Subgroups — C₂×#20252411 #27080999

Order 12032.

2890 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#20252411	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₈×D₁₈₈	C₂	1	4	yes	maximal, complemented
4	C₂×#15689188	C₂	1	4	yes	maximal, complemented
5	C₂×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊C₈×D₄₇	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₈₈	C₄	1	1	yes	characteristic
9	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
10	C₂²×C₈×D₄₇	C₂²	1	8	yes	complemented
11	C₂×C₄×D₁₈₈	C₄	1	2	yes	—
12	C₂×C₄×D₁₈₈	C₄	1	2	yes	—
13	C₂×C₄×D₁₈₈	C₄	1	8	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
15	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
16	C₂×C₄×D₁₈₈	C₂²	1	8	yes	—
17	C₂²×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
18	C₂²×(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
19	C₈×D₁₈₈	C₂²	1	32	yes	complemented
20	#15689188	C₂²	1	32	yes	complemented
21	#15689176	C₂²	1	8	yes	complemented
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	8	yes	complemented
25	C₂²⋊C₈×D₄₇	C₂²	1	32	yes	complemented
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#431	C₂²	1	8	yes	complemented
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
32	C₂⁴×D₄₇	C₂×C₄	1	2	yes	—
33	C₂²×D₁₈₈	C₈	1	16	yes	complemented
34	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
35	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
36	C₂²×D₁₈₈	C₂×C₄	1	8	yes	—
37	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
38	C₂²×C₄×D₄₇	—	4	8	no	—
39	C₂²×C₄×D₄₇	C₂×C₄	1	8	yes	—
40	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
41	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
42	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
44	C₂×C₈×D₄₇	—	4	16	no	—
45	C₂×C₈×D₄₇	C₂³	1	32	yes	complemented
46	C₄×D₁₈₈	C₂×C₄	1	8	yes	—
47	C₄×D₁₈₈	C₂×C₄	1	8	yes	—
48	C₄×D₁₈₈	C₂×C₄	1	16	yes	—
49	C₄×D₁₈₈	C₂×C₄	1	16	yes	—
50	C₄×D₁₈₈	C₂³	1	8	yes	—
51	C₄×D₁₈₈	C₂³	1	8	yes	—
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
56	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	16	yes	—
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	complemented
59	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
60	(C₂×D₄₇)⋊C₈	C₂³	1	32	yes	complemented
61	C₄×C₄₇⋊C₈	C₂³	1	8	yes	complemented
62	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
72	C₄⋊C₈×C₄₇	C₂³	1	8	yes	complemented
73	C₂²⋊C₈×C₄₇	C₂³	1	8	yes	—
74	C₄×C₈×C₄₇	C₂³	1	8	yes	complemented
75	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂³×D₄₇	—	4	4	no	—
77	C₂³×D₄₇	—	4	4	no	—
78	C₂³×D₄₇	C₂×C₈	1	16	yes	complemented
79	C₂³×D₄₇	C₂²×C₄	1	4	yes	—
80	C₂³×D₄₇	C₂²×C₄	1	8	yes	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	complemented
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	4	4	no	—
95	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
97	C₂×D₁₈₈	C₂×C₈	1	16	yes	complemented
98	C₂×D₁₈₈	C₂×C₈	1	16	yes	complemented
99	C₂×D₁₈₈	C₂×C₈	1	64	yes	complemented
100	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
101	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
102	C₂×C₄×D₄₇	—	2	16	no	—
