Subgroups — #26421941

Order 12032.

1698 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251765	C₂	1	2	yes	maximal
2	#20248761	C₂	1	2	yes	maximal
3	#20248630	C₂	1	2	yes	maximal
4	#20248618	C₂	1	4	yes	maximal
5	#20248604	C₂	1	2	yes	maximal
6	#20247959	C₂	1	4	yes	maximal
7	#20247160	C₂	1	4	yes	maximal
8	#20246448	C₂	1	2	yes	maximal
9	#20246347	C₂	1	2	yes	maximal
10	#20246347	C₂	1	2	yes	maximal
11	C₄⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal
12	C₄×#13094024	C₂	1	1	yes	maximal, characteristic
13	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
14	C₄₇×#2868	C₂	1	1	yes	maximal, characteristic
15	C₂×#13094024	C₂²	1	1	yes	characteristic
16	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
17	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
19	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
21	#15689062	C₂²	1	8	yes	—
22	#15689061	C₂²	1	8	yes	—
23	#15689053	C₂²	1	8	yes	—
24	#15689030	C₂²	1	4	yes	—
25	#15689030	C₂²	1	4	yes	—
26	#15689030	C₂²	1	4	yes	—
27	#15689029	C₂²	1	2	yes	—
28	#15689028	C₂²	1	4	yes	—
29	#15689028	C₂²	1	4	yes	—
30	#15689028	C₂²	1	4	yes	—
31	#15689022	C₂²	1	4	yes	—
32	#15689022	C₂²	1	4	yes	—
33	#15689022	C₂²	1	4	yes	—
34	#15689021	C₂²	1	2	yes	—
35	#15689021	C₂²	1	2	yes	—
36	#15689009	C₂²	1	8	yes	—
37	#15689004	C₂²	1	8	yes	—
38	#15689004	C₂²	1	8	yes	—
39	#15688993	C₂²	1	1	yes	characteristic
40	#15688988	C₂²	1	4	yes	—
41	#15688988	C₂²	1	4	yes	—
42	#15688988	C₂²	1	4	yes	—
43	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
44	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
45	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
46	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
47	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
48	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
49	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
50	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
52	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
54	C₄²×Dic₄₇	C₂²	1	2	yes	—
55	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
56	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
57	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
58	C₄₇×#384	C₂²	1	2	yes	—
59	C₄₇×#384	C₂²	1	2	yes	—
60	C₄₇×#384	C₂²	1	2	yes	—
61	C₄₇×#384	C₂²	1	2	yes	—
62	C₄³×C₄₇	C₂²	1	1	yes	characteristic
63	C₂²×Dic₉₄	C₂³	1	2	yes	—
64	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
65	#13094024	—	2	4	no	—
66	Q₈×Dic₄₇	—	4	8	no	—
67	C₄×Dic₉₄	—	2	4	no	—
68	C₄×Dic₉₄	—	2	4	no	—
69	C₄×Dic₉₄	—	2	8	no	—
70	C₄×Dic₉₄	Q₈	1	8	yes	complemented
71	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
79	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
80	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
81	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
