Subgroups — #27087507

Order 12032.

2208 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689673	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254360	C₂	1	4	yes	maximal, complemented
3	#20254349	C₂	1	4	yes	maximal, complemented
4	#20254340	C₂	1	2	yes	maximal, complemented
5	#20254333	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254326	C₂	1	1	yes	maximal, characteristic, complemented
7	#20254317	C₂	1	2	yes	maximal, complemented
8	#20254310	C₂	1	1	yes	maximal, characteristic, complemented
9	#20254303	C₂	1	1	yes	maximal, characteristic, complemented
10	#20253814	C₂	1	2	yes	maximal, complemented
11	#20253713	C₂	1	2	yes	maximal, complemented
12	#20252843	C₂	1	4	yes	maximal, complemented
13	#20252604	C₂	1	4	yes	maximal, complemented
14	C₂×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625350	C₂²	1	2	yes	—
17	C₂×#13094044	C₂²	1	8	yes	complemented
18	#15689673	—	2	1	no	—
19	#15689673	—	2	1	no	—
20	#15689673	—	2	1	no	—
21	#15689673	—	2	1	no	—
22	#15689673	C₂²	1	2	yes	—
23	#15689673	C₂²	1	2	yes	—
24	#15689673	C₂²	1	2	yes	—
25	#15689673	C₂²	1	2	yes	—
26	C₂×#13094024	C₂²	1	1	yes	characteristic
27	C₂×#13094021	C₂²	1	1	yes	characteristic
28	C₂×#13094012	C₂²	1	2	yes	—
29	C₂×#13093998	—	2	1	no	—
30	C₂×#13093998	—	2	1	no	—
31	C₂×C₄×D₁₈₈	—	2	1	no	—
32	C₂×C₄×D₁₈₈	—	2	1	no	—
33	#15689505	C₂²	1	8	yes	complemented
34	#15689502	C₂²	1	2	yes	complemented
35	#15689499	C₂²	1	2	yes	complemented
36	#15689497	C₂²	1	2	yes	complemented
37	#15689495	C₂²	1	2	yes	complemented
38	#15689480	C₂²	1	8	yes	complemented
39	#15689475	C₂²	1	2	yes	complemented
40	#15689475	C₂²	1	2	yes	complemented
41	#15689471	C₂²	1	2	yes	complemented
42	#15689471	C₂²	1	2	yes	complemented
43	#15689345	C₂²	1	8	yes	complemented
44	#15689338	C₂²	1	8	yes	complemented
45	#15689333	C₂²	1	4	yes	complemented
46	#15689328	C₂²	1	4	yes	complemented
47	#15689323	C₂²	1	4	yes	complemented
48	#15689318	C₂²	1	4	yes	complemented
49	#15689283	C₂²	1	8	yes	complemented
50	#15689278	C₂²	1	4	yes	—
51	#15689273	C₂²	1	4	yes	—
52	#15689266	C₂²	1	8	yes	complemented
53	#15689261	C₂²	1	4	yes	—
54	#15689256	C₂²	1	4	yes	—
55	#15689176	C₂²	1	1	yes	characteristic
56	#15689176	C₂²	1	1	yes	characteristic
57	#15689176	C₂²	1	2	yes	—
58	#15689176	C₂²	1	2	yes	complemented
59	#15689176	C₂²	1	2	yes	complemented
60	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
61	#15689117	C₂²	1	8	yes	complemented
62	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
63	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
64	C₄₇×#533	C₂²	1	1	yes	characteristic
65	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
66	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
67	C₄₇×#532	C₂²	1	1	yes	characteristic
68	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
69	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
70	C₄₇×#529	—	2	1	no	—
71	C₄₇×#529	—	2	1	no	—
72	C₄₇×#529	—	2	1	no	—
73	C₄₇×#529	—	2	1	no	—
74	C₄₇×#529	C₂²	1	2	yes	—
75	C₄₇×#529	C₂²	1	2	yes	complemented
76	C₄₇×#525	—	2	1	no	—
77	C₄₇×#525	—	2	1	no	—
78	C₄₇×#525	C₂²	1	2	yes	—
79	C₄×#41×C₄₇	—	2	1	no	—
