Subgroups — #27096915

Order 12032.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257189	C₂	1	2	yes	maximal, complemented
2	#20256348	C₂	1	4	yes	maximal, complemented
3	#20256289	C₂	1	4	yes	maximal, complemented
4	#20256256	C₂	1	4	yes	maximal, complemented
5	#20256256	C₂	1	2	yes	maximal, complemented
6	Q₈×D₃₇₆	C₂	1	2	yes	maximal, complemented
7	#20253927	C₂	1	2	yes	maximal, complemented
8	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253220	C₂	1	4	yes	maximal, complemented
10	#20253187	C₂	1	2	yes	maximal, complemented
11	#20252241	C₂	1	2	yes	maximal
12	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
13	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
15	#15689834	—	2	2	no	—
16	#15689833	C₂²	1	4	yes	complemented
17	#15689833	C₂²	1	8	yes	complemented
18	#15689829	—	2	4	no	—
19	Q₈×D₁₈₈	C₂²	1	4	yes	complemented
20	#15689788	—	2	2	no	—
21	#15689751	C₂²	1	4	yes	—
22	#15689748	—	2	4	no	—
23	#15689680	C₂²	1	2	yes	—
24	C₂²⋊Q₈×D₄₇	—	2	4	no	—
25	#15689597	C₂²	1	4	yes	—
26	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
27	#15689532	C₂²	1	8	yes	complemented
28	#15689528	C₂²	1	1	yes	characteristic, complemented
29	#15689528	C₂²	1	4	yes	complemented
30	#15689528	C₂²	1	1	yes	characteristic, complemented
31	#15689525	C₂²	1	2	yes	complemented
32	#15689525	C₂²	1	4	yes	complemented
33	#15689525	C₂²	1	2	yes	complemented
34	#15689521	C₂²	1	2	yes	complemented
35	#15689424	C₂²	1	8	yes	complemented
36	#15689424	C₂²	1	8	yes	complemented
37	#15689424	C₂²	1	8	yes	complemented
38	#15689414	C₂²	1	4	yes	complemented
39	#15689414	C₂²	1	8	yes	complemented
40	#15689404	C₂²	1	4	yes	complemented
41	#15689404	C₂²	1	8	yes	complemented
42	#15689236	C₂²	1	8	yes	—
43	C₄×D₃₇₆	C₂²	1	4	yes	—
44	C₄×D₃₇₆	C₂²	1	2	yes	—
45	C₄×D₃₇₆	C₂²	1	4	yes	—
46	C₄×D₃₇₆	C₂²	1	2	yes	—
47	C₄×D₃₇₆	C₂²	1	2	yes	—
48	C₄×D₃₇₆	C₂²	1	2	yes	—
49	#15689165	C₂²	1	4	yes	—
50	#15689161	C₂²	1	2	yes	—
51	#15689161	C₂²	1	2	yes	—
52	C₂×#13093958	C₂²	1	1	yes	characteristic
53	#15689129	C₂²	1	4	yes	—
54	C₂×#13093946	C₂²	1	2	yes	—
55	C₄₇×#533	C₂²	1	1	yes	characteristic
56	C₄₇×#446	C₂²	1	2	yes	complemented
57	C₄₇×#446	C₂²	1	2	yes	complemented
58	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
59	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
60	C₄₇×#424	C₂²	1	2	yes	—
61	C₄₇×#423	C₂²	1	1	yes	characteristic
62	C₄₇×#405	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×Q₈×D₄₇	—	2	4	no	—
65	C₂²×D₁₈₈	C₂³	1	2	yes	—
66	C₂²×C₄×D₄₇	—	2	2	no	—
67	C₂×D₃₇₆	Q₈	1	8	yes	complemented
68	C₂×D₃₇₆	C₂³	1	2	yes	—
69	C₂×D₃₇₆	C₂³	1	2	yes	—
70	#13094024	C₂³	1	8	yes	—
71	#13094024	C₂³	1	2	yes	—
72	#13094024	C₂³	1	2	yes	—
73	#13094023	—	2	4	no	—
74	#13094016	C₂³	1	8	yes	—
