Subgroups — #26221171

Order 12032.

982 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245795	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244152	C₂	1	2	yes	maximal, complemented
4	#20244147	C₂	1	2	yes	maximal, complemented
5	#20243583	C₂	1	2	yes	maximal
6	#20243578	C₂	1	2	yes	maximal
7	#20243285	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₇×#432	C₂	1	1	yes	maximal, characteristic
9	C₂×#13093983	—	2	1	no	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	—	2	1	no	—
13	C₂×#13093958	C₂²	1	4	yes	—
14	C₂×#13093956	C₂²	1	4	yes	—
15	#15688993	C₂²	1	1	yes	characteristic
16	#15688993	C₂²	1	1	yes	characteristic
17	#15688989	—	2	1	no	—
18	#15688983	—	2	1	no	—
19	#15688983	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	—	2	1	no	—
22	C₄×C₄⋊Dic₄₇	—	2	1	no	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	C₂×C₄₇⋊#95	—	2	1	no	—
27	#15688886	C₂²	1	4	yes	—
28	#15688886	C₂²	1	4	yes	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#432	C₄	1	8	yes	complemented
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
33	C₂×#97×C₄₇	C₂²	1	2	yes	—
34	C₂³×Dic₄₇	—	2	1	no	—
35	C₂³×Dic₄₇	—	2	1	no	—
36	#13093983	—	4	4	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	—	2	4	no	—
40	C₂×C₄⋊Dic₄₇	—	2	4	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	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×C₂²⋊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	—	4	4	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	C₂³	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
71	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
72	#97×C₄₇	C₂×C₄	1	8	yes	complemented
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	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×Q₈	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₄₇	—	2	4	no	—
101	C₂×C₈×C₄₇	—	2	4	no	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
103	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
104	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
105	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₂²⋊Dic₄₇	—	4	4	no	—
110	C₄⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	—	2	4	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	4	no	—
115	C₄⋊Dic₄₇	—	2	4	no	—
116	C₄⋊Dic₄₇	—	4	2	no	—
117	C₄⋊Dic₄₇	—	4	2	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	C₄⋊Dic₄₇	#41	1	4	yes	—
121	C₄⋊Dic₄₇	#41	1	4	yes	—
122	C₄×Dic₄₇	—	4	4	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	4	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
131	C₂³×C₄₇	#137	1	2	yes	—
132	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	8	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₄₇	#137	1	2	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	4	8	no	—
159	C₂×Dic₄₇	—	4	8	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	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	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₈×C₄₇	—	2	8	no	—
171	#21365	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	#428	1	4	yes	—
179	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₇	#525	1	1	yes	characteristic
181	C₂²×C₄₇	#525	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	#428	1	4	yes	—
191	C₄×C₄₇	C₄×#41	1	2	yes	—
192	C₄×C₄₇	#533	1	2	yes	—
193	Dic₄₇	—	4	4	no	—
194	Dic₄₇	—	4	4	no	—
195	Dic₄₇	—	8	2	no	—
196	Dic₄₇	—	8	2	no	—
197	C₂×#432	D₄₇	1	1	yes	characteristic
198	#2285	—	47	1	no	—
199	C₂×C₄×C₄⋊C₄	—	47	1	no	—
200	#1948	—	47	2	no	—
201	#1947	—	47	2	no	—
202	#1853	—	47	2	no	—
203	#1852	—	47	2	no	—
204	#1776	—	47	4	no	—
205	C₂×C₄₇	—	2	4	no	—
206	C₂×C₄₇	#2296	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
208	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
209	C₂×C₄₇	#3109	1	1	yes	characteristic
210	C₂×C₄₇	#3110	1	1	yes	characteristic
211	C₂×C₄₇	#3112	1	1	yes	characteristic
212	C₂×C₄₇	#3113	1	1	yes	characteristic
213	C₂×#117	—	94	1	no	—
214	C₂²×C₄⋊C₄	—	47	1	no	—
215	C₂²×C₄⋊C₄	—	47	1	no	—
216	C₂²×C₄²	—	94	1	no	—
217	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
218	#432	Dic₄₇	1	8	yes	complemented
219	C₂×#107	—	47	4	no	—
220	C₂×#106	—	47	4	no	—
221	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
222	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
223	C₂×#97	C₂×D₄₇	1	2	yes	—
224	#384	—	47	1	no	—
225	#384	—	47	1	no	—
226	#382	—	94	1	no	—
227	#380	—	47	2	no	—
228	#380	—	94	1	no	—
229	C₄×C₄⋊C₄	—	47	2	no	—
230	C₄×C₄⋊C₄	—	47	2	no	—
231	C₄×C₄⋊C₄	—	47	2	no	—
232	C₄×C₄⋊C₄	—	94	1	no	—
233	C₄×C₄⋊C₄	—	94	1	no	—
234	C₄×C₄⋊C₄	—	94	1	no	—
235	C₂×#95	—	94	1	no	—
