Subgroups — #26232855

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689851	C₂	1	1	yes	maximal, characteristic
2	Q₈×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20244381	C₂	1	2	yes	maximal
4	#20244380	C₂	1	2	yes	maximal
5	#20244377	C₂	1	1	yes	maximal, characteristic
6	#20244376	C₂	1	1	yes	maximal, characteristic
7	#20243381	C₂	1	2	yes	maximal
8	#20243381	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093942	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093942	C₂	1	2	yes	maximal
11	Q₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689851	—	2	1	no	—
13	#15689851	—	2	2	no	—
14	#15689851	—	2	1	no	—
15	#15689851	—	2	1	no	—
16	#15689851	—	2	2	no	—
17	#15689851	—	2	1	no	—
18	C₂×#13094024	C₂²	1	1	yes	characteristic
19	C₂×#13094022	C₄	1	2	yes	—
20	C₂×#13094016	C₂²	1	2	yes	—
21	C₂×#13094014	C₄	1	4	yes	—
22	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
23	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
24	C₂×#13093989	C₄	1	2	yes	—
25	#15689254	—	2	2	no	—
26	#15689254	—	2	1	no	—
27	Q₈×C₄₇⋊C₈	—	2	1	no	—
28	#15689147	C₂²	1	1	yes	characteristic
29	#15689147	C₂²	1	2	yes	—
30	C₂×#13093942	C₂²	1	2	yes	—
31	C₂×#13093942	C₂²	1	1	yes	characteristic
32	C₂×#13093942	C₂²	1	1	yes	characteristic
33	C₄×#10625329	C₂²	1	1	yes	characteristic
34	C₄×#10625329	C₂²	1	2	yes	—
35	#15688891	C₂²	1	2	yes	—
36	#15688891	C₂²	1	2	yes	—
37	#15688891	C₂²	1	2	yes	—
38	#15688891	C₂²	1	2	yes	—
39	#15688891	C₂²	1	1	yes	characteristic
40	#15688891	C₂²	1	2	yes	—
41	#15688891	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#446	—	2	2	no	—
44	C₄₇×#446	—	2	1	no	—
45	C₈×Q₈×C₄₇	—	2	1	no	—
46	C₄₇×#423	C₂²	1	1	yes	characteristic
47	C₄₇×#423	C₂²	1	2	yes	—
48	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
49	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
50	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
51	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
52	C₂×#10625329	C₂³	1	1	yes	characteristic
53	C₂×#10625329	C₂³	1	2	yes	—
54	C₂×#10625329	C₂³	1	1	yes	characteristic
55	#13094024	—	2	1	no	—
56	#13094024	—	2	1	no	—
57	#13094024	—	2	1	no	—
58	#13094024	—	2	1	no	—
59	#13094022	—	2	2	no	—
60	#13094022	—	2	2	no	—
61	#13094022	—	2	4	no	—
62	#13094016	—	2	2	no	—
63	#13094016	—	2	2	no	—
64	#13094016	—	2	2	no	—
65	#13094016	—	2	2	no	—
66	#13094014	—	2	4	no	—
67	#13094014	—	2	4	no	—
68	#13094014	—	2	4	no	—
69	#13094014	—	2	4	no	—
70	C₄×Dic₉₄	—	2	2	no	—
71	C₄×Dic₉₄	—	2	2	no	—
72	C₄×Dic₉₄	—	2	2	no	—
73	C₄×Dic₉₄	—	2	2	no	—
74	C₄×Dic₉₄	—	2	1	no	—
75	C₄×Dic₉₄	—	2	1	no	—
76	C₄×Dic₉₄	—	2	1	no	—
77	C₄×Dic₉₄	—	2	1	no	—
78	#13093989	—	2	4	no	—
79	#13093989	—	2	2	no	—
80	#13093989	—	2	2	no	—
81	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
84	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
85	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
87	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
88	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
89	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
90	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
91	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
92	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
93	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
94	#13093942	—	2	2	no	—
95	#13093942	—	2	4	no	—
96	#13093942	Q₈	1	4	yes	complemented
97	#13093935	—	2	2	no	—
98	#13093935	—	2	1	no	—
99	C₄×C₄₇⋊C₈	—	2	2	no	—
100	C₄×C₄₇⋊C₈	—	2	1	no	—
101	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
103	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
105	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×Q₈×C₄₇	D₄	1	2	yes	—