103	C₂×C₄×D₄₇	—	4	16	no	—
104	C₂×C₄×D₄₇	—	4	16	no	—
105	C₂×C₄×D₄₇	—	4	8	no	—
106	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
107	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
108	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
109	C₂×C₈×C₄₇	—	2	8	no	—
110	C₂×C₈×C₄₇	C₂⁴	1	8	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	C₂⁴	1	2	yes	—
116	C₄²×C₄₇	C₂⁴	1	2	yes	—
117	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
118	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
119	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
121	C₂×C₄₇⋊C₈	—	2	8	no	—
122	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
123	C₈×D₄₇	—	4	32	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
127	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
128	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	8	no	—
130	C₂²×D₄₇	—	2	8	no	—
131	C₂²×D₄₇	—	4	8	no	—
132	C₂²×D₄₇	—	4	32	no	—
133	C₂²×D₄₇	—	4	8	no	—
134	C₂²×D₄₇	C₂²×C₈	1	16	yes	—
135	C₂²×D₄₇	C₂²×C₈	1	32	yes	complemented
136	C₂²×D₄₇	C₂³×C₄	1	8	yes	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×C₈	1	16	yes	complemented
146	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
153	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	4	8	no	—
156	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
157	D₁₈₈	C₂²×C₈	1	32	yes	complemented
158	D₁₈₈	C₂²×C₈	1	32	yes	complemented
159	C₄×D₄₇	—	2	16	no	—
160	C₄×D₄₇	—	2	16	no	—
161	C₄×D₄₇	—	4	16	no	—
162	C₈×C₄₇	—	2	8	no	—
163	C₄₇⋊C₈	—	2	8	no	—
164	C₂×#2972	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	8	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	#518	1	2	yes	—
169	C₂²×C₄₇	C₂³×C₈	1	4	yes	—
170	C₂²×C₄₇	C₂³×C₈	1	2	yes	—
171	C₂²×C₄₇	#568	1	2	yes	—
172	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
173	C₂×D₄₇	—	2	8	no	—
174	C₂×D₄₇	—	2	32	no	—
175	C₂×D₄₇	—	2	8	no	—
176	C₂×D₄₇	—	4	32	no	—
177	C₂×D₄₇	C₂³×C₈	1	16	yes	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	#518	1	2	yes	—
182	C₄×C₄₇	C₂³×C₈	1	4	yes	—
183	C₄×C₄₇	C₂³×C₈	1	4	yes	—
184	C₄×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
185	Dic₄₇	—	2	8	no	—
186	C₂²×C₄×D₄	—	47	1	no	—
187	#2972	—	47	16	no	—
188	C₂×C₈×D₄	—	47	4	no	—
189	C₂×C₈×D₄	—	47	4	no	—
190	C₂×#431	—	47	1	no	—
191	C₂×#431	D₄₇	1	1	yes	characteristic, complemented
192	C₂²×C₂²⋊C₈	—	47	4	no	—
193	C₂×C₄₇	—	2	4	no	—
194	C₂×C₄₇	#2972	1	4	yes	complemented
195	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
196	C₂×C₄₇	C₂⁴×C₈	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
198	D₄₇	—	2	16	no	—
199	C₂³×D₄	—	47	1	no	—
200	C₂⁴×C₄	—	47	2	no	—
201	C₂³×C₈	—	47	8	no	—
202	C₂×C₄×D₄	—	47	2	no	—
203	C₂×C₄×D₄	—	47	2	no	—
204	C₂×C₄×D₄	—	47	8	no	—
205	C₂×C₄×D₄	—	47	2	no	—
206	C₂×C₄×D₄	—	47	2	no	—
207	C₂×C₄×D₄	—	47	8	no	—
208	C₂²×C₄⋊C₄	—	47	1	no	—
209	C₂²×C₂²⋊C₄	—	47	2	no	—
210	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
211	C₈×D₄	—	47	32	no	—
212	C₈×D₄	—	47	32	no	—
213	#431	—	47	8	no	—
214	#431	C₂×D₄₇	1	8	yes	complemented
215	C₂×C₄⋊C₈	—	47	2	no	—
216	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	complemented
