Group #26132507 — subgroups

Subgroups — #26132507

Order 12032.

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

normal subgroups only

This group has 430 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	C₂×#15689081	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688905	C₂	1	1	yes	maximal, characteristic
3	#20241469	C₂	1	2	yes	maximal, complemented
4	#20241467	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#349	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₂×#13093983	C₄	1	1	yes	characteristic
8	C₂×#13093964	C₂²	1	2	yes	—
9	#15689081	—	2	2	no	—
10	#15689081	—	2	2	no	—
11	C₂×#13093934	C₄	1	1	yes	characteristic
12	C₂×#13093934	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₄₇	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
15	#15688905	—	2	2	no	—
16	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#349	—	2	2	no	—
19	C₂²×C₄₇⋊C₈	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#13093983	—	2	2	no	—
25	#13093983	C₈	1	4	yes	—
26	C₂×C₄⋊Dic₄₇	—	2	1	no	—
27	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
28	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	#13093964	—	2	2	no	—
31	#13093964	—	2	2	no	—
32	C₂×C₄₇⋊C₁₆	—	2	2	no	—
33	#13093934	—	2	2	no	—
34	#13093934	—	2	1	no	—
35	#13093934	—	2	1	no	—
36	C₈×Dic₄₇	—	2	2	no	—
37	C₈×Dic₄₇	—	2	1	no	—
38	C₈×Dic₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	—	2	2	no	—
42	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
43	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
44	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	M₃₂×C₄₇	—	2	2	no	—
47	M₃₂×C₄₇	—	2	2	no	—
48	C₂×C₁₆×C₄₇	—	2	2	no	—
49	C₂⁴×C₄₇	M₁₆	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	—	2	1	no	—
51	C₂²×C₄×C₄₇	—	2	1	no	—
52	C₂²×C₄×C₄₇	—	2	1	no	—
53	C₂²×C₄×C₄₇	—	2	1	no	—
54	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₄₇	M₁₆	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
58	C₂²×Dic₄₇	—	2	1	no	—
59	C₂²×Dic₄₇	—	2	1	no	—
60	M₁₆×C₄₇	—	2	4	no	—
61	M₁₆×C₄₇	—	2	4	no	—
62	C₂×C₈×C₄₇	—	2	1	no	—
63	C₂×C₈×C₄₇	—	2	1	no	—
64	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₄₇	#41	1	2	yes	—
68	C₂×C₈×C₄₇	#41	1	2	yes	—
69	C₂²⋊Dic₄₇	—	2	4	no	—
70	C₄⋊Dic₄₇	—	2	4	no	—
71	C₄×Dic₄₇	—	2	1	no	—
72	C₄×Dic₄₇	—	2	1	no	—
73	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
74	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
75	C₂×C₄₇⋊C₈	—	2	8	no	—
76	C₂×C₄₇⋊C₈	—	2	1	no	—
77	C₂×C₄₇⋊C₈	—	2	1	no	—
78	C₂×C₄₇⋊C₈	—	2	1	no	—
79	C₂×C₄₇⋊C₈	—	2	1	no	—
80	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
81	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
82	C₁₆×C₄₇	—	4	2	no	—
83	C₄₇⋊C₁₆	—	4	2	no	—
84	C₂³×C₄₇	—	2	1	no	—
85	C₂³×C₄₇	—	2	1	no	—
86	C₂³×C₄₇	—	4	2	no	—
87	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
88	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₄₇	—	2	1	no	—
90	C₂×C₄×C₄₇	—	2	1	no	—
91	C₂×C₄×C₄₇	—	2	2	no	—
92	C₂×C₄×C₄₇	—	2	2	no	—
93	C₂×C₄×C₄₇	—	2	2	no	—
94	C₂×C₄×C₄₇	—	2	2	no	—
95	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
96	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
101	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
102	C₂×Dic₄₇	—	2	2	no	—
103	C₂×Dic₄₇	—	2	2	no	—
104	C₂×Dic₄₇	—	4	2	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₈×C₄₇	—	2	2	no	—
107	C₈×C₄₇	#123	1	2	yes	—
108	C₈×C₄₇	#123	1	2	yes	—
109	C₄₇⋊C₈	—	2	2	no	—
110	C₄₇⋊C₈	—	2	2	no	—
111	#12850	—	47	1	no	maximal, Sylow
112	C₂²×C₄₇	—	2	2	no	—
113	C₂²×C₄₇	—	2	2	no	—
114	C₂²×C₄₇	—	4	2	no	—
115	C₂²×C₄₇	—	4	2	no	—
116	C₂²×C₄₇	—	4	2	no	—
117	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
118	C₂²×C₄₇	#432	1	1	yes	characteristic
119	C₂²×C₄₇	#432	1	1	yes	characteristic
120	C₄×C₄₇	—	2	2	no	—
121	C₄×C₄₇	#381	1	1	yes	characteristic
122	C₄×C₄₇	#407	1	1	yes	characteristic
123	C₄×C₄₇	#431	1	1	yes	characteristic
124	C₄×C₄₇	#431	1	1	yes	characteristic
125	Dic₄₇	—	4	2	no	—
126	Dic₄₇	—	4	2	no	—
