Subgroups — #26214730

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689080	C₂	1	2	yes	maximal, complemented
4	#20245852	C₂	1	1	yes	maximal, characteristic
5	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243173	C₂	1	2	yes	maximal, complemented
9	#20243165	C₂	1	2	yes	maximal, complemented
10	#20243157	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093981	C₂²	1	2	yes	—
16	#15689202	C₄	1	8	yes	complemented
17	C₈×D₁₈₈	C₄	1	8	yes	complemented
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	#15689080	—	2	8	no	—
23	C₂×#13093934	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
26	#15689025	C₄	1	2	yes	—
27	#15689021	C₄	1	2	yes	—
28	#15689014	C₄	1	4	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄³×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
43	C₂×#10625324	—	2	4	no	—
44	C₂×#10625324	—	2	4	no	—
45	C₂×#10625324	C₂×C₄	1	8	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂×C₈×D₄₇	—	2	4	no	—
49	C₂×C₈×D₄₇	—	2	4	no	—
50	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
53	#13093981	—	2	4	no	—
54	#13093981	—	2	4	no	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
63	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
64	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
65	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
66	#13093934	—	2	4	no	—
67	C₄×C₄₇⋊C₈	—	2	4	no	—
68	C₈×Dic₄₇	—	2	4	no	—
69	C₄₇⋊#95	C₂×C₄	1	4	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#97×C₄₇	—	2	2	no	—
81	#97×C₄₇	—	2	2	no	—
82	#97×C₄₇	—	2	2	no	—
83	#97×C₄₇	D₄	1	4	yes	complemented
84	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
85	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
86	C₂³×D₄₇	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	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂×D₁₈₈	—	2	4	no	—
95	C₂×D₁₈₈	C₄²	1	4	yes	—
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×C₄×D₄₇	—	2	2	no	—
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	2	no	—
100	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
101	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₄₇	#41	1	2	yes	—
113	C₂×C₈×C₄₇	#41	1	2	yes	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	2	1	no	—
117	C₄²×C₄₇	—	4	2	no	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	#41	1	2	yes	—
122	(C₂×D₄₇)⋊C₄	—	2	8	no	—
123	(C₂×D₄₇)⋊C₄	—	4	4	no	—
124	(C₂×D₄₇)⋊C₄	C₄²	1	8	yes	—
125	C₄⋊Dic₄₇	—	2	4	no	—
126	C₄⋊Dic₄₇	C₄²	1	4	yes	—
127	Dic₄₇⋊C₄	—	2	8	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
136	#10625324	—	2	16	no	—
137	C₈×D₄₇	—	2	16	no	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	2	4	no	—
142	C₂²×D₄₇	—	2	4	no	—
143	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
153	C₂×C₄×C₄₇	#131	1	4	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×D₄	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×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	4	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
166	D₁₈₈	—	2	8	no	—
167	C₄×D₄₇	—	2	4	no	—
168	C₄×D₄₇	—	2	4	no	—
169	C₄×D₄₇	—	2	4	no	—
170	C₄×D₄₇	—	2	4	no	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₈×C₄₇	C₄×D₄	1	4	yes	—
174	C₈×C₄₇	C₄×D₄	1	4	yes	—
175	C₄₇⋊C₈	—	2	4	no	—
176	C₄₇⋊C₈	—	2	4	no	—
