Group #26372726 — subgroups

Subgroups — #26372726

Order 12032.

488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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	#20254020	C₂	1	2	yes	maximal, complemented
2	#20245533	C₂	1	2	yes	maximal, complemented
3	#20245529	C₂	1	2	yes	maximal, complemented
4	#20245496	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245482	C₂	1	2	yes	maximal, complemented
6	#20245449	C₂	1	2	yes	maximal, complemented
7	#20245441	C₂	1	2	yes	maximal, complemented
8	#20245148	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2218	C₂	1	1	yes	maximal, characteristic
10	#15689740	—	2	2	no	—
11	C₂×Dic₃₇₆	C₂²	1	1	yes	characteristic
12	C₂×#13093968	C₂²	1	2	yes	—
13	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
14	#15689527	C₂²	1	2	yes	—
15	#15689506	C₂²	1	2	yes	—
16	#15689481	—	2	2	no	—
17	#15689367	—	2	2	no	—
18	#15689364	C₂²	1	2	yes	—
19	#15689220	—	2	2	no	—
20	#15689217	C₂²	1	2	yes	—
21	D₈×Dic₄₇	C₂²	1	2	yes	—
22	#15689078	C₂²	1	1	yes	characteristic
23	#15688951	C₂²	1	1	yes	characteristic
24	#15688950	C₂²	1	2	yes	—
25	Dic₄₇⋊C₁₆	C₂²	1	2	yes	—
26	Dic₄₇⋊C₁₆	C₂²	1	2	yes	—
27	#15688928	C₂²	1	2	yes	—
28	#15688926	C₂²	1	2	yes	—
29	#15688924	C₂²	1	2	yes	—
30	C₂×D₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#466	C₂²	1	2	yes	—
33	C₄₇×#367	C₂²	1	1	yes	characteristic
34	C₄₇×#357	C₂²	1	2	yes	—
35	C₂×Dic₁₈₈	C₂³	1	2	yes	—
36	C₂×#10625335	—	2	2	no	—
37	C₂×#10625329	D₄	1	1	yes	characteristic
38	#13094023	—	2	2	no	—
39	#13094017	—	4	2	no	—
40	#13094011	—	2	2	no	—
41	#13094011	—	4	2	no	—
42	#13094005	—	4	2	no	—
43	#13094003	—	2	2	no	—
44	#13094001	—	4	2	no	—
45	#13093989	—	2	2	no	—
46	D₄×Dic₄₇	—	2	2	no	—
47	#13093983	D₄	1	1	yes	characteristic
48	Dic₃₇₆	—	4	1	no	—
49	#13093968	—	4	2	no	—
50	C₂×C₄₇⋊C₁₆	—	4	1	no	—
51	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
52	#13093958	C₂³	1	2	yes	—
53	#13093957	—	2	2	no	—
54	#13093949	—	2	2	no	—
55	#13093947	—	2	2	no	—
56	#13093945	—	2	2	no	—
57	#13093934	D₄	1	2	yes	—
58	C₈×Dic₄₇	C₂³	1	2	yes	—
59	C₂×D₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	#121×C₄₇	—	2	2	no	—
62	D₁₆×C₄₇	—	4	1	no	—
63	M₃₂×C₄₇	—	4	1	no	—
64	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
66	#107×C₄₇	C₂³	1	2	yes	—
67	#102×C₄₇	—	2	2	no	—
68	C₂×D₄×C₄₇	—	2	2	no	—
69	C₂×D₄×C₄₇	—	4	2	no	—
70	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×Dic₄₇	—	4	2	no	—
72	C₂×Dic₉₄	—	2	2	no	—
73	C₂×Dic₉₄	—	4	2	no	—
74	D₈×C₄₇	—	2	2	no	—
75	D₈×C₄₇	—	2	2	no	—
76	C₂×C₈×C₄₇	—	2	1	no	—
77	C₂×C₈×C₄₇	—	2	1	no	—
78	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
80	C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂²⋊C₄×C₄₇	—	4	2	no	—
82	C₂²⋊Dic₄₇	—	4	2	no	—
83	C₂²⋊Dic₄₇	—	4	2	no	—
84	C₂²⋊Dic₄₇	—	4	2	no	—