127	C₂×#405	—	47	1	no	—
128	C₂×#349	—	47	1	no	—
129	C₂×#349	D₄₇	1	1	yes	characteristic
130	#1376	—	47	2	no	—
131	#1375	—	47	2	no	—
132	C₂×C₄₇	—	2	1	no	—
133	C₂×C₄₇	—	2	1	no	—
134	C₂×C₄₇	—	4	2	no	—
135	C₂×C₄₇	#1817	1	1	yes	characteristic
136	C₂×C₄₇	#2166	1	2	yes	—
137	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
138	C₂³×C₈	—	47	1	no	—
139	C₂×#117	—	47	1	no	—
140	C₂×M₃₂	—	47	2	no	—
141	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
142	#405	—	94	2	no	—
143	#405	—	94	2	no	—
144	C₂×#97	—	47	1	no	—
145	C₂×#97	—	47	1	no	—
146	C₂×C₄×C₈	—	47	1	no	—
147	C₂×C₄×C₈	—	47	1	no	—
148	#349	—	2	2	no	—
149	#349	—	94	2	no	—
150	C₄₇	#12850	1	1	yes	characteristic, complemented, Sylow
151	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
152	C₂×M₁₆	—	2	2	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	D₁₈₈	1	2	yes	—
155	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
156	C₂²×C₈	—	47	1	no	—
157	C₂²×C₈	—	47	1	no	—
158	C₂²×C₈	—	94	2	no	—
159	C₂²×C₈	—	94	2	no	—
160	C₂²×C₈	—	94	2	no	—
161	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
162	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
163	#117	—	47	4	no	—
164	#117	—	94	2	no	—
165	C₂×C₄⋊C₄	—	94	1	no	—
166	C₂×C₂²⋊C₄	—	94	1	no	—
167	C₂×C₄²	—	47	1	no	—
168	C₂×C₄²	—	47	1	no	—
169	M₃₂	—	2	2	no	—
170	M₃₂	—	2	2	no	—
171	M₃₂	—	94	2	no	—
172	M₃₂	—	94	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	C₂×C₁₆	—	94	2	no	—
175	#97	—	94	2	no	—
176	#97	—	94	1	no	—
177	#97	—	94	1	no	—
178	C₄×C₈	—	94	2	no	—
179	C₄×C₈	—	94	1	no	—
180	C₄×C₈	—	94	1	no	—
181	C₂⁴	#10625324	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	94	1	no	—
187	C₂²×C₄	—	94	1	no	—
188	C₂²×C₄	C₈×D₄₇	1	2	yes	—
189	C₂²×C₄	#10625324	1	1	yes	characteristic
190	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
191	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
192	M₁₆	—	2	4	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	47	2	no	—
197	C₂×C₈	—	47	2	no	—
198	C₂×C₈	—	94	8	no	—
199	C₂×C₈	—	94	1	no	—
200	C₂×C₈	—	94	1	no	—
201	C₂×C₈	—	94	1	no	—
202	C₂×C₈	—	94	1	no	—
203	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
204	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
205	C₂×C₈	#10625352	1	2	yes	—
206	C₂×C₈	#10625352	1	2	yes	—
207	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
208	C₄⋊C₄	—	94	4	no	—
209	C₂²⋊C₄	—	94	4	no	—
210	C₄²	—	47	2	no	—
211	C₄²	—	47	2	no	—
212	C₄²	—	94	1	no	—
213	C₄²	—	94	1	no	—
214	C₁₆	—	4	2	no	—
215	C₁₆	—	188	2	no	—
216	C₂³	—	2	1	no	—
217	C₂³	—	2	1	no	—
218	C₂³	—	4	2	no	—
219	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
220	C₂³	C₂×#10625324	1	1	yes	characteristic
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	94	2	no	—
228	C₂×C₄	—	94	2	no	—
229	C₂×C₄	—	188	2	no	—
230	C₂×C₄	—	188	2	no	—
231	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
232	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
233	C₂×C₄	#13093980	1	1	yes	characteristic
234	C₂×C₄	#13093980	1	1	yes	characteristic
235	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
236	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
237	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
238	C₈	—	2	2	no	—
239	C₈	—	94	2	no	—
240	C₈	—	94	2	no	—
241	C₈	#13094005	1	2	yes	—
242	C₈	#13094008	1	2	yes	—
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	4	2	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	2	no	—
248	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
249	C₂²	#15689177	1	1	yes	characteristic
250	C₂²	#15689177	1	1	yes	characteristic
251	C₄	—	2	2	no	—
252	C₄	—	188	2	no	—
253	C₄	—	188	2	no	—
254	C₄	#15688984	1	1	yes	characteristic
255	C₄	#15689086	1	1	yes	characteristic
256	C₄	#15689173	1	1	yes	characteristic
257	C₄	#15689173	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	4	2	no	—
261	C₂	#20243454	1	1	yes	characteristic
262	C₂	#20245201	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689081

