Group #26133170 — subgroups

Subgroups — #26133170

Order 12032.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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	C₂³×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252082	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688908	C₂	1	2	yes	maximal, complemented
4	#20241478	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2112	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13094030	C₂²	1	1	yes	characteristic
7	#15689634	C₄	1	1	yes	characteristic
8	C₂²×C₄₇⋊C₁₆	—	2	4	no	—
9	C₂²×C₄₇⋊C₁₆	—	2	2	no	—
10	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	—
11	#15689194	—	2	2	no	—
12	C₈×C₂²⋊D₄₇	—	2	2	no	—
13	#15689149	C₄	1	1	yes	characteristic
14	#15689089	C₄	1	1	yes	characteristic
15	#15689087	C₄	1	1	yes	characteristic
16	#15689078	C₂²	1	1	yes	characteristic
17	#15688908	—	2	4	no	—
18	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
20	C₄₇×C₂²⋊C₁₆	—	2	2	no	—
21	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
22	#13094030	—	2	2	no	—
23	#13094030	—	2	2	no	—
24	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
25	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
26	C₂×#10625324	—	2	1	no	—
27	C₂×C₈×D₄₇	—	2	1	no	—
28	#13094007	—	2	1	no	—
29	#13094003	C₈	1	2	yes	—
30	#13093998	C₈	1	2	yes	—
31	#13093993	—	2	1	no	—
32	C₄×C₂²⋊D₄₇	—	2	2	no	—
33	#13093983	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄₇⋊C₁₆	—	2	8	no	—
35	C₂×C₄₇⋊C₁₆	—	2	2	no	—
36	C₂×C₄₇⋊C₁₆	—	2	2	no	—
37	C₂×C₄₇⋊C₁₆	D₄	1	4	yes	complemented
38	Dic₄₇⋊C₈	—	2	2	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
40	(C₂×D₄₇)⋊C₈	—	2	2	no	—
41	#13093934	—	2	1	no	—
42	C₈×Dic₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₈×C₄₇	D₄	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	M₃₂×C₄₇	—	2	2	no	—
51	M₃₂×C₄₇	—	2	2	no	—
52	C₂×C₁₆×C₄₇	—	2	2	no	—
53	C₂⁴×C₄₇	M₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
58	C₂²×C₄×C₄₇	M₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₄₇	—	2	2	no	—
61	C₂×C₂²⋊D₄₇	—	2	1	no	—
62	#10625350	—	2	2	no	—
63	#10625350	—	2	2	no	—
64	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
65	C₂×C₄×D₄₇	—	2	1	no	—
66	C₂×Dic₉₄	C₂×C₈	1	1	yes	characteristic
67	C₂×C₈×C₄₇	—	2	2	no	—
68	C₂×C₈×C₄₇	—	2	2	no	—
69	C₂×C₈×C₄₇	—	2	4	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
72	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₄₇	#41	1	2	yes	—
76	C₂²⋊Dic₄₇	—	2	2	no	—
77	C₂²⋊Dic₄₇	—	2	1	no	—
78	(C₂×D₄₇)⋊C₄	—	2	2	no	—
79	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
80	Dic₄₇⋊C₄	—	2	2	no	—
81	C₄×Dic₄₇	—	2	1	no	—
82	#10625329	—	2	2	no	—
83	#10625329	—	2	2	no	—
84	C₂×C₄₇⋊C₈	—	2	1	no	—
85	C₂×C₄₇⋊C₈	—	2	1	no	—
86	#10625324	—	4	1	no	—
87	#10625324	—	4	1	no	—
