	C₂²×C₄₇	#421	1	2	yes	—
109	C₄×C₄₇	—	2	2	no	—
110	C₄×C₄₇	—	4	2	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	#405	1	2	yes	—
113	C₄×C₄₇	#433	1	2	yes	—
114	C₄×C₄₇	#440	1	2	yes	—
115	C₄×C₄₇	#441	1	2	yes	—
116	Dic₄₇	—	4	2	no	—
117	Dic₄₇	—	4	2	no	—
118	Dic₄₇	—	8	2	no	—
119	#2295	—	47	1	no	—
120	#1767	D₄₇	1	1	yes	characteristic
121	#1744	—	47	1	no	—
122	C₂×Q₈⋊C₈	—	47	2	no	—
123	#1279	—	47	2	no	—
124	C₂×C₄₇	#1495	1	2	yes	—
125	C₂×C₄₇	#1497	1	2	yes	—
126	C₂×C₄₇	#1750	1	1	yes	characteristic
127	C₂×C₄₇	#1759	1	1	yes	characteristic
128	C₂×C₄₇	#1763	1	1	yes	characteristic
129	C₂×C₄×Q₈	—	47	1	no	—
130	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
131	C₂×#97	—	2	1	no	—
132	C₂×C₄×C₈	—	47	2	no	—
133	#391	—	47	2	no	—
134	#389	—	47	2	no	—
135	#387	—	94	2	no	—
136	C₄×C₄⋊C₄	—	47	1	no	—
137	C₄×C₄⋊C₄	—	94	1	no	—
138	#376	—	94	1	no	—
139	C₄³	C₂×D₄₇	1	1	yes	characteristic
140	#336	—	2	1	no	—
141	#336	—	94	2	no	—
142	Q₈⋊C₈	—	47	8	no	—
143	C₄₇	#8178	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	47	1	no	—
145	C₂²×C₈	—	2	2	no	—
146	C₂²×C₈	—	94	2	no	—
147	C₄×Q₈	—	47	4	no	—
148	C₄×Q₈	—	94	2	no	—
149	C₂×C₄⋊C₄	—	47	1	no	—
150	C₂×C₄⋊C₄	—	47	2	no	—
151	C₂×C₄⋊C₄	—	94	1	no	—
152	C₂×C₄⋊C₄	—	94	2	no	—
153	C₂×C₄²	—	94	1	no	—
154	C₂×C₄²	—	94	1	no	—
155	C₂×C₄²	C₄×D₄₇	1	2	yes	—
156	C₂×C₄²	D₁₈₈	1	2	yes	—
157	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
158	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
159	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
160	C₄⋊C₈	—	2	2	no	—
161	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
162	#97	—	4	2	no	—
163	C₄×C₈	—	47	4	no	—
164	C₄×C₈	—	94	2	no	—
165	#95	—	94	2	no	—
166	#95	—	94	2	no	—
167	#95	—	94	2	no	—
168	#95	—	94	1	no	—
169	C₂×Q₈	—	47	2	no	—
170	C₂×Q₈	—	94	1	no	—
171	C₂×Q₈	—	94	4	no	—
172	C₂²×C₄	—	94	1	no	—
173	C₂²×C₄	—	94	1	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
180	C₂×C₈	—	2	4	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	94	4	no	—
184	C₂×C₈	—	188	4	no	—
185	C₄⋊C₄	—	47	2	no	—
186	C₄⋊C₄	—	94	1	no	—
187	C₄⋊C₄	—	94	4	no	—
188	C₄⋊C₄	—	94	4	no	—
189	C₄⋊C₄	—	188	4	no	—
190	C₄²	—	2	4	no	—
191	C₄²	—	2	1	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	2	1	no	—
194	C₄²	—	4	2	no	—
195	C₄²	—	94	4	no	—
196	C₄²	—	188	1	no	—
197	C₄²	—	188	1	no	—
198	C₄²	C₂×C₄×D₄₇	1	2	yes	—
199	C₄²	#10625350	1	2	yes	—
200	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
201	Q₈	—	94	4	no	—
202	Q₈	—	188	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	94	2	no	—
211	C₂×C₄	—	94	2	no	—
212	C₂×C₄	—	188	2	no	—
213	C₂×C₄	—	188	2	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	—	188	2	no	—
216	C₂×C₄	—	188	2	no	—
217	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
218	C₂×C₄	#13093981	1	1	yes	characteristic
219	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
220	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
221	C₂×C₄	#13094032	1	4	yes	—
222	C₂×C₄	#13094050	1	1	yes	characteristic
223	C₂×C₄	#13094054	1	2	yes	—
224	C₂×C₄	#13094055	1	1	yes	characteristic
225	C₈	—	4	4	no	—
226	C₈	—	188	4	no	—
227	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
228	C₂²	#15689091	1	2	yes	—
229	C₂²	#15689122	1	1	yes	characteristic
230	C₂²	#15689131	1	1	yes	characteristic
231	C₂²	#15689139	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	4	2	no	—
234	C₄	—	4	2	no	—
235	C₄	—	376	2	no	—
236	C₄	—	188	2	no	—
237	C₄	—	188	2	no	—
238	C₄	#15689080	1	2	yes	—
239	C₄	#15689185	1	2	yes	—
240	C₄	#15689223	1	2	yes	—
241	C₄	#15689228	1	2	yes	—
242	C₂	#20241851	1	2	yes	—
243	C₂	#20241860	1	2	yes	—
244	C₂	#20243157	1	1	yes	characteristic
245	C₂	#20243201	1	1	yes	characteristic
246	C₂	#20243221	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20245865

