Group #26133021 — subgroups

Subgroups — #26133021

Order 12032.

396 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 107 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×#15689229	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688938	C₂	1	1	yes	maximal, characteristic
3	#20245109	C₂	1	1	yes	maximal, characteristic
4	#20244139	C₂	1	1	yes	maximal, characteristic
5	#20241495	C₂	1	1	yes	maximal, characteristic
6	#20241467	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₇×#365	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#13093989	—	2	1	no	—
10	C₂×#13093964	C₂²	1	1	yes	characteristic
11	#15689229	—	2	2	no	—
12	#15689229	—	2	2	no	—
13	#15689161	C₂²	1	1	yes	characteristic
14	#15689151	—	2	1	no	—
15	C₂×#13093947	—	2	1	no	—
16	C₂×#13093934	C₂²	1	1	yes	characteristic
17	#15688938	—	2	2	no	—
18	#15688928	C₄	1	4	yes	complemented
19	#15688884	—	2	1	no	—
20	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#365	—	2	2	no	—
24	C₂²×Dic₉₄	—	2	1	no	—
25	C₂×Dic₁₈₈	—	2	1	no	—
26	C₂×Dic₁₈₈	—	2	1	no	—
27	C₂×Dic₁₈₈	—	2	1	no	—
28	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₈₈	D₄	1	2	yes	—
30	C₂×Dic₁₈₈	Q₈	1	2	yes	—
31	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
32	#13093989	—	2	4	no	—
33	#13093989	—	4	2	no	—
34	#13093983	—	2	1	no	—
35	C₂×Dic₄₇⋊C₄	—	4	1	no	—
36	C₂×C₄×Dic₄₇	—	4	1	no	—
37	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
38	#13093964	—	2	1	no	—
39	#13093964	—	2	1	no	—
40	C₂×C₄₇⋊C₁₆	—	2	1	no	—
41	#13093958	C₂×C₄	1	2	yes	—
42	#13093956	—	2	1	no	—
43	Dic₄₇⋊C₈	—	4	2	no	—
44	#13093947	—	2	4	no	—
45	#13093934	—	2	1	no	—
46	#13093934	—	2	1	no	—
47	C₂×M₁₆×C₄₇	—	2	1	no	—
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
50	M₃₂×C₄₇	—	2	1	no	—
51	M₃₂×C₄₇	—	2	1	no	—
52	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	—
53	#108×C₄₇	—	2	1	no	—
54	#108×C₄₇	—	2	1	no	—
55	#106×C₄₇	—	2	1	no	—
56	#106×C₄₇	D₄	1	2	yes	—
57	C₂²×C₄×C₄₇	—	4	1	no	—
58	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×Dic₄₇	—	2	1	no	—
60	C₂²×Dic₄₇	—	4	1	no	—
61	C₂×Dic₉₄	—	2	2	no	—
62	C₂×Dic₉₄	—	2	2	no	—
63	C₂×Dic₉₄	—	2	2	no	—
64	C₂×Dic₉₄	—	4	1	no	—
65	C₂×Dic₉₄	—	4	1	no	—
66	C₂×Dic₉₄	—	4	1	no	—
67	M₁₆×C₄₇	—	4	1	no	—
68	M₁₆×C₄₇	—	4	1	no	—
69	C₂×C₈×C₄₇	—	4	1	no	—
70	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
75	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
76	C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₄⋊C₄×C₄₇	—	4	1	no	—
78	C₂²⋊Dic₄₇	—	4	1	no	—
79	C₄⋊Dic₄₇	—	2	2	no	—
80	Dic₄₇⋊C₄	—	4	4	no	—
81	C₄×Dic₄₇	—	2	1	no	—
82	C₄×Dic₄₇	—	4	4	no	—
83	C₄×Dic₄₇	—	4	1	no	—
84	C₄×Dic₄₇	SD₁₆	1	2	yes	—
85	C₂×C₄₇⋊C₈	—	2	1	no	—
86	C₂×C₄₇⋊C₈	—	2	1	no	—
