Group #26113634 — subgroups

Subgroups — #26113634

Order 12032.

538 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 139 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	#20252412	C₂	1	1	yes	maximal, characteristic
2	#20243380	C₂	1	1	yes	maximal, characteristic
3	#20242069	C₂	1	2	yes	maximal, complemented
4	#20241291	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2563	C₂	1	1	yes	maximal, characteristic
6	D₄×C₄₇⋊C₈	—	2	4	no	—
7	#15689176	C₂²	1	2	yes	—
8	#15689147	C₂²	1	2	yes	—
9	C₂×#13093941	—	2	1	no	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
11	#15688892	—	2	1	no	—
12	#15688872	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#393	C₄	1	4	yes	—
16	C₄₇×#390	—	2	1	no	—
17	C₄₇×#382	—	2	1	no	—
18	C₄₇×#380	—	2	2	no	—
19	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#10625329	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	4	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
25	#13093941	—	4	2	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	D₄	1	2	yes	—
32	C₄⋊Q₈×C₄₇	—	2	2	no	—
33	C₄⋊Q₈×C₄₇	—	2	2	no	—
34	C₄×D₄×C₄₇	—	2	2	no	—
35	C₄×D₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₄₇	—	2	1	no	—
43	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
44	#95×C₄₇	—	2	4	no	—
45	#95×C₄₇	C₂×C₄	1	2	yes	—
46	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
47	C₂×Q₈×C₄₇	—	2	4	no	—
48	C₂×Q₈×C₄₇	—	8	2	no	—
49	C₂×D₄×C₄₇	—	2	2	no	—
50	C₂×D₄×C₄₇	—	2	2	no	—
51	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
52	C₂×D₄×C₄₇	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	4	4	no	—
58	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₄⋊C₄×C₄₇	—	4	2	no	—
64	C₄⋊C₄×C₄₇	—	4	1	no	—
65	C₄⋊C₄×C₄₇	—	4	2	no	—
66	C₄⋊C₄×C₄₇	—	4	1	no	—
67	C₂²⋊C₄×C₄₇	—	2	4	no	—
68	C₂²⋊C₄×C₄₇	—	8	4	no	—
69	C₄²×C₄₇	—	4	2	no	—
70	C₄²×C₄₇	C₂×D₄	1	2	yes	—
71	C₄²×C₄₇	#41	1	2	yes	—
72	#10625329	—	4	2	no	—
73	#10625329	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	2	4	no	—
75	C₂×C₄₇⋊C₈	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	8	4	no	—
77	C₂³×C₄₇	—	2	2	no	—
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	—	4	2	no	—
80	C₂³×C₄₇	—	4	2	no	—
81	C₂³×C₄₇	#103	1	4	yes	—
82	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	Q₈×C₄₇	—	8	4	no	—
84	D₄×C₄₇	—	2	4	no	—
85	D₄×C₄₇	—	2	4	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	4	1	no	—
89	C₂×C₄×C₄₇	—	4	4	no	—
90	C₂×C₄×C₄₇	—	4	2	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	—	4	4	no	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	—	4	2	no	—
96	C₂×C₄×C₄₇	—	8	2	no	—
97	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#121	1	2	yes	—
100	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
101	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
103	C₂×C₄×C₄₇	#135	1	2	yes	—
104	C₄₇⋊C₈	—	4	4	no	—
105	C₄₇⋊C₈	—	8	2	no	—
106	#9391	—	47	1	no	maximal, Sylow
107	C₂²×C₄₇	—	2	1	no	—
108	C₂²×C₄₇	—	2	1	no	—
109	C₂²×C₄₇	—	2	4	no	—
110	C₂²×C₄₇	—	4	4	no	—
111	C₂²×C₄₇	—	4	2	no	—
112	C₂²×C₄₇	—	4	2	no	—
113	C₂²×C₄₇	—	8	2	no	—
114	C₂²×C₄₇	#386	1	1	yes	characteristic
115	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
116	C₂²×C₄₇	#416	1	1	yes	characteristic
117	C₄×C₄₇	—	2	1	no	—
118	C₄×C₄₇	—	2	2	no	—
119	C₄×C₄₇	—	4	2	no	—
120	C₄×C₄₇	—	8	2	no	—
121	C₄×C₄₇	—	8	2	no	—
122	C₄×C₄₇	#455	1	2	yes	—
123	C₄×C₄₇	#465	1	2	yes	—
124	C₄×C₄₇	#467	1	2	yes	—
125	#2972	—	47	1	no	—
126	#2563	D₄₇	1	1	yes	characteristic
127	#1800	—	47	1	no	—
128	#1548	—	47	2	no	—
129	#1303	—	47	2	no	—