82	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
83	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
84	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
85	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
86	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
89	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
91	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
92	C₄₇⋊#95	C₂³	1	2	yes	—
93	C₄₇⋊#95	C₂³	1	2	yes	—
94	C₄₇⋊#95	C₂³	1	2	yes	—
95	C₄₇⋊#95	C₂³	1	4	yes	—
96	C₄₇⋊#95	C₂³	1	4	yes	—
97	C₄₇⋊#95	C₂³	1	8	yes	—
98	C₄₇⋊#95	C₂³	1	8	yes	—
99	C₄₇⋊#95	C₂³	1	8	yes	—
100	C₄₇⋊#95	C₂³	1	8	yes	—
101	C₄₇⋊#95	C₂³	1	8	yes	—
102	C₄₇⋊#95	C₂³	1	8	yes	—
103	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₄₇	—	2	8	no	—
105	C₄⋊Q₈×C₄₇	—	2	8	no	—
106	C₄⋊Q₈×C₄₇	—	4	4	no	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×Q₈×C₄₇	—	2	8	no	—
121	C₂×Q₈×C₄₇	—	2	8	no	—
122	C₂×Q₈×C₄₇	—	2	8	no	—
123	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
132	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
133	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
134	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
135	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
136	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
137	C₂×Dic₉₄	—	2	2	no	—
138	C₂×Dic₉₄	—	2	2	no	—
139	C₂×Dic₉₄	—	2	4	no	—
140	C₂×Dic₉₄	—	2	4	no	—
141	C₂×Dic₉₄	—	2	4	no	—
142	C₂×Dic₉₄	C₂×Q₈	1	4	yes	—
143	C₄⋊C₄×C₄₇	—	2	8	no	—
144	C₄⋊C₄×C₄₇	—	2	8	no	—
145	C₄⋊C₄×C₄₇	—	2	8	no	—
146	C₄⋊C₄×C₄₇	—	2	8	no	—
147	C₄⋊C₄×C₄₇	—	4	4	no	—
148	C₄⋊C₄×C₄₇	—	4	4	no	—
149	C₄²×C₄₇	—	2	2	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
153	C₄²×C₄₇	#41	1	4	yes	—
154	C₄²×C₄₇	#41	1	4	yes	—
155	C₄²×C₄₇	#41	1	4	yes	—
156	C₄⋊Dic₄₇	—	2	2	no	—
157	C₄⋊Dic₄₇	—	2	2	no	—
158	C₄⋊Dic₄₇	—	2	4	no	—
159	C₄⋊Dic₄₇	—	2	4	no	—
160	C₄⋊Dic₄₇	—	2	4	no	—
161	C₄⋊Dic₄₇	—	2	4	no	—
162	C₄⋊Dic₄₇	—	2	4	no	—
163	C₄⋊Dic₄₇	—	4	8	no	—
164	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
165	Dic₄₇⋊C₄	—	2	4	no	—
166	Dic₄₇⋊C₄	—	2	4	no	—
167	Dic₄₇⋊C₄	—	2	8	no	—
168	Dic₄₇⋊C₄	C₂×Q₈	1	8	yes	—
169	C₄×Dic₄₇	—	2	4	no	—
170	C₄×Dic₄₇	—	2	4	no	—
171	C₄×Dic₄₇	—	2	8	no	—
172	C₄×Dic₄₇	—	2	4	no	—
173	C₄×Dic₄₇	—	2	4	no	—
174	C₄×Dic₄₇	—	2	4	no	—
175	C₄×Dic₄₇	—	4	8	no	—
176	C₄×Dic₄₇	C₂×Q₈	1	8	yes	—
177	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
178	Q₈×C₄₇	—	4	16	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	8	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	—	2	8	no	—
188	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
189	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
190	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
192	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
193	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
196	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