107	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
109	C₄×Q₈×C₄₇	D₄	1	2	yes	—
110	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
113	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
114	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₄₇	—	2	2	no	—
116	C₄⋊C₈×C₄₇	—	2	1	no	—
117	C₄⋊C₈×C₄₇	—	2	2	no	—
118	C₄⋊C₈×C₄₇	—	2	1	no	—
119	#97×C₄₇	—	2	2	no	—
120	#97×C₄₇	—	2	1	no	—
121	C₄×C₈×C₄₇	—	2	2	no	—
122	C₄×C₈×C₄₇	—	2	1	no	—
123	C₂×Q₈×C₄₇	—	4	2	no	—
124	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
134	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
135	C₂×Dic₉₄	—	2	1	no	—
136	C₂×Dic₉₄	—	2	1	no	—
137	C₂×Dic₉₄	—	2	1	no	—
138	C₂×Dic₉₄	—	2	1	no	—
139	C₂×Dic₉₄	—	2	2	no	—
140	C₂×Dic₉₄	—	2	2	no	—
141	C₂×Dic₉₄	—	4	4	no	—
142	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
143	C₂×Dic₉₄	#41	1	2	yes	—
144	M₁₆×C₄₇	—	2	1	no	—
145	M₁₆×C₄₇	—	2	2	no	—
146	M₁₆×C₄₇	—	2	1	no	—
147	M₁₆×C₄₇	—	2	2	no	—
148	M₁₆×C₄₇	—	2	1	no	—
149	M₁₆×C₄₇	C₂×Q₈	1	2	yes	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
157	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
158	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
159	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
160	C₄²×C₄₇	C₂×D₄	1	2	yes	—
161	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂×D₄	1	2	yes	—
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	2	yes	—
165	C₄²×C₄₇	C₂×D₄	1	2	yes	—
166	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₄⋊Dic₄₇	—	2	2	no	—
169	C₄⋊Dic₄₇	—	2	2	no	—
170	C₄⋊Dic₄₇	—	2	1	no	—
171	C₄⋊Dic₄₇	—	2	1	no	—
172	C₄⋊Dic₄₇	—	2	2	no	—
173	C₄⋊Dic₄₇	—	2	2	no	—
174	Dic₄₇⋊C₄	—	2	4	no	—
175	Dic₄₇⋊C₄	—	2	4	no	—
176	Dic₄₇⋊C₄	—	2	2	no	—
177	Dic₄₇⋊C₄	—	2	2	no	—
178	Dic₄₇⋊C₄	—	2	4	no	—
179	Dic₄₇⋊C₄	—	2	4	no	—
180	Dic₄₇⋊C₄	—	2	4	no	—
181	Dic₄₇⋊C₄	—	2	4	no	—
182	C₄×Dic₄₇	—	2	4	no	—
183	C₄×Dic₄₇	—	2	4	no	—
184	C₄×Dic₄₇	—	2	2	no	—
185	C₄×Dic₄₇	—	2	2	no	—
186	#10625329	—	2	1	no	—
187	#10625329	—	2	1	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	2	1	no	—
190	#10625329	—	2	2	no	—
191	#10625329	C₂×Q₈	1	2	yes	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	2	1	no	—
195	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	Q₈×C₄₇	—	2	2	no	—
197	Q₈×C₄₇	—	2	2	no	—
198	Q₈×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
216	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×Dic₄₇	—	2	2	no	—
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	4	4	no	—
222	C₂×Dic₄₇	—	4	2	no	—
223	C₂×Dic₄₇	C₄×Q₈	1	4	yes	—
224	Dic₉₄	—	2	2	no	—
225	Dic₉₄	—	2	2	no	—
226	Dic₉₄	—	2	2	no	—
227	Dic₉₄	—	2	2	no	—
228	Dic₉₄	—	4	4	no	—
229	Dic₉₄	—	4	4	no	—
230	C₈×C₄₇	—	2	2	no	—
231	C₈×C₄₇	—	4	1	no	—
232	C₈×C₄₇	—	4	2	no	—
233	C₄₇⋊C₈	—	2	2	no	—
234	C₄₇⋊C₈	—	4	2	no	—
235	C₄₇⋊C₈	—	4	1	no	—
236	#22517	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
241	C₂²×C₄₇	#519	1	1	yes	characteristic
242	C₄×C₄₇	—	2	1	no	—
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	—	2	1	no	—
249	C₄×C₄₇	#413	1	2	yes	—
250	C₄×C₄₇	#548	1	1	yes	characteristic
251	C₄×C₄₇	#548	1	1	yes	characteristic
252	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
253	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
254	Dic₄₇	—	2	4	no	—
255	Dic₄₇	—	4	4	no	—
256	Dic₄₇	—	4	2	no	—
257	C₂×#557	—	47	1	no	—
258	Q₈×M₁₆	—	47	1	no	—
259	Q₈×M₁₆	D₄₇	1	1	yes	characteristic
260	#1998	—	47	2	no	—
261	#1998	—	47	2	no	—
262	#1997	—	47	1	no	—
263	#1997	—	47	1	no	—
264	#1801	—	47	2	no	—
265	#1801	—	47	1	no	—
266	C₄×#101	—	47	2	no	—
267	C₄×#101	—	47	1	no	—
268	C₂×C₄₇	—	2	1	no	—
269	C₂×C₄₇	—	2	1	no	—
270	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
