Group #26107221 — subgroups

Subgroups — #26107221

Order 12032.

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

normal subgroups only

This group has 540 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	#20245955	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×Dic₄₇	C₂	1	2	yes	maximal
3	C₂×#15688871	C₂	1	2	yes	maximal
4	#20241271	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×#13093989	C₄	1	2	yes	—
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₈×Dic₄₇	—	2	2	no	—
10	#15689028	C₄	1	2	yes	—
11	#15689019	—	2	2	no	—
12	C₄⋊C₄×Dic₄₇	—	2	2	no	—
13	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15688877	—	2	2	no	—
15	#15688871	C₄	1	8	yes	complemented
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#384	C₂²	1	1	yes	characteristic
18	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	#13094024	—	2	1	no	—
21	#13094024	—	2	1	no	—
22	#13094024	C₂×C₄	1	4	yes	—
23	#13093989	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×Dic₄₇⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₄₇	—	2	2	no	—
27	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
30	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
33	C₈×Dic₄₇	—	4	4	no	—
34	C₄₇⋊#95	—	2	4	no	—
35	C₂²×C₈×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
39	C₄⋊C₈×C₄₇	—	2	2	no	—
40	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
41	C₂²×C₄×C₄₇	—	2	2	no	—
42	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
44	C₂²×Dic₄₇	—	2	2	no	—
45	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
47	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×Dic₉₄	—	2	2	no	—
49	C₂×Dic₉₄	—	4	2	no	—
50	C₂×Dic₉₄	—	4	2	no	—
51	C₂×Dic₉₄	C₄²	1	4	yes	—
52	C₂×C₈×C₄₇	—	2	4	no	—
53	C₂×C₈×C₄₇	—	4	2	no	—
54	C₂×C₈×C₄₇	—	4	2	no	—
55	C₄⋊C₄×C₄₇	—	4	2	no	—
56	C₄⋊C₄×C₄₇	—	4	2	no	—
57	C₄⋊C₄×C₄₇	—	4	2	no	—
58	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
59	C₄²×C₄₇	#41	1	1	yes	characteristic
60	C₄²×C₄₇	#41	1	1	yes	characteristic
61	C₄⋊Dic₄₇	—	2	4	no	—
62	C₄⋊Dic₄₇	—	2	4	no	—
63	Dic₄₇⋊C₄	—	4	4	no	—
64	C₄×Dic₄₇	—	2	2	no	—
65	C₄×Dic₄₇	—	2	2	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	4	1	no	—
68	C₄×Dic₄₇	—	4	4	no	—
69	C₄×Dic₄₇	SD₁₆	1	4	yes	—
70	C₄×Dic₄₇	Q₁₆	1	4	yes	—
71	C₂×C₄₇⋊C₈	—	2	4	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	—	4	2	no	—
78	C₂×C₄×C₄₇	—	4	4	no	—
79	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
84	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
85	C₂×C₄×C₄₇	#135	1	2	yes	—
86	C₂×C₄×C₄₇	#135	1	2	yes	—
87	C₂×Dic₄₇	—	2	2	no	—
88	C₂×Dic₄₇	—	2	2	no	—
89	C₂×Dic₄₇	—	2	4	no	—
90	C₂×Dic₄₇	—	2	1	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	4	2	no	—
93	C₂×Dic₄₇	—	4	2	no	—
94	C₂×Dic₄₇	#100	1	2	yes	—
95	C₂×Dic₄₇	#103	1	4	yes	—
96	C₂×Dic₄₇	#103	1	4	yes	—
97	Dic₉₄	—	4	4	no	—
98	Dic₉₄	—	4	4	no	—
99	C₈×C₄₇	—	4	4	no	—
100	C₄₇⋊C₈	—	4	4	no	—
101	C₄×#333	—	47	1	no	maximal, Sylow
102	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
104	C₂²×C₄₇	#413	1	1	yes	characteristic
105	C₂²×C₄₇	C₂×#103	1	2	yes	—
106	C₂²×C₄₇	#416	1	2	yes	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	—	8	2	no	—
110	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
111	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
112	C₄×C₄₇	C₄×Q₁₆	1	2	yes	—
113	C₄×C₄₇	C₄×Q₁₆	1	2	yes	—
114	Dic₄₇	—	2	4	no	—
115	Dic₄₇	—	4	1	no	—
116	Dic₄₇	—	4	4	no	—
117	Dic₄₇	#333	1	4	yes	complemented
118	C₄×C₄⋊Q₈	—	47	1	no	—
119	C₄×C₄⋊C₈	—	47	2	no	—
120	C₂×#333	—	47	2	no	—