85	C₂²⋊Dic₄₇	—	4	2	no	—
86	C₂²⋊Dic₄₇	D₈	1	1	yes	characteristic
87	C₂²⋊Dic₄₇	D₈	1	1	yes	characteristic
88	#10625335	—	4	4	no	—
89	C₄⋊Dic₄₇	—	2	2	no	—
90	C₄⋊Dic₄₇	D₈	1	2	yes	—
91	Dic₄₇⋊C₄	—	4	2	no	—
92	Dic₄₇⋊C₄	—	4	2	no	—
93	Dic₄₇⋊C₄	—	4	2	no	—
94	C₄×Dic₄₇	—	4	2	no	—
95	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
96	#10625329	—	4	1	no	—
97	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
98	Dic₁₈₈	—	2	2	no	—
99	Dic₁₈₈	—	2	2	no	—
100	C₁₆×C₄₇	—	2	1	no	—
101	C₁₆×C₄₇	—	2	1	no	—
102	C₄₇⋊C₁₆	—	2	2	no	—
103	C₂³×C₄₇	—	4	2	no	—
104	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
105	D₄×C₄₇	—	4	2	no	—
106	D₄×C₄₇	—	4	2	no	—
107	D₄×C₄₇	—	16	2	no	—
108	C₂×C₄×C₄₇	—	2	1	no	—
109	C₂×C₄×C₄₇	—	2	1	no	—
110	C₂×C₄×C₄₇	—	4	2	no	—
111	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
113	C₂×Dic₄₇	—	4	2	no	—
114	C₂×Dic₄₇	—	4	2	no	—
115	C₂×Dic₄₇	—	16	2	no	—
116	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
117	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
118	Dic₉₄	—	4	2	no	—
119	Dic₉₄	—	4	2	no	—
120	Dic₉₄	—	16	2	no	—
121	C₈×C₄₇	—	2	1	no	—
122	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
123	C₈×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
124	C₄₇⋊C₈	—	2	2	no	—
125	#33829	—	47	1	no	maximal, Sylow
126	C₂²×C₄₇	—	2	2	no	—
127	C₂²×C₄₇	—	2	1	no	—
128	C₂²×C₄₇	—	8	2	no	—
129	C₂²×C₄₇	—	8	2	no	—
130	C₂²×C₄₇	—	8	2	no	—
131	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
132	C₄×C₄₇	—	2	1	no	—
133	C₄×C₄₇	—	8	2	no	—
134	C₄×C₄₇	#537	1	1	yes	characteristic
135	C₄×C₄₇	#575	1	1	yes	characteristic
136	Dic₄₇	—	2	2	no	—
137	Dic₄₇	—	2	2	no	—
138	Dic₄₇	—	8	2	no	—
139	Dic₄₇	—	8	2	no	—
140	#3175	—	47	2	no	—
141	#2226	—	47	2	no	—
142	#2225	—	47	2	no	—
143	#2219	—	47	1	no	—
144	#2218	D₄₇	1	1	yes	characteristic
145	#2217	—	47	2	no	—
146	#2211	—	47	2	no	—
147	#2210	—	47	2	no	—
148	#2151	—	47	1	no	—
149	C₂×C₄₇	—	4	1	no	—
150	C₂×C₄₇	—	16	2	no	—
151	C₂×C₄₇	#3245	1	1	yes	characteristic
152	C₂×C₄₇	#3416	1	2	yes	—
153	#542	—	94	2	no	—
154	C₂×Q₃₂	—	47	1	no	—
155	C₂×SD₃₂	—	47	2	no	—
156	C₂×D₁₆	C₂×D₄₇	1	1	yes	characteristic
157	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
158	C₂²×C₁₆	—	47	1	no	—
159	#500	—	47	2	no	—
160	#495	—	47	2	no	—
161	#489	—	94	2	no	—
162	#468	—	94	2	no	—
163	#467	—	47	2	no	—
164	#466	C₂×D₄₇	1	2	yes	—
165	#440	—	94	2	no	—
166	C₄×Q₁₆	—	47	2	no	—
167	C₄×D₈	—	47	2	no	—
168	#405	—	47	1	no	—
169	#367	—	47	1	no	—
170	#367	—	47	2	no	—
171	#367	C₂×D₄₇	1	1	yes	characteristic
172	C₄⋊C₁₆	—	47	2	no	—
173	C₄⋊C₁₆	—	47	2	no	—
174	#358	—	47	2	no	—
175	#358	—	47	2	no	—
176	#357	—	47	2	no	—
177	#357	C₂×D₄₇	1	2	yes	—
178	C₄₇	#33829	1	1	yes	characteristic, complemented, Sylow
179	C₂×Q₁₆	—	47	2	no	—
180	C₂×SD₁₆	—	94	2	no	—
181	C₂×D₈	C₂²×D₄₇	1	2	yes	—