272	C₂×C₄₇	#2889	1	1	yes	characteristic
273	#557	—	94	1	no	—
274	#557	—	94	2	no	—
275	#557	—	94	1	no	—
276	#557	—	94	1	no	—
277	#557	—	94	2	no	—
278	#557	—	94	1	no	—
279	C₂×C₄⋊Q₈	—	47	2	no	—
280	C₂×C₄⋊Q₈	—	47	1	no	—
281	C₂×#125	—	47	4	no	—
282	C₂×#125	—	47	2	no	—
283	C₂×C₄×Q₈	—	47	2	no	—
284	C₂×C₄×Q₈	—	47	2	no	—
285	C₂×C₄×Q₈	—	47	1	no	—
286	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
287	#446	—	2	2	no	—
288	#446	—	2	1	no	—
289	#446	—	94	2	no	—
290	#446	—	94	1	no	—
291	C₈×Q₈	—	2	1	no	—
292	C₈×Q₈	—	94	1	no	—
293	#423	—	47	1	no	—
294	#423	—	47	2	no	—
295	#423	C₂×D₄₇	1	1	yes	characteristic
296	#423	C₂×D₄₇	1	2	yes	—
297	C₂×#101	—	47	1	no	—
298	C₂×#101	—	47	1	no	—
299	C₂×#101	—	47	2	no	—
300	C₄×M₁₆	—	47	1	no	—
301	C₄×M₁₆	—	47	2	no	—
302	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
303	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
304	#343	—	47	2	no	—
305	#343	—	47	2	no	—
306	#343	—	47	2	no	—
307	#343	—	47	2	no	—
308	#343	—	47	2	no	—
309	#343	—	47	1	no	—
310	#343	—	47	1	no	—
311	C₄₇	#22517	1	1	yes	characteristic, complemented, Sylow
312	C₂²×Q₈	—	47	2	no	—
313	C₂²×Q₈	—	47	1	no	—
314	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
315	C₂×M₁₆	—	47	1	no	—
316	C₂×M₁₆	—	47	1	no	—
317	C₂×M₁₆	—	47	2	no	—
318	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
319	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
320	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
321	C₄⋊Q₈	—	94	2	no	—
322	C₄⋊Q₈	—	94	2	no	—
323	C₄⋊Q₈	—	94	4	no	—
324	C₄⋊Q₈	—	94	1	no	—
325	C₄⋊Q₈	—	94	1	no	—
326	C₄⋊Q₈	—	94	1	no	—
327	C₄⋊Q₈	—	94	1	no	—
328	#125	—	94	4	no	—
329	#125	—	94	4	no	—
330	#125	—	94	4	no	—
331	#125	—	94	4	no	—
332	#125	—	94	2	no	—
333	#125	—	94	2	no	—
334	#125	—	94	2	no	—
335	#125	—	94	2	no	—
336	C₄×Q₈	—	94	4	no	—
337	C₄×Q₈	—	94	2	no	—
338	C₄×Q₈	—	94	2	no	—
339	C₄×Q₈	—	94	2	no	—
340	C₄×Q₈	—	94	2	no	—
341	C₄×Q₈	—	94	1	no	—
342	C₄×Q₈	—	94	1	no	—
343	C₄×Q₈	—	94	2	no	—
344	C₄×Q₈	—	94	2	no	—
345	C₄×Q₈	—	94	1	no	—
346	C₄×Q₈	—	94	1	no	—
347	C₄×Q₈	D₁₈₈	1	1	yes	characteristic
348	C₄×Q₈	D₁₈₈	1	2	yes	—
349	C₄×Q₈	D₁₈₈	1	1	yes	characteristic
350	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
351	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
352	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	—	47	2	no	—
354	C₂×C₄⋊C₄	—	47	4	no	—
355	C₂×C₄⋊C₄	—	47	4	no	—
356	C₂×C₄⋊C₄	—	47	4	no	—
357	C₂×C₄⋊C₄	—	47	2	no	—
358	C₂×C₄⋊C₄	—	47	1	no	—
359	C₂×C₄⋊C₄	—	47	2	no	—
360	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
362	C₂×C₄²	—	47	4	no	—
363	C₂×C₄²	—	47	2	no	—
364	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	C₄⋊C₈	—	2	2	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	94	2	no	—
371	C₄⋊C₈	—	94	1	no	—
372	C₄⋊C₈	—	94	2	no	—
373	C₄⋊C₈	—	94	1	no	—
374	#101	—	47	4	no	—
375	#101	—	94	2	no	—
376	#101	—	94	4	no	—
377	#97	—	2	2	no	—
378	#97	—	2	1	no	—
379	#97	—	94	2	no	—
380	#97	—	94	1	no	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	2	1	no	—
383	C₄×C₈	—	94	2	no	—
384	C₄×C₈	—	94	1	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	—	47	2	no	—
387	C₂×Q₈	—	47	2	no	—
388	C₂×Q₈	—	94	2	no	—
389	C₂×Q₈	—	94	2	no	—
390	C₂×Q₈	—	94	1	no	—
391	C₂×Q₈	—	94	1	no	—
392	C₂×Q₈	—	94	1	no	—
393	C₂×Q₈	—	94	1	no	—
394	C₂×Q₈	—	188	4	no	—
395	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
396	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
397	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
398	C₂²×C₄	—	47	2	no	—
399	C₂²×C₄	—	47	2	no	—
400	C₂²×C₄	—	47	4	no	—
401	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
403	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