75	#13094016	C₂³	1	4	yes	—
76	#13094015	—	2	4	no	—
77	#13094004	—	2	8	no	—
78	#13094004	—	2	4	no	—
79	#13094003	—	2	2	no	—
80	#13094003	—	2	2	no	—
81	#13094002	—	2	8	no	—
82	#13094002	—	2	8	no	—
83	#13094002	—	2	8	no	—
84	#13094001	—	2	8	no	—
85	#13094000	—	2	8	no	—
86	#13094000	—	2	4	no	—
87	C₄×Dic₉₄	—	2	2	no	—
88	C₄×Dic₉₄	—	2	2	no	—
89	C₄×D₁₈₈	—	2	2	no	—
90	C₄×D₁₈₈	—	2	2	no	—
91	C₄×D₁₈₈	C₂³	1	8	yes	—
92	C₄×D₁₈₈	C₂³	1	8	yes	—
93	C₄×D₁₈₈	C₂³	1	4	yes	—
94	C₄×D₁₈₈	C₂³	1	4	yes	—
95	#13093986	—	2	4	no	—
96	#13093986	—	2	4	no	—
97	#13093983	C₂³	1	4	yes	—
98	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
99	C₄⋊C₄×D₄₇	—	2	8	no	—
100	C₄⋊C₄×D₄₇	—	2	4	no	—
101	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
102	C₂²⋊C₄×D₄₇	—	2	8	no	—
103	#13093958	C₂³	1	2	yes	—
104	#13093958	C₂³	1	2	yes	—
105	#13093958	C₂³	1	2	yes	—
106	#13093958	C₂³	1	2	yes	—
107	#13093958	C₂³	1	2	yes	—
108	#13093958	C₂³	1	8	yes	—
109	#13093958	C₂³	1	2	yes	—
110	#13093956	C₂³	1	4	yes	—
111	#13093956	C₂³	1	4	yes	—
112	#13093956	C₂³	1	8	yes	—
113	#13093946	C₂³	1	8	yes	—
114	#13093946	C₂³	1	8	yes	—
115	#13093946	C₂³	1	4	yes	—
116	#13093946	C₂³	1	4	yes	—
117	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
121	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
122	#125×C₄₇	D₄	1	2	yes	—
123	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
125	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
126	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
127	#117×C₄₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
130	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
131	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
132	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
133	#97×C₄₇	C₂³	1	4	yes	—
134	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₇	C₂³	1	4	yes	—
138	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₂³×D₄₇	—	2	2	no	—
140	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
141	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₄₇	—	2	2	no	—
146	Q₈×D₄₇	—	8	8	no	—
147	C₂×D₁₈₈	—	2	2	no	—
148	C₂×D₁₈₈	—	2	4	no	—
149	C₂×D₁₈₈	C₂×Q₈	1	8	yes	complemented
150	C₂×D₁₈₈	C₂⁴	1	4	yes	—
151	C₂×C₄×D₄₇	—	2	4	no	—
152	C₂×C₄×D₄₇	—	2	8	no	—
153	C₂×C₄×D₄₇	—	2	8	no	—
154	C₂×C₄×D₄₇	—	2	4	no	—
155	C₂×C₄×D₄₇	—	8	4	no	—
156	C₂×Dic₉₄	—	2	2	no	—
157	C₂×Dic₉₄	—	2	2	no	—
158	C₂×Dic₉₄	—	2	8	no	—
159	M₁₆×C₄₇	—	2	4	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
162	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
165	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
171	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
174	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₄²×C₄₇	C₂⁴	1	4	yes	—