C₂

yes

maximal, characteristic

#20243134

C₂

yes

maximal, characteristic

C₂×#15688853

C₂

yes

maximal

#20241227

C₂

yes

maximal

C₄₇×#1767

C₂

yes

maximal, characteristic

C₂×C₄×Dic₉₄

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

#15689029

C₄

yes

—

#15689021

C₄

yes

—

#15689007

—

C₄×Dic₄₇⋊C₄

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

—

C₄

yes

complemented

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×#97×C₄₇

—

C₄³×C₄₇

C₂²

yes

characteristic

C₄₇×#336

—

C₂²×Dic₉₄

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄×Dic₉₄

—

C₄×Dic₉₄

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

C₂×C₄

yes

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

#97×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄²

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₄²

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

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×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

100

Dic₉₄

—

101

C₈×C₄₇

—

102

C₄₇⋊C₈

—

103

#8178

—

maximal, Sylow

104

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

105

C₂²×C₄₇

#408

yes

—

106

C₂²×C₄₇

#417

yes

characteristic

107

C₂²×C₄₇

#419

yes

characteristic

108

C₂²×C₄₇

#421

yes

—

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

#405

yes

—

113

C₄×C₄₇

#433

yes

—

114

C₄×C₄₇

#440

yes

—

115

C₄×C₄₇

#441

yes

—

116

Dic₄₇

—

117

Dic₄₇

—

118

Dic₄₇

—

119

#2295

—

120

#1767

D₄₇

yes

characteristic

121

#1744

—

122

C₂×Q₈⋊C₈

—

123

#1279

—

124

C₂×C₄₇

#1495

yes

—

125

C₂×C₄₇

#1497

yes

—

126

C₂×C₄₇

#1750

yes

characteristic

127

C₂×C₄₇

#1759

yes

characteristic

128

C₂×C₄₇

#1763

yes

characteristic

129

C₂×C₄×Q₈

—

130

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

131

C₂×#97

—

132

C₂×C₄×C₈

—

133

#391

—

134

#389

—

135

#387

—

136

C₄×C₄⋊C₄

—

137

C₄×C₄⋊C₄

—

138

#376

—

139

C₄³

C₂×D₄₇

yes

characteristic

140

#336

—

141

#336

—

142

Q₈⋊C₈

—

143

C₄₇

#8178

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

C₄×D₄₇

yes

—

156

C₂×C₄²

D₁₈₈

yes

—

157

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

158

C₂×C₄²

C₂²⋊D₄₇

yes

characteristic

159

C₂×C₄²

C₂²×D₄₇

yes

characteristic

160

C₄⋊C₈

—

161

C₄⋊C₈

C₄×D₄₇

yes

—

162

#97

—

163

C₄×C₈

—

164

C₄×C₈

—

165

#95

—

166

#95

—

167

#95

—

168

#95

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

176

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

177

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

178

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

188

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

188

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

188

—

197

C₄²

—

188

—

198

C₄²

C₂×C₄×D₄₇

yes

—

199

C₄²

#10625350

yes

—

200

C₂³

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

201

Q₈

—

202

Q₈

—

188

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

188

—

213

C₂×C₄

—

188

—

214

C₂×C₄

—

188

—

215

C₂×C₄

—

188

—

216

C₂×C₄

—

188

—

217

C₂×C₄

C₄²×D₄₇

yes

characteristic

218

C₂×C₄

#13093981

yes

characteristic

219

C₂×C₄

C₄×C₂²⋊D₄₇

yes

—

220

C₂×C₄

C₄×D₁₈₈

yes

—

221

C₂×C₄

#13094032

yes

—

222

C₂×C₄

#13094050

yes

characteristic

223

C₂×C₄

#13094054

yes

—

224

C₂×C₄

#13094055

yes

characteristic

225

C₈

—

226

C₈

—

188

—

227

C₂²

C₄×(C₂×D₄₇)⋊C₄

yes

characteristic

228

C₂²

#15689091

yes

—

229

C₂²

#15689122

yes

characteristic

230

C₂²

#15689131

yes

characteristic

231

C₂²

#15689139

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

376

—

236

C₄

—

188

—

237

C₄

—

188

—

238

C₄

#15689080

yes

—

239

C₄

#15689185

yes

—

240

C₄

#15689223

yes

—

241

C₄

#15689228

yes

—

242

C₂

#20241851

yes

—

243

C₂

#20241860

yes

—

244

C₂

#20243157

yes

characteristic

245

C₂

#20243201

yes

characteristic

246

C₂

#20243221

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1767	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1767	D₄₇
hypocenter	C₄₇	#8178
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1767

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1767

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1767

N	H ≅ G/N	type
15. #15688853	C₄	semidirect
143. C₄₇	#8178	semidirect

H ≅ G/N

type

15. #15688853

C₄

semidirect

143. C₄₇

#8178

semidirect

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

subgroup	index
#20245865	2
#20243134	2
C₂×#15688853	2
#20241227	2
C₄₇×#1767	2
#8178	47

subgroup

index

C₄₇×#1767

Subgroups — #26106923

Conjugacy classes of subgroups

Complements

Maximal subgroups