Group #26134437 — subgroups

Subgroups — #26134437

Order 12032.

522 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 159 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×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₄₇)⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
6	C₂×C₄×D₁₈₈	C₄	1	1	yes	characteristic
7	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
8	C₈×D₁₈₈	—	2	2	no	—
9	C₈×D₁₈₈	—	2	2	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
12	C₄⋊(C₄₇⋊C₁₆)	—	2	2	no	—
13	(C₂×D₄₇)⋊C₁₆	—	2	8	no	—
14	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#346	—	2	2	no	—
17	C₂²×D₁₈₈	C₈	1	1	yes	characteristic
18	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
19	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
20	C₂×C₈×D₄₇	—	2	4	no	—
21	C₂×C₈×D₄₇	—	2	2	no	—
22	C₂×C₈×D₄₇	—	2	2	no	—
23	C₂×C₈×D₄₇	—	2	4	no	—
24	C₄×D₁₈₈	—	2	2	no	—
25	C₄×D₁₈₈	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₄	C₈	1	2	yes	—
28	C₂×C₄₇⋊C₁₆	—	2	4	no	—
29	C₂×C₄₇⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	(C₂×D₄₇)⋊C₈	—	2	4	no	—
32	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₁₆×C₄₇	—	2	2	no	—
36	C₂×C₁₆×C₄₇	—	2	2	no	—
37	C₂×C₁₆×C₄₇	D₄	1	4	yes	complemented
38	C₄×C₈×C₄₇	D₄	1	2	yes	—
39	C₄×C₈×C₄₇	D₄	1	2	yes	—
40	C₂³×D₄₇	C₂×C₈	1	2	yes	—
41	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
44	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
45	C₂×D₁₈₈	—	2	4	no	—
46	C₂×D₁₈₈	—	2	2	no	—
47	C₂×C₄×D₄₇	—	2	2	no	—
48	C₂×C₄×D₄₇	—	2	4	no	—
49	C₂×C₄×D₄₇	—	2	2	no	—
50	C₂×C₄×D₄₇	—	2	4	no	—
51	C₂×C₈×C₄₇	—	2	2	no	—
52	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
53	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
55	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₄₇	#41	1	2	yes	—
57	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₄₇	M₁₆	1	2	yes	—
59	(C₂×D₄₇)⋊C₄	—	2	4	no	—
60	C₄⋊Dic₄₇	—	2	2	no	—
61	C₂×C₄₇⋊C₈	—	2	2	no	—
62	C₂×C₄₇⋊C₈	—	2	4	no	—
63	C₈×D₄₇	—	4	4	no	—
64	C₈×D₄₇	—	4	2	no	—
65	C₈×D₄₇	—	4	2	no	—
66	C₁₆×C₄₇	—	2	4	no	—
67	C₄₇⋊C₁₆	—	4	2	no	—
68	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
69	C₂²×D₄₇	—	2	2	no	—
70	C₂²×D₄₇	—	2	4	no	—
71	C₂²×D₄₇	—	2	2	no	—
72	C₂²×D₄₇	—	2	4	no	—
73	C₂²×D₄₇	M₃₂	1	4	yes	—
74	C₂×C₄×C₄₇	—	2	2	no	—
75	C₂×C₄×C₄₇	—	2	2	no	—
76	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
77	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
80	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₄₇	#131	1	2	yes	—
82	C₂×Dic₄₇	—	2	2	no	—
83	C₂×Dic₄₇	—	2	4	no	—
84	D₁₈₈	—	2	8	no	—
85	C₄×D₄₇	—	4	2	no	—
86	C₄×D₄₇	—	4	2	no	—
87	C₄×D₄₇	—	4	4	no	—
88	C₈×C₄₇	—	2	2	no	—
89	C₈×C₄₇	#121	1	2	yes	—
90	C₈×C₄₇	#124	1	1	yes	characteristic
91	C₈×C₄₇	#127	1	1	yes	characteristic
92	C₄₇⋊C₈	—	4	2	no	—
93	#13190	—	47	1	no	maximal, Sylow
94	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₂²×C₄₇	C₈×D₄	1	2	yes	—
96	C₂²×C₄₇	C₂×M₃₂	1	2	yes	—
97	C₂²×C₄₇	#504	1	2	yes	—
98	C₂×D₄₇	—	2	4	no	—
99	C₂×D₄₇	—	2	8	no	—
100	C₂×D₄₇	—	4	2	no	—
101	C₂×D₄₇	—	4	4	no	—
102	C₂×D₄₇	—	4	2	no	—
103	C₄×C₄₇	—	2	2	no	—
104	C₄×C₄₇	—	2	2	no	—
105	C₄×C₄₇	#390	1	1	yes	characteristic
106	C₄×C₄₇	#408	1	1	yes	characteristic
107	C₄×C₄₇	#436	1	2	yes	—
108	Dic₄₇	—	4	2	no	—
109	C₂×C₈×D₄	—	47	1	no	—
110	C₂×C₄⋊C₁₆	—	47	1	no	—
111	C₂×C₂²⋊C₁₆	—	47	4	no	—
112	C₂×#346	D₄₇	1	1	yes	characteristic, complemented
113	C₂×C₄₇	#1954	1	1	yes	characteristic
114	C₂×C₄₇	#2112	1	1	yes	characteristic
115	C₂×C₄₇	#2113	1	1	yes	characteristic
