Subgroups — #26124465

Order 12032.

814 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	C₂²×#13093958	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688886	C₂	1	2	yes	maximal
3	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
4	#20241618	C₂	1	2	yes	maximal
5	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×#13093958	—	2	4	no	—
9	C₂×#13093958	—	2	2	no	—
10	C₂×C₄₇⋊#95	—	2	2	no	—
11	C₂×C₄₇⋊#95	—	2	2	no	—
12	#15688886	—	2	4	no	—
13	#15688886	C₄	1	4	yes	complemented
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#336	—	2	2	no	—
18	C₂³×Dic₄₇	—	2	2	no	—
19	C₂³×Dic₄₇	—	2	2	no	—
20	C₂×C₄⋊Dic₄₇	—	2	2	no	—
21	C₂×C₄⋊Dic₄₇	—	2	2	no	—
22	C₂×C₄⋊Dic₄₇	—	2	2	no	—
23	C₂×C₄⋊Dic₄₇	—	2	2	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×C₄⋊Dic₄₇	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
32	#13093958	—	2	8	no	—
33	C₄₇⋊#95	—	4	4	no	—
34	C₄₇⋊#95	—	4	4	no	—
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	—	2	2	no	—
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	—	2	1	no	—
41	C₂²×C₈×C₄₇	—	2	2	no	—
42	C₂²×C₈×C₄₇	—	2	2	no	—
43	C₂²×C₈×C₄₇	—	2	1	no	—
44	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₄₇	D₄	1	2	yes	—
46	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
47	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
48	C₂×C₄²×C₄₇	—	2	1	no	—
49	C₂×C₄²×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	1	no	—
52	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	—	2	1	no	—
54	C₂²×C₄×C₄₇	—	2	1	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	1	no	—
58	C₂²×C₄×C₄₇	—	2	1	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	D₈	1	2	yes	—
62	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
63	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	#41	1	2	yes	—
69	C₂²×C₄×C₄₇	#41	1	2	yes	—
70	C₂²×C₄×C₄₇	#41	1	2	yes	—
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
73	C₂²×Dic₄₇	—	2	4	no	—
74	C₂²×Dic₄₇	—	2	4	no	—
75	C₂²×Dic₄₇	—	4	2	no	—
76	C₂²×Dic₄₇	—	4	2	no	—
77	C₂²×Dic₄₇	—	4	2	no	—
78	C₂²×Dic₄₇	—	4	2	no	—
79	C₂²×Dic₄₇	—	4	2	no	—
80	C₂²×Dic₄₇	—	4	2	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂×C₈×C₄₇	—	2	4	no	—
88	C₂×C₈×C₄₇	—	2	2	no	—
89	C₂×C₈×C₄₇	—	2	4	no	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	4	1	no	—
94	C₂×C₈×C₄₇	—	4	2	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	C₄⋊C₄	1	4	yes	—
97	C₄²×C₄₇	—	4	1	no	—
98	C₄²×C₄₇	—	4	1	no	—
99	C₄²×C₄₇	—	4	2	no	—
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	2	4	no	—
103	C₄⋊Dic₄₇	—	2	4	no	—
104	C₄⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	4	2	no	—
106	C₄⋊Dic₄₇	—	4	2	no	—
107	C₄⋊Dic₄₇	—	4	2	no	—
108	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
109	C₂³×C₄₇	#121	1	1	yes	characteristic
110	C₂³×C₄₇	#121	1	2	yes	—
111	C₂³×C₄₇	#123	1	2	yes	—
112	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