87	C₂×C₄₇⋊C₈	—	2	1	no	—
88	Dic₁₈₈	—	2	2	no	—
89	Dic₁₈₈	—	2	2	no	—
90	Dic₁₈₈	—	2	2	no	—
91	Dic₁₈₈	C₄⋊C₄	1	4	yes	—
92	C₁₆×C₄₇	—	2	2	no	—
93	C₄₇⋊C₁₆	—	4	1	no	—
94	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₄₇	—	4	2	no	—
96	C₂×C₄×C₄₇	—	8	2	no	—
97	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
102	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×Dic₄₇	—	2	2	no	—
104	C₂×Dic₄₇	—	4	2	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₂×Dic₄₇	—	4	2	no	—
107	C₂×Dic₄₇	—	4	2	no	—
108	C₂×Dic₄₇	—	4	2	no	—
109	Dic₉₄	—	2	4	no	—
110	Dic₉₄	—	4	2	no	—
111	Dic₉₄	—	4	2	no	—
112	Dic₉₄	—	4	2	no	—
113	C₈×C₄₇	—	8	1	no	—
114	C₈×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
116	C₈×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
117	C₈×C₄₇	#123	1	1	yes	characteristic
118	C₄₇⋊C₈	—	4	1	no	—
119	#12957	—	47	1	no	maximal, Sylow
120	C₂²×C₄₇	—	2	2	no	—
121	C₂²×C₄₇	#442	1	1	yes	characteristic
122	C₂²×C₄₇	#450	1	1	yes	characteristic
123	C₂²×C₄₇	#478	1	1	yes	characteristic
124	C₄×C₄₇	—	8	2	no	—
125	C₄×C₄₇	#385	1	1	yes	characteristic
126	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
127	C₄×C₄₇	#449	1	1	yes	characteristic
128	C₄×C₄₇	#476	1	1	yes	characteristic
129	Dic₄₇	—	4	2	no	—
130	Dic₄₇	—	4	4	no	—
131	Dic₄₇	—	8	2	no	—
132	C₂×#441	—	47	1	no	—
133	C₂×#365	D₄₇	1	1	yes	characteristic
134	C₂×#362	—	47	1	no	—
135	#2141	—	47	1	no	—
136	#1946	—	47	1	no	—
137	#1386	—	47	1	no	—
138	#1375	—	47	1	no	—
139	C₂×C₄₇	—	2	1	no	—
140	C₂×C₄₇	—	2	1	no	—
141	C₂×C₄₇	#1864	1	1	yes	characteristic
142	C₂×C₄₇	#2180	1	2	yes	—
143	C₂²×Q₁₆	—	47	1	no	—
144	C₂×C₄×Q₈	—	94	1	no	—
145	C₂×M₃₂	—	47	1	no	—
146	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
147	#441	—	94	2	no	—
148	#441	—	94	2	no	—
149	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
150	#427	—	47	1	no	—
151	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
152	#424	—	94	1	no	—
153	C₂×#103	—	94	1	no	—
154	C₂×#97	—	47	1	no	—
155	#365	—	2	2	no	—
156	#362	—	94	2	no	—
157	#358	—	47	4	no	—
158	#339	—	94	1	no	—
159	C₄₇	#12957	1	1	yes	characteristic, complemented, Sylow
160	C₂²×Q₈	—	94	1	no	—
161	C₂×Q₁₆	—	47	2	no	—
162	C₂×Q₁₆	—	47	2	no	—
163	C₂×Q₁₆	—	47	2	no	—
164	C₂×Q₁₆	—	94	1	no	—
165	C₂×Q₁₆	—	94	1	no	—
166	C₂×Q₁₆	—	94	1	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂²×C₈	—	47	1	no	—
169	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
170	C₄×Q₈	—	94	4	no	—
171	C₄×Q₈	—	188	2	no	—
172	#117	—	94	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	188	1	no	—
175	C₂×C₄²	—	47	1	no	—
176	C₂×C₄²	—	188	1	no	—
177	M₃₂	—	2	1	no	—
178	M₃₂	—	2	1	no	—
179	M₃₂	—	94	1	no	—
180	M₃₂	—	94	1	no	—
181	C₂×C₁₆	—	94	1	no	—
