Group #26107233 — subgroups

Subgroups — #26107233

Order 12032.

684 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 173 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	#127×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20243243	C₂	1	2	yes	maximal, complemented
3	C₂×#15688867	C₂	1	1	yes	maximal, characteristic
4	#20241272	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#331	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×Dic₄₇	—	2	2	no	—
7	C₂×D₄×Dic₄₇	C₄	1	2	yes	—
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×#13093934	—	2	2	no	—
10	#15689026	—	2	2	no	—
11	#15689026	C₄	1	2	yes	—
12	#15688993	C₂²	1	1	yes	characteristic
13	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15688877	—	2	2	no	—
15	#15688867	C₄	1	4	yes	complemented
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#331	C₄	1	4	yes	complemented
19	C₂³×Dic₄₇	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	D₄×Dic₄₇	—	4	4	no	—
22	D₄×Dic₄₇	—	4	4	no	—
23	D₄×Dic₄₇	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
27	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
28	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
31	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
34	#13093934	—	4	4	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₄₇	—	2	2	no	—
38	#127×C₄₇	—	2	2	no	—
39	#127×C₄₇	C₂×C₄	1	2	yes	—
40	#127×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₄₇	—	2	2	no	—
43	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
44	C₂⁴×C₄₇	—	2	2	no	—
45	C₂×D₄×C₄₇	—	2	2	no	—
46	C₂×D₄×C₄₇	—	2	4	no	—
47	C₂×D₄×C₄₇	—	2	4	no	—
48	C₂×D₄×C₄₇	—	4	2	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	C₂×D₄×C₄₇	—	4	2	no	—
54	C₂×D₄×C₄₇	C₄²	1	4	yes	—
55	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
57	C₂²×Dic₄₇	—	2	2	no	—
58	C₂²×Dic₄₇	—	4	8	no	—
59	C₂²×Dic₄₇	—	4	4	no	—
60	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
62	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₄₇	—	2	4	no	—
64	C₂×C₈×C₄₇	—	4	2	no	—
65	C₂×C₈×C₄₇	—	4	2	no	—
66	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₄₇	#41	1	2	yes	—
69	C₂²⋊Dic₄₇	—	4	4	no	—
70	C₂²⋊Dic₄₇	—	4	8	no	—
71	C₄⋊Dic₄₇	—	4	2	no	—
72	C₄⋊Dic₄₇	—	4	2	no	—
73	C₄⋊Dic₄₇	—	4	2	no	—
74	C₄×Dic₄₇	—	2	2	no	—
75	C₄×Dic₄₇	—	2	2	no	—
76	C₄×Dic₄₇	—	2	2	no	—
77	C₄×Dic₄₇	—	2	2	no	—
78	C₄×Dic₄₇	—	2	2	no	—
79	C₄×Dic₄₇	—	4	1	no	—
80	C₂×C₄₇⋊C₈	—	2	4	no	—
81	C₂×C₄₇⋊C₈	—	4	2	no	—
82	C₂×C₄₇⋊C₈	—	4	2	no	—
83	C₂³×C₄₇	—	2	4	no	—
84	C₂³×C₄₇	—	4	2	no	—
85	C₂³×C₄₇	—	4	2	no	—
86	C₂³×C₄₇	—	4	4	no	—
87	C₂³×C₄₇	—	4	4	no	—
88	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	D₄×C₄₇	—	4	4	no	—
90	D₄×C₄₇	—	4	4	no	—
91	D₄×C₄₇	—	4	4	no	—
92	D₄×C₄₇	—	4	4	no	—
93	D₄×C₄₇	—	4	4	no	—
