Group #26119286 — subgroups

Subgroups — #26119286

Order 12032.

588 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20248417	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244316	C₂	1	2	yes	maximal
3	#20241271	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1957	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094023	—	2	2	no	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×#13093945	—	2	2	no	—
9	C₂×#13093945	—	2	2	no	—
10	#15689043	—	2	2	no	—
11	#15689019	—	2	2	no	—
12	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#102×C₄₇	—	2	2	no	—
15	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#384	C₂²	1	1	yes	characteristic
17	C₂²×Dic₉₄	—	2	2	no	—
18	C₂²×C₄₇⋊C₈	—	2	2	no	—
19	#13094023	—	4	4	no	—
20	#13094023	—	4	4	no	—
21	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
23	C₂×Dic₄₇⋊C₄	—	2	4	no	—
24	C₂×C₄×Dic₄₇	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	#13093945	—	4	4	no	—
28	#13093945	—	4	4	no	—
29	C₄₇⋊#95	—	2	2	no	—
30	C₄₇⋊#95	—	2	2	no	—
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	—	2	1	no	—
33	C₂²×C₈×C₄₇	—	2	1	no	—
34	#127×C₄₇	—	2	1	no	—
35	#127×C₄₇	—	2	2	no	—
36	#127×C₄₇	Q₈	1	2	yes	complemented
37	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	#102×C₄₇	—	4	4	no	—
41	C₄×C₈×C₄₇	—	2	2	no	—
42	C₂⁴×C₄₇	—	4	1	no	—
43	C₂×D₄×C₄₇	—	2	4	no	—
44	C₂×D₄×C₄₇	—	2	2	no	—
45	C₂×D₄×C₄₇	—	4	2	no	—
46	C₂×D₄×C₄₇	—	4	2	no	—
47	C₂×D₄×C₄₇	—	4	2	no	—
48	C₂×D₄×C₄₇	—	4	1	no	—
49	C₂×D₄×C₄₇	—	4	2	no	—
50	C₂×D₄×C₄₇	—	4	2	no	—
51	C₂×D₄×C₄₇	—	4	2	no	—
52	C₂×D₄×C₄₇	—	4	2	no	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
56	C₂²×Dic₄₇	—	2	2	no	—
57	C₂²×Dic₄₇	—	2	2	no	—
58	C₂×Dic₉₄	—	4	8	no	—
59	C₂×Dic₉₄	—	8	2	no	—
60	C₂×C₈×C₄₇	—	2	2	no	—
61	C₂×C₈×C₄₇	—	4	1	no	—
62	C₂×C₈×C₄₇	—	4	1	no	—
63	C₄⋊C₄×C₄₇	—	4	2	no	—
64	C₄⋊C₄×C₄₇	—	4	2	no	—
65	C₄⋊C₄×C₄₇	—	4	2	no	—
66	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₄₇	#41	1	1	yes	characteristic
68	C₄²×C₄₇	#41	1	2	yes	—
69	C₄⋊Dic₄₇	—	2	2	no	—
70	C₄⋊Dic₄₇	—	2	2	no	—
71	C₄⋊Dic₄₇	D₈	1	4	yes	—
72	C₄⋊Dic₄₇	SD₁₆	1	4	yes	—
73	Dic₄₇⋊C₄	—	4	8	no	—
74	C₄×Dic₄₇	—	4	2	no	—
75	C₄×Dic₄₇	—	4	2	no	—
76	C₂×C₄₇⋊C₈	—	4	2	no	—
77	C₂×C₄₇⋊C₈	—	4	2	no	—
78	C₂×C₄₇⋊C₈	—	4	2	no	—
79	C₂³×C₄₇	—	4	2	no	—
80	C₂³×C₄₇	—	8	2	no	—
81	C₂³×C₄₇	—	8	2	no	—
82	C₂³×C₄₇	—	8	1	no	—
83	C₂³×C₄₇	—	8	1	no	—
84	C₂³×C₄₇	#120	1	1	yes	characteristic
85	D₄×C₄₇	—	4	4	no	—
86	D₄×C₄₇	—	4	4	no	—
87	D₄×C₄₇	—	4	4	no	—
88	D₄×C₄₇	—	8	2	no	—
89	D₄×C₄₇	—	8	2	no	—
90	D₄×C₄₇	—	8	2	no	—
91	C₂×C₄×C₄₇	—	2	1	no	—
