Group #20247696 — subgroups

Subgroups — #20247696

Order 6016.

624 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13094005	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689053	C₂	1	2	yes	maximal, complemented
4	#15689048	C₂	1	2	yes	maximal, complemented
5	#15689021	C₂	1	2	yes	maximal, complemented
6	#15688984	C₂	1	2	yes	maximal, complemented
7	#15688983	C₂	1	2	yes	maximal, complemented
8	#15688983	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₄₇	C₂²	1	2	yes	—
11	#13094005	—	2	8	no	—
12	C₂×C₄⋊Dic₄₇	—	2	4	no	—
13	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
17	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
19	C₄₇⋊#95	C₂²	1	4	yes	—
20	C₄₇⋊#95	C₂²	1	2	yes	—
21	C₄₇⋊#95	C₂²	1	4	yes	—
22	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₄₇	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
31	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
32	C₂×D₄×C₄₇	—	2	2	no	—
33	C₂×D₄×C₄₇	—	2	2	no	—
34	C₂×D₄×C₄₇	D₄	1	4	yes	—
35	C₂²×C₄×C₄₇	—	2	4	no	—
36	C₂²×C₄×C₄₇	—	2	2	no	—
37	C₂²×C₄×C₄₇	—	2	4	no	—
38	C₂²×C₄×C₄₇	D₄	1	4	yes	—
39	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₇	—	2	4	no	—
45	C₂²×Dic₄₇	—	2	4	no	—
46	C₂²×Dic₄₇	—	2	4	no	—
47	C₂²×Dic₄₇	C₂³	1	4	yes	—
48	C₂²×Dic₄₇	C₂³	1	4	yes	—
49	C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂²⋊C₄×C₄₇	—	2	2	no	—
51	C₂²⋊C₄×C₄₇	—	2	2	no	—
52	C₄²×C₄₇	—	2	2	no	—
53	C₂²⋊Dic₄₇	—	2	4	no	—
54	C₂²⋊Dic₄₇	—	2	8	no	—
55	C₄⋊Dic₄₇	—	2	4	no	—
56	C₄⋊Dic₄₇	—	2	4	no	—
57	C₄⋊Dic₄₇	—	2	4	no	—
58	Dic₄₇⋊C₄	—	2	8	no	—
59	C₂³×C₄₇	—	2	2	no	—
60	C₂³×C₄₇	—	2	2	no	—
61	C₂³×C₄₇	—	2	1	no	—
62	C₂³×C₄₇	—	2	2	no	—
63	C₂³×C₄₇	—	2	1	no	—
64	C₂³×C₄₇	—	2	2	no	—
65	C₂³×C₄₇	C₂×D₄	1	2	yes	—
66	C₂³×C₄₇	C₂×D₄	1	2	yes	—
67	C₂³×C₄₇	C₂×D₄	1	2	yes	—
68	C₂³×C₄₇	#41	1	2	yes	—
69	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
70	D₄×C₄₇	—	2	8	no	—
71	C₂×C₄×C₄₇	—	2	1	no	—
72	C₂×C₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	1	no	—
74	C₂×C₄×C₄₇	—	2	8	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	2	no	—
79	C₂×C₄×C₄₇	—	4	4	no	—
80	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	#41	1	4	yes	—
84	C₂×Dic₄₇	—	2	4	no	—
85	C₂×Dic₄₇	—	2	4	no	—
86	C₂×Dic₄₇	—	2	4	no	—
87	C₂×Dic₄₇	—	2	4	no	—
88	C₂×Dic₄₇	—	2	4	no	—
89	C₂×Dic₄₇	—	2	4	no	—
90	C₂×Dic₄₇	—	4	8	no	—
91	C₂²×C₄₇	—	2	2	no	—
92	C₂²×C₄₇	—	2	2	no	—
93	C₂²×C₄₇	—	2	4	no	—
94	C₂²×C₄₇	—	2	4	no	—
95	C₂²×C₄₇	—	2	2	no	—
96	C₂²×C₄₇	—	2	4	no	—
97	C₂²×C₄₇	—	4	1	no	—
98	C₂²×C₄₇	—	4	1	no	—
99	C₂²×C₄₇	—	4	2	no	—
100	C₂²×C₄₇	#121	1	4	yes	—
101	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
102	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#41	1	2	yes	—
104	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
105	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
106	C₄×C₄₇	—	2	2	no	—
107	C₄×C₄₇	—	2	2	no	—
108	C₄×C₄₇	—	4	1	no	—
109	C₄×C₄₇	—	4	1	no	—
110	C₄×C₄₇	#123	1	4	yes	complemented
111	Dic₄₇	—	4	4	no	—
112	Dic₄₇	—	4	4	no	—
113	#2486	—	47	1	no	maximal, Sylow
114	C₂×C₄₇	—	2	4	no	—
115	C₂×C₄₇	—	4	2	no	—
116	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
117	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
118	C₂×C₄₇	#536	1	1	yes	characteristic
119	C₂×C₄₇	#547	1	2	yes	—
120	C₂×C₄₇	#552	1	2	yes	—
121	C₂×#123	—	47	2	no	—
122	C₂×C₄×D₄	D₄₇	1	1	yes	characteristic
123	C₂²×C₄⋊C₄	—	47	1	no	—
124	#398	—	47	2	no	—
125	#397	—	47	2	no	—
126	#389	—	47	2	no	—