198	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
200	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
201	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
202	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	2	2	no	—
206	C₂×Dic₄₇	—	2	2	no	—
207	C₂×Dic₄₇	—	2	2	no	—
208	C₂×Dic₄₇	—	2	2	no	—
209	C₂×Dic₄₇	—	2	4	no	—
210	C₂×Dic₄₇	—	2	4	no	—
211	C₂×Dic₄₇	—	2	4	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	4	no	—
214	C₂×Dic₄₇	—	2	2	no	—
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	—	2	2	no	—
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
220	C₂×Dic₄₇	C₂²×Q₈	1	4	yes	—
221	Dic₉₄	—	2	8	no	—
222	Dic₉₄	—	4	8	no	—
223	#36598	—	47	1	no	maximal, Sylow
224	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
225	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
226	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
227	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	4	8	no	—
235	C₄×C₄₇	#533	1	4	yes	—
236	C₄×C₄₇	#556	1	4	yes	—
237	C₄×C₄₇	#557	1	4	yes	—
238	C₄×C₄₇	#559	1	4	yes	—
239	Dic₄₇	—	2	4	no	—
240	Dic₄₇	—	2	4	no	—
241	Dic₄₇	—	4	4	no	—
242	Dic₄₇	—	4	2	no	—
243	Dic₄₇	—	4	2	no	—
244	Dic₄₇	—	4	4	no	—
245	#2868	D₄₇	1	1	yes	characteristic
246	#2862	—	47	2	no	—
247	#2582	—	47	2	no	—
248	#2571	—	47	2	no	—
249	#2570	—	47	4	no	—
250	#2568	—	47	2	no	—
251	#2511	—	47	4	no	—
252	#2446	—	47	4	no	—
253	#2365	—	47	2	no	—
254	#2355	—	47	2	no	—
255	#2355	—	47	2	no	—
256	C₄×C₄⋊Q₈	—	47	1	no	—
257	C₄×C₄⋊Q₈	—	47	2	no	—
258	C₄²×Q₈	—	47	1	no	—
259	C₂×C₄₇	C₂×#533	1	1	yes	characteristic
260	C₂×C₄₇	C₂×#556	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#557	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#559	1	1	yes	characteristic
263	C₂×C₄₇	#3503	1	1	yes	characteristic
264	C₂×C₄₇	#3509	1	1	yes	characteristic
265	C₂×C₄₇	#3511	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	—	47	1	no	—
267	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
268	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
269	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
270	C₂×C₄×Q₈	—	47	4	no	—
271	C₂×C₄×Q₈	—	47	1	no	—
272	C₂×C₄×Q₈	—	47	2	no	—
273	C₂×C₄×Q₈	—	47	1	no	—
274	C₂×C₄×Q₈	—	47	1	no	—
275	#400	—	47	8	no	—
276	#400	—	47	8	no	—
277	#398	—	47	8	no	—
278	#391	—	47	4	no	—
279	#391	—	47	4	no	—
280	#391	—	47	4	no	—
281	#391	—	47	4	no	—
282	#391	—	47	4	no	—
283	#391	—	47	4	no	—
284	#391	—	47	2	no	—
285	#389	—	47	4	no	—
286	#389	—	47	4	no	—
287	#389	—	47	4	no	—
288	#389	—	47	2	no	—
289	#389	—	47	2	no	—
290	#387	—	47	8	no	—
291	#387	—	47	8	no	—
292	#387	—	47	8	no	—
293	#384	—	47	1	no	—
294	#384	C₂×D₄₇	1	2	yes	—
295	#384	C₂×D₄₇	1	2	yes	—
296	#384	C₂×D₄₇	1	2	yes	—
297	#384	C₂×D₄₇	1	2	yes	—
298	#382	—	47	4	no	—
299	#382	—	47	4	no	—
300	#382	—	47	4	no	—
301	C₄×C₄⋊C₄	—	47	4	no	—
302	C₄×C₄⋊C₄	—	47	4	no	—