80	C₄×#41×C₄₇	—	2	1	no	—
81	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
82	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	C₂×#10625350	—	2	2	no	—
84	C₂×#10625350	—	2	2	no	—
85	C₂×#10625350	—	4	8	no	—
86	C₂×#10625350	C₂³	1	4	yes	—
87	C₂×#10625350	C₂³	1	4	yes	—
88	C₂²×Dic₉₄	C₂³	1	2	yes	—
89	C₂²×D₁₈₈	—	2	1	no	—
90	C₂²×D₁₈₈	—	2	1	no	—
91	C₂²×D₁₈₈	C₂³	1	2	yes	—
92	C₂²×C₂²⋊D₄₇	—	2	2	no	—
93	C₂²×C₄×D₄₇	—	2	2	no	—
94	#13094044	—	4	16	no	—
95	C₂×#10625337	C₂³	1	8	yes	—
96	C₂×#10625335	C₂³	1	8	yes	—
97	C₂×#10625336	C₂³	1	8	yes	—
98	C₂×#10625334	C₂³	1	8	yes	—
99	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
100	#13094024	—	2	1	no	—
101	#13094024	—	2	1	no	—
102	#13094024	C₂³	1	2	yes	—
103	#13094024	C₂³	1	2	yes	—
104	#13094021	—	2	1	no	—
105	#13094021	—	2	1	no	—
106	#13094021	C₂³	1	2	yes	—
107	#13094021	C₂³	1	2	yes	—
108	#13094012	—	2	2	no	—
109	#13094012	—	2	2	no	—
110	#13094012	C₂³	1	4	yes	—
111	#13094012	C₂³	1	4	yes	—
112	#13093998	—	2	2	no	—
113	#13093998	—	2	2	no	—
114	#13093998	—	2	2	no	—
115	#13093998	—	2	2	no	—
116	#13093998	—	2	2	no	—
117	#13093998	—	2	2	no	—
118	#13093998	—	2	2	no	—
119	#13093998	—	2	2	no	—
120	C₄×D₁₈₈	—	2	2	no	—
121	C₄×D₁₈₈	—	2	2	no	—
122	C₄×D₁₈₈	—	2	2	no	—
123	C₄×D₁₈₈	—	2	2	no	—
124	C₄×D₁₈₈	—	2	2	no	—
125	C₄×D₁₈₈	—	2	2	no	—
126	C₄×D₁₈₈	—	2	2	no	—
127	C₄×D₁₈₈	—	2	2	no	—
128	C₂×C₄⋊Dic₄₇	—	2	1	no	—
129	C₂×C₄⋊Dic₄₇	—	2	1	no	—
130	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
131	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
133	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
134	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
135	#13093947	C₂³	1	8	yes	—
136	#13093947	C₂³	1	8	yes	—
137	#13093944	C₂³	1	8	yes	—
138	#13093944	C₂³	1	8	yes	—
139	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
140	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
141	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
142	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
143	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
144	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
145	C₂×#41×C₄₇	—	2	1	no	—
146	C₂×#41×C₄₇	—	2	1	no	—
147	C₂×#41×C₄₇	C₂³	1	2	yes	—
148	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
149	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
150	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
154	#127×C₄₇	C₂³	1	1	yes	characteristic
155	#126×C₄₇	—	2	2	no	—
156	#126×C₄₇	—	2	2	no	—
157	#125×C₄₇	—	2	1	no	—
158	#125×C₄₇	—	2	1	no	—
159	#125×C₄₇	C₂³	1	2	yes	—
160	#124×C₄₇	—	2	1	no	—
161	#124×C₄₇	—	2	1	no	—
162	#124×C₄₇	C₂³	1	2	yes	—
163	#123×C₄₇	—	2	2	no	—
164	#123×C₄₇	—	2	2	no	—
165	#123×C₄₇	—	2	2	no	—
166	C₂²⋊Q₈×C₄₇	—	2	1	no	—
167	C₂²⋊Q₈×C₄₇	—	2	1	no	—
168	C₂²⋊Q₈×C₄₇	—	2	1	no	—
169	C₂²⋊Q₈×C₄₇	—	2	1	no	—
170	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
171	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
172	#121×C₄₇	—	2	1	no	—
173	#121×C₄₇	—	2	1	no	—
174	#121×C₄₇	—	2	1	no	—
175	#121×C₄₇	—	2	1	no	—
176	#121×C₄₇	C₂³	1	2	yes	—
177	#121×C₄₇	C₂³	1	2	yes	—
178	#120×C₄₇	—	2	2	no	—
