Group #26107309 — subgroups

Subgroups — #26107309

Order 12032.

376 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 121 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	#20252318	C₂	1	1	yes	maximal, characteristic
2	#20242052	C₂	1	1	yes	maximal, characteristic
3	#20241982	C₂	1	1	yes	maximal, characteristic
4	#20241675	C₂	1	1	yes	maximal, characteristic
5	#20241669	C₂	1	1	yes	maximal, characteristic
6	#20241277	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1299	C₂	1	1	yes	maximal, characteristic
8	#15689680	C₂²	1	1	yes	characteristic
9	#15689250	—	2	1	no	—
10	#15689250	—	2	1	no	—
11	#15689247	—	2	1	no	—
12	#15689247	—	2	1	no	—
13	#15689176	C₂²	1	1	yes	characteristic
14	#15689151	C₄	1	2	yes	—
15	#15689081	C₄	1	2	yes	—
16	C₄×#10625329	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	#15688870	C₄	1	2	yes	—
19	#15688868	C₄	1	2	yes	—
20	#15688864	C₄	1	4	yes	—
21	#15688845	—	2	1	no	—
22	#15688845	—	2	1	no	—
23	#15688845	—	2	1	no	—
24	C₈×C₄₇⋊C₈	—	2	1	no	—
25	C₄₇×#431	C₂²	1	1	yes	characteristic
26	C₄₇×#423	C₂²	1	1	yes	characteristic
27	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#10625329	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
31	#13094024	C₂×C₄	1	1	yes	characteristic
32	#13094024	C₂×C₄	1	1	yes	characteristic
33	#13094016	C₂×C₄	1	2	yes	—
34	#13094003	—	2	1	no	—
35	#13094003	—	2	1	no	—
36	C₄×Dic₉₄	—	2	1	no	—
37	C₄×Dic₉₄	—	2	1	no	—
38	#13093983	C₂×C₄	1	2	yes	—
39	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
40	Dic₄₇⋊C₈	—	2	2	no	—
41	Dic₄₇⋊C₈	—	2	2	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
43	#13093935	C₂×C₄	1	2	yes	—
44	#13093934	—	2	2	no	—
45	C₄×C₄₇⋊C₈	—	2	1	no	—
46	C₄×C₄₇⋊C₈	—	2	1	no	—
47	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
48	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
49	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
50	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
51	C₈×Dic₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	1	no	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₄₇	—	2	1	no	—
56	C₄⋊C₈×C₄₇	—	2	1	no	—
57	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
58	C₂²⋊C₈×C₄₇	—	2	1	no	—
59	#97×C₄₇	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₄₇	—	2	1	no	—
61	C₄×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
65	C₂×Dic₉₄	—	2	1	no	—
66	C₂×Dic₉₄	—	2	1	no	—
67	M₁₆×C₄₇	—	4	2	no	—
68	M₁₆×C₄₇	—	4	2	no	—
69	C₂×C₈×C₄₇	—	2	2	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	—	2	2	no	—
