Subgroups — #26106530

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#20241284	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	—	2	1	no	—
6	#15689180	—	2	1	no	—
7	#15689180	C₄	1	2	yes	—
8	#15689176	—	2	1	no	—
9	#15689176	C₄	1	2	yes	—
10	#15689147	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	#15689087	—	2	1	no	—
18	C₄×#10625329	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#432	—	2	1	no	—
21	C₄₇×#432	C₄	1	2	yes	—
22	C₄₇×#431	—	2	1	no	—
23	C₄₇×#431	C₂²	1	2	yes	—
24	C₄₇×#423	—	2	1	no	—
25	C₄₇×#407	C₄	1	2	yes	—
26	C₄×M₁₆×C₄₇	—	2	1	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	4	4	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
37	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
40	#13093935	—	2	2	no	—
41	C₄×C₄₇⋊C₈	—	2	2	no	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₄₇	—	2	2	no	—
59	C₄⋊C₈×C₄₇	—	2	2	no	—
60	C₂²⋊C₈×C₄₇	—	2	2	no	—
61	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
62	#97×C₄₇	—	2	2	no	—
63	C₄×C₈×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	—	2	4	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	4	2	no	—
69	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
87	M₁₆×C₄₇	—	4	4	no	—
88	C₂×C₈×C₄₇	—	2	4	no	—
89	C₄²×C₄₇	C₄²	1	1	yes	characteristic
90	C₄²×C₄₇	C₄²	1	1	yes	characteristic
91	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
105	#10625329	—	4	2	no	—
106	#10625329	—	4	2	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	4	4	no	—
110	C₂×C₄₇⋊C₈	—	4	4	no	—
111	C₂×C₄₇⋊C₈	—	4	4	no	—
112	C₂³×C₄₇	—	2	2	no	—
113	C₂³×C₄₇	—	2	2	no	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	#95	1	1	yes	characteristic
116	C₂³×C₄₇	#95	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₄₇	—	2	2	no	—
119	C₂×C₄×C₄₇	—	2	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	2	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	4	1	no	—
133	C₂×C₄×C₄₇	—	4	1	no	—
134	C₂×C₄×C₄₇	—	4	1	no	—
135	C₂×C₄×C₄₇	—	4	1	no	—
136	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
137	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#108	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₄₇	#137	1	2	yes	—
151	C₈×C₄₇	—	4	4	no	—
152	C₄₇⋊C₈	—	4	4	no	—
153	C₄₇⋊C₈	—	4	4	no	—
154	#8082	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	1	no	—
157	C₂²×C₄₇	—	2	1	no	—
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	#341	1	2	yes	—
163	C₂²×C₄₇	#344	1	2	yes	—
164	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
165	C₂²×C₄₇	#428	1	2	yes	—
166	C₄×C₄₇	—	2	1	no	—
167	C₄×C₄₇	—	2	1	no	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	—	2	1	no	—
171	C₄×C₄₇	—	2	1	no	—
172	C₄×C₄₇	—	2	1	no	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	#341	1	2	yes	—
175	C₄×C₄₇	#417	1	2	yes	—
176	C₄×C₄₇	#418	1	1	yes	characteristic
177	C₄×C₄₇	#419	1	1	yes	characteristic
178	C₄×C₄₇	C₂×#108	1	2	yes	—
179	#2920	—	47	1	no	—
180	#2920	D₄₇	1	1	yes	characteristic
181	C₂²×C₄⋊C₈	—	47	1	no	—
182	#1301	—	47	4	no	—
183	C₂×C₄₇	—	2	2	no	—
184	C₂×C₄₇	—	2	2	no	—
185	C₂×C₄₇	—	2	2	no	—
186	C₂×C₄₇	#1736	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#341	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
189	C₂³×C₈	—	94	1	no	—
190	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
191	#432	—	2	1	no	—
192	#432	—	47	2	no	—
193	#432	—	94	1	no	—
194	#432	Dic₄₇	1	2	yes	—
195	#431	—	2	1	no	—
196	#431	—	47	2	no	—
197	#431	—	94	1	no	—
198	#431	C₂×D₄₇	1	2	yes	—
199	#423	—	2	1	no	—
200	#423	—	47	2	no	—
201	C₂×C₄⋊C₈	—	47	2	no	—
202	C₂×C₄⋊C₈	—	47	2	no	—
203	C₂×C₄⋊C₈	—	47	2	no	—
204	C₂×C₄⋊C₈	—	94	1	no	—
205	C₂×C₄⋊C₈	—	94	1	no	—
206	C₂×C₄⋊C₈	—	94	1	no	—
207	#407	—	94	1	no	—
208	#407	Dic₄₇	1	2	yes	—
209	C₄×M₁₆	—	2	1	no	—
210	C₄×M₁₆	—	94	1	no	—
211	C₄₇	#8082	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
213	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
214	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	94	2	no	—
217	C₂²×C₈	—	94	2	no	—
218	C₂²×C₈	—	94	2	no	—
219	C₂²×C₈	—	94	2	no	—
220	C₂²×C₈	—	188	4	no	—
221	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
226	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
228	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	47	4	no	—
236	C₄⋊C₈	—	47	4	no	—
237	C₄⋊C₈	—	94	2	no	—
238	C₄⋊C₈	—	94	2	no	—
239	C₄⋊C₈	—	94	2	no	—
240	C₄⋊C₈	—	94	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	C₂²⋊C₈	—	94	2	no	—
243	C₂²⋊C₈	—	94	2	no	—
244	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
245	#97	—	2	2	no	—
246	#97	—	94	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	94	2	no	—
249	C₂⁴	C₄⋊Dic₄₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
256	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
272	M₁₆	—	4	4	no	—
273	M₁₆	—	188	2	no	—
274	M₁₆	—	188	2	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	94	4	no	—
277	C₂×C₈	—	94	4	no	—
278	C₂×C₈	—	188	4	no	—
279	C₂×C₈	—	188	4	no	—
280	C₂×C₈	—	188	4	no	—
281	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
282	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
283	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
284	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
287	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
288	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
289	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
290	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
291	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
292	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	C₄₇⋊#95	1	1	yes	characteristic
301	C₂³	C₄₇⋊#95	1	1	yes	characteristic
302	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
324	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
325	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
327	C₂×C₄	#13093959	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
334	C₂×C₄	#13094052	1	2	yes	—
335	C₂×C₄	#13094057	1	2	yes	—
336	C₈	—	4	4	no	—
337	C₈	—	188	4	no	—
338	C₈	—	188	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	#15688887	1	2	yes	—
347	C₂²	#15688893	1	2	yes	—
348	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
349	C₂²	#15689165	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	#15688887	1	2	yes	—
359	C₄	#15689125	1	2	yes	—
360	C₄	#15689129	1	1	yes	characteristic
361	C₄	#15689133	1	1	yes	characteristic
362	C₄	C₂×#13093959	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	#20243108	1	1	yes	characteristic
367	C₂	C₂×#15688887	1	1	yes	characteristic
368	C₂	C₂×#15688893	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂⁴×C₄₇	C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#8082
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #20241284	C₂	semidirect
211. C₄₇	#8082	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
#20241284	2
C₄₇×#2920	2
#8082	47