Group #26133162 — subgroups

Subgroups — #26133162

Order 12032.

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

normal subgroups only

This group has 488 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	#20252080	C₂	1	1	yes	maximal, characteristic
2	#20245009	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244998	C₂	1	2	yes	maximal, complemented
4	#20241473	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
7	#15689630	C₄	1	1	yes	characteristic
8	C₂×#13093964	C₂²	1	2	yes	—
9	#15689192	—	2	2	no	—
10	C₈×C₂²⋊D₄₇	—	2	2	no	—
11	#15689151	C₄	1	1	yes	characteristic
12	#15689090	C₄	1	1	yes	characteristic
13	#15689086	C₄	1	1	yes	characteristic
14	#15689078	C₂²	1	1	yes	characteristic
15	#15688905	—	2	2	no	—
16	(C₂×D₄₇)⋊C₁₆	—	2	4	no	—
17	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#504	—	2	4	no	—
19	C₂×M₃₂×C₄₇	—	2	2	no	—
20	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₄₇	—	2	2	no	—
25	C₂×C₈×D₄₇	—	2	1	no	—
26	C₂×C₈×D₄₇	—	2	1	no	—
27	C₂×C₈×D₄₇	—	2	2	no	—
28	#13094005	C₈	1	2	yes	—
29	#13094000	—	2	1	no	—
30	#13093995	—	2	1	no	—
31	#13093992	C₈	1	2	yes	—
32	C₄×C₂²⋊D₄₇	—	2	2	no	—
33	#13093983	C₂×C₄	1	1	yes	characteristic
34	#13093964	—	2	2	no	—
35	#13093964	—	2	2	no	—
36	C₂×C₄₇⋊C₁₆	—	2	2	no	—
37	Dic₄₇⋊C₈	—	2	2	no	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
39	(C₂×D₄₇)⋊C₈	—	2	2	no	—
40	#13093934	—	2	1	no	—
41	C₈×Dic₄₇	—	2	1	no	—
42	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
43	#131×C₄₇	—	2	2	no	—
44	#131×C₄₇	—	2	2	no	—
45	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
47	C₂²×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	M₃₂×C₄₇	—	2	4	no	—
50	M₃₂×C₄₇	—	2	2	no	—
51	M₃₂×C₄₇	—	2	2	no	—
52	C₂×C₁₆×C₄₇	—	2	4	no	—
53	C₂×C₁₆×C₄₇	D₄	1	4	yes	complemented
54	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
55	#41×C₄₇	—	2	2	no	—
56	#41×C₄₇	—	2	2	no	—
57	C₂×Q₈×C₄₇	M₁₆	1	1	yes	characteristic
58	C₂×D₄×C₄₇	C₂×C₈	1	2	yes	—
59	C₂×D₄×C₄₇	M₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₄₇	—	2	2	no	—
63	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
64	C₂×C₄×D₄₇	—	2	1	no	—
65	C₂×C₄×D₄₇	—	2	2	no	—
66	C₂×C₄×D₄₇	—	2	1	no	—
67	C₂×C₄×D₄₇	—	2	2	no	—
68	M₁₆×C₄₇	—	2	2	no	—
69	M₁₆×C₄₇	—	2	4	no	—
70	C₂×C₈×C₄₇	—	2	2	no	—
71	C₂×C₈×C₄₇	—	2	2	no	—
72	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₄₇	#41	1	2	yes	—
77	C₂²⋊Dic₄₇	—	2	2	no	—
78	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
79	(C₂×D₄₇)⋊C₄	—	2	2	no	—
80	C₄⋊Dic₄₇	—	2	1	no	—
81	Dic₄₇⋊C₄	—	2	2	no	—
82	C₄×Dic₄₇	—	2	1	no	—
83	#10625329	—	2	2	no	—
84	C₂×C₄₇⋊C₈	—	2	1	no	—
85	C₂×C₄₇⋊C₈	—	2	1	no	—
86	C₂×C₄₇⋊C₈	—	2	2	no	—
87	C₈×D₄₇	—	4	1	no	—
88	C₈×D₄₇	—	4	2	no	—
89	C₈×D₄₇	—	4	1	no	—
90	C₁₆×C₄₇	—	2	4	no	—
91	C₄₇⋊C₁₆	—	4	2	no	—