72	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²⋊Dic₄₇	—	2	2	no	—
77	C₄⋊Dic₄₇	—	2	1	no	—
78	C₄⋊Dic₄₇	—	2	1	no	—
79	C₄⋊Dic₄₇	C₄²	1	2	yes	—
80	C₄⋊Dic₄₇	C₄²	1	2	yes	—
81	Dic₄₇⋊C₄	—	2	2	no	—
82	Dic₄₇⋊C₄	—	2	2	no	—
83	C₄×Dic₄₇	—	2	2	no	—
84	#10625329	—	2	4	no	—
85	C₂×C₄₇⋊C₈	—	2	2	no	—
86	C₂×C₄₇⋊C₈	—	2	2	no	—
87	C₂×C₄₇⋊C₈	—	2	2	no	—
88	C₂×C₄₇⋊C₈	—	4	1	no	—
89	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
93	C₂³×C₄₇	#117	1	1	yes	characteristic
94	C₂×C₄×C₄₇	—	2	1	no	—
95	C₂×C₄×C₄₇	—	2	1	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
104	C₂×Dic₄₇	—	2	2	no	—
105	C₂×Dic₄₇	—	2	2	no	—
106	Dic₉₄	—	4	2	no	—
107	Dic₉₄	—	4	2	no	—
108	C₈×C₄₇	—	4	2	no	—
109	C₈×C₄₇	—	4	2	no	—
110	C₈×C₄₇	—	4	2	no	—
111	C₄₇⋊C₈	—	2	4	no	—
112	C₄₇⋊C₈	—	2	1	no	—
113	C₄₇⋊C₈	—	2	1	no	—
114	C₄₇⋊C₈	—	2	1	no	—
115	C₄₇⋊C₈	—	4	2	no	—
116	C₄₇⋊C₈	#101	1	2	yes	—
117	#8246	—	47	1	no	maximal, Sylow
118	C₂²×C₄₇	—	2	1	no	—
119	C₂²×C₄₇	—	2	1	no	—
120	C₂²×C₄₇	—	2	1	no	—
121	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
122	C₄×C₄₇	—	2	1	no	—
123	C₄×C₄₇	—	2	1	no	—
124	C₄×C₄₇	—	2	1	no	—
125	C₄×C₄₇	C₂×#101	1	1	yes	characteristic
126	C₄×C₄₇	#413	1	1	yes	characteristic
127	C₄×C₄₇	#443	1	2	yes	—
128	C₄×C₄₇	#444	1	2	yes	—
129	Dic₄₇	—	4	2	no	—
130	Dic₄₇	—	4	2	no	—
131	#2960	—	47	1	no	—
132	#1544	—	47	1	no	—
133	#1526	—	47	1	no	—
134	#1451	—	47	1	no	—
135	C₈×M₁₆	—	47	1	no	—
136	#1299	—	47	1	no	—
137	#1299	D₄₇	1	1	yes	characteristic
138	C₂×C₄₇	—	4	1	no	—
139	C₂×C₄₇	C₄×#101	1	1	yes	characteristic
140	C₂×C₄₇	#1764	1	1	yes	characteristic
141	C₂×C₄₇	#1765	1	1	yes	characteristic
142	#533	—	47	1	no	—
143	#446	—	94	1	no	—
144	#446	—	94	1	no	—
145	C₈×Q₈	—	94	1	no	—
146	C₈×Q₈	—	94	1	no	—
147	#431	—	47	1	no	—
148	#431	C₂×D₄₇	1	1	yes	characteristic
149	#424	—	47	2	no	—
150	#423	C₂×D₄₇	1	1	yes	characteristic
151	#405	—	47	2	no	—
152	C₄×M₁₆	—	47	1	no	—
153	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
154	C₂×C₄×C₈	—	47	1	no	—
155	#332	—	47	2	no	—
156	#332	—	47	2	no	—
157	#330	—	47	4	no	—
158	#322	—	94	1	no	—
159	#322	—	94	1	no	—
160	#322	—	94	1	no	—
161	C₈²	—	94	1	no	—
162	C₄₇	#8246	1	1	yes	characteristic, complemented, Sylow
163	C₂×M₁₆	—	2	1	no	—
164	C₂×M₁₆	—	94	1	no	—
165	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
166	C₂²×C₈	—	47	1	no	—
167	C₂²×C₈	—	47	1	no	—
168	C₄⋊Q₈	—	47	1	no	—
169	C₄⋊Q₈	—	47	1	no	—
170	#125	—	47	2	no	—
171	C₂²⋊Q₈	—	94	1	no	—
172	C₂²⋊Q₈	—	94	1	no	—
173	C₄×Q₈	—	94	1	no	—
174	C₄×Q₈	—	94	1	no	—
175	#117	—	47	2	no	—
176	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