177	#20495	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×#131	1	2	yes	—
182	C₂²×C₄₇	#568	1	2	yes	—
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	—	2	4	no	—
185	C₂×D₄₇	—	2	4	no	—
186	C₂×D₄₇	—	4	4	no	—
187	C₂×D₄₇	—	4	4	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	4	no	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	#405	1	4	yes	complemented
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
195	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	4	4	no	—
198	C₂×#436	—	47	1	no	—
199	C₂×C₈×D₄	—	47	1	no	—
200	C₂×#405	—	47	2	no	—
201	#2293	—	47	1	no	—
202	#1770	—	47	1	no	—
203	C₈×C₄⋊C₄	—	47	1	no	—
204	C₄×C₄⋊C₈	—	47	1	no	—
205	#1753	—	47	2	no	—
206	#1752	—	47	2	no	—
207	#1750	—	47	2	no	—
208	C₄×#97	D₄₇	1	1	yes	characteristic, complemented
209	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
211	C₂×C₄₇	#2875	1	1	yes	characteristic
212	C₂×C₄₇	#2935	1	2	yes	—
213	C₂×C₄₇	#2969	1	2	yes	—
214	D₄₇	—	4	4	no	—
215	C₂²×M₁₆	—	47	2	no	—
216	C₂³×C₈	—	47	2	no	—
217	C₂×C₄×D₄	—	47	1	no	—
218	C₂×#117	—	47	2	no	—
219	#436	—	47	8	no	—
220	C₈×D₄	—	47	8	no	—
221	C₂×C₄⋊C₈	—	47	1	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₂²⋊C₈	—	47	2	no	—
224	C₂×C₂²⋊C₈	—	47	2	no	—
225	#405	—	94	8	no	—
226	C₂×#97	—	47	2	no	—
227	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
229	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
230	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄×C₈	—	47	2	no	—
232	C₂×C₄×C₈	—	47	2	no	—
233	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
235	#390	—	47	2	no	—
236	#389	—	47	2	no	—
237	#388	—	47	4	no	—
238	C₄×C₄⋊C₄	—	47	1	no	—
239	C₄×C₂²⋊C₄	—	47	2	no	—
240	C₄³	C₂×D₄₇	1	1	yes	characteristic
241	#336	—	47	2	no	—
242	#336	—	47	2	no	—
243	#336	—	47	2	no	—
244	C₄₇	#20495	1	1	yes	characteristic, complemented, Sylow
245	C₂²×D₄	—	47	1	no	—
246	C₂³×C₄	—	47	2	no	—
247	C₂×M₁₆	—	47	8	no	—
248	C₂×M₁₆	—	94	4	no	—
249	C₂×M₁₆	—	94	4	no	—
250	C₂²×C₈	—	47	2	no	—
251	C₂²×C₈	—	47	2	no	—
252	C₂²×C₈	—	47	8	no	—
253	C₂²×C₈	—	94	4	no	—
254	C₂²×C₈	—	94	4	no	—
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
259	C₄×D₄	—	47	4	no	—
260	C₄×D₄	—	47	4	no	—
261	#117	—	94	4	no	—
262	#117	—	94	4	no	—
263	C₂×C₄⋊C₄	—	47	1	no	—
264	C₂×C₄⋊C₄	—	47	4	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₂²⋊C₄	—	47	2	no	—
267	C₂×C₂²⋊C₄	—	47	4	no	—
268	C₂×C₂²⋊C₄	—	47	4	no	—
269	C₂×C₄²	—	47	2	no	—
270	C₂×C₄²	C₄×D₄₇	1	2	yes	—
271	C₂×C₄²	C₄×D₄₇	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₄⋊C₈	—	47	4	no	—
276	C₄⋊C₈	—	47	4	no	—
277	C₂²⋊C₈	—	47	8	no	—
278	C₂²⋊C₈	—	47	8	no	—
279	#97	—	2	2	no	—
280	#97	—	2	2	no	—
281	#97	—	2	2	no	—
282	#97	—	94	4	no	—
283	#97	D₁₈₈	1	4	yes	complemented
284	C₄×C₈	—	94	4	no	—
285	C₄×C₈	—	94	4	no	—
286	C₄×C₈	C₄×D₄₇	1	4	yes	—
287	C₄×C₈	C₄×D₄₇	1	4	yes	—
288	#95	—	47	4	no	—
289	#95	—	47	2	no	—
290	C₂⁴	—	47	2	no	—
291	C₂×D₄	—	47	4	no	—
292	C₂×D₄	—	94	4	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	4	no	—
295	C₂²×C₄	—	47	4	no	—
296	C₂²×C₄	—	47	4	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
304	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
306	M₁₆	—	94	16	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	47	4	no	—
