Subgroups — #26268125

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689400	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20248306	C₂	1	1	yes	maximal, characteristic
4	#20244879	C₂	1	2	yes	maximal, complemented
5	#20244773	C₂	1	2	yes	maximal
6	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244146	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244118	C₂	1	2	yes	maximal, complemented
9	#20244070	C₂	1	2	yes	maximal
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094000	—	2	1	no	—
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	#15689400	—	2	4	no	—
15	Q₈×C₄₇⋊C₈	—	2	4	no	—
16	C₂×#13093957	C₂²	1	2	yes	—
17	C₂×#13093957	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093944	C₂²	1	1	yes	characteristic
21	C₂×#13093944	C₂²	1	2	yes	—
22	C₂×#13093944	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
25	#15689045	—	2	2	no	—
26	#15689025	C₂²	1	2	yes	—
27	#15689021	C₂²	1	2	yes	—
28	#15688993	C₂²	1	1	yes	characteristic
29	#15688980	—	2	1	no	—
30	#15688885	C₂²	1	1	yes	characteristic
31	#15688885	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
36	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#398	—	2	2	no	—
39	C₄₇×#391	—	2	1	no	—
40	C₄₇×#389	C₂²	1	2	yes	—
41	C₄₇×#389	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	1	no	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	#13094000	—	4	4	no	—
49	C₄×D₁₈₈	—	2	2	no	—
50	C₄×D₁₈₈	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	C₂×C₄⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×Dic₄₇⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	#13093957	—	2	4	no	—
60	#13093957	—	2	4	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
63	#13093944	—	2	2	no	—
64	#13093944	—	2	4	no	—
65	#13093944	Q₈	1	4	yes	complemented
66	C₄×C₄₇⋊C₈	—	2	2	no	—
67	C₄×C₄₇⋊C₈	—	2	4	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₂²×Q₈×C₄₇	—	2	1	no	—
70	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₇	—	2	2	no	—
72	C₄⋊Q₈×C₄₇	—	2	2	no	—
73	C₄⋊Q₈×C₄₇	—	4	4	no	—
74	C₄×Q₈×C₄₇	—	2	2	no	—
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	—	2	1	no	—
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#95×C₄₇	—	2	1	no	—
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	2	no	—
90	C₂³×D₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	4	2	no	—
94	C₂×Q₈×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	4	2	no	—
96	C₂×Q₈×C₄₇	D₈	1	4	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
113	C₂×C₄×D₄₇	—	4	2	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	4	4	no	—
124	C₄⋊C₄×C₄₇	—	4	4	no	—
125	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₄₇	#41	1	2	yes	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	4	2	no	—
130	C₄²×C₄₇	C₂×D₄	1	2	yes	—
131	C₄²×C₄₇	#41	1	2	yes	—
132	(C₂×D₄₇)⋊C₄	—	4	2	no	—
133	(C₂×D₄₇)⋊C₄	—	4	4	no	—
134	(C₂×D₄₇)⋊C₄	—	8	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	—	8	1	no	—
141	Dic₄₇⋊C₄	—	4	4	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
150	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
151	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	2	no	—
153	C₂²×D₄₇	—	4	1	no	—
154	C₂²×D₄₇	—	4	1	no	—
155	C₂²×D₄₇	—	4	1	no	—
156	C₂²×D₄₇	—	4	1	no	—
157	C₂²×D₄₇	—	4	1	no	—
158	C₂²×D₄₇	—	4	1	no	—
159	Q₈×C₄₇	—	2	8	no	—
160	Q₈×C₄₇	—	8	4	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	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	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	#121	1	2	yes	—
