Group #26109125 — subgroups

Subgroups — #26109125

Order 12032.

478 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 147 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×#15689174	C₂	1	1	yes	maximal, characteristic
2	#20243365	C₂	1	2	yes	maximal
3	C₂×#15688873	C₂	1	2	yes	maximal, complemented
4	#20241223	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1277	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
7	#15689174	—	2	4	no	—
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×Dic₄₇⋊C₈	C₄	1	2	yes	—
10	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
11	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15688877	—	2	2	no	—
14	#15688873	—	2	4	no	—
15	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
19	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
24	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
25	C₄²×D₄₇	—	2	2	no	—
26	C₄²×D₄₇	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
29	Dic₄₇⋊C₈	—	2	4	no	—
30	(C₂×D₄₇)⋊C₈	—	2	4	no	—
31	(C₂×D₄₇)⋊C₈	—	4	4	no	—
32	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
33	C₂²×C₈×C₄₇	—	2	2	no	—
34	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₄₇	—	2	2	no	—
37	C₄⋊C₈×C₄₇	—	2	2	no	—
38	C₄×C₈×C₄₇	—	2	2	no	—
39	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
43	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×D₄₇	—	2	2	no	—
47	C₂×C₄×D₄₇	—	2	1	no	—
48	C₂×C₄×D₄₇	—	2	1	no	—
49	C₂×C₄×D₄₇	—	2	1	no	—
50	C₂×C₄×D₄₇	—	2	1	no	—
51	C₂×C₄×D₄₇	—	2	2	no	—
52	C₂×C₄×D₄₇	—	2	2	no	—
53	C₂×C₄×D₄₇	—	2	2	no	—
54	C₂×C₄×D₄₇	—	4	2	no	—
55	C₂×C₄×D₄₇	SD₁₆	1	4	yes	—
56	C₂×C₈×C₄₇	—	2	2	no	—
57	C₂×C₈×C₄₇	—	2	2	no	—
58	C₂×C₈×C₄₇	—	2	2	no	—
59	C₂×C₈×C₄₇	—	4	2	no	—
60	C₂×C₈×C₄₇	—	4	2	no	—
61	C₂×C₈×C₄₇	—	4	2	no	—
62	C₄²×C₄₇	C₂×D₄	1	2	yes	—
63	C₄²×C₄₇	#41	1	2	yes	—
64	C₄×Dic₄₇	—	2	1	no	—
65	C₄×Dic₄₇	—	2	1	no	—
66	C₄×Dic₄₇	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₂×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₄₇⋊C₈	—	2	2	no	—
70	C₂×C₄₇⋊C₈	—	4	2	no	—
71	C₂×C₄₇⋊C₈	—	4	2	no	—
72	C₂×C₄₇⋊C₈	—	4	2	no	—
73	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
74	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂²×D₄₇	—	2	1	no	—
76	C₂²×D₄₇	—	2	2	no	—
77	C₂²×D₄₇	—	2	1	no	—
78	C₂²×D₄₇	—	2	2	no	—
79	C₂²×D₄₇	#106	1	2	yes	—
80	C₂×C₄×C₄₇	—	2	2	no	—
81	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
83	C₂×C₄×C₄₇	#121	1	2	yes	—
84	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₄₇	#131	1	2	yes	—
