Subgroups — #27097394

Order 12032.

1986 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257242	C₂	1	2	yes	maximal, complemented
2	#20256478	C₂	1	4	yes	maximal, complemented
3	#20256410	C₂	1	4	yes	maximal, complemented
4	#20256401	C₂	1	4	yes	maximal, complemented
5	#20256377	C₂	1	2	yes	maximal, complemented
6	#20256363	C₂	1	2	yes	maximal, complemented
7	#20253874	C₂	1	2	yes	maximal, complemented
8	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252929	C₂	1	4	yes	maximal, complemented
10	#20252854	C₂	1	2	yes	maximal, complemented
11	#20252265	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13094052	C₂²	1	4	yes	—
15	C₂×#13094046	C₂²	1	2	yes	—
16	C₂×#13094046	C₂²	1	2	yes	—
17	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
18	#15689858	C₂²	1	8	yes	complemented
19	#15689846	C₂²	1	4	yes	complemented
20	#15689839	—	2	2	no	—
21	#15689826	—	2	4	no	—
22	#15689795	C₂²	1	4	yes	complemented
23	#15689776	—	2	2	no	—
24	#15689713	—	2	4	no	—
25	#15689692	C₂²	1	4	yes	—
26	#15689673	C₂²	1	2	yes	—
27	#15689636	—	2	4	no	—
28	#15689603	C₂²	1	4	yes	—
29	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
30	#15689512	C₂²	1	8	yes	—
31	#15689507	C₂²	1	4	yes	—
32	#15689507	C₂²	1	2	yes	complemented
33	#15689507	C₂²	1	2	yes	complemented
34	#15689503	C₂²	1	1	yes	characteristic, complemented
35	#15689500	C₂²	1	4	yes	—
36	#15689500	C₂²	1	1	yes	characteristic, complemented
37	#15689496	C₂²	1	2	yes	complemented
38	#15689346	C₂²	1	8	yes	complemented
39	#15689339	C₂²	1	8	yes	complemented
40	#15689339	C₂²	1	8	yes	complemented
41	#15689329	C₂²	1	4	yes	complemented
42	#15689324	C₂²	1	8	yes	complemented
43	#15689319	C₂²	1	8	yes	complemented
44	#15689319	C₂²	1	4	yes	complemented
45	#15689225	C₂²	1	8	yes	complemented
46	C₄×Dic₁₈₈	C₂²	1	4	yes	complemented
47	C₄×D₃₇₆	C₂²	1	2	yes	—
48	C₄×D₃₇₆	C₂²	1	2	yes	—
49	C₄×D₃₇₆	C₂²	1	2	yes	—
50	C₄×D₃₇₆	C₂²	1	2	yes	—
51	C₄×D₃₇₆	C₂²	1	4	yes	complemented
52	C₂×#13093958	C₂²	1	1	yes	characteristic
53	#15689125	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×#10625354	—	2	4	no	—
65	C₂×#10625350	C₂³	1	4	yes	—
66	C₂²×D₁₈₈	C₂³	1	2	yes	—
67	C₂²×C₄×D₄₇	—	2	2	no	—
68	#13094052	—	4	8	no	—
69	#13094046	—	2	8	no	—
70	#13094046	—	4	4	no	—
71	C₂×Dic₁₈₈	C₂³	1	2	yes	—
72	C₂×Dic₁₈₈	C₂³	1	2	yes	—
73	C₂×#10625325	C₂³	1	4	yes	—
74	C₂×#10625325	C₂³	1	4	yes	—
75	C₂×#10625325	C₂³	1	8	yes	—
76	C₂×D₃₇₆	—	2	4	no	—
77	C₂×D₃₇₆	C₂³	1	2	yes	—
78	C₂×D₃₇₆	C₂³	1	2	yes	—
79	C₂×D₃₇₆	C₂³	1	2	yes	—
80	C₂×D₃₇₆	C₂³	1	8	yes	—
81	C₂×D₃₇₆	C₂³	1	2	yes	—
82	#13094024	C₂³	1	2	yes	—
83	#13094021	C₂³	1	2	yes	—
84	#13094021	C₂³	1	8	yes	—
85	#13094019	—	2	8	no	—
86	#13094013	—	2	8	no	—
87	#13094012	C₂³	1	8	yes	—
88	#13094012	C₂³	1	4	yes	—
89	#13094009	—	2	8	no	—
90	#13094009	—	2	8	no	—
91	#13094000	—	2	4	no	—
92	#13093999	—	2	4	no	—
93	#13093999	—	2	8	no	—
94	#13093999	—	2	4	no	—