113	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
114	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
115	C₂³×C₄₇	#135	1	1	yes	characteristic
116	C₂³×C₄₇	#135	1	1	yes	characteristic
117	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
118	C₂³×C₄₇	#137	1	2	yes	—
119	C₂×C₄×C₄₇	—	2	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	4	1	no	—
124	C₂×C₄×C₄₇	—	4	1	no	—
125	C₂×C₄×C₄₇	—	4	1	no	—
126	C₂×C₄×C₄₇	—	4	1	no	—
127	C₂×C₄×C₄₇	—	4	2	no	—
128	C₂×C₄×C₄₇	—	4	2	no	—
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#117	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#123	1	2	yes	—
139	C₂×C₄×C₄₇	#124	1	2	yes	—
140	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#125	1	2	yes	—
143	C₂×C₄×C₄₇	#125	1	2	yes	—
144	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#126	1	2	yes	—
146	C₂×C₄×C₄₇	#126	1	2	yes	—
147	C₂×Dic₄₇	—	4	4	no	—
148	C₂×Dic₄₇	—	4	4	no	—
149	C₂×Dic₄₇	—	4	4	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	4	no	—
152	C₂×Dic₄₇	—	4	4	no	—
153	C₂×Dic₄₇	—	8	2	no	—
154	C₂×Dic₄₇	—	8	2	no	—
155	C₂×Dic₄₇	—	8	2	no	—
156	C₂×Dic₄₇	—	8	2	no	—
157	C₂×Dic₄₇	—	8	2	no	—
158	C₂×Dic₄₇	—	8	2	no	—
159	C₂×Dic₄₇	—	8	2	no	—
160	C₂×Dic₄₇	—	8	2	no	—
161	C₈×C₄₇	—	2	4	no	—
162	C₈×C₄₇	—	4	2	no	—
163	#11256	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	#388	1	2	yes	—
165	C₂²×C₄₇	#389	1	1	yes	characteristic
166	C₂²×C₄₇	#394	1	1	yes	characteristic
167	C₂²×C₄₇	#397	1	1	yes	characteristic
168	C₂²×C₄₇	#398	1	2	yes	—
169	C₂²×C₄₇	C₄×D₈	1	1	yes	characteristic
170	C₂²×C₄₇	C₄×Q₁₆	1	1	yes	characteristic
171	C₂²×C₄₇	#440	1	2	yes	—
172	C₂²×C₄₇	#459	1	2	yes	—
173	C₂²×C₄₇	#462	1	2	yes	—
174	C₂²×C₄₇	#463	1	2	yes	—
175	C₂²×C₄₇	#464	1	2	yes	—
176	C₂²×C₄₇	#466	1	1	yes	characteristic
177	C₂²×C₄₇	#467	1	1	yes	characteristic
178	C₂²×C₄₇	#469	1	1	yes	characteristic
179	C₂²×C₄₇	#470	1	1	yes	characteristic
180	C₂²×C₄₇	#480	1	2	yes	—
181	C₂²×C₄₇	#482	1	2	yes	—
182	C₂²×C₄₇	#484	1	2	yes	—
183	C₂²×C₄₇	#485	1	2	yes	—
184	C₂²×C₄₇	#499	1	1	yes	characteristic
185	C₂²×C₄₇	#500	1	1	yes	characteristic
186	C₂²×C₄₇	#501	1	2	yes	—
187	C₄×C₄₇	—	4	2	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	#382	1	1	yes	characteristic
190	C₄×C₄₇	#385	1	1	yes	characteristic
191	C₄×C₄₇	#387	1	2	yes	—
192	C₄×C₄₇	#393	1	1	yes	characteristic
193	C₄×C₄₇	#400	1	1	yes	characteristic
194	C₄×C₄₇	#400	1	2	yes	—
195	Dic₄₇	—	8	4	no	—
196	Dic₄₇	—	8	4	no	—
197	C₂²×#107	—	47	1	no	—
198	C₂×#340	—	47	1	no	—
199	C₂×#340	—	47	2	no	—
200	C₂×#336	D₄₇	1	1	yes	characteristic
201	C₄⋊#95	—	47	2	no	—
202	C₂×C₄₇	#1442	1	1	yes	characteristic
203	C₂×C₄₇	#1925	1	2	yes	—
204	C₂×C₄₇	#1928	1	2	yes	—
205	C₂×C₄₇	#1942	1	1	yes	characteristic
206	C₂×C₄₇	#1944	1	1	yes	characteristic
207	C₂×C₄₇	#2054	1	1	yes	characteristic
208	C₂×C₄₇	#2056	1	1	yes	characteristic
209	C₂×C₄₇	#2075	1	1	yes	characteristic
210	C₂×C₄₇	#2076	1	1	yes	characteristic
211	C₂×C₄₇	#2083	1	2	yes	—