88	C₈×D₄₇	—	4	2	no	—
89	C₁₆×C₄₇	—	4	2	no	—
90	C₄₇⋊C₁₆	—	2	4	no	—
91	C₂³×C₄₇	—	2	4	no	—
92	C₂³×C₄₇	—	2	2	no	—
93	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
94	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
95	C₂²×D₄₇	—	2	1	no	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	2	no	—
98	C₂×C₄×C₄₇	—	2	2	no	—
99	C₂×C₄×C₄₇	—	2	4	no	—
100	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
101	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₄₇	#131	1	2	yes	—
105	C₂²⋊D₄₇	—	4	4	no	—
106	C₂²⋊D₄₇	—	4	2	no	—
107	C₂×Dic₄₇	—	2	2	no	—
108	C₂×Dic₄₇	—	2	1	no	—
109	D₁₈₈	—	2	2	no	—
110	C₄×D₄₇	—	4	1	no	—
111	C₄×D₄₇	—	4	1	no	—
112	Dic₉₄	—	2	2	no	—
113	C₈×C₄₇	—	2	2	no	—
114	C₈×C₄₇	#120	1	1	yes	characteristic
115	C₈×C₄₇	#121	1	2	yes	—
116	C₈×C₄₇	#123	1	1	yes	characteristic
117	C₄₇⋊C₈	—	4	1	no	—
118	C₄₇⋊C₈	—	4	1	no	—
119	#12983	—	47	1	no	maximal, Sylow
120	C₂²×C₄₇	—	2	8	no	—
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	—	2	2	no	—
123	C₂²×C₄₇	—	2	2	no	—
124	C₂²×C₄₇	#350	1	4	yes	complemented
125	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
126	C₂²×C₄₇	#435	1	2	yes	—
127	C₂×D₄₇	—	4	2	no	—
128	C₂×D₄₇	—	4	1	no	—
129	C₄×C₄₇	—	2	2	no	—
130	C₄×C₄₇	#386	1	1	yes	characteristic
131	C₄×C₄₇	#408	1	1	yes	characteristic
132	C₄×C₄₇	C₈×D₄	1	2	yes	—
133	Dic₄₇	—	4	2	no	—
134	Dic₄₇	—	4	1	no	—
135	C₂³×C₁₆	—	47	1	no	—
136	#2929	—	47	1	no	—
137	C₂×#350	—	47	2	no	—
138	#2112	D₄₇	1	1	yes	characteristic, complemented
139	#1379	—	47	2	no	—
140	C₂×C₄₇	—	2	4	no	—
141	C₂×C₄₇	—	2	2	no	—
142	C₂×C₄₇	#1869	1	1	yes	characteristic
143	C₂×C₄₇	C₂×#350	1	2	yes	—
144	D₄₇	—	8	1	no	—
145	C₂×#131	—	47	1	no	—
146	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
147	#525	—	47	1	no	—
148	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
149	C₂²×C₁₆	—	47	2	no	—
150	C₂²×C₁₆	—	94	4	no	—
151	C₂²×C₁₆	—	94	2	no	—
152	#435	—	94	2	no	—
153	C₈×D₄	—	94	2	no	—
154	#424	—	47	1	no	—
155	#408	—	47	1	no	—
156	#407	—	47	1	no	—
157	#405	—	47	1	no	—
158	#350	—	94	4	no	—
159	C₂²⋊C₁₆	—	2	2	no	—
160	C₄₇	#12983	1	1	yes	characteristic, complemented, Sylow
161	C₂×#41	—	47	1	no	—
162	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
163	#131	—	94	2	no	—
164	#131	—	94	2	no	—
165	C₂×M₁₆	—	47	1	no	—
166	C₂×M₁₆	—	47	1	no	—
167	C₂×M₁₆	—	94	1	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	2	no	—
170	C₂²×C₈	—	94	1	no	—
171	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
172	C₂²×C₈	D₁₈₈	1	2	yes	—
173	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
174	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
175	#123	—	94	1	no	—
176	C₂²⋊Q₈	—	47	2	no	—
177	#121	—	47	2	no	—
178	#120	—	94	1	no	—
179	C₄×D₄	—	94	2	no	—
180	#117	—	47	1	no	—
181	M₃₂	—	2	2	no	—