127	#381	—	47	2	no	—
128	#380	—	47	2	no	—
129	#380	—	47	1	no	—
130	C₄₇	#2486	1	1	yes	characteristic, complemented, Sylow
131	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
132	C₂³×C₄	—	47	2	no	—
133	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
134	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
135	#123	—	94	8	no	—
136	C₄×D₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	47	2	no	—
138	C₂×C₄⋊C₄	—	47	2	no	—
139	C₂×C₄⋊C₄	—	47	4	no	—
140	C₂×C₄⋊C₄	—	47	2	no	—
141	C₂×C₄⋊C₄	—	94	4	no	—
142	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
143	C₂×C₂²⋊C₄	—	47	2	no	—
144	C₂×C₂²⋊C₄	—	47	4	no	—
145	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
146	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
147	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
148	#95	—	47	4	no	—
149	#95	—	47	2	no	—
150	#95	—	47	4	no	—
151	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
152	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
153	C₂×D₄	—	2	2	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	D₁₈₈	1	4	yes	—
156	C₂²×C₄	—	2	4	no	—
157	C₂²×C₄	—	2	4	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	47	4	no	—
160	C₂²×C₄	—	47	4	no	—
161	C₂²×C₄	—	94	4	no	—
162	C₂²×C₄	—	94	4	no	—
163	C₂²×C₄	—	94	4	no	—
164	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
165	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
166	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
167	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
168	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
169	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	94	8	no	—
172	C₄⋊C₄	—	94	4	no	—
173	C₄⋊C₄	—	94	4	no	—
174	C₄⋊C₄	—	94	4	no	—
175	C₂²⋊C₄	—	2	2	no	—
176	C₂²⋊C₄	—	2	2	no	—
177	C₂²⋊C₄	—	94	4	no	—
178	C₂²⋊C₄	—	94	8	no	—
179	C₄²	—	2	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	2	no	—
182	C₂³	—	2	1	no	—
183	C₂³	—	2	2	no	—
184	C₂³	—	2	1	no	—
185	C₂³	—	2	2	no	—
186	C₂³	C₂×D₁₈₈	1	2	yes	—
187	C₂³	C₂×D₁₈₈	1	2	yes	—
188	C₂³	#10625350	1	2	yes	—
189	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
190	C₂³	C₂³×D₄₇	1	1	yes	characteristic
191	D₄	—	2	8	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	94	4	no	—
202	C₂×C₄	—	94	4	no	—
203	C₂×C₄	—	94	4	no	—
204	C₂×C₄	—	94	4	no	—
205	C₂×C₄	—	94	4	no	—
206	C₂×C₄	—	94	4	no	—
207	C₂×C₄	—	188	8	no	—
208	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
209	C₂×C₄	#10625352	1	4	yes	—
210	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
211	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
212	C₂²	—	2	4	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	2	4	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	4	2	no	—
219	C₂²	—	4	1	no	—
220	C₂²	—	4	1	no	—
221	C₂²	#13093998	1	4	yes	—
222	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
223	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
224	C₂²	C₂×#10625352	1	2	yes	—
225	C₂²	C₂×#10625350	1	1	yes	characteristic
226	C₂²	#13094071	1	2	yes	—
227	C₄	—	2	2	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	1	no	—
231	C₄	—	188	4	no	—
232	C₄	—	188	4	no	—
233	C₄	#13094005	1	4	yes	complemented
234	C₂	—	2	4	no	—
235	C₂	—	4	2	no	—
236	C₂	C₂×#13093998	1	1	yes	characteristic
237	C₂	C₂×#13094005	1	1	yes	characteristic
238	C₂	#15689694	1	1	yes	characteristic
239	C₂	#15689777	1	2	yes	—
240	C₂	#15689813	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094005