177	C₄⋊C₈	—	2	1	no	—
178	C₄⋊C₈	—	2	1	no	—
179	C₄⋊C₈	—	47	2	no	—
180	C₄⋊C₈	—	94	2	no	—
181	C₄⋊C₈	—	94	2	no	—
182	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
183	C₂²⋊C₈	—	2	1	no	—
184	C₂²⋊C₈	—	94	1	no	—
185	#97	—	47	2	no	—
186	#97	—	94	2	no	—
187	#97	C₄×D₄₇	1	2	yes	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	2	1	no	—
190	C₄×C₈	—	47	1	no	—
191	C₄×C₈	—	47	1	no	—
192	C₄×C₈	—	47	1	no	—
193	C₄×C₈	—	47	1	no	—
194	C₄×C₈	—	94	2	no	—
195	C₄×C₈	—	94	1	no	—
196	C₄×C₈	—	94	1	no	—
197	C₂×Q₈	—	94	1	no	—
198	C₂×Q₈	—	94	1	no	—
199	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
200	C₂²×C₄	#10625352	1	1	yes	characteristic
201	C₂²×C₄	#10625354	1	1	yes	characteristic
202	M₁₆	—	4	2	no	—
203	M₁₆	—	4	2	no	—
204	M₁₆	—	94	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	2	2	no	—
208	C₂×C₈	—	47	1	no	—
209	C₂×C₈	—	47	1	no	—
210	C₂×C₈	—	47	1	no	—
211	C₂×C₈	—	47	1	no	—
212	C₂×C₈	—	94	2	no	—
213	C₂×C₈	—	94	2	no	—
214	C₂×C₈	—	94	2	no	—
215	C₂×C₈	—	188	1	no	—
216	C₄⋊C₄	—	47	2	no	—
217	C₄⋊C₄	—	47	2	no	—
218	C₄⋊C₄	—	94	2	no	—
219	C₄⋊C₄	—	94	1	no	—
220	C₄⋊C₄	—	94	2	no	—
221	C₄⋊C₄	—	94	1	no	—
222	C₂²⋊C₄	—	94	2	no	—
223	C₄²	—	94	2	no	—
224	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
225	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
226	C₄²	D₄×D₄₇	1	1	yes	characteristic
227	C₄²	D₄×D₄₇	1	1	yes	characteristic
228	C₂³	#13093982	1	1	yes	characteristic
229	Q₈	—	188	2	no	—
230	Q₈	—	188	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	94	2	no	—
236	C₂×C₄	—	94	2	no	—
237	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
238	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
239	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
240	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#13093986	1	1	yes	characteristic
242	C₂×C₄	#13093986	1	1	yes	characteristic
243	C₈	—	4	2	no	—
244	C₈	—	4	2	no	—
245	C₈	—	4	2	no	—
246	C₈	—	47	2	no	—
247	C₈	—	94	4	no	—
248	C₈	—	94	1	no	—
249	C₈	—	94	1	no	—
250	C₈	—	94	1	no	—
251	C₈	—	188	2	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	#15688970	1	1	yes	characteristic
256	C₄	—	2	1	no	—
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	188	2	no	—
260	C₄	—	188	2	no	—
261	C₄	#101×D₄₇	1	1	yes	characteristic
262	C₄	#15689104	1	1	yes	characteristic
263	C₄	#15689239	1	2	yes	—
264	C₄	#15689242	1	2	yes	—
265	C₂	—	4	1	no	—
266	C₂	#20243183	1	1	yes	characteristic
267	C₂	#20243224	1	1	yes	characteristic
268	C₂	#20243229	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252318