312	C₂×C₈	—	47	4	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	2	no	—
317	C₂×C₈	—	94	16	no	—
318	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
319	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
320	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
321	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
322	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
323	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
324	C₂×C₈	#10625350	1	2	yes	—
325	C₂×C₈	#10625350	1	2	yes	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	94	8	no	—
328	C₄⋊C₄	—	94	4	no	—
329	C₂²⋊C₄	—	47	8	no	—
330	C₂²⋊C₄	—	94	8	no	—
331	C₂²⋊C₄	—	188	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	2	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	2	no	—
338	C₄²	C₂×C₄×D₄₇	1	2	yes	—
339	C₄²	C₂×C₄×D₄₇	1	2	yes	—
340	C₄²	C₂×D₁₈₈	1	2	yes	—
341	C₄²	#10625350	1	2	yes	—
342	C₂³	—	47	4	no	—
343	C₂³	—	94	2	no	—
344	C₂³	—	94	2	no	—
345	C₂³	—	94	4	no	—
346	C₂³	—	94	4	no	—
347	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
348	D₄	—	94	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	4	no	—
365	C₂×C₄	C₄²×D₄₇	1	2	yes	—
366	C₂×C₄	C₄²×D₄₇	1	2	yes	—
367	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
368	C₂×C₄	#13094032	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
372	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
373	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	94	4	no	—
378	C₈	—	94	4	no	—
379	C₈	C₄×D₁₈₈	1	4	yes	—
380	C₈	C₄×D₁₈₈	1	4	yes	—
381	C₂²	—	94	4	no	—
382	C₂²	—	94	4	no	—
383	C₂²	—	94	4	no	—
384	C₂²	—	188	4	no	—
385	C₂²	—	188	4	no	—
386	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
387	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
388	C₂²	C₄×#10625350	1	1	yes	characteristic
389	C₂²	C₂×#13094032	1	2	yes	—
390	C₂²	#15689889	1	2	yes	—
391	C₄	—	2	2	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	94	4	no	—
395	C₄	—	188	4	no	—
396	C₄	#15689080	1	4	yes	complemented
397	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
398	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
399	C₄	C₄×#10625350	1	1	yes	characteristic
400	C₄	C₄×#10625350	1	1	yes	characteristic
401	C₂	—	188	4	no	—
402	C₂	C₄²×D₁₈₈	1	1	yes	characteristic
403	C₂	C₂×#15689080	1	1	yes	characteristic
404	C₂	#20251813	1	1	yes	characteristic
405	C₂	#20252134	1	2	yes	—
406	C₂	#20252392	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#97	D₄₇
hypocenter	C₄₇	#20495
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
3. C₂×#15689080	C₂	semidirect
5. #20243255	C₂	semidirect
6. C₈×C₄⋊Dic₄₇	C₂	semidirect
7. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
8. #20243173	C₂	semidirect
9. #20243165	C₂	semidirect
10. #20243157	C₂	semidirect
11. C₄×#97×C₄₇	C₂	semidirect
16. #15689202	C₄	semidirect
17. C₈×D₁₈₈	C₄	semidirect
83. #97×C₄₇	D₄	semidirect
191. C₄×C₄₇	#405	semidirect
208. C₄×#97	D₄₇	semidirect
244. C₄₇	#20495	semidirect
283. #97	D₁₈₈	semidirect
396. C₄	#15689080	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×C₈×D₁₈₈	2
C₂×#15689080	2
#20245852	2
#20243255	2
C₈×C₄⋊Dic₄₇	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243173	2
#20243165	2
#20243157	2
C₄×#97×C₄₇	2
#20495	47