Subgroups — #26223780

Order 12032.

842 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
3	#20246658	C₂	1	1	yes	maximal, characteristic
4	#20244111	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243948	C₂	1	2	yes	maximal, complemented
6	#20243567	C₂	1	2	yes	maximal
7	#20243369	C₂	1	1	yes	maximal, characteristic
8	#20243259	C₂	1	2	yes	maximal, complemented
9	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243168	C₂	1	2	yes	maximal
11	C₄₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093981	C₂²	1	1	yes	characteristic
15	Q₈×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	#15689080	—	2	4	no	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	#15689061	C₄	1	1	yes	characteristic
27	#15689058	C₄	1	1	yes	characteristic
28	#15689056	C₄	1	2	yes	—
29	#15689045	C₄	1	2	yes	—
30	#15689042	C₄	1	1	yes	characteristic
31	#15689034	C₄	1	1	yes	characteristic
32	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625324	—	2	2	no	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	Q₈	1	4	yes	complemented
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	—	2	2	no	—
53	#13093981	—	2	2	no	—
54	#13093981	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
68	Dic₄₇⋊C₈	—	2	4	no	—
69	(C₂×D₄₇)⋊C₈	—	2	4	no	—
70	#13093934	—	2	2	no	—
71	#13093934	—	2	4	no	—
72	C₄×C₄₇⋊C₈	—	2	4	no	—
73	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
74	C₈×Dic₄₇	—	2	2	no	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₄₇⋊#95	C₂×C₄	1	2	yes	—
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	2	yes	—
80	C₄₇⋊#95	C₂×C₄	1	2	yes	—
81	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₄₇	—	2	2	no	—
86	C₄×Q₈×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	#97×C₄₇	—	2	2	no	—
93	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
111	C₂×C₄×D₄₇	#41	1	2	yes	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	(C₂×D₄₇)⋊C₄	—	2	2	no	—
128	(C₂×D₄₇)⋊C₄	—	2	2	no	—
129	(C₂×D₄₇)⋊C₄	—	2	4	no	—
130	(C₂×D₄₇)⋊C₄	—	4	2	no	—
131	C₄⋊Dic₄₇	—	4	2	no	—
132	Dic₄₇⋊C₄	—	2	2	no	—
133	Dic₄₇⋊C₄	—	2	2	no	—
134	Dic₄₇⋊C₄	—	2	4	no	—
135	Dic₄₇⋊C₄	—	4	2	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
147	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
148	C₂×C₄₇⋊C₈	#41	1	2	yes	—
149	#10625324	—	2	8	no	—
150	C₈×D₄₇	—	2	8	no	—
151	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	—	2	1	no	—
154	C₂²×D₄₇	—	2	2	no	—
155	C₂²×D₄₇	—	2	2	no	—
156	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
157	Q₈×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	#131	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
187	C₄×D₄₇	—	2	2	no	—
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₄₇⋊C₈	—	2	2	no	—
195	C₄₇⋊C₈	—	4	2	no	—
196	C₄₇⋊C₈	C₂²⋊Q₈	1	4	yes	—
197	#21602	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
200	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#131	1	2	yes	—
202	C₂²×C₄₇	#568	1	2	yes	—
203	C₂×D₄₇	—	2	4	no	—
204	C₂×D₄₇	—	2	2	no	—
205	C₂×D₄₇	—	4	1	no	—
206	C₂×D₄₇	—	4	1	no	—
207	C₂×D₄₇	—	4	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₄×C₄₇	#525	1	1	yes	characteristic
214	C₄×C₄₇	#529	1	1	yes	characteristic
215	C₄×C₄₇	#533	1	1	yes	characteristic
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	1	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	4	2	no	—
221	C₂×C₈×Q₈	—	47	1	no	—
222	C₂×#405	—	47	1	no	—
223	#2396	—	47	1	no	—
224	#1985	D₄₇	1	1	yes	characteristic, complemented
225	#1940	—	47	1	no	—
226	#1916	—	47	2	no	—
227	#1850	—	47	2	no	—
228	#1798	—	47	1	no	—
229	#1771	—	47	2	no	—
230	#1770	—	47	1	no	—
231	#1753	—	47	2	no	—
232	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₄₇	#2929	1	1	yes	characteristic
234	C₂×C₄₇	#2932	1	1	yes	characteristic
235	C₂×C₄₇	#2962	1	2	yes	—
236	C₂×C₄₇	#2969	1	2	yes	—
237	D₄₇	—	4	2	no	—
238	C₂²×M₁₆	—	47	1	no	—
239	C₂³×C₈	—	47	1	no	—
240	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂×#117	—	47	1	no	—
242	C₈×Q₈	—	94	4	no	—
243	C₂×C₄⋊C₈	—	47	2	no	—
244	C₂×C₄⋊C₈	—	47	1	no	—
245	C₂×C₄⋊C₈	—	47	2	no	—
246	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
247	C₂×C₂²⋊C₈	—	47	2	no	—
248	#405	—	94	4	no	—
249	C₂×#97	—	47	1	no	—
250	C₂×#97	—	47	2	no	—
251	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
252	C₂×C₄×C₈	—	47	1	no	—
253	C₂×C₄×C₈	—	47	1	no	—
254	C₂×C₄×C₈	—	47	2	no	—
255	#400	—	47	1	no	—
256	#399	—	47	1	no	—
257	#398	—	47	2	no	—
258	#396	—	47	2	no	—
259	#395	—	47	1	no	—
260	#393	—	47	1	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₄⋊C₄	—	47	2	no	—