86	C₂×C₄×C₄₇	#131	1	2	yes	—
87	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
89	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
90	C₂×Dic₄₇	—	2	1	no	—
91	C₂×Dic₄₇	—	2	1	no	—
92	C₂×Dic₄₇	—	2	1	no	—
93	C₂×Dic₄₇	—	2	1	no	—
94	C₂×Dic₄₇	—	2	2	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	#106	1	2	yes	—
97	C₄×D₄₇	—	2	4	no	—
98	C₄×D₄₇	—	2	4	no	—
99	C₄×D₄₇	—	4	4	no	—
100	C₄×D₄₇	—	4	2	no	—
101	C₄×D₄₇	—	4	1	no	—
102	C₄×D₄₇	—	4	1	no	—
103	C₈×C₄₇	—	4	2	no	—
104	C₈×C₄₇	—	8	2	no	—
105	C₄₇⋊C₈	—	2	4	no	—
106	C₄₇⋊C₈	—	8	2	no	—
107	#8598	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	#380	1	1	yes	characteristic
109	C₂²×C₄₇	#424	1	2	yes	—
110	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
111	C₂²×C₄₇	#427	1	1	yes	characteristic
112	C₂²×C₄₇	#430	1	2	yes	—
113	C₂×D₄₇	—	2	2	no	—
114	C₂×D₄₇	—	2	4	no	—
115	C₂×D₄₇	—	4	1	no	—
116	C₂×D₄₇	—	4	1	no	—
117	C₂×D₄₇	—	4	2	no	—
118	C₄×C₄₇	—	2	2	no	—
119	C₄×C₄₇	#408	1	2	yes	—
120	C₄×C₄₇	#433	1	1	yes	characteristic
121	C₄×C₄₇	#433	1	1	yes	characteristic
122	C₄×C₄₇	#465	1	2	yes	—
123	C₄×C₄₇	#465	1	2	yes	—
124	Dic₄₇	—	2	2	no	—
125	Dic₄₇	—	4	1	no	—
126	Dic₄₇	—	4	1	no	—
127	C₂×#431	—	47	1	no	—
128	#1797	—	47	2	no	—
129	C₂×#334	—	47	2	no	—
130	#1277	—	47	1	no	—
131	#1277	D₄₇	1	1	yes	characteristic, complemented
132	C₂×C₄₇	#1570	1	2	yes	—
133	C₂×C₄₇	#1572	1	2	yes	—
134	C₂×C₄₇	#1798	1	1	yes	characteristic
135	C₂×C₄₇	#1807	1	1	yes	characteristic
136	C₂×C₄₇	#1811	1	1	yes	characteristic
137	D₄₇	—	4	2	no	—
138	C₂²×C₄²	—	47	1	no	—
139	#431	—	94	4	no	—
140	C₂×C₄⋊C₈	—	47	2	no	—
141	C₂×C₄⋊C₈	—	47	2	no	—
142	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
143	C₂×C₂²⋊C₈	—	47	2	no	—
144	C₂×C₂²⋊C₈	—	94	2	no	—
145	C₂×C₄×C₈	—	47	1	no	—
146	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
147	#336	—	94	2	no	—
148	#334	—	94	4	no	—
149	C₄₇	#8598	1	1	yes	characteristic, complemented, Sylow
150	C₂³×C₄	—	47	1	no	—
151	C₂³×C₄	—	47	1	no	—
152	C₂³×C₄	—	47	1	no	—
153	C₂²×C₈	—	2	2	no	—
154	C₂²×C₈	—	47	2	no	—
155	C₂²×C₈	—	94	2	no	—
156	C₂²×C₈	C₄×D₄₇	1	2	yes	—
157	C₂×C₄²	—	47	1	no	—
158	C₂×C₄²	—	47	1	no	—
159	C₂×C₄²	—	47	1	no	—
160	C₂×C₄²	—	94	2	no	—
161	C₂×C₄²	—	94	2	no	—
162	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	94	4	no	—
166	C₄⋊C₈	—	94	2	no	—
167	C₄⋊C₈	—	94	2	no	—
168	C₂²⋊C₈	—	94	4	no	—
169	C₂²⋊C₈	—	188	4	no	—
170	C₄×C₈	—	2	2	no	—
171	C₄×C₈	—	47	4	no	—
172	C₂⁴	—	47	1	no	—
173	C₂²×C₄	—	47	1	no	—
174	C₂²×C₄	—	47	4	no	—
175	C₂²×C₄	—	47	1	no	—