179	C₂²⋊Dic₄₇	—	2	4	no	—
180	(C₂×D₄₇)⋊C₄	—	2	8	no	—
181	(C₂×D₄₇)⋊C₄	—	2	8	no	—
182	(C₂×D₄₇)⋊C₄	—	2	4	no	—
183	(C₂×D₄₇)⋊C₄	—	2	4	no	—
184	C₄⋊Dic₄₇	—	2	2	no	—
185	C₄⋊Dic₄₇	—	2	8	no	—
186	C₄⋊Dic₄₇	—	2	2	no	—
187	C₄⋊Dic₄₇	—	2	2	no	—
188	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
189	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
190	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
191	Dic₄₇⋊C₄	—	2	4	no	—
192	Dic₄₇⋊C₄	—	2	8	no	—
193	Dic₄₇⋊C₄	—	2	8	no	—
194	Dic₄₇⋊C₄	—	2	4	no	—
195	C₄×Dic₄₇	—	2	4	no	—
196	D₃₇₆	C₂×Q₈	1	8	yes	complemented
197	D₃₇₆	C₂×Q₈	1	8	yes	complemented
198	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₂²×D₄₇	—	2	4	no	—
200	C₂²×D₄₇	—	2	8	no	—
201	C₂²×D₄₇	—	8	2	no	—
202	C₂²×D₄₇	—	8	2	no	—
203	Q₈×C₄₇	—	2	4	no	—
204	Q₈×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
216	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	2	4	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	8	2	no	—
221	D₁₈₈	—	2	8	no	—
222	D₁₈₈	—	2	4	no	—
223	D₁₈₈	C₂²×Q₈	1	8	yes	—
224	C₄×D₄₇	—	4	8	no	—
225	C₄×D₄₇	—	8	8	no	—
226	C₄×D₄₇	—	8	4	no	—
227	C₄×D₄₇	—	8	8	no	—
228	Dic₉₄	—	4	4	no	—
229	Dic₉₄	—	8	2	no	—
230	Dic₉₄	—	8	8	no	—
231	C₈×C₄₇	—	2	1	no	—
232	C₈×C₄₇	—	2	1	no	—
233	C₈×C₄₇	—	2	4	no	—
234	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
235	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
236	#61370	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
240	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
241	C₂×D₄₇	—	2	8	no	—
242	C₂×D₄₇	—	4	4	no	—
243	C₂×D₄₇	—	4	4	no	—
244	C₂×D₄₇	—	8	8	no	—
245	C₄×C₄₇	—	2	1	no	—
246	C₄×C₄₇	—	2	4	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	—	2	4	no	—
249	C₄×C₄₇	—	2	1	no	—
250	C₄×C₄₇	D₄×Q₈	1	2	yes	—
251	C₄×C₄₇	#576	1	2	yes	—
252	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
253	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	Dic₄₇	—	4	4	no	—
255	Dic₄₇	—	4	4	no	—
256	Dic₄₇	—	4	4	no	—
257	#3501	—	47	2	no	—
258	#3389	—	47	4	no	—
259	#3384	—	47	4	no	—
260	#3380	—	47	2	no	—
261	#3380	—	47	4	no	—
262	Q₈×D₈	—	47	2	no	—
263	#3164	—	47	2	no	—
264	#3160	—	47	1	no	—
265	#3081	—	47	4	no	—
266	#3077	—	47	2	no	—
267	#2960	D₄₇	1	1	yes	characteristic, complemented
268	#2948	—	47	2	no	—
269	C₂×C₄×D₈	—	47	1	no	—
270	C₂×C₄₇	—	2	2	no	—
271	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
272	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
273	C₂×C₄₇	#3584	1	1	yes	characteristic
274	D₄₇	—	4	8	no	—
275	C₂²×D₈	—	47	1	no	—
276	#554	—	47	4	no	—
277	#554	—	47	8	no	—
278	#554	—	94	2	no	—
279	#554	—	94	4	no	—
280	D₄×Q₈	—	47	4	no	—
281	D₄×Q₈	—	94	2	no	—
282	#544	—	47	4	no	—
283	#543	—	94	4	no	—
284	#533	—	47	2	no	—