121	#1296	—	47	1	no	—
122	#1296	D₄₇	1	1	yes	characteristic
123	C₂×C₄₇	C₂×#333	1	1	yes	characteristic
124	C₂×C₄₇	#1542	1	2	yes	—
125	C₂×C₄₇	#1543	1	1	yes	characteristic
126	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
127	C₂×C₄₇	C₄×#103	1	2	yes	—
128	C₂×C₄⋊Q₈	—	47	1	no	—
129	C₂×C₄×Q₈	—	47	2	no	—
130	C₂×C₄⋊C₈	—	47	2	no	—
131	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
132	C₂×C₄×C₈	—	94	2	no	—
133	#391	—	47	2	no	—
134	#389	—	94	2	no	—
135	#384	C₂×D₄₇	1	1	yes	characteristic
136	C₄×C₄⋊C₄	—	94	2	no	—
137	C₄³	—	47	1	no	—
138	#336	—	94	2	no	—
139	#333	—	47	8	no	—
140	C₄₇	C₄×#333	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	2	no	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	94	2	no	—
144	C₄⋊Q₈	—	47	4	no	—
145	C₄⋊Q₈	—	94	1	no	—
146	C₄⋊Q₈	—	94	1	no	—
147	C₄×Q₈	—	188	4	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	94	2	no	—
150	C₂×C₄⋊C₄	—	94	2	no	—
151	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
152	C₂×C₄²	—	47	2	no	—
153	C₂×C₄²	—	47	1	no	—
154	C₂×C₄²	—	47	2	no	—
155	C₂×C₄²	—	47	1	no	—
156	C₂×C₄²	—	94	2	no	—
157	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	47	4	no	—
160	C₄⋊C₈	—	94	2	no	—
161	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
162	C₄×C₈	—	188	4	no	—
163	#95	—	94	4	no	—
164	C₂×Q₈	—	47	4	no	—
165	C₂×Q₈	—	94	2	no	—
166	C₂×Q₈	—	188	2	no	—
167	C₂×Q₈	—	188	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	47	1	no	—
170	C₂²×C₄	—	47	2	no	—
171	C₂²×C₄	—	47	1	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
174	C₂²×C₄	D₄×D₄₇	1	2	yes	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₂×C₈	—	94	4	no	—
179	C₂×C₈	—	188	2	no	—
180	C₂×C₈	—	188	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	94	4	no	—
185	C₄⋊C₄	—	94	4	no	—
186	C₄⋊C₄	—	188	4	no	—
187	C₄²	—	47	4	no	—
188	C₄²	—	47	4	no	—
189	C₄²	—	94	2	no	—
190	C₄²	—	94	2	no	—
191	C₄²	—	94	2	no	—
192	C₄²	—	188	1	no	—
193	C₄²	—	188	4	no	—
194	C₄²	C₂×C₄×D₄₇	1	2	yes	—
195	C₄²	#10625352	1	1	yes	characteristic
196	C₄²	#10625354	1	1	yes	characteristic
197	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
198	Q₈	—	188	4	no	—
199	Q₈	—	188	4	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	47	2	no	—
205	C₂×C₄	—	47	4	no	—
206	C₂×C₄	—	47	4	no	—
207	C₂×C₄	—	94	2	no	—
208	C₂×C₄	—	94	2	no	—
209	C₂×C₄	—	94	4	no	—
210	C₂×C₄	—	94	1	no	—
211	C₂×C₄	—	94	2	no	—
212	C₂×C₄	—	188	2	no	—
213	C₂×C₄	—	188	2	no	—
214	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
215	C₂×C₄	#13093982	1	1	yes	characteristic
216	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
217	C₂×C₄	#13093986	1	2	yes	—
218	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
219	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
220	C₂×C₄	#13094043	1	2	yes	—
221	C₂×C₄	#13094045	1	2	yes	—
222	C₈	—	4	4	no	—
223	C₈	—	188	4	no	—
224	C₂²	#15688970	1	1	yes	characteristic
225	C₂²	#100×D₄₇	1	1	yes	characteristic
226	C₂²	#15689106	1	1	yes	characteristic
227	C₂²	#103×D₄₇	1	2	yes	—
228	C₂²	#15689116	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	8	2	no	—
232	C₄	—	47	4	no	—
233	C₄	—	94	4	no	—
234	C₄	—	188	1	no	—
235	C₄	—	188	4	no	—
236	C₄	#15689210	1	2	yes	—
237	C₄	#15689214	1	2	yes	—
238	C₄	#15689215	1	2	yes	—
239	C₄	#15689217	1	2	yes	—
240	C₂	#333×D₄₇	1	1	yes	characteristic
241	C₂	#20242044	1	2	yes	—
242	C₂	#20242047	1	1	yes	characteristic
243	C₂	#20243179	1	1	yes	characteristic
244	C₂	#20243207	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20245955

