Subgroups — C₂×#20241952 #26183622

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688989	C₂	1	1	yes	maximal, characteristic
3	#20241952	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688860	C₂	1	4	yes	maximal
5	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	#15689176	—	2	2	no	—
8	#15689176	C₂²	1	4	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
12	#15688989	—	2	2	no	—
13	#15688989	C₂²	1	4	yes	—
14	C₂×C₄₇⋊#95	—	2	1	no	—
15	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
16	#15688860	C₂²	1	16	yes	—
17	C₄₇×#533	—	2	2	no	—
18	C₄₇×#533	—	2	2	no	—
19	C₄₇×#533	C₄	1	4	yes	complemented
20	C₄₇×#533	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₂×#125×C₄₇	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
27	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	complemented
28	C₂×#117×C₄₇	—	2	1	no	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×Dic₄₇	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	4	4	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
35	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
37	C₄×C₄₇⋊C₈	—	2	4	no	—
38	C₄₇⋊#95	—	2	4	no	—
39	C₄₇⋊#95	—	2	2	no	—
40	C₄₇⋊#95	C₂³	1	4	yes	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
49	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
50	#125×C₄₇	—	2	4	no	—
51	#125×C₄₇	—	2	4	no	—
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	2	no	—
55	C₂²⋊Q₈×C₄₇	—	2	2	no	—
56	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
57	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
58	C₄×Q₈×C₄₇	—	2	4	no	—
59	C₄×Q₈×C₄₇	—	2	4	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	4	4	no	—
84	C₂×Q₈×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
97	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	—	4	4	no	—
108	C₂²×Dic₄₇	—	4	4	no	—
109	C₂²×Dic₄₇	—	4	4	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	8	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	2	4	no	—
120	C₄²×C₄₇	—	2	8	no	—
121	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	2	yes	—
129	C₄⋊Dic₄₇	—	4	8	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
137	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₇	—	4	4	no	—
140	Q₈×C₄₇	—	4	4	no	—
141	Q₈×C₄₇	—	4	8	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	1	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	#103	1	8	yes	—
157	C₂×C₄×C₄₇	#103	1	4	yes	—
158	C₂×C₄×C₄₇	#103	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
166	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×Dic₄₇	—	4	4	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	4	4	no	—
172	C₂×Dic₄₇	—	8	8	no	—
173	C₄₇⋊C₈	—	4	4	no	—
174	C₂×#1518	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	#410	1	2	yes	—
182	C₂²×C₄₇	C₂×#103	1	2	yes	—
183	C₂²×C₄₇	C₂×#103	1	2	yes	—
184	C₂²×C₄₇	#421	1	2	yes	—
185	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
187	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	C₂×#103	1	4	yes	—
197	C₄×C₄₇	C₂×#103	1	4	yes	—
198	Dic₄₇	—	8	4	no	—
199	C₂×#533	D₄₇	1	1	yes	characteristic
200	C₂×#431	—	47	1	no	—
201	C₂×#382	—	47	1	no	—
202	#1518	—	47	8	no	—
203	C₂×#328	—	47	4	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	2	2	no	—
207	C₂×C₄₇	#1518	1	4	yes	complemented
208	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
209	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
211	#533	—	2	2	no	—
212	#533	—	2	2	no	—
213	#533	Dic₄₇	1	4	yes	complemented
214	#533	C₂×D₄₇	1	4	yes	—
215	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
216	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
217	C₂×#125	—	2	1	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
220	C₂×C₄×Q₈	—	2	1	no	—
221	C₂×C₄×Q₈	Dic₄₇	1	2	yes	complemented
222	C₂×#117	—	2	1	no	—
223	C₂²×C₄⋊C₄	—	94	1	no	—
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	#431	—	47	4	no	—
226	#431	—	94	2	no	—
227	C₂×C₄⋊C₈	—	94	1	no	—
228	C₂×C₂²⋊C₈	—	47	2	no	—
229	C₂×C₄×C₈	—	94	1	no	—
230	#382	—	47	4	no	—
231	#382	—	94	2	no	—
232	C₂×#95	—	47	2	no	—
233	C₂×#95	—	94	1	no	—
234	#328	—	47	16	no	—
235	C₄₇	C₂×#1518	1	1	yes	characteristic, complemented, Sylow
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
238	C₂³×C₄	—	94	2	no	—