285	#533	C₂×D₄₇	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	—	94	4	no	—
287	#518	—	47	4	no	—
288	C₂×C₄×D₄	—	47	2	no	—
289	#501	—	47	8	no	—
290	#500	—	47	1	no	—
291	#500	—	47	4	no	—
292	#500	—	47	1	no	—
293	#499	—	47	2	no	—
294	#499	—	47	4	no	—
295	#499	—	47	2	no	—
296	#498	—	47	2	no	—
297	#478	—	47	8	no	—
298	#478	—	47	8	no	—
299	#478	—	47	8	no	—
300	#476	—	47	4	no	—
301	#476	—	47	8	no	—
302	#474	—	47	4	no	—
303	#474	—	47	8	no	—
304	#446	C₂×D₄₇	1	2	yes	complemented
305	#446	C₂×D₄₇	1	2	yes	complemented
306	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
307	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
308	#442	—	47	8	no	—
309	C₄×D₈	—	47	2	no	—
310	C₄×D₈	—	47	4	no	—
311	C₄×D₈	—	47	2	no	—
312	C₄×D₈	—	47	4	no	—
313	C₄×D₈	—	47	2	no	—
314	C₄×D₈	—	47	2	no	—
315	#428	—	47	4	no	—
316	#427	—	47	2	no	—
317	#427	—	47	2	no	—
318	C₂×#107	—	47	1	no	—
319	#424	C₂×D₄₇	1	2	yes	—
320	#423	C₂×D₄₇	1	1	yes	characteristic
321	#418	—	47	4	no	—
322	C₂×#102	—	47	2	no	—
323	#405	C₂×D₄₇	1	2	yes	—
324	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
325	C₄₇	#61370	1	1	yes	characteristic, complemented, Sylow
326	C₂²×Q₈	—	94	4	no	—
327	C₂²×D₄	—	47	2	no	—
328	C₂³×C₄	—	94	2	no	—
329	C₂×D₈	—	47	8	no	—
330	C₂×D₈	—	47	2	no	—
331	C₂×D₈	—	47	2	no	—
332	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
333	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₄⋊Q₈	—	47	2	no	—
336	C₄⋊Q₈	—	47	2	no	—
337	C₄⋊Q₈	—	47	8	no	—
338	C₄⋊Q₈	—	94	4	no	—
339	C₄⋊Q₈	D₁₈₈	1	1	yes	characteristic
340	C₄⋊Q₈	D₁₈₈	1	1	yes	characteristic
341	#125	—	47	4	no	—
342	#125	—	47	8	no	—
343	#125	—	94	4	no	—
344	#125	D₁₈₈	1	2	yes	—
345	C₂²⋊Q₈	—	94	4	no	—
346	C₂²⋊Q₈	—	94	8	no	—
347	C₂²⋊Q₈	—	94	2	no	—
348	C₂²⋊Q₈	—	94	2	no	—
349	C₂²⋊Q₈	—	94	4	no	—
350	C₂²⋊Q₈	—	94	8	no	—
351	C₂²⋊Q₈	—	94	8	no	—
352	C₂²⋊Q₈	—	94	8	no	—
353	C₂²⋊Q₈	—	94	8	no	—
354	C₂²⋊Q₈	—	94	8	no	—
355	C₂²⋊Q₈	D₁₈₈	1	2	yes	—
356	C₂²⋊Q₈	D₁₈₈	1	2	yes	—
357	C₄×Q₈	—	94	2	no	—
358	C₄×Q₈	—	94	2	no	—
359	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
360	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
361	C₄×D₄	—	47	4	no	—
362	C₄×D₄	—	47	4	no	—
363	C₄×D₄	—	47	8	no	—
364	C₄×D₄	—	47	8	no	—
365	C₄×D₄	—	94	4	no	—
366	C₄×D₄	—	94	4	no	—
367	C₄×D₄	—	94	2	no	—
368	C₄×D₄	—	94	2	no	—
369	#117	—	47	4	no	—
370	#117	C₂²×D₄₇	1	2	yes	—
371	C₂×C₄⋊C₄	—	47	2	no	—
372	C₂×C₄⋊C₄	—	94	8	no	—
373	C₂×C₄⋊C₄	—	94	4	no	—
374	C₂×C₂²⋊C₄	—	94	2	no	—
375	C₂×C₂²⋊C₄	—	94	8	no	—
376	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
377	#107	—	47	2	no	—
378	#107	—	47	2	no	—
379	#107	—	47	2	no	—
380	#107	—	47	2	no	—
381	#107	—	47	2	no	—
382	#107	—	47	2	no	—
383	#107	—	47	8	no	—
384	#106	—	47	4	no	—
385	#106	—	47	4	no	—
386	#106	—	47	8	no	—