182	C₂×C₁₆	C₄×D₄₇	1	2	yes	—
183	#108	—	2	1	no	—
184	#108	—	2	1	no	—
185	#107	—	47	2	no	—
186	#106	—	2	1	no	—
187	#106	—	94	1	no	—
188	#106	C₂²⋊D₄₇	1	2	yes	—
189	C₄⋊C₈	—	188	2	no	—
190	#103	—	94	4	no	—
191	#97	—	94	1	no	—
192	#97	—	94	1	no	—
193	C₂×Q₈	—	94	2	no	—
194	C₂×Q₈	—	94	2	no	—
195	C₂×Q₈	—	94	2	no	—
196	C₂×Q₈	—	188	1	no	—
197	C₂×Q₈	—	188	1	no	—
198	C₂×Q₈	—	188	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	94	1	no	—
201	C₂²×C₄	—	188	1	no	—
202	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
203	Q₁₆	—	47	4	no	—
204	Q₁₆	—	94	2	no	—
205	Q₁₆	—	94	2	no	—
206	Q₁₆	—	94	2	no	—
207	M₁₆	—	4	1	no	—
208	M₁₆	—	4	1	no	—
209	C₂×C₈	—	4	1	no	—
210	C₂×C₈	—	94	1	no	—
211	C₂×C₈	—	94	1	no	—
212	C₂×C₈	—	94	1	no	—
213	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
214	C₂×C₈	#10625350	1	1	yes	characteristic
215	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
216	C₂×C₈	Q₈×D₄₇	1	1	yes	characteristic
217	C₂×C₈	#10625354	1	1	yes	characteristic
218	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
219	C₄⋊C₄	—	2	2	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	94	2	no	—
222	C₄⋊C₄	—	188	4	no	—
223	C₂²⋊C₄	—	188	1	no	—
224	C₄²	—	47	2	no	—
225	C₄²	—	94	1	no	—
226	C₄²	—	188	4	no	—
227	C₄²	—	188	1	no	—
228	C₁₆	—	2	2	no	—
229	C₁₆	—	188	1	no	—
230	C₂³	#13094051	1	1	yes	characteristic
231	Q₈	—	94	4	no	—
232	Q₈	—	188	2	no	—
233	Q₈	—	188	2	no	—
234	Q₈	—	188	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	8	2	no	—
237	C₂×C₄	—	94	2	no	—
238	C₂×C₄	—	188	2	no	—
239	C₂×C₄	—	188	2	no	—
240	C₂×C₄	—	188	2	no	—
241	C₂×C₄	—	188	2	no	—
242	C₂×C₄	—	188	2	no	—
243	C₂×C₄	#13093986	1	1	yes	characteristic
244	C₂×C₄	#13093992	1	1	yes	characteristic
245	C₂×C₄	#13094002	1	1	yes	characteristic
246	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
247	C₂×C₄	#13094045	1	1	yes	characteristic
248	C₂×C₄	#13094051	1	1	yes	characteristic
249	C₈	—	8	1	no	—
250	C₈	—	188	1	no	—
251	C₈	C₄⋊C₄×D₄₇	1	1	yes	characteristic
252	C₈	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
253	C₈	#13094000	1	1	yes	characteristic
254	C₈	#13094009	1	1	yes	characteristic
255	C₂²	—	2	2	no	—
256	C₂²	#15689234	1	1	yes	characteristic
257	C₂²	#15689272	1	1	yes	characteristic
258	C₂²	#15689422	1	1	yes	characteristic
259	C₄	—	8	2	no	—
260	C₄	—	376	2	no	—
261	C₄	—	188	2	no	—
262	C₄	—	188	4	no	—
263	C₄	#15688994	1	1	yes	characteristic
264	C₄	#15689210	1	1	yes	characteristic
265	C₄	#15689267	1	1	yes	characteristic
266	C₄	#15689412	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	1	no	—
269	C₂	#20243646	1	1	yes	characteristic
270	C₂	#20245278	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689229

