Group #26133658 — subgroups

Subgroups — #26133658

Order 12032.

508 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂³×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252969	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688929	C₂	1	2	yes	maximal, complemented
4	#20241485	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094046	C₂²	1	1	yes	characteristic
7	#15689634	—	2	1	no	—
8	C₂²×C₄₇⋊C₁₆	—	2	4	no	—
9	C₂²×C₄₇⋊C₁₆	—	2	2	no	—
10	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	#15689364	C₄	1	2	yes	—
12	#15689359	C₄	1	2	yes	—
13	#15689352	—	2	2	no	—
14	#15689161	C₂²	1	1	yes	characteristic
15	#15689120	—	2	1	no	—
16	#15688929	—	2	4	no	—
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#108×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#407	—	2	1	no	—
20	C₄₇×#341	—	2	1	no	—
21	C₂×#10625350	—	2	1	no	—
22	#13094046	—	2	2	no	—
23	#13094046	—	2	2	no	—
24	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
25	C₂×#10625325	—	2	1	no	—
26	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
27	#13094007	—	4	1	no	—
28	#13094003	—	2	2	no	—
29	#13093998	—	2	2	no	—
30	#13093993	—	4	1	no	—
31	C₄×C₂²⋊D₄₇	—	4	2	no	—
32	#13093983	—	2	1	no	—
33	C₂×C₄₇⋊C₁₆	—	2	8	no	—
34	C₂×C₄₇⋊C₁₆	—	2	2	no	—
35	C₂×C₄₇⋊C₁₆	—	2	2	no	—
36	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	complemented
37	#13093958	C₂×C₄	1	2	yes	—
38	#13093956	—	2	1	no	—
39	#13093949	—	2	2	no	—
40	#13093946	—	2	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂×M₁₆×C₄₇	—	2	2	no	—
43	C₂²×C₈×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	#108×C₄₇	—	2	2	no	—
50	#108×C₄₇	—	2	2	no	—
51	C₂²⋊C₈×C₄₇	—	4	2	no	—
52	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₇	D₈	1	2	yes	—
57	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂×C₂²⋊D₄₇	—	4	2	no	—
60	C₂×C₂²⋊D₄₇	—	4	1	no	—
61	#10625350	—	4	2	no	—
62	#10625350	—	4	2	no	—
63	C₂×D₁₈₈	—	2	1	no	—
64	C₂×C₄×D₄₇	—	4	1	no	—
65	C₂×Dic₉₄	—	2	1	no	—
66	M₁₆×C₄₇	—	4	2	no	—
67	M₁₆×C₄₇	—	4	2	no	—
68	C₂×C₈×C₄₇	—	2	2	no	—
69	C₂×C₈×C₄₇	—	2	4	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	—	2	2	no	—
72	C₂×C₈×C₄₇	—	4	2	no	—
73	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₄₇	#41	1	2	yes	—
78	C₂²⋊Dic₄₇	—	4	2	no	—
79	C₂²⋊Dic₄₇	—	4	1	no	—
80	(C₂×D₄₇)⋊C₄	—	4	2	no	—
81	C₄⋊Dic₄₇	—	2	2	no	—
82	Dic₄₇⋊C₄	—	4	2	no	—
83	C₄×Dic₄₇	—	4	1	no	—
84	Dic₁₈₈	—	2	2	no	—
85	D₃₇₆	—	2	2	no	—
86	#10625325	—	4	1	no	—
87	#10625325	—	4	1	no	—
88	C₄₇⋊C₁₆	—	2	4	no	—
89	C₂³×C₄₇	—	2	4	no	—
90	C₂³×C₄₇	—	2	2	no	—
91	C₂³×C₄₇	#102	1	2	yes	—