92	C₂×C₄×C₄₇	—	2	1	no	—
93	C₂×C₄×C₄₇	—	4	4	no	—
94	C₂×C₄×C₄₇	—	4	2	no	—
95	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
96	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
97	C₂×C₄×C₄₇	#124	1	2	yes	—
98	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
100	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
101	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₄₇	#137	1	2	yes	—
103	C₂×Dic₄₇	—	2	4	no	—
104	C₂×Dic₄₇	—	2	4	no	—
105	C₂×Dic₄₇	—	4	2	no	—
106	C₂×Dic₄₇	—	4	2	no	—
107	C₂×Dic₄₇	—	4	2	no	—
108	C₂×Dic₄₇	—	4	2	no	—
109	Dic₉₄	—	8	8	no	—
110	C₈×C₄₇	—	4	2	no	—
111	C₄₇⋊C₈	—	8	2	no	—
112	#10348	—	47	1	no	maximal, Sylow
113	C₂²×C₄₇	—	8	4	no	—
114	C₂²×C₄₇	—	8	2	no	—
115	C₂²×C₄₇	—	16	1	no	—
116	C₂²×C₄₇	—	16	1	no	—
117	C₂²×C₄₇	—	16	2	no	—
118	C₂²×C₄₇	#393	1	1	yes	characteristic
119	C₂²×C₄₇	#447	1	2	yes	—
120	C₂²×C₄₇	#448	1	2	yes	—
121	C₂²×C₄₇	#453	1	1	yes	characteristic
122	C₂²×C₄₇	#454	1	1	yes	characteristic
123	C₄×C₄₇	—	2	1	no	—
124	C₄×C₄₇	—	2	1	no	—
125	C₄×C₄₇	—	8	2	no	—
126	C₄×C₄₇	#474	1	2	yes	—
127	C₄×C₄₇	#476	1	2	yes	—
128	C₄×C₄₇	#486	1	2	yes	—
129	C₄×C₄₇	#489	1	2	yes	—
130	Dic₄₇	—	4	4	no	—
131	Dic₄₇	—	4	4	no	—
132	#2551	—	47	1	no	—
133	#1982	—	47	2	no	—
134	#1957	D₄₇	1	1	yes	characteristic
135	#1296	—	47	1	no	—
136	#1279	—	47	2	no	—
137	C₂×C₄₇	—	16	2	no	—
138	C₂×C₄₇	#1619	1	1	yes	characteristic
139	C₂×C₄₇	#1623	1	1	yes	characteristic
140	C₂×C₄₇	#1627	1	2	yes	—
141	C₂×C₄₇	#2023	1	2	yes	—
142	C₂×C₄₇	#2027	1	1	yes	characteristic
143	C₂×C₄⋊Q₈	—	94	2	no	—
144	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
145	C₂×C₄⋊C₈	—	47	2	no	—
146	C₂×#102	—	2	2	no	—
147	C₂×#102	—	94	2	no	—
148	C₂×#102	—	94	2	no	—
149	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
150	#395	—	94	2	no	—
151	#389	—	94	2	no	—
152	#384	C₂×D₄₇	1	1	yes	characteristic
153	C₄×C₄⋊C₄	—	47	2	no	—
154	C₄₇	#10348	1	1	yes	characteristic, complemented, Sylow
155	C₂²×Q₈	—	94	2	no	—
156	C₂²×D₄	—	2	2	no	—
157	C₂²×D₄	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	94	2	no	—
160	C₄⋊Q₈	—	188	4	no	—
161	C₄⋊Q₈	—	188	4	no	—
162	#127	—	2	1	no	—
163	#127	—	2	2	no	—
164	#127	Dic₉₄	1	2	yes	complemented
165	C₂×C₄⋊C₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	47	2	no	—
167	C₂×C₄⋊C₄	—	47	2	no	—
168	C₂×C₄⋊C₄	—	94	4	no	—
169	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
170	C₂×C₄²	—	94	2	no	—
171	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
172	C₄⋊C₈	—	94	2	no	—
173	C₄⋊C₈	—	94	2	no	—
174	#102	—	4	4	no	—
175	#102	—	188	4	no	—
176	#102	—	188	4	no	—