212	C₂×C₄₇	#2085	1	2	yes	—
213	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
214	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	—	47	2	no	—
216	C₂²×C₄⋊C₄	—	47	2	no	—
217	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#107	—	94	4	no	—
219	C₂×#107	—	94	2	no	—
220	C₂×#95	—	94	2	no	—
221	C₂×#95	—	94	2	no	—
222	#340	—	47	4	no	—
223	#340	—	94	4	no	—
224	#336	—	2	2	no	—
225	C₄₇	#11256	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	—	94	2	no	—
227	C₂³×C₄	—	94	2	no	—
228	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
229	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
230	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	2	2	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	Dic₉₄	1	2	yes	—
238	C₂²×C₈	Dic₉₄	1	2	yes	—
239	C₂²×C₈	C₄×D₄₇	1	2	yes	—
240	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
241	C₂×C₄⋊C₄	—	47	4	no	—
242	C₂×C₄⋊C₄	—	47	4	no	—
243	C₂×C₄⋊C₄	—	94	2	no	—
244	C₂×C₄⋊C₄	—	94	2	no	—
245	C₂×C₄⋊C₄	—	94	2	no	—
246	C₂×C₄⋊C₄	—	94	2	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	—	94	2	no	—
251	C₂×C₄⋊C₄	—	94	2	no	—
252	C₂×C₄⋊C₄	—	94	2	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	1	no	—
257	#107	—	94	8	no	—
258	#95	—	188	4	no	—
259	#95	—	188	4	no	—
260	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	94	4	no	—
270	C₂²×C₄	—	94	4	no	—
271	C₂²×C₄	—	188	2	no	—
272	C₂²×C₄	—	188	2	no	—
273	C₂²×C₄	—	188	2	no	—
274	C₂²×C₄	—	188	2	no	—
275	C₂²×C₄	—	188	2	no	—
276	C₂²×C₄	—	188	2	no	—
277	C₂²×C₄	—	188	2	no	—
278	C₂²×C₄	—	188	2	no	—
279	C₂²×C₄	—	188	2	no	—
280	C₂²×C₄	—	188	2	no	—
281	C₂²×C₄	—	188	2	no	—
282	C₂²×C₄	—	188	2	no	—
283	C₂²×C₄	D₃₇₆	1	2	yes	—
284	C₂²×C₄	Dic₁₈₈	1	2	yes	—
285	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
286	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	#10625350	1	1	yes	characteristic
289	C₂²×C₄	#10625350	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₄₇	1	2	yes	—
291	C₂²×C₄	#10625352	1	2	yes	—
292	C₂²×C₄	#10625352	1	2	yes	—
293	C₂²×C₄	#10625354	1	2	yes	—
294	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	4	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	Dic₄₇⋊C₄	1	4	yes	—
305	C₄⋊C₄	—	94	4	no	—
306	C₄⋊C₄	—	94	4	no	—
307	C₄⋊C₄	—	94	4	no	—
308	C₄⋊C₄	—	94	4	no	—
309	C₄⋊C₄	—	188	2	no	—
310	C₄⋊C₄	—	188	2	no	—
311	C₄⋊C₄	—	188	2	no	—
312	C₄⋊C₄	—	188	2	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	2	no	—
316	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
317	C₂³	#13093998	1	1	yes	characteristic
318	C₂³	#13093999	1	2	yes	—
319	C₂³	#13094008	1	2	yes	—
320	C₂³	#13094024	1	1	yes	characteristic
321	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
322	C₂³	C₂×Dic₁₈₈	1	1	yes	characteristic
323	C₂³	#13094046	1	1	yes	characteristic
324	C₂³	#13094046	1	1	yes	characteristic
325	C₂³	#13094052	1	2	yes	—
