Group #26118634 — subgroups

Subgroups — #26118634

Order 12032.

560 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15689419	C₂	1	2	yes	maximal
2	#20248761	C₂	1	1	yes	maximal, characteristic
3	#20244189	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688853	C₂	1	2	yes	maximal
5	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094024	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
8	#15689419	—	2	4	no	—
9	#15689419	—	2	4	no	—
10	C₂×#13093958	—	2	2	no	—
11	C₂×#13093949	—	2	2	no	—
12	C₂×#13093947	—	2	2	no	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15689053	—	2	2	no	—
15	#15689028	—	2	2	no	—
16	#15689022	—	2	2	no	—
17	#15688853	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#384	C₂²	1	1	yes	characteristic
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×Dic₉₄	D₄	1	2	yes	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	#13094024	—	2	2	no	—
24	#13094024	—	2	1	no	—
25	#13094024	D₄	1	2	yes	—
26	C₄×Dic₉₄	—	2	2	no	—
27	C₄×Dic₉₄	—	2	2	no	—
28	C₄×Dic₉₄	—	2	2	no	—
29	C₄×Dic₉₄	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
33	C₂×Dic₄₇⋊C₄	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	#13093958	—	2	8	no	—
36	#13093949	—	2	8	no	—
37	#13093947	—	4	4	no	—
38	C₄×C₄₇⋊C₈	—	2	2	no	—
39	C₄₇⋊#95	—	2	4	no	—
40	C₄₇⋊#95	—	2	2	no	—
41	C₂²×C₈×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
44	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₄₇	—	2	2	no	—
46	C₄⋊C₈×C₄₇	D₄	1	4	yes	—
47	C₂²×C₄×C₄₇	—	2	2	no	—
48	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂²×Dic₄₇	—	2	2	no	—
52	C₂²×Dic₄₇	—	4	1	no	—
53	C₂×Dic₉₄	—	2	2	no	—
54	C₂×Dic₉₄	—	2	2	no	—
55	C₂×Dic₉₄	—	2	2	no	—
56	C₂×Dic₉₄	—	2	2	no	—
57	C₂×Dic₉₄	—	2	2	no	—
58	C₂×Dic₉₄	—	2	2	no	—
59	C₂×Dic₉₄	—	4	2	no	—
60	C₂×Dic₉₄	—	4	2	no	—
61	C₂×Dic₉₄	—	4	1	no	—
62	C₂×Dic₉₄	Q₁₆	1	4	yes	—
63	C₂×C₈×C₄₇	—	2	4	no	—
64	C₂×C₈×C₄₇	—	4	2	no	—
65	C₂×C₈×C₄₇	—	4	2	no	—
66	C₄⋊C₄×C₄₇	—	4	2	no	—
67	C₄⋊C₄×C₄₇	—	4	2	no	—
68	C₄⋊C₄×C₄₇	—	4	2	no	—
69	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₄₇	C₂×D₄	1	2	yes	—
71	C₄²×C₄₇	#41	1	1	yes	characteristic
72	C₄⋊Dic₄₇	—	2	4	no	—
73	C₄⋊Dic₄₇	—	2	2	no	—
74	C₄⋊Dic₄₇	—	2	2	no	—
75	C₄⋊Dic₄₇	—	4	2	no	—
76	C₄⋊Dic₄₇	—	8	2	no	—
77	Dic₄₇⋊C₄	—	4	2	no	—
78	Dic₄₇⋊C₄	—	4	2	no	—
79	C₄×Dic₄₇	—	4	2	no	—
80	C₄×Dic₄₇	—	4	2	no	—
81	C₂×C₄₇⋊C₈	—	2	2	no	—
82	C₂×C₄₇⋊C₈	—	4	1	no	—
83	C₂×C₄₇⋊C₈	—	4	1	no	—
84	C₂³×C₄₇	#120	1	1	yes	characteristic
85	C₂×C₄×C₄₇	—	2	1	no	—
86	C₂×C₄×C₄₇	—	2	1	no	—
