Subgroups — C₂×#20244377 #26220938

Order 12032.

1342 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20244377	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688891	C₂	1	4	yes	maximal
5	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₉₄	C₄	1	2	yes	—
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂×#13094024	—	2	1	no	—
9	C₂×#13094024	—	2	1	no	—
10	C₂×#13094024	—	2	2	no	—
11	C₂×#13094024	—	2	1	no	—
12	C₂×#13094024	—	2	1	no	—
13	C₂×#13094024	—	2	2	no	—
14	C₂×#13094024	C₄	1	4	yes	—
15	C₂×#13094024	C₂²	1	4	yes	—
16	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
17	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	#15689147	—	2	2	no	—
19	#15689147	C₂²	1	4	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
22	#15688891	C₂²	1	16	yes	—
23	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₄×M₁₆×C₄₇	—	2	2	no	—
26	C₄×M₁₆×C₄₇	C₂²	1	4	yes	—
27	C₂×#97×C₄₇	—	2	1	no	—
28	C₂×C₄×C₈×C₄₇	—	2	1	no	—
29	C₂²×Dic₉₄	—	2	2	no	—
30	C₂²×Dic₉₄	—	2	4	no	—
31	C₂²×Dic₉₄	—	2	2	no	—
32	C₂²×Dic₉₄	—	4	8	no	—
33	C₂²×Dic₉₄	C₂×C₄	1	8	yes	—
34	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	8	no	—
37	C₂×#10625329	C₂³	1	4	yes	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	#13094024	—	2	4	no	—
40	#13094024	—	2	4	no	—
41	#13094024	—	2	4	no	—
42	#13094024	—	2	4	no	—
43	#13094024	—	2	4	no	—
44	#13094024	—	2	4	no	—
45	#13094024	—	2	4	no	—
46	#13094024	—	2	4	no	—
47	C₂×C₄⋊Dic₄₇	—	2	2	no	—
48	C₂×C₄⋊Dic₄₇	—	2	4	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
57	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	4	no	—
64	C₂×M₁₆×C₄₇	Q₈	1	8	yes	complemented
65	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
66	C₂²×C₈×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
75	#97×C₄₇	—	2	4	no	—
76	C₄×C₈×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₄₇	#41	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	4	8	no	—
99	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
100	C₂×Dic₉₄	—	2	8	no	—
101	C₂×Dic₉₄	—	2	8	no	—
102	C₂×Dic₉₄	—	4	8	no	—
103	C₂×Dic₉₄	—	4	16	no	—
104	C₂×Dic₉₄	—	4	8	no	—
105	C₂×Dic₉₄	—	4	16	no	—
106	M₁₆×C₄₇	—	2	8	no	—
107	M₁₆×C₄₇	—	2	4	no	—
108	M₁₆×C₄₇	C₂×Q₈	1	8	yes	complemented
109	C₂×C₈×C₄₇	—	2	8	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
112	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
113	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
114	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
115	C₄²×C₄₇	C₂×D₄	1	2	yes	—
116	C₄²×C₄₇	C₂×D₄	1	2	yes	—
117	C₄²×C₄₇	C₂×D₄	1	2	yes	—
118	C₄²×C₄₇	C₂×D₄	1	2	yes	—
119	C₄⋊Dic₄₇	—	2	8	no	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄⋊Dic₄₇	—	2	8	no	—
123	C₄⋊Dic₄₇	—	2	4	no	—
124	C₄⋊Dic₄₇	—	2	4	no	—
125	#10625329	—	2	8	no	—
126	#10625329	—	4	4	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	C₂×C₄₇⋊C₈	—	4	4	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₄₇	C₄×Q₈	1	4	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	#100	1	4	yes	—
142	C₂×C₄×C₄₇	#101	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
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×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
152	C₂×C₄×C₄₇	#124	1	2	yes	—
153	C₂×C₄×C₄₇	#124	1	2	yes	—
154	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
160	C₂×Dic₄₇	—	2	8	no	—