177	C₄×C₈	—	2	2	no	—
178	#95	—	94	2	no	—
179	#95	—	94	2	no	—
180	C₂⁴	—	4	1	no	—
181	C₂×Q₈	—	376	2	no	—
182	C₂×Q₈	—	188	8	no	—
183	C₂×D₄	—	2	4	no	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	2	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	2	no	—
191	C₂×D₄	—	4	2	no	—
192	C₂×D₄	—	4	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	94	2	no	—
195	C₂²×C₄	—	94	2	no	—
196	C₂²×C₄	D₄×D₄₇	1	2	yes	—
197	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
198	C₂×C₈	—	2	2	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	1	no	—
201	C₂×C₈	—	188	2	no	—
202	C₂×C₈	—	188	2	no	—
203	C₂×C₈	—	188	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	47	4	no	—
208	C₄⋊C₄	—	47	4	no	—
209	C₄⋊C₄	—	94	2	no	—
210	C₄⋊C₄	—	94	2	no	—
211	C₄⋊C₄	—	188	8	no	—
212	C₄²	—	188	2	no	—
213	C₄²	—	188	2	no	—
214	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
215	C₄²	#10625350	1	1	yes	characteristic
216	C₄²	#10625352	1	2	yes	—
217	C₂³	—	4	2	no	—
218	C₂³	—	8	2	no	—
219	C₂³	—	8	2	no	—
220	C₂³	—	8	1	no	—
221	C₂³	—	8	1	no	—
222	C₂³	#13093992	1	1	yes	characteristic
223	Q₈	—	376	8	no	—
224	D₄	—	4	4	no	—
225	D₄	—	4	4	no	—
226	D₄	—	4	4	no	—
227	D₄	—	8	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	4	4	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	94	4	no	—
235	C₂×C₄	—	94	4	no	—
236	C₂×C₄	—	188	2	no	—
237	C₂×C₄	—	188	2	no	—
238	C₂×C₄	—	188	2	no	—
239	C₂×C₄	—	188	2	no	—
240	C₂×C₄	#13094001	1	2	yes	—
241	C₂×C₄	#13094003	1	1	yes	characteristic
242	C₂×C₄	#13094010	1	2	yes	—
243	C₂×C₄	#13094011	1	1	yes	characteristic
244	C₂×C₄	D₈×D₄₇	1	2	yes	—
245	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
246	C₂×C₄	#13094048	1	2	yes	—
247	C₂×C₄	#13094053	1	2	yes	—
248	C₈	—	4	2	no	—
249	C₈	—	376	2	no	—
250	C₂²	—	8	4	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	16	1	no	—
253	C₂²	—	16	1	no	—
254	C₂²	—	16	2	no	—
255	C₂²	#15689035	1	1	yes	characteristic
256	C₂²	#15689255	1	2	yes	—
257	C₂²	#15689260	1	2	yes	—
258	C₂²	#15689290	1	1	yes	characteristic
259	C₂²	#15689295	1	1	yes	characteristic
260	C₄	—	2	1	no	—
261	C₄	—	2	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	188	4	no	—
264	C₄	—	188	4	no	—
265	C₄	#15689401	1	2	yes	—
266	C₄	#15689411	1	2	yes	—
267	C₄	#15689468	1	2	yes	—
268	C₄	#15689481	1	2	yes	—
269	C₂	—	16	2	no	—
270	C₂	#20242440	1	1	yes	characteristic
271	C₂	#20242464	1	1	yes	characteristic
272	C₂	#20242488	1	2	yes	—
273	C₂	#20244522	1	2	yes	—
274	C₂	#20244544	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20248417