87	C₂×C₄×C₄₇	—	4	4	no	—
88	C₂×C₄×C₄₇	—	4	2	no	—
89	C₂×C₄×C₄₇	#120	1	2	yes	—
90	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#121	1	2	yes	—
92	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
94	C₂×C₄×C₄₇	#135	1	2	yes	—
95	C₂×C₄×C₄₇	#137	1	2	yes	—
96	C₂×C₄×C₄₇	#137	1	2	yes	—
97	C₂×Dic₄₇	—	2	4	no	—
98	C₂×Dic₄₇	—	4	2	no	—
99	C₂×Dic₄₇	—	4	2	no	—
100	C₂×Dic₄₇	—	4	2	no	—
101	C₂×Dic₄₇	—	4	2	no	—
102	C₂×Dic₄₇	—	4	2	no	—
103	C₂×Dic₄₇	—	4	2	no	—
104	C₂×Dic₄₇	—	8	1	no	—
105	C₂×Dic₄₇	—	8	1	no	—
106	Dic₉₄	—	2	4	no	—
107	Dic₉₄	—	2	4	no	—
108	Dic₉₄	—	4	2	no	—
109	Dic₉₄	—	4	2	no	—
110	Dic₉₄	—	4	4	no	—
111	Dic₉₄	—	8	2	no	—
112	C₈×C₄₇	—	4	4	no	—
113	C₄₇⋊C₈	—	4	2	no	—
114	#10237	—	47	1	no	maximal, Sylow
115	C₂²×C₄₇	#392	1	1	yes	characteristic
116	C₂²×C₄₇	#451	1	2	yes	—
117	C₂²×C₄₇	#452	1	2	yes	—
118	C₂²×C₄₇	#453	1	1	yes	characteristic
119	C₂²×C₄₇	#454	1	1	yes	characteristic
120	C₄×C₄₇	—	2	1	no	—
121	C₄×C₄₇	—	2	1	no	—
122	C₄×C₄₇	—	8	2	no	—
123	C₄×C₄₇	#451	1	2	yes	—
124	C₄×C₄₇	#452	1	2	yes	—
125	C₄×C₄₇	#467	1	2	yes	—
126	C₄×C₄₇	#470	1	2	yes	—
127	Dic₄₇	—	4	4	no	—
128	Dic₄₇	—	8	2	no	—
129	Dic₄₇	—	8	2	no	—
130	C₂×#477	—	47	2	no	—
131	#2582	—	47	1	no	—
132	#1956	—	47	1	no	—
133	C₂×Q₈⋊C₈	—	47	2	no	—
134	#1296	D₄₇	1	1	yes	characteristic
135	C₂×C₄₇	#1630	1	1	yes	characteristic
136	C₂×C₄₇	#1633	1	1	yes	characteristic
137	C₂×C₄₇	#1636	1	2	yes	—
138	C₂×C₄₇	#2001	1	2	yes	—
139	C₂×C₄₇	#2006	1	1	yes	characteristic
140	C₂×C₄⋊Q₈	—	47	1	no	—
141	C₂×C₄×Q₈	—	47	2	no	—
142	#477	—	94	4	no	—
143	#477	—	94	4	no	—
144	C₂×#107	—	94	2	no	—
145	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
146	C₂×#103	—	94	2	no	—
147	C₂×#103	—	94	2	no	—
148	C₂×C₄×C₈	—	47	1	no	—
149	#398	—	94	2	no	—
150	#391	—	94	2	no	—
151	#389	—	94	2	no	—
152	#384	C₂×D₄₇	1	1	yes	characteristic
153	Q₈⋊C₈	—	94	4	no	—
154	C₄₇	#10237	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	47	2	no	—
156	C₂²×Q₈	—	94	1	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	94	1	no	—
159	C₄⋊Q₈	—	47	2	no	—
160	C₄⋊Q₈	—	94	2	no	—
161	C₄⋊Q₈	—	94	1	no	—
162	C₄×Q₈	—	94	2	no	—
163	C₄×Q₈	—	94	2	no	—
164	C₄×Q₈	—	94	2	no	—
165	C₄×Q₈	—	94	2	no	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	47	2	no	—
168	C₂×C₄⋊C₄	—	94	2	no	—
169	C₂×C₄⋊C₄	—	94	2	no	—
170	C₂×C₄⋊C₄	—	94	2	no	—
171	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
172	C₂×C₄²	—	94	2	no	—
173	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
174	#107	—	94	8	no	—
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	D₁₈₈	1	4	yes	—
