Group #26132503 — subgroups

Subgroups — #26132503

Order 12032.

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

normal subgroups only

This group has 462 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×M₁₆×Dic₄₇	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	C₂²×#10625329	C₄	1	1	yes	characteristic
7	C₂²×C₄×Dic₄₇	C₄	1	1	yes	characteristic
8	C₂×#13093964	C₂²	1	2	yes	—
9	M₁₆×Dic₄₇	—	2	2	no	—
10	M₁₆×Dic₄₇	—	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	C₂³×Dic₄₇	—	2	1	no	—
20	C₂×#10625329	—	2	2	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂×#10625329	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₄₇	—	2	2	no	—
26	C₂×C₄×Dic₄₇	—	2	1	no	—
27	C₂×C₄×Dic₄₇	C₈	1	4	yes	—
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	4	no	—
60	C₂²×Dic₄₇	—	2	1	no	—
61	C₂²×Dic₄₇	—	4	4	no	—
62	M₁₆×C₄₇	—	2	4	no	—
63	M₁₆×C₄₇	—	2	4	no	—
64	C₂×C₈×C₄₇	—	2	1	no	—
65	C₂×C₈×C₄₇	—	2	1	no	—
66	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₄₇	#41	1	2	yes	—
70	C₂×C₈×C₄₇	#41	1	2	yes	—
71	C₄×Dic₄₇	—	2	4	no	—
72	C₄×Dic₄₇	—	2	1	no	—
73	C₄×Dic₄₇	—	2	1	no	—
74	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
75	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
76	#10625329	—	2	8	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	—	2	1	no	—
81	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
82	C₂×C₄₇⋊C₈	M₁₆	1	2	yes	—
83	C₁₆×C₄₇	—	4	2	no	—
84	C₄₇⋊C₁₆	—	4	2	no	—
85	C₂³×C₄₇	—	2	1	no	—
86	C₂³×C₄₇	—	2	1	no	—
87	C₂³×C₄₇	—	4	2	no	—
88	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
89	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₄₇	—	2	1	no	—
91	C₂×C₄×C₄₇	—	2	1	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	—	2	2	no	—
96	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
97	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
99	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
100	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
103	C₂×Dic₄₇	—	2	4	no	—
104	C₂×Dic₄₇	—	2	2	no	—
105	C₂×Dic₄₇	—	2	2	no	—
106	C₂×Dic₄₇	—	4	8	no	—
107	C₂×Dic₄₇	—	4	2	no	—
108	C₈×C₄₇	—	2	2	no	—
109	C₈×C₄₇	#123	1	2	yes	—
110	C₈×C₄₇	#123	1	2	yes	—
111	C₄₇⋊C₈	—	2	2	no	—
112	C₄₇⋊C₈	—	2	2	no	—
113	#12849	—	47	1	no	maximal, Sylow
114	C₂²×C₄₇	—	2	2	no	—
115	C₂²×C₄₇	—	2	2	no	—
116	C₂²×C₄₇	—	4	2	no	—
117	C₂²×C₄₇	—	4	2	no	—
118	C₂²×C₄₇	—	4	2	no	—
119	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
120	C₂²×C₄₇	#432	1	1	yes	characteristic
121	C₂²×C₄₇	#432	1	1	yes	characteristic
122	C₄×C₄₇	—	2	2	no	—
123	C₄×C₄₇	#381	1	1	yes	characteristic
124	C₄×C₄₇	#407	1	1	yes	characteristic
125	C₄×C₄₇	#431	1	1	yes	characteristic
126	C₄×C₄₇	#431	1	1	yes	characteristic
127	Dic₄₇	—	2	4	no	—
128	Dic₄₇	—	4	2	no	—
129	C₂×C₄×M₁₆	—	47	1	no	—
130	C₂×#349	—	47	1	no	—
131	C₂×#349	D₄₇	1	1	yes	characteristic
132	#1376	—	47	2	no	—
133	#1375	—	47	2	no	—
134	C₂×C₄₇	—	2	1	no	—
135	C₂×C₄₇	—	2	1	no	—
136	C₂×C₄₇	—	4	2	no	—
137	C₂×C₄₇	#1817	1	1	yes	characteristic
138	C₂×C₄₇	#2165	1	2	yes	—
139	C₂²×M₁₆	—	47	1	no	—
140	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
141	C₂²×C₄²	—	47	1	no	—
142	C₂×M₃₂	—	47	2	no	—
143	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
144	C₄×M₁₆	—	94	2	no	—
145	C₄×M₁₆	—	94	2	no	—
146	C₂×#97	—	47	1	no	—
147	C₂×#97	—	47	1	no	—
148	C₂×C₄×C₈	—	47	1	no	—