95	#13093999	—	2	4	no	—
96	#13093998	—	2	2	no	—
97	#13093998	—	2	2	no	—
98	#13093994	—	2	8	no	—
99	C₄×Dic₉₄	C₂³	1	8	yes	—
100	C₄×D₁₈₈	—	2	2	no	—
101	C₄×D₁₈₈	—	2	2	no	—
102	C₄×D₁₈₈	—	2	2	no	—
103	C₄×D₁₈₈	—	2	2	no	—
104	C₄×D₁₈₈	C₂³	1	8	yes	—
105	C₄×D₁₈₈	C₂³	1	4	yes	—
106	C₄×D₁₈₈	C₂³	1	4	yes	—
107	#13093986	—	2	8	no	—
108	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
109	#13093982	—	2	4	no	—
110	#13093982	—	2	4	no	—
111	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
112	C₄⋊C₄×D₄₇	—	2	4	no	—
113	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
114	#13093958	C₂³	1	2	yes	—
115	#13093958	C₂³	1	2	yes	—
116	#13093949	C₂³	1	8	yes	—
117	#13093946	C₂³	1	8	yes	—
118	#13093946	C₂³	1	4	yes	—
119	#13093946	C₂³	1	4	yes	—
120	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
125	#125×C₄₇	D₄	1	2	yes	—
126	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
127	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
128	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
129	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
130	#117×C₄₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
133	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
134	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
135	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
136	#97×C₄₇	C₂³	1	4	yes	—
137	C₄×C₈×C₄₇	C₂³	1	4	yes	—
138	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
142	C₂³×D₄₇	—	2	2	no	—
143	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂×C₂²⋊D₄₇	—	2	4	no	—
149	C₂²×Dic₄₇	—	2	2	no	—
150	#10625354	—	8	8	no	—
151	#10625350	—	2	8	no	—
152	#10625350	—	2	8	no	—
153	C₂×D₁₈₈	—	2	4	no	—
154	C₂×D₁₈₈	—	2	4	no	—
155	C₂×D₁₈₈	—	2	2	no	—
156	C₂×D₁₈₈	—	2	2	no	—
157	C₂×D₁₈₈	—	2	8	no	—
158	C₂×D₁₈₈	—	2	2	no	—
159	C₂×D₁₈₈	—	2	8	no	—
160	C₂×D₁₈₈	C₂⁴	1	4	yes	—
161	C₂×D₁₈₈	C₂⁴	1	4	yes	—
162	C₂×C₄×D₄₇	—	2	4	no	—
163	C₂×C₄×D₄₇	—	2	4	no	—
164	C₂×C₄×D₄₇	—	2	8	no	—
165	C₂×C₄×D₄₇	—	2	4	no	—
166	C₂×C₄×D₄₇	—	8	4	no	—
167	C₂×Dic₉₄	C₂⁴	1	4	yes	—
168	M₁₆×C₄₇	—	2	4	no	—
169	C₂×C₈×C₄₇	—	2	2	no	—
170	C₂×C₈×C₄₇	#41	1	4	yes	complemented
171	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
174	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
178	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
179	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
180	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
183	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
187	C₄²×C₄₇	C₂⁴	1	4	yes	—
188	(C₂×D₄₇)⋊C₄	—	2	4	no	—
189	(C₂×D₄₇)⋊C₄	—	2	4	no	—
190	(C₂×D₄₇)⋊C₄	—	2	8	no	—
191	(C₂×D₄₇)⋊C₄	—	2	8	no	—
192	(C₂×D₄₇)⋊C₄	—	2	4	no	—
193	(C₂×D₄₇)⋊C₄	—	2	8	no	—
194	(C₂×D₄₇)⋊C₄	—	2	4	no	—
195	C₄⋊Dic₄₇	—	2	2	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	C₄⋊Dic₄₇	—	2	2	no	—
198	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
199	Dic₄₇⋊C₄	—	2	8	no	—