92	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
93	C₂²×D₄₇	—	4	1	no	—
94	C₂×C₄×C₄₇	—	2	2	no	—
95	C₂×C₄×C₄₇	—	2	2	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	4	no	—
98	C₂×C₄×C₄₇	#102	1	2	yes	—
99	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₄₇	#121	1	2	yes	—
101	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₄₇	#135	1	2	yes	—
103	C₂²⋊D₄₇	—	8	4	no	—
104	C₂²⋊D₄₇	—	8	2	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₂×Dic₄₇	—	4	1	no	—
107	D₁₈₈	—	4	1	no	—
108	D₁₈₈	—	4	1	no	—
109	C₄×D₄₇	—	8	2	no	—
110	Dic₉₄	—	4	1	no	—
111	Dic₉₄	—	4	1	no	—
112	C₈×C₄₇	—	2	2	no	—
113	C₈×C₄₇	—	8	2	no	—
114	C₈×C₄₇	C₄×D₄	1	2	yes	—
115	C₈×C₄₇	#120	1	1	yes	characteristic
116	C₈×C₄₇	#123	1	1	yes	characteristic
117	#13063	—	47	1	no	maximal, Sylow
118	C₂²×C₄₇	—	2	8	no	—
119	C₂²×C₄₇	—	2	2	no	—
120	C₂²×C₄₇	—	2	2	no	—
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	#359	1	4	yes	complemented
123	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
124	C₂²×C₄₇	#465	1	2	yes	—
125	C₂×D₄₇	—	8	2	no	—
126	C₂×D₄₇	—	8	1	no	—
127	C₄×C₄₇	—	2	2	no	—
128	C₄×C₄₇	#386	1	1	yes	characteristic
129	C₄×C₄₇	#416	1	1	yes	characteristic
130	C₄×C₄₇	#466	1	2	yes	—
131	Dic₄₇	—	8	2	no	—
132	Dic₄₇	—	8	1	no	—
133	C₂³×C₁₆	—	47	1	no	—
134	#3050	—	47	1	no	—
135	C₂×#359	—	47	2	no	—
136	#1810	D₄₇	1	1	yes	characteristic, complemented
137	#1382	—	47	2	no	—
138	C₂×C₄₇	—	2	4	no	—
139	C₂×C₄₇	—	2	2	no	—
140	C₂×C₄₇	#1893	1	1	yes	characteristic
141	C₂×C₄₇	C₂×#359	1	2	yes	—
142	D₄₇	—	16	1	no	—
143	C₂×#135	—	47	1	no	—
144	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
145	#525	—	94	1	no	—
146	C₂²×C₁₆	—	47	2	no	—
147	C₂²×C₁₆	—	94	4	no	—
148	C₂²×C₁₆	—	94	2	no	—
149	#467	—	47	2	no	—
150	#466	—	47	2	no	—
151	#465	—	94	2	no	—
152	C₂×#108	C₂×D₄₇	1	2	yes	—
153	#427	—	47	1	no	—
154	#416	—	94	1	no	—
155	#407	—	2	1	no	—
156	#359	—	94	4	no	—
157	#341	—	2	1	no	—
158	C₄₇	#13063	1	1	yes	characteristic, complemented, Sylow
159	C₂×#41	—	94	1	no	—
160	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
161	#135	—	94	2	no	—
162	#135	—	94	2	no	—
163	C₂×Q₁₆	—	47	1	no	—
164	C₂×SD₁₆	—	94	1	no	—
165	C₂×D₈	—	47	1	no	—
166	C₂×M₁₆	—	2	2	no	—
167	C₂²×C₈	—	2	2	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	C₄×D₄₇	1	2	yes	—
170	C₂²×C₈	D₁₈₈	1	2	yes	—
171	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
172	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
173	#123	—	188	1	no	—
174	C₂²⋊Q₈	—	94	2	no	—
175	#121	—	94	2	no	—
176	#120	—	188	1	no	—
177	C₄×D₄	—	188	2	no	—
178	#117	—	94	1	no	—
179	C₂×C₁₆	—	47	4	no	—
180	C₂×C₁₆	—	94	8	no	—
