Subgroups — #26185231

Order 12032.

924 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252520	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252513	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242123	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242118	C₂	1	2	yes	maximal, complemented
5	#20242093	C₂	1	2	yes	maximal, complemented
6	#20242073	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242065	C₂	1	2	yes	maximal, complemented
8	#20242060	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242050	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242045	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3511	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	1	no	—
13	Q₈×C₄₇⋊C₈	—	2	1	no	—
14	#15689201	—	2	1	no	—
15	#15689201	—	2	2	no	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	#15689180	C₂²	1	2	yes	—
19	#15689176	C₂²	1	1	yes	characteristic
20	#15689176	C₂²	1	2	yes	—
21	#15689176	C₂²	1	1	yes	characteristic
22	#15689147	C₂²	1	1	yes	characteristic
23	#15689147	C₂²	1	1	yes	characteristic
24	#15689147	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
26	#15688872	C₂²	1	1	yes	characteristic
27	#15688872	C₂²	1	2	yes	—
28	#15688872	C₂²	1	1	yes	characteristic
29	#15688869	C₂²	1	2	yes	—
30	#15688869	C₂²	1	2	yes	—
31	#15688869	C₂²	1	2	yes	—
32	#15688869	C₂²	1	2	yes	—
33	#15688867	C₂²	1	1	yes	characteristic
34	#15688867	C₂²	1	1	yes	characteristic
35	#15688867	C₂²	1	2	yes	—
36	C₄₇×#556	—	2	1	no	—
37	C₄₇×#555	—	2	1	no	—
38	C₄₇×#554	—	2	1	no	—
39	C₄₇×#553	—	2	2	no	—
40	C₄₇×#548	—	2	2	no	—
41	C₄₇×#547	—	2	1	no	—
42	C₄₇×#542	C₄	1	4	yes	—
43	C₄₇×#537	C₄	1	2	yes	—
44	C₄₇×#533	C₂²	1	2	yes	—
45	C₄₇×#532	C₂²	1	1	yes	characteristic
46	C₄₇×#532	C₂²	1	2	yes	—
47	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#520	C₄	1	2	yes	—
49	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	#13093935	—	2	2	no	—
69	C₄×C₄₇⋊C₈	—	2	1	no	—
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	2	no	—
73	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂²×Q₈×C₄₇	—	2	1	no	—
76	C₄⋊Q₈×C₄₇	—	2	1	no	—
77	C₄⋊Q₈×C₄₇	—	2	1	no	—
78	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
81	#127×C₄₇	C₂³	1	1	yes	characteristic
82	#126×C₄₇	—	2	4	no	—
83	#125×C₄₇	—	2	2	no	—
84	#124×C₄₇	—	2	4	no	—
85	#124×C₄₇	—	2	2	no	—
86	#124×C₄₇	C₂×C₄	1	2	yes	—
87	#123×C₄₇	—	2	4	no	—
88	C₂²⋊Q₈×C₄₇	—	2	2	no	—
89	C₂²⋊Q₈×C₄₇	—	2	2	no	—
90	C₂²⋊Q₈×C₄₇	—	2	4	no	—
91	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
92	#121×C₄₇	—	2	2	no	—
93	#121×C₄₇	—	2	4	no	—
94	#121×C₄₇	—	2	1	no	—
95	#121×C₄₇	—	2	1	no	—
96	#121×C₄₇	—	2	2	no	—
97	#121×C₄₇	C₂×C₄	1	4	yes	—
98	C₄×Q₈×C₄₇	—	2	2	no	—
99	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
100	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
102	C₄×D₄×C₄₇	—	2	4	no	—
103	C₄×D₄×C₄₇	—	2	1	no	—
104	C₄×D₄×C₄₇	—	2	2	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
107	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
108	C₄×D₄×C₄₇	D₄	1	2	yes	—
109	C₄×D₄×C₄₇	D₄	1	2	yes	—
110	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
111	#117×C₄₇	—	2	2	no	—
112	#117×C₄₇	—	2	2	no	—
113	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
114	#117×C₄₇	C₂×C₄	1	2	yes	—
115	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
116	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
120	#41×C₄₇	—	4	2	no	—
121	#41×C₄₇	—	4	4	no	—
122	#41×C₄₇	—	8	2	no	—
123	#41×C₄₇	—	8	2	no	—
124	C₂×Q₈×C₄₇	—	2	2	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	—	8	1	no	—
127	C₂×Q₈×C₄₇	—	8	1	no	—
128	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	4	no	—
132	C₂×D₄×C₄₇	—	2	1	no	—
133	C₂×D₄×C₄₇	—	2	1	no	—
134	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
136	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	—	2	4	no	—
148	C₄⋊C₄×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	—	2	1	no	—
152	C₄⋊C₄×C₄₇	—	2	1	no	—
153	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
156	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
157	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
158	C₂²⋊C₄×C₄₇	—	2	4	no	—
159	C₂²⋊C₄×C₄₇	—	2	4	no	—
160	C₂²⋊C₄×C₄₇	—	2	4	no	—
161	C₂²⋊C₄×C₄₇	—	2	2	no	—
162	C₂²⋊C₄×C₄₇	—	2	2	no	—
163	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
164	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
165	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
