Group #26109196 — subgroups

Subgroups — #26109196

Order 12032.

486 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 137 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×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#20243380	C₂	1	1	yes	maximal, characteristic
3	#20242143	C₂	1	2	yes	maximal, complemented
4	#20241262	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₄	1	2	yes	—
7	D₄×C₄₇⋊C₈	—	2	2	no	—
8	D₄×C₄₇⋊C₈	—	2	2	no	—
9	#15689147	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13093941	—	2	1	no	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15688892	—	2	1	no	—
15	#15688873	—	2	2	no	—
16	#15688873	—	2	2	no	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#423	C₂²	1	2	yes	—
19	C₂×#100×C₄₇	—	2	1	no	—
20	C₄₇×#343	—	2	1	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	4	4	no	—
25	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	#13093941	—	4	2	no	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
33	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
34	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
35	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₄×D₄×C₄₇	—	2	2	no	—
39	C₄×D₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₄₇	Q₈	1	2	yes	—
42	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₄₇	—	2	2	no	—
44	C₄⋊C₈×C₄₇	—	2	2	no	—
45	#100×C₄₇	—	4	2	no	—
46	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
47	C₂×D₄×C₄₇	—	2	2	no	—
48	C₂×D₄×C₄₇	—	2	2	no	—
49	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
50	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
51	C₂²×C₄×C₄₇	—	2	2	no	—
52	C₂²×C₄×C₄₇	—	2	2	no	—
53	C₂²×C₄×C₄₇	—	4	2	no	—
54	C₂²×C₄×C₄₇	—	4	2	no	—
55	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
59	M₁₆×C₄₇	—	4	2	no	—
60	M₁₆×C₄₇	—	4	2	no	—
61	C₂×C₈×C₄₇	—	4	2	no	—
62	C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₄²×C₄₇	C₂×D₄	1	2	yes	—
65	C₄²×C₄₇	#41	1	2	yes	—
66	#10625329	—	4	2	no	—
67	#10625329	—	4	2	no	—
68	C₂×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	4	1	no	—
71	C₂×C₄₇⋊C₈	—	4	4	no	—
72	C₂×C₄₇⋊C₈	—	4	4	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
76	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	—	2	2	no	—
80	C₂³×C₄₇	—	4	2	no	—
81	C₂³×C₄₇	—	4	2	no	—
82	C₂³×C₄₇	#106	1	4	yes	—
83	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
84	D₄×C₄₇	—	2	4	no	—
85	D₄×C₄₇	—	2	4	no	—
86	C₂×C₄×C₄₇	—	2	1	no	—
87	C₂×C₄×C₄₇	—	2	1	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	—	4	1	no	—
90	C₂×C₄×C₄₇	—	4	4	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	—	4	2	no	—
93	C₂×C₄×C₄₇	—	4	2	no	—
94	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
96	C₂×C₄×C₄₇	#121	1	2	yes	—
97	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₇	#135	1	2	yes	—
101	C₈×C₄₇	—	8	2	no	—
102	C₄₇⋊C₈	—	2	1	no	—
103	C₄₇⋊C₈	—	2	2	no	—
104	C₄₇⋊C₈	—	4	2	no	—
105	C₄₇⋊C₈	—	8	2	no	—
106	C₄₇⋊C₈	#100	1	2	yes	complemented
107	#8614	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	—	2	1	no	—
109	C₂²×C₄₇	—	2	1	no	—
110	C₂²×C₄₇	—	2	4	no	—
111	C₂²×C₄₇	—	4	4	no	—
112	C₂²×C₄₇	—	4	4	no	—
113	C₂²×C₄₇	—	4	2	no	—
114	C₂²×C₄₇	—	4	2	no	—
115	C₂²×C₄₇	#380	1	1	yes	characteristic
116	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
117	C₂²×C₄₇	#427	1	1	yes	characteristic
118	C₄×C₄₇	—	2	1	no	—
119	C₄×C₄₇	—	2	2	no	—
120	C₄×C₄₇	—	4	2	no	—
121	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
122	C₄×C₄₇	#413	1	1	yes	characteristic
123	C₄×C₄₇	#465	1	2	yes	—
124	C₄×C₄₇	#465	1	2	yes	—
125	C₂×C₈×D₄	—	47	1	no	—