263	C₄×C₂²⋊C₄	—	47	2	no	—
264	#336	—	47	2	no	—
265	#336	—	47	2	no	—
266	#336	—	47	2	no	—
267	#336	C₂×D₄₇	1	2	yes	—
268	#336	C₂×D₄₇	1	2	yes	—
269	C₄₇	#21602	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
271	C₂³×C₄	—	47	1	no	—
272	C₂×M₁₆	—	47	4	no	—
273	C₂×M₁₆	—	94	2	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂²×C₈	—	47	1	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	—	47	2	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₂²×C₈	—	94	2	no	—
281	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
282	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	#117	—	94	2	no	—
287	#117	—	94	2	no	—
288	C₂×C₄⋊C₄	—	47	1	no	—
289	C₂×C₄⋊C₄	—	47	1	no	—
290	C₂×C₄⋊C₄	—	47	2	no	—
291	C₂×C₄⋊C₄	—	47	2	no	—
292	C₂×C₄⋊C₄	—	47	2	no	—
293	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	47	1	no	—
296	C₂×C₂²⋊C₄	—	47	1	no	—
297	C₂×C₂²⋊C₄	—	47	2	no	—
298	C₂×C₂²⋊C₄	—	47	2	no	—
299	C₂×C₄²	—	47	1	no	—
300	C₂×C₄²	—	47	2	no	—
301	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	94	4	no	—
305	C₄⋊C₈	—	94	4	no	—
306	C₄⋊C₈	—	94	2	no	—
307	C₂²⋊C₈	—	94	4	no	—
308	#97	—	2	2	no	—
309	#97	—	94	4	no	—
310	#97	—	94	2	no	—
311	C₄×C₈	—	47	4	no	—
312	C₄×C₈	—	94	4	no	—
313	C₄×C₈	—	94	2	no	—
314	#95	—	47	2	no	—
315	#95	—	47	2	no	—
316	#95	—	47	2	no	—
317	#95	—	47	1	no	—
318	#95	—	47	1	no	—
319	#95	—	47	2	no	—
320	C₂⁴	—	47	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	47	2	no	—
327	C₂²×C₄	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	2	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
335	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
338	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
339	M₁₆	—	94	8	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	47	2	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	47	2	no	—
350	C₂×C₈	—	47	2	no	—
351	C₂×C₈	—	94	8	no	—
352	C₂×C₈	—	94	1	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	Q₈×D₄₇	1	2	yes	—
358	C₂×C₈	#10625354	1	2	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	94	2	no	—
362	C₄⋊C₄	—	94	2	no	—
363	C₄⋊C₄	—	94	4	no	—
364	C₄⋊C₄	—	188	2	no	—
365	C₄⋊C₄	—	188	2	no	—
366	C₂²⋊C₄	—	94	2	no	—
367	C₂²⋊C₄	—	94	2	no	—
368	C₂²⋊C₄	—	94	4	no	—
369	C₂²⋊C₄	—	188	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	94	1	no	—
373	C₄²	—	94	2	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	2	no	—
376	C₄²	D₄×D₄₇	1	2	yes	—
377	C₄²	#10625352	1	2	yes	—
378	C₂³	—	47	2	no	—
379	C₂³	—	94	1	no	—
380	C₂³	—	94	1	no	—
381	C₂³	—	94	2	no	—
382	C₂³	—	94	2	no	—
383	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
384	Q₈	—	2	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	47	2	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	1	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
410	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
411	C₂×C₄	#13094032	1	4	yes	—
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
414	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
415	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	47	4	no	—
422	C₈	—	94	2	no	—
423	C₈	—	188	2	no	—
424	C₂²	—	94	2	no	—
425	C₂²	—	94	4	no	—
426	C₂²	—	188	1	no	—
427	C₂²	—	188	1	no	—
428	C₂²	—	188	2	no	—
429	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
430	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
431	C₂²	C₄×#10625354	1	1	yes	characteristic
432	C₂²	C₂×#13094032	1	2	yes	—
433	C₂²	#15689888	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	94	2	no	—
439	C₄	—	188	1	no	—
440	C₄	—	188	1	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
444	C₄	#15689636	1	1	yes	characteristic
445	C₄	#15689652	1	1	yes	characteristic
446	C₄	#15689678	1	1	yes	characteristic
447	C₂	—	188	2	no	—
448	C₂	#20245926	1	1	yes	characteristic
449	C₂	#20252078	1	1	yes	characteristic
450	C₂	#20252103	1	1	yes	characteristic
451	C₂	#20252336	1	2	yes	—
452	C₂	#20252394	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1985	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1985	D₄₇
hypocenter	C₄₇	#21602
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1985

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20244111	C₂	semidirect
5. #20243948	C₂	semidirect
8. #20243259	C₂	semidirect
9. #20243258	C₂	semidirect
11. C₄₇×#1985	C₂	semidirect
46. C₂×#10625324	Q₈	semidirect
224. #1985	D₄₇	semidirect
269. C₄₇	#21602	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₄₇⋊C₈	2
C₂×#15689080	2
#20246658	2
#20244111	2
#20243948	2
#20243567	2
#20243369	2
#20243259	2
#20243258	2
#20243168	2
C₄₇×#1985	2
#21602	47