166	C₄²×C₄₇	—	2	4	no	—
167	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
168	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₄₇	C₂×D₄	1	2	yes	—
170	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₇	C₂×D₄	1	2	yes	—
173	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
174	#10625329	—	8	1	no	—
175	#10625329	—	8	2	no	—
176	#10625329	—	8	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	1	no	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	—	2	1	no	—
181	C₂×C₄₇⋊C₈	—	2	2	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	—	8	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	Q₈×C₄₇	—	2	2	no	—
188	Q₈×C₄₇	—	4	2	no	—
189	Q₈×C₄₇	—	4	2	no	—
190	Q₈×C₄₇	—	4	2	no	—
191	Q₈×C₄₇	—	8	2	no	—
192	D₄×C₄₇	—	2	2	no	—
193	D₄×C₄₇	—	4	2	no	—
194	D₄×C₄₇	—	4	2	no	—
195	D₄×C₄₇	—	4	4	no	—
196	D₄×C₄₇	—	4	1	no	—
197	D₄×C₄₇	—	4	1	no	—
198	D₄×C₄₇	—	4	1	no	—
199	D₄×C₄₇	—	4	1	no	—
200	D₄×C₄₇	—	8	4	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	1	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	8	4	no	—
215	C₂×C₄×C₄₇	—	8	2	no	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₄₇⋊C₈	—	4	2	no	—
226	C₄₇⋊C₈	—	4	1	no	—
227	C₄₇⋊C₈	—	4	1	no	—
228	C₄₇⋊C₈	—	4	1	no	—
229	C₄₇⋊C₈	—	4	2	no	—
230	C₄₇⋊C₈	—	4	1	no	—
231	#17781	—	47	1	no	maximal, Sylow
232	C₂²×C₄₇	—	2	1	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	2	2	no	—
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	C₂²×C₂²⋊C₄	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	1	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	—	4	2	no	—
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	#413	1	2	yes	—
251	C₄×C₄₇	#576	1	1	yes	characteristic
252	C₄×C₄₇	#577	1	1	yes	characteristic
253	C₄×C₄₇	#577	1	1	yes	characteristic
254	C₄×C₄₇	#578	1	1	yes	characteristic
255	#3511	D₄₇	1	1	yes	characteristic
256	#2991	—	47	1	no	—
257	#2990	—	47	1	no	—
258	#1560	—	47	1	no	—
259	#1559	—	47	2	no	—
260	#1553	—	47	2	no	—
261	#1549	—	47	1	no	—
262	#1547	—	47	2	no	—
263	#1546	—	47	1	no	—
264	#1543	—	47	1	no	—
265	#1542	—	47	2	no	—
266	C₂×C₄₇	—	4	1	no	—
267	C₂×C₄₇	—	4	2	no	—
268	C₂×C₄₇	—	8	2	no	—
269	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
270	C₂×C₄₇	#2897	1	1	yes	characteristic
271	C₂×C₄₇	#2898	1	1	yes	characteristic
272	#556	—	2	1	no	—
273	#555	—	2	1	no	—
274	#554	—	2	1	no	—
275	#553	—	2	2	no	—
276	#548	—	2	2	no	—
277	#547	—	2	1	no	—
278	#542	Dic₄₇	1	4	yes	—
279	#537	Dic₄₇	1	2	yes	—
280	#533	C₂×D₄₇	1	2	yes	—
281	#532	C₂×D₄₇	1	1	yes	characteristic
282	#532	C₂×D₄₇	1	2	yes	—
283	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
284	#520	Dic₄₇	1	2	yes	—
285	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
286	#446	—	94	1	no	—
287	C₈×Q₈	—	94	1	no	—
288	#436	—	94	1	no	—
289	#436	—	94	2	no	—
290	#435	—	94	2	no	—
291	C₈×D₄	—	94	1	no	—
292	#432	—	47	2	no	—
293	#431	—	47	2	no	—
294	#431	—	47	1	no	—
295	#431	—	47	1	no	—
296	#423	—	47	1	no	—
297	#423	—	47	2	no	—
298	#423	—	47	1	no	—
299	C₂×C₄⋊C₈	—	47	2	no	—
300	#333	—	47	1	no	—
301	#333	—	47	2	no	—
302	#333	—	47	1	no	—
303	#332	—	47	2	no	—
304	#332	—	47	2	no	—
305	#332	—	47	2	no	—
306	#332	—	47	2	no	—
307	#331	—	47	1	no	—
308	#331	—	47	1	no	—
309	#331	—	47	2	no	—
310	C₄₇	#17781	1	1	yes	characteristic, complemented, Sylow
311	C₂×#41	—	2	2	no	—
312	C₂×#41	C₂×Dic₄₇	1	2	yes	—
313	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂×M₁₆	—	94	1	no	—
316	C₂×M₁₆	—	94	1	no	—
317	C₂×M₁₆	—	94	2	no	—
318	C₂²×C₈	—	94	2	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
322	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
323	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
324	#127	C₂²×D₄₇	1	1	yes	characteristic
325	#126	—	2	4	no	—
326	#125	—	2	2	no	—
327	#124	—	2	4	no	—
328	#124	—	2	2	no	—
329	#124	C₂×Dic₄₇	1	2	yes	—
330	#123	—	2	4	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
335	#121	—	2	2	no	—
336	#121	—	2	4	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	2	no	—
340	#121	C₂×Dic₄₇	1	4	yes	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
343	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
344	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	1	no	—
349	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
350	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
351	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
