Subgroups — #27097390

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	#20257240	C₂	1	2	yes	maximal, complemented
2	#20256474	C₂	1	4	yes	maximal, complemented
3	#20256406	C₂	1	4	yes	maximal, complemented
4	#20256400	C₂	1	4	yes	maximal, complemented
5	#20256374	C₂	1	2	yes	maximal, complemented
6	#20256362	C₂	1	2	yes	maximal, complemented
7	#20253869	C₂	1	2	yes	maximal, complemented
8	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252932	C₂	1	4	yes	maximal, complemented
10	#20252852	C₂	1	2	yes	maximal, complemented
11	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
12	#20252262	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13094050	C₂²	1	4	yes	—
15	C₂×#13094046	C₂²	1	2	yes	—
16	C₂×#13094046	C₂²	1	2	yes	—
17	#15689856	C₂²	1	8	yes	complemented
18	#15689843	C₂²	1	4	yes	complemented
19	#15689838	—	2	2	no	—
20	#15689823	—	2	4	no	—
21	#15689794	C₂²	1	4	yes	complemented
22	#15689778	—	2	2	no	—
23	#15689711	—	2	4	no	—
24	#15689690	C₂²	1	4	yes	—
25	#15689680	C₂²	1	1	yes	characteristic
26	#15689673	C₂²	1	2	yes	—
27	#15689634	—	2	4	no	—
28	#15689604	C₂²	1	4	yes	—
29	#15689511	C₂²	1	8	yes	—
30	#15689507	C₂²	1	2	yes	complemented
31	#15689507	C₂²	1	2	yes	complemented
32	#15689506	C₂²	1	4	yes	—
33	#15689503	C₂²	1	1	yes	characteristic, complemented
34	#15689500	C₂²	1	1	yes	characteristic, complemented
35	#15689498	C₂²	1	4	yes	—
36	#15689496	C₂²	1	2	yes	complemented
37	#15689344	C₂²	1	8	yes	complemented
38	#15689338	C₂²	1	8	yes	complemented
39	#15689337	C₂²	1	8	yes	complemented
40	#15689328	C₂²	1	4	yes	complemented
41	#15689322	C₂²	1	8	yes	complemented
42	#15689318	C₂²	1	4	yes	complemented
43	#15689317	C₂²	1	8	yes	complemented
44	#15689253	C₂²	1	2	yes	complemented
45	#15689253	C₂²	1	2	yes	complemented
46	C₈×Dic₉₄	C₂²	1	2	yes	complemented
47	C₈×Dic₉₄	C₂²	1	2	yes	complemented
48	#15689222	C₂²	1	8	yes	complemented
49	#15689217	C₂²	1	4	yes	complemented
50	#15689205	C₂²	1	4	yes	complemented
51	#15689149	C₂²	1	2	yes	—
52	#15689147	C₂²	1	1	yes	characteristic
53	#15689122	C₂²	1	4	yes	—
54	#15689078	C₂²	1	2	yes	—
55	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
57	C₄×D₈×C₄₇	C₂²	1	2	yes	—
58	C₄×D₈×C₄₇	C₂²	1	2	yes	—
59	C₄×D₈×C₄₇	C₂²	1	2	yes	—
60	C₄×D₈×C₄₇	C₂²	1	2	yes	—
61	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
62	C₂×#102×C₄₇	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×#10625350	—	2	4	no	—
65	C₂×#10625350	C₂³	1	4	yes	—
66	#13094050	—	4	8	no	—
67	#13094046	—	2	8	no	—
68	#13094046	—	4	4	no	—
69	C₂×Dic₁₈₈	C₂³	1	2	yes	—
70	C₂×Dic₁₈₈	C₂³	1	2	yes	—
71	C₂×#10625325	C₂³	1	4	yes	—
72	C₂×#10625325	C₂³	1	4	yes	—
73	C₂×#10625335	C₂³	1	8	yes	—
74	C₂×D₃₇₆	C₂³	1	2	yes	—
75	C₂×D₃₇₆	C₂³	1	2	yes	—
76	C₂×#10625334	C₂³	1	8	yes	—
77	C₂×#10625329	C₂³	1	2	yes	—
78	#13094024	D₄	1	1	yes	characteristic
79	#13094024	D₄	1	1	yes	characteristic
80	#13094024	C₂³	1	2	yes	—
81	#13094021	C₂³	1	2	yes	—
82	#13094020	C₂³	1	8	yes	—
83	#13094017	—	2	8	no	—
84	#13094016	D₄	1	2	yes	—
85	#13094012	C₂³	1	4	yes	—
86	#13094011	C₂³	1	8	yes	—
87	#13094010	—	2	8	no	—
88	#13094007	—	2	8	no	—
89	#13094006	—	2	8	no	—