179	C₄×Q₈×C₄₇	—	2	1	no	—
180	C₄×Q₈×C₄₇	—	2	1	no	—
181	C₄×Q₈×C₄₇	—	2	1	no	—
182	C₄×Q₈×C₄₇	—	2	1	no	—
183	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
184	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
185	C₄×D₄×C₄₇	—	2	2	no	—
186	C₄×D₄×C₄₇	—	2	2	no	—
187	C₄×D₄×C₄₇	—	2	2	no	—
188	C₄×D₄×C₄₇	—	2	2	no	—
189	C₄×D₄×C₄₇	—	2	2	no	—
190	C₄×D₄×C₄₇	—	2	2	no	—
191	C₄×D₄×C₄₇	—	2	1	no	—
192	C₄×D₄×C₄₇	—	2	1	no	—
193	C₄×D₄×C₄₇	—	2	1	no	—
194	C₄×D₄×C₄₇	—	2	1	no	—
195	C₄×D₄×C₄₇	C₂³	1	2	yes	—
196	C₄×D₄×C₄₇	C₂³	1	2	yes	—
197	#117×C₄₇	—	2	1	no	—
198	#117×C₄₇	—	2	1	no	—
199	#117×C₄₇	—	2	2	no	—
200	#117×C₄₇	—	2	2	no	—
201	#117×C₄₇	—	2	2	no	—
202	#117×C₄₇	C₂³	1	2	yes	—
203	C₂×C₄²×C₄₇	—	2	2	no	—
204	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
205	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
206	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
207	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
208	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
209	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
210	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
216	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
217	C₂³×D₄₇	—	2	2	no	—
218	#41×C₄₇	—	2	8	no	—
219	#41×C₄₇	—	4	4	no	—
220	#41×C₄₇	—	4	4	no	—
221	C₂×Q₈×C₄₇	—	2	1	no	—
222	C₂×Q₈×C₄₇	—	2	1	no	—
223	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
224	C₂×D₄×C₄₇	—	2	2	no	—
225	C₂×D₄×C₄₇	—	2	2	no	—
226	C₂×D₄×C₄₇	—	2	2	no	—
227	C₂×D₄×C₄₇	—	2	1	no	—
228	C₂×D₄×C₄₇	—	2	1	no	—
229	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₄₇	—	2	4	no	—
231	C₂²×C₄×C₄₇	—	2	4	no	—
232	C₂²×C₄×C₄₇	—	2	2	no	—
233	C₂²×C₄×C₄₇	—	2	2	no	—
234	C₂²×C₄×C₄₇	—	2	2	no	—
235	C₂²×C₄×C₄₇	—	4	2	no	—
236	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₂²⋊D₄₇	—	2	4	no	—
255	C₂×C₂²⋊D₄₇	—	2	4	no	—
256	C₂×C₂²⋊D₄₇	—	4	8	no	—
257	C₂²×Dic₄₇	—	2	2	no	—
258	#10625350	—	2	16	no	—
259	#10625350	—	4	8	no	—
260	#10625350	—	4	8	no	—
261	#10625350	—	4	8	no	—
262	C₂×D₁₈₈	—	2	2	no	—
263	C₂×D₁₈₈	—	2	2	no	—
264	C₂×D₁₈₈	—	2	2	no	—
265	C₂×D₁₈₈	—	2	2	no	—
266	C₂×D₁₈₈	—	2	2	no	—
267	C₂×D₁₈₈	—	4	4	no	—
268	C₂×D₁₈₈	—	4	4	no	—
269	C₂×D₁₈₈	—	4	4	no	—
270	C₂×D₁₈₈	C₂⁴	1	4	yes	—
271	C₂×C₄×D₄₇	—	2	4	no	—
272	C₂×C₄×D₄₇	—	2	4	no	—
273	C₂×C₄×D₄₇	—	4	8	no	—
274	C₂×Dic₉₄	—	2	2	no	—
275	C₂×Dic₉₄	—	4	4	no	—
276	C₂×Dic₉₄	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₄₇	—	2	1	no	—
278	C₄⋊C₄×C₄₇	—	2	1	no	—
279	C₄⋊C₄×C₄₇	—	2	1	no	—
280	C₄⋊C₄×C₄₇	—	2	1	no	—
281	C₄⋊C₄×C₄₇	—	2	2	no	—
282	C₄⋊C₄×C₄₇	—	2	2	no	—
283	C₄⋊C₄×C₄₇	—	2	2	no	—
284	C₄⋊C₄×C₄₇	—	2	2	no	—
285	C₄⋊C₄×C₄₇	—	2	2	no	—
286	C₄⋊C₄×C₄₇	—	2	2	no	—
287	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
289	C₂²⋊C₄×C₄₇	—	2	2	no	—
290	C₂²⋊C₄×C₄₇	—	2	2	no	—
291	C₂²⋊C₄×C₄₇	—	2	2	no	—
292	C₂²⋊C₄×C₄₇	—	2	2	no	—
293	C₂²⋊C₄×C₄₇	—	2	2	no	—
294	C₂²⋊C₄×C₄₇	—	2	2	no	—
295	C₂²⋊C₄×C₄₇	—	2	2	no	—
296	C₂²⋊C₄×C₄₇	—	2	2	no	—
297	C₂²⋊C₄×C₄₇	—	2	2	no	—
298	C₄²×C₄₇	—	2	2	no	—
299	C₄²×C₄₇	—	2	2	no	—
300	C₄²×C₄₇	—	2	2	no	—
301	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
314	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