178	C₂×C₄×C₄₇	#121	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
180	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₄₇	#135	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	D₁₈₈	—	2	2	no	—
195	D₁₈₈	—	2	2	no	—
196	D₁₈₈	—	4	1	no	—
197	D₁₈₈	—	4	1	no	—
198	C₄×D₄₇	—	8	4	no	—
199	C₄₇⋊C₈	—	2	4	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	#25469	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₂²×C₄₇	#548	1	1	yes	characteristic
205	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
208	C₂²×C₄₇	#577	1	1	yes	characteristic
209	C₂²×C₄₇	#578	1	1	yes	characteristic
210	C₂×D₄₇	—	4	2	no	—
211	C₂×D₄₇	—	4	2	no	—
212	C₂×D₄₇	—	4	2	no	—
213	C₂×D₄₇	—	8	1	no	—
214	C₂×D₄₇	—	8	1	no	—
215	C₂×D₄₇	—	8	1	no	—
216	C₂×D₄₇	—	8	1	no	—
217	C₄×C₄₇	—	2	4	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	8	2	no	—
223	C₄×C₄₇	#466	1	4	yes	—
224	C₄×C₄₇	#533	1	1	yes	characteristic
225	C₄×C₄₇	#541	1	1	yes	characteristic
226	C₄×C₄₇	#547	1	1	yes	characteristic
227	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
228	Dic₄₇	—	8	2	no	—
229	Dic₄₇	—	8	1	no	—
230	C₂×#474	—	47	1	no	—
231	C₂×C₈×Q₈	—	47	1	no	—
232	#2546	D₄₇	1	1	yes	characteristic, complemented
233	#2538	—	47	1	no	—
234	#2086	—	47	2	no	—
235	#2067	—	47	2	no	—
236	#1990	—	47	1	no	—
237	#1947	—	47	1	no	—
238	#1942	—	47	2	no	—
239	#1934	—	47	2	no	—
240	C₄×#102	—	47	1	no	—
241	C₂×C₄₇	#2429	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
243	C₂×C₄₇	#3063	1	1	yes	characteristic
244	C₂×C₄₇	#3358	1	1	yes	characteristic
245	C₂×C₄₇	#3364	1	1	yes	characteristic
246	C₂×C₄₇	Q₈×D₈	1	1	yes	characteristic
247	C₂×C₄₇	#3381	1	1	yes	characteristic
248	D₄₇	—	8	2	no	—
249	C₂×C₄⋊Q₈	—	2	1	no	—
250	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	—	94	1	no	—
252	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₄×D₄	—	47	1	no	—
254	#474	—	94	4	no	—
255	C₈×Q₈	—	94	4	no	—
256	C₂×#107	—	47	2	no	—
257	C₂×#107	—	47	2	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×C₄⋊C₈	—	47	2	no	—
260	C₂×#102	—	47	1	no	—
261	C₂×#102	—	47	1	no	—
262	C₂×#102	—	47	2	no	—
263	C₂×C₄×C₈	—	47	2	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	#398	—	2	2	no	—
266	#396	—	94	2	no	—
267	#391	—	2	1	no	—
268	#390	—	47	2	no	—
269	#389	—	47	2	no	—
270	#389	C₂×D₄₇	1	2	yes	—
271	#389	C₂×D₄₇	1	2	yes	—
272	#384	—	47	1	no	—
273	#380	—	94	1	no	—
274	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
275	#340	—	47	2	no	—
276	#340	—	47	1	no	—
277	#340	—	47	2	no	—
278	#340	—	47	2	no	—
279	#340	—	47	1	no	—
280	C₄₇	#25469	1	1	yes	characteristic, complemented, Sylow
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂²×D₄	—	47	1	no	—
284	C₂³×C₄	—	94	1	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	4	4	no	—
291	C₂²⋊Q₈	—	188	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	94	2	no	—
295	C₄×D₄	—	94	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	47	2	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	2	no	—
303	C₂×C₄⋊C₄	—	94	1	no	—
304	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	94	2	no	—
310	C₂×C₂²⋊C₄	—	94	1	no	—
311	C₂×C₂²⋊C₄	—	94	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	—	94	4	no	—
316	#107	—	94	4	no	—
317	C₄⋊C₈	—	47	4	no	—
318	C₄⋊C₈	—	94	4	no	—
319	#102	—	47	4	no	—
320	#102	—	94	4	no	—
321	#102	—	94	2	no	—
322	C₄×C₈	—	94	4	no	—
323	C₄×C₈	—	94	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	94	2	no	—