161	C₂×Dic₄₇	—	4	8	no	—
162	C₂×Dic₄₇	—	4	8	no	—
163	C₂×Dic₄₇	—	4	8	no	—
164	Dic₉₄	—	4	16	no	—
165	Dic₉₄	—	4	16	no	—
166	C₈×C₄₇	—	2	8	no	—
167	C₄₇⋊C₈	—	4	4	no	—
168	C₂×#1997	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	8	no	—
174	C₂²×C₄₇	#391	1	2	yes	—
175	C₂²×C₄₇	#391	1	2	yes	—
176	C₂²×C₄₇	C₂×#100	1	2	yes	—
177	C₂²×C₄₇	C₂×#101	1	2	yes	—
178	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	#391	1	2	yes	—
183	C₄×C₄₇	#391	1	2	yes	—
184	C₄×C₄₇	C₂×#100	1	4	yes	—
185	C₄×C₄₇	C₂×#101	1	4	yes	—
186	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
187	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	Dic₄₇	—	4	8	no	—
190	C₂²×C₄⋊Q₈	—	47	1	no	—
191	C₂×#423	—	47	1	no	—
192	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
193	#1997	—	47	8	no	—
194	C₂×#343	—	47	4	no	—
195	C₂×C₄₇	—	2	2	no	—
196	C₂×C₄₇	—	2	2	no	—
197	C₂×C₄₇	#1997	1	4	yes	complemented
198	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
199	C₂×C₄₇	C₂²×#100	1	1	yes	characteristic
200	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
201	C₂³×Q₈	—	47	2	no	—
202	C₂²×M₁₆	—	47	2	no	—
203	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
204	C₂×C₄⋊Q₈	—	47	4	no	—
205	C₂×C₄⋊Q₈	—	47	4	no	—
206	C₂×C₄⋊Q₈	—	94	1	no	—
207	C₂×C₄⋊Q₈	—	94	1	no	—
208	C₂×C₄⋊Q₈	—	94	2	no	—
209	C₂×C₄⋊Q₈	—	94	1	no	—
210	C₂×C₄⋊Q₈	—	94	1	no	—
211	C₂×C₄⋊Q₈	—	94	2	no	—
212	C₂²×C₄⋊C₄	—	47	2	no	—
213	C₂²×C₄⋊C₄	—	47	2	no	—
214	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
215	#423	—	47	4	no	—
216	#423	—	94	2	no	—
217	C₂×C₄⋊C₈	—	94	1	no	—
218	C₂×C₄⋊C₈	—	94	1	no	—
219	C₄×M₁₆	—	2	2	no	—
220	C₄×M₁₆	C₂×D₄₇	1	4	yes	—
221	C₂×#97	—	2	1	no	—
222	C₂×C₄×C₈	—	2	1	no	—
223	#343	—	47	16	no	—
224	C₄₇	C₂×#1997	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₈	—	47	8	no	—
226	C₂²×Q₈	—	94	4	no	—
227	C₂²×Q₈	—	94	2	no	—
228	C₂²×Q₈	—	94	2	no	—
229	C₂²×Q₈	—	188	8	no	—
230	C₂³×C₄	—	47	4	no	—
231	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	47	4	no	—
237	C₂×M₁₆	—	94	2	no	—
238	C₂×M₁₆	—	94	8	no	—
239	C₂×M₁₆	Dic₉₄	1	8	yes	complemented
240	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	94	2	no	—
243	C₄⋊Q₈	—	94	4	no	—
244	C₄⋊Q₈	—	94	4	no	—
245	C₄⋊Q₈	—	94	4	no	—
246	C₄⋊Q₈	—	94	4	no	—
247	C₄⋊Q₈	—	94	4	no	—
248	C₄⋊Q₈	—	94	4	no	—
249	C₄⋊Q₈	—	94	4	no	—
250	C₄⋊Q₈	—	94	4	no	—
251	C₂×C₄⋊C₄	—	47	8	no	—
252	C₂×C₄⋊C₄	—	47	4	no	—
253	C₂×C₄⋊C₄	—	47	4	no	—
254	C₂×C₄⋊C₄	—	94	4	no	—
255	C₂×C₄⋊C₄	—	94	2	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄²	C₄×D₄₇	1	2	yes	—
262	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
263	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
264	C₂×C₄²	D₁₈₈	1	2	yes	—
265	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	C₄⋊C₈	—	94	4	no	—
270	C₄⋊C₈	—	94	4	no	—
271	#97	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
274	C₂×Q₈	—	94	8	no	—
275	C₂×Q₈	—	94	8	no	—
276	C₂×Q₈	—	188	16	no	—
277	C₂×Q₈	—	188	8	no	—
278	C₂×Q₈	—	188	16	no	—
279	C₂×Q₈	—	188	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	47	8	no	—
283	C₂²×C₄	—	94	4	no	—
284	C₂²×C₄	—	94	4	no	—
285	C₂²×C₄	—	188	8	no	—
286	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
287	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
288	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
293	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