315	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
316	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
317	#10625337	—	4	8	no	—
318	#10625336	—	4	8	no	—
319	#10625335	—	4	8	no	—
320	#10625334	—	4	8	no	—
321	(C₂×D₄₇)⋊C₄	—	2	4	no	—
322	(C₂×D₄₇)⋊C₄	—	2	4	no	—
323	(C₂×D₄₇)⋊C₄	—	2	4	no	—
324	(C₂×D₄₇)⋊C₄	—	2	4	no	—
325	C₄⋊Dic₄₇	—	2	2	no	—
326	C₄⋊Dic₄₇	—	2	2	no	—
327	C₄⋊Dic₄₇	—	2	2	no	—
328	C₄⋊Dic₄₇	—	2	2	no	—
329	C₂×C₄₇⋊C₈	—	2	8	no	—
330	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
331	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
332	C₂³×C₄₇	—	2	2	no	—
333	C₂³×C₄₇	—	2	2	no	—
334	C₂³×C₄₇	—	2	2	no	—
335	C₂³×C₄₇	—	4	1	no	—
336	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
337	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
338	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
339	C₂²×D₄₇	—	2	4	no	—
340	C₂²×D₄₇	—	4	4	no	—
341	C₂²×D₄₇	—	4	4	no	—
342	C₂²×D₄₇	—	4	4	no	—
343	Q₈×C₄₇	—	2	4	no	—
344	Q₈×C₄₇	—	4	2	no	—
345	Q₈×C₄₇	—	4	2	no	—
346	D₄×C₄₇	—	2	4	no	—
347	D₄×C₄₇	—	4	4	no	—
348	D₄×C₄₇	—	4	4	no	—
349	D₄×C₄₇	—	4	4	no	—
350	D₄×C₄₇	—	4	2	no	—
351	D₄×C₄₇	—	4	2	no	—
352	C₂×C₄×C₄₇	—	2	2	no	—
353	C₂×C₄×C₄₇	—	2	2	no	—
354	C₂×C₄×C₄₇	—	2	2	no	—
355	C₂×C₄×C₄₇	—	2	2	no	—
356	C₂×C₄×C₄₇	—	2	2	no	—
357	C₂×C₄×C₄₇	—	2	2	no	—
358	C₂×C₄×C₄₇	—	2	2	no	—
359	C₂×C₄×C₄₇	—	2	2	no	—
360	C₂×C₄×C₄₇	—	2	2	no	—
361	C₂×C₄×C₄₇	—	2	2	no	—
362	C₂×C₄×C₄₇	—	2	2	no	—
363	C₂×C₄×C₄₇	—	2	2	no	—
364	C₂×C₄×C₄₇	—	2	2	no	—
365	C₂×C₄×C₄₇	—	2	2	no	—
366	C₂×C₄×C₄₇	—	2	2	no	—
367	C₂×C₄×C₄₇	—	2	2	no	—
368	C₂×C₄×C₄₇	—	4	1	no	—
369	C₂×C₄×C₄₇	—	4	1	no	—
370	C₂×C₄×C₄₇	—	4	1	no	—
371	C₂×C₄×C₄₇	—	4	4	no	—
372	C₂×C₄×C₄₇	—	4	4	no	—
373	C₂×C₄×C₄₇	—	4	4	no	—
374	C₂×C₄×C₄₇	#135	1	4	yes	complemented
375	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
387	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
388	C₂²⋊D₄₇	—	4	8	no	—
389	C₂²⋊D₄₇	—	4	8	no	—
390	C₂×Dic₄₇	—	2	4	no	—
391	C₂×Dic₄₇	—	4	4	no	—
392	D₁₈₈	—	2	8	no	—
393	D₁₈₈	—	4	4	no	—
394	D₁₈₈	—	4	4	no	—
395	D₁₈₈	—	4	4	no	—
396	D₁₈₈	—	4	4	no	—
397	D₁₈₈	—	4	4	no	—
398	C₄×D₄₇	—	4	8	no	—
399	C₄×D₄₇	—	4	8	no	—
400	Dic₉₄	—	2	8	no	—
401	Dic₉₄	—	4	4	no	—
402	C₄₇⋊C₈	—	2	4	no	—
403	C₄₇⋊C₈	—	2	4	no	—
404	#60782	—	47	1	no	maximal, Sylow
405	C₂²×C₄₇	—	2	1	no	—
406	C₂²×C₄₇	—	2	1	no	—
407	C₂²×C₄₇	—	2	1	no	—
408	C₂²×C₄₇	—	2	1	no	—
409	C₂²×C₄₇	—	2	1	no	—
410	C₂²×C₄₇	—	2	1	no	—
411	C₂²×C₄₇	—	2	1	no	—
412	C₂²×C₄₇	—	4	4	no	—
413	C₂²×C₄₇	—	4	2	no	—
414	C₂²×C₄₇	—	4	2	no	—
415	C₂²×C₄₇	—	4	2	no	—
416	C₂²×C₄₇	#535	1	2	yes	—
417	C₂²×C₄₇	C₂×#135	1	2	yes	—
418	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
419	C₂×D₄₇	—	4	4	no	—
420	C₂×D₄₇	—	4	4	no	—
421	C₂×D₄₇	—	4	4	no	—
422	C₂×D₄₇	—	8	8	no	—
423	C₄×C₄₇	—	2	1	no	—
424	C₄×C₄₇	—	2	1	no	—
425	C₄×C₄₇	—	2	1	no	—
426	C₄×C₄₇	—	2	1	no	—
427	C₄×C₄₇	—	2	1	no	—
428	C₄×C₄₇	—	2	1	no	—
429	C₄×C₄₇	—	2	1	no	—
430	C₄×C₄₇	—	4	2	no	—
431	C₄×C₄₇	—	4	2	no	—
432	C₄×C₄₇	—	4	2	no	—
433	C₄×C₄₇	#535	1	2	yes	—
434	C₄×C₄₇	C₂×#135	1	2	yes	—
435	C₄×C₄₇	C₂×#135	1	2	yes	—
436	C₄×C₄₇	#575	1	2	yes	—
437	C₄×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
