Subgroups — #26369143

Order 12032.

1176 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251871	C₂	1	2	yes	maximal, complemented
2	#20245083	C₂	1	2	yes	maximal, complemented
3	#20245077	C₂	1	4	yes	maximal, complemented
4	#20245073	C₂	1	2	yes	maximal, complemented
5	C₂×#15688922	C₂	1	4	yes	maximal, complemented
6	C₄₇×#3499	C₂	1	1	yes	maximal, characteristic
7	#15689890	—	2	2	no	—
8	#15689107	—	2	4	no	—
9	#15689107	C₂²	1	4	yes	—
10	C₂×#13093943	—	2	2	no	—
11	C₂×#13093943	C₂²	1	8	yes	—
12	#15688922	C₂²	1	4	yes	—
13	#15688922	C₂²	1	8	yes	—
14	#15688920	C₂²	1	4	yes	—
15	C₂×2₋¹⁺⁴×C₄₇	C₄	1	1	yes	characteristic
16	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
17	D₄×Q₈×C₄₇	—	2	2	no	—
18	C₄₇×#547	—	2	4	no	—
19	C₄₇×#547	—	2	2	no	—
20	C₄₇×#536	C₄	1	1	yes	characteristic
21	C₄₇×#536	C₄	1	2	yes	—
22	C₄₇×#536	C₂²	1	1	yes	characteristic
23	C₄₇×#536	C₂²	1	2	yes	—
24	C₄₇×#532	C₄	1	2	yes	—
25	C₄₇×#532	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
28	C₄×#41×C₄₇	C₄	1	1	yes	characteristic
29	#13094031	—	4	8	no	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	2	8	no	—
32	#13093943	—	2	8	no	—
33	#13093943	C₂³	1	8	yes	—
34	#13093941	—	2	4	no	—
35	2₋¹⁺⁴×C₄₇	—	4	4	no	—
36	2₋¹⁺⁴×C₄₇	—	4	4	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	1	no	—
39	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
40	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
42	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×#41×C₄₇	D₄	1	4	yes	—
44	C₂×#41×C₄₇	D₄	1	2	yes	—
45	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₄₇	—	2	1	no	—
47	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
51	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	—	2	4	no	—
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
55	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
56	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
57	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
59	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
60	#124×C₄₇	C₂×C₄	1	2	yes	—
61	#124×C₄₇	C₂×C₄	1	2	yes	—
62	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
63	#124×C₄₇	C₂³	1	1	yes	characteristic
64	#123×C₄₇	—	2	4	no	—
65	#123×C₄₇	—	2	2	no	—
66	#123×C₄₇	—	2	2	no	—
67	#123×C₄₇	—	2	4	no	—
68	C₂²⋊Q₈×C₄₇	—	2	2	no	—
69	C₂²⋊Q₈×C₄₇	—	2	4	no	—
70	C₂²⋊Q₈×C₄₇	—	2	4	no	—
71	C₂²⋊Q₈×C₄₇	—	2	2	no	—
72	#121×C₄₇	—	2	4	no	—
73	#121×C₄₇	—	2	2	no	—
74	C₄×Q₈×C₄₇	—	2	1	no	—
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	—	2	1	no	—
77	C₄×D₄×C₄₇	—	2	4	no	—
78	C₄×D₄×C₄₇	—	2	2	no	—
79	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
80	#117×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
85	#41×C₄₇	—	2	4	no	—
86	#41×C₄₇	—	2	8	no	—
87	#41×C₄₇	—	4	2	no	—
88	#41×C₄₇	—	4	4	no	—
89	#41×C₄₇	—	4	8	no	—
90	#41×C₄₇	—	4	4	no	—
91	#41×C₄₇	—	4	2	no	—
92	#41×C₄₇	—	4	8	no	—
93	#41×C₄₇	—	4	4	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	4	4	no	—
97	C₂×Q₈×C₄₇	—	4	2	no	—
98	C₂×Q₈×C₄₇	—	4	4	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	—	4	4	no	—
101	C₂×Q₈×C₄₇	—	4	4	no	—
102	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
104	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
113	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₄₇	—	2	4	no	—
131	C₄⋊C₄×C₄₇	—	2	4	no	—
132	C₄⋊C₄×C₄₇	—	2	4	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	1	no	—
138	C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂²⋊C₄×C₄₇	—	2	4	no	—
140	C₂²⋊C₄×C₄₇	—	2	2	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	—	2	1	no	—
145	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	#10625329	—	2	8	no	—
149	#10625329	—	4	8	no	—
150	#10625329	—	4	4	no	—
151	C₂×C₄₇⋊C₈	—	4	8	no	—
152	C₂×C₄₇⋊C₈	—	4	4	no	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	Q₈×C₄₇	—	2	2	no	—
158	Q₈×C₄₇	—	2	4	no	—
159	Q₈×C₄₇	—	4	2	no	—
160	Q₈×C₄₇	—	4	4	no	—
161	Q₈×C₄₇	—	4	1	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	Q₈×C₄₇	—	4	1	no	—
164	Q₈×C₄₇	—	4	4	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	2	8	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	4	1	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	4	1	no	—
171	D₄×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	4	no	—
174	D₄×C₄₇	#99	1	4	yes	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	8	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	4	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
197	C₄₇⋊C₈	—	4	8	no	—
198	#33372	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	C₂×#99	1	4	yes	—
207	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	4	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	4	1	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	4	1	no	—
217	C₄×C₄₇	C₂×#99	1	2	yes	—
218	#3499	D₄₇	1	1	yes	characteristic
219	#2889	—	47	2	no	—
220	#2135	—	47	2	no	—
221	#2133	—	47	4	no	—
222	#2132	—	47	2	no	—
223	C₂×#356	—	47	4	no	—
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	—	2	4	no	—
226	C₂×C₄₇	—	4	1	no	—
227	C₂×C₄₇	—	4	2	no	—
228	C₂×C₄₇	—	8	1	no	—
229	C₂×C₄₇	C₂²×#99	1	1	yes	characteristic