92	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
93	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
94	C₂²×D₄₇	—	2	1	no	—
95	C₂²×D₄₇	—	2	2	no	—
96	C₂²×D₄₇	—	4	2	no	—
97	Q₈×C₄₇	—	2	2	no	—
98	D₄×C₄₇	—	2	4	no	—
99	D₄×C₄₇	—	2	2	no	—
100	C₂×C₄×C₄₇	—	2	2	no	—
101	C₂×C₄×C₄₇	—	2	2	no	—
102	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
103	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₄₇	#131	1	2	yes	—
107	C₂²⋊D₄₇	—	4	4	no	—
108	C₂×Dic₄₇	—	2	2	no	—
109	C₂×Dic₄₇	—	2	1	no	—
110	C₂×Dic₄₇	—	2	2	no	—
111	C₄×D₄₇	—	4	1	no	—
112	C₄×D₄₇	—	4	1	no	—
113	C₄×D₄₇	—	4	2	no	—
114	C₈×C₄₇	—	2	2	no	—
115	C₈×C₄₇	#120	1	1	yes	characteristic
116	C₈×C₄₇	#121	1	2	yes	—
117	C₈×C₄₇	#123	1	1	yes	characteristic
118	C₄₇⋊C₈	—	4	1	no	—
119	C₄₇⋊C₈	—	4	1	no	—
120	#12981	—	47	1	no	maximal, Sylow
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	—	4	1	no	—
123	C₂²×C₄₇	—	4	2	no	—
124	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₂²×C₄₇	C₈×D₄	1	2	yes	—
126	C₂×D₄₇	—	2	2	no	—
127	C₂×D₄₇	—	2	4	no	—
128	C₂×D₄₇	—	4	1	no	—
129	C₂×D₄₇	—	4	2	no	—
130	C₂×D₄₇	—	4	1	no	—
131	C₄×C₄₇	—	2	2	no	—
132	C₄×C₄₇	#386	1	1	yes	characteristic
133	C₄×C₄₇	#408	1	1	yes	characteristic
134	C₄×C₄₇	#435	1	2	yes	—
135	Dic₄₇	—	4	2	no	—
136	Dic₄₇	—	4	1	no	—
137	#3407	D₄₇	1	1	yes	characteristic, complemented
138	#2929	—	47	1	no	—
139	#2115	—	47	1	no	—
140	#2112	—	47	2	no	—
141	#1378	—	47	2	no	—
142	C₂×C₄₇	—	2	1	no	—
143	C₂×C₄₇	—	2	2	no	—
144	C₂×C₄₇	—	4	2	no	—
145	C₂×C₄₇	#1869	1	1	yes	characteristic
146	D₄₇	—	4	2	no	—
147	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
148	C₂³×C₈	—	47	1	no	—
149	#525	—	47	1	no	—
150	#504	—	2	4	no	—
151	C₂×M₃₂	—	2	2	no	—
152	C₂×M₃₂	—	47	2	no	—
153	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
154	#435	—	94	2	no	—
155	C₈×D₄	—	94	2	no	—
156	#424	—	47	1	no	—
157	#408	—	47	1	no	—
158	#407	—	47	1	no	—
159	#405	—	47	1	no	—
160	#349	—	94	2	no	—
161	C₂²⋊C₁₆	—	94	4	no	—
162	C₄₇	#12981	1	1	yes	characteristic, complemented, Sylow
163	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
164	C₂³×C₄	—	47	1	no	—
165	#131	—	2	2	no	—
166	#131	—	2	2	no	—
167	C₂×M₁₆	—	47	1	no	—
168	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
169	C₂×M₁₆	D₁₈₈	1	2	yes	—
170	C₂²×C₈	—	47	1	no	—
171	C₂²×C₈	—	94	1	no	—
172	C₂²×C₈	—	94	2	no	—
173	C₂²×C₈	—	94	2	no	—
174	C₂²×C₈	—	94	1	no	—
175	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
176	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
177	#123	—	47	2	no	—
178	C₂²⋊Q₈	—	94	1	no	—
179	#121	—	94	1	no	—
180	#120	—	47	2	no	—
181	C₄×D₄	—	94	2	no	—
182	#117	—	47	1	no	—
183	M₃₂	—	2	4	no	—
184	M₃₂	—	2	2	no	—
185	M₃₂	—	2	2	no	—
186	M₃₂	—	94	2	no	—
187	M₃₂	—	94	2	no	—
188	C₂×C₁₆	—	2	4	no	—
189	C₂×C₁₆	—	94	2	no	—