176	C₂²×C₄	—	47	1	no	—
177	C₂²×C₄	—	94	2	no	—
178	C₂²×C₄	—	94	1	no	—
179	C₂²×C₄	—	94	1	no	—
180	C₂²×C₄	—	94	1	no	—
181	C₂²×C₄	—	94	1	no	—
182	C₂²×C₄	—	94	2	no	—
183	C₂²×C₄	—	94	2	no	—
184	C₂²×C₄	—	94	2	no	—
185	C₂²×C₄	—	188	2	no	—
186	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
187	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
188	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	—	2	2	no	—
191	C₂×C₈	—	2	2	no	—
192	C₂×C₈	—	4	2	no	—
193	C₂×C₈	—	4	2	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	47	4	no	—
196	C₂×C₈	—	94	2	no	—
197	C₂×C₈	—	94	2	no	—
198	C₂×C₈	—	188	2	no	—
199	C₂×C₈	—	188	2	no	—
200	C₂×C₈	—	188	2	no	—
201	C₄²	—	94	1	no	—
202	C₄²	—	94	1	no	—
203	C₄²	—	94	2	no	—
204	C₄²	—	94	2	no	—
205	C₄²	#10625350	1	2	yes	—
206	C₄²	D₄×D₄₇	1	2	yes	—
207	C₂³	—	47	2	no	—
208	C₂³	—	94	1	no	—
209	C₂³	—	94	2	no	—
210	C₂³	—	94	1	no	—
211	C₂³	—	94	2	no	—
212	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	47	2	no	—
215	C₂×C₄	—	94	1	no	—
216	C₂×C₄	—	94	1	no	—
217	C₂×C₄	—	94	4	no	—
218	C₂×C₄	—	94	4	no	—
219	C₂×C₄	—	94	1	no	—
220	C₂×C₄	—	94	1	no	—
221	C₂×C₄	—	94	2	no	—
222	C₂×C₄	—	94	2	no	—
223	C₂×C₄	—	188	4	no	—
224	C₂×C₄	—	188	2	no	—
225	C₂×C₄	—	188	1	no	—
226	C₂×C₄	—	188	1	no	—
227	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
228	C₂×C₄	#13093981	1	1	yes	characteristic
229	C₂×C₄	#13093997	1	2	yes	—
230	C₂×C₄	#13094002	1	2	yes	—
231	C₂×C₄	#13094030	1	2	yes	—
232	C₂×C₄	#13094032	1	2	yes	—
233	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
234	C₂×C₄	#13094043	1	1	yes	characteristic
235	C₂×C₄	#13094047	1	1	yes	characteristic
236	C₈	—	4	2	no	—
237	C₈	—	8	2	no	—
238	C₈	—	94	4	no	—
239	C₈	—	376	2	no	—
240	C₂²	—	94	2	no	—
241	C₂²	—	94	4	no	—
242	C₂²	—	188	1	no	—
243	C₂²	—	188	1	no	—
244	C₂²	—	188	2	no	—
245	C₂²	#15688982	1	1	yes	characteristic
246	C₂²	#15689148	1	2	yes	—
247	C₂²	#106×D₄₇	1	1	yes	characteristic
248	C₂²	#15689160	1	1	yes	characteristic
249	C₂²	#15689170	1	2	yes	—
250	C₄	—	2	2	no	—
251	C₄	—	94	2	no	—
252	C₄	—	188	1	no	—
253	C₄	—	188	1	no	—
254	C₄	#15689088	1	2	yes	—
255	C₄	#15689182	1	1	yes	characteristic
256	C₄	#15689185	1	1	yes	characteristic
257	C₄	#15689351	1	2	yes	—
258	C₄	#15689355	1	2	yes	—
259	C₂	—	188	2	no	—
260	C₂	#20242157	1	2	yes	—
261	C₂	#20242167	1	2	yes	—
262	C₂	#20243371	1	1	yes	characteristic
263	C₂	#20243412	1	1	yes	characteristic
264	C₂	#20243429	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689174