94	D₄×C₄₇	—	4	4	no	—
95	C₂×C₄×C₄₇	—	2	1	no	—
96	C₂×C₄×C₄₇	—	2	1	no	—
97	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
99	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
100	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
101	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
102	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
104	C₂×C₄×C₄₇	#137	1	2	yes	—
105	C₂×Dic₄₇	—	2	2	no	—
106	C₂×Dic₄₇	—	2	1	no	—
107	C₂×Dic₄₇	—	2	2	no	—
108	C₂×Dic₄₇	—	2	2	no	—
109	C₂×Dic₄₇	—	2	2	no	—
110	C₂×Dic₄₇	—	2	2	no	—
111	C₂×Dic₄₇	—	4	2	no	—
112	C₂×Dic₄₇	—	4	4	no	—
113	C₂×Dic₄₇	—	8	8	no	—
114	C₂×Dic₄₇	#100	1	2	yes	—
115	C₈×C₄₇	—	4	4	no	—
116	C₄₇⋊C₈	—	4	4	no	—
117	#8231	—	47	1	no	maximal, Sylow
118	C₂²×C₄₇	—	4	4	no	—
119	C₂²×C₄₇	—	4	8	no	—
120	C₂²×C₄₇	—	8	2	no	—
121	C₂²×C₄₇	—	8	4	no	—
122	C₂²×C₄₇	—	8	2	no	—
123	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
125	C₂²×C₄₇	#413	1	1	yes	characteristic
126	C₂²×C₄₇	#417	1	2	yes	—
127	C₂²×C₄₇	#418	1	2	yes	—
128	C₄×C₄₇	—	2	1	no	—
129	C₄×C₄₇	—	2	1	no	—
130	C₄×C₄₇	#440	1	2	yes	—
131	C₄×C₄₇	#440	1	2	yes	—
132	C₄×C₄₇	#442	1	2	yes	—
133	C₄×C₄₇	#442	1	2	yes	—
134	Dic₄₇	—	2	2	no	—
135	Dic₄₇	—	4	2	no	—
136	Dic₄₇	—	4	1	no	—
137	Dic₄₇	—	8	2	no	—
138	C₄×#127	—	47	1	no	—
139	#1767	—	47	2	no	—
140	C₂×#331	—	47	1	no	—
141	C₂×#331	D₄₇	1	1	yes	characteristic
142	#1296	—	47	2	no	—
143	C₂×C₄₇	—	8	4	no	—
144	C₂×C₄₇	#1555	1	1	yes	characteristic
145	C₂×C₄₇	#1557	1	2	yes	—
146	C₂×C₄₇	#1560	1	1	yes	characteristic
147	C₂×C₄₇	C₄×#100	1	1	yes	characteristic
148	C₂×C₄₇	#1762	1	2	yes	—
149	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
150	C₂×C₄×D₄	—	47	2	no	—
151	C₂×C₄×D₄	—	94	2	no	—
152	C₂×C₄⋊C₈	—	47	2	no	—
153	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
154	C₂×#97	—	94	2	no	—
155	#390	—	47	2	no	—
156	#390	—	94	2	no	—
157	#384	—	47	1	no	—
158	C₄³	—	47	1	no	—
159	#336	—	94	2	no	—
160	#331	—	47	4	no	—
161	#331	Dic₄₇	1	4	yes	complemented
162	C₄₇	#8231	1	1	yes	characteristic, complemented, Sylow
163	C₂²×D₄	—	2	2	no	—
164	C₂²×D₄	C₄×D₄₇	1	2	yes	—
165	C₂³×C₄	—	94	2	no	—
166	C₂²×C₈	—	2	2	no	—
167	C₂²×C₈	—	94	2	no	—
168	#127	—	2	2	no	—
169	#127	C₄×D₄₇	1	2	yes	—
170	#127	C₂×Dic₄₇	1	2	yes	—
171	C₄×D₄	—	188	4	no	—
172	C₄×D₄	—	188	4	no	—
173	C₄×D₄	—	188	4	no	—
174	C₂×C₄⋊C₄	—	47	2	no	—
175	C₂×C₄⋊C₄	—	94	2	no	—
176	C₂×C₂²⋊C₄	—	94	2	no	—
177	C₂×C₂²⋊C₄	—	94	4	no	—
178	C₂×C₄²	—	47	1	no	—
179	C₂×C₄²	—	47	2	no	—
180	C₂×C₄²	—	47	2	no	—
181	C₂×C₄²	—	47	1	no	—
182	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
183	C₄⋊C₈	—	2	2	no	—
184	C₄⋊C₈	—	47	4	no	—
185	C₄⋊C₈	—	94	2	no	—
186	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
187	#97	—	188	4	no	—
188	C₂⁴	—	2	2	no	—