116	C₂×C₄₇	#2168	1	4	yes	—
117	D₄₇	—	4	4	no	—
118	C₂³×C₈	—	47	2	no	—
119	C₂×C₄×D₄	—	47	1	no	—
120	C₂²×C₁₆	—	47	2	no	—
121	C₂²×C₁₆	C₂×D₄₇	1	2	yes	—
122	C₈×D₄	—	94	2	no	—
123	C₈×D₄	—	94	2	no	—
124	C₂×C₄⋊C₈	—	47	1	no	—
125	C₂×C₂²⋊C₈	—	47	2	no	—
126	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
127	C₄⋊C₁₆	—	94	2	no	—
128	C₂²⋊C₁₆	—	94	8	no	—
129	#346	—	2	2	no	—
130	C₄₇	#13190	1	1	yes	characteristic, complemented, Sylow
131	C₂²×D₄	—	47	1	no	—
132	C₂³×C₄	—	47	2	no	—
133	C₂²×C₈	—	47	2	no	—
134	C₂²×C₈	—	94	4	no	—
135	C₂²×C₈	—	94	2	no	—
136	C₂²×C₈	—	94	4	no	—
137	C₂²×C₈	—	94	2	no	—
138	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
139	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
140	C₄×D₄	—	94	2	no	—
141	C₄×D₄	—	94	2	no	—
142	C₂×C₄⋊C₄	—	47	1	no	—
143	C₂×C₂²⋊C₄	—	47	2	no	—
144	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
145	C₂×C₁₆	—	2	2	no	—
146	C₂×C₁₆	—	2	2	no	—
147	C₂×C₁₆	—	94	4	no	—
148	C₂×C₁₆	—	94	2	no	—
149	C₂×C₁₆	D₁₈₈	1	4	yes	complemented
150	C₄⋊C₈	—	94	2	no	—
151	C₂²⋊C₈	—	94	4	no	—
152	C₄×C₈	D₁₈₈	1	2	yes	—
153	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
154	C₂⁴	—	47	2	no	—
155	C₂×D₄	—	94	4	no	—
156	C₂×D₄	—	94	2	no	—
157	C₂²×C₄	—	47	2	no	—
158	C₂²×C₄	—	94	2	no	—
159	C₂²×C₄	—	94	4	no	—
160	C₂²×C₄	—	94	2	no	—
161	C₂²×C₄	—	94	4	no	—
162	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
163	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	94	2	no	—
167	C₂×C₈	—	94	4	no	—
168	C₂×C₈	—	188	4	no	—
169	C₂×C₈	—	188	2	no	—
170	C₂×C₈	—	188	2	no	—
171	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
172	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
173	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
174	C₂×C₈	#10625350	1	2	yes	—
175	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
176	C₄⋊C₄	—	94	2	no	—
177	C₂²⋊C₄	—	94	4	no	—
178	C₄²	#10625324	1	2	yes	—
179	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
180	C₁₆	—	2	4	no	—
181	C₁₆	—	188	2	no	—
182	C₂³	—	47	4	no	—
183	C₂³	—	94	2	no	—
184	C₂³	—	94	4	no	—
185	C₂³	—	94	2	no	—
186	C₂³	—	94	4	no	—
187	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
188	D₄	—	94	8	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	94	2	no	—
192	C₂×C₄	—	94	4	no	—
193	C₂×C₄	—	188	2	no	—
194	C₂×C₄	—	188	2	no	—
195	C₂×C₄	—	188	4	no	—
196	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
197	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
198	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
199	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
200	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
201	C₂×C₄	#13094030	1	2	yes	—
202	C₈	—	2	2	no	—
203	C₈	—	188	2	no	—
204	C₈	#13093998	1	2	yes	—
205	C₈	#13094012	1	1	yes	characteristic
206	C₈	#13094021	1	1	yes	characteristic
207	C₂²	—	94	4	no	—
208	C₂²	—	94	8	no	—
209	C₂²	—	188	2	no	—
210	C₂²	—	188	2	no	—
211	C₂²	—	188	4	no	—
212	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
213	C₂²	C₈×D₁₈₈	1	2	yes	—
214	C₂²	M₃₂×D₄₇	1	2	yes	—
215	C₂²	#15689541	1	2	yes	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	188	2	no	—
219	C₄	#15689025	1	1	yes	characteristic
220	C₄	#15689089	1	1	yes	characteristic
221	C₄	#15689202	1	2	yes	—
222	C₂	—	188	4	no	—
223	C₂	#20244182	1	1	yes	characteristic
224	C₂	#20244998	1	1	yes	characteristic
225	C₂	#20245003	1	1	yes	characteristic
226	C₂	#20245215	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₁₈₈

