Subgroups — #26187243

Order 12032.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253392	C₂	1	1	yes	maximal, characteristic
2	#20252337	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252123	C₂	1	1	yes	maximal, characteristic
4	#20242293	C₂	1	2	yes	maximal, complemented
5	#20242263	C₂	1	2	yes	maximal, complemented
6	#20242248	C₂	1	2	yes	maximal, complemented
7	#20242203	C₂	1	2	yes	maximal, complemented
8	#20242164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
10	#20241677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₇	—	2	1	no	—
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	#15689451	C₄	1	2	yes	—
15	#15689410	C₄	1	1	yes	characteristic
16	#15689410	C₄	1	1	yes	characteristic
17	#15689325	C₄	1	1	yes	characteristic
18	#15689325	C₄	1	1	yes	characteristic
19	#15689273	C₄	1	2	yes	—
20	#15689254	—	2	2	no	—
21	#15689254	C₂²	1	2	yes	complemented
22	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
23	C₄×#10625336	C₂²	1	2	yes	—
24	C₄×#10625336	C₂²	1	2	yes	—
25	#15689200	C₂²	1	2	yes	—
26	#15689193	—	2	2	no	—
27	#15689188	C₂²	1	2	yes	—
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689150	—	2	1	no	—
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	#15689086	—	2	1	no	—
32	#15689079	—	2	1	no	—
33	C₄×#10625329	C₂²	1	1	yes	characteristic
34	#15688875	C₂²	1	2	yes	complemented
35	#15688875	C₂²	1	2	yes	complemented
36	#15688852	C₂²	1	1	yes	characteristic
37	#15688852	C₂²	1	1	yes	characteristic
38	#15688852	C₂²	1	1	yes	characteristic
39	#15688852	C₂²	1	1	yes	characteristic
40	#15688845	C₂²	1	2	yes	complemented
41	#15688844	C₂²	1	2	yes	complemented
42	C₄₇×#533	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
46	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
47	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₇	—	2	1	no	—
49	C₂×#10625336	C₂×C₄	1	2	yes	—
50	C₂×#10625336	C₂×C₄	1	2	yes	—
51	C₂×#10625329	D₄	1	1	yes	characteristic
52	C₂×#10625329	D₄	1	1	yes	characteristic
53	C₂×#10625324	—	2	2	no	—
54	M₁₆×D₄₇	—	4	4	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂×C₈×D₄₇	—	2	2	no	—
57	C₄×D₁₈₈	—	2	1	no	—
58	C₄×D₁₈₈	—	2	1	no	—
59	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
60	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
61	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
65	#13093955	C₂×C₄	1	2	yes	—
66	#13093955	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
71	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
72	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
74	#13093948	C₂×C₄	1	2	yes	—
75	#13093948	C₂×C₄	1	2	yes	—
76	#13093944	C₂×C₄	1	2	yes	—
77	#13093944	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
79	(C₂×D₄₇)⋊C₈	—	2	2	no	—
80	(C₂×D₄₇)⋊C₈	—	2	2	no	—
81	#13093935	—	2	2	no	—
82	#13093935	D₄	1	2	yes	—
83	C₄×C₄₇⋊C₈	—	2	2	no	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂²×C₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#125×C₄₇	—	2	1	no	—
91	C₂²⋊Q₈×C₄₇	—	2	1	no	—
92	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
95	#117×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂³×D₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	2	1	no	—
109	C₂×D₁₈₈	—	2	2	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	4	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	1	no	—
118	C₂×C₄×D₄₇	—	4	2	no	—
119	C₂×C₄×D₄₇	—	4	2	no	—
120	M₁₆×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	#10625336	—	2	4	no	—
138	#10625336	—	4	2	no	—
139	(C₂×D₄₇)⋊C₄	—	2	1	no	—
140	(C₂×D₄₇)⋊C₄	—	2	1	no	—
141	(C₂×D₄₇)⋊C₄	—	2	1	no	—
142	(C₂×D₄₇)⋊C₄	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	#10625329	—	2	2	no	—
147	#10625329	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	4	2	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	4	4	no	—
157	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	4	2	no	—
161	C₂²×D₄₇	—	4	2	no	—
162	C₂²×D₄₇	—	8	1	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	8	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₄₇	#137	1	2	yes	—
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	D₁₈₈	—	2	1	no	—
183	D₁₈₈	—	2	1	no	—
184	D₁₈₈	—	2	1	no	—
185	D₁₈₈	—	4	2	no	—
186	D₁₈₈	#131	1	2	yes	—
187	C₄×D₄₇	—	4	1	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	2	no	—
192	C₄×D₄₇	—	4	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	4	1	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	2	2	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	1	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	#18000	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	#440	1	2	yes	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	4	1	no	—
209	C₂×D₄₇	—	4	1	no	—
210	C₂×D₄₇	—	4	1	no	—
211	C₂×D₄₇	—	4	1	no	—
212	C₂×D₄₇	—	4	1	no	—
213	C₂×D₄₇	—	8	4	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	1	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	#440	1	2	yes	—
220	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
221	C₄×C₄₇	#568	1	1	yes	characteristic
222	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
224	Dic₄₇	—	4	1	no	—
225	Dic₄₇	—	4	1	no	—
226	#3101	—	47	1	no	—
227	#2962	—	47	1	no	—
228	D₄×M₁₆	—	47	1	no	—
229	#1592	—	47	2	no	—
230	#1588	—	47	2	no	—
231	#1585	—	47	2	no	—
232	SD₁₆⋊C₈	—	47	2	no	—
233	#1571	—	47	1	no	—
234	#1493	D₄₇	1	1	yes	characteristic, complemented
235	C₂×D₄⋊C₈	—	47	1	no	—