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	2	4	no	—
191	C₂×D₄	—	2	4	no	—
192	C₂×D₄	—	4	2	no	—
193	C₂×D₄	—	4	2	no	—
194	C₂×D₄	—	4	2	no	—
195	C₂×D₄	—	4	2	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂×D₄	—	4	2	no	—
198	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
199	C₂²×C₄	—	47	1	no	—
200	C₂²×C₄	—	47	1	no	—
201	C₂²×C₄	—	47	2	no	—
202	C₂²×C₄	—	94	2	no	—
203	C₂²×C₄	—	188	4	no	—
204	C₂²×C₄	—	188	8	no	—
205	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
206	C₂²×C₄	D₄×D₄₇	1	2	yes	—
207	C₂×C₈	—	2	4	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	—	94	4	no	—
211	C₂×C₈	—	188	2	no	—
212	C₂×C₈	—	188	2	no	—
213	C₄⋊C₄	—	188	2	no	—
214	C₄⋊C₄	—	188	2	no	—
215	C₄⋊C₄	—	188	2	no	—
216	C₂²⋊C₄	—	188	4	no	—
217	C₂²⋊C₄	—	188	8	no	—
218	C₄²	—	94	2	no	—
219	C₄²	—	94	2	no	—
220	C₄²	—	94	2	no	—
221	C₄²	—	94	2	no	—
222	C₄²	—	94	2	no	—
223	C₄²	—	188	1	no	—
224	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
225	C₄²	#10625352	1	2	yes	—
226	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
227	C₂³	—	2	4	no	—
228	C₂³	—	4	2	no	—
229	C₂³	—	4	2	no	—
230	C₂³	—	4	4	no	—
231	C₂³	—	4	4	no	—
232	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
233	D₄	—	4	4	no	—
234	D₄	—	4	4	no	—
235	D₄	—	4	4	no	—
236	D₄	—	4	4	no	—
237	D₄	—	4	4	no	—
238	D₄	—	4	4	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	47	2	no	—
242	C₂×C₄	—	94	2	no	—
243	C₂×C₄	—	94	1	no	—
244	C₂×C₄	—	94	2	no	—
245	C₂×C₄	—	94	2	no	—
246	C₂×C₄	—	94	2	no	—
247	C₂×C₄	—	94	2	no	—
248	C₂×C₄	—	376	8	no	—
249	C₂×C₄	—	188	2	no	—
250	C₂×C₄	—	188	4	no	—
251	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
252	C₂×C₄	#13093980	1	1	yes	characteristic
253	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
254	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
255	C₂×C₄	#13094048	1	2	yes	—
256	C₂×C₄	#13094048	1	2	yes	—
257	C₂×C₄	#13094051	1	2	yes	—
258	C₂×C₄	#13094053	1	2	yes	—
259	C₈	—	4	4	no	—
260	C₈	—	188	4	no	—
261	C₂²	—	4	8	no	—
262	C₂²	—	4	4	no	—
263	C₂²	—	8	2	no	—
264	C₂²	—	8	4	no	—
265	C₂²	—	8	2	no	—
266	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
267	C₂²	#100×D₄₇	1	1	yes	characteristic
268	C₂²	#15689104	1	1	yes	characteristic
269	C₂²	#15689121	1	2	yes	—
270	C₂²	#15689126	1	2	yes	—
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	94	2	no	—
274	C₄	—	376	2	no	—
275	C₄	—	188	2	no	—
276	C₄	—	188	1	no	—
277	C₄	#15689220	1	2	yes	—
278	C₄	#15689224	1	2	yes	—
279	C₄	#15689232	1	2	yes	—
280	C₄	#15689235	1	2	yes	—
281	C₂	—	8	4	no	—
282	C₂	#20242100	1	1	yes	characteristic
283	C₂	#20242107	1	2	yes	—
284	C₂	#20242120	1	1	yes	characteristic
285	C₂	#100×Dic₄₇	1	1	yes	characteristic
286	C₂	#20243215	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#127×Dic₄₇