182	M₃₂	—	2	2	no	—
183	C₂×C₁₆	—	2	2	no	—
184	C₂×C₁₆	—	47	4	no	—
185	C₂×C₁₆	—	94	8	no	—
186	C₂×C₁₆	—	94	2	no	—
187	C₂×C₁₆	—	94	2	no	—
188	C₄⋊C₈	—	94	2	no	—
189	C₂²⋊C₈	—	94	2	no	—
190	C₂²⋊C₈	—	94	2	no	—
191	#97	—	94	1	no	—
192	C₄×C₈	—	94	1	no	—
193	C₂⁴	#10625324	1	1	yes	characteristic
194	#41	—	94	2	no	—
195	#41	—	94	2	no	—
196	C₂×Q₈	—	47	1	no	—
197	C₂×D₄	—	47	1	no	—
198	C₂×D₄	—	94	2	no	—
199	C₂×D₄	—	94	1	no	—
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	94	1	no	—
203	C₂²×C₄	C₈×D₄₇	1	2	yes	—
204	C₂²×C₄	#10625324	1	1	yes	characteristic
205	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
206	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
207	M₁₆	—	94	2	no	—
208	M₁₆	—	94	2	no	—
209	M₁₆	—	188	1	no	—
210	M₁₆	—	188	1	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	94	1	no	—
216	C₂×C₈	—	94	1	no	—
217	C₂×C₈	—	188	2	no	—
218	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
219	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
220	C₂×C₈	D₄×D₄₇	1	2	yes	—
221	C₂×C₈	#10625352	1	2	yes	—
222	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
223	C₄⋊C₄	—	47	2	no	—
224	C₄⋊C₄	—	94	2	no	—
225	C₂²⋊C₄	—	94	2	no	—
226	C₂²⋊C₄	—	94	1	no	—
227	C₂²⋊C₄	—	94	2	no	—
228	C₄²	—	94	1	no	—
229	C₁₆	—	4	2	no	—
230	C₁₆	—	94	4	no	—
231	C₂³	—	2	4	no	—
232	C₂³	—	2	2	no	—
233	C₂³	—	94	1	no	—
234	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
235	C₂³	C₂×#10625324	1	1	yes	characteristic
236	Q₈	—	94	2	no	—
237	D₄	—	94	2	no	—
238	D₄	—	188	4	no	—
239	D₄	—	188	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	4	no	—
244	C₂×C₄	—	94	2	no	—
245	C₂×C₄	—	94	1	no	—
246	C₂×C₄	—	188	1	no	—
247	C₂×C₄	—	188	1	no	—
248	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
249	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
250	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
251	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
252	C₂×C₄	#13094032	1	2	yes	—
253	C₈	—	2	2	no	—
254	C₈	—	188	1	no	—
255	C₈	—	188	1	no	—
256	C₈	#13093994	1	1	yes	characteristic
257	C₈	#13093996	1	2	yes	—
258	C₈	#13094008	1	1	yes	characteristic
259	C₂²	—	2	8	no	—
260	C₂²	—	2	2	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	188	2	no	—
264	C₂²	—	188	1	no	—
265	C₂²	#15688908	1	4	yes	complemented
266	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
267	C₂²	#15689191	1	2	yes	—
268	C₄	—	2	2	no	—
269	C₄	—	188	2	no	—
270	C₄	—	188	1	no	—
271	C₄	#15689000	1	1	yes	characteristic
272	C₄	#15689091	1	1	yes	characteristic
273	C₄	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
274	C₂	—	2	4	no	—
275	C₂	—	2	2	no	—
276	C₂	—	376	1	no	—
277	C₂	#20243678	1	1	yes	characteristic
278	C₂	C₂×#15688908	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#20252082