303	C₄×C₄⋊C₄	—	47	4	no	—
304	C₄×C₄⋊C₄	—	47	2	no	—
305	C₄×C₄⋊C₄	—	47	2	no	—
306	C₄×C₄⋊C₄	—	47	2	no	—
307	C₄×C₄⋊C₄	—	47	1	no	—
308	C₄×C₄⋊C₄	—	47	1	no	—
309	C₄×C₄⋊C₄	—	47	1	no	—
310	C₄×C₄⋊C₄	—	47	2	no	—
311	C₄×C₄⋊C₄	—	47	2	no	—
312	C₄³	—	47	2	no	—
313	C₄³	C₂×D₄₇	1	1	yes	characteristic
314	C₄₇	#36598	1	1	yes	characteristic, complemented, Sylow
315	C₂²×Q₈	—	47	1	no	—
316	C₂²×Q₈	—	47	2	no	—
317	C₂²×Q₈	C₂²×D₄₇	1	4	yes	—
318	C₄⋊Q₈	—	2	8	no	—
319	C₄⋊Q₈	—	2	8	no	—
320	C₄⋊Q₈	—	4	4	no	—
321	C₄⋊Q₈	—	94	4	no	—
322	C₄×Q₈	—	47	8	no	—
323	C₄×Q₈	—	94	4	no	—
324	C₄×Q₈	—	94	4	no	—
325	C₄×Q₈	—	94	8	no	—
326	C₄×Q₈	—	188	8	no	—
327	C₂×C₄⋊C₄	—	47	2	no	—
328	C₂×C₄⋊C₄	—	47	1	no	—
329	C₂×C₄⋊C₄	—	47	2	no	—
330	C₂×C₄⋊C₄	—	47	2	no	—
331	C₂×C₄⋊C₄	—	47	2	no	—
332	C₂×C₄⋊C₄	—	47	4	no	—
333	C₂×C₄⋊C₄	—	47	1	no	—
334	C₂×C₄⋊C₄	—	47	2	no	—
335	C₂×C₄⋊C₄	—	47	1	no	—
336	C₂×C₄⋊C₄	—	47	2	no	—
337	C₂×C₄⋊C₄	—	47	2	no	—
338	C₂×C₄⋊C₄	—	47	2	no	—
339	C₂×C₄⋊C₄	—	47	8	no	—
340	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
341	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
342	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
343	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
344	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
345	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
346	C₂×C₄²	—	47	2	no	—
347	C₂×C₄²	—	47	2	no	—
348	C₂×C₄²	—	47	2	no	—
349	C₂×C₄²	—	47	2	no	—
350	C₂×C₄²	—	47	4	no	—
351	C₂×C₄²	—	47	2	no	—
352	C₂×C₄²	—	47	2	no	—
353	C₂×C₄²	—	47	8	no	—
354	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
359	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
360	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
361	#95	—	47	2	no	—
362	#95	—	47	2	no	—
363	#95	—	47	2	no	—
364	#95	—	47	8	no	—
365	#95	—	47	8	no	—
366	#95	—	47	4	no	—
367	#95	—	47	4	no	—
368	#95	—	47	8	no	—
369	#95	—	47	8	no	—
370	#95	—	47	8	no	—
371	#95	—	47	8	no	—
372	C₂×Q₈	—	2	8	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	47	4	no	—
376	C₂×Q₈	—	94	2	no	—
377	C₂×Q₈	—	94	4	no	—
378	C₂×Q₈	—	94	2	no	—
379	C₂×Q₈	—	94	4	no	—
380	C₂×Q₈	—	94	4	no	—
381	C₂²×C₄	—	47	2	no	—
382	C₂²×C₄	—	47	2	no	—
383	C₂²×C₄	—	47	2	no	—
384	C₂²×C₄	—	47	4	no	—
385	C₂²×C₄	—	47	2	no	—
386	C₂²×C₄	—	47	4	no	—
387	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
388	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
394	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	—	47	8	no	—
402	C₄⋊C₄	—	47	4	no	—
403	C₄⋊C₄	—	94	4	no	—
404	C₄⋊C₄	—	94	2	no	—
405	C₄⋊C₄	—	94	4	no	—
406	C₄⋊C₄	—	94	4	no	—
407	C₄⋊C₄	—	94	4	no	—
408	C₄⋊C₄	—	94	8	no	—
409	C₄⋊C₄	—	94	4	no	—
410	C₄⋊C₄	—	94	2	no	—
411	C₄⋊C₄	—	94	4	no	—
412	C₄⋊C₄	—	94	4	no	—
413	C₄⋊C₄	—	188	8	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	47	8	no	—
418	C₄²	—	94	4	no	—
419	C₄²	—	94	4	no	—
420	C₄²	—	94	8	no	—
421	C₄²	—	94	4	no	—