294	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
295	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
298	C₂²×C₄	#10625350	1	4	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
302	M₁₆	—	2	8	no	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	94	8	no	—
305	M₁₆	—	188	4	no	—
306	M₁₆	C₂×Dic₉₄	1	8	yes	complemented
307	C₂×C₈	—	2	8	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	188	4	no	—
311	C₄⋊C₄	—	94	8	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	—	94	4	no	—
314	C₄⋊C₄	—	94	8	no	—
315	C₄⋊C₄	—	94	4	no	—
316	C₄⋊C₄	—	94	4	no	—
317	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
318	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
319	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
320	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
321	C₄²	C₂×D₁₈₈	1	2	yes	—
322	C₄²	C₂×D₁₈₈	1	2	yes	—
323	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
324	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
328	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
329	C₂³	C₄×Dic₉₄	1	4	yes	—
330	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
331	Q₈	—	188	16	no	—
332	Q₈	—	188	16	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	94	8	no	—
340	C₂×C₄	—	188	8	no	—
341	C₂×C₄	—	188	8	no	—
342	C₂×C₄	—	188	8	no	—
343	C₂×C₄	#13093940	1	4	yes	—
344	C₂×C₄	#13093942	1	4	yes	—
345	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
346	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
347	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
350	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
351	C₂×C₄	C₄×Dic₉₄	1	4	yes	—
352	C₂×C₄	#13094003	1	4	yes	—
353	C₂×C₄	#13094003	1	4	yes	—
354	C₂×C₄	#13094012	1	2	yes	—
355	C₂×C₄	#13094012	1	2	yes	—
356	C₂×C₄	#13094024	1	2	yes	—
357	C₂×C₄	#13094024	1	2	yes	—
358	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
360	C₂×C₄	C₂²×Dic₉₄	1	2	yes	—
361	C₂×C₄	C₂×#10625350	1	2	yes	—
362	C₈	—	2	8	no	—
363	C₈	—	188	4	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	#15689029	1	2	yes	—
370	C₂²	#15689029	1	2	yes	—
371	C₂²	C₂×#13093940	1	2	yes	—
372	C₂²	C₂×#13093942	1	2	yes	—
373	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
374	C₂²	C₂×C₄×Dic₉₄	1	2	yes	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	188	8	no	—
378	C₄	#15689029	1	2	yes	—
379	C₄	#15689029	1	2	yes	—
380	C₄	C₂×#13093940	1	4	yes	—
381	C₄	C₂×#13093942	1	4	yes	—
382	C₄	C₂×#13094003	1	2	yes	—
383	C₄	C₂×#13094012	1	1	yes	characteristic
384	C₄	C₂×#13094024	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	#20244377	1	4	yes	direct product factor
388	C₂	C₂×#15689029	1	1	yes	characteristic
389	C₂	C₂²×#13093940	1	1	yes	characteristic
390	C₂	C₂²×#13093942	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₂×#1997
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20244377	C₂	direct (N × H)
64. C₂×M₁₆×C₄₇	Q₈	semidirect
108. M₁₆×C₄₇	C₂×Q₈	semidirect
197. C₂×C₄₇	#1997	semidirect
224. C₄₇	C₂×#1997	semidirect
239. C₂×M₁₆	Dic₉₄	semidirect
306. M₁₆	C₂×Dic₉₄	semidirect
387. C₂	#20244377	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×#13094024	2
C₂×#15689147	2
#20244377	2
C₂×#15688891	2
C₂×C₄×M₁₆×C₄₇	2
C₂×#1997	47

Subgroups — C2×#20244377 #26220938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244377 #26220938