C₂

yes

maximal, characteristic

C₂×#15688938

C₂

yes

maximal, characteristic

#20245109

C₂

yes

maximal, characteristic

#20244139

C₂

yes

maximal, characteristic

#20241495

C₂

yes

maximal, characteristic

#20241467

C₂

yes

maximal, characteristic

C₂×C₄₇×#365

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

C₂²

yes

characteristic

C₂×#13093989

—

C₂×#13093964

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

#15688938

—

#15688928

C₄

yes

complemented

#15688884

—

C₂×M₃₂×C₄₇

C₂²

yes

characteristic

C₂×#108×C₄₇

C₂²

yes

characteristic

C₂×#106×C₄₇

C₂²

yes

characteristic

C₄₇×#365

—

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂×Dic₁₈₈

D₄

yes

—

C₂×Dic₁₈₈

Q₈

yes

—

C₂²×C₄₇⋊C₈

D₄

yes

—

—

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

D₄

yes

characteristic

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093958

C₂×C₄

yes

—

#13093956

—

Dic₄₇⋊C₈

—

#13093947

—

#13093934

—

#13093934

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₇

—

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂×C₄

yes

—

#108×C₄₇

—

#108×C₄₇

—

#106×C₄₇

—

#106×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×Q₈

yes

C₂×C₈×C₄₇

yes

C₂×C₈×C₄₇

yes

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

SD₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

C₄⋊C₄

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

100

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₄₇

#135

yes

characteristic

102

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

Dic₉₄

—

110

Dic₉₄

—

111

Dic₉₄

—

112

Dic₉₄

—

113

C₈×C₄₇

—

114

C₈×C₄₇

C₂×C₄⋊C₄

yes

characteristic

115

C₈×C₄₇

C₄×D₄

yes

characteristic

116

C₈×C₄₇

C₂²⋊Q₈

yes

characteristic

117

C₈×C₄₇

#123

yes

characteristic

118

C₄₇⋊C₈

—

119

#12957

—

maximal, Sylow

120

C₂²×C₄₇

—

121

C₂²×C₄₇

#442

yes

characteristic

122

C₂²×C₄₇

#450

yes

characteristic

123

C₂²×C₄₇

#478

yes

characteristic

124

C₄×C₄₇

—

125

C₄×C₄₇

#385

yes

characteristic

126

C₄×C₄₇

C₄×SD₁₆

yes

characteristic

127

C₄×C₄₇

#449

yes

characteristic

128

C₄×C₄₇

#476

yes

characteristic

129

Dic₄₇

—

130

Dic₄₇

—

131

Dic₄₇

—

132

C₂×#441

—

133

C₂×#365

D₄₇

yes

characteristic

134

C₂×#362

—

135

#2141

—

136

#1946

—

137

#1386

—

138

#1375

—

139

C₂×C₄₇

—

140

C₂×C₄₇

—

141

C₂×C₄₇

#1864

yes

characteristic

142

C₂×C₄₇

#2180

yes

—

143

C₂²×Q₁₆

—

144

C₂×C₄×Q₈

—

145

C₂×M₃₂

—

146

C₂×M₃₂

C₂×D₄₇

yes

characteristic

147

#441

—

148

#441

—

149

C₂×#108

C₂×D₄₇

yes

characteristic

150

#427

—

151

C₂×#106

C₂×D₄₇

yes

characteristic

152

#424

—

153

C₂×#103

—

154

C₂×#97

—

155

#365

—

156

#362

—

157

#358

—

158

#339

—

159

C₄₇

#12957

yes

characteristic, complemented, Sylow

160

C₂²×Q₈

—

161

C₂×Q₁₆

—

162

C₂×Q₁₆

—

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₂²×C₈

C₂²×D₄₇

yes

characteristic

170

C₄×Q₈

—

171

C₄×Q₈

—

188

—

172

#117

—

173

C₂×C₄⋊C₄

—

174

C₂×C₄⋊C₄

—

188

—

175