177	#103	—	94	8	no	—
178	#103	—	188	4	no	—
179	C₄×C₈	—	94	2	no	—
180	#95	—	94	4	no	—
181	#95	—	94	2	no	—
182	C₂×Q₈	—	47	4	no	—
183	C₂×Q₈	—	94	2	no	—
184	C₂×Q₈	—	94	2	no	—
185	C₂×Q₈	—	94	2	no	—
186	C₂×Q₈	—	94	2	no	—
187	C₂×Q₈	—	94	2	no	—
188	C₂×Q₈	—	94	2	no	—
189	C₂×Q₈	—	188	2	no	—
190	C₂×Q₈	—	188	2	no	—
191	C₂×Q₈	—	188	1	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	94	2	no	—
194	C₂²×C₄	—	94	2	no	—
195	C₂²×C₄	—	188	1	no	—
196	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
197	C₂²×C₄	D₄×D₄₇	1	2	yes	—
198	C₂×C₈	—	2	4	no	—
199	C₂×C₈	—	4	2	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	94	2	no	—
202	C₂×C₈	—	188	1	no	—
203	C₂×C₈	—	188	1	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	94	4	no	—
208	C₄⋊C₄	—	94	2	no	—
209	C₄⋊C₄	—	94	2	no	—
210	C₄⋊C₄	—	376	2	no	—
211	C₄⋊C₄	—	188	2	no	—
212	C₄⋊C₄	—	188	2	no	—
213	C₄⋊C₄	—	188	2	no	—
214	C₄²	—	188	2	no	—
215	C₄²	—	188	2	no	—
216	C₄²	C₂×D₁₈₈	1	2	yes	—
217	C₄²	D₄×D₄₇	1	1	yes	characteristic
218	C₄²	#10625354	1	1	yes	characteristic
219	C₂³	#13093994	1	1	yes	characteristic
220	Q₈	—	94	4	no	—
221	Q₈	—	94	4	no	—
222	Q₈	—	376	2	no	—
223	Q₈	—	188	4	no	—
224	Q₈	—	188	2	no	—
225	Q₈	—	188	2	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	4	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	94	4	no	—
231	C₂×C₄	—	376	1	no	—
232	C₂×C₄	—	376	1	no	—
233	C₂×C₄	—	188	2	no	—
234	C₂×C₄	—	188	2	no	—
235	C₂×C₄	—	188	2	no	—
236	C₂×C₄	—	188	2	no	—
237	C₂×C₄	—	188	2	no	—
238	C₂×C₄	—	188	2	no	—
239	C₂×C₄	#13093994	1	2	yes	—
240	C₂×C₄	#13093999	1	1	yes	characteristic
241	C₂×C₄	#13093999	1	2	yes	—
242	C₂×C₄	#13094021	1	1	yes	characteristic
243	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
244	C₂×C₄	#13094043	1	2	yes	—
245	C₂×C₄	#13094053	1	2	yes	—
246	C₂×C₄	#13094053	1	2	yes	—
247	C₈	—	4	4	no	—
248	C₈	—	188	2	no	—
249	C₂²	#15689033	1	1	yes	characteristic
250	C₂²	#15689280	1	2	yes	—
251	C₂²	#15689286	1	2	yes	—
252	C₂²	#15689293	1	1	yes	characteristic
253	C₂²	#15689298	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	8	2	no	—
257	C₄	—	376	2	no	—
258	C₄	—	376	2	no	—
259	C₄	—	188	4	no	—
260	C₄	#15689280	1	2	yes	—
261	C₄	#15689286	1	2	yes	—
262	C₄	#15689365	1	2	yes	—
263	C₄	#15689382	1	2	yes	—
264	C₂	#20242510	1	1	yes	characteristic
265	C₂	#20242529	1	1	yes	characteristic
266	C₂	#20242547	1	2	yes	—
267	C₂	#20244399	1	2	yes	—
268	C₂	#20244432	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689419