328	C₂⁴	—	94	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	#10625334	1	4	yes	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	1	no	—
337	C₂×D₄	—	94	1	no	—
338	C₂×D₄	—	94	1	no	—
339	C₂×D₄	—	94	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	188	2	no	—
347	C₂²×C₄	—	188	2	no	—
348	C₂²×C₄	—	188	2	no	—
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	C₂×C₈	—	47	4	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	1	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	376	1	no	—
377	C₄⋊C₄	—	188	4	no	—
378	C₄⋊C₄	—	188	2	no	—
379	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
380	C₄⋊C₄	#10625354	1	2	yes	—
381	C₂²⋊C₄	—	376	2	no	—
382	C₂²⋊C₄	—	188	2	no	—
383	C₂²⋊C₄	—	188	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	D₄×D₄₇	1	2	yes	—
388	C₄²	#10625352	1	2	yes	—
389	C₂³	—	94	2	no	—
390	C₂³	—	188	1	no	—
391	C₂³	—	188	1	no	—
392	C₂³	—	188	1	no	—
393	C₂³	—	188	1	no	—
394	C₂³	—	188	1	no	—
395	C₂³	—	188	1	no	—
396	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
397	Q₈	—	2	8	no	—
398	Q₈	—	8	4	no	—
399	D₄	—	94	2	no	—
400	D₄	—	94	2	no	—
401	D₄	—	188	1	no	—
402	D₄	—	188	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	376	4	no	—
420	C₂×C₄	—	188	2	no	—
421	C₂×C₄	—	188	1	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	1	no	—
424	C₂×C₄	—	188	1	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	#13093996	1	2	yes	—
427	C₂×C₄	#13093996	1	2	yes	—
428	C₂×C₄	C₂×#10625334	1	4	yes	—
429	C₂×C₄	C₂×#10625334	1	2	yes	—
430	C₂×C₄	#13094044	1	2	yes	—
431	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
434	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
435	C₂×C₄	#13094072	1	1	yes	characteristic
436	C₂×C₄	#13094072	1	1	yes	characteristic
437	C₈	—	94	4	no	—
438	C₈	—	94	2	no	—
439	C₈	—	188	1	no	—
440	C₂²	—	376	1	no	—
441	C₂²	—	376	1	no	—
442	C₂²	—	376	1	no	—
443	C₂²	—	376	1	no	—
444	C₂²	—	188	2	no	—
445	C₂²	—	188	2	no	—
446	C₂²	—	188	2	no	—
447	C₂²	C₂×#13093996	1	1	yes	characteristic
448	C₂²	#15689784	1	1	yes	characteristic
449	C₂²	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
450	C₂²	C₂²×#10625334	1	1	yes	characteristic
451	C₂²	C₂×#13094044	1	1	yes	characteristic
452	C₂²	#15689931	1	1	yes	characteristic
453	C₂²	#15689938	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	376	2	no	—
461	C₄	—	376	1	no	—
462	C₄	#15689357	1	4	yes	—
463	C₄	#15689678	1	1	yes	characteristic
464	C₄	#15689734	1	1	yes	characteristic
465	C₄	#15689776	1	1	yes	characteristic
466	C₄	#15689788	1	1	yes	characteristic
467	C₂	—	376	2	no	—
468	C₂	#20246990	1	1	yes	characteristic
469	C₂	C₂×#15689357	1	1	yes	characteristic
470	C₂	#20253075	1	1	yes	characteristic
471	C₂	#20256023	1	1	yes	characteristic
472	C₂	#20256073	1	1	yes	characteristic
473	C₂	Q₈×#10625334	1	1	yes	characteristic
474	C₂	#20256259	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2546	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
hypercenter	#2546	D₄₇
hypocenter	C₄₇	#25469
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ #2546

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20244879	C₂	semidirect
6. #20244350	C₂	semidirect
7. #20244146	C₂	semidirect
8. #20244118	C₂	semidirect
11. C₄₇×#2546	C₂	semidirect
65. #13093944	Q₈	semidirect
232. #2546	D₄₇	semidirect
280. C₄₇	#25469	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689400	2
C₂×Q₈×C₄₇⋊C₈	2
#20248306	2
#20244879	2
#20244773	2
#20244350	2
#20244146	2
#20244118	2
#20244070	2
C₄×#13093944	2
C₄₇×#2546	2
#25469	47