405	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	47	2	no	—
412	M₁₆	—	94	1	no	—
413	M₁₆	—	94	1	no	—
414	M₁₆	—	94	2	no	—
415	M₁₆	—	94	1	no	—
416	M₁₆	—	94	2	no	—
417	M₁₆	Q₈×D₄₇	1	2	yes	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	94	1	no	—
422	C₂×C₈	—	94	2	no	—
423	C₂×C₈	—	94	1	no	—
424	C₄⋊C₄	—	94	2	no	—
425	C₄⋊C₄	—	94	2	no	—
426	C₄⋊C₄	—	94	4	no	—
427	C₄⋊C₄	—	94	4	no	—
428	C₄⋊C₄	—	94	4	no	—
429	C₄⋊C₄	—	94	4	no	—
430	C₄⋊C₄	—	94	4	no	—
431	C₄⋊C₄	—	94	4	no	—
432	C₄⋊C₄	—	94	2	no	—
433	C₄⋊C₄	—	94	2	no	—
434	C₄⋊C₄	—	94	1	no	—
435	C₄⋊C₄	—	94	2	no	—
436	C₄⋊C₄	—	94	1	no	—
437	C₄⋊C₄	—	94	2	no	—
438	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
439	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
440	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
441	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
442	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
443	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
444	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
445	C₄²	—	94	4	no	—
446	C₄²	—	94	4	no	—
447	C₄²	—	94	2	no	—
448	C₄²	—	94	2	no	—
449	C₄²	C₂×D₁₈₈	1	2	yes	—
450	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
451	C₄²	C₂×D₁₈₈	1	2	yes	—
452	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
454	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
455	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
456	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	94	2	no	—
462	Q₈	—	94	2	no	—
463	Q₈	—	94	2	no	—
464	Q₈	—	94	2	no	—
465	Q₈	—	188	4	no	—
466	Q₈	—	188	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	47	4	no	—
472	C₂×C₄	—	94	2	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	2	no	—
475	C₂×C₄	—	94	4	no	—
476	C₂×C₄	—	188	2	no	—
477	C₂×C₄	—	188	4	no	—
478	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
479	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
480	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
481	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
482	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
483	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
484	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
485	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
486	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
488	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
489	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
490	C₂×C₄	#13094071	1	1	yes	characteristic
491	C₂×C₄	#13094072	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	1	no	—
495	C₈	—	94	2	no	—
496	C₈	—	188	2	no	—
497	C₈	—	188	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
501	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
502	C₂²	#15689599	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	94	4	no	—
511	C₄	—	188	4	no	—
512	C₄	—	188	2	no	—
513	C₄	#15689105	1	2	yes	—
514	C₄	#15689780	1	1	yes	characteristic
515	C₄	#15689785	1	1	yes	characteristic
516	C₄	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
517	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	Q₈×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
521	C₂	C₂×#15689105	1	1	yes	characteristic
522	C₂	#20251870	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₇)⋊C₄
commutator, prime radical	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×M₁₆	D₄₇
hypocenter	C₄₇	#22517
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
96. #13093942	Q₈	semidirect
311. C₄₇	#22517	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689851	2
Q₈×#10625329	2
#20244381	2
#20244380	2
#20244377	2
#20244376	2
#20243381	2
C₄×#13093942	2
Q₈×M₁₆×C₄₇	2
#22517	47