236	#1451	—	47	1	no	—
237	C₂×C₄₇	—	2	2	no	—
238	C₂×C₄₇	#2933	1	1	yes	characteristic
239	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
240	C₂×C₄₇	#2956	1	1	yes	characteristic
241	D₄₇	—	4	2	no	—
242	D₄₇	—	8	1	no	—
243	C₂²×M₁₆	—	94	1	no	—
244	#533	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄×D₄	—	47	1	no	—
246	#483	—	47	2	no	—
247	#476	—	47	1	no	—
248	#476	—	47	1	no	—
249	#461	—	47	1	no	—
250	#461	—	47	1	no	—
251	#450	—	47	2	no	—
252	#446	—	47	2	no	—
253	#446	—	94	2	no	—
254	C₈×Q₈	—	47	2	no	—
255	C₄×SD₁₆	—	47	2	no	—
256	C₄×SD₁₆	—	47	2	no	—
257	#436	—	47	2	no	—
258	#435	—	94	2	no	—
259	C₈×D₄	—	47	2	no	—
260	#431	—	47	1	no	—
261	#424	—	94	1	no	—
262	#423	C₂×D₄₇	1	1	yes	characteristic
263	C₂×C₄⋊C₈	—	47	1	no	—
264	#407	—	94	1	no	—
265	#405	—	94	1	no	—
266	C₄×M₁₆	—	47	1	no	—
267	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
268	#335	—	47	2	no	—
269	#335	—	47	2	no	—
270	Q₈⋊C₈	C₂×D₄₇	1	2	yes	complemented
271	Q₈⋊C₈	C₂×D₄₇	1	2	yes	complemented
272	D₄⋊C₈	—	47	1	no	—
273	D₄⋊C₈	—	47	1	no	—
274	D₄⋊C₈	—	47	1	no	—
275	D₄⋊C₈	—	47	1	no	—
276	#322	—	47	2	no	—
277	#322	—	47	2	no	—
278	C₄₇	#18000	1	1	yes	characteristic, complemented, Sylow
279	C₂²×D₄	—	47	1	no	—
280	C₂³×C₄	—	94	1	no	—
281	C₂×SD₁₆	—	47	2	no	—
282	C₂×SD₁₆	—	47	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	47	1	no	—
285	C₂×M₁₆	—	47	1	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	188	4	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₂²×C₈	—	94	1	no	—
291	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
292	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
298	C₄×D₄	—	47	1	no	—
299	C₄×D₄	—	47	1	no	—
300	C₄×D₄	—	47	1	no	—
301	C₄×D₄	—	47	1	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	—	94	1	no	—
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	47	1	no	—
306	C₂×C₂²⋊C₄	—	94	1	no	—
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	#106	—	47	2	no	—
309	#106	—	47	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	47	1	no	—
312	C₄⋊C₈	—	47	1	no	—
313	C₄⋊C₈	—	47	1	no	—
314	C₄⋊C₈	—	47	1	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	—	94	1	no	—
318	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
319	#103	—	47	2	no	—
320	#103	—	47	2	no	—
321	#102	—	47	2	no	—
322	#102	—	47	2	no	—
323	C₂²⋊C₈	—	47	2	no	—
324	C₂²⋊C₈	—	94	2	no	—
325	C₂²⋊C₈	—	94	2	no	—
326	#97	—	47	2	no	—
327	#97	—	94	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	47	2	no	—
330	C₄×C₈	—	47	2	no	—
331	C₄×C₈	—	94	2	no	—
332	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₂⁴	—	94	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
337	C₂×D₄	—	47	1	no	—
338	C₂×D₄	—	47	1	no	—
339	C₂×D₄	—	94	2	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂×D₄	—	188	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	188	2	no	—
348	C₂²×C₄	—	188	2	no	—
349	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	#10625352	1	1	yes	characteristic
352	SD₁₆	—	94	4	no	—
353	SD₁₆	—	188	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	94	2	no	—
356	M₁₆	—	94	2	no	—
357	M₁₆	—	188	4	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	47	2	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	188	4	no	—
369	C₂×C₈	—	188	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	47	1	no	—
376	C₄⋊C₄	—	47	1	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	94	1	no	—
381	C₂²⋊C₄	—	94	1	no	—
382	C₂²⋊C₄	—	94	1	no	—
383	C₂²⋊C₄	—	94	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
386	C₄²	D₄×D₄₇	1	1	yes	characteristic
387	C₄²	#10625352	1	1	yes	characteristic
388	C₄²	C₂³×D₄₇	1	1	yes	characteristic
389	C₂³	—	94	1	no	—
390	C₂³	—	94	1	no	—
391	C₂³	—	376	1	no	—
392	C₂³	—	188	2	no	—
393	C₂³	—	188	2	no	—
394	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	47	2	no	—
399	D₄	—	94	1	no	—
400	D₄	—	94	1	no	—
401	D₄	—	94	1	no	—
402	D₄	—	188	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	94	1	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	188	2	no	—
411	C₂×C₄	—	188	2	no	—
412	C₂×C₄	—	188	2	no	—
413	C₂×C₄	—	188	1	no	—
414	C₂×C₄	—	188	1	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	—	188	1	no	—
417	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
418	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
420	C₂×C₄	#13094051	1	2	yes	—
421	C₂×C₄	#13094056	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₈	—	94	2	no	—
429	C₈	—	94	2	no	—
430	C₈	—	94	2	no	—
431	C₈	—	94	2	no	—
432	C₈	—	188	1	no	—
433	C₈	—	188	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	376	4	no	—
438	C₂²	—	188	1	no	—
439	C₂²	—	188	1	no	—
440	C₂²	—	188	1	no	—
441	C₂²	—	188	1	no	—
442	C₂²	—	188	1	no	—
443	C₂²	#15689226	1	2	yes	—
444	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	188	1	no	—
451	C₄	—	188	1	no	—
452	C₄	#15689226	1	2	yes	—
453	C₄	#131×D₄₇	1	1	yes	characteristic
454	C₄	#15689888	1	1	yes	characteristic
455	C₄	C₂×#13094051	1	1	yes	characteristic
456	C₄	C₂×#13094056	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	376	1	no	—
459	C₂	—	188	2	no	—
460	C₂	#20252118	1	1	yes	characteristic
461	C₂	C₂×#15689226	1	1	yes	characteristic
462	C₂	#20252294	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1493	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1493	D₄₇
hypocenter	C₄₇	#18000
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1493