90	#13094003	—	2	4	no	—
91	#13094003	D₄	1	2	yes	—
92	#13094003	D₄	1	2	yes	—
93	#13093998	—	2	2	no	—
94	#13093998	—	2	2	no	—
95	#13093998	—	2	4	no	—
96	#13093997	—	2	8	no	—
97	#13093995	—	2	4	no	—
98	#13093995	—	2	4	no	—
99	#13093993	—	2	8	no	—
100	C₄×Dic₉₄	C₂³	1	2	yes	—
101	C₄×Dic₉₄	C₂³	1	2	yes	—
102	#13093989	C₂³	1	8	yes	—
103	C₄×D₁₈₈	—	2	2	no	—
104	C₄×D₁₈₈	—	2	2	no	—
105	#13093986	C₂³	1	8	yes	—
106	C₄×C₂²⋊D₄₇	—	2	8	no	—
107	C₄×C₂²⋊D₄₇	—	2	8	no	—
108	#13093983	—	2	4	no	—
109	#13093983	C₂³	1	2	yes	—
110	#13093982	—	2	4	no	—
111	C₄⋊C₄×D₄₇	—	2	4	no	—
112	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
113	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
114	Dic₄₇⋊C₈	C₂³	1	4	yes	—
115	Dic₄₇⋊C₈	C₂³	1	4	yes	—
116	#13093947	C₂³	1	8	yes	—
117	#13093944	C₂³	1	8	yes	—
118	#13093934	C₂³	1	4	yes	—
119	C₈×Dic₄₇	C₂³	1	4	yes	—
120	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₄₇	—	2	2	no	—
122	C₂×D₈×C₄₇	—	2	4	no	—
123	C₂×D₈×C₄₇	C₂³	1	2	yes	—
124	C₂×D₈×C₄₇	C₂³	1	2	yes	—
125	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₄×D₄×C₄₇	—	2	2	no	—
128	C₄×D₄×C₄₇	—	2	2	no	—
129	C₄×D₄×C₄₇	C₂³	1	4	yes	—
130	C₄×D₄×C₄₇	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
133	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
134	#107×C₄₇	C₂³	1	2	yes	—
135	#107×C₄₇	C₂³	1	2	yes	—
136	#102×C₄₇	C₂³	1	4	yes	—
137	#102×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	C₂⁴×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	2	4	no	—
145	C₂×D₄×C₄₇	—	2	4	no	—
146	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	4	no	—
150	C₂²×C₄×C₄₇	—	8	4	no	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₂×C₂²⋊D₄₇	—	2	4	no	—
155	C₂×C₂²⋊D₄₇	—	2	8	no	—
156	C₂×C₂²⋊D₄₇	—	2	8	no	—
157	#10625350	—	2	8	no	—
158	#10625350	—	2	8	no	—
159	#10625350	—	8	8	no	—
160	C₂×D₁₈₈	—	2	2	no	—
161	C₂×D₁₈₈	—	2	2	no	—
162	C₂×D₁₈₈	C₂⁴	1	4	yes	—
163	C₂×C₄×D₄₇	—	2	4	no	—
164	C₂×C₄×D₄₇	—	2	8	no	—
165	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
166	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
167	C₂×Dic₉₄	C₂⁴	1	4	yes	—
168	D₈×C₄₇	—	2	4	no	—
169	D₈×C₄₇	—	2	4	no	—
170	C₂×C₈×C₄₇	—	2	2	no	—
171	C₂×C₈×C₄₇	#41	1	4	yes	complemented
172	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
178	C₂²⋊C₄×C₄₇	—	2	4	no	—
179	C₂²⋊C₄×C₄₇	—	2	4	no	—
180	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
183	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
184	C₂²⋊Dic₄₇	—	2	8	no	—
185	C₂²⋊Dic₄₇	—	2	8	no	—
186	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
187	#10625335	—	4	8	no	—
188	#10625334	—	4	8	no	—
189	(C₂×D₄₇)⋊C₄	—	2	4	no	—
190	(C₂×D₄₇)⋊C₄	—	2	4	no	—
191	(C₂×D₄₇)⋊C₄	—	2	8	no	—
192	C₄⋊Dic₄₇	—	2	2	no	—
193	C₄⋊Dic₄₇	—	2	2	no	—
194	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
195	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
196	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
197	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
198	Dic₄₇⋊C₄	—	2	8	no	—
199	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
200	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