217	C₂×C₂²⋊C₈	—	47	2	no	—
218	C₂×C₂²⋊C₈	—	47	8	no	—
219	C₂×C₂²⋊C₈	—	47	32	no	—
220	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
221	C₂×C₄×C₈	—	47	2	no	—
222	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	complemented
223	C₄₇	C₂×#2972	1	1	yes	characteristic, complemented, Sylow
224	C₂⁵	—	47	2	no	—
225	C₂²×D₄	—	47	16	no	—
226	C₂²×D₄	—	47	2	no	—
227	C₂²×D₄	—	47	2	no	—
228	C₂²×D₄	—	47	8	no	—
229	C₂³×C₄	—	47	2	no	—
230	C₂³×C₄	—	47	4	no	—
231	C₂³×C₄	—	47	4	no	—
232	C₂³×C₄	—	47	8	no	—
233	C₂³×C₄	—	47	8	no	—
234	C₂³×C₄	—	188	8	no	—
235	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
236	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂²×C₈	—	47	4	no	—
239	C₂²×C₈	—	47	32	no	—
240	C₂²×C₈	—	188	16	no	—
241	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
242	C₄×D₄	—	47	8	no	—
243	C₄×D₄	—	47	8	no	—
244	C₄×D₄	—	47	16	no	—
245	C₄×D₄	—	47	16	no	—
246	C₄×D₄	—	47	8	no	—
247	C₄×D₄	—	47	8	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	—	47	8	no	—
251	C₂×C₂²⋊C₄	—	47	4	no	—
252	C₂×C₂²⋊C₄	—	47	4	no	—
253	C₂×C₂²⋊C₄	—	47	16	no	—
254	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₄×D₄₇	1	4	yes	—
257	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₄⋊C₈	—	47	8	no	—
261	C₄⋊C₈	C₂²×D₄₇	1	8	yes	complemented
262	C₂²⋊C₈	—	47	8	no	—
263	C₂²⋊C₈	—	47	32	no	—
264	C₂²⋊C₈	C₂²×D₄₇	1	8	yes	—
265	C₄×C₈	—	47	8	no	—
266	C₄×C₈	C₂²×D₄₇	1	8	yes	complemented
267	C₂⁴	—	47	4	no	—
268	C₂⁴	—	47	16	no	—
269	C₂⁴	—	47	8	no	—
270	C₂⁴	—	188	4	no	—
271	C₂⁴	—	188	4	no	—
272	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
273	C₂×D₄	—	47	16	no	—
274	C₂×D₄	—	47	16	no	—
275	C₂×D₄	—	47	64	no	—
276	C₂×D₄	—	47	8	no	—
277	C₂×D₄	—	47	8	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	47	4	no	—
281	C₂²×C₄	—	47	8	no	—
282	C₂²×C₄	—	47	8	no	—
283	C₂²×C₄	—	47	8	no	—
284	C₂²×C₄	—	47	16	no	—
285	C₂²×C₄	—	94	16	no	—
286	C₂²×C₄	—	188	16	no	—
287	C₂²×C₄	—	188	16	no	—
288	C₂²×C₄	—	188	8	no	—
289	C₂²×C₄	—	188	4	no	—
290	C₂²×C₄	C₈×D₄₇	1	8	yes	complemented
291	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
299	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
300	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
301	C₂×C₈	—	2	8	no	—
302	C₂×C₈	—	47	8	no	—
303	C₂×C₈	—	94	8	no	—
304	C₂×C₈	—	188	32	no	—
305	C₂×C₈	C₂³×D₄₇	1	8	yes	—
306	C₄⋊C₄	—	47	8	no	—
307	C₄⋊C₄	—	47	8	no	—
308	C₂²⋊C₄	—	47	16	no	—
309	C₂²⋊C₄	—	47	16	no	—
310	C₄²	C₂×C₄×D₄₇	1	4	yes	—
311	C₄²	C₂×C₄×D₄₇	1	4	yes	—
312	C₄²	C₂×C₄×D₄₇	1	2	yes	—
313	C₄²	C₂×C₄×D₄₇	1	2	yes	—
314	C₄²	C₂³×D₄₇	1	2	yes	—
315	C₄²	C₂³×D₄₇	1	2	yes	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	47	16	no	—
319	C₂³	—	47	8	no	—
320	C₂³	—	47	32	no	—
321	C₂³	—	94	8	no	—
322	C₂³	—	94	8	no	—
323	C₂³	—	188	8	no	—
324	C₂³	—	188	8	no	—
325	C₂³	—	188	32	no	—
326	C₂³	C₂×C₈×D₄₇	1	4	yes	—
327	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
328	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
329	D₄	—	47	32	no	—
330	D₄	—	47	32	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	47	8	no	—
338	C₂×C₄	—	94	8	no	—
339	C₂×C₄	—	94	16	no	—
340	C₂×C₄	—	94	16	no	—