230	C₂×2₋¹⁺⁴	Dic₄₇	1	1	yes	characteristic
231	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
232	#568	—	94	2	no	—
233	D₄×Q₈	—	2	2	no	—
234	#547	—	2	4	no	—
235	#547	—	2	2	no	—
236	#536	Dic₄₇	1	1	yes	characteristic
237	#536	Dic₄₇	1	2	yes	—
238	#536	C₂×D₄₇	1	1	yes	characteristic
239	#536	C₂×D₄₇	1	2	yes	—
240	#532	Dic₄₇	1	2	yes	—
241	#532	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
244	C₄×#41	Dic₄₇	1	1	yes	characteristic
245	#413	—	47	4	no	—
246	#413	—	94	4	no	—
247	C₂×#101	—	47	8	no	—
248	C₂×#101	—	94	2	no	—
249	#356	—	47	4	no	—
250	#356	—	47	8	no	—
251	#355	—	47	4	no	—
252	C₄₇	#33372	1	1	yes	characteristic, complemented, Sylow
253	2₋¹⁺⁴	—	4	4	no	—
254	2₋¹⁺⁴	—	4	4	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	1	no	—
257	C₂×#41	C₂×Dic₄₇	1	2	yes	—
258	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
259	C₂×#41	C₂×Dic₄₇	1	2	yes	—
260	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
261	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
262	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
263	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
266	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
267	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
269	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
270	#131	—	188	8	no	—
271	C₂×M₁₆	—	94	8	no	—
272	C₂×M₁₆	—	94	4	no	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
276	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
277	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
278	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
279	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
280	#127	C₂×Dic₄₇	1	1	yes	characteristic
281	#124	C₂×Dic₄₇	1	2	yes	—
282	#124	C₂×Dic₄₇	1	2	yes	—
283	#124	C₂×Dic₄₇	1	1	yes	characteristic
284	#124	C₂²×D₄₇	1	1	yes	characteristic
285	#123	—	2	4	no	—
286	#123	—	2	2	no	—
287	#123	—	2	2	no	—
288	#123	—	2	4	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	#121	—	2	4	no	—
294	#121	—	2	2	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	#117	C₂×Dic₄₇	1	1	yes	characteristic
301	#117	C₂×Dic₄₇	1	2	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
306	#101	—	47	8	no	—
307	#101	—	94	8	no	—
308	#100	—	94	4	no	—
309	#41	—	2	8	no	—
310	#41	—	2	4	no	—
311	#41	—	4	2	no	—
312	#41	—	4	4	no	—
313	#41	—	4	8	no	—
314	#41	—	4	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	8	no	—
317	#41	—	4	4	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
327	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
328	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
329	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
331	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
332	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
337	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
338	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
339	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
340	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
341	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
349	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
350	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
354	M₁₆	—	94	8	no	—
355	M₁₆	—	188	8	no	—
356	M₁₆	—	188	4	no	—
357	C₂×C₈	—	188	8	no	—
358	C₂×C₈	—	188	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
375	C₄²	C₂²×Dic₄₇	1	2	yes	—
376	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
379	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
380	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	4	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	4	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	1	no	—
388	Q₈	—	4	4	no	—
389	Q₈	—	4	2	no	—
390	D₄	—	2	8	no	—
391	D₄	—	2	4	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	#13093939	1	4	yes	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
418	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
421	C₈	—	188	8	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	1	no	—
429	C₂²	C₂×#13093939	1	4	yes	—
430	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	C₂×#13093939	1	2	yes	—
441	C₂	—	2	1	no	—
442	C₂	—	2	4	no	—
443	C₂	—	4	1	no	—
444	C₂	—	4	2	no	—
445	C₂	—	8	1	no	—
446	C₂	C₂²×#13093939	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×#13093939
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂×Q₈	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3499	C₂
socle	C₂×C₄₇	C₂²×#99
cosocle	C₂×Q₈×C₄₇	C₂⁴
hypercenter	#3499	D₄₇
hypocenter	C₄₇	#33372
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×D₄ ◁ C₂×2₋¹⁺⁴ ◁ #3499

Complements

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

N	H ≅ G/N	type
1. #20251871	C₂	semidirect
2. #20245083	C₂	semidirect
3. #20245077	C₂	semidirect
4. #20245073	C₂	semidirect
5. C₂×#15688922	C₂	semidirect
252. C₄₇	#33372	semidirect

Maximal subgroups

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

subgroup	index
#20251871	2
#20245083	2
#20245077	2
#20245073	2
C₂×#15688922	2
C₄₇×#3499	2
#33372	47