201	C₄×Dic₄₇	—	2	8	no	—
202	C₄×Dic₄₇	C₂⁴	1	4	yes	—
203	#10625329	—	2	4	no	—
204	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
205	Dic₁₈₈	—	2	4	no	—
206	Dic₁₈₈	—	4	2	no	—
207	D₃₇₆	—	2	4	no	—
208	D₃₇₆	—	4	2	no	—
209	#10625325	—	2	8	no	—
210	#10625325	—	4	4	no	—
211	C₂³×C₄₇	—	2	4	no	—
212	C₂³×C₄₇	—	4	4	no	—
213	C₂³×C₄₇	—	8	2	no	—
214	C₂³×C₄₇	—	8	2	no	—
215	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₂²×D₄₇	—	2	4	no	—
217	D₄×C₄₇	—	2	4	no	—
218	D₄×C₄₇	—	2	4	no	—
219	D₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	8	no	—
224	C₂×C₄×C₄₇	—	8	4	no	—
225	C₂×C₄×C₄₇	—	8	2	no	—
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
232	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
233	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
234	C₂²⋊D₄₇	—	4	8	no	—
235	C₂²⋊D₄₇	—	8	8	no	—
236	C₂²⋊D₄₇	—	8	8	no	—
237	C₂×Dic₄₇	—	2	4	no	—
238	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
239	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
240	D₁₈₈	—	2	4	no	—
241	D₁₈₈	—	2	4	no	—
242	D₁₈₈	—	4	4	no	—
243	D₁₈₈	—	8	2	no	—
244	C₄×D₄₇	—	4	8	no	—
245	C₄×D₄₇	—	8	8	no	—
246	Dic₉₄	—	2	4	no	—
247	Dic₉₄	—	2	4	no	—
248	Dic₉₄	—	2	4	no	—
249	Dic₉₄	—	4	2	no	—
250	C₈×C₄₇	—	2	1	no	—
251	C₈×C₄₇	—	2	1	no	—
252	C₈×C₄₇	C₂×#41	1	2	yes	—
253	C₈×C₄₇	C₂×#41	1	2	yes	—
254	C₄₇⋊C₈	—	2	4	no	—
255	#61406	—	47	1	no	maximal, Sylow
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	4	4	no	—
259	C₂²×C₄₇	—	4	4	no	—
260	C₂²×C₄₇	—	4	4	no	—
261	C₂²×C₄₇	—	8	8	no	—
262	C₂²×C₄₇	#550	1	2	yes	—
263	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
264	C₂×D₄₇	—	4	4	no	—
265	C₂×D₄₇	—	4	4	no	—
266	C₂×D₄₇	—	4	4	no	—
267	C₄×C₄₇	—	2	1	no	—
268	C₄×C₄₇	—	2	1	no	—
269	C₄×C₄₇	—	2	1	no	—
270	C₄×C₄₇	—	4	4	no	—
271	C₄×C₄₇	#550	1	2	yes	—
272	C₄×C₄₇	#576	1	2	yes	—
273	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
274	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
275	Dic₄₇	—	2	4	no	—
276	Dic₄₇	—	2	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	—	47	1	no	—
289	#2951	—	47	2	no	—
290	C₂×C₄×D₈	D₄₇	1	1	yes	characteristic, complemented
291	C₂×C₄₇	—	2	2	no	—
292	C₂×C₄₇	—	8	4	no	—
293	C₂×C₄₇	C₂×#550	1	1	yes	characteristic
294	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
295	C₂×C₄₇	#3584	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
310	#532	—	47	2	no	—
311	#525	—	94	4	no	—
312	#520	—	47	4	no	—
313	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
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	—	47	2	no	—
330	#446	—	47	2	no	—
331	C₈×Q₈	—	47	2	no	—
332	C₈×Q₈	—	47	2	no	—
333	#440	—	47	8	no	—
334	C₄×Q₁₆	—	47	4	no	—
335	C₄×D₈	—	47	4	no	—
336	C₄×D₈	C₂×D₄₇	1	2	yes	—
337	C₄×D₈	C₂×D₄₇	1	2	yes	—
338	C₄×D₈	C₂×D₄₇	1	2	yes	—
339	C₄×D₈	C₂×D₄₇	1	2	yes	—
340	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
341	#424	—	47	2	no	—
342	#423	—	47	1	no	—
343	#417	—	47	4	no	—
344	C₂×#102	C₂×D₄₇	1	2	yes	—
345	#405	—	47	2	no	—
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	C₂²×D₄₇	1	2	yes	—
351	C₂³×C₄	—	2	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	8	no	—
358	C₂×SD₁₆	—	47	4	no	—
