Subgroups — C₂×#20243974 #26218415

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689021	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243974	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
14	C₂²×C₄×Dic₄₇	—	2	1	no	—
15	C₂×#13093956	C₄	1	8	yes	complemented
16	C₂×#13093956	C₂²	1	4	yes	—
17	#15689021	—	2	2	no	—
18	#15689021	C₂²	1	4	yes	—
19	C₄×C₄⋊Dic₄₇	—	2	2	no	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
21	C₂×C₄₇⋊#95	—	2	1	no	—
22	C₂×C₄₇⋊#95	—	2	1	no	—
23	#15688886	C₂²	1	4	yes	—
24	#15688886	C₂²	1	4	yes	—
25	#15688886	C₂²	1	4	yes	—
26	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#336	C₂²	1	4	yes	—
30	C₂³×Dic₄₇	—	2	1	no	—
31	C₂³×Dic₄₇	—	2	1	no	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂³×Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	—	2	1	no	—
36	C₂×C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	4	no	—
51	C₂×Dic₄₇⋊C₄	—	4	4	no	—
52	C₂×C₄×Dic₄₇	—	2	4	no	—
53	C₂×C₄×Dic₄₇	—	4	4	no	—
54	#13093956	C₂×C₄	1	16	yes	complemented
55	C₄₇⋊#95	—	2	4	no	—
56	C₄₇⋊#95	—	2	4	no	—
57	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	2	2	no	—
65	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₄₇	—	2	4	no	—
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	2	4	no	—
92	C₂²×Dic₄₇	—	2	2	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	—	4	2	no	—
98	C₂²×Dic₄₇	—	4	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂²×Dic₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	—	4	2	no	—
105	C₂×C₈×C₄₇	—	2	8	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	4	4	no	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₇	—	2	4	no	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	4	2	no	—
125	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
126	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
127	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
128	Dic₄₇⋊C₄	—	4	8	no	—
129	C₄×Dic₄₇	—	4	8	no	—
130	C₂³×C₄₇	C₄×D₄	1	2	yes	—
131	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
132	C₂³×C₄₇	#123	1	2	yes	—
133	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
134	C₂³×C₄₇	#135	1	2	yes	—
135	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
136	C₂³×C₄₇	#137	1	2	yes	—
137	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	#117	1	4	yes	—
146	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₄₇	#123	1	2	yes	—
150	C₂×C₄×C₄₇	#125	1	4	yes	—
151	C₂×C₄×C₄₇	#126	1	4	yes	—
152	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	8	no	—
169	C₂×Dic₄₇	—	4	8	no	—
170	C₂×Dic₄₇	—	4	8	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	8	4	no	—
175	C₈×C₄₇	—	2	4	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₂×#1920	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	#387	1	4	yes	—
179	C₂²×C₄₇	C₄×SD₁₆	1	4	yes	—
180	C₂²×C₄₇	#440	1	4	yes	—
181	C₂²×C₄₇	#476	1	4	yes	—
182	C₂²×C₄₇	#479	1	4	yes	—
183	C₂²×C₄₇	#482	1	4	yes	—
184	C₂²×C₄₇	#483	1	4	yes	—
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
188	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	#387	1	4	yes	—
195	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
196	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
199	Dic₄₇	—	4	4	no	—
200	Dic₄₇	—	4	4	no	—
201	Dic₄₇	—	4	4	no	—
202	Dic₄₇	—	8	2	no	—
203	C₂²×#106	—	47	1	no	—
204	C₂×#389	—	47	1	no	—
205	C₂×C₄×C₄⋊C₄	—	47	1	no	—
206	#1920	—	47	8	no	—
207	C₂×#340	—	47	1	no	—
208	C₂×#340	—	47	1	no	—
209	C₂×#340	—	47	1	no	—
210	C₂×#336	D₄₇	1	1	yes	characteristic
211	C₂×C₄₇	#1920	1	8	yes	complemented
212	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
213	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#479	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#483	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#482	1	1	yes	characteristic
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	—	47	1	no	—
222	C₂²×C₄⋊C₄	—	47	1	no	—
223	C₂²×C₄⋊C₄	—	47	1	no	—
224	C₂²×C₄⋊C₄	—	47	1	no	—
225	C₂²×C₄⋊C₄	—	94	1	no	—
226	C₂²×C₄²	—	94	1	no	—
227	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#106	—	47	8	no	—
229	C₂×#106	—	47	4	no	—
230	#389	—	47	4	no	—
231	#389	—	94	2	no	—
232	C₄×C₄⋊C₄	—	47	4	no	—
233	C₄×C₄⋊C₄	—	94	2	no	—
234	C₂×#95	—	94	1	no	—
235	C₂×#95	—	94	1	no	—
236	#340	—	47	4	no	—
237	#340	—	47	4	no	—
238	#340	—	47	4	no	—
239	#336	C₂×D₄₇	1	4	yes	—
240	C₄₇	C₂×#1920	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	—	94	1	no	—
242	C₂³×C₄	—	94	1	no	—
243	C₂³×C₄	—	94	1	no	—
244	C₂³×C₄	—	94	1	no	—
245	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
246	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	C₄×D₄₇	1	4	yes	—