C₂

yes

maximal

#20248761

C₂

yes

maximal, characteristic

#20244189

C₂

yes

maximal, characteristic

C₂×#15688853

C₂

yes

maximal

C₄₇×#1296

C₂

yes

maximal, characteristic

C₂×#13094024

C₂²

yes

characteristic

C₂×C₄×Dic₉₄

C₂²

yes

—

—

—

—

—

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#384

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂²×Dic₉₄

D₄

yes

—

C₂²×C₄₇⋊C₈

—

#13094024

—

#13094024

—

#13094024

D₄

yes

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

#13093958

—

#13093949

—

#13093947

—

C₄×C₄₇⋊C₈

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#120

yes

—

C₂×C₄×C₄₇

#121

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

#127

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₂×C₄×C₄₇

#135

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×C₄×C₄₇

#137

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

100

C₂×Dic₄₇

—

101

C₂×Dic₄₇

—

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

Dic₉₄

—

107

Dic₉₄

—

108

Dic₉₄

—

109

Dic₉₄

—

110

Dic₉₄

—

111

Dic₉₄

—

112

C₈×C₄₇

—

113

C₄₇⋊C₈

—

114

#10237

—

maximal, Sylow

115

C₂²×C₄₇

#392

yes

characteristic

116

C₂²×C₄₇

#451

yes

—

117

C₂²×C₄₇

#452

yes

—

118

C₂²×C₄₇

#453

yes

characteristic

119

C₂²×C₄₇

#454

yes

characteristic

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

—

123

C₄×C₄₇

#451

yes

—

124

C₄×C₄₇

#452

yes

—

125

C₄×C₄₇

#467

yes

—

126

C₄×C₄₇

#470

yes

—

127

Dic₄₇

—

128

Dic₄₇

—

129

Dic₄₇

—

130

C₂×#477

—

131

#2582

—

132

#1956

—

133

C₂×Q₈⋊C₈

—

134

#1296

D₄₇

yes

characteristic

135

C₂×C₄₇

#1630

yes

characteristic

136

C₂×C₄₇

#1633

yes

characteristic

137

C₂×C₄₇

#1636

yes

—

138

C₂×C₄₇

#2001

yes

—

139

C₂×C₄₇

#2006

yes

characteristic

140

C₂×C₄⋊Q₈

—

141

C₂×C₄×Q₈

—

142

#477

—

143

#477

—

144

C₂×#107

—

145

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

146

C₂×#103

—

147

C₂×#103

—

148

C₂×C₄×C₈

—

149

#398

—

150

#391

—

151

#389

—

152

#384

C₂×D₄₇

yes

characteristic

153

Q₈⋊C₈

—

154

C₄₇

#10237

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×Q₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₄⋊Q₈

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×Q₈

—

165

C₄×Q₈

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

171

C₂×C₄⋊C₄

D₁₈₈

yes

—

172

C₂×C₄²

—

173

C₂×C₄²

C₂²×D₄₇

yes

characteristic

174

#107

—

175

C₄⋊C₈

—

176

C₄⋊C₈

D₁₈₈

yes

—

177

#103

—

178

#103

—

188

—

179

C₄×C₈

—

180

#95

—

181

#95

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

188

—

190

C₂×Q₈

—

188

—

191

C₂×Q₈

—

188

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

188

—

196

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

197

C₂²×C₄

D₄×D₄₇

yes

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

188

—

203

C₂×C₈

—

188

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

376

—

211

C₄⋊C₄

—

188

—

212

C₄⋊C₄

—

188

—

213

C₄⋊C₄

—

188

—

214

C₄²

—

188

—

215

C₄²

—

188

—

216

C₄²

C₂×D₁₈₈

yes

—

217

C₄²

D₄×D₄₇

yes

characteristic

218

C₄²

#10625354

yes

characteristic

219

C₂³

#13093994

yes

characteristic

220

Q₈

—

221

Q₈

—

222

Q₈

—

376

—

223

Q₈

—

188

—

224

Q₈

—

188

—

225

Q₈

—

188

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

376

—

232

C₂×C₄

—

376

—

233

C₂×C₄

—

188

—

234

C₂×C₄

—

188

—

235

C₂×C₄

—

188

—

236

C₂×C₄

—

188

—

237

C₂×C₄

—

188

—

238

C₂×C₄

—

188

—

239

C₂×C₄

#13093994

yes

—

240

C₂×C₄

#13093999

yes

characteristic

241

C₂×C₄

#13093999

yes

—

242

C₂×C₄

#13094021

yes

characteristic

243

C₂×C₄

Q₁₆×D₄₇

yes

—

244

C₂×C₄

#13094043

yes

—

245

C₂×C₄

#13094053

yes

—

246

C₂×C₄

#13094053

yes

—

247

C₈

—

248

C₈

—

188

—

249

C₂²

#15689033

yes

characteristic

250

C₂²

#15689280

yes

—

251

C₂²

#15689286

yes

—

252

C₂²

#15689293

yes

characteristic

253

C₂²

#15689298

yes

characteristic

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

376

—

258

C₄

—

376

—

259

C₄

—

188

—

260

C₄

#15689280

yes

—

261

C₄

#15689286

yes

—

262

C₄

#15689365

yes

—

263

C₄

#15689382

yes

—

264

C₂

#20242510

yes

characteristic

265

C₂

#20242529

yes

characteristic

266

C₂

#20242547

yes

—

267

C₂

#20244399

yes

—

268

C₂

#20244432

yes

characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle, prime radical	C₂³×C₄₇	#120
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#10237
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#13093994

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1296

C₂

C₂³×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
154. C₄₇	#10237	semidirect

H ≅ G/N

type

154. C₄₇

#10237

semidirect

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

subgroup	index
C₂×#15689419	2
#20248761	2
#20244189	2
C₂×#15688853	2
C₄₇×#1296	2
#10237	47

subgroup

index

C₄₇×#1296

Subgroups — #26118634

Conjugacy classes of subgroups

Complements

Maximal subgroups