387	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
388	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
389	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
390	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
391	#102	—	47	4	no	—
392	#102	—	47	4	no	—
393	#102	—	47	8	no	—
394	#102	—	47	8	no	—
395	#97	C₂²×D₄₇	1	4	yes	—
396	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₄₇	1	4	yes	—
401	C₂⁴	—	94	2	no	—
402	C₂×Q₈	—	94	2	no	—
403	C₂×Q₈	—	94	8	no	—
404	C₂×Q₈	—	94	2	no	—
405	C₂×Q₈	—	376	8	no	—
406	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
407	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
408	C₂×D₄	—	47	8	no	—
409	C₂×D₄	—	47	4	no	—
410	C₂×D₄	—	94	2	no	—
411	C₂×D₄	—	94	4	no	—
412	C₂²×C₄	—	94	2	no	—
413	C₂²×C₄	—	94	8	no	—
414	C₂²×C₄	—	94	8	no	—
415	C₂²×C₄	—	94	4	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	—	376	4	no	—
418	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
421	D₈	—	47	8	no	—
422	D₈	—	47	8	no	—
423	M₁₆	—	2	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
426	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
427	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₄₇	1	4	yes	—
429	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
430	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
431	C₄⋊C₄	—	47	4	no	—
432	C₄⋊C₄	—	47	4	no	—
433	C₄⋊C₄	—	47	4	no	—
434	C₄⋊C₄	—	94	4	no	—
435	C₄⋊C₄	—	94	8	no	—
436	C₄⋊C₄	—	94	8	no	—
437	C₄⋊C₄	—	94	4	no	—
438	C₄⋊C₄	—	94	2	no	—
439	C₄⋊C₄	—	94	2	no	—
440	C₄⋊C₄	—	94	8	no	—
441	C₄⋊C₄	—	94	2	no	—
442	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
443	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
444	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
445	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
446	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
447	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
448	C₂²⋊C₄	—	94	4	no	—
449	C₂²⋊C₄	—	94	8	no	—
450	C₂²⋊C₄	—	94	8	no	—
451	C₂²⋊C₄	—	94	4	no	—
452	C₂²⋊C₄	—	94	4	no	—
453	C₂²⋊C₄	C₂×D₁₈₈	1	4	yes	—
454	C₄²	—	94	4	no	—
455	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
456	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
457	C₄²	C₂³×D₄₇	1	1	yes	characteristic
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₄²	C₂³×D₄₇	1	4	yes	—
460	C₂³	—	94	8	no	—
461	C₂³	—	94	4	no	—
462	C₂³	—	376	2	no	—
463	C₂³	—	376	2	no	—
464	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	376	2	no	—
468	Q₈	—	376	8	no	—
469	Q₈	—	188	4	no	—
470	D₄	—	47	8	no	—
471	D₄	—	94	8	no	—
472	D₄	—	94	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	94	4	no	—
476	C₂×C₄	—	94	4	no	—
477	C₂×C₄	—	94	4	no	—
478	C₂×C₄	—	376	8	no	—
479	C₂×C₄	—	376	4	no	—