422	C₄²	—	94	4	no	—
423	C₄²	—	94	4	no	—
424	C₄²	—	188	8	no	—
425	C₄²	#10625352	1	4	yes	—
426	C₄²	#10625352	1	4	yes	—
427	C₄²	Q₈×D₄₇	1	4	yes	—
428	C₄²	#10625354	1	4	yes	—
429	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
430	Q₈	—	4	16	no	—
431	Q₈	—	94	8	no	—
432	Q₈	—	188	8	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	47	4	no	—
443	C₂×C₄	—	47	4	no	—
444	C₂×C₄	—	94	2	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	94	2	no	—
447	C₂×C₄	—	94	2	no	—
448	C₂×C₄	—	94	2	no	—
449	C₂×C₄	—	94	4	no	—
450	C₂×C₄	—	94	2	no	—
451	C₂×C₄	—	94	4	no	—
452	C₂×C₄	—	94	4	no	—
453	C₂×C₄	—	94	2	no	—
454	C₂×C₄	—	94	4	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	94	2	no	—
457	C₂×C₄	—	94	2	no	—
458	C₂×C₄	—	94	4	no	—
459	C₂×C₄	—	94	4	no	—
460	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
461	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
462	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
463	C₂×C₄	C₂×#10625352	1	2	yes	—
464	C₂×C₄	C₂×#10625352	1	2	yes	—
465	C₂×C₄	C₂×#10625352	1	2	yes	—
466	C₂×C₄	C₂×#10625352	1	2	yes	—
467	C₂×C₄	C₂×#10625352	1	2	yes	—
468	C₂×C₄	C₂×#10625352	1	2	yes	—
469	C₂×C₄	C₂×#10625354	1	2	yes	—
470	C₂×C₄	C₂×#10625354	1	2	yes	—
471	C₂×C₄	C₂×#10625354	1	2	yes	—
472	C₂×C₄	#13094069	1	2	yes	—
473	C₂×C₄	#13094072	1	2	yes	—
474	C₂×C₄	#13094072	1	2	yes	—
475	C₂²	C₂²×Q₈×D₄₇	1	1	yes	characteristic
476	C₂²	C₂²×#10625352	1	1	yes	characteristic
477	C₂²	C₂²×#10625352	1	1	yes	characteristic
478	C₂²	C₂²×#10625354	1	1	yes	characteristic
479	C₂²	C₂×#13094069	1	1	yes	characteristic
480	C₂²	C₂×#13094072	1	1	yes	characteristic
481	C₂²	C₂×#13094072	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	8	no	—
486	C₄	—	94	4	no	—
487	C₄	—	94	4	no	—
488	C₄	—	188	2	no	—
489	C₄	—	188	4	no	—
490	C₄	—	188	4	no	—
491	C₄	—	188	2	no	—
492	C₄	#15689678	1	4	yes	—
493	C₄	#15689847	1	4	yes	—
494	C₄	#15689848	1	4	yes	—
495	C₄	#15689859	1	4	yes	—
496	C₂	C₂×#15689678	1	1	yes	characteristic
497	C₂	C₂×#15689847	1	1	yes	characteristic
498	C₂	C₂×#15689848	1	1	yes	characteristic
499	C₂	C₂×#15689859	1	1	yes	characteristic
500	C₂	#20257204	1	1	yes	characteristic
501	C₂	#20257272	1	1	yes	characteristic
502	C₂	#20257301	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator, socle, prime radical, cosocle	C₂³×C₄₇	C₂⁵
Fitting	C₄₇×#2868	C₂
hypercenter	#2868	D₄₇
hypocenter	C₄₇	#36598
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #2868

Complements

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

N	H ≅ G/N	type
70. C₄×Dic₉₄	Q₈	semidirect
314. C₄₇	#36598	semidirect

Maximal subgroups

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

subgroup	index
#20251765	2
#20248761	2
#20248630	2
#20248618	2
#20248604	2
#20247959	2
#20247160	2
#20246448	2
#20246347	2
C₄⋊Q₈×Dic₄₇	2
C₄×#13094024	2
C₄²×Dic₉₄	2
C₄₇×#2868	2
#36598	47