C₂

yes

maximal

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15689053

C₂

yes

maximal, complemented

#15689048

C₂

yes

maximal, complemented

#15689021

C₂

yes

maximal, complemented

#15688984

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

#13094005

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×D₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

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

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

100

C₂²×C₄₇

#121

yes

—

101

C₂²×C₄₇

C₂²×D₄

yes

characteristic

102

C₂²×C₄₇

C₂²×D₄

yes

characteristic

103

C₂²×C₄₇

C₂×#41

yes

—

104

C₂²×C₄₇

C₂×#41

yes

characteristic

105

C₂²×C₄₇

2₋¹⁺⁴

yes

—

106

C₄×C₄₇

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#123

yes

complemented

111

Dic₄₇

—

112

Dic₄₇

—

113

#2486

—

maximal, Sylow

114

C₂×C₄₇

—

115

C₂×C₄₇

—

116

C₂×C₄₇

C₂×#121

yes

characteristic

117

C₂×C₄₇

C₂×#123

yes

characteristic

118

C₂×C₄₇

#536

yes

characteristic

119

C₂×C₄₇

#547

yes

—

120

C₂×C₄₇

#552

yes

—

121

C₂×#123

—

122

C₂×C₄×D₄

D₄₇

yes

characteristic

123

C₂²×C₄⋊C₄

—

124

#398

—

125

#397

—

126

#389

—

127

#381

—

128

#380

—

129

#380

—

130

C₄₇

#2486

yes

characteristic, complemented, Sylow

131

C₂²×D₄

C₂×D₄₇

yes

characteristic

132

C₂³×C₄

—

133

C₂³×C₄

C₂×D₄₇

yes

characteristic

134

C₂³×C₄

C₂×D₄₇

yes

characteristic

135

#123

—

136

C₄×D₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

143

C₂×C₂²⋊C₄

—

144

C₂×C₂²⋊C₄

—

145

C₂×C₂²⋊C₄

C₂×D₄₇

yes

characteristic

146

C₂×C₂²⋊C₄

C₂×D₄₇

yes

characteristic

147

C₂×C₄²

C₂×D₄₇

yes

characteristic

148

#95

—

149

#95

—

150

#95

—

151

C₂⁴

C₂²×D₄₇

yes

characteristic

152

C₂⁴

C₂²×D₄₇

yes

characteristic

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

D₁₈₈

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂²⋊D₄₇

yes

—

165

C₂²×C₄

C₂²×D₄₇

yes

characteristic

166

C₂²×C₄

C₂²×D₄₇

yes

characteristic

167

C₂²×C₄

C₂²×D₄₇

yes

characteristic

168

C₂²×C₄

C₂²×D₄₇

yes

characteristic

169

C₂²×C₄

C₂²×D₄₇

yes

characteristic

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₂²⋊C₄

—

179

C₄²

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

C₂×D₁₈₈

yes

—

187

C₂³

C₂×D₁₈₈

yes

—

188

C₂³

#10625350

yes

—

189

C₂³

C₂×C₂²⋊D₄₇

yes

—

190

C₂³

C₂³×D₄₇

yes

characteristic

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

188

—

208

C₂×C₄

C₂×D₁₈₈

yes

—

209

C₂×C₄

#10625352

yes

—

210

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

211

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

#13093998

yes

—

222

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

223

C₂²

C₂²×D₁₈₈

yes

characteristic

224

C₂²

C₂×#10625352

yes

—

225

C₂²

C₂×#10625350

yes

characteristic

226

C₂²

#13094071

yes

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

188

—

232

C₄

—

188

—

233

C₄

#13094005

yes

complemented

234

C₂

—

235

C₂

—

236

C₂

C₂×#13093998

yes

characteristic

237

C₂

C₂×#13094005

yes

characteristic

238

C₂

#15689694

yes

characteristic

239

C₂

#15689777

yes

—

240

C₂

#15689813

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×C₄×D₄×C₄₇	C₂
hypercenter	C₂×C₄×D₄	D₄₇
hypocenter	C₄₇	#2486
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×C₄×D₄×C₄₇

C₂

hypercenter

C₂×C₄×D₄

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×C₄×D₄

N	H ≅ G/N	type
2. C₂²×C₄⋊Dic₄₇	C₂	semidirect
3. #15689053	C₂	semidirect
4. #15689048	C₂	semidirect
5. #15689021	C₂	semidirect
6. #15688984	C₂	semidirect
7. #15688983	C₂	semidirect
8. #15688983	C₂	semidirect
110. C₄×C₄₇	#123	semidirect
130. C₄₇	#2486	semidirect
233. C₄	#13094005	semidirect

H ≅ G/N

type

2. C₂²×C₄⋊Dic₄₇

C₂

semidirect

3. #15689053

C₂

semidirect

4. #15689048

C₂

semidirect

5. #15689021

C₂

semidirect

6. #15688984

C₂

semidirect

7. #15688983

C₂

semidirect

8. #15688983

C₂

semidirect

110. C₄×C₄₇

#123

semidirect

130. C₄₇

#2486

semidirect

233. C₄

#13094005

semidirect

Subgroups — #20247696

Conjugacy classes of subgroups

Complements