190	C₂×C₁₆	C₂²⋊D₄₇	1	4	yes	complemented
191	C₄⋊C₈	—	94	2	no	—
192	C₂²⋊C₈	—	94	2	no	—
193	C₂²⋊C₈	—	94	2	no	—
194	#97	—	94	1	no	—
195	C₄×C₈	—	94	1	no	—
196	C₂⁴	—	47	1	no	—
197	#41	—	2	2	no	—
198	#41	—	2	2	no	—
199	C₂×Q₈	#10625324	1	1	yes	characteristic
200	C₂×D₄	—	94	2	no	—
201	C₂×D₄	C₈×D₄₇	1	2	yes	—
202	C₂×D₄	#10625324	1	1	yes	characteristic
203	C₂²×C₄	—	47	1	no	—
204	C₂²×C₄	—	94	1	no	—
205	C₂²×C₄	—	94	2	no	—
206	C₂²×C₄	—	94	1	no	—
207	C₂²×C₄	—	94	2	no	—
208	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
209	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
210	M₁₆	—	2	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	94	2	no	—
213	C₂×C₈	—	2	2	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	94	1	no	—
216	C₂×C₈	—	94	1	no	—
217	C₂×C₈	—	94	2	no	—
218	C₂×C₈	—	188	1	no	—
219	C₂×C₈	—	188	2	no	—
220	C₂×C₈	—	188	1	no	—
221	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
222	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
223	C₂×C₈	#10625350	1	2	yes	—
224	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
225	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
226	C₄⋊C₄	—	94	2	no	—
227	C₄⋊C₄	—	94	1	no	—
228	C₂²⋊C₄	—	47	2	no	—
229	C₂²⋊C₄	—	94	2	no	—
230	C₂²⋊C₄	—	94	2	no	—
231	C₄²	—	94	1	no	—
232	C₁₆	—	2	4	no	—
233	C₁₆	—	188	2	no	—
234	C₂³	—	94	1	no	—
235	C₂³	—	94	2	no	—
236	C₂³	—	188	2	no	—
237	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
238	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
239	Q₈	—	2	2	no	—
240	D₄	—	2	4	no	—
241	D₄	—	2	2	no	—
242	D₄	—	188	4	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	94	2	no	—
246	C₂×C₄	—	94	1	no	—
247	C₂×C₄	—	94	2	no	—
248	C₂×C₄	—	188	1	no	—
249	C₂×C₄	—	188	1	no	—
250	C₂×C₄	—	188	2	no	—
251	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
252	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
253	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
254	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
255	C₂×C₄	#13094030	1	2	yes	—
256	C₈	—	2	2	no	—
257	C₈	—	188	1	no	—
258	C₈	—	188	1	no	—
259	C₈	#13093993	1	1	yes	characteristic
260	C₈	#13093998	1	2	yes	—
261	C₈	#13094007	1	1	yes	characteristic
262	C₂²	—	2	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	94	2	no	—
266	C₂²	—	94	4	no	—
267	C₂²	—	188	1	no	—
268	C₂²	—	188	2	no	—
269	C₂²	—	188	1	no	—
270	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
271	C₂²	C₈×C₂²⋊D₄₇	1	2	yes	—
272	C₄	—	2	2	no	—
273	C₄	—	188	2	no	—
274	C₄	—	188	1	no	—
275	C₄	#15689002	1	1	yes	characteristic
276	C₄	#15689089	1	1	yes	characteristic
277	C₄	#15689194	1	2	yes	—
278	C₂	—	2	1	no	—
279	C₂	—	2	2	no	—
280	C₂	—	4	2	no	—
281	C₂	—	188	2	no	—
282	C₂	#20243680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20252080