239	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂²×C₈	—	94	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
246	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
247	#125	—	2	4	no	—
248	#125	—	2	4	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
254	C₂²⋊Q₈	C₂²×D₄₇	1	4	yes	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
259	#117	—	2	4	no	—
260	#117	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	94	4	no	—
267	C₂×C₄⋊C₄	—	188	4	no	—
268	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
272	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
274	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
275	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
278	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
279	C₄⋊C₈	—	94	4	no	—
280	C₂²⋊C₈	—	47	4	no	—
281	C₂²⋊C₈	—	94	2	no	—
282	C₄×C₈	—	94	4	no	—
283	#95	—	47	4	no	—
284	#95	—	94	2	no	—
285	#95	—	94	4	no	—
286	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	94	4	no	—
297	C₂²×C₄	—	188	4	no	—
298	C₂²×C₄	—	188	4	no	—
299	C₂²×C₄	—	188	4	no	—
300	C₂²×C₄	#10625336	1	4	yes	—
301	C₂²×C₄	#10625337	1	4	yes	—
302	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
305	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
306	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
315	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	—	188	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	188	8	no	—
326	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₄²	—	2	8	no	—
330	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
331	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
332	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
333	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
334	C₄²	C₂²×Dic₄₇	1	2	yes	—
335	C₄²	C₂²×Dic₄₇	1	2	yes	—
336	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
337	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
341	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
342	C₂³	C₂×#10625336	1	2	yes	—
343	C₂³	C₂×#10625337	1	2	yes	—
344	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
345	Q₈	—	4	4	no	—
346	Q₈	—	4	8	no	—
347	Q₈	—	4	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	376	8	no	—
363	C₂×C₄	—	188	4	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	4	no	—
366	C₂×C₄	#13093948	1	8	yes	—
367	C₂×C₄	#13093948	1	4	yes	—
368	C₂×C₄	#13093948	1	4	yes	—
369	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
373	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
375	C₂×C₄	C₂×#10625336	1	4	yes	—
376	C₂×C₄	C₂×#10625337	1	4	yes	—
377	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₈	—	188	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	#15689097	1	2	yes	—
387	C₂²	C₂×#13093948	1	2	yes	—
388	C₂²	C₂×#13093948	1	2	yes	—
389	C₂²	#15689140	1	2	yes	—
390	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
391	C₂²	C₂²×#10625336	1	1	yes	characteristic
392	C₂²	C₂²×#10625337	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	4	4	no	—
400	C₄	—	4	4	no	—
401	C₄	—	376	4	no	—
402	C₄	C₂×#13093948	1	4	yes	—
403	C₄	C₂×#13093948	1	4	yes	—
404	C₂	—	2	1	no	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	#20241952	1	4	yes	direct product factor
408	C₂	C₂×#15689097	1	1	yes	characteristic
409	C₂	C₂²×#13093948	1	1	yes	characteristic
410	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#1518
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20241952	C₂	direct (N × H)
19. C₄₇×#533	C₄	semidirect
21. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
22. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
27. C₂×C₄×Q₈×C₄₇	C₄	semidirect
48. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
49. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
61. C₄×Q₈×C₄₇	C₂×C₄	semidirect
207. C₂×C₄₇	#1518	semidirect
213. #533	Dic₄₇	semidirect
215. C₂×C₄⋊Q₈	Dic₄₇	semidirect
216. C₂×C₄⋊Q₈	Dic₄₇	semidirect
221. C₂×C₄×Q₈	Dic₄₇	semidirect
235. C₄₇	C₂×#1518	semidirect
245. C₄⋊Q₈	C₂×Dic₄₇	semidirect
246. C₄⋊Q₈	C₂×Dic₄₇	semidirect
258. C₄×Q₈	C₂×Dic₄₇	semidirect
407. C₂	#20241952	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
C₂×#15688989	2
#20241952	2
C₂×#15688860	2
C₂×C₄₇×#533	2
C₂×#1518	47

Subgroups — C2×#20241952 #26183622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241952 #26183622