181	C₂×C₁₆	—	94	2	no	—
182	C₂×C₁₆	—	94	2	no	—
183	#108	—	2	2	no	—
184	#108	—	2	2	no	—
185	#107	—	47	2	no	—
186	#106	—	94	1	no	—
187	#103	—	94	2	no	—
188	#102	—	94	2	no	—
189	C₂²⋊C₈	—	4	2	no	—
190	C₂⁴	#10625336	1	1	yes	characteristic
191	#41	—	188	2	no	—
192	#41	—	188	2	no	—
193	C₂×Q₈	—	94	1	no	—
194	C₂×D₄	—	94	1	no	—
195	C₂×D₄	—	188	2	no	—
196	C₂×D₄	—	188	1	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	188	1	no	—
200	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
201	C₂²×C₄	#10625334	1	2	yes	—
202	C₂²×C₄	#10625336	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
204	Q₁₆	—	94	2	no	—
205	SD₁₆	—	188	1	no	—
206	SD₁₆	—	188	1	no	—
207	D₈	—	94	2	no	—
208	M₁₆	—	4	2	no	—
209	M₁₆	—	4	2	no	—
210	C₂×C₈	—	2	2	no	—
211	C₂×C₈	—	2	4	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	4	2	no	—
215	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
216	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
217	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
218	C₂×C₈	D₄×D₄₇	1	2	yes	—
219	C₂×C₈	#10625352	1	2	yes	—
220	C₄⋊C₄	—	94	2	no	—
221	C₄⋊C₄	—	188	2	no	—
222	C₂²⋊C₄	—	188	2	no	—
223	C₂²⋊C₄	—	188	1	no	—
224	C₂²⋊C₄	—	188	2	no	—
225	C₄²	—	188	1	no	—
226	C₁₆	—	94	4	no	—
227	C₂³	—	2	2	no	—
228	C₂³	—	2	4	no	—
229	C₂³	—	188	1	no	—
230	C₂³	#13093944	1	2	yes	—
231	C₂³	C₂×#10625336	1	1	yes	characteristic
232	Q₈	—	188	1	no	—
233	Q₈	—	188	1	no	—
234	D₄	—	376	2	no	—
235	D₄	—	376	4	no	—
236	D₄	—	188	1	no	—
237	D₄	—	188	1	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	376	2	no	—
243	C₂×C₄	—	188	2	no	—
244	C₂×C₄	—	188	1	no	—
245	C₂×C₄	#13093944	1	2	yes	—
246	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#13093996	1	2	yes	—
248	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
249	C₂×C₄	#13094044	1	2	yes	—
250	C₈	—	2	2	no	—
251	C₈	—	8	2	no	—
252	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
253	C₈	#13093994	1	1	yes	characteristic
254	C₈	#13094008	1	1	yes	characteristic
255	C₂²	—	2	8	no	—
256	C₂²	—	2	2	no	—
257	C₂²	—	2	2	no	—
258	C₂²	—	2	2	no	—
259	C₂²	—	376	1	no	—
260	C₂²	—	376	2	no	—
261	C₂²	#15688929	1	4	yes	complemented
262	C₂²	C₂×#13093944	1	1	yes	characteristic
263	C₂²	#15689354	1	2	yes	—
264	C₄	—	2	2	no	—
265	C₄	—	376	1	no	—
266	C₄	—	376	2	no	—
267	C₄	#15689000	1	1	yes	characteristic
268	C₄	#15689117	1	1	yes	characteristic
269	C₄	#15689357	1	2	yes	—
270	C₂	—	2	2	no	—
271	C₂	—	2	4	no	—
272	C₂	—	752	1	no	—
273	C₂	#20243814	1	1	yes	characteristic
274	C₂	C₂×#15688929	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#20252969