438	Dic₄₇	—	4	4	no	—
439	#3444	D₄₇	1	1	yes	characteristic, complemented
440	C₂×#532	—	47	1	no	—
441	#3212	—	47	4	no	—
442	#3211	—	47	4	no	—
443	#3210	—	47	2	no	—
444	#3209	—	47	1	no	—
445	#3208	—	47	1	no	—
446	#3207	—	47	2	no	—
447	#3206	—	47	1	no	—
448	#3205	—	47	1	no	—
449	#3147	—	47	2	no	—
450	#3131	—	47	2	no	—
451	#3035	—	47	4	no	—
452	#3002	—	47	4	no	—
453	C₂×#431	—	47	1	no	—
454	C₂×C₄₇	—	2	2	no	—
455	C₂×C₄₇	—	2	2	no	—
456	C₂×C₄₇	—	4	1	no	—
457	C₂×C₄₇	—	8	2	no	—
458	C₂×C₄₇	C₂×#535	1	1	yes	characteristic
459	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
460	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
461	D₄₇	—	8	4	no	—
462	C₂²×#41	—	47	2	no	—
463	C₂×#135	—	47	8	no	—
464	#533	C₂×D₄₇	1	1	yes	characteristic
465	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
466	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
467	#532	—	47	2	no	—
468	#532	—	47	2	no	—
469	#532	—	47	2	no	—
470	#532	—	47	2	no	—
471	#532	—	94	1	no	—
472	#532	—	94	1	no	—
473	#532	—	94	1	no	—
474	#532	—	94	1	no	—
475	#532	C₂×D₄₇	1	1	yes	characteristic
476	#532	C₂×D₄₇	1	1	yes	characteristic, complemented
477	#532	C₂×D₄₇	1	1	yes	characteristic, complemented
478	C₂×C₄⋊Q₈	—	47	1	no	—
479	C₂×#127	—	47	1	no	—
480	#529	—	2	1	no	—
481	#529	—	2	1	no	—
482	#529	—	2	1	no	—
483	#529	—	2	1	no	—
484	#529	C₂×D₄₇	1	2	yes	—
485	#529	C₂×D₄₇	1	2	yes	complemented
486	C₂×#124	—	47	2	no	—
487	#525	—	2	1	no	—
488	#525	—	2	1	no	—
489	#525	C₂×D₄₇	1	2	yes	—
490	C₂×#121	—	94	1	no	—
491	C₂×#121	—	94	1	no	—
492	C₄×#41	—	2	1	no	—
493	C₄×#41	—	2	1	no	—
494	C₄×#41	C₂×D₄₇	1	2	yes	complemented
495	C₂×C₄×D₄	—	94	1	no	—
496	C₂×C₄×D₄	—	94	1	no	—
497	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
498	#495	—	47	8	no	—
499	#494	—	47	2	no	—
500	#493	—	47	2	no	—
501	#492	—	47	2	no	—
502	#492	—	47	2	no	—
503	#488	—	47	8	no	—
504	#487	—	47	2	no	—
505	#487	—	47	2	no	—
506	#486	—	47	2	no	—
507	#486	—	47	2	no	—
508	#464	—	47	8	no	—
509	#463	—	47	8	no	—
510	#462	—	47	4	no	—
511	#461	—	47	4	no	—
512	#460	—	47	4	no	—
513	#459	—	47	4	no	—
514	#452	—	47	8	no	—
515	#451	—	47	4	no	—
516	#450	—	47	4	no	—
517	#449	—	47	8	no	—
518	#448	—	47	4	no	—
519	#447	—	47	4	no	—
520	#431	—	47	1	no	—
521	#431	—	47	1	no	—
522	#431	—	47	2	no	—
523	#431	—	47	2	no	—
524	#431	—	47	2	no	—
525	C₂×C₄⋊C₈	—	47	2	no	—
526	#416	—	47	8	no	—
527	C₂×C₂²⋊C₈	—	47	2	no	—
528	C₂×C₄×C₈	—	47	2	no	—
529	C₄₇	#60782	1	1	yes	characteristic, complemented, Sylow
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	1	no	—
532	C₂×#41	—	47	4	no	—
533	C₂×#41	—	47	4	no	—
534	C₂×#41	—	94	2	no	—
535	C₂×#41	—	94	2	no	—
536	C₂×#41	—	188	8	no	—
537	C₂×#41	C₂²×D₄₇	1	2	yes	—
538	C₂²×Q₈	—	47	2	no	—
539	C₂²×D₄	—	47	2	no	—
540	C₂²×D₄	—	94	2	no	—
541	C₂²×D₄	—	94	1	no	—
542	C₂²×D₄	—	94	1	no	—
543	C₂³×C₄	—	94	2	no	—
544	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
545	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
546	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
547	#135	—	188	16	no	—
548	C₂×Q₁₆	—	47	8	no	—
549	C₂×SD₁₆	—	47	8	no	—
550	C₂×SD₁₆	—	47	8	no	—