C₂

yes

maximal, characteristic

#20243365

C₂

yes

maximal

C₂×#15688873

C₂

yes

maximal, complemented

#20241223

C₂

yes

maximal, characteristic, complemented

C₄₇×#1277

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₄₇

C₂²

yes

characteristic

#15689174

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×Dic₄₇⋊C₈

C₄

yes

—

C₂×(C₂×D₄₇)⋊C₈

—

C₂×(C₂×D₄₇)⋊C₈

C₄

yes

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688877

—

#15688873

—

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×D₄₇

D₄

yes

characteristic

C₂²×C₄×D₄₇

Q₈

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄×Dic₄₇

Q₈

yes

characteristic

C₄²×D₄₇

—

C₄²×D₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

Dic₄₇⋊C₈

—

(C₂×D₄₇)⋊C₈

—

(C₂×D₄₇)⋊C₈

—

C₄×C₄₇⋊C₈

D₄

yes

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

—

C₄×C₈×C₄₇

—

C₂³×D₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂²×Dic₄₇

C₄⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₄⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

SD₁₆

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂×D₄

yes

—

C₄²×C₄₇

#41

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

#106

yes

—

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

#131

yes

—

C₂×C₄×C₄₇

#131

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#106

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

100

C₄×D₄₇

—

101

C₄×D₄₇

—

102

C₄×D₄₇

—

103

C₈×C₄₇

—

104

C₈×C₄₇

—

105

C₄₇⋊C₈

—

106

C₄₇⋊C₈

—

107

#8598

—

maximal, Sylow

108

C₂²×C₄₇

#380

yes

characteristic

109

C₂²×C₄₇

#424

yes

—

110

C₂²×C₄₇

C₂×#106

yes

characteristic

111

C₂²×C₄₇

#427

yes

characteristic

112

C₂²×C₄₇

#430

yes

—

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₂×D₄₇

—

117

C₂×D₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

#408

yes

—

120

C₄×C₄₇

#433

yes

characteristic

121

C₄×C₄₇

#433

yes

characteristic

122

C₄×C₄₇

#465

yes

—

123

C₄×C₄₇

#465

yes

—

124

Dic₄₇

—

125

Dic₄₇

—

126

Dic₄₇

—

127

C₂×#431

—

128

#1797

—

129

C₂×#334

—

130

#1277

—

131

#1277

D₄₇

yes

characteristic, complemented

132

C₂×C₄₇

#1570

yes

—

133

C₂×C₄₇

#1572

yes

—

134

C₂×C₄₇

#1798

yes

characteristic

135

C₂×C₄₇

#1807

yes

characteristic

136

C₂×C₄₇

#1811

yes

characteristic

137

D₄₇

—

138

C₂²×C₄²

—

139

#431

—

140

C₂×C₄⋊C₈

—

141

C₂×C₄⋊C₈

—

142

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

143

C₂×C₂²⋊C₈

—

144

C₂×C₂²⋊C₈

—

145

C₂×C₄×C₈

—

146

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

147

#336

—

148

#334

—

149

C₄₇

#8598

yes

characteristic, complemented, Sylow

150

C₂³×C₄

—

151

C₂³×C₄

—

152

C₂³×C₄

—

153

C₂²×C₈

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₂²×C₈

C₄×D₄₇

yes

—

157

C₂×C₄²

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

C₂×C₄²

—

161

C₂×C₄²

—

162

C₂×C₄²

C₂²×D₄₇

yes

characteristic

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

168

C₂²⋊C₈

—

169

C₂²⋊C₈

—

188

—

170

C₄×C₈

—

171

C₄×C₈

—

172

C₂⁴

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

188

—

186

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

187

C₂²×C₄

D₄×D₄₇

yes

characteristic

188

C₂²×C₄

Q₈×D₄₇

yes

characteristic

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

188

—

199

C₂×C₈

—

188

—

200

C₂×C₈

—

188

—

201

C₄²

—

202

C₄²

—

203

C₄²

—

204

C₄²

—

205

C₄²

#10625350

yes

—

206

C₄²

D₄×D₄₇

yes

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

C₄⋊C₄×D₄₇

yes

characteristic

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

188

—

224

C₂×C₄

—

188

—

225

C₂×C₄

—

188

—

226

C₂×C₄

—

188

—

227

C₂×C₄

C₂²⋊C₄×D₄₇

yes

characteristic

228

C₂×C₄

#13093981

yes

characteristic

229

C₂×C₄

#13093997

yes

—

230

C₂×C₄

#13094002

yes

—

231

C₂×C₄

#13094030

yes

—

232

C₂×C₄

#13094032

yes

—

233

C₂×C₄

SD₁₆×D₄₇

yes

—

234

C₂×C₄

#13094043

yes

characteristic

235

C₂×C₄

#13094047

yes

characteristic

236

C₈

—

237

C₈

—

238

C₈

—

239

C₈

—

376

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

188

—

243

C₂²

—

188

—

244

C₂²

—

188

—

245

C₂²

#15688982

yes

characteristic

246

C₂²

#15689148

yes

—

247

C₂²

#106×D₄₇

yes

characteristic

248

C₂²

#15689160

yes

characteristic

249

C₂²

#15689170

yes

—

250

C₄

—

251

C₄

—

252

C₄

—

188

—

253

C₄

—

188

—

254

C₄

#15689088

yes

—

255

C₄

#15689182

yes

characteristic

256

C₄

#15689185

yes

characteristic

257

C₄

#15689351

yes

—

258

C₄

#15689355

yes

—

259

C₂

—

188

—

260

C₂

#20242157

yes

—

261

C₂

#20242167

yes

—

262

C₂

#20243371

yes

characteristic

263

C₂

#20243412

yes

characteristic

264

C₂

#20243429

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1277	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1277	D₄₇
hypocenter	C₄₇	#8598
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

subgroup

G/H

center

C₂²×C₄

D₄×D₄₇

commutator

C₂²×C₄×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1277

C₂

socle

C₂³×C₄₇

C₂×C₄⋊C₄

prime radical

C₂³×D₄₇

C₄⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

N	H ≅ G/N	type
3. C₂×#15688873	C₂	semidirect
4. #20241223	C₂	semidirect
5. C₄₇×#1277	C₂	semidirect
131. #1277	D₄₇	semidirect
149. C₄₇	#8598	semidirect

H ≅ G/N

type

3. C₂×#15688873

C₂

semidirect

4. #20241223

C₂

semidirect

5. C₄₇×#1277

C₂

semidirect

131. #1277

D₄₇

semidirect

149. C₄₇

#8598

semidirect

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

subgroup	index
C₂×#15689174	2
#20243365	2
C₂×#15688873	2
#20241223	2
C₄₇×#1277	2
#8598	47

subgroup

index

C₄₇×#1277

Subgroups — #26109125

Conjugacy classes of subgroups

Complements

Maximal subgroups