C₂

yes

maximal, characteristic, complemented

#20244316

C₂

yes

maximal

#20241271

C₂

yes

maximal, characteristic, complemented

#20241228

C₂

yes

maximal, complemented

C₄₇×#1957

C₂

yes

maximal, characteristic

C₂×#13094023

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

—

—

—

—

C₄×C₄⋊Dic₄₇

C₂²

yes

—

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×#102×C₄₇

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×#384

C₂²

yes

characteristic

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

—

#13094023

—

#13094023

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄⋊Dic₄₇

D₄

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

#13093945

—

#13093945

—

C₄₇⋊#95

—

C₄₇⋊#95

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×C₈×C₄₇

—

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

Q₈

yes

complemented

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#102×C₄₇

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×Q₈

yes

C₄²×C₄₇

yes

C₄²×C₄₇

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₈

yes

—

C₄⋊Dic₄₇

SD₁₆

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#120

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₄₇

#124

yes

—

C₂×C₄×C₄₇

#124

yes

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

—

100

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

101

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

102

C₂×C₄×C₄₇

#137

yes

—

103

C₂×Dic₄₇

—

104

C₂×Dic₄₇

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

Dic₉₄

—

110

C₈×C₄₇

—

111

C₄₇⋊C₈

—

112

#10348

—

maximal, Sylow

113

C₂²×C₄₇

—

114

C₂²×C₄₇

—

115

C₂²×C₄₇

—

116

C₂²×C₄₇

—

117

C₂²×C₄₇

—

118

C₂²×C₄₇

#393

yes

characteristic

119

C₂²×C₄₇

#447

yes

—

120

C₂²×C₄₇

#448

yes

—

121

C₂²×C₄₇

#453

yes

characteristic

122

C₂²×C₄₇

#454

yes

characteristic

123

C₄×C₄₇

—

124

C₄×C₄₇

—

125

C₄×C₄₇

—

126

C₄×C₄₇

#474

yes

—

127

C₄×C₄₇

#476

yes

—

128

C₄×C₄₇

#486

yes

—

129

C₄×C₄₇

#489

yes

—

130

Dic₄₇

—

131

Dic₄₇

—

132

#2551

—

133

#1982

—

134

#1957

D₄₇

yes

characteristic

135

#1296

—

136

#1279

—

137

C₂×C₄₇

—

138

C₂×C₄₇

#1619

yes

characteristic

139

C₂×C₄₇

#1623

yes

characteristic

140

C₂×C₄₇

#1627

yes

—

141

C₂×C₄₇

#2023

yes

—

142

C₂×C₄₇

#2027

yes

characteristic

143

C₂×C₄⋊Q₈

—

144

C₂×#127

C₂×D₄₇

yes

characteristic

145

C₂×C₄⋊C₈

—

146

C₂×#102

—

147

C₂×#102

—

148

C₂×#102

—

149

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

150

#395

—

151

#389

—

152

#384

C₂×D₄₇

yes

characteristic

153

C₄×C₄⋊C₄

—

154

C₄₇

#10348

yes

characteristic, complemented, Sylow

155

C₂²×Q₈

—

156

C₂²×D₄

—

157

C₂²×D₄

—

158

C₂²×C₈

—

159

C₂²×C₈

—

160

C₄⋊Q₈

—

188

—

161

C₄⋊Q₈

—

188

—

162

#127

—

163

#127

—

164

#127

Dic₉₄

yes

complemented

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

C₂²⋊D₄₇

yes

—

170

C₂×C₄²

—

171

C₂×C₄²

C₂²×D₄₇

yes

characteristic

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#102

—

175

#102

—

188

—

176

#102

—

188

—

177

C₄×C₈

—

178

#95

—

179

#95

—

180

C₂⁴

—

181

C₂×Q₈

—

376

—

182

C₂×Q₈

—

188

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

D₄×D₄₇

yes

—

197

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

188

—

202

C₂×C₈

—

188

—

203

C₂×C₈

—

188

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₄⋊C₄

—

211

C₄⋊C₄

—

188

—

212

C₄²

—

188

—

213

C₄²

—

188

—

214

C₄²

C₂×Dic₉₄

yes

characteristic

215

C₄²

#10625350

yes

characteristic

216

C₄²

#10625352

yes

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

#13093992

yes

characteristic

223

Q₈

—

376

—

224

D₄

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

188

—

237

C₂×C₄

—

188

—

238

C₂×C₄

—

188

—

239

C₂×C₄

—

188

—

240

C₂×C₄

#13094001

yes

—

241

C₂×C₄

#13094003

yes

characteristic

242

C₂×C₄

#13094010

yes

—

243

C₂×C₄

#13094011

yes

characteristic

244

C₂×C₄

D₈×D₄₇

yes

—

245

C₂×C₄

SD₁₆×D₄₇

yes

—

246

C₂×C₄

#13094048

yes

—

247

C₂×C₄

#13094053

yes

—

248

C₈

—

249

C₈

—

376

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

#15689035

yes

characteristic

256

C₂²

#15689255

yes

—

257

C₂²

#15689260

yes

—

258

C₂²

#15689290

yes

characteristic

259

C₂²

#15689295

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

—

188

—

264

C₄

—

188

—

265

C₄

#15689401

yes

—

266

C₄

#15689411

yes

—

267

C₄

#15689468

yes

—

268

C₄

#15689481

yes

—

269

C₂

—

270

C₂

#20242440

yes

characteristic

271

C₂

#20242464

yes

characteristic

272

C₂

#20242488

yes

—

273

C₂

#20244522

yes

—

274

C₂

#20244544

yes

characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator, cosocle	C₂×C₄²×C₄₇	C₂³
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1957	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	#1957	D₄₇
hypocenter	C₄₇	#10348
LCS	G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1957

subgroup

G/H

center

C₂³

#13093992

commutator, cosocle

C₂×C₄²×C₄₇

C₂³

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1957

C₂

socle

C₂³×C₄₇

#120

prime radical

C₂×#127×C₄₇

C₂²

D₄₇

C₄₇

G ▷ C₂×C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1957

N	H ≅ G/N	type
1. #20248417	C₂	semidirect
3. #20241271	C₂	semidirect
4. #20241228	C₂	semidirect
36. #127×C₄₇	Q₈	semidirect
154. C₄₇	#10348	semidirect
164. #127	Dic₉₄	semidirect

H ≅ G/N

type

1. #20248417

C₂

semidirect

3. #20241271

C₂

semidirect

4. #20241228

C₂

semidirect

36. #127×C₄₇

Q₈

semidirect

154. C₄₇

#10348

semidirect

164. #127

Dic₉₄

semidirect

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

subgroup	index
#20248417	2
#20244316	2
#20241271	2
#20241228	2
C₄₇×#1957	2
#10348	47

subgroup

index

C₄₇×#1957

Subgroups — #26119286

Conjugacy classes of subgroups

Complements

Maximal subgroups