182	C₂×M₁₆	—	47	1	no	—
183	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
184	C₄⋊Q₈	—	94	2	no	—
185	#126	—	188	2	no	—
186	#124	—	94	2	no	—
187	#124	—	188	2	no	—
188	#123	—	188	2	no	—
189	C₂²⋊Q₈	—	94	2	no	—
190	C₂²⋊Q₈	—	188	2	no	—
191	#121	—	2	2	no	—
192	C₄×Q₈	—	94	2	no	—
193	C₄×D₄	—	94	2	no	—
194	#117	—	47	1	no	—
195	Q₃₂	—	188	1	no	—
196	SD₃₂	—	188	2	no	—
197	D₁₆	—	4	1	no	—
198	M₃₂	—	4	1	no	—
199	C₂×C₁₆	—	47	2	no	—
200	C₂×C₁₆	—	188	1	no	—
201	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
202	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
203	#107	—	47	2	no	—
204	#107	—	94	2	no	—
205	#107	C₂²×D₄₇	1	2	yes	—
206	#103	—	94	2	no	—
207	#103	—	94	2	no	—
208	#102	—	2	2	no	—
209	#102	—	94	2	no	—
210	#97	—	47	2	no	—
211	C₄×C₈	—	47	2	no	—
212	C₂×Q₈	—	94	2	no	—
213	C₂×Q₈	—	188	2	no	—
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	—	4	2	no	—
216	C₂²×C₄	—	188	2	no	—
217	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
218	Q₁₆	—	94	2	no	—
219	Q₁₆	—	94	2	no	—
220	SD₁₆	—	188	4	no	—
221	D₈	—	2	2	no	—
222	D₈	—	2	2	no	—
223	M₁₆	—	188	1	no	—
224	C₂×C₈	—	2	1	no	—
225	C₂×C₈	—	2	1	no	—
226	C₂×C₈	—	47	2	no	—
227	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
228	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
229	C₄⋊C₄	—	2	2	no	—
230	C₄⋊C₄	—	47	2	no	—
231	C₄⋊C₄	—	94	2	no	—
232	C₄⋊C₄	—	188	2	no	—
233	C₄⋊C₄	—	188	2	no	—
234	C₄⋊C₄	—	188	2	no	—
235	C₂²⋊C₄	—	4	2	no	—
236	C₂²⋊C₄	—	47	1	no	—
237	C₂²⋊C₄	—	47	1	no	—
238	C₂²⋊C₄	—	188	2	no	—
239	C₂²⋊C₄	—	188	2	no	—
240	C₂²⋊C₄	—	188	2	no	—
241	C₂²⋊C₄	—	188	2	no	—
242	C₄²	—	47	2	no	—
243	C₄²	—	188	2	no	—
244	C₁₆	—	2	1	no	—
245	C₁₆	—	2	1	no	—
246	C₁₆	—	94	2	no	—
247	C₂³	—	4	2	no	—
248	C₂³	D₈×D₄₇	1	1	yes	characteristic
249	Q₈	—	188	2	no	—
250	Q₈	—	188	2	no	—
251	Q₈	—	752	2	no	—
252	D₄	—	4	2	no	—
253	D₄	—	4	2	no	—
254	D₄	—	16	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	47	2	no	—
259	C₂×C₄	—	47	2	no	—
260	C₂×C₄	—	188	2	no	—
261	C₂×C₄	—	188	2	no	—
262	C₂×C₄	—	752	2	no	—
263	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
264	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
265	C₈	—	2	1	no	—
266	C₈	—	94	2	no	—
267	C₈	#13094069	1	1	yes	characteristic
268	C₈	#13094071	1	1	yes	characteristic
269	C₂²	—	2	2	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	8	2	no	—
272	C₂²	—	8	2	no	—
273	C₂²	—	8	2	no	—
274	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	8	2	no	—
277	C₄	—	94	2	no	—
278	C₄	—	94	2	no	—
279	C₄	—	376	2	no	—
280	C₄	—	376	2	no	—
281	C₄	#15689700	1	1	yes	characteristic
282	C₄	#15689920	1	1	yes	characteristic
283	C₂	—	4	1	no	—
284	C₂	—	16	2	no	—
285	C₂	#20254694	1	1	yes	characteristic
286	C₂	#20256534	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20254020

