Subgroups — #26219743

Order 12032.

1026 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689161	C₂	1	2	yes	maximal
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
4	#20244158	C₂	1	4	yes	maximal, complemented
5	#20244152	C₂	1	2	yes	maximal, complemented
6	#20244147	C₂	1	2	yes	maximal, complemented
7	#20243105	C₂	1	2	yes	maximal
8	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	C₂²	1	2	yes	—
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689161	—	2	8	no	—
13	C₂×#13093958	C₂²	1	4	yes	—
14	C₂×#13093956	C₂²	1	4	yes	—
15	#15688993	C₂²	1	2	yes	—
16	#15688989	C₂²	1	2	yes	—
17	#15688983	—	2	1	no	—
18	#15688983	—	2	1	no	—
19	C₄×C₄⋊Dic₄₇	—	2	1	no	—
20	C₄×C₄⋊Dic₄₇	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
22	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
24	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
25	#15688969	—	2	1	no	—
26	C₄²×Dic₄₇	—	2	1	no	—
27	#15688886	C₂²	1	4	yes	—
28	#15688886	C₂²	1	4	yes	—
29	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₇	C₄	1	8	yes	complemented
32	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
35	#13093983	—	2	2	no	—
36	#13093983	—	2	2	no	—
37	#13093983	—	2	4	no	—
38	#13093983	—	2	4	no	—
39	#13093983	D₄	1	4	yes	—
40	#13093983	Q₈	1	4	yes	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
47	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄×Dic₄₇	—	2	1	no	—
50	C₂×C₄×Dic₄₇	—	2	1	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	#13093958	—	2	8	no	—
55	#13093956	—	2	8	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₄₇⋊#95	—	2	2	no	—
60	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	—	2	4	no	—
64	C₂²×C₈×C₄₇	—	2	4	no	—
65	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
75	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
76	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	2	16	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
104	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
105	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂²⋊Dic₄₇	—	2	4	no	—
111	C₂²⋊Dic₄₇	—	2	4	no	—
112	C₂²⋊Dic₄₇	—	4	4	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	—	4	4	no	—
119	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
120	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
121	C₄×Dic₄₇	—	2	4	no	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	4	no	—
125	C₄×Dic₄₇	—	4	4	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂³×C₄₇	#121	1	2	yes	—
130	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
144	C₂×C₄×C₄₇	#121	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	#125	1	4	yes	—
147	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
148	C₂×C₄×C₄₇	#135	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	4	4	no	—
164	C₈×C₄₇	—	2	4	no	—
165	C₈×C₄₇	—	2	4	no	—
166	#21169	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	#389	1	4	yes	—
172	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#135	1	2	yes	—
176	C₂²×C₄₇	#575	1	2	yes	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	#389	1	4	yes	—
181	C₄×C₄₇	#427	1	4	yes	complemented
182	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
183	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
185	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	Dic₄₇	—	4	4	no	—
187	Dic₄₇	—	4	4	no	—
188	Dic₄₇	—	8	4	no	—
189	C₂×#427	—	47	2	no	—
190	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
191	#2285	—	47	1	no	—
192	C₄×#117	—	47	1	no	—
193	#1949	—	47	4	no	—
194	#1948	—	47	2	no	—
195	#1947	—	47	2	no	—
196	#1735	—	47	2	no	—
197	C₂×C₄₇	—	2	4	no	—
198	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
200	C₂×C₄₇	#2911	1	1	yes	characteristic
201	C₂×C₄₇	#3035	1	2	yes	—
202	C₂×C₄₇	#3076	1	2	yes	—
203	C₂³×C₈	C₂×D₄₇	1	2	yes	—
204	C₂×#117	—	47	1	no	—
205	C₂×#117	—	47	1	no	—
206	C₂×#117	—	47	2	no	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	#427	—	94	8	no	—
209	C₂×#107	—	47	4	no	—
210	C₂×#106	—	47	4	no	—
211	C₂×C₄⋊C₈	Dic₄₇	1	8	yes	complemented
212	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
215	#384	—	47	2	no	—
216	#382	—	47	2	no	—
217	#380	—	94	1	no	—
218	#380	—	94	1	no	—
219	C₄×C₄⋊C₄	—	47	2	no	—
220	C₄×C₄⋊C₄	—	47	2	no	—
221	C₄×C₄⋊C₄	—	94	1	no	—
222	C₄×C₄⋊C₄	—	94	1	no	—
223	C₄×C₂²⋊C₄	—	94	1	no	—
224	C₄×C₂²⋊C₄	—	94	1	no	—
225	#376	—	94	1	no	—
226	C₄³	—	94	1	no	—
227	#340	—	47	4	no	—
228	#340	—	47	4	no	—
229	C₄₇	#21169	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
231	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