480	C₂×C₄	—	376	8	no	—
481	C₂×C₄	—	376	2	no	—
482	C₂×C₄	—	188	8	no	—
483	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
487	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
488	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
490	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
491	C₂×C₄	#13094071	1	2	yes	—
492	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	4	no	—
496	C₈	C₂×Q₈×D₄₇	1	2	yes	—
497	C₈	C₂×Q₈×D₄₇	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	94	8	no	—
501	C₂²	—	376	8	no	—
502	C₂²	—	188	4	no	—
503	C₂²	—	188	4	no	—
504	C₂²	Q₈×D₁₈₈	1	2	yes	—
505	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	188	4	no	—
512	C₄	—	188	4	no	—
513	C₄	—	188	4	no	—
514	C₄	Q₈×D₁₈₈	1	2	yes	—
515	C₄	#15689928	1	2	yes	—
516	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
517	C₄	C₂×#13094071	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	188	8	no	—
520	C₂	C₂×Q₈×D₁₈₈	1	1	yes	characteristic
521	C₂	C₂×#15689928	1	1	yes	characteristic
522	C₂	#20258162	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2960	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂²×D₃₇₆	C₂²
hypercenter	#2960	D₄₇
hypocenter	C₄₇	#61370
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #20257189	C₂	semidirect
2. #20256348	C₂	semidirect
3. #20256289	C₂	semidirect
4. #20256256	C₂	semidirect
5. #20256256	C₂	semidirect
6. Q₈×D₃₇₆	C₂	semidirect
7. #20253927	C₂	semidirect
8. #20253902	C₂	semidirect
9. #20253220	C₂	semidirect
10. #20253187	C₂	semidirect
13. C₄₇×#2960	C₂	semidirect
16. #15689833	C₂²	semidirect
17. #15689833	C₂²	semidirect
19. Q₈×D₁₈₈	C₂²	semidirect
27. #15689532	C₂²	semidirect
28. #15689528	C₂²	semidirect
29. #15689528	C₂²	semidirect
30. #15689528	C₂²	semidirect
31. #15689525	C₂²	semidirect
32. #15689525	C₂²	semidirect
33. #15689525	C₂²	semidirect
34. #15689521	C₂²	semidirect
35. #15689424	C₂²	semidirect
36. #15689424	C₂²	semidirect
37. #15689424	C₂²	semidirect
38. #15689414	C₂²	semidirect
39. #15689414	C₂²	semidirect
40. #15689404	C₂²	semidirect
41. #15689404	C₂²	semidirect
56. C₄₇×#446	C₂²	semidirect
57. C₄₇×#446	C₂²	semidirect
58. C₈×Q₈×C₄₇	C₂²	semidirect
59. C₈×Q₈×C₄₇	C₂²	semidirect
67. C₂×D₃₇₆	Q₈	semidirect
149. C₂×D₁₈₈	C₂×Q₈	semidirect
161. C₂×C₈×C₄₇	C₂×Q₈	semidirect
196. D₃₇₆	C₂×Q₈	semidirect
197. D₃₇₆	C₂×Q₈	semidirect
267. #2960	D₄₇	semidirect
304. #446	C₂×D₄₇	semidirect
305. #446	C₂×D₄₇	semidirect
306. C₈×Q₈	C₂×D₄₇	semidirect
307. C₈×Q₈	C₂×D₄₇	semidirect
325. C₄₇	#61370	semidirect
425. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20257189	2
#20256348	2
#20256289	2
#20256256	2
Q₈×D₃₇₆	2
#20253927	2
#20253902	2
#20253220	2
#20253187	2
#20252241	2
C₂×C₄×D₃₇₆	2
C₄₇×#2960	2
#61370	47