200	C₄×Dic₄₇	—	2	8	no	—
201	Dic₁₈₈	—	2	4	no	—
202	Dic₁₈₈	—	4	2	no	—
203	D₃₇₆	—	2	4	no	—
204	D₃₇₆	—	2	4	no	—
205	D₃₇₆	—	2	4	no	—
206	D₃₇₆	—	4	2	no	—
207	D₃₇₆	—	4	8	no	—
208	#10625325	—	2	8	no	—
209	#10625325	—	4	4	no	—
210	#10625325	—	4	8	no	—
211	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂²×D₄₇	—	2	4	no	—
213	C₂²×D₄₇	—	2	4	no	—
214	C₂²×D₄₇	—	4	4	no	—
215	C₂²×D₄₇	—	8	2	no	—
216	C₂²×D₄₇	—	8	2	no	—
217	Q₈×C₄₇	—	2	4	no	—
218	Q₈×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	4	1	no	—
221	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
229	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
230	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
231	C₂²⋊D₄₇	—	4	8	no	—
232	C₂×Dic₄₇	—	2	4	no	—
233	C₂×Dic₄₇	—	2	4	no	—
234	C₂×Dic₄₇	—	8	2	no	—
235	D₁₈₈	—	2	4	no	—
236	D₁₈₈	—	2	4	no	—
237	D₁₈₈	—	2	4	no	—
238	D₁₈₈	—	2	4	no	—
239	D₁₈₈	—	4	4	no	—
240	D₁₈₈	—	4	4	no	—
241	D₁₈₈	—	8	2	no	—
242	D₁₈₈	—	8	8	no	—
243	D₁₈₈	—	8	8	no	—
244	C₄×D₄₇	—	4	8	no	—
245	C₄×D₄₇	—	4	8	no	—
246	C₄×D₄₇	—	8	4	no	—
247	C₄×D₄₇	—	8	8	no	—
248	Dic₉₄	—	2	4	no	—
249	Dic₉₄	—	2	4	no	—
250	C₈×C₄₇	—	2	1	no	—
251	C₈×C₄₇	—	2	4	no	—
252	C₈×C₄₇	—	2	1	no	—
253	C₈×C₄₇	C₂×#41	1	2	yes	—
254	C₈×C₄₇	C₂×#41	1	2	yes	—
255	#61406	—	47	1	no	maximal, Sylow
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	#550	1	2	yes	—
259	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
260	C₂×D₄₇	—	4	4	no	—
261	C₂×D₄₇	—	4	4	no	—
262	C₂×D₄₇	—	4	4	no	—
263	C₂×D₄₇	—	4	4	no	—
264	C₂×D₄₇	—	4	4	no	—
265	C₂×D₄₇	—	4	4	no	—
266	C₂×D₄₇	—	8	8	no	—
267	C₄×C₄₇	—	2	1	no	—
268	C₄×C₄₇	—	2	4	no	—
269	C₄×C₄₇	—	2	1	no	—
270	C₄×C₄₇	—	2	1	no	—
271	C₄×C₄₇	—	2	4	no	—
272	C₄×C₄₇	#550	1	2	yes	—
273	C₄×C₄₇	#576	1	2	yes	—
274	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
275	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
276	Dic₄₇	—	4	4	no	—
277	Dic₄₇	—	4	4	no	—
278	#3506	—	47	2	no	—
279	#3403	—	47	4	no	—
280	#3397	—	47	4	no	—
281	#3396	—	47	4	no	—
282	#3393	—	47	2	no	—
283	#3391	—	47	2	no	—
284	#3155	—	47	2	no	—
285	#3147	—	47	1	no	—
286	#3045	—	47	4	no	—
287	#3036	—	47	2	no	—
288	#2960	D₄₇	1	1	yes	characteristic, complemented
289	#2951	—	47	2	no	—
290	C₂×C₄×D₈	—	47	1	no	—
291	C₂×C₄₇	—	2	2	no	—
292	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
293	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
294	C₂×C₄₇	#3584	1	1	yes	characteristic
295	D₄₇	—	8	4	no	—
296	D₄₇	—	8	4	no	—
297	C₂×AGL(1,ℤ/8)	—	47	4	no	—
298	C₂×#135	—	47	2	no	—
299	C₂×#135	—	47	2	no	—
300	C₂²×D₈	—	47	1	no	—
301	#559	—	47	8	no	—
302	#556	—	47	4	no	—
303	#555	—	94	2	no	—
304	#553	—	94	4	no	—
305	#550	—	47	4	no	—
306	#547	—	94	2	no	—
307	#538	—	94	4	no	—
308	#535	—	47	4	no	—
309	#533	C₂×D₄₇	1	1	yes	characteristic
310	#532	—	47	2	no	—
311	#525	—	94	4	no	—
312	#520	—	47	4	no	—
313	C₂×C₄×D₄	—	47	2	no	—
314	#496	—	47	8	no	—
315	#495	—	47	4	no	—