149	C₂×C₄×C₈	—	47	1	no	—
150	#349	—	2	2	no	—
151	#349	—	94	2	no	—
152	C₄₇	#12849	1	1	yes	characteristic, complemented, Sylow
153	C₂³×C₄	—	94	1	no	—
154	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	—	2	2	no	—
157	C₂×M₁₆	—	94	2	no	—
158	C₂×M₁₆	—	94	2	no	—
159	C₂×M₁₆	—	94	2	no	—
160	C₂×M₁₆	D₁₈₈	1	2	yes	—
161	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
162	C₂²×C₈	—	47	1	no	—
163	C₂²×C₈	—	47	1	no	—
164	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
165	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
166	C₂×C₄²	—	47	4	no	—
167	C₂×C₄²	—	47	1	no	—
168	C₂×C₄²	—	47	1	no	—
169	C₂×C₄²	—	94	1	no	—
170	C₂×C₄²	—	94	2	no	—
171	M₃₂	—	2	2	no	—
172	M₃₂	—	2	2	no	—
173	M₃₂	—	94	2	no	—
174	M₃₂	—	94	2	no	—
175	C₂×C₁₆	—	2	2	no	—
176	C₂×C₁₆	—	94	2	no	—
177	#97	—	94	2	no	—
178	#97	—	94	1	no	—
179	#97	—	94	1	no	—
180	C₄×C₈	—	94	2	no	—
181	C₄×C₈	—	94	1	no	—
182	C₄×C₈	—	94	1	no	—
183	C₂⁴	#10625324	1	1	yes	characteristic
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	94	1	no	—
189	C₂²×C₄	—	94	4	no	—
190	C₂²×C₄	—	94	1	no	—
191	C₂²×C₄	—	188	4	no	—
192	C₂²×C₄	C₈×D₄₇	1	2	yes	—
193	C₂²×C₄	#10625324	1	1	yes	characteristic
194	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
195	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
196	M₁₆	—	2	4	no	—
197	M₁₆	—	2	4	no	—
198	M₁₆	—	94	8	no	—
199	C₂×C₈	—	2	1	no	—
200	C₂×C₈	—	2	1	no	—
201	C₂×C₈	—	47	2	no	—
202	C₂×C₈	—	47	2	no	—
203	C₂×C₈	—	94	1	no	—
204	C₂×C₈	—	94	1	no	—
205	C₂×C₈	—	94	1	no	—
206	C₂×C₈	—	94	1	no	—
207	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
208	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
209	C₂×C₈	#10625352	1	2	yes	—
210	C₂×C₈	#10625352	1	2	yes	—
211	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
212	C₄²	—	47	2	no	—
213	C₄²	—	47	2	no	—
214	C₄²	—	94	4	no	—
215	C₄²	—	94	1	no	—
216	C₄²	—	94	1	no	—
217	C₁₆	—	4	2	no	—
218	C₁₆	—	188	2	no	—
219	C₂³	—	2	1	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	4	2	no	—
222	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
223	C₂³	C₂×#10625324	1	1	yes	characteristic
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	94	4	no	—
231	C₂×C₄	—	94	2	no	—
232	C₂×C₄	—	94	2	no	—
233	C₂×C₄	—	188	8	no	—
234	C₂×C₄	—	188	2	no	—
235	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
236	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
237	C₂×C₄	#13093980	1	1	yes	characteristic
238	C₂×C₄	#13093980	1	1	yes	characteristic
239	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
240	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
241	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
242	C₈	—	2	2	no	—
243	C₈	—	94	2	no	—
244	C₈	—	94	2	no	—
245	C₈	#13094005	1	2	yes	—
246	C₈	#13094008	1	2	yes	—
247	C₂²	—	2	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
253	C₂²	#15689177	1	1	yes	characteristic
254	C₂²	#15689177	1	1	yes	characteristic
255	C₄	—	2	2	no	—
256	C₄	—	94	4	no	—
257	C₄	—	188	2	no	—
258	C₄	#15688984	1	1	yes	characteristic
259	C₄	#15689086	1	1	yes	characteristic
260	C₄	#15689173	1	1	yes	characteristic
261	C₄	#15689173	1	1	yes	characteristic
262	C₂	—	2	1	no	—
263	C₂	—	2	1	no	—
264	C₂	—	4	2	no	—
265	C₂	#20243454	1	1	yes	characteristic
266	C₂	#20245197	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×M₁₆×Dic₄₇