C₂

yes

maximal, characteristic

#20245009

C₂

yes

maximal, characteristic, complemented

#20244998

C₂

yes

maximal, complemented

#20241473

C₂

yes

maximal, complemented

C₄₇×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₇

C₂²

yes

characteristic

#15689630

C₄

yes

characteristic

C₂×#13093964

C₂²

yes

—

#15689192

—

C₈×C₂²⋊D₄₇

—

#15689151

C₄

yes

characteristic

#15689090

C₄

yes

characteristic

#15689086

C₄

yes

characteristic

#15689078

C₂²

yes

characteristic

#15688905

—

(C₂×D₄₇)⋊C₁₆

—

C₂×#131×C₄₇

C₂²

yes

characteristic

C₄₇×#504

—

C₂×M₃₂×C₄₇

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂²×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×#10625329

C₂×C₄

yes

characteristic

C₂²×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

—

#13094005

C₈

yes

—

#13094000

—

#13093995

—

#13093992

C₈

yes

—

C₄×C₂²⋊D₄₇

—

#13093983

C₂×C₄

yes

characteristic

#13093964

—

#13093964

—

C₂×C₄₇⋊C₁₆

—

Dic₄₇⋊C₈

—

C₂²⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

#13093934

—

C₈×Dic₄₇

—

C₂×#41×C₄₇

C₂×C₄

yes

characteristic

#131×C₄₇

—

#131×C₄₇

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

complemented

C₂³×D₄₇

C₂×C₈

yes

characteristic

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

M₁₆

yes

characteristic

C₂×D₄×C₄₇

C₂×C₈

yes

—

C₂×D₄×C₄₇

M₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

C₂×C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

M₁₆×C₄₇

—

M₁₆×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×C₈

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₈×D₄₇

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂²⋊C₈

yes

—

C₂³×C₄₇

C₂²×C₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

100

C₂×C₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

103

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₄₇

C₄×D₄

yes

—

105

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₄₇

#131

yes

—

107

C₂²⋊D₄₇

—

108

C₂×Dic₄₇

—

109

C₂×Dic₄₇

—

110

C₂×Dic₄₇

—

111

C₄×D₄₇

—

112

C₄×D₄₇

—

113

C₄×D₄₇

—

114

C₈×C₄₇

—

115

C₈×C₄₇

#120

yes

characteristic

116

C₈×C₄₇

#121

yes

—

117

C₈×C₄₇

#123

yes

characteristic

118

C₄₇⋊C₈

—

119

C₄₇⋊C₈

—

120

#12981

—

maximal, Sylow

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

125

C₂²×C₄₇

C₈×D₄

yes

—

126

C₂×D₄₇

—

127

C₂×D₄₇

—

128

C₂×D₄₇

—

129

C₂×D₄₇

—

130

C₂×D₄₇

—

131

C₄×C₄₇

—

132

C₄×C₄₇

#386

yes

characteristic

133

C₄×C₄₇

#408

yes

characteristic

134

C₄×C₄₇

#435

yes

—

135

Dic₄₇

—

136

Dic₄₇

—

137

#3407

D₄₇

yes

characteristic, complemented

138

#2929

—

139

#2115

—

140

#2112

—

141

#1378

—

142

C₂×C₄₇

—

143

C₂×C₄₇

—

144

C₂×C₄₇

—

145

C₂×C₄₇

#1869

yes

characteristic

146

D₄₇

—

147

C₂×#131

C₂×D₄₇

yes

characteristic

148

C₂³×C₈

—

149

#525

—

150

#504

—

151

C₂×M₃₂

—

152

C₂×M₃₂

—

153

C₂×M₃₂

C₂×D₄₇

yes

—

154

#435

—

155

C₈×D₄

—

156

#424

—

157

#408

—

158

#407

—

159

#405

—

160

#349

—

161

C₂²⋊C₁₆

—

162

C₄₇

#12981

yes

characteristic, complemented, Sylow

163

C₂×#41

C₄×D₄₇

yes

characteristic

164

C₂³×C₄

—

165

#131

—

166

#131

—

167

C₂×M₁₆

—

168

C₂×M₁₆

C₄×D₄₇

yes

characteristic

169

C₂×M₁₆

D₁₈₈

yes

—

170

C₂²×C₈

—

171

C₂²×C₈

—

172

C₂²×C₈

—

173

C₂²×C₈

—

174

C₂²×C₈

—

175

C₂²×C₈

C₂²⋊D₄₇

yes

—

176

C₂²×C₈

C₂²×D₄₇

yes

characteristic