551	C₂×D₈	—	47	8	no	—
552	C₂²×C₈	—	47	4	no	—
553	C₄⋊Q₈	—	47	2	no	—
554	C₄⋊Q₈	—	47	2	no	—
555	C₄⋊Q₈	—	94	1	no	—
556	C₄⋊Q₈	—	94	1	no	—
557	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
558	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
559	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
560	#127	—	47	2	no	—
561	#127	—	47	2	no	—
562	#127	—	94	1	no	—
563	#127	—	94	1	no	—
564	#127	C₂²×D₄₇	1	1	yes	characteristic
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#125	—	2	1	no	—
568	#125	—	2	1	no	—
569	#125	C₂²×D₄₇	1	2	yes	—
570	#124	—	2	1	no	—
571	#124	—	2	1	no	—
572	#124	—	47	4	no	—
573	#124	—	47	4	no	—
574	#124	—	94	2	no	—
575	#124	—	94	2	no	—
576	#124	C₂²×D₄₇	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
585	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
586	#121	—	2	1	no	—
587	#121	—	2	1	no	—
588	#121	—	2	1	no	—
589	#121	—	2	1	no	—
590	#121	—	94	2	no	—
591	#121	—	94	2	no	—
592	#121	—	94	2	no	—
593	#121	—	94	2	no	—
594	#121	—	94	2	no	—
595	#121	—	94	2	no	—
596	#121	—	94	2	no	—
597	#121	—	94	2	no	—
598	#121	C₂²×D₄₇	1	2	yes	—
599	#121	C₂²×D₄₇	1	2	yes	—
600	#120	—	2	2	no	—
601	C₄×Q₈	—	2	1	no	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	1	no	—
605	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
606	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	94	2	no	—
618	C₄×D₄	—	94	2	no	—
619	C₄×D₄	—	94	2	no	—
620	C₄×D₄	—	94	2	no	—
621	C₄×D₄	—	94	2	no	—
622	C₄×D₄	—	94	2	no	—
623	C₄×D₄	—	94	2	no	—
624	C₄×D₄	—	94	2	no	—
625	C₄×D₄	C₂²×D₄₇	1	2	yes	—
626	C₄×D₄	C₂²×D₄₇	1	2	yes	—
627	#117	—	2	1	no	—
628	#117	—	2	1	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	C₂²×D₄₇	1	2	yes	—
633	C₂×C₄⋊C₄	—	94	1	no	—
634	C₂×C₄⋊C₄	—	94	1	no	—
635	C₂×C₂²⋊C₄	—	94	2	no	—
636	C₂×C₂²⋊C₄	—	94	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
639	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
640	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
641	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
642	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
643	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
644	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
645	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
646	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
647	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
648	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
649	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
650	C₄⋊C₈	—	47	2	no	—
651	C₄⋊C₈	—	47	2	no	—
652	C₄⋊C₈	—	47	4	no	—
653	#103	—	47	8	no	—
654	#103	—	47	8	no	—
655	#102	—	47	8	no	—
656	#102	—	47	8	no	—
657	C₂²⋊C₈	—	47	2	no	—
658	C₂²⋊C₈	—	47	2	no	—
659	C₂²⋊C₈	—	47	4	no	—
660	C₄×C₈	—	47	2	no	—
661	C₄×C₈	—	47	2	no	—
662	C₄×C₈	—	47	4	no	—
663	C₂⁴	—	94	2	no	—
664	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
665	#41	—	2	8	no	—
666	#41	—	4	4	no	—
667	#41	—	4	4	no	—
668	#41	—	94	16	no	—
669	#41	—	188	8	no	—
670	#41	—	188	8	no	—
671	#41	—	188	8	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	47	4	no	—
675	C₂×Q₈	—	94	2	no	—
676	C₂×Q₈	—	188	4	no	—
