Subgroups — #26214564

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689179	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093982	C₂	1	1	yes	maximal, characteristic
4	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243171	C₂	1	2	yes	maximal
8	#20243168	C₂	1	2	yes	maximal
9	#20243135	C₂	1	2	yes	maximal, complemented
10	C₄×#13093934	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₄	1	2	yes	—
15	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
16	#15689179	C₄	1	8	yes	complemented
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
19	C₄×#10625324	C₄	1	8	yes	complemented
20	C₂×#13093934	C₂²	1	2	yes	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	2	yes	—
23	C₂×#13093934	C₂²	1	1	yes	characteristic
24	C₂×#13093934	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
30	#15688970	C₄	1	2	yes	—
31	#15688968	C₄	1	2	yes	—
32	C₄²×Dic₄₇	C₂²	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625324	—	2	2	no	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	—	2	2	no	—
47	C₂×#10625324	—	2	2	no	—
48	C₂×#10625324	C₂×C₄	1	4	yes	—
49	C₂×#10625324	C₂×C₄	1	4	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	#13093982	—	2	8	no	—
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
56	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₄²×D₄₇	C₂×C₄	1	4	yes	—
63	C₄²×D₄₇	C₂×C₄	1	4	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
65	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
66	#13093934	—	2	4	no	—
67	#13093934	—	2	4	no	—
68	#13093934	C₂×C₄	1	4	yes	—
69	#13093934	C₂×C₄	1	4	yes	—
70	#13093934	C₂×C₄	1	8	yes	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
82	C₄×C₈×C₄₇	—	2	4	no	—
83	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
84	#95×C₄₇	C₂×C₄	1	2	yes	—
85	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₄₇	—	2	4	no	—
95	C₂×C₄×D₄₇	—	2	1	no	—
96	C₂×C₄×D₄₇	—	2	1	no	—
97	C₂×C₄×D₄₇	—	2	1	no	—
98	C₂×C₄×D₄₇	—	2	1	no	—
99	C₂×C₄×D₄₇	—	4	2	no	—
100	C₂×C₄×D₄₇	C₄²	1	4	yes	—
101	C₂×C₄×D₄₇	C₄²	1	4	yes	—
102	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₄₇	#41	1	2	yes	—
112	C₂×C₈×C₄₇	#41	1	2	yes	—
113	C₄⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
118	(C₂×D₄₇)⋊C₄	—	2	8	no	—
119	C₄⋊Dic₄₇	—	2	4	no	—
120	C₄×Dic₄₇	—	2	8	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	C₄²	1	4	yes	—
125	C₄×Dic₄₇	C₄²	1	4	yes	—
126	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
127	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	#41	1	2	yes	—
136	C₂×C₄₇⋊C₈	#41	1	2	yes	—
137	#10625324	—	2	8	no	—
138	#10625324	—	2	8	no	—
139	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
140	C₂²×D₄₇	—	2	1	no	—
141	C₂²×D₄₇	—	2	1	no	—
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	—	2	2	no	—
144	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
151	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	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×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
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	2	yes	—
166	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
167	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	8	no	—
173	C₄×D₄₇	—	4	4	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	2	4	no	—
176	C₈×C₄₇	#117	1	4	yes	complemented
177	C₄₇⋊C₈	—	2	2	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	#117	1	4	yes	complemented
180	#20480	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
182	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
183	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
184	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
185	C₂²×C₄₇	#568	1	2	yes	—
186	C₂×D₄₇	—	2	2	no	—
187	C₂×D₄₇	—	2	2	no	—
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	8	no	—
193	C₄×C₄₇	C₄×M₁₆	1	4	yes	—
194	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
195	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
196	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
197	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	2	2	no	—
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	4	4	no	—
202	C₂×#432	—	47	1	no	—
203	C₂×C₄×M₁₆	—	47	1	no	—
204	C₄×#117	—	47	1	no	—
205	#1770	—	47	1	no	—
206	#1770	—	47	1	no	—
207	C₈×C₄⋊C₄	—	47	1	no	—
208	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
209	#1753	—	47	2	no	—
210	#1753	—	47	2	no	—
211	#1745	—	47	2	no	—
212	C₄×#97	—	47	2	no	—
213	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
214	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
215	C₂×C₄₇	#2873	1	1	yes	characteristic
216	C₂×C₄₇	#2970	1	2	yes	—
217	C₂×C₄₇	#2971	1	2	yes	—
218	D₄₇	—	4	2	no	—
219	C₂²×M₁₆	—	47	1	no	—
220	C₂²×M₁₆	—	47	1	no	—
221	C₂×#117	—	47	2	no	—
222	C₂²×C₄²	—	47	1	no	—
223	#432	—	47	8	no	—
224	C₂×C₄⋊C₈	—	47	1	no	—
225	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	47	2	no	—
227	C₄×M₁₆	—	47	8	no	—
228	C₂×#97	—	47	1	no	—
229	C₂×#97	—	47	1	no	—
230	C₂×#97	—	47	2	no	—
231	C₂×#97	—	47	2	no	—
232	C₂×#97	—	47	2	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	2	no	—