C₂

yes

maximal, characteristic

C₂×#15688929

C₂

yes

maximal, complemented

#20241485

C₂

yes

maximal, complemented

C₄₇×#1810

C₂

yes

maximal, characteristic, complemented

C₂×#13094046

C₂²

yes

characteristic

#15689634

—

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689364

C₄

yes

—

#15689359

C₄

yes

—

#15689352

—

#15689161

C₂²

yes

characteristic

#15689120

—

#15688929

—

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂×#108×C₄₇

C₂²

yes

—

C₄₇×#407

—

C₄₇×#341

—

C₂×#10625350

—

#13094046

—

#13094046

—

C₂×Dic₁₈₈

C₂×C₄

yes

characteristic

C₂×#10625325

—

C₂×D₃₇₆

C₂×C₄

yes

—

—

—

—

C₄×C₂²⋊D₄₇

—

#13093983

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

complemented

#13093958

C₂×C₄

yes

—

#13093956

—

#13093949

—

#13093946

—

C₂³×C₄×C₄₇

D₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

#108×C₄₇

—

#108×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

—

C₂²×C₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

#10625325

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₄₇

#121

yes

—

101

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

102

C₂×C₄×C₄₇

#135

yes

—

103

C₂²⋊D₄₇

—

104

C₂²⋊D₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

D₁₈₈

—

108

D₁₈₈

—

109

C₄×D₄₇

—

110

Dic₉₄

—

111

Dic₉₄

—

112

C₈×C₄₇

—

113

C₈×C₄₇

—

114

C₈×C₄₇

C₄×D₄

yes

—

115

C₈×C₄₇

#120

yes

characteristic

116

C₈×C₄₇

yes

117

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

#359

yes

complemented

123

C₂²×C₄₇

C₂×#102

yes

characteristic

124

C₂²×C₄₇

#465

yes

—

125

C₂×D₄₇

—

126

C₂×D₄₇

—

127

C₄×C₄₇

—

128

C₄×C₄₇

#386

yes

characteristic

129

C₄×C₄₇

#416

yes

characteristic

130

C₄×C₄₇

#466

yes

—

131

Dic₄₇

—

132

Dic₄₇

—

133

C₂³×C₁₆

—

134

#3050

—

135

C₂×#359

—

136

#1810

D₄₇

yes

characteristic, complemented

137

#1382

—

138

C₂×C₄₇

—

139

C₂×C₄₇

—

140

C₂×C₄₇

#1893

yes

characteristic

141

C₂×C₄₇

C₂×#359

yes

—

142

D₄₇

—

143

C₂×#135

—

144

C₂³×C₈

C₂×D₄₇

yes

characteristic

145

#525

—

146

C₂²×C₁₆

—

147

C₂²×C₁₆

—

148

C₂²×C₁₆

—

149

#467

—

150

#466

—

151

#465

—

152

C₂×#108

C₂×D₄₇

yes

—

153

#427

—

154

#416

—

155

#407

—

156

#359

—

157

#341

—

158

C₄₇

#13063

yes

characteristic, complemented, Sylow

159

C₂×#41

—

160

C₂³×C₄

C₂²⋊D₄₇

yes

characteristic

161

#135

—

162

#135

—

163

C₂×Q₁₆

—

164

C₂×SD₁₆

—

165

C₂×D₈

—

166

C₂×M₁₆

—

167

C₂²×C₈

—

168

C₂²×C₈

—

169

C₂²×C₈

C₄×D₄₇

yes

—

170

C₂²×C₈

D₁₈₈

yes

—

171

C₂²×C₈

C₂²⋊D₄₇

yes

characteristic

172

C₂²×C₈

C₂²×D₄₇

yes

characteristic

173

#123

—

188

—

174

C₂²⋊Q₈

—

175

#121

—

176

#120

—

188

—

177

C₄×D₄

—

188

—

178

#117

—

179

C₂×C₁₆

—

180

C₂×C₁₆

—

181

C₂×C₁₆

—

182

C₂×C₁₆

—

183

#108

—

184

#108

—

185

#107

—

186

#106

—

187

#103

—

188

#102

—

189

C₂²⋊C₈

—

190

C₂⁴

#10625336

yes

characteristic

191

#41

—

188

—

192

#41

—

188

—

193

C₂×Q₈

—

194

C₂×D₄

—

195

C₂×D₄

—

188

—

196

C₂×D₄

—

188