C₂

yes

maximal, characteristic

#20242052

C₂

yes

maximal, characteristic

#20241982

C₂

yes

maximal, characteristic

#20241675

C₂

yes

maximal, characteristic

#20241669

C₂

yes

maximal, characteristic

#20241277

C₂

yes

maximal, characteristic

C₄₇×#1299

C₂

yes

maximal, characteristic

#15689680

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#15689151

C₄

yes

—

#15689081

C₄

yes

—

C₄×#10625329

C₂²

yes

characteristic

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688870

C₄

yes

—

#15688868

C₄

yes

—

#15688864

C₄

yes

—

#15688845

—

#15688845

—

#15688845

—

C₈×C₄₇⋊C₈

—

C₄₇×#431

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

characteristic

C₄×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

#13094024

C₂×C₄

yes

characteristic

#13094024

C₂×C₄

yes

characteristic

#13094016

C₂×C₄

yes

—

#13094003

—

#13094003

—

C₄×Dic₉₄

—

C₄×Dic₉₄

—

#13093983

C₂×C₄

yes

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

—

Dic₄₇⋊C₈

—

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

#13093935

C₂×C₄

yes

—

#13093934

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

characteristic

C₄×C₄₇⋊C₈

D₄

yes

characteristic

C₄×C₄₇⋊C₈

D₄

yes

characteristic

C₄×C₄₇⋊C₈

D₄

yes

characteristic

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

—

C₂²⋊C₈×C₄₇

—

#97×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

C₂²×C₄×C₄₇

yes

C₂²×C₄×C₄₇

yes

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₄²

yes

—

C₄⋊Dic₄₇

C₄²

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

100

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

101

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

102

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

103

C₂×C₄×C₄₇

C₄×D₄

yes

characteristic

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

Dic₉₄

—

107

Dic₉₄

—

108

C₈×C₄₇

—

109

C₈×C₄₇

—

110

C₈×C₄₇

—

111

C₄₇⋊C₈

—

112

C₄₇⋊C₈

—

113

C₄₇⋊C₈

—

114

C₄₇⋊C₈

—

115

C₄₇⋊C₈

—

116

C₄₇⋊C₈

#101

yes

—

117

#8246

—

maximal, Sylow

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

122

C₄×C₄₇

—

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

C₂×#101

yes

characteristic

126

C₄×C₄₇

#413

yes

characteristic

127

C₄×C₄₇

#443

yes

—

128

C₄×C₄₇

#444

yes

—

129

Dic₄₇

—

130

Dic₄₇

—

131

#2960

—

132

#1544

—

133

#1526

—

134

#1451

—

135

C₈×M₁₆

—

136

#1299

—

137

#1299

D₄₇

yes

characteristic

138

C₂×C₄₇

—

139

C₂×C₄₇

C₄×#101

yes

characteristic

140

C₂×C₄₇

#1764

yes

characteristic

141

C₂×C₄₇

#1765

yes

characteristic

142

#533

—

143

#446

—

144

#446

—

145

C₈×Q₈

—

146

C₈×Q₈

—

147

#431

—

148

#431

C₂×D₄₇

yes

characteristic

149

#424

—

150

#423

C₂×D₄₇

yes

characteristic

151

#405

—

152

C₄×M₁₆

—

153

C₄×M₁₆

C₂×D₄₇

yes

characteristic

154

C₂×C₄×C₈

—

155

#332

—

156

#332

—

157

#330

—

158

#322

—

159

#322

—

160

#322

—

161

C₈²

—

162

C₄₇

#8246

yes

characteristic, complemented, Sylow

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂×M₁₆

C₄×D₄₇

yes

—

166

C₂²×C₈

—

167

C₂²×C₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

#125

—

171

C₂²⋊Q₈

—

172

C₂²⋊Q₈

—

173

C₄×Q₈

—

174

C₄×Q₈

—

175

#117

—

176

C₂×C₄²

C₂²×D₄₇

yes

characteristic

177

C₄⋊C₈

—

178

C₄⋊C₈

—

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

C₄×D₄₇

yes

—

183

C₂²⋊C₈

—

184

C₂²⋊C₈

—

185

#97

—

186

#97

—

187

#97

C₄×D₄₇

yes

—

188

C₄×C₈

—

189

C₄×C₈

—

190

C₄×C₈

—

191

C₄×C₈

—

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

200

C₂²×C₄

#10625352

yes

characteristic

201

C₂²×C₄

#10625354

yes

characteristic

202

M₁₆

—

203

M₁₆

—

204

M₁₆

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

188

—

216

C₄⋊C₄

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₂²⋊C₄

—

223

C₄²

—

224

C₄²

C₂×C₄×D₄₇

yes

characteristic

225

C₄²

C₂×C₄×D₄₇

yes

characteristic

226

C₄²

D₄×D₄₇

yes

characteristic

227

C₄²

D₄×D₄₇

yes

characteristic

228

C₂³

#13093982

yes

characteristic

229

Q₈

—

188

—

230

Q₈

—

188

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

C₄²×D₄₇

yes

characteristic

238

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

239

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

characteristic

240

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

characteristic

241

C₂×C₄

#13093986

yes

characteristic

242

C₂×C₄

#13093986

yes

characteristic

243

C₈

—

244

C₈

—

245

C₈

—

246

C₈

—

247

C₈

—

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

188

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

#15688970

yes

characteristic

256

C₄

—

257

C₄

—

258

C₄

—

259

C₄

—

188

—

260

C₄

—

188

—

261

C₄

#101×D₄₇

yes

characteristic

262

C₄

#15689104

yes

characteristic

263

C₄

#15689239

yes

—

264

C₄

#15689242

yes

—

265

C₂

—

266

C₂

#20243183

yes

characteristic

267

C₂

#20243224

yes

characteristic

268

C₂

#20243229

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1299	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂³×C₄₇	#117
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1299	D₄₇
hypocenter	C₄₇	#8246
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1299

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1299

C₂

socle

C₂²×C₄₇

C₄×C₂²⋊C₄

prime radical

C₂³×C₄₇

#117

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1299

N	H ≅ G/N	type
162. C₄₇	#8246	semidirect

H ≅ G/N

type

162. C₄₇

#8246

semidirect

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

subgroup	index
#20252318	2
#20242052	2
#20241982	2
#20241675	2
#20241669	2
#20241277	2
C₄₇×#1299	2
#8246	47

subgroup

index

C₄₇×#1299

Subgroups — #26107309

Conjugacy classes of subgroups

Complements

Maximal subgroups