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

C₂²×#10625329

C₄

yes

characteristic

C₂²×C₄×Dic₄₇

C₄

yes

characteristic

C₂×#13093964

C₂²

yes

—

M₁₆×Dic₄₇

—

M₁₆×Dic₄₇

—

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

—

C₂³×Dic₄₇

—

C₂×#10625329

—

C₂×#10625329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₈

yes

—

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

—

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

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₈

yes

—

C₄×Dic₄₇

C₂×C₈

yes

—

#10625329

—

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

100

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

101

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

102

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₈×C₄₇

—

109

C₈×C₄₇

#123

yes

—

110

C₈×C₄₇

#123

yes

—

111

C₄₇⋊C₈

—

112

C₄₇⋊C₈

—

113

#12849

—

maximal, Sylow

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

120

C₂²×C₄₇

#432

yes

characteristic

121

C₂²×C₄₇

#432

yes

characteristic

122

C₄×C₄₇

—

123

C₄×C₄₇

#381

yes

characteristic

124

C₄×C₄₇

#407

yes

characteristic

125

C₄×C₄₇

#431

yes

characteristic

126

C₄×C₄₇

#431

yes

characteristic

127

Dic₄₇

—

128

Dic₄₇

—

129

C₂×C₄×M₁₆

—

130

C₂×#349

—

131

C₂×#349

D₄₇

yes

characteristic

132

#1376

—

133

#1375

—

134

C₂×C₄₇

—

135

C₂×C₄₇

—

136

C₂×C₄₇

—

137

C₂×C₄₇

#1817

yes

characteristic

138

C₂×C₄₇

#2165

yes

—

139

C₂²×M₁₆

—

140

C₂²×M₁₆

C₂×D₄₇

yes

characteristic

141

C₂²×C₄²

—

142

C₂×M₃₂

—

143

C₂×M₃₂

C₂×D₄₇

yes

—

144

C₄×M₁₆

—

145

C₄×M₁₆

—

146

C₂×#97

—

147

C₂×#97

—

148

C₂×C₄×C₈

—

149

C₂×C₄×C₈

—

150

#349

—

151

#349

—

152

C₄₇

#12849

yes

characteristic, complemented, Sylow

153

C₂³×C₄

—

154

C₂³×C₄

C₄×D₄₇

yes

characteristic

155

C₂×M₁₆

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

158

C₂×M₁₆

—

159

C₂×M₁₆

—

160

C₂×M₁₆

D₁₈₈

yes

—

161

C₂×M₁₆

C₂²⋊D₄₇

yes

—

162

C₂²×C₈

—

163

C₂²×C₈

—

164

C₂²×C₈

C₄×D₄₇

yes

characteristic

165

C₂²×C₈

C₂²×D₄₇

yes

characteristic

166

C₂×C₄²

—

167

C₂×C₄²

—

168

C₂×C₄²

—

169

C₂×C₄²

—

170

C₂×C₄²

—

171

M₃₂

—

172

M₃₂

—

173

M₃₂

—

174

M₃₂

—

175

C₂×C₁₆

—

176

C₂×C₁₆

—

177

#97

—

178

#97

—

179

#97

—

180

C₄×C₈

—

181

C₄×C₈

—

182

C₄×C₈

—

183

C₂⁴

#10625324

yes

characteristic

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

188

—

192

C₂²×C₄

C₈×D₄₇

yes

—

193

C₂²×C₄

#10625324

yes

characteristic

194

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

195

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

208

C₂×C₈

C₂×D₁₈₈

yes

characteristic

209

C₂×C₈

#10625352

yes

—

210

C₂×C₈

#10625352

yes

—

211

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

212

C₄²

—

213

C₄²

—

214

C₄²

—

215

C₄²

—

216

C₄²

—

217

C₁₆

—

218

C₁₆

—

188

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

(C₂×D₄₇)⋊C₈

yes

—

223

C₂³

C₂×#10625324

yes

characteristic

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

188

—

234

C₂×C₄

—

188

—

235

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

236

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

237

C₂×C₄

#13093980

yes

characteristic

238

C₂×C₄

#13093980

yes

characteristic

239

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

240

C₂×C₄

M₁₆×D₄₇

yes

characteristic

241

C₂×C₄

M₁₆×D₄₇

yes

characteristic

242

C₈

—

243

C₈

—

244

C₈

—

245

C₈

#13094005

yes

—

246

C₈

#13094008

yes

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

253

C₂²

#15689177

yes

characteristic

254

C₂²

#15689177

yes

characteristic

255

C₄

—

256

C₄

—

257

C₄

—

188

—

258

C₄

#15688984

yes

characteristic

259

C₄

#15689086

yes

characteristic

260

C₄

#15689173

yes

characteristic

261

C₄

#15689173

yes

characteristic

262

C₂

—

263

C₂

—

264

C₂

—

265

C₂

#20243454

yes

characteristic

266

C₂

#20245197

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	#12849
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
152. C₄₇	#12849	semidirect

H ≅ G/N

type

3. #20241469

C₂

semidirect

4. #20241467

C₂

semidirect

152. C₄₇

#12849

semidirect

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

subgroup	index
C₂×M₁₆×Dic₄₇	2
C₂×#15688905	2
#20241469	2
#20241467	2
C₂×C₄₇×#349	2
#12849	47

subgroup

index

C₂×M₁₆×Dic₄₇

C₂×C₄₇×#349

Subgroups — #26132503

Conjugacy classes of subgroups

Complements

Maximal subgroups