Subgroups — #26186246

Order 12032.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242250	C₂	1	2	yes	maximal, complemented
4	#20242243	C₂	1	2	yes	maximal, complemented
5	C₈×#10625336	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242174	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241830	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241801	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	—	2	1	no	—
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	#15689456	C₄	1	1	yes	characteristic
15	#15689439	C₄	1	1	yes	characteristic
16	#15689420	C₄	1	2	yes	—
17	#15689335	C₄	1	2	yes	—
18	#15689273	C₄	1	1	yes	characteristic
19	#15689256	C₄	1	1	yes	characteristic
20	C₄×#10625336	C₂²	1	2	yes	—
21	C₄×#10625334	C₂²	1	2	yes	—
22	C₈×D₁₈₈	—	2	1	no	—
23	C₈×D₁₈₈	—	2	1	no	—
24	C₈×D₁₈₈	C₂²	1	2	yes	—
25	C₈×D₁₈₈	C₂²	1	2	yes	—
26	#15689176	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
29	C₄×#10625329	C₂²	1	1	yes	characteristic
30	#15688875	C₂²	1	2	yes	complemented
31	#15688873	C₂²	1	2	yes	complemented
32	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
34	#15688850	C₂²	1	2	yes	—
35	#15688850	C₂²	1	2	yes	—
36	#15688845	C₂²	1	2	yes	complemented
37	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
38	C₄₇×#529	C₂²	1	1	yes	characteristic
39	C₄₇×#446	C₂²	1	1	yes	characteristic, complemented
40	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#436	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#435	—	2	1	no	—
43	C₈×D₄×C₄₇	—	2	1	no	—
44	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	C₄₇×#433	—	2	1	no	—
46	C₄₇×#432	C₂²	1	1	yes	characteristic
47	C₄₇×#405	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
49	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₇	—	2	1	no	—
51	C₂×#10625336	C₂×C₄	1	2	yes	—
52	C₂×#10625334	C₂×C₄	1	2	yes	—
53	C₂×#10625329	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₇	—	2	2	no	—
56	C₂×C₈×D₄₇	—	2	2	no	—
57	C₂×C₈×D₄₇	—	4	4	no	—
58	C₄×D₁₈₈	—	2	1	no	—
59	C₄×D₁₈₈	—	2	1	no	—
60	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
61	C₄×D₁₈₈	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
64	#13093957	C₂×C₄	1	2	yes	—
65	#13093955	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
67	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	#13093948	C₂×C₄	1	2	yes	—
70	#13093945	C₂×C₄	1	2	yes	—
71	#13093944	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
77	#13093935	—	2	1	no	—
78	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
84	#126×C₄₇	—	2	1	no	—
85	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
86	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
87	#123×C₄₇	—	2	1	no	—
88	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
93	#117×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	1	no	—
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₇	—	2	1	no	—
100	C₂²⋊C₈×C₄₇	—	2	1	no	—
101	C₂²⋊C₈×C₄₇	—	2	1	no	—
102	#97×C₄₇	—	2	1	no	—
103	#97×C₄₇	—	2	1	no	—
104	C₄×C₈×C₄₇	—	2	1	no	—
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂³×D₄₇	—	2	1	no	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	2	1	no	—
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×D₁₈₈	—	2	4	no	—
120	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
121	C₂×C₄×D₄₇	—	2	2	no	—
122	C₂×C₄×D₄₇	—	2	2	no	—
123	C₂×C₄×D₄₇	—	4	2	no	—
124	C₂×C₄×D₄₇	—	4	2	no	—
125	M₁₆×C₄₇	—	4	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	4	1	no	—
130	C₂×C₈×C₄₇	—	4	2	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₄₇	—	2	1	no	—
142	C₂²⋊C₄×C₄₇	—	2	1	no	—
143	C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₂²⋊C₄×C₄₇	—	2	1	no	—
145	C₂²⋊C₄×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₇	#41	1	1	yes	characteristic
150	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
151	#10625336	—	2	4	no	—
152	#10625334	—	2	4	no	—
153	(C₂×D₄₇)⋊C₄	—	2	2	no	—