236	#340	—	47	4	no	—
237	#340	—	47	4	no	—
238	C₄₇	#21365	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	94	1	no	—
240	C₂³×C₄	—	94	1	no	—
241	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
242	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
243	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
245	#117	—	188	4	no	—
246	C₂×C₄⋊C₄	—	47	2	no	—
247	C₂×C₄⋊C₄	—	47	2	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	—	94	4	no	—
251	C₂×C₄⋊C₄	—	94	4	no	—
252	C₂×C₄⋊C₄	—	94	1	no	—
253	C₂×C₄⋊C₄	—	94	1	no	—
254	C₂×C₄⋊C₄	—	94	1	no	—
255	C₂×C₄⋊C₄	—	94	1	no	—
256	C₂×C₄⋊C₄	—	94	1	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₂²⋊C₄	—	94	2	no	—
259	C₂×C₄²	—	94	2	no	—
260	C₂×C₄²	—	94	2	no	—
261	C₂×C₄²	—	94	2	no	—
262	C₂×C₄²	—	188	4	no	—
263	C₂×C₄²	Dic₉₄	1	4	yes	—
264	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
265	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
266	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	#107	—	94	8	no	—
270	#106	—	94	8	no	—
271	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
272	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
273	#97	C₂×Dic₄₇	1	8	yes	complemented
274	#95	—	94	2	no	—
275	#95	—	94	2	no	—
276	#95	—	94	2	no	—
277	#95	—	94	2	no	—
278	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	94	4	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	—	188	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
296	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
297	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
298	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
304	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
308	C₄⋊C₄	—	47	4	no	—
309	C₄⋊C₄	—	47	4	no	—
310	C₄⋊C₄	—	94	4	no	—
311	C₄⋊C₄	—	94	4	no	—
312	C₄⋊C₄	—	94	2	no	—
313	C₄⋊C₄	—	94	2	no	—
314	C₄⋊C₄	—	94	4	no	—
315	C₄⋊C₄	—	94	4	no	—
316	C₄⋊C₄	—	188	2	no	—
317	C₄⋊C₄	—	188	2	no	—
318	C₄⋊C₄	—	188	2	no	—
319	C₄⋊C₄	—	188	2	no	—
320	C₂²⋊C₄	—	188	4	no	—
321	C₄²	—	188	4	no	—
322	C₄²	—	188	4	no	—
323	C₄²	—	188	4	no	—
324	C₄²	C₄⋊Dic₄₇	1	4	yes	—
325	C₄²	C₄⋊Dic₄₇	1	4	yes	—
326	C₄²	C₂×Dic₉₄	1	2	yes	—
327	C₄²	C₂×Dic₉₄	1	2	yes	—
328	C₄²	C₂²×Dic₄₇	1	2	yes	—
329	C₄²	C₂²×Dic₄₇	1	2	yes	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
335	C₂³	#13094052	1	2	yes	—
336	C₂³	#13094057	1	2	yes	—
337	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	94	4	no	—
351	C₂×C₄	—	94	4	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	—	188	2	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	8	no	—
359	C₂×C₄	—	188	8	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
365	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
366	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
367	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
368	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
369	C₂×C₄	#13094052	1	2	yes	—
370	C₂×C₄	#13094057	1	2	yes	—
371	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	2	yes	—
374	C₂×C₄	#41×D₄₇	1	2	yes	—
375	C₈	—	2	8	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	#15689165	1	4	yes	—
383	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
384	C₂²	#15689635	1	1	yes	characteristic
385	C₂²	#15689635	1	1	yes	characteristic
386	C₂²	C₂×#13094052	1	1	yes	characteristic
387	C₂²	C₂×#13094052	1	1	yes	characteristic
388	C₂²	C₂×#13094057	1	1	yes	characteristic
389	C₂²	C₂×#13094057	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	376	2	no	—
395	C₄	—	376	2	no	—
396	C₄	—	188	4	no	—
397	C₄	—	188	4	no	—
398	C₄	#15689165	1	4	yes	—
399	C₄	#41×Dic₄₇	1	2	yes	—
400	C₄	#15689676	1	2	yes	—
401	C₂	—	2	4	no	—
402	C₂	#20245872	1	1	yes	characteristic
403	C₂	C₂×#15689165	1	1	yes	characteristic
404	C₂	C₂×#15689165	1	1	yes	characteristic
405	C₂	#20253480	1	1	yes	characteristic
406	C₂	#20253488	1	1	yes	characteristic
407	C₂	#20253511	1	1	yes	characteristic
408	C₂	#20253519	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#432	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#432	D₄₇
hypocenter	C₄₇	#21365
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #20244152	C₂	semidirect
4. #20244147	C₂	semidirect
7. #20243285	C₂	semidirect
30. C₄₇×#432	C₄	semidirect
70. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
72. #97×C₄₇	C₂×C₄	semidirect
218. #432	Dic₄₇	semidirect
238. C₄₇	#21365	semidirect
271. C₄⋊C₈	C₂×Dic₄₇	semidirect
273. #97	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20245795	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244152	2
#20244147	2
#20243583	2
#20243578	2
#20243285	2
C₂×C₄₇×#432	2
#21365	47