341	C₂×C₄	—	188	16	no	—
342	C₂×C₄	—	188	8	no	—
343	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
344	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
345	C₂×C₄	C₂×C₈×D₄₇	1	16	yes	complemented
346	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
347	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
351	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
352	C₂×C₄	#13094070	1	4	yes	—
353	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
354	C₈	—	2	8	no	—
355	C₈	—	94	8	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	8	no	—
359	C₂²	—	47	16	no	—
360	C₂²	—	94	8	no	—
361	C₂²	—	94	8	no	—
362	C₂²	—	94	32	no	—
363	C₂²	—	188	32	no	—
364	C₂²	#15689597	1	2	yes	—
365	C₂²	C₂²×C₈×D₄₇	1	4	yes	—
366	C₂²	C₂²×C₈×D₄₇	1	2	yes	—
367	C₂²	#15689889	1	2	yes	—
368	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	94	8	no	—
373	C₄	#15689597	1	2	yes	—
374	C₄	C₂²×C₈×D₄₇	1	4	yes	—
375	C₄	C₂²×C₈×D₄₇	1	4	yes	—
376	C₄	C₂×#13094070	1	2	yes	—
377	C₂	—	2	4	no	—
378	C₂	—	94	16	no	—
379	C₂	#20252411	1	4	yes	direct product factor
380	C₂	C₂×#15689597	1	1	yes	characteristic
381	C₂	C₂³×C₈×D₄₇	1	1	yes	characteristic
382	C₂	C₂×#15689889	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂×C₄₇	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₁₈₈	C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	C₂×#2972
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #20252411	C₂	direct (N × H)
3. C₂×C₈×D₁₈₈	C₂	semidirect
4. C₂×#15689188	C₂	semidirect
5. C₂×#15689176	C₂	semidirect
6. C₂×C₂²⋊C₈×D₄₇	C₂	semidirect
7. C₂×C₄₇×#431	C₂	semidirect
10. C₂²×C₈×D₄₇	C₂²	semidirect
19. C₈×D₁₈₈	C₂²	semidirect
20. #15689188	C₂²	semidirect
21. #15689176	C₂²	semidirect
22. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
24. C₂×(C₂×D₄₇)⋊C₈	C₂²	semidirect
25. C₂²⋊C₈×D₄₇	C₂²	semidirect
26. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
28. C₄₇×#431	C₂²	semidirect
29. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
31. C₂×C₄×C₈×C₄₇	C₂²	semidirect
33. C₂²×D₁₈₈	C₈	semidirect
45. C₂×C₈×D₄₇	C₂³	semidirect
58. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
60. (C₂×D₄₇)⋊C₈	C₂³	semidirect
61. C₄×C₄₇⋊C₈	C₂³	semidirect
72. C₄⋊C₈×C₄₇	C₂³	semidirect
74. C₄×C₈×C₄₇	C₂³	semidirect
78. C₂³×D₄₇	C₂×C₈	semidirect
83. C₂²×C₄×C₄₇	C₂×C₈	semidirect
97. C₂×D₁₈₈	C₂×C₈	semidirect
98. C₂×D₁₈₈	C₂×C₈	semidirect
99. C₂×D₁₈₈	C₂×C₈	semidirect
135. C₂²×D₄₇	C₂²×C₈	semidirect
145. C₂×C₄×C₄₇	C₂²×C₈	semidirect
157. D₁₈₈	C₂²×C₈	semidirect
158. D₁₈₈	C₂²×C₈	semidirect
191. C₂×#431	D₄₇	semidirect
194. C₂×C₄₇	#2972	semidirect
214. #431	C₂×D₄₇	semidirect
216. C₂×C₄⋊C₈	C₂×D₄₇	semidirect
222. C₂×C₄×C₈	C₂×D₄₇	semidirect
223. C₄₇	C₂×#2972	semidirect
261. C₄⋊C₈	C₂²×D₄₇	semidirect
266. C₄×C₈	C₂²×D₄₇	semidirect
290. C₂²×C₄	C₈×D₄₇	semidirect
345. C₂×C₄	C₂×C₈×D₄₇	semidirect
379. C₂	#20252411	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₁₈₈	2
#20252411	2
C₂×C₈×D₁₈₈	2
C₂×#15689188	2
C₂×#15689176	2
C₂×C₂²⋊C₈×D₄₇	2
C₂×C₄₇×#431	2
C₂×#2972	47

Subgroups — C2×#20252411 #27080999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252411 #27080999