130	C₂×C₄₇	—	2	1	no	—
131	C₂×C₄₇	—	2	1	no	—
132	C₂×C₄₇	—	4	4	no	—
133	C₂×C₄₇	#1885	1	1	yes	characteristic
134	C₂×C₄₇	#1892	1	1	yes	characteristic
135	C₂×C₄₇	#1914	1	1	yes	characteristic
136	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
137	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
138	C₈×D₄	—	94	4	no	—
139	#431	—	47	2	no	—
140	#423	—	47	2	no	—
141	C₂×#100	—	94	1	no	—
142	C₂×C₂²⋊C₈	—	94	2	no	—
143	#393	Dic₄₇	1	4	yes	—
144	#390	—	2	1	no	—
145	#382	—	2	1	no	—
146	#380	—	2	2	no	—
147	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
148	#343	—	94	1	no	—
149	#333	—	94	4	no	—
150	C₄₇	#9391	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
152	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
153	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
154	C₂×M₁₆	—	94	2	no	—
155	C₂²×C₈	—	94	4	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	C₄×D₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	1	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
164	C₂×C₂²⋊C₄	—	2	4	no	—
165	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
166	C₂×C₄²	—	2	1	no	—
167	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
168	C₄⋊C₈	—	47	4	no	—
169	C₄⋊C₈	—	94	2	no	—
170	C₄⋊C₈	—	94	2	no	—
171	#100	—	188	2	no	—
172	C₂²⋊C₈	—	94	4	no	—
173	C₂²⋊C₈	—	94	2	no	—
174	C₄×C₈	—	94	2	no	—
175	#95	—	2	4	no	—
176	#95	C₂×Dic₄₇	1	2	yes	—
177	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
178	C₂×Q₈	—	2	4	no	—
179	C₂×Q₈	—	8	2	no	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	2	2	no	—
182	C₂×D₄	#10625336	1	2	yes	—
183	C₂×D₄	#10625337	1	2	yes	—
184	C₂²×C₄	—	2	2	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	4	4	no	—
189	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
190	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
192	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
193	M₁₆	—	188	2	no	—
194	M₁₆	—	188	2	no	—
195	C₂×C₈	—	94	4	no	—
196	C₂×C₈	—	376	4	no	—
197	C₂×C₈	—	188	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	4	2	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	1	no	—
203	C₂²⋊C₄	—	2	4	no	—
204	C₂²⋊C₄	—	8	4	no	—
205	C₄²	—	4	2	no	—
206	C₄²	D₄×D₄₇	1	2	yes	—
207	C₄²	#10625352	1	2	yes	—
208	C₂³	—	2	2	no	—
209	C₂³	—	2	2	no	—
210	C₂³	—	4	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	#13093948	1	4	yes	—
213	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
214	Q₈	—	8	4	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	2	no	—
228	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
229	C₂×C₄	#13093992	1	1	yes	characteristic
230	C₂×C₄	#13093996	1	2	yes	—
231	C₂×C₄	#13094005	1	1	yes	characteristic
232	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
233	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
234	C₂×C₄	#13094044	1	2	yes	—
235	C₈	—	376	2	no	—
236	C₈	—	188	4	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	4	no	—
240	C₂²	—	4	4	no	—
241	C₂²	—	4	2	no	—
242	C₂²	—	4	2	no	—
243	C₂²	—	8	2	no	—
244	C₂²	#15689003	1	1	yes	characteristic
245	C₂²	C₂×#13093948	1	1	yes	characteristic
246	C₂²	#15689119	1	1	yes	characteristic
247	C₄	—	2	1	no	—
248	C₄	—	2	2	no	—
249	C₄	—	4	2	no	—
250	C₄	—	8	2	no	—
251	C₄	—	8	2	no	—
252	C₄	#15689300	1	2	yes	—
253	C₄	#15689354	1	2	yes	—
254	C₄	#15689362	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	#20243777	1	1	yes	characteristic
259	C₂	#20243812	1	1	yes	characteristic
260	C₂	#20243936	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252412