C₂

yes

maximal, characteristic

C₄⋊C₈×Dic₄₇

C₂

yes

maximal

C₂×#15688871

C₂

yes

maximal

#20241271

C₂

yes

maximal, characteristic

C₄₇×#1296

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×#13093989

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×C₈×Dic₄₇

—

#15689028

C₄

yes

—

#15689019

—

C₄⋊C₄×Dic₄₇

—

C₄²×Dic₄₇

C₂²

yes

characteristic

#15688877

—

#15688871

C₄

yes

complemented

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#384

C₂²

yes

characteristic

C₂²×Dic₉₄

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

—

#13094024

—

#13094024

—

#13094024

C₂×C₄

yes

—

#13093989

—

C₂×C₄⋊Dic₄₇

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

C₈×Dic₄₇

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₂²⋊C₄

yes

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₄²

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

—

C₄²×C₄₇

yes

C₄²×C₄₇

yes

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

SD₁₆

yes

—

C₄×Dic₄₇

Q₁₆

yes

—

C₂×C₄₇⋊C₈

—

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×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#100

yes

—

C₂×Dic₄₇

#103

yes

—

C₂×Dic₄₇

#103

yes

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

C₄×#333

—

maximal, Sylow

102

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

103

C₂²×C₄₇

C₂×#100

yes

characteristic

104

C₂²×C₄₇

#413

yes

characteristic

105

C₂²×C₄₇

C₂×#103

yes

—

106

C₂²×C₄₇

#416

yes

—

107

C₄×C₄₇

—

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

C₄×SD₁₆

yes

—

111

C₄×C₄₇

C₄×SD₁₆

yes

—

112

C₄×C₄₇

C₄×Q₁₆

yes

—

113

C₄×C₄₇

C₄×Q₁₆

yes

—

114

Dic₄₇

—

115

Dic₄₇

—

116

Dic₄₇

—

117

Dic₄₇

#333

yes

complemented

118

C₄×C₄⋊Q₈

—

119

C₄×C₄⋊C₈

—

120

C₂×#333

—

121

#1296

—

122

#1296

D₄₇

yes

characteristic

123

C₂×C₄₇

C₂×#333

yes

characteristic

124

C₂×C₄₇

#1542

yes

—

125

C₂×C₄₇

#1543

yes

characteristic

126

C₂×C₄₇

C₄×#100

yes

characteristic

127

C₂×C₄₇

C₄×#103

yes

—

128

C₂×C₄⋊Q₈

—

129

C₂×C₄×Q₈

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

132

C₂×C₄×C₈

—

133

#391

—

134

#389

—

135

#384

C₂×D₄₇

yes

characteristic

136

C₄×C₄⋊C₄

—

137

C₄³

—

138

#336

—

139

#333

—

140

C₄₇

C₄×#333

yes

characteristic, complemented, Sylow

141

C₂²×Q₈

—

142

C₂²×C₈

—

143

C₂²×C₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

—

147

C₄×Q₈

—

188

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

C₄×D₄₇

yes

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₂×C₄²

—

155

C₂×C₄²

—

156

C₂×C₄²

—

157

C₂×C₄²

C₂²×D₄₇

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

—

161

C₄⋊C₈

C₄×D₄₇

yes

—

162

C₄×C₈

—

188

—

163

#95

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

188

—

167

C₂×Q₈

—

188

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

174

C₂²×C₄

D₄×D₄₇

yes

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

188

—

180

C₂×C₈

—

188

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

188

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

188

—

193

C₄²

—

188

—

194

C₄²

C₂×C₄×D₄₇

yes

—

195

C₄²

#10625352

yes

characteristic

196

C₄²

#10625354

yes

characteristic

197

C₂³

C₂²⋊C₄×D₄₇

yes

characteristic

198

Q₈

—

188

—

199

Q₈

—

188

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

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

C₄²×D₄₇

yes

characteristic

215

C₂×C₄

#13093982

yes

characteristic

216

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

217

C₂×C₄

#13093986

yes

—

218

C₂×C₄

SD₁₆×D₄₇

yes

—

219

C₂×C₄

Q₁₆×D₄₇

yes

—

220

C₂×C₄

#13094043

yes

—

221

C₂×C₄

#13094045

yes

—

222

C₈

—

223

C₈

—

188

—

224

C₂²

#15688970

yes

characteristic

225

C₂²

#100×D₄₇

yes

characteristic

226

C₂²

#15689106

yes

characteristic

227

C₂²

#103×D₄₇

yes

—

228

C₂²

#15689116

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

188

—

235

C₄

—

188

—

236

C₄

#15689210

yes

—

237

C₄

#15689214

yes

—

238

C₄

#15689215

yes

—

239

C₄

#15689217

yes

—

240

C₂

#333×D₄₇

yes

characteristic

241

C₂

#20242044

yes

—

242

C₂

#20242047

yes

characteristic

243

C₂

#20243179

yes

characteristic

244

C₂

#20243207

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	C₄×#333
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1296

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
15. #15688871	C₄	semidirect
117. Dic₄₇	#333	semidirect
140. C₄₇	C₄×#333	semidirect

H ≅ G/N

type

15. #15688871

C₄

semidirect

117. Dic₄₇

#333

semidirect

140. C₄₇

C₄×#333

semidirect

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

subgroup	index
#20245955	2
C₄⋊C₈×Dic₄₇	2
C₂×#15688871	2
#20241271	2
C₄₇×#1296	2
C₄×#333	47

subgroup

index

C₄⋊C₈×Dic₄₇

C₄₇×#1296

Subgroups — #26107221

Conjugacy classes of subgroups

Complements

Maximal subgroups