C₂

yes

maximal, characteristic

#20243243

C₂

yes

maximal, complemented

C₂×#15688867

C₂

yes

maximal, characteristic

#20241272

C₂

yes

maximal, complemented

C₂×C₄₇×#331

C₂

yes

maximal, characteristic

C₂×D₄×Dic₄₇

—

C₂×D₄×Dic₄₇

C₄

yes

—

C₂×C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

C₂×#13093934

—

#15689026

—

#15689026

C₄

yes

—

#15688993

C₂²

yes

characteristic

C₄²×Dic₄₇

C₂²

yes

characteristic

#15688877

—

#15688867

C₄

yes

complemented

C₂×#127×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#331

C₄

yes

complemented

C₂³×Dic₄₇

—

C₂²×C₄₇⋊C₈

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

D₄×Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂×C₄

yes

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₂²⋊Dic₄₇

—

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₄₇

D₄

yes

—

C₂×C₄×Dic₄₇

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

C₂×C₄

yes

complemented

#13093934

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

#127×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂×C₄

yes

complemented

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

C₄²

yes

—

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₇

C₂²⋊C₄

yes

—

C₂²×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

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

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₇

#117

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

100

C₂×C₄×C₄₇

C₄×D₄

yes

—

101

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

102

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

104

C₂×C₄×C₄₇

#137

yes

—

105

C₂×Dic₄₇

—

106

C₂×Dic₄₇

—

107

C₂×Dic₄₇

—

108

C₂×Dic₄₇

—

109

C₂×Dic₄₇

—

110

C₂×Dic₄₇

—

111

C₂×Dic₄₇

—

112

C₂×Dic₄₇

—

113

C₂×Dic₄₇

—

114

C₂×Dic₄₇

#100

yes

—

115

C₈×C₄₇

—

116

C₄₇⋊C₈

—

117

#8231

—

maximal, Sylow

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

C₄×C₂²⋊C₄

yes

characteristic

124

C₂²×C₄₇

C₂×#100

yes

characteristic

125

C₂²×C₄₇

#413

yes

characteristic

126

C₂²×C₄₇

#417

yes

—

127

C₂²×C₄₇

#418

yes

—

128

C₄×C₄₇

—

129

C₄×C₄₇

—

130

C₄×C₄₇

#440

yes

—

131

C₄×C₄₇

#440

yes

—

132

C₄×C₄₇

#442

yes

—

133

C₄×C₄₇

#442

yes

—

134

Dic₄₇

—

135

Dic₄₇

—

136

Dic₄₇

—

137

Dic₄₇

—

138

C₄×#127

—

139

#1767

—

140

C₂×#331

—

141

C₂×#331

D₄₇

yes

characteristic

142

#1296

—

143

C₂×C₄₇

—

144

C₂×C₄₇

#1555

yes

characteristic

145

C₂×C₄₇

#1557

yes

—

146

C₂×C₄₇

#1560

yes

characteristic

147

C₂×C₄₇

C₄×#100

yes

characteristic

148

C₂×C₄₇

#1762

yes

—

149

C₂×#127

C₂×D₄₇

yes

characteristic

150

C₂×C₄×D₄

—

151

C₂×C₄×D₄

—

152

C₂×C₄⋊C₈

—

153

C₂×C₄⋊C₈

C₂×D₄₇

yes

—

154

C₂×#97

—

155

#390

—

156

#390

—

157

#384

—

158

C₄³

—

159

#336

—

160

#331

—

161

#331

Dic₄₇

yes

complemented

162

C₄₇

#8231

yes

characteristic, complemented, Sylow

163

C₂²×D₄

—

164

C₂²×D₄

C₄×D₄₇

yes

—

165

C₂³×C₄

—

166

C₂²×C₈

—

167

C₂²×C₈

—

168

#127

—

169

#127

C₄×D₄₇

yes

—

170

#127

C₂×Dic₄₇

yes

—

171

C₄×D₄

—

188

—

172

C₄×D₄

—

188

—

173

C₄×D₄

—

188

—

174

C₂×C₄⋊C₄

—

175

C₂×C₄⋊C₄

—

176

C₂×C₂²⋊C₄

—

177

C₂×C₂²⋊C₄

—

178

C₂×C₄²

—

179

C₂×C₄²

—

180

C₂×C₄²

—

181