C₂

yes

maximal, characteristic

C₂×#15688905

C₂

yes

maximal, characteristic

#20241469

C₂

yes

maximal, complemented

#20241467

C₂

yes

maximal, complemented

C₂×C₄₇×#349

C₂

yes

maximal, characteristic

C₂³×C₄₇⋊C₈

C₄

yes

characteristic

C₂×#13093983

C₄

yes

characteristic

C₂×#13093964

C₂²

yes

—

#15689081

—

#15689081

—

C₂×#13093934

C₄

yes

characteristic

C₂×#13093934

C₂²

yes

characteristic

C₂×C₈×Dic₄₇

C₄

yes

characteristic

C₂×C₈×Dic₄₇

C₂²

yes

characteristic

#15688905

—

C₂²×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₃₂×C₄₇

C₂²

yes

—

C₄₇×#349

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

#13093983

—

#13093983

C₈

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

#13093934

—

#13093934

—

#13093934

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

D₄

yes

—

C₂×M₁₆×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂⁴×C₄₇

M₁₆

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₈

yes

—

C₄×Dic₄₇

C₂×C₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

M₁₆

yes

—

C₂×C₄₇⋊C₈

M₁₆

yes

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₈

yes

—

C₂³×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

100

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

101

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

102

C₂×Dic₄₇

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₈×C₄₇

—

107

C₈×C₄₇

#123

yes

—

108

C₈×C₄₇

#123

yes

—

109

C₄₇⋊C₈

—

110

C₄₇⋊C₈

—

111

#12850

—

maximal, Sylow

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

118

C₂²×C₄₇

#432

yes

characteristic

119

C₂²×C₄₇

#432

yes

characteristic

120

C₄×C₄₇

—

121

C₄×C₄₇

#381

yes

characteristic

122

C₄×C₄₇

#407

yes

characteristic

123

C₄×C₄₇

#431

yes

characteristic

124

C₄×C₄₇

#431

yes

characteristic

125

Dic₄₇

—

126

Dic₄₇

—

127

C₂×#405

—

128

C₂×#349

—

129

C₂×#349

D₄₇

yes

characteristic

130

#1376

—

131

#1375

—

132

C₂×C₄₇

—

133

C₂×C₄₇

—

134

C₂×C₄₇

—

135

C₂×C₄₇

#1817

yes

characteristic

136

C₂×C₄₇

#2166

yes

—

137

C₂²×M₁₆

C₂×D₄₇

yes

characteristic

138

C₂³×C₈

—

139

C₂×#117

—

140

C₂×M₃₂

—

141

C₂×M₃₂

C₂×D₄₇

yes

—

142

#405

—

143

#405

—

144

C₂×#97

—

145

C₂×#97

—

146

C₂×C₄×C₈

—

147

C₂×C₄×C₈

—

148

#349

—

149

#349

—

150

C₄₇

#12850

yes

characteristic, complemented, Sylow

151

C₂³×C₄

C₄×D₄₇

yes

characteristic

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

D₁₈₈

yes

—

155

C₂×M₁₆

C₂²⋊D₄₇

yes

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

C₄×D₄₇

yes

characteristic

162

C₂²×C₈

C₂²×D₄₇

yes

characteristic

163

#117

—

164

#117

—

165

C₂×C₄⋊C₄

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₄²