C₂

yes

maximal, characteristic

C₂×#15688908

C₂

yes

maximal, complemented

#20241478

C₂

yes

maximal, complemented

C₄₇×#2112

C₂

yes

maximal, characteristic, complemented

C₂×#13094030

C₂²

yes

characteristic

#15689634

C₄

yes

characteristic

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

—

C₂²×C₄₇⋊C₁₆

C₂²

yes

—

#15689194

—

C₈×C₂²⋊D₄₇

—

#15689149

C₄

yes

characteristic

#15689089

C₄

yes

characteristic

#15689087

C₄

yes

characteristic

#15689078

C₂²

yes

characteristic

#15688908

—

C₂³×C₈×C₄₇

C₂²

yes

characteristic

C₂×M₃₂×C₄₇

C₂²

yes

—

C₄₇×C₂²⋊C₁₆

—

C₂×#10625350

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10625329

C₂×C₄

yes

characteristic

C₂×#10625324

—

C₂×C₈×D₄₇

—

#13094007

—

#13094003

C₈

yes

—

#13093998

C₈

yes

—

#13093993

—

C₄×C₂²⋊D₄₇

—

#13093983

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

complemented

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

#13093934

—

C₈×Dic₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

—

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

yes

—

C₂²×C₄×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

M₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

C₂×C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₂×C₈

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₂×C₈

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

#10625324

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₈

yes

—

C₂³×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

100

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

101

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

102

C₂×C₄×C₄₇

C₄×D₄

yes

—

103

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

104

C₂×C₄×C₄₇

#131

yes

—

105

C₂²⋊D₄₇

—

106

C₂²⋊D₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

D₁₈₈

—

110

C₄×D₄₇

—

111

C₄×D₄₇

—

112

Dic₉₄

—

113

C₈×C₄₇

—

114

C₈×C₄₇

#120

yes

characteristic

115

C₈×C₄₇

#121

yes

—

116

C₈×C₄₇

#123

yes

characteristic

117

C₄₇⋊C₈

—

118

C₄₇⋊C₈

—

119

#12983

—

maximal, Sylow

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

#350

yes

complemented

125

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

126

C₂²×C₄₇

#435

yes

—

127

C₂×D₄₇

—

128

C₂×D₄₇

—

129

C₄×C₄₇

—

130

C₄×C₄₇

#386

yes

characteristic

131

C₄×C₄₇

#408

yes

characteristic

132

C₄×C₄₇

C₈×D₄

yes

—

133

Dic₄₇

—

134

Dic₄₇

—

135

C₂³×C₁₆

—

136

#2929

—

137

C₂×#350

—

138

#2112

D₄₇

yes

characteristic, complemented

139

#1379

—

140

C₂×C₄₇

—

141

C₂×C₄₇

—

142

C₂×C₄₇

#1869

yes

characteristic

143

C₂×C₄₇

C₂×#350

yes

—

144

D₄₇

—

145

C₂×#131

—

146

C₂³×C₈

C₂×D₄₇

yes

characteristic

147

#525

—

148

C₂×M₃₂

C₂×D₄₇

yes

—

149

C₂²×C₁₆

—

150

C₂²×C₁₆

—

151

C₂²×C₁₆

—

152

#435

—

153

C₈×D₄

—

154

#424

—

155

#408

—

156

#407

—

157

#405

—

158

#350

—

159

C₂²⋊C₁₆

—

160

C₄₇

#12983

yes

characteristic, complemented, Sylow

161

C₂×#41

—

162

C₂³×C₄

C₄×D₄₇

yes

characteristic

163

#131

—

164

#131

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

168

C₂²×C₈

—

169

C₂²×C₈

—

170

C₂²×C₈

—

171

C₂²×C₈

C₄×D₄₇

yes

characteristic

172

C₂²×C₈

D₁₈₈

yes

—

173

C₂²×C₈

C₂²⋊D₄₇

yes

—

174

C₂²×C₈

C₂²×D₄₇

yes

characteristic

175

#123

—

176

C₂²⋊Q₈

—