C₂

yes

maximal, complemented

#20245533

C₂

yes

maximal, complemented

#20245529

C₂

yes

maximal, complemented

#20245496

C₂

yes

maximal, characteristic, complemented

#20245482

C₂

yes

maximal, complemented

#20245449

C₂

yes

maximal, complemented

#20245441

C₂

yes

maximal, complemented

#20245148

C₂

yes

maximal, characteristic, complemented

C₄₇×#2218

C₂

yes

maximal, characteristic

#15689740

—

C₂×Dic₃₇₆

C₂²

yes

characteristic

C₂×#13093968

C₂²

yes

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

characteristic

#15689527

C₂²

yes

—

#15689506

C₂²

yes

—

#15689481

—

#15689367

—

#15689364

C₂²

yes

—

#15689220

—

#15689217

C₂²

yes

—

D₈×Dic₄₇

C₂²

yes

—

#15689078

C₂²

yes

characteristic

#15688951

C₂²

yes

characteristic

#15688950

C₂²

yes

—

Dic₄₇⋊C₁₆

C₂²

yes

—

Dic₄₇⋊C₁₆

C₂²

yes

—

#15688928

C₂²

yes

—

#15688926

C₂²

yes

—

#15688924

C₂²

yes

—

C₂×D₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₃₂×C₄₇

C₂²

yes

characteristic

C₄₇×#466

C₂²

yes

—

C₄₇×#367

C₂²

yes

characteristic

C₄₇×#357

C₂²

yes

—

C₂×Dic₁₈₈

C₂³

yes

—

C₂×#10625335

—

C₂×#10625329

D₄

yes

—

—

—

—

—

—

—

—

D₄×Dic₄₇

—

#13093983

D₄

yes

characteristic

Dic₃₇₆

—

#13093968

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂³

yes

—

#13093958

C₂³

yes

—

—

—

—

—

D₄

yes

—

C₈×Dic₄₇

C₂³

yes

—

C₂×D₈×C₄₇

C₂³

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#121×C₄₇

—

D₁₆×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

C₂×C₁₆×C₄₇

C₂³

yes

characteristic

#107×C₄₇

C₂³

yes

—

#102×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

D₈×C₄₇

—

D₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂⁴

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

D₈

yes

characteristic

C₂²⋊Dic₄₇

D₈

yes

characteristic

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₈

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×D₄

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×D₄

yes

—

Dic₁₈₈

—

Dic₁₈₈

—

100

C₁₆×C₄₇

—

101

C₁₆×C₄₇

—

102

C₄₇⋊C₁₆

—

103

C₂³×C₄₇

—

104

C₂³×C₄₇

C₂×D₈

yes

characteristic

105

D₄×C₄₇

—

106

D₄×C₄₇

—

107

D₄×C₄₇

—

108

C₂×C₄×C₄₇

—

109

C₂×C₄×C₄₇

—

110

C₂×C₄×C₄₇

—

111

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

112

C₂×C₄×C₄₇

C₂²×D₄

yes

characteristic

113

C₂×Dic₄₇

—

114

C₂×Dic₄₇

—

115

C₂×Dic₄₇

—

116

C₂×Dic₄₇

C₂×D₈

yes

—

117

C₂×Dic₄₇

C₂×D₈

yes

—

118

Dic₉₄

—

119

Dic₉₄

—

120

Dic₉₄

—

121

C₈×C₄₇

—

122

C₈×C₄₇

H(5,𝔽₂)