326	C₂³	#13094057	1	2	yes	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	376	2	no	—
338	C₂×C₄	—	376	2	no	—
339	C₂×C₄	—	376	2	no	—
340	C₂×C₄	—	376	2	no	—
341	C₂×C₄	—	376	2	no	—
342	C₂×C₄	—	376	2	no	—
343	C₂×C₄	—	376	2	no	—
344	C₂×C₄	—	376	2	no	—
345	C₂×C₄	—	188	4	no	—
346	C₂×C₄	—	188	4	no	—
347	C₂×C₄	—	188	4	no	—
348	C₂×C₄	—	188	4	no	—
349	C₂×C₄	—	188	4	no	—
350	C₂×C₄	—	188	4	no	—
351	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
352	C₂×C₄	#13093982	1	2	yes	—
353	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
354	C₂×C₄	C₄×Dic₉₄	1	1	yes	characteristic
355	C₂×C₄	#13093992	1	1	yes	characteristic
356	C₂×C₄	#13094001	1	2	yes	—
357	C₂×C₄	#13094001	1	2	yes	—
358	C₂×C₄	#13094003	1	1	yes	characteristic
359	C₂×C₄	#13094005	1	1	yes	characteristic
360	C₂×C₄	#13094009	1	2	yes	—
361	C₂×C₄	#13094010	1	2	yes	—
362	C₂×C₄	#13094011	1	1	yes	characteristic
363	C₂×C₄	#13094013	1	1	yes	characteristic
364	C₂×C₄	#13094015	1	2	yes	—
365	C₂×C₄	#13094015	1	2	yes	—
366	C₂×C₄	#13094016	1	1	yes	characteristic
367	C₂×C₄	#13094017	1	2	yes	—
368	C₂×C₄	#13094019	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₂²	#15689015	1	2	yes	—
372	C₂²	#15689021	1	1	yes	characteristic
373	C₂²	#15689040	1	1	yes	characteristic
374	C₂²	#15689048	1	1	yes	characteristic
375	C₂²	#15689055	1	2	yes	—
376	C₂²	C₄×D₃₇₆	1	1	yes	characteristic
377	C₂²	C₄×Dic₁₈₈	1	1	yes	characteristic
378	C₂²	#15689225	1	2	yes	—
379	C₂²	#15689319	1	2	yes	—
380	C₂²	#15689334	1	2	yes	—
381	C₂²	#15689339	1	2	yes	—
382	C₂²	#15689346	1	2	yes	—
383	C₂²	#15689359	1	1	yes	characteristic
384	C₂²	#15689364	1	1	yes	characteristic
385	C₂²	#15689376	1	1	yes	characteristic
386	C₂²	#15689381	1	1	yes	characteristic
387	C₂²	#15689437	1	2	yes	—
388	C₂²	#15689448	1	2	yes	—
389	C₂²	#15689459	1	2	yes	—
390	C₂²	#15689465	1	2	yes	—
391	C₂²	#15689525	1	1	yes	characteristic
392	C₂²	#15689528	1	1	yes	characteristic
393	C₂²	#15689532	1	2	yes	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	376	4	no	—
397	C₄	—	376	4	no	—
398	C₄	#15688988	1	1	yes	characteristic
399	C₄	#15688995	1	1	yes	characteristic
400	C₄	#15689010	1	2	yes	—
401	C₄	#15689035	1	1	yes	characteristic
402	C₄	#15689062	1	1	yes	characteristic
403	C₄	#15689065	1	2	yes	—
404	C₂	#20241644	1	1	yes	characteristic
405	C₂	#20244009	1	2	yes	—
406	C₂	#20244030	1	2	yes	—
407	C₂	#20244121	1	1	yes	characteristic
408	C₂	#20244131	1	1	yes	characteristic
409	C₂	#20244699	1	1	yes	characteristic
410	C₂	#20244711	1	1	yes	characteristic
411	C₂	#20244811	1	1	yes	characteristic
412	C₂	#20244816	1	1	yes	characteristic
413	C₂	#20244861	1	2	yes	—
414	C₂	#20244871	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11256
LCS	G ▷ C₂²×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
13. #15688886	C₄	semidirect
225. C₄₇	#11256	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093958	2
C₂×#15688886	2
#20241618	2
C₂×C₄₇×#336	2
#11256	47