316	#495	—	47	2	no	—
317	#495	—	47	2	no	—
318	#494	—	47	1	no	—
319	#493	—	47	4	no	—
320	#493	—	47	1	no	—
321	#492	—	47	2	no	—
322	#464	—	47	8	no	—
323	#463	—	47	8	no	—
324	#463	—	47	8	no	—
325	#461	—	47	4	no	—
326	#460	—	47	8	no	—
327	#459	—	47	4	no	—
328	#459	—	47	8	no	—
329	#446	C₂×D₄₇	1	2	yes	complemented
330	#446	C₂×D₄₇	1	2	yes	complemented
331	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
332	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
333	#440	—	47	8	no	—
334	C₄×Q₁₆	—	47	4	no	—
335	C₄×D₈	—	47	2	no	—
336	C₄×D₈	—	47	4	no	—
337	C₄×D₈	—	47	2	no	—
338	C₄×D₈	—	47	2	no	—
339	C₄×D₈	—	47	2	no	—
340	C₂×#107	—	47	1	no	—
341	#424	C₂×D₄₇	1	2	yes	—
342	#423	C₂×D₄₇	1	1	yes	characteristic
343	#417	—	47	4	no	—
344	C₂×#102	—	47	2	no	—
345	#405	C₂×D₄₇	1	2	yes	—
346	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
347	C₄₇	#61406	1	1	yes	characteristic, complemented, Sylow
348	C₂×#41	—	47	4	no	—
349	C₂×#41	—	94	4	no	—
350	C₂²×D₄	—	47	2	no	—
351	C₂³×C₄	—	94	2	no	—
352	AGL(1,ℤ/8)	—	188	8	no	—
353	#135	—	94	8	no	—
354	#135	—	188	4	no	—
355	C₂×Q₁₆	—	47	2	no	—
356	C₂×Q₁₆	—	47	2	no	—
357	C₂×SD₁₆	—	47	4	no	—
358	C₂×SD₁₆	—	47	4	no	—
359	C₂×SD₁₆	—	47	8	no	—
360	C₂×D₈	—	47	2	no	—
361	C₂×D₈	—	47	2	no	—
362	C₂×D₈	—	47	2	no	—
363	C₂×D₈	—	47	2	no	—
364	C₂×D₈	—	47	8	no	—
365	C₂×D₈	—	94	4	no	—
366	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
367	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
368	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
369	C₄⋊Q₈	—	47	2	no	—
370	C₄⋊Q₈	D₁₈₈	1	1	yes	characteristic
371	C₄⋊Q₈	D₁₈₈	1	1	yes	characteristic
372	#127	—	47	2	no	—
373	#127	—	47	8	no	—
374	#126	—	94	8	no	—
375	#125	D₁₈₈	1	2	yes	—
376	#124	—	47	4	no	—
377	#124	—	47	8	no	—
378	#124	—	94	8	no	—
379	#123	—	94	8	no	—
380	#123	—	94	8	no	—
381	C₂²⋊Q₈	—	94	4	no	—
382	C₂²⋊Q₈	D₁₈₈	1	2	yes	—
383	C₂²⋊Q₈	D₁₈₈	1	2	yes	—
384	#121	—	94	2	no	—
385	#121	—	94	2	no	—
386	#121	—	94	4	no	—
387	#121	—	94	4	no	—
388	#121	—	94	4	no	—
389	#121	—	94	8	no	—
390	#120	—	94	8	no	—
391	C₄×Q₈	—	47	8	no	—
392	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
393	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
394	C₄×D₄	—	47	4	no	—
395	C₄×D₄	—	47	4	no	—
396	C₄×D₄	—	47	8	no	—
397	C₄×D₄	—	94	8	no	—
398	C₄×D₄	—	94	8	no	—
399	C₄×D₄	—	94	2	no	—
400	C₄×D₄	—	94	2	no	—
401	C₄×D₄	—	94	2	no	—
402	C₄×D₄	—	94	2	no	—
403	#117	—	94	4	no	—
404	#117	—	94	4	no	—
405	#117	C₂²×D₄₇	1	2	yes	—
406	C₂×C₄⋊C₄	—	47	2	no	—
407	C₂×C₄⋊C₄	—	94	4	no	—
408	C₂×C₂²⋊C₄	—	94	2	no	—
409	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
410	#107	—	47	2	no	—
411	#107	—	47	2	no	—
412	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
413	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
414	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
415	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