126	#1800	—	47	1	no	—
127	#1800	D₄₇	1	1	yes	characteristic
128	#1566	—	47	2	no	—
129	#1292	—	47	2	no	—
130	C₂×C₄₇	—	2	1	no	—
131	C₂×C₄₇	—	2	1	no	—
132	C₂×C₄₇	—	4	4	no	—
133	C₂×C₄₇	#1800	1	1	yes	characteristic
134	C₂×C₄₇	#1807	1	1	yes	characteristic
135	C₂×C₄₇	#1813	1	1	yes	characteristic
136	C₂³×C₈	—	47	2	no	—
137	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
138	C₈×D₄	—	94	2	no	—
139	C₈×D₄	—	94	2	no	—
140	#423	—	47	2	no	—
141	#423	C₂×D₄₇	1	2	yes	—
142	C₂×C₄⋊C₈	—	47	1	no	—
143	C₂×#100	—	2	1	no	—
144	C₂×#100	—	94	1	no	—
145	C₂×C₂²⋊C₈	—	47	2	no	—
146	C₂×C₄×C₈	—	47	1	no	—
147	#343	—	2	1	no	—
148	#343	—	94	1	no	—
149	#334	—	94	2	no	—
150	#334	—	94	2	no	—
151	C₄₇	#8614	1	1	yes	characteristic, complemented, Sylow
152	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
153	C₂³×C₄	C₄×D₄₇	1	2	yes	—
154	C₂×M₁₆	—	2	2	no	—
155	C₂×M₁₆	—	94	2	no	—
156	C₂²×C₈	—	47	1	no	—
157	C₂²×C₈	—	47	1	no	—
158	C₂²×C₈	—	47	2	no	—
159	C₂²×C₈	—	94	2	no	—
160	C₂²×C₈	—	94	2	no	—
161	C₂²×C₈	—	188	4	no	—
162	C₄×D₄	—	2	2	no	—
163	C₄×D₄	—	2	2	no	—
164	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
165	C₂×C₂²⋊C₄	Dic₉₄	1	2	yes	—
166	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	94	2	no	—
170	C₄⋊C₈	—	94	2	no	—
171	C₄⋊C₈	—	94	2	no	—
172	#100	—	4	2	no	—
173	#100	—	188	2	no	—
174	C₂²⋊C₈	—	94	4	no	—
175	C₄×C₈	—	47	2	no	—
176	C₄×C₈	—	47	2	no	—
177	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	2	2	no	—
180	C₂×D₄	#10625335	1	2	yes	—
181	C₂×D₄	#10625336	1	2	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	—	2	2	no	—
184	C₂²×C₄	—	4	2	no	—
185	C₂²×C₄	—	4	2	no	—
186	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
187	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
190	M₁₆	—	4	2	no	—
191	M₁₆	—	4	2	no	—
192	M₁₆	—	188	2	no	—
193	M₁₆	—	188	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	47	1	no	—
196	C₂×C₈	—	47	2	no	—
197	C₂×C₈	—	47	1	no	—
198	C₂×C₈	—	94	2	no	—
199	C₂×C₈	—	94	2	no	—
200	C₂×C₈	—	188	4	no	—
201	C₂×C₈	—	188	1	no	—
202	C₂×C₈	—	188	4	no	—
203	C₂×C₈	—	188	2	no	—
204	C₂×C₈	—	188	2	no	—
205	C₄⋊C₄	—	2	2	no	—
206	C₂²⋊C₄	—	2	4	no	—
207	C₄²	D₄×D₄₇	1	2	yes	—
208	C₄²	#10625352	1	2	yes	—
209	C₂³	—	2	2	no	—
210	C₂³	—	2	2	no	—
211	C₂³	—	4	2	no	—
212	C₂³	—	4	2	no	—
213	C₂³	#13093955	1	4	yes	—
214	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
215	D₄	—	2	4	no	—
216	D₄	—	2	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
226	C₂×C₄	#13093980	1	1	yes	characteristic
227	C₂×C₄	#13093996	1	2	yes	—
228	C₂×C₄	#13094001	1	2	yes	—
229	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
230	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
231	C₂×C₄	#13094044	1	2	yes	—
232	C₈	—	8	2	no	—
233	C₈	—	47	2	no	—
234	C₈	—	94	1	no	—
235	C₈	—	94	2	no	—
236	C₈	—	376	2	no	—
237	C₈	—	188	2	no	—
238	C₂²	—	2	1	no	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	4	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	4	no	—
243	C₂²	—	4	2	no	—
244	C₂²	—	4	2	no	—
245	C₂²	#15688981	1	1	yes	characteristic
246	C₂²	C₂×#13093955	1	1	yes	characteristic
247	C₂²	#15689159	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	2	2	no	—
250	C₄	—	4	2	no	—
251	C₄	#100×D₄₇	1	1	yes	characteristic
252	C₄	#15689104	1	1	yes	characteristic
253	C₄	#15689350	1	2	yes	—
254	C₄	#15689354	1	2	yes	—
255	C₂	—	2	1	no	—
256	C₂	—	2	1	no	—
257	C₂	—	4	4	no	—
258	C₂	#20243378	1	1	yes	characteristic
259	C₂	#20243411	1	1	yes	characteristic
260	C₂	#20243436	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