yes

characteristic

123

C₈×C₄₇

2₋¹⁺⁴

yes

characteristic

124

C₄₇⋊C₈

—

125

#33829

—

maximal, Sylow

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

—

131

C₂²×C₄₇

C₂²×D₈

yes

characteristic

132

C₄×C₄₇

—

133

C₄×C₄₇

—

134

C₄×C₄₇

#537

yes

characteristic

135

C₄×C₄₇

#575

yes

characteristic

136

Dic₄₇

—

137

Dic₄₇

—

138

Dic₄₇

—

139

Dic₄₇

—

140

#3175

—

141

#2226

—

142

#2225

—

143

#2219

—

144

#2218

D₄₇

yes

characteristic

145

#2217

—

146

#2211

—

147

#2210

—

148

#2151

—

149

C₂×C₄₇

—

150

C₂×C₄₇

—

151

C₂×C₄₇

#3245

yes

characteristic

152

C₂×C₄₇

#3416

yes

—

153

#542

—

154

C₂×Q₃₂

—

155

C₂×SD₃₂

—

156

C₂×D₁₆

C₂×D₄₇

yes

characteristic

157

C₂×M₃₂

C₂×D₄₇

yes

characteristic

158

C₂²×C₁₆

—

159

#500

—

160

#495

—

161

#489

—

162

#468

—

163

#467

—

164

#466

C₂×D₄₇

yes

—

165

#440

—

166

C₄×Q₁₆

—

167

C₄×D₈

—

168

#405

—

169

#367

—

170

#367

—

171

#367

C₂×D₄₇

yes

characteristic

172

C₄⋊C₁₆

—

173

C₄⋊C₁₆

—

174

#358

—

175

#358

—

176

#357

—

177

#357

C₂×D₄₇

yes

—

178

C₄₇

#33829

yes

characteristic, complemented, Sylow

179

C₂×Q₁₆

—

180

C₂×SD₁₆

—

181

C₂×D₈

C₂²×D₄₇

yes

—

182

C₂×M₁₆

—

183

C₂²×C₈

C₂²×D₄₇

yes

characteristic

184

C₄⋊Q₈

—

185

#126

—

188

—

186

#124

—

187

#124

—

188

—

188

#123

—

188

—

189

C₂²⋊Q₈

—

190

C₂²⋊Q₈

—

188

—

191

#121

—

192

C₄×Q₈

—

193

C₄×D₄

—

194

#117

—

195

Q₃₂

—

188

—

196

SD₃₂

—

188

—

197

D₁₆

—

198

M₃₂

—

199

C₂×C₁₆

—

200

C₂×C₁₆

—

188

—

201

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

202

C₂×C₁₆

C₂²×D₄₇

yes

characteristic

203

#107

—

204

#107

—

205

#107

C₂²×D₄₇

yes

—

206

#103

—

207

#103

—

208

#102

—

209

#102

—

210

#97

—

211

C₄×C₈

—

212

C₂×Q₈

—

213

C₂×Q₈

—

188

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂²×C₄

—

188

—

217

C₂²×C₄

D₄×D₄₇

yes

characteristic

218

Q₁₆

—

219

Q₁₆

—

220

SD₁₆

—

188

—

221

D₈

—

222

D₈

—

223

M₁₆

—

188

—

224

C₂×C₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

D₄×D₄₇

yes

characteristic

228

C₂×C₈

C₂³×D₄₇

yes

characteristic

229

C₄⋊C₄

—

230

C₄⋊C₄

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

188

—

233