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, complemented

C₂×C₄₇×#346

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₇

C₂²

yes

—

C₂×C₄×D₁₈₈

C₄

yes

characteristic

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

C₈×D₁₈₈

—

C₈×D₁₈₈

—

C₂×C₄⋊(C₄₇⋊C₈)

C₄

yes

characteristic

C₂×(C₂×D₄₇)⋊C₈

C₄

yes

—

C₄⋊(C₄₇⋊C₁₆)

—

(C₂×D₄₇)⋊C₁₆

—

C₂²×C₁₆×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#346

—

C₂²×D₁₈₈

C₈

yes

characteristic

C₂²×C₄×D₄₇

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₄×D₁₈₈

—

C₄×D₁₈₈

—

C₂×C₄⋊Dic₄₇

C₈

yes

characteristic

C₂×(C₂×D₄₇)⋊C₄

C₈

yes

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₄⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

complemented

C₄×C₈×C₄₇

D₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂³×D₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₈

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₄²×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

M₁₆

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₈×D₄₇

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂²×C₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

M₃₂

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

#131

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

#121

yes

—

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

—

#13190

—

maximal, Sylow

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₄₇

C₈×D₄

yes

—

C₂²×C₄₇

C₂×M₃₂

yes

—

C₂²×C₄₇

#504

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

100

C₂×D₄₇

—

101

C₂×D₄₇

—

102

C₂×D₄₇

—

103

C₄×C₄₇

—

104

C₄×C₄₇

—

105

C₄×C₄₇

#390

yes

characteristic

106

C₄×C₄₇

#408

yes

characteristic

107

C₄×C₄₇

#436

yes

—

108

Dic₄₇

—

109

C₂×C₈×D₄

—

110

C₂×C₄⋊C₁₆

—

111

C₂×C₂²⋊C₁₆

—

112

C₂×#346

D₄₇

yes

characteristic, complemented

113

C₂×C₄₇

#1954

yes

characteristic

114

C₂×C₄₇

#2112

yes

characteristic

115

C₂×C₄₇

#2113

yes

characteristic

116

C₂×C₄₇

#2168

yes

—

117

D₄₇

—

118

C₂³×C₈

—

119

C₂×C₄×D₄

—

120

C₂²×C₁₆

—

121

C₂²×C₁₆

C₂×D₄₇

yes

—

122

C₈×D₄

—

123

C₈×D₄

—

124

C₂×C₄⋊C₈

—

125

C₂×C₂²⋊C₈

—

126

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

127

C₄⋊C₁₆

—

128

C₂²⋊C₁₆

—

129

#346

—

130

C₄₇

#13190

yes

characteristic, complemented, Sylow

131

C₂²×D₄

—

132

C₂³×C₄

—

133

C₂²×C₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

C₄×D₄₇

yes

characteristic

139

C₂²×C₈

C₂²×D₄₇

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

C₂×C₄²

C₄×D₄₇

yes

characteristic

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

—

148

C₂×C₁₆

—

149

C₂×C₁₆

D₁₈₈

yes

complemented

150

C₄⋊C₈

—

151

C₂²⋊C₈

—

152

C₄×C₈

D₁₈₈

yes

—

153

C₄×C₈

C₂²⋊D₄₇

yes

—

154

C₂⁴

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

C₈×D₄₇

yes

characteristic

163

C₂²×C₄

C₈×D₄₇

yes

characteristic

164