254	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
255	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
256	C₂×C₄⋊C₄	—	47	4	no	—
257	C₂×C₄⋊C₄	—	47	4	no	—
258	C₂×C₄⋊C₄	—	47	4	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	—	47	2	no	—
263	C₂×C₄⋊C₄	—	94	1	no	—
264	C₂×C₄⋊C₄	—	94	1	no	—
265	C₂×C₄⋊C₄	—	94	1	no	—
266	C₂×C₄⋊C₄	—	94	2	no	—
267	C₂×C₄⋊C₄	—	94	2	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	2	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	4	no	—
273	C₂×C₄⋊C₄	—	188	4	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	94	4	no	—
277	C₂×C₄²	—	188	4	no	—
278	C₂×C₄²	D₁₈₈	1	2	yes	—
279	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
280	#106	—	47	16	no	—
281	#95	—	94	4	no	—
282	#95	—	94	4	no	—
283	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	94	4	no	—
290	C₂²×C₄	—	94	4	no	—
291	C₂²×C₄	—	94	4	no	—
292	C₂²×C₄	—	94	2	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	—	94	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	—	188	2	no	—
299	C₂²×C₄	—	188	2	no	—
300	C₂²×C₄	—	188	2	no	—
301	C₂²×C₄	—	188	2	no	—
302	C₂²×C₄	—	188	2	no	—
303	C₂²×C₄	—	188	2	no	—
304	C₂²×C₄	—	188	2	no	—
305	C₂²×C₄	#10625325	1	4	yes	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
307	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
308	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
309	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
310	C₂²×C₄	#10625350	1	2	yes	—
311	C₂²×C₄	#10625352	1	2	yes	—
312	C₂²×C₄	#10625352	1	2	yes	—
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
315	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
324	C₄⋊C₄	—	47	4	no	—
325	C₄⋊C₄	—	47	4	no	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	94	4	no	—
328	C₄⋊C₄	—	94	4	no	—
329	C₄⋊C₄	—	94	4	no	—
330	C₄⋊C₄	—	94	2	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	94	2	no	—
335	C₄⋊C₄	—	188	8	no	—
336	C₄⋊C₄	—	188	2	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	188	8	no	—
341	C₂³	C₄×D₁₈₈	1	2	yes	—
342	C₂³	#13094004	1	2	yes	—
343	C₂³	#13094008	1	2	yes	—
344	C₂³	C₂×#10625325	1	2	yes	—
345	C₂³	#13094046	1	2	yes	—
346	C₂³	#13094052	1	2	yes	—
347	C₂³	#13094057	1	2	yes	—
348	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	94	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	376	4	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	8	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	8	no	—
371	C₂×C₄	—	188	8	no	—
372	C₂×C₄	#13093980	1	4	yes	—
373	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
374	C₂×C₄	#13093989	1	4	yes	—
375	C₂×C₄	#13094004	1	2	yes	—
376	C₂×C₄	#13094008	1	2	yes	—
377	C₂×C₄	#13094014	1	4	yes	—
378	C₂×C₄	#13094017	1	4	yes	—
379	C₂×C₄	C₂×#10625325	1	4	yes	—
380	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
385	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
386	C₈	—	2	4	no	—
387	C₈	—	4	2	no	—
388	C₂²	#15689008	1	4	yes	—
389	C₂²	C₄×#10625325	1	4	yes	—
390	C₂²	#15689225	1	4	yes	—
391	C₂²	#15689414	1	4	yes	—
392	C₂²	#15689431	1	4	yes	—
393	C₂²	#15689448	1	4	yes	—
394	C₂²	#15689454	1	4	yes	—
395	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
396	C₂²	C₂×#13094004	1	1	yes	characteristic
397	C₂²	C₂×#13094008	1	1	yes	characteristic
398	C₂²	C₂²×#10625325	1	1	yes	characteristic
399	C₂²	C₂×#13094046	1	1	yes	characteristic
400	C₂²	C₂×#13094052	1	1	yes	characteristic
401	C₂²	C₂×#13094057	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	4	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	4	no	—
406	C₄	—	188	4	no	—
407	C₄	—	188	4	no	—
408	C₄	#15689008	1	4	yes	—
409	C₄	C₂×#13093980	1	1	yes	characteristic
410	C₄	C₂×#13093989	1	1	yes	characteristic
411	C₄	C₂×#13094014	1	1	yes	characteristic
412	C₄	C₂×#13094017	1	1	yes	characteristic
413	C₂	#20243974	1	8	yes	direct product factor
414	C₂	C₂×#15689008	1	1	yes	characteristic
415	C₂	C₂×C₄×#10625325	1	1	yes	characteristic
416	C₂	C₂×#15689225	1	1	yes	characteristic
417	C₂	C₂×#15689414	1	1	yes	characteristic
418	C₂	C₂×#15689431	1	1	yes	characteristic
419	C₂	C₂×#15689454	1	1	yes	characteristic
420	C₂	C₂×#15689448	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	C₂×#1920
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
4. #20243974	C₂	direct (N × H)
15. C₂×#13093956	C₄	semidirect
54. #13093956	C₂×C₄	semidirect
211. C₂×C₄₇	#1920	semidirect
240. C₄₇	C₂×#1920	semidirect
413. C₂	#20243974	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×#13093956	2
C₂×#15689021	2
C₂×C₄×C₄⋊Dic₄₇	2
#20243974	2
C₂×#15688886	2
C₂×C₄₇×#336	2
C₂×#1920	47

Subgroups — C2×#20243974 #26218415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243974 #26218415