177

#121

—

178

#120

—

179

C₄×D₄

—

180

#117

—

181

M₃₂

—

182

M₃₂

—

183

C₂×C₁₆

—

184

C₂×C₁₆

—

185

C₂×C₁₆

—

186

C₂×C₁₆

—

187

C₂×C₁₆

—

188

C₄⋊C₈

—

189

C₂²⋊C₈

—

190

C₂²⋊C₈

—

191

#97

—

192

C₄×C₈

—

193

C₂⁴

#10625324

yes

characteristic

194

#41

—

195

#41

—

196

C₂×Q₈

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

C₈×D₄₇

yes

—

204

C₂²×C₄

#10625324

yes

characteristic

205

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

206

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

207

M₁₆

—

208

M₁₆

—

209

M₁₆

—

188

—

210

M₁₆

—

188

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

188

—

218

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

219

C₂×C₈

C₂×D₁₈₈

yes

characteristic

220

C₂×C₈

D₄×D₄₇

yes

—

221

C₂×C₈

#10625352

yes

—

222

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₂²⋊C₄

—

226

C₂²⋊C₄

—

227

C₂²⋊C₄

—

228

C₄²

—

229

C₁₆

—

230

C₁₆

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

(C₂×D₄₇)⋊C₈

yes

—

235

C₂³

C₂×#10625324

yes

characteristic

236

Q₈

—

237

D₄

—

238

D₄

—

188

—

239

D₄

—

188

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

188

—

247

C₂×C₄

—

188

—

248

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

249

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

250

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

251

C₂×C₄

C₂×C₈×D₄₇

yes

characteristic

252

C₂×C₄

#13094032

yes

—

253

C₈

—

254

C₈

—

188

—

255

C₈

—

188

—

256

C₈

#13093994

yes

characteristic

257

C₈

#13093996

yes

—

258

C₈

#13094008

yes

characteristic

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

188

—

264

C₂²

—

188

—

265

C₂²

#15688908

yes

complemented

266

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

267

C₂²

#15689191

yes

—

268

C₄

—

269

C₄

—

188

—

270

C₄

—

188

—

271

C₄

#15689000

yes

characteristic

272

C₄

#15689091

yes

characteristic

273

C₄

(C₂²⋊D₄₇)⋊C₈

yes

—

274

C₂

—

275

C₂

—

276

C₂

—

376

—

277

C₂

#20243678

yes

characteristic

278

C₂

C₂×#15688908

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#2112	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	#15689634	C₄
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#2112	D₄₇
hypocenter	C₄₇	#12983
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#2112

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₈

prime radical

#15689634

C₄

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
1. C₂³×C₄₇⋊C₁₆	C₂	semidirect
3. C₂×#15688908	C₂	semidirect
4. #20241478	C₂	semidirect
5. C₄₇×#2112	C₂	semidirect
37. C₂×C₄₇⋊C₁₆	D₄	semidirect
124. C₂²×C₄₇	#350	semidirect
138. #2112	D₄₇	semidirect
160. C₄₇	#12983	semidirect
265. C₂²	#15688908	semidirect

H ≅ G/N

type

1. C₂³×C₄₇⋊C₁₆

C₂

semidirect

3. C₂×#15688908

C₂

semidirect

4. #20241478

C₂

semidirect

5. C₄₇×#2112

C₂

semidirect

37. C₂×C₄₇⋊C₁₆

D₄

semidirect

124. C₂²×C₄₇

#350

semidirect

138. #2112

D₄₇

semidirect

160. C₄₇

#12983

semidirect

265. C₂²

#15688908

semidirect

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

subgroup	index
C₂³×C₄₇⋊C₁₆	2
#20252082	2
C₂×#15688908	2
#20241478	2
C₄₇×#2112	2
#12983	47

subgroup

index

C₂³×C₄₇⋊C₁₆

C₄₇×#2112

Subgroups — #26133170

Conjugacy classes of subgroups

Complements

Maximal subgroups