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

188

—

200

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

201

C₂²×C₄

#10625334

yes

—

202

C₂²×C₄

#10625336

yes

characteristic

203

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

204

Q₁₆

—

205

SD₁₆

—

188

—

206

SD₁₆

—

188

—

207

D₈

—

208

M₁₆

—

209

M₁₆

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

216

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

217

C₂×C₈

C₂×D₁₈₈

yes

characteristic

218

C₂×C₈

D₄×D₄₇

yes

—

219

C₂×C₈

#10625352

yes

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

188

—

222

C₂²⋊C₄

—

188

—

223

C₂²⋊C₄

—

188

—

224

C₂²⋊C₄

—

188

—

225

C₄²

—

188

—

226

C₁₆

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

188

—

230

C₂³

#13093944

yes

—

231

C₂³

C₂×#10625336

yes

characteristic

232

Q₈

—

188

—

233

Q₈

—

188

—

234

D₄

—

376

—

235

D₄

—

376

—

236

D₄

—

188

—

237

D₄

—

188

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

376

—

243

C₂×C₄

—

188

—

244

C₂×C₄

—

188

—

245

C₂×C₄

#13093944

yes

—

246

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

247

C₂×C₄

#13093996

yes

—

248

C₂×C₄

C₂×#10625334

yes

characteristic

249

C₂×C₄

#13094044

yes

—

250

C₈

—

251

C₈

—

252

C₈

(C₂²⋊D₄₇)⋊C₄

yes

—

253

C₈

#13093994

yes

characteristic

254

C₈

#13094008

yes

characteristic

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

376

—

260

C₂²

—

376

—

261

C₂²

#15688929

yes

complemented

262

C₂²

C₂×#13093944

yes

characteristic

263

C₂²

#15689354

yes

—

264

C₄

—

265

C₄

—

376

—

266

C₄

—

376

—

267

C₄

#15689000

yes

characteristic

268

C₄

#15689117

yes

characteristic

269

C₄

#15689357

yes

—

270

C₂

—

271

C₂

—

272

C₂

—

752

—

273

C₂

#20243814

yes

characteristic

274

C₂

C₂×#15688929

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1810	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	#20252969	C₂
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1810	D₄₇
hypocenter	C₄₇	#13063
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂×C₄

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#1810

C₂

C₂²×C₄₇

C₂

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
1. C₂³×C₄₇⋊C₁₆	C₂	semidirect
3. C₂×#15688929	C₂	semidirect
4. #20241485	C₂	semidirect
5. C₄₇×#1810	C₂	semidirect
36. C₂×C₄₇⋊C₁₆	D₄	semidirect
122. C₂²×C₄₇	#359	semidirect
136. #1810	D₄₇	semidirect
158. C₄₇	#13063	semidirect
261. C₂²	#15688929	semidirect

H ≅ G/N

type

1. C₂³×C₄₇⋊C₁₆

C₂

semidirect

3. C₂×#15688929

C₂

semidirect

4. #20241485

C₂

semidirect

5. C₄₇×#1810

C₂

semidirect

36. C₂×C₄₇⋊C₁₆

D₄

semidirect

122. C₂²×C₄₇

#359

semidirect

136. #1810

D₄₇

semidirect

158. C₄₇

#13063

semidirect

261. C₂²

#15688929

semidirect

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

subgroup	index
C₂³×C₄₇⋊C₁₆	2
#20252969	2
C₂×#15688929	2
#20241485	2
C₄₇×#1810	2
#13063	47

subgroup

index

C₂³×C₄₇⋊C₁₆

C₄₇×#1810

Subgroups — #26133658

Conjugacy classes of subgroups

Complements

Maximal subgroups