Complements

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

N	H ≅ G/N	type
2. #20252337	C₂	semidirect
4. #20242293	C₂	semidirect
5. #20242263	C₂	semidirect
6. #20242248	C₂	semidirect
7. #20242203	C₂	semidirect
8. #20242164	C₂	semidirect
10. #20241677	C₂	semidirect
11. C₄₇×#1493	C₂	semidirect
21. #15689254	C₂²	semidirect
22. Q₈×C₄₇⋊C₈	C₂²	semidirect
34. #15688875	C₂²	semidirect
35. #15688875	C₂²	semidirect
40. #15688845	C₂²	semidirect
41. #15688844	C₂²	semidirect
45. C₄₇×Q₈⋊C₈	C₂²	semidirect
46. C₄₇×Q₈⋊C₈	C₂²	semidirect
234. #1493	D₄₇	semidirect
270. Q₈⋊C₈	C₂×D₄₇	semidirect
271. Q₈⋊C₈	C₂×D₄₇	semidirect
278. C₄₇	#18000	semidirect

Maximal subgroups

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

subgroup	index
#20253392	2
#20252337	2
#20252123	2
#20242293	2
#20242263	2
#20242248	2
#20242203	2
#20242164	2
C₂×#15688852	2
#20241677	2
C₄₇×#1493	2
#18000	47