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

188

—

169

C₂×C₈

—

188

—

170

C₂×C₈

—

188

—

171

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

172

C₂×C₈

C₂×D₁₈₈

yes

—

173

C₂×C₈

C₂×D₁₈₈

yes

characteristic

174

C₂×C₈

#10625350

yes

—

175

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

176

C₄⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

#10625324

yes

—

179

C₄²

(C₂×D₄₇)⋊C₄

yes

—

180

C₁₆

—

181

C₁₆

—

188

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

C₂×C₈×D₄₇

yes

characteristic

188

D₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

188

—

194

C₂×C₄

—

188

—

195

C₂×C₄

—

188

—

196

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

197

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

198

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

199

C₂×C₄

C₄×D₁₈₈

yes

—

200

C₂×C₄

C₂×#10625324

yes

characteristic

201

C₂×C₄

#13094030

yes

—

202

C₈

—

203

C₈

—

188

—

204

C₈

#13093998

yes

—

205

C₈

#13094012

yes

characteristic

206

C₈

#13094021

yes

characteristic

207

C₂²

—

208

C₂²

—

209

C₂²

—

188

—

210

C₂²

—

188

—

211

C₂²

—

188

—

212

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

213

C₂²

C₈×D₁₈₈

yes

—

214

C₂²

M₃₂×D₄₇

yes

—

215

C₂²

#15689541

yes

—

216

C₄

—

217

C₄

—

218

C₄

—

188

—

219

C₄

#15689025

yes

characteristic

220

C₄

#15689089

yes

characteristic

221

C₄

#15689202

yes

—

222

C₂

—

188

—

223

C₂

#20244182

yes

characteristic

224

C₂

#20244998

yes

characteristic

225

C₂

#20245003

yes

characteristic

226

C₂

#20245215

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂²×C₈
Fitting	C₂×C₄₇×#346	C₂
prime radical	C₂²×D₁₈₈	C₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×#346	D₄₇
hypocenter	C₄₇	#13190
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#346

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₄₇

commutator, socle

C₂³×C₄₇

C₂²×C₈

Fitting

C₂×C₄₇×#346

C₂

prime radical

C₂²×D₁₈₈

C₈

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₈ ◁ C₂×#346

N	H ≅ G/N	type
2. C₂×C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
3. C₂×(C₂×D₄₇)⋊C₁₆	C₂	semidirect
4. C₂×C₄₇×#346	C₂	semidirect
37. C₂×C₁₆×C₄₇	D₄	semidirect
112. C₂×#346	D₄₇	semidirect
130. C₄₇	#13190	semidirect
149. C₂×C₁₆	D₁₈₈	semidirect

H ≅ G/N

type

2. C₂×C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

3. C₂×(C₂×D₄₇)⋊C₁₆

C₂

semidirect

4. C₂×C₄₇×#346

C₂

semidirect

37. C₂×C₁₆×C₄₇

D₄

semidirect

112. C₂×#346

D₄₇

semidirect

130. C₄₇

#13190

semidirect

149. C₂×C₁₆

D₁₈₈

semidirect

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

subgroup	index
C₂×C₈×D₁₈₈	2
C₂×C₄⋊(C₄₇⋊C₁₆)	2
C₂×(C₂×D₄₇)⋊C₁₆	2
C₂×C₄₇×#346	2
#13190	47

subgroup

index

C₂×C₈×D₁₈₈

C₂×C₄⋊(C₄₇⋊C₁₆)

C₂×(C₂×D₄₇)⋊C₁₆

C₂×C₄₇×#346

#13190

Subgroups — #26134437

Conjugacy classes of subgroups

Complements

Maximal subgroups