416	#103	—	47	8	no	—
417	#102	—	47	4	no	—
418	#102	—	47	4	no	—
419	#102	—	47	8	no	—
420	#97	C₂²×D₄₇	1	4	yes	—
421	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₄₇	1	4	yes	—
426	C₂⁴	—	94	2	no	—
427	#41	—	94	8	no	—
428	#41	—	94	8	no	—
429	#41	—	376	8	no	—
430	C₂×Q₈	—	47	4	no	—
431	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
432	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
433	C₂×D₄	—	47	4	no	—
434	C₂×D₄	—	47	4	no	—
435	C₂×D₄	—	94	4	no	—
436	C₂×D₄	—	94	8	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	8	no	—
439	C₂×D₄	—	94	2	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	4	no	—
442	C₂×D₄	—	94	4	no	—
443	C₂²×C₄	—	94	2	no	—
444	C₂²×C₄	—	94	8	no	—
445	C₂²×C₄	—	94	4	no	—
446	C₂²×C₄	—	94	4	no	—
447	C₂²×C₄	—	94	4	no	—
448	C₂²×C₄	—	376	4	no	—
449	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
451	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
452	Q₁₆	—	94	4	no	—
453	Q₁₆	—	188	2	no	—
454	SD₁₆	—	94	8	no	—
455	SD₁₆	—	188	4	no	—
456	SD₁₆	—	188	8	no	—
457	D₈	—	94	4	no	—
458	D₈	—	94	4	no	—
459	D₈	—	94	4	no	—
460	D₈	—	188	2	no	—
461	D₈	—	188	8	no	—
462	M₁₆	—	2	4	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	#10625354	1	4	yes	complemented
465	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
466	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
467	C₂×C₈	C₂³×D₄₇	1	4	yes	—
468	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
469	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
470	C₄⋊C₄	—	47	4	no	—
471	C₄⋊C₄	—	94	8	no	—
472	C₄⋊C₄	—	94	2	no	—
473	C₄⋊C₄	—	94	2	no	—
474	C₄⋊C₄	—	94	2	no	—
475	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
476	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
477	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
478	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
479	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
480	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
481	C₂²⋊C₄	—	94	4	no	—
482	C₂²⋊C₄	—	94	4	no	—
483	C₂²⋊C₄	—	94	8	no	—
484	C₂²⋊C₄	—	94	8	no	—
485	C₂²⋊C₄	—	94	4	no	—
486	C₂²⋊C₄	—	94	8	no	—
487	C₂²⋊C₄	—	94	4	no	—
488	C₂²⋊C₄	C₂×D₁₈₈	1	4	yes	—
489	C₄²	—	94	8	no	—
490	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
491	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
492	C₄²	C₂³×D₄₇	1	1	yes	characteristic
493	C₄²	C₂³×D₄₇	1	1	yes	characteristic
494	C₄²	C₂³×D₄₇	1	4	yes	—
495	C₂³	—	94	4	no	—
496	C₂³	—	94	4	no	—
497	C₂³	—	376	2	no	—
498	C₂³	—	376	2	no	—
499	C₂³	—	188	4	no	—
500	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
501	Q₈	—	2	4	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	94	4	no	—
504	Q₈	—	94	4	no	—
505	D₄	—	94	4	no	—
506	D₄	—	94	4	no	—
507	D₄	—	94	4	no	—
508	D₄	—	94	4	no	—
509	D₄	—	376	2	no	—
510	D₄	—	376	8	no	—
511	D₄	—	376	8	no	—
512	D₄	—	188	8	no	—
513	D₄	—	188	4	no	—