352	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
353	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	C₂×Dic₄₇	1	1	yes	characteristic
357	#117	C₂×Dic₄₇	1	2	yes	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
361	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
363	C₄⋊C₈	—	47	1	no	—
364	C₄⋊C₈	—	47	2	no	—
365	C₄⋊C₈	—	47	1	no	—
366	C₄⋊C₈	—	47	2	no	—
367	C₄⋊C₈	—	47	1	no	—
368	C₄⋊C₈	—	47	1	no	—
369	C₄⋊C₈	—	94	2	no	—
370	C₄⋊C₈	—	94	1	no	—
371	C₄⋊C₈	—	94	1	no	—
372	C₄⋊C₈	—	94	2	no	—
373	C₂²⋊C₈	—	94	1	no	—
374	C₂²⋊C₈	—	94	1	no	—
375	C₂²⋊C₈	—	94	2	no	—
376	C₂²⋊C₈	—	94	2	no	—
377	#97	—	94	2	no	—
378	C₄×C₈	—	94	1	no	—
379	C₄×C₈	—	94	1	no	—
380	C₄×C₈	—	94	2	no	—
381	#41	—	4	2	no	—
382	#41	—	4	4	no	—
383	#41	—	8	2	no	—
384	#41	—	8	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	8	1	no	—
388	C₂×Q₈	—	8	1	no	—
389	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
390	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
396	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
397	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
403	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
405	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
407	M₁₆	—	376	1	no	—
408	M₁₆	—	376	2	no	—
409	M₁₆	—	376	1	no	—
410	C₂×C₈	—	94	1	no	—
411	C₂×C₈	—	94	1	no	—
412	C₂×C₈	—	94	1	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	2	no	—
415	C₂×C₈	—	94	2	no	—
416	C₂×C₈	—	376	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
425	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
426	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
427	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
428	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
435	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
436	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
437	C₄²	—	2	4	no	—
438	C₄²	C₂²×Dic₄₇	1	2	yes	—
439	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
440	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
441	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
442	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
443	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
444	C₄²	C₂³×D₄₇	1	1	yes	characteristic
445	C₂³	—	2	2	no	—
446	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
447	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
448	Q₈	—	2	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	8	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	4	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	1	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	1	no	—
461	D₄	—	8	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
478	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
479	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
480	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
481	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
482	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
484	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
486	C₈	—	188	2	no	—
487	C₈	—	188	1	no	—
488	C₈	—	188	1	no	—
489	C₈	—	188	2	no	—
490	C₈	—	188	1	no	—
491	C₈	—	188	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₄	#15689107	1	2	yes	—
511	C₄	#15689926	1	1	yes	characteristic
512	C₄	#15689931	1	1	yes	characteristic
513	C₄	#15689934	1	1	yes	characteristic
514	C₄	#15689938	1	1	yes	characteristic
515	C₂	—	4	1	no	—
516	C₂	—	4	2	no	—
517	C₂	—	8	2	no	—
518	C₂	C₂×#15689107	1	1	yes	characteristic
519	C₂	#20251914	1	1	yes	characteristic
520	C₂	#20251921	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3511	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3511	D₄₇
hypocenter	C₄₇	#17781
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3511

Complements

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

N	H ≅ G/N	type
1. #20252520	C₂	semidirect
2. #20252513	C₂	semidirect
3. #20242123	C₂	semidirect
4. #20242118	C₂	semidirect
5. #20242093	C₂	semidirect
6. #20242073	C₂	semidirect
7. #20242065	C₂	semidirect
8. #20242060	C₂	semidirect
9. #20242050	C₂	semidirect
10. #20242045	C₂	semidirect
310. C₄₇	#17781	semidirect

Maximal subgroups

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

subgroup	index
#20252520	2
#20252513	2
#20242123	2
#20242118	2
#20242093	2
#20242073	2
#20242065	2
#20242060	2
#20242050	2
#20242045	2
C₄₇×#3511	2
#17781	47