C₂×C₄²

—

176

C₂×C₄²

—

188

—

177

M₃₂

—

178

M₃₂

—

179

M₃₂

—

180

M₃₂

—

181

C₂×C₁₆

—

182

C₂×C₁₆

C₄×D₄₇

yes

—

183

#108

—

184

#108

—

185

#107

—

186

#106

—

187

#106

—

188

#106

C₂²⋊D₄₇

yes

—

189

C₄⋊C₈

—

188

—

190

#103

—

191

#97

—

192

#97

—

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

188

—

197

C₂×Q₈

—

188

—

198

C₂×Q₈

—

188

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

188

—

202

C₂²×C₄

D₄×D₄₇

yes

characteristic

203

Q₁₆

—

204

Q₁₆

—

205

Q₁₆

—

206

Q₁₆

—

207

M₁₆

—

208

M₁₆

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

214

C₂×C₈

#10625350

yes

characteristic

215

C₂×C₈

D₄×D₄₇

yes

characteristic

216

C₂×C₈

Q₈×D₄₇

yes

characteristic

217

C₂×C₈

#10625354

yes

characteristic

218

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

188

—

223

C₂²⋊C₄

—

188

—

224

C₄²

—

225

C₄²

—

226

C₄²

—

188

—

227

C₄²

—

188

—

228

C₁₆

—

229

C₁₆

—

188

—

230

C₂³

#13094051

yes

characteristic

231

Q₈

—

232

Q₈

—

188

—

233

Q₈

—

188

—

234

Q₈

—

188

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

188

—

239

C₂×C₄

—

188

—

240

C₂×C₄

—

188

—

241

C₂×C₄

—

188

—

242

C₂×C₄

—

188

—

243

C₂×C₄

#13093986

yes

characteristic

244

C₂×C₄

#13093992

yes

characteristic

245

C₂×C₄

#13094002

yes

characteristic

246

C₂×C₄

SD₁₆×D₄₇

yes

characteristic

247

C₂×C₄

#13094045

yes

characteristic

248

C₂×C₄

#13094051

yes

characteristic

249

C₈

—

250

C₈

—

188

—

251

C₈

C₄⋊C₄×D₄₇

yes

characteristic

252

C₈

C₄×C₂²⋊D₄₇

yes

characteristic

253

C₈

#13094000

yes

characteristic

254

C₈

#13094009

yes

characteristic

255

C₂²

—

256

C₂²

#15689234

yes

characteristic

257

C₂²

#15689272

yes

characteristic

258

C₂²

#15689422

yes

characteristic

259

C₄

—

260

C₄

—

376

—

261

C₄

—

188

—

262

C₄

—

188

—

263

C₄

#15688994

yes

characteristic

264

C₄

#15689210

yes

characteristic

265

C₄

#15689267

yes

characteristic

266

C₄

#15689412

yes

characteristic

267

C₂

—

268

C₂

—

269

C₂

#20243646

yes

characteristic

270

C₂

#20245278

yes

—

	subgroup	G/H
center	C₂²	#15689234
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×#365	C₂
socle	C₂²×C₄₇	#442
prime radical	C₂³×C₄₇	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×#365	D₄₇
hypocenter	C₄₇	#12957
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

subgroup

G/H

center

C₂²

#15689234

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×#365

C₂

C₂²×C₄₇

C₂³×C₄₇

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

N	H ≅ G/N	type
18. #15688928	C₄	semidirect
159. C₄₇	#12957	semidirect

H ≅ G/N

type

18. #15688928

C₄

semidirect

159. C₄₇

#12957

semidirect

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

subgroup	index
C₂×#15689229	2
C₂×#15688938	2
#20245109	2
#20244139	2
#20241495	2
#20241467	2
C₂×C₄₇×#365	2
#12957	47

subgroup

index

C₂×C₄₇×#365

Subgroups — #26133021

Conjugacy classes of subgroups

Complements

Maximal subgroups