514	D₄	—	188	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	94	4	no	—
518	C₂×C₄	—	94	4	no	—
519	C₂×C₄	—	376	4	no	—
520	C₂×C₄	—	376	8	no	—
521	C₂×C₄	—	376	2	no	—
522	C₂×C₄	—	188	8	no	—
523	C₂×C₄	—	188	8	no	—
524	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
525	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
529	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
531	C₂×C₄	C₂×#10625354	1	2	yes	—
532	C₂×C₄	#13094070	1	2	yes	—
533	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	4	no	—
537	C₈	C₂×#10625354	1	2	yes	—
538	C₈	C₂×#10625354	1	2	yes	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	376	8	no	—
542	C₂²	—	188	4	no	—
543	C₂²	—	188	4	no	—
544	C₂²	—	188	4	no	—
545	C₂²	—	188	4	no	—
546	C₂²	—	188	4	no	—
547	C₂²	—	188	4	no	—
548	C₂²	#15689795	1	2	yes	—
549	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	4	no	—
555	C₄	—	188	4	no	—
556	C₄	—	188	4	no	—
557	C₄	#15689795	1	2	yes	—
558	C₄	#15689928	1	2	yes	—
559	C₄	C₂²×#10625354	1	1	yes	characteristic
560	C₄	C₂×#13094070	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	376	4	no	—
563	C₂	—	376	4	no	—
564	C₂	C₂×#15689795	1	1	yes	characteristic
565	C₂	C₂×#15689928	1	1	yes	characteristic
566	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
hypercenter	#2960	D₄₇
hypocenter	C₄₇	#61406
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. #20257242	C₂	semidirect
2. #20256478	C₂	semidirect
3. #20256410	C₂	semidirect
4. #20256401	C₂	semidirect
5. #20256377	C₂	semidirect
6. #20256363	C₂	semidirect
7. #20253874	C₂	semidirect
8. #20253816	C₂	semidirect
9. #20252929	C₂	semidirect
10. #20252854	C₂	semidirect
11. #20252265	C₂	semidirect
12. C₂×C₄×D₃₇₆	C₂	semidirect
13. C₄₇×#2960	C₂	semidirect
18. #15689858	C₂²	semidirect
19. #15689846	C₂²	semidirect
22. #15689795	C₂²	semidirect
32. #15689507	C₂²	semidirect
33. #15689507	C₂²	semidirect
34. #15689503	C₂²	semidirect
36. #15689500	C₂²	semidirect
37. #15689496	C₂²	semidirect
38. #15689346	C₂²	semidirect
39. #15689339	C₂²	semidirect
40. #15689339	C₂²	semidirect
41. #15689329	C₂²	semidirect
42. #15689324	C₂²	semidirect
43. #15689319	C₂²	semidirect
44. #15689319	C₂²	semidirect
45. #15689225	C₂²	semidirect
46. C₄×Dic₁₈₈	C₂²	semidirect
51. C₄×D₃₇₆	C₂²	semidirect
56. C₄₇×#446	C₂²	semidirect
57. C₄₇×#446	C₂²	semidirect
58. C₈×Q₈×C₄₇	C₂²	semidirect
59. C₈×Q₈×C₄₇	C₂²	semidirect
170. C₂×C₈×C₄₇	#41	semidirect
288. #2960	D₄₇	semidirect
329. #446	C₂×D₄₇	semidirect
330. #446	C₂×D₄₇	semidirect
331. C₈×Q₈	C₂×D₄₇	semidirect
332. C₈×Q₈	C₂×D₄₇	semidirect
347. C₄₇	#61406	semidirect
464. C₂×C₈	#10625354	semidirect

Maximal subgroups

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

subgroup	index
#20257242	2
#20256478	2
#20256410	2
#20256401	2
#20256377	2
#20256363	2
#20253874	2
#20253816	2
#20252929	2
#20252854	2
#20252265	2
C₂×C₄×D₃₇₆	2
C₄₇×#2960	2
#61406	47