C₄⋊C₄

—

188

—

234

C₄⋊C₄

—

188

—

235

C₂²⋊C₄

—

236

C₂²⋊C₄

—

237

C₂²⋊C₄

—

238

C₂²⋊C₄

—

188

—

239

C₂²⋊C₄

—

188

—

240

C₂²⋊C₄

—

188

—

241

C₂²⋊C₄

—

188

—

242

C₄²

—

243

C₄²

—

188

—

244

C₁₆

—

245

C₁₆

—

246

C₁₆

—

247

C₂³

—

248

C₂³

D₈×D₄₇

yes

characteristic

249

Q₈

—

188

—

250

Q₈

—

188

—

251

Q₈

—

752

—

252

D₄

—

253

D₄

—

254

D₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

188

—

261

C₂×C₄

—

188

—

262

C₂×C₄

—

752

—

263

C₂×C₄

D₈×D₄₇

yes

characteristic

264

C₂×C₄

C₂×D₄×D₄₇

yes

characteristic

265

C₈

—

266

C₈

—

267

C₈

#13094069

yes

characteristic

268

C₈

#13094071

yes

characteristic

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

C₂×D₈×D₄₇

yes

characteristic

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

376

—

280

C₄

—

376

—

281

C₄

#15689700

yes

characteristic

282

C₄

#15689920

yes

characteristic

283

C₂

—

284

C₂

—

285

C₂

#20254694

yes

characteristic

286

C₂

#20256534

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting, prime radical	C₄₇×#2218	C₂
socle	C₂²×C₄₇	C₂²×D₈
hypercenter	#2218	D₄₇
hypocenter	C₄₇	#33829
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2218

subgroup

G/H

center

C₂²

C₂×D₈×D₄₇

commutator, cosocle

C₂×C₈×C₄₇

C₂⁴

Frattini

C₂×C₈

C₂³×D₄₇

Fitting, prime radical

C₄₇×#2218

C₂

socle

C₂²×C₄₇

C₂²×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2218

N	H ≅ G/N	type
1. #20254020	C₂	semidirect
2. #20245533	C₂	semidirect
3. #20245529	C₂	semidirect
4. #20245496	C₂	semidirect
5. #20245482	C₂	semidirect
6. #20245449	C₂	semidirect
7. #20245441	C₂	semidirect
8. #20245148	C₂	semidirect
178. C₄₇	#33829	semidirect

H ≅ G/N

type

1. #20254020

C₂

semidirect

2. #20245533

C₂

semidirect

3. #20245529

C₂

semidirect

4. #20245496

C₂

semidirect

5. #20245482

C₂

semidirect

6. #20245449

C₂

semidirect

7. #20245441

C₂

semidirect

8. #20245148

C₂

semidirect

178. C₄₇

#33829

semidirect

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

subgroup	index
#20254020	2
#20245533	2
#20245529	2
#20245496	2
#20245482	2
#20245449	2
#20245441	2
#20245148	2
C₄₇×#2218	2
#33829	47

subgroup

index

C₄₇×#2218

Subgroups — #26372726

Conjugacy classes of subgroups

Complements

Maximal subgroups