359	C₂×SD₁₆	—	47	4	no	—
360	C₂×D₈	—	2	4	no	—
361	C₂×D₈	—	47	8	no	—
362	C₂×D₈	—	47	2	no	—
363	C₂×D₈	—	47	2	no	—
364	C₂×D₈	C₂²×D₄₇	1	2	yes	—
365	C₂×D₈	C₂²×D₄₇	1	2	yes	—
366	C₂×M₁₆	—	47	2	no	—
367	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
368	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
369	C₄⋊Q₈	—	47	1	no	—
370	C₄⋊Q₈	—	47	1	no	—
371	C₄⋊Q₈	—	47	2	no	—
372	#127	—	47	8	no	—
373	#127	—	47	2	no	—
374	#126	—	94	8	no	—
375	#125	—	47	2	no	—
376	#124	—	47	8	no	—
377	#124	—	47	4	no	—
378	#124	—	94	8	no	—
379	#123	—	94	8	no	—
380	#123	—	94	8	no	—
381	C₂²⋊Q₈	—	47	2	no	—
382	C₂²⋊Q₈	—	47	2	no	—
383	C₂²⋊Q₈	—	94	4	no	—
384	#121	—	94	8	no	—
385	#121	—	94	4	no	—
386	#121	—	94	4	no	—
387	#121	—	94	4	no	—
388	#121	—	94	2	no	—
389	#121	—	94	2	no	—
390	#120	—	94	8	no	—
391	C₄×Q₈	—	47	2	no	—
392	C₄×Q₈	—	47	2	no	—
393	C₄×Q₈	—	47	8	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	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	C₂²×D₄₇	1	4	yes	—
402	C₄×D₄	C₂²×D₄₇	1	4	yes	—
403	#117	—	47	2	no	—
404	#117	—	94	4	no	—
405	#117	—	94	4	no	—
406	C₂×C₄⋊C₄	—	94	4	no	—
407	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
410	#107	C₂²×D₄₇	1	2	yes	—
411	#107	C₂²×D₄₇	1	2	yes	—
412	C₄⋊C₈	—	47	4	no	—
413	C₄⋊C₈	—	47	4	no	—
414	C₄⋊C₈	—	47	2	no	—
415	C₄⋊C₈	—	47	2	no	—
416	#103	—	47	8	no	—
417	#102	—	47	8	no	—
418	#102	C₂²×D₄₇	1	4	yes	—
419	#102	C₂²×D₄₇	1	4	yes	—
420	#97	—	47	4	no	—
421	C₄×C₈	—	47	4	no	—
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	1	yes	characteristic
426	C₂⁴	—	2	2	no	—
427	#41	—	94	8	no	—
428	#41	—	94	8	no	—
429	#41	—	376	8	no	—
430	C₂×Q₈	—	47	2	no	—
431	C₂×Q₈	—	47	2	no	—
432	C₂×Q₈	—	47	4	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	47	4	no	—
437	C₂×D₄	—	94	8	no	—
438	C₂×D₄	—	94	8	no	—
439	C₂×D₄	—	94	4	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	2	no	—
442	C₂×D₄	C₂³×D₄₇	1	4	yes	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	8	4	no	—
447	C₂²×C₄	—	94	8	no	—
448	C₂²×C₄	—	94	4	no	—
449	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
450	C₂²×C₄	D₄×D₄₇	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	—	2	4	no	—
458	D₈	—	2	4	no	—
459	D₈	—	94	4	no	—
460	D₈	—	188	2	no	—
461	D₈	—	188	8	no	—
462	M₁₆	—	94	4	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	47	4	no	—
465	C₂×C₈	#10625350	1	4	yes	complemented
466	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
467	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
468	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
469	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	47	4	no	—
472	C₄⋊C₄	—	47	4	no	—
473	C₄⋊C₄	—	47	2	no	—
474	C₄⋊C₄	—	47	2	no	—
475	C₄⋊C₄	—	47	2	no	—
476	C₄⋊C₄	—	47	2	no	—
477	C₄⋊C₄	—	94	8	no	—
478	C₄⋊C₄	—	94	2	no	—
479	C₄⋊C₄	—	94	2	no	—
480	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	47	4	no	—
484	C₂²⋊C₄	—	94	8	no	—
485	C₂²⋊C₄	—	94	8	no	—
486	C₂²⋊C₄	—	94	8	no	—
487	C₂²⋊C₄	—	94	4	no	—
488	C₂²⋊C₄	—	94	4	no	—
489	C₄²	—	47	4	no	—
490	C₄²	—	94	8	no	—
491	C₄²	D₄×D₄₇	1	1	yes	characteristic
492	C₄²	D₄×D₄₇	1	1	yes	characteristic
493	C₄²	C₂³×D₄₇	1	1	yes	characteristic