#20243380

C₂

yes

maximal, characteristic

#20242143

C₂

yes

maximal, complemented

#20241262

C₂

yes

maximal, complemented

C₄₇×#1800

C₂

yes

maximal, characteristic

C₂³×C₄₇⋊C₈

C₄

yes

—

D₄×C₄₇⋊C₈

—

D₄×C₄₇⋊C₈

—

#15689147

C₂²

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₂×#13093941

—

C₂×C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

—

—

—

C₂×C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄₇×#423

C₂²

yes

—

C₂×#100×C₄₇

—

C₄₇×#343

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093941

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×D₄×C₄₇

D₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

—

C₄×D₄×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

Q₈

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

#100×C₄₇

—

C₂⁴×C₄₇

C₄⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

SD₁₆

yes

—

C₂×D₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₄⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#106

yes

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

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×C₂²⋊C₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

100

C₂×C₄×C₄₇

#135

yes

—

101

C₈×C₄₇

—

102

C₄₇⋊C₈

—

103

C₄₇⋊C₈

—

104

C₄₇⋊C₈

—

105

C₄₇⋊C₈

—

106

C₄₇⋊C₈

yes

107

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

#380

yes

characteristic

116

C₂²×C₄₇

C₂×#106

yes

characteristic

117

C₂²×C₄₇

#427

yes

characteristic

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₄×C₄₇

—

121

C₄×C₄₇

C₂×#100

yes

characteristic

122

C₄×C₄₇

#413

yes

characteristic

123

C₄×C₄₇

#465

yes

—

124

C₄×C₄₇

#465

yes

—

125

C₂×C₈×D₄

—

126

#1800

—

127

#1800

D₄₇

yes

characteristic

128

#1566

—

129

#1292

—

130

C₂×C₄₇

—

131

C₂×C₄₇

—

132

C₂×C₄₇

—

133

C₂×C₄₇

#1800

yes

characteristic

134

C₂×C₄₇

#1807

yes

characteristic

135

C₂×C₄₇

#1813

yes

characteristic

136

C₂³×C₈

—

137

C₂×C₄×D₄

C₂×D₄₇

yes

characteristic

138

C₈×D₄

—

139

C₈×D₄

—

140

#423

—

141

#423

C₂×D₄₇

yes

—

142

C₂×C₄⋊C₈

—

143

C₂×#100

—

144

C₂×#100

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₄×C₈

—

147

#343

—

148

#343

—

149

#334

—

150

#334

—

151

C₄₇

#8614

yes

characteristic, complemented, Sylow

152

C₂²×D₄

C₂²⋊D₄₇

yes

characteristic

153

C₂³×C₄

C₄×D₄₇

yes

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

—

188

—

162

C₄×D₄

—

163

C₄×D₄

—

164

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

characteristic

165

C₂×C₂²⋊C₄

Dic₉₄

yes

—

166

C₂×C₄²

C₂²×D₄₇

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

169

C₄⋊C₈

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

#100

—

173

#100

—

188

—

174

C₂²⋊C₈

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₂⁴

Dic₄₇⋊C₄

yes

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

#10625335

yes

—

181

C₂×D₄

#10625336

yes

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

C₂²×C₄

Dic₄₇⋊C₄

yes

—

187

C₂²×C₄

C₂×Dic₉₄

yes

characteristic

188

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

189

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

190

M₁₆

—

191

M₁₆

—

192

M₁₆

—

188

—

193

M₁₆

—

188

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

188

—

201

C₂×C₈

—

188

—

202

C₂×C₈

—

188

—

203

C₂×C₈

—

188

—

204

C₂×C₈

—

188

—

205

C₄⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

D₄×D₄₇

yes

—

208

C₄²

#10625352

yes

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

—

213

C₂³

#13093955

yes

—

214

C₂³

C₂×Dic₄₇⋊C₄

yes

characteristic

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

C₂²⋊C₄×D₄₇

yes

characteristic

226

C₂×C₄

#13093980

yes

characteristic

227

C₂×C₄

#13093996

yes

—

228

C₂×C₄

#13094001

yes

—

229

C₂×C₄

C₂×#10625336

yes

characteristic

230

C₂×C₄

C₂×#10625335

yes

characteristic

231

C₂×C₄

#13094044

yes

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

376

—

237

C₈

—

188

—

238

C₂²

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

#15688981

yes

characteristic

246

C₂²

C₂×#13093955

yes

characteristic

247

C₂²

#15689159

yes

characteristic

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

#100×D₄₇

yes

characteristic

252

C₄

#15689104

yes

characteristic

253

C₄

#15689350

yes

—

254

C₄

#15689354

yes

—

255

C₂

—

256

C₂

—

257

C₂

—

258

C₂

#20243378

yes

characteristic

259

C₂

#20243411

yes

characteristic

260

C₂

#20243436

yes

characteristic

	subgroup	G/H
center	C₂²	#15688981
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1800	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1800	D₄₇
hypocenter	C₄₇	#8614
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1800

subgroup

G/H

center

C₂²

#15688981

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1800

C₂

socle

C₂²×C₄₇

#380

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 ◁ #1800

N	H ≅ G/N	type
3. #20242143	C₂	semidirect
4. #20241262	C₂	semidirect
106. C₄₇⋊C₈	#100	semidirect
151. C₄₇	#8614	semidirect

H ≅ G/N

type

3. #20242143

C₂

semidirect

4. #20241262

C₂

semidirect

106. C₄₇⋊C₈

#100

semidirect

151. C₄₇

#8614

semidirect

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
#20243380	2
#20242143	2
#20241262	2
C₄₇×#1800	2
#8614	47

subgroup

index

C₂×D₄×C₄₇⋊C₈

C₄₇×#1800

Subgroups — #26109196

Conjugacy classes of subgroups

Complements

Maximal subgroups