C₂×C₄²

—

182

C₂×C₄²

C₂²×D₄₇

yes

characteristic

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

C₄⋊C₈

C₂×Dic₄₇

yes

complemented

187

#97

—

188

—

188

C₂⁴

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

C₄×Dic₄₇

yes

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

188

—

204

C₂²×C₄

—

188

—

205

C₂²×C₄

C₂×C₄×D₄₇

yes

characteristic

206

C₂²×C₄

D₄×D₄₇

yes

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

188

—

212

C₂×C₈

—

188

—

213

C₄⋊C₄

—

188

—

214

C₄⋊C₄

—

188

—

215

C₄⋊C₄

—

188

—

216

C₂²⋊C₄

—

188

—

217

C₂²⋊C₄

—

188

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

223

C₄²

—

188

—

224

C₄²

C₂×C₄×D₄₇

yes

characteristic

225

C₄²

#10625352

yes

—

226

C₄²

C₂²×Dic₄₇

yes

characteristic

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

C₂²⋊C₄×D₄₇

yes

characteristic

233

D₄

—

234

D₄

—

235

D₄

—

236

D₄

—

237

D₄

—

238

D₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

376

—

249

C₂×C₄

—

188

—

250

C₂×C₄

—

188

—

251

C₂×C₄

C₂×C₄×Dic₄₇

yes

characteristic

252

C₂×C₄

#13093980

yes

characteristic

253

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

254

C₂×C₄

D₄×Dic₄₇

yes

—

255

C₂×C₄

#13094048

yes

—

256

C₂×C₄

#13094048

yes

—

257

C₂×C₄

#13094051

yes

—

258

C₂×C₄

#13094053

yes

—

259

C₈

—

260

C₈

—

188

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

C₂²⋊C₄×Dic₄₇

yes

characteristic

267

C₂²

#100×D₄₇

yes

characteristic

268

C₂²

#15689104

yes

characteristic

269

C₂²

#15689121

yes

—

270

C₂²

#15689126

yes

—

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

376

—

275

C₄

—

188

—

276

C₄

—

188

—

277

C₄

#15689220

yes

—

278

C₄

#15689224

yes

—

279

C₄

#15689232

yes

—

280

C₄

#15689235

yes

—

281

C₂

—

282

C₂

#20242100

yes

characteristic

283

C₂

#20242107

yes

—

284

C₂

#20242120

yes

characteristic

285

C₂

#100×Dic₄₇

yes

characteristic

286

C₂

#20243215

yes

—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#331	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#331	D₄₇
hypocenter	C₄₇	#8231
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

subgroup

G/H

center

C₂³

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₂×C₄₇×#331

C₂

socle

C₂³×C₄₇

C₂×C₂²⋊C₄

prime radical

C₂×#127×C₄₇

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#331

N	H ≅ G/N	type
2. #20243243	C₂	semidirect
4. #20241272	C₂	semidirect
15. #15688867	C₄	semidirect
18. C₄₇×#331	C₄	semidirect
33. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
43. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
161. #331	Dic₄₇	semidirect
162. C₄₇	#8231	semidirect
186. C₄⋊C₈	C₂×Dic₄₇	semidirect

H ≅ G/N

type

2. #20243243

C₂

semidirect

4. #20241272

C₂

semidirect

15. #15688867

C₄

semidirect

18. C₄₇×#331

C₄

semidirect

33. C₄⋊(C₄₇⋊C₈)

C₂×C₄

semidirect

43. C₄⋊C₈×C₄₇

C₂×C₄

semidirect

161. #331

Dic₄₇

semidirect

162. C₄₇

#8231

semidirect

186. C₄⋊C₈

C₂×Dic₄₇

semidirect

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

subgroup	index
#127×Dic₄₇	2
#20243243	2
C₂×#15688867	2
#20241272	2
C₂×C₄₇×#331	2
#8231	47

subgroup

index

#127×Dic₄₇

C₂×C₄₇×#331

Subgroups — #26107233

Conjugacy classes of subgroups

Complements

Maximal subgroups