177

#123

—

178

C₂²⋊Q₈

—

179

#121

—

180

#120

—

181

C₄×D₄

—

182

#117

—

183

M₃₂

—

184

M₃₂

—

185

M₃₂

—

186

M₃₂

—

187

M₃₂

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

190

C₂×C₁₆

C₂²⋊D₄₇

yes

complemented

191

C₄⋊C₈

—

192

C₂²⋊C₈

—

193

C₂²⋊C₈

—

194

#97

—

195

C₄×C₈

—

196

C₂⁴

—

197

#41

—

198

#41

—

199

C₂×Q₈

#10625324

yes

characteristic

200

C₂×D₄

—

201

C₂×D₄

C₈×D₄₇

yes

—

202

C₂×D₄

#10625324

yes

characteristic

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

209

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

210

M₁₆

—

211

M₁₆

—

212

M₁₆

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

188

—

219

C₂×C₈

—

188

—

220

C₂×C₈

—

188

—

221

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

222

C₂×C₈

C₂×D₁₈₈

yes

characteristic

223

C₂×C₈

#10625350

yes

—

224

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

225

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₂²⋊C₄

—

229

C₂²⋊C₄

—

230

C₂²⋊C₄

—

231

C₄²

—

232

C₁₆

—

233

C₁₆

—

188

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

188

—

237

C₂³

(C₂×D₄₇)⋊C₈

yes

—

238

C₂³

C₂×C₈×D₄₇

yes

characteristic

239

Q₈

—

240

D₄

—

241

D₄

—

242

D₄

—

188

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

188

—

249

C₂×C₄

—

188

—

250

C₂×C₄

—

188

—

251

C₂×C₄

(C₂×D₄₇)⋊C₈

yes

—

252

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

253

C₂×C₄

C₄×C₂²⋊D₄₇

yes

—

254

C₂×C₄

C₂×#10625324

yes

characteristic

255

C₂×C₄

#13094030

yes

—

256

C₈

—

257

C₈

—

188

—

258

C₈

—

188

—

259

C₈

#13093993

yes

characteristic

260

C₈

#13093998

yes

—

261

C₈

#13094007

yes

characteristic

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

188

—

268

C₂²

—

188

—

269

C₂²

—

188

—

270

C₂²

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

271

C₂²

C₈×C₂²⋊D₄₇

yes

—

272

C₄

—

273

C₄

—

188

—

274

C₄

—

188

—

275

C₄

#15689002

yes

characteristic

276

C₄

#15689089

yes

characteristic

277

C₄

#15689194

yes

—

278

C₂

—

279

C₂

—

280

C₂

—

281

C₂

—

188

—

282

C₂

#20243680

yes

characteristic

	subgroup	G/H
center	C₈	#13093993
commutator	C₂³×C₄₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#3407	C₂
socle	C₂×C₄₇	#1869
prime radical	#15689630	C₄
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#3407	D₄₇
hypocenter	C₄₇	#12981
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

subgroup

G/H

center

C₈

#13093993

commutator

C₂³×C₄₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#3407

C₂

C₂×C₄₇

C₄

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3407

N	H ≅ G/N	type
2. #20245009	C₂	semidirect
3. #20244998	C₂	semidirect
4. #20241473	C₂	semidirect
5. C₄₇×#3407	C₂	semidirect
53. C₂×C₁₆×C₄₇	D₄	semidirect
137. #3407	D₄₇	semidirect
162. C₄₇	#12981	semidirect
190. C₂×C₁₆	C₂²⋊D₄₇	semidirect

H ≅ G/N

type

2. #20245009

C₂

semidirect

3. #20244998

C₂

semidirect

4. #20241473

C₂

semidirect

5. C₄₇×#3407

C₂

semidirect

53. C₂×C₁₆×C₄₇

D₄

semidirect

137. #3407

D₄₇

semidirect

162. C₄₇

#12981

semidirect

190. C₂×C₁₆

C₂²⋊D₄₇

semidirect

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

subgroup	index
#20252080	2
#20245009	2
#20244998	2
#20241473	2
C₄₇×#3407	2
#12981	47

subgroup

index

C₄₇×#3407

Subgroups — #26133162

Conjugacy classes of subgroups

Complements

Maximal subgroups