—

168

C₂×C₄²

—

169

M₃₂

—

170

M₃₂

—

171

M₃₂

—

172

M₃₂

—

173

C₂×C₁₆

—

174

C₂×C₁₆

—

175

#97

—

176

#97

—

177

#97

—

178

C₄×C₈

—

179

C₄×C₈

—

180

C₄×C₈

—

181

C₂⁴

#10625324

yes

characteristic

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

C₈×D₄₇

yes

—

189

C₂²×C₄

#10625324

yes

characteristic

190

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

191

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

204

C₂×C₈

C₂×D₁₈₈

yes

characteristic

205

C₂×C₈

#10625352

yes

—

206

C₂×C₈

#10625352

yes

—

207

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₁₆

—

215

C₁₆

—

188

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

(C₂×D₄₇)⋊C₈

yes

—

220

C₂³

C₂×#10625324

yes

characteristic

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

188

—

230

C₂×C₄

—

188

—

231

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

232

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

233

C₂×C₄

#13093980

yes

characteristic

234

C₂×C₄

#13093980

yes

characteristic

235

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

236

C₂×C₄

M₁₆×D₄₇

yes

characteristic

237

C₂×C₄

M₁₆×D₄₇

yes

characteristic

238

C₈

—

239

C₈

—

240

C₈

—

241

C₈

#13094005

yes

—

242

C₈

#13094008

yes

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

249

C₂²

#15689177

yes

characteristic

250

C₂²

#15689177

yes

characteristic

251

C₄

—

252

C₄

—

188

—

253

C₄

—

188

—

254

C₄

#15688984

yes

characteristic

255

C₄

#15689086

yes

characteristic

256

C₄

#15689173

yes

characteristic

257

C₄

#15689173

yes

characteristic

258

C₂

—

259

C₂

—

260

C₂

—

261

C₂

#20243454

yes

characteristic

262

C₂

#20245201

yes

—

	subgroup	G/H
center	C₂×C₄	#13093980
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×#349	C₂
socle	C₂²×C₄₇	#432
prime radical	C₂⁴×C₄₇	M₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×#349	D₄₇
hypocenter	C₄₇	#12850
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

subgroup

G/H

center

C₂×C₄

#13093980

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×#349

C₂

socle

C₂²×C₄₇

#432

prime radical

C₂⁴×C₄₇

M₁₆

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

N	H ≅ G/N	type
3. #20241469	C₂	semidirect
4. #20241467	C₂	semidirect
150. C₄₇	#12850	semidirect

H ≅ G/N

type

3. #20241469

C₂

semidirect

4. #20241467

C₂

semidirect

150. C₄₇

#12850

semidirect

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

subgroup	index
C₂×#15689081	2
C₂×#15688905	2
#20241469	2
#20241467	2
C₂×C₄₇×#349	2
#12850	47

subgroup

index

C₂×C₄₇×#349

Subgroups — #26132507

Conjugacy classes of subgroups

Complements

Maximal subgroups