Subgroups — C₂×#20242098 #26184661

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
3	#20242098	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688872	C₂	1	2	yes	maximal, complemented
5	C₂×#15688869	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
7	#15689180	—	2	2	no	—
8	#15689180	C₂²	1	4	yes	—
9	#15689176	—	2	2	no	—
10	#15689176	C₂²	1	4	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×#13093935	—	2	1	no	—
16	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
17	#15688872	C₂²	1	8	yes	complemented
18	#15688869	C₂²	1	8	yes	complemented
19	C₄₇×#533	—	2	2	no	—
20	C₄₇×#533	—	2	2	no	—
21	C₄₇×#533	C₄	1	4	yes	—
22	C₄₇×#533	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₄₇	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
30	C₂×#117×C₄₇	—	2	1	no	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
37	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
40	#13093935	—	2	4	no	—
41	C₄×C₄₇⋊C₈	—	2	4	no	—
42	C₂²×Q₈×C₄₇	—	2	1	no	—
43	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₄₇	—	2	1	no	—
48	C₄⋊Q₈×C₄₇	—	2	1	no	—
49	C₄⋊Q₈×C₄₇	—	2	1	no	—
50	C₄⋊Q₈×C₄₇	—	2	1	no	—
51	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
52	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
53	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
55	#125×C₄₇	—	2	4	no	—
56	#125×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
61	C₄×Q₈×C₄₇	—	2	4	no	—
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	C₄×Q₈×C₄₇	—	2	4	no	—
64	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
65	#117×C₄₇	—	2	4	no	—
66	#117×C₄₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	D₄	1	2	yes	—
80	C₂×C₄²×C₄₇	D₄	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
83	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	4	4	no	—
88	C₂×Q₈×C₄₇	—	4	4	no	—
89	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	8	no	—
111	C₄⋊C₄×C₄₇	—	2	8	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
117	C₂²⋊C₄×C₄₇	—	2	8	no	—
118	C₄²×C₄₇	—	2	8	no	—
119	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	—	2	4	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂×C₄₇⋊C₈	—	4	4	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	Q₈×C₄₇	—	4	4	no	—
139	Q₈×C₄₇	—	4	4	no	—
140	Q₈×C₄₇	—	4	4	no	—
141	Q₈×C₄₇	—	4	4	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	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	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	1	yes	characteristic
162	C₂×C₄×C₄₇	#135	1	4	yes	—
163	C₂×C₄×C₄₇	#137	1	4	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₄₇⋊C₈	—	4	4	no	—
168	C₄₇⋊C₈	—	4	4	no	—
169	C₂×#1554	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	4	4	no	—
174	C₂²×C₄₇	#413	1	2	yes	—
175	C₂²×C₄₇	#416	1	2	yes	—
176	C₂²×C₄₇	#419	1	2	yes	—
177	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	2	2	no	—
183	C₄×C₄₇	—	4	4	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	#416	1	2	yes	—
186	C₄×C₄₇	#419	1	2	yes	—
187	C₄×C₄₇	C₂×#135	1	2	yes	—
188	C₄×C₄₇	C₂×#137	1	2	yes	—
189	C₂×#533	D₄₇	1	1	yes	characteristic
190	C₂×#432	—	47	1	no	—
191	C₂×#431	—	47	1	no	—
192	#1554	—	47	8	no	—
193	C₂×#333	—	47	2	no	—
194	C₂×#332	—	47	2	no	—
195	C₂×C₄₇	—	4	2	no	—
196	C₂×C₄₇	#1554	1	4	yes	complemented
197	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
200	#533	—	2	2	no	—
201	#533	—	2	2	no	—
202	#533	Dic₄₇	1	4	yes	—
203	#533	C₂×D₄₇	1	4	yes	—
204	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂×#125	—	2	1	no	—
207	C₂×C₂²⋊Q₈	—	2	1	no	—
208	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
211	C₂×#117	—	2	1	no	—
212	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
213	#432	—	47	4	no	—
214	#432	—	94	2	no	—
215	#431	—	47	4	no	—
216	#431	—	94	2	no	—
217	C₂×C₄⋊C₈	—	47	2	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₂²⋊C₈	—	94	1	no	—
220	C₂×C₂²⋊C₈	—	94	1	no	—
221	C₂×#97	—	94	1	no	—
222	C₂×C₄×C₈	—	94	1	no	—
223	#333	—	47	8	no	—
224	#332	—	47	8	no	—
225	C₄₇	C₂×#1554	1	1	yes	characteristic, complemented, Sylow
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
228	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
230	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
231	C₂²×C₈	—	94	2	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
238	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
239	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
240	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
241	#125	—	2	4	no	—
242	#125	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₂²⋊Q₈	—	2	4	no	—
246	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
251	#117	—	2	4	no	—
252	#117	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
263	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
266	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	C₄⋊C₈	—	47	4	no	—
270	C₄⋊C₈	—	47	4	no	—
271	C₄⋊C₈	—	94	2	no	—
272	C₄⋊C₈	—	94	2	no	—
273	C₂²⋊C₈	—	94	4	no	—
274	C₂²⋊C₈	—	94	4	no	—
275	#97	—	94	4	no	—
276	C₄×C₈	—	94	4	no	—
277	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	4	4	no	—
283	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
290	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
297	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂×C₈	—	94	4	no	—
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	188	4	no	—
304	C₂×C₈	—	188	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₄²	—	2	8	no	—
317	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
318	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
319	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
320	C₄²	C₂²×Dic₄₇	1	2	yes	—
321	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
323	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
324	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
326	C₄²	C₂³×D₄₇	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
331	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	Q₈	—	4	4	no	—
333	Q₈	—	4	4	no	—
334	Q₈	—	4	4	no	—
335	Q₈	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
356	C₂×C₄	#13094044	1	4	yes	—
357	C₂×C₄	#13094055	1	4	yes	—
358	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₈	—	188	4	no	—
362	C₈	—	188	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	#15689107	1	2	yes	—
368	C₂²	#15689119	1	2	yes	—
369	C₂²	#15689132	1	2	yes	—
370	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	4	no	—
378	C₄	#15689119	1	2	yes	—
379	C₄	#15689132	1	2	yes	—
380	C₄	C₂×#13094044	1	2	yes	—
381	C₄	C₂×#13094055	1	2	yes	—
382	C₂	—	4	2	no	—
383	C₂	#20242098	1	4	yes	direct product factor
384	C₂	C₂×#15689107	1	1	yes	characteristic
385	C₂	C₂×#15689119	1	1	yes	characteristic
386	C₂	C₂×#15689132	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#1554
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. #20242098	C₂	direct (N × H)
4. C₂×#15688872	C₂	semidirect
5. C₂×#15688869	C₂	semidirect
17. #15688872	C₂²	semidirect
18. #15688869	C₂²	semidirect
196. C₂×C₄₇	#1554	semidirect
225. C₄₇	C₂×#1554	semidirect
383. C₂	#20242098	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×#15689180	2
C₂×#15689176	2
#20242098	2
C₂×#15688872	2
C₂×#15688869	2
C₂×C₄₇×#533	2
C₂×#1554	47

Subgroups — C2×#20242098 #26184661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242098 #26184661