494	C₄²	C₂³×D₄₇	1	1	yes	characteristic
495	C₂³	—	2	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	8	2	no	—
498	C₂³	—	8	2	no	—
499	C₂³	—	94	4	no	—
500	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
501	Q₈	—	94	4	no	—
502	Q₈	—	94	4	no	—
503	Q₈	—	94	4	no	—
504	Q₈	—	188	2	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	4	4	no	—
508	D₄	—	94	4	no	—
509	D₄	—	94	4	no	—
510	D₄	—	376	2	no	—
511	D₄	—	376	8	no	—
512	D₄	—	376	8	no	—
513	D₄	—	188	8	no	—
514	D₄	—	188	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	47	4	no	—
522	C₂×C₄	—	47	4	no	—
523	C₂×C₄	—	94	4	no	—
524	C₂×C₄	—	376	8	no	—
525	C₂×C₄	—	188	8	no	—
526	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
527	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
528	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
530	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
531	C₂×C₄	C₂×#10625350	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	—	94	4	no	—
537	C₈	C₂×#10625350	1	2	yes	—
538	C₈	C₂×#10625350	1	2	yes	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	8	8	no	—
545	C₂²	—	188	4	no	—
546	C₂²	—	188	4	no	—
547	C₂²	—	188	4	no	—
548	C₂²	#15689794	1	2	yes	—
549	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	4	4	no	—
554	C₄	—	94	4	no	—
555	C₄	—	94	4	no	—
556	C₄	—	188	4	no	—
557	C₄	#15689794	1	2	yes	—
558	C₄	#15689924	1	2	yes	—
559	C₄	C₂²×#10625350	1	1	yes	characteristic
560	C₄	C₂×#13094070	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	8	4	no	—
563	C₂	—	376	4	no	—
564	C₂	C₂×#15689794	1	1	yes	characteristic
565	C₂	C₂×#15689924	1	1	yes	characteristic
566	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₂×C₄×D₈	D₄₇
hypocenter	C₄₇	#61406
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #20257240	C₂	semidirect
2. #20256474	C₂	semidirect
3. #20256406	C₂	semidirect
4. #20256400	C₂	semidirect
5. #20256374	C₂	semidirect
6. #20256362	C₂	semidirect
7. #20253869	C₂	semidirect
8. #20253816	C₂	semidirect
9. #20252932	C₂	semidirect
10. #20252852	C₂	semidirect
11. #20252322	C₂	semidirect
12. #20252262	C₂	semidirect
13. C₂×C₄×D₈×C₄₇	C₂	semidirect
17. #15689856	C₂²	semidirect
18. #15689843	C₂²	semidirect
21. #15689794	C₂²	semidirect
30. #15689507	C₂²	semidirect
31. #15689507	C₂²	semidirect
33. #15689503	C₂²	semidirect
34. #15689500	C₂²	semidirect
36. #15689496	C₂²	semidirect
37. #15689344	C₂²	semidirect
38. #15689338	C₂²	semidirect
39. #15689337	C₂²	semidirect
40. #15689328	C₂²	semidirect
41. #15689322	C₂²	semidirect
42. #15689318	C₂²	semidirect
43. #15689317	C₂²	semidirect
44. #15689253	C₂²	semidirect
45. #15689253	C₂²	semidirect
46. C₈×Dic₉₄	C₂²	semidirect
47. C₈×Dic₉₄	C₂²	semidirect
48. #15689222	C₂²	semidirect
49. #15689217	C₂²	semidirect
50. #15689205	C₂²	semidirect
171. C₂×C₈×C₄₇	#41	semidirect
290. C₂×C₄×D₈	D₄₇	semidirect
347. C₄₇	#61406	semidirect
465. C₂×C₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257240	2
#20256474	2
#20256406	2
#20256400	2
#20256374	2
#20256362	2
#20253869	2
#20253816	2
#20252932	2
#20252852	2
#20252322	2
#20252262	2
C₂×C₄×D₈×C₄₇	2
#61406	47