232	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂×Dic₄₇	1	8	yes	—
236	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
237	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
238	#117	—	47	4	no	—
239	#117	—	47	4	no	—
240	#117	—	94	2	no	—
241	#117	—	94	2	no	—
242	#117	—	94	4	no	—
243	#117	—	94	4	no	—
244	C₂×C₄⋊C₄	—	47	2	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	—	47	4	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₂²⋊C₄	—	94	1	no	—
250	C₂×C₂²⋊C₄	—	94	1	no	—
251	C₂×C₂²⋊C₄	—	94	2	no	—
252	C₂×C₄²	—	94	1	no	—
253	C₂×C₄²	—	94	1	no	—
254	C₂×C₄²	—	94	2	no	—
255	C₂×C₄²	—	94	2	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	Dic₉₄	1	4	yes	—
258	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
259	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
260	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	#107	—	94	8	no	—
264	#106	—	94	8	no	—
265	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
266	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
267	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	—
268	#95	—	94	2	no	—
269	#95	—	94	2	no	—
270	#95	—	94	2	no	—
271	#95	—	94	2	no	—
272	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	94	2	no	—
276	C₂²×C₄	—	94	2	no	—
277	C₂²×C₄	—	94	4	no	—
278	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
279	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
280	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
281	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
286	C₂²×C₄	D₄×D₄₇	1	2	yes	—
287	C₂²×C₄	#10625352	1	2	yes	—
288	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
289	C₂²×C₄	#10625354	1	2	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
292	C₂×C₈	—	2	16	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
298	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
299	C₄⋊C₄	—	47	4	no	—
300	C₄⋊C₄	—	47	4	no	—
301	C₄⋊C₄	—	94	2	no	—
302	C₄⋊C₄	—	94	2	no	—
303	C₄⋊C₄	—	94	4	no	—
304	C₄⋊C₄	—	94	4	no	—
305	C₄⋊C₄	—	188	4	no	—
306	C₄⋊C₄	—	188	4	no	—
307	C₂²⋊C₄	—	94	4	no	—
308	C₂²⋊C₄	—	94	4	no	—
309	C₂²⋊C₄	—	188	4	no	—
310	C₄²	—	94	4	no	—
311	C₄²	—	94	4	no	—
312	C₄²	—	188	4	no	—
313	C₄²	—	188	4	no	—
314	C₄²	—	188	4	no	—
315	C₄²	C₄⋊Dic₄₇	1	4	yes	—
316	C₄²	C₄⋊Dic₄₇	1	4	yes	—
317	C₄²	C₂×Dic₉₄	1	2	yes	—
318	C₄²	C₂×Dic₉₄	1	2	yes	—
319	C₄²	C₂²×Dic₄₇	1	2	yes	—
320	C₄²	C₂²×Dic₄₇	1	2	yes	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
324	C₂³	#13093999	1	2	yes	—
325	C₂³	#13094004	1	2	yes	—
326	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	94	4	no	—
333	C₂×C₄	—	94	4	no	—
334	C₂×C₄	—	188	4	no	—
335	C₂×C₄	—	188	4	no	—
336	C₂×C₄	—	188	4	no	—
337	C₂×C₄	—	188	2	no	—
338	C₂×C₄	—	188	2	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
343	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
344	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
345	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
347	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
348	C₂×C₄	#13093999	1	2	yes	—
349	C₂×C₄	#13094004	1	2	yes	—
350	C₂×C₄	#13094015	1	4	yes	—
351	C₂×C₄	#13094023	1	4	yes	—
352	C₂×C₄	#13094046	1	4	yes	—
353	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	#15689022	1	4	yes	—
366	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
367	C₂²	C₂×#13093999	1	1	yes	characteristic
368	C₂²	C₂×#13094004	1	1	yes	characteristic
369	C₂²	C₂×#13094046	1	2	yes	—
370	C₂²	#15689923	1	2	yes	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	376	4	no	—
375	C₄	—	188	4	no	—
376	C₄	—	188	4	no	—
377	C₄	#15689022	1	4	yes	—
378	C₄	#15689161	1	4	yes	complemented
379	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
380	C₄	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
381	C₄	C₂×#13094015	1	1	yes	characteristic
382	C₄	C₂×#13094023	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×#15689022	1	1	yes	characteristic
385	C₂	C₂×#15689161	1	1	yes	characteristic
386	C₂	#20251978	1	1	yes	characteristic
387	C₂	#20252845	1	2	yes	—
388	C₂	#20253178	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#21169
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #20244158	C₂	semidirect
5. #20244152	C₂	semidirect
6. #20244147	C₂	semidirect
31. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
181. C₄×C₄₇	#427	semidirect
211. C₂×C₄⋊C₈	Dic₄₇	semidirect
229. C₄₇	#21169	semidirect
378. C₄	#15689161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689161	2
#20245795	2
C₄×#13093983	2
#20244158	2
#20244152	2
#20244147	2
#20243105	2
C₂²×C₄⋊C₈×C₄₇	2
#21169	47