154	(C₂×D₄₇)⋊C₄	—	2	2	no	—
155	C₄⋊Dic₄₇	—	2	1	no	—
156	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
157	#10625329	—	2	4	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	4	2	no	—
161	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
162	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
163	C₈×D₄₇	—	4	4	no	—
164	C₈×D₄₇	—	4	4	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂²×D₄₇	—	2	4	no	—
168	C₂²×D₄₇	—	2	2	no	—
169	C₂²×D₄₇	—	4	2	no	—
170	C₂²×D₄₇	—	4	2	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	D₁₈₈	—	2	4	no	—
192	D₁₈₈	—	2	2	no	—
193	D₁₈₈	#131	1	4	yes	—
194	C₄×D₄₇	—	4	4	no	—
195	C₄×D₄₇	—	4	2	no	—
196	C₄×D₄₇	—	4	2	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	2	1	no	—
199	C₈×C₄₇	—	2	1	no	—
200	C₈×C₄₇	—	4	1	no	—
201	C₈×C₄₇	—	4	1	no	—
202	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
203	C₄₇⋊C₈	—	2	4	no	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	2	2	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	#17910	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	4	1	no	—
211	C₂²×C₄₇	—	4	1	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	#443	1	2	yes	—
214	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂×D₄₇	—	2	4	no	—
216	C₂×D₄₇	—	4	8	no	—
217	C₂×D₄₇	—	4	2	no	—
218	C₂×D₄₇	—	4	2	no	—
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	—	4	1	no	—
225	C₄×C₄₇	—	4	1	no	—
226	C₄×C₄₇	C₂×#131	1	2	yes	—
227	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₄₇	#575	1	1	yes	characteristic
229	Dic₄₇	—	4	2	no	—
230	#3105	—	47	1	no	—
231	#2966	D₄₇	1	1	yes	characteristic, complemented
232	C₂×C₈×D₄	—	47	1	no	—
233	#1586	—	47	2	no	—
234	#1585	—	47	2	no	—
235	C₈×SD₁₆	—	47	2	no	—
236	C₈×D₈	—	47	2	no	—
237	#1573	—	47	1	no	—
238	#1490	—	47	1	no	—
239	#1483	—	47	1	no	—
240	C₈×M₁₆	—	47	1	no	—
241	C₂×C₄₇	—	2	2	no	—
242	C₂×C₄₇	—	8	1	no	—
243	C₂×C₄₇	#2929	1	1	yes	characteristic
244	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
246	D₄₇	—	4	4	no	—
247	C₂³×C₈	—	94	1	no	—
248	#529	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×D₄	—	47	1	no	—
250	#484	—	47	1	no	—
251	#481	—	47	1	no	—
252	#478	—	47	2	no	—
253	#463	—	47	2	no	—
254	#450	—	47	1	no	—
255	#447	—	47	1	no	—
256	#446	C₂×D₄₇	1	1	yes	characteristic, complemented
257	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
258	C₄×SD₁₆	—	47	2	no	—
259	C₄×D₈	—	47	2	no	—
260	#436	C₂×D₄₇	1	1	yes	characteristic, complemented
261	#435	—	2	1	no	—
262	C₈×D₄	—	2	1	no	—
263	C₈×D₄	—	47	2	no	—
264	C₈×D₄	—	47	2	no	—
265	C₈×D₄	—	94	1	no	—
266	C₈×D₄	—	94	1	no	—
267	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
268	#433	—	2	1	no	—
269	#432	C₂×D₄₇	1	1	yes	characteristic
270	#431	—	47	1	no	—
271	C₂×C₄⋊C₈	—	47	1	no	—
272	C₂×C₂²⋊C₈	—	94	1	no	—
273	#405	—	2	1	no	—
274	C₄×M₁₆	—	47	1	no	—
275	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
276	#335	—	47	2	no	—
277	#334	—	47	2	no	—
278	Q₈⋊C₈	—	47	2	no	—
279	D₄⋊C₈	—	47	2	no	—
280	D₄⋊C₈	—	47	2	no	—
281	D₄⋊C₈	—	47	2	no	—
282	#322	—	47	2	no	—
283	C₈²	—	47	2	no	—
284	C₄₇	#17910	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	—	47	1	no	—
286	C₂³×C₄	—	94	1	no	—
287	C₂×SD₁₆	—	47	2	no	—
288	C₂×D₈	—	47	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	94	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	94	1	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	—	94	2	no	—
295	C₂²×C₈	—	188	4	no	—
296	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
298	#126	—	2	1	no	—
299	#125	C₄×D₄₇	1	1	yes	characteristic
300	#124	C₄×D₄₇	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
303	#121	C₄×D₄₇	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	47	2	no	—
307	C₄×D₄	—	47	2	no	—
308	C₄×D₄	—	94	1	no	—
309	C₄×D₄	—	94	1	no	—
310	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₂²⋊C₄	—	94	1	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	47	2	no	—