235	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₄×C₄⋊C₄	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	1	no	—
239	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
240	C₄×C₂²⋊C₄	—	47	2	no	—
241	C₄×C₂²⋊C₄	—	47	2	no	—
242	#376	—	47	2	no	—
243	C₄³	—	47	2	no	—
244	#336	—	47	2	no	—
245	#336	—	47	2	no	—
246	#336	—	47	2	no	—
247	#336	C₂×D₄₇	1	2	yes	—
248	C₄₇	#20480	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	47	1	no	—
250	C₂³×C₄	—	47	1	no	—
251	C₂³×C₄	—	47	1	no	—
252	C₂×M₁₆	—	47	4	no	—
253	C₂×M₁₆	—	47	4	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	—	47	2	no	—
261	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
263	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	#117	—	94	8	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
267	C₂×C₂²⋊C₄	—	47	4	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	4	no	—
272	C₂×C₄²	—	47	4	no	—
273	C₂×C₄²	—	47	4	no	—
274	C₂×C₄²	—	47	2	no	—
275	C₂×C₄²	—	47	4	no	—
276	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
277	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊C₈	—	47	4	no	—
279	C₄⋊C₈	C₄×D₄₇	1	4	yes	—
280	C₂²⋊C₈	—	47	8	no	—
281	#97	—	47	4	no	—
282	#97	—	47	4	no	—
283	#97	—	47	8	no	—
284	#97	—	94	4	no	—
285	#97	—	94	4	no	—
286	C₄×C₈	—	2	4	no	—
287	C₄×C₈	—	47	4	no	—
288	C₄×C₈	—	94	4	no	—
289	C₄×C₈	C₄×D₄₇	1	4	yes	—
290	#95	—	47	4	no	—
291	#95	—	47	2	no	—
292	#95	C₄×D₄₇	1	2	yes	—
293	C₂⁴	—	47	1	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	4	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	47	2	no	—
300	C₂²×C₄	—	47	4	no	—
301	C₂²×C₄	—	47	4	no	—
302	C₂²×C₄	—	94	4	no	—
303	C₂²×C₄	—	94	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	—	94	1	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
310	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
312	M₁₆	—	94	8	no	—
313	M₁₆	—	94	8	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	47	2	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	47	2	no	—
321	C₂×C₈	—	47	2	no	—
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
328	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
329	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
330	C₂×C₈	#10625352	1	2	yes	—
331	C₂×C₈	#10625354	1	2	yes	—
332	C₄⋊C₄	—	94	4	no	—
333	C₄⋊C₄	#10625324	1	8	yes	complemented
334	C₂²⋊C₄	—	94	8	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	47	4	no	—
338	C₄²	—	47	4	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	94	8	no	—
342	C₄²	—	94	2	no	—
343	C₄²	—	94	2	no	—
344	C₄²	—	188	4	no	—
345	C₄²	C₂×C₄×D₄₇	1	2	yes	—
346	C₄²	C₂×C₄×D₄₇	1	2	yes	—
347	C₂³	—	47	2	no	—
348	C₂³	—	94	1	no	—
349	C₂³	—	94	1	no	—
350	C₂³	—	94	2	no	—
351	C₂³	—	94	2	no	—
352	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	47	2	no	—
357	C₂×C₄	—	47	2	no	—
358	C₂×C₄	—	47	2	no	—
359	C₂×C₄	—	94	1	no	—
360	C₂×C₄	—	94	1	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	8	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	4	no	—
369	C₂×C₄	—	94	4	no	—
370	C₂×C₄	—	94	4	no	—
371	C₂×C₄	—	188	4	no	—
372	C₂×C₄	C₄²×D₄₇	1	2	yes	—
373	C₂×C₄	C₄²×D₄₇	1	2	yes	—
374	C₂×C₄	C₂×#10625324	1	8	yes	—
375	C₂×C₄	C₂×#10625324	1	4	yes	—
376	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
379	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	4	no	—
384	C₈	—	47	4	no	—
385	C₈	—	94	2	no	—
386	C₈	—	94	4	no	—
387	C₈	#13093982	1	4	yes	complemented
388	C₂²	—	94	2	no	—
389	C₂²	—	94	2	no	—
390	C₂²	—	94	2	no	—
391	C₂²	—	188	2	no	—
392	C₂²	—	188	2	no	—
393	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
394	C₂²	C₄×#10625352	1	1	yes	characteristic
395	C₂²	C₄×#10625354	1	1	yes	characteristic
396	C₂²	C₂²×#10625324	1	2	yes	—
397	C₂²	#15689888	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	2	8	no	—
400	C₄	—	94	2	no	—
401	C₄	—	94	2	no	—
402	C₄	—	94	2	no	—
403	C₄	—	188	4	no	—
404	C₄	C₄×#10625324	1	4	yes	—
405	C₄	#117×D₄₇	1	1	yes	characteristic
406	C₄	C₂×#13093982	1	1	yes	characteristic
407	C₄	C₄×#10625352	1	1	yes	characteristic
408	C₄	C₄×#10625354	1	1	yes	characteristic
409	C₂	—	188	2	no	—
410	C₂	C₄×#13093982	1	1	yes	characteristic
411	C₂	C₂×C₄×#10625324	1	1	yes	characteristic
412	C₂	#20251804	1	1	yes	characteristic
413	C₂	#20252396	1	2	yes	—
414	C₂	#20252407	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#20480
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20243258	C₂	semidirect
5. #20243255	C₂	semidirect
6. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
9. #20243135	C₂	semidirect
10. C₄×#13093934	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
16. #15689179	C₄	semidirect
19. C₄×#10625324	C₄	semidirect
113. C₄⋊C₄×C₄₇	M₁₆	semidirect
176. C₈×C₄₇	#117	semidirect
179. C₄₇⋊C₈	#117	semidirect
208. C₈×C₄⋊C₄	D₄₇	semidirect
248. C₄₇	#20480	semidirect
333. C₄⋊C₄	#10625324	semidirect
387. C₈	#13093982	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689179	2
C₂×C₄×#10625324	2
C₄×#13093982	2
#20243258	2
#20243255	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243171	2
#20243168	2
#20243135	2
C₄×#13093934	2
C₈×C₄⋊C₄×C₄₇	2
#20480	47