C₂

yes

maximal, characteristic

#20243380

C₂

yes

maximal, characteristic

#20242069

C₂

yes

maximal, complemented

#20241291

C₂

yes

maximal, complemented

C₄₇×#2563

C₂

yes

maximal, characteristic

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

C₂×#13093941

—

C₂×C₂²⋊(C₄₇⋊C₈)

—

#15688892

—

#15688872

—

C₂×C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#393

C₄

yes

—

C₄₇×#390

—

C₄₇×#382

—

C₄₇×#380

—

C₄×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093941

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

D₄

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#95×C₄₇

—

#95×C₄₇

C₂×C₄

yes

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

SD₁₆

yes

—

C₂×D₄×C₄₇

Q₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#103

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

100

C₂×C₄×C₄₇

#123

yes

characteristic

101

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

102

C₂×C₄×C₄₇

C₂×Q₁₆

yes

characteristic

103

C₂×C₄×C₄₇

#135

yes

—

104

C₄₇⋊C₈

—

105

C₄₇⋊C₈

—

106

#9391

—

maximal, Sylow

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

#386

yes

characteristic

115

C₂²×C₄₇

C₂×#103

yes

characteristic

116

C₂²×C₄₇

#416

yes

characteristic

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

—

122

C₄×C₄₇

#455

yes

—

123

C₄×C₄₇

#465

yes

—

124

C₄×C₄₇

#467

yes

—

125

#2972

—

126

#2563

D₄₇

yes

characteristic

127

#1800

—

128

#1548

—

129

#1303

—

130

C₂×C₄₇

—

131

C₂×C₄₇

—

132

C₂×C₄₇

—

133

C₂×C₄₇

#1885

yes

characteristic

134

C₂×C₄₇

#1892

yes

characteristic

135

C₂×C₄₇

#1914

yes

characteristic

136

C₂×C₄⋊Q₈

C₂×D₄₇

yes

characteristic

137

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

138

C₈×D₄

—

139

#431

—

140

#423

—

141

C₂×#100

—

142

C₂×C₂²⋊C₈

—

143

#393

Dic₄₇

yes

—

144

#390

—

145

#382

—

146

#380

—

147

C₄×C₄⋊C₄

C₂×D₄₇

yes

characteristic

148

#343

—

149

#333

—

150

C₄₇

#9391

yes

characteristic, complemented, Sylow

151

C₂²×Q₈

C₂×Dic₄₇

yes

—

152

C₂²×D₄

C₂²⋊D₄₇

yes

characteristic

153

C₂³×C₄

C₂²⋊D₄₇

yes

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

C₄×D₄

—

159

C₄×D₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

164

C₂×C₂²⋊C₄

—

165

C₂×C₂²⋊C₄

C₂×Dic₄₇

yes

—

166

C₂×C₄²

—

167

C₂×C₄²

C₂²×D₄₇

yes

characteristic

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

#100

—

188

—

172

C₂²⋊C₈

—

173

C₂²⋊C₈

—

174

C₄×C₈

—

175

#95

—

176

#95

C₂×Dic₄₇

yes

—

177

C₂⁴

C₂²⋊Dic₄₇

yes

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

#10625336

yes

—

183

C₂×D₄

#10625337

yes

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

190

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

191

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

192

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

193

M₁₆

—

188

—

194

M₁₆

—

188

—

195

C₂×C₈

—

196

C₂×C₈

—

376

—

197

C₂×C₈

—

188

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₄²

—

206

C₄²

D₄×D₄₇

yes

—

207

C₄²

#10625352

yes

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#13093948

yes

—

213

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

D₄×Dic₄₇

yes

—

229

C₂×C₄

#13093992

yes

characteristic

230

C₂×C₄

#13093996

yes

—

231

C₂×C₄

#13094005

yes

characteristic

232

C₂×C₄

C₂×#10625336

yes

characteristic

233

C₂×C₄

C₂×#10625337

yes

characteristic

234

C₂×C₄

#13094044

yes

—

235

C₈

—

376

—

236

C₈

—

188

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

#15689003

yes

characteristic

245

C₂²

C₂×#13093948

yes

characteristic

246

C₂²

#15689119

yes

characteristic

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

#15689300

yes

—

253

C₄

#15689354

yes

—

254

C₄

#15689362

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

#20243777

yes

characteristic

259

C₂

#20243812

yes

characteristic

260

C₂

#20243936

yes

characteristic

	subgroup	G/H
center	C₂²	#15689003
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2563	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2563	D₄₇
hypocenter	C₄₇	#9391
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2563

subgroup

G/H

center

C₂²

#15689003

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#2563

C₂

socle

C₂²×C₄₇

#386

prime radical

C₂²×D₄×C₄₇

D₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2563

N	H ≅ G/N	type
3. #20242069	C₂	semidirect
4. #20241291	C₂	semidirect
150. C₄₇	#9391	semidirect

H ≅ G/N

type

3. #20242069

C₂

semidirect

4. #20241291

C₂

semidirect

150. C₄₇

#9391

semidirect

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

subgroup	index
#20252412	2
#20243380	2
#20242069	2
#20241291	2
C₄₇×#2563	2
#9391	47

subgroup

index

C₄₇×#2563

Subgroups — #26113634

Conjugacy classes of subgroups

Complements

Maximal subgroups