316	#106	—	47	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	47	2	no	—
320	C₄⋊C₈	—	47	2	no	—
321	C₄⋊C₈	—	94	1	no	—
322	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
323	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
324	#103	—	47	2	no	—
325	#102	—	47	2	no	—
326	#102	—	47	2	no	—
327	#102	—	47	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	2	1	no	—
331	C₂²⋊C₈	—	47	1	no	—
332	C₂²⋊C₈	—	47	1	no	—
333	C₂²⋊C₈	—	94	2	no	—
334	C₂²⋊C₈	—	94	2	no	—
335	#97	—	2	1	no	—
336	#97	—	2	1	no	—
337	#97	—	94	1	no	—
338	C₄×C₈	—	2	1	no	—
339	C₄×C₈	—	47	2	no	—
340	C₄×C₈	—	47	2	no	—
341	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
342	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₂⁴	—	94	1	no	—
346	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	47	2	no	—
349	C₂×D₄	—	94	4	no	—
350	C₂×D₄	—	94	1	no	—
351	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	188	2	no	—
357	C₂²×C₄	—	188	2	no	—
358	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	#10625350	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
361	SD₁₆	—	94	4	no	—
362	D₈	—	94	4	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	—	94	4	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	47	2	no	—
371	C₂×C₈	—	47	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	188	4	no	—
375	C₂×C₈	—	188	2	no	—
376	C₂×C₈	—	188	4	no	—
377	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	47	2	no	—
386	C₄⋊C₄	—	94	1	no	—
387	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	94	2	no	—
395	C₂²⋊C₄	—	94	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₄²	#10625350	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	2	1	no	—
402	C₂³	—	94	4	no	—
403	C₂³	—	94	2	no	—
404	C₂³	—	188	2	no	—
405	C₂³	—	188	2	no	—
406	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	47	4	no	—
411	D₄	—	94	4	no	—
412	D₄	—	94	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	188	4	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	94	4	no	—
439	C₈	—	94	2	no	—
440	C₈	—	94	2	no	—
441	C₈	—	188	2	no	—
442	C₈	#13094049	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	94	4	no	—
449	C₂²	—	188	8	no	—
450	C₂²	—	188	2	no	—
451	C₂²	—	188	2	no	—
452	C₂²	#15689238	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	188	2	no	—
462	C₄	#131×D₄₇	1	2	yes	—
463	C₄	C₂×#13094049	1	1	yes	characteristic
464	C₄	#15689921	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	188	4	no	—
468	C₂	#20252080	1	1	yes	characteristic
469	C₂	C₄×#13094049	1	1	yes	characteristic
470	C₂	C₂×#15689238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2966	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689256	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2966	D₄₇
hypocenter	C₄₇	#17910
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₁₈₈	C₂	semidirect
3. #20242250	C₂	semidirect
4. #20242243	C₂	semidirect
5. C₈×#10625336	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242174	C₂	semidirect
8. #20241830	C₂	semidirect
9. #20241801	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₄₇×#2966	C₂	semidirect
30. #15688875	C₂²	semidirect
31. #15688873	C₂²	semidirect
32. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
33. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. #15688845	C₂²	semidirect
37. C₈×C₄₇⋊C₈	C₂²	semidirect
39. C₄₇×#446	C₂²	semidirect
40. C₈×Q₈×C₄₇	C₂²	semidirect
41. C₄₇×#436	C₂²	semidirect
44. C₈×D₄×C₄₇	C₂²	semidirect
231. #2966	D₄₇	semidirect
256. #446	C₂×D₄₇	semidirect
257. C₈×Q₈	C₂×D₄₇	semidirect
260. #436	C₂×D₄₇	semidirect
267. C₈×D₄	C₂×D₄₇	semidirect
284. C₄₇	#17910	semidirect

Maximal subgroups

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

subgroup	index
#20253431	2
C₂×C₈×D₁₈₈	2
#20242250	2
#20242243	2
C₈×#10625336	2
C₈×#10625334	2
#20242174	2
#20241830	2
#20241801	2
C₈×#10625329	2
C₄₇×#2966	2
#17910	47