677	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	47	4	no	—
684	C₂×D₄	—	94	4	no	—
685	C₂×D₄	—	94	4	no	—
686	C₂×D₄	—	94	2	no	—
687	C₂×D₄	—	94	2	no	—
688	C₂×D₄	—	94	2	no	—
689	C₂×D₄	—	94	2	no	—
690	C₂×D₄	—	94	2	no	—
691	C₂×D₄	—	188	4	no	—
692	C₂×D₄	—	188	4	no	—
693	C₂×D₄	—	188	8	no	—
694	C₂×D₄	—	188	4	no	—
695	C₂×D₄	C₂³×D₄₇	1	2	yes	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	94	2	no	—
703	C₂²×C₄	—	94	4	no	—
704	C₂²×C₄	—	94	4	no	—
705	C₂²×C₄	—	188	8	no	—
706	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
709	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
710	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
711	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
712	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
715	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
716	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
717	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
718	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
719	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
720	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
721	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
722	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
723	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
724	Q₁₆	—	188	8	no	—
725	SD₁₆	—	188	8	no	—
726	SD₁₆	—	188	8	no	—
727	D₈	—	188	8	no	—
728	C₂×C₈	—	47	4	no	—
729	C₂×C₈	—	47	4	no	—
730	C₂×C₈	—	94	8	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	94	2	no	—
742	C₄⋊C₄	—	94	2	no	—
743	C₄⋊C₄	—	94	2	no	—
744	C₄⋊C₄	—	94	2	no	—
745	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
746	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	94	4	no	—
757	C₂²⋊C₄	—	94	4	no	—
758	C₂²⋊C₄	—	94	4	no	—
759	C₂²⋊C₄	—	94	4	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
764	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
765	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
766	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
767	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
768	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
769	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
770	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
771	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
772	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
773	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
774	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
775	C₄²	C₂³×D₄₇	1	1	yes	characteristic
776	C₄²	C₂³×D₄₇	1	1	yes	characteristic
777	C₄²	C₂³×D₄₇	1	1	yes	characteristic
778	C₄²	C₂³×D₄₇	1	1	yes	characteristic
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	1	no	—
783	C₂³	—	94	4	no	—
784	C₂³	—	188	4	no	—
785	C₂³	—	188	4	no	—
786	C₂³	—	188	4	no	—
787	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
788	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
789	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
790	Q₈	—	2	4	no	—
791	Q₈	—	4	2	no	—
792	Q₈	—	4	2	no	—
793	Q₈	—	94	8	no	—
794	Q₈	—	188	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	94	8	no	—
802	D₄	—	188	4	no	—
803	D₄	—	188	4	no	—
804	D₄	—	188	8	no	—
805	D₄	—	188	8	no	—
806	D₄	—	188	4	no	—
807	D₄	—	188	4	no	—
808	D₄	—	188	4	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	94	4	no	—
832	C₂×C₄	—	188	8	no	—
833	C₂×C₄	—	188	4	no	—
834	C₂×C₄	—	188	8	no	—
835	C₂×C₄	#13094044	1	4	yes	complemented
836	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
838	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
839	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
842	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
843	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
844	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
847	C₂×C₄	#13094070	1	4	yes	—
848	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
849	C₈	—	94	4	no	—
850	C₈	—	94	4	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	4	4	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	376	8	no	—
863	C₂²	—	188	4	no	—
864	C₂²	—	188	4	no	—
865	C₂²	—	188	4	no	—
866	C₂²	#15689687	1	2	yes	—
867	C₂²	C₂×#13094044	1	2	yes	—
868	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	188	4	no	—
880	C₄	#15689687	1	2	yes	—
881	C₄	C₂×#13094044	1	2	yes	—
882	C₄	C₂×#13094044	1	2	yes	—
883	C₄	#15689921	1	2	yes	—
884	C₄	C₂×#13094070	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	2	no	—
889	C₂	—	376	4	no	—
890	C₂	C₂×#15689687	1	1	yes	characteristic
891	C₂	C₂²×#13094044	1	1	yes	characteristic
892	C₂	C₂×#15689921	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3444	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#60782
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂×#15689673	C₂	semidirect
2. #20254360	C₂	semidirect
3. #20254349	C₂	semidirect
4. #20254340	C₂	semidirect
5. #20254333	C₂	semidirect
6. #20254326	C₂	semidirect
7. #20254317	C₂	semidirect
8. #20254310	C₂	semidirect
9. #20254303	C₂	semidirect
10. #20253814	C₂	semidirect
11. #20253713	C₂	semidirect
12. #20252843	C₂	semidirect
13. #20252604	C₂	semidirect
14. C₂×#15689176	C₂	semidirect
15. C₄₇×#3444	C₂	semidirect
17. C₂×#13094044	C₂²	semidirect
33. #15689505	C₂²	semidirect
34. #15689502	C₂²	semidirect
35. #15689499	C₂²	semidirect
36. #15689497	C₂²	semidirect
37. #15689495	C₂²	semidirect
38. #15689480	C₂²	semidirect
39. #15689475	C₂²	semidirect
40. #15689475	C₂²	semidirect
41. #15689471	C₂²	semidirect
42. #15689471	C₂²	semidirect
43. #15689345	C₂²	semidirect
44. #15689338	C₂²	semidirect
45. #15689333	C₂²	semidirect
46. #15689328	C₂²	semidirect
47. #15689323	C₂²	semidirect
48. #15689318	C₂²	semidirect
49. #15689283	C₂²	semidirect
52. #15689266	C₂²	semidirect
58. #15689176	C₂²	semidirect
59. #15689176	C₂²	semidirect
60. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
61. #15689117	C₂²	semidirect
63. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
65. C₄₇×#533	C₂²	semidirect
66. C₄₇×#533	C₂²	semidirect
68. C₄₇×#532	C₂²	semidirect
69. C₄₇×#532	C₂²	semidirect
75. C₄₇×#529	C₂²	semidirect
81. C₄×#41×C₄₇	C₂²	semidirect
374. C₂×C₄×C₄₇	#135	semidirect
439. #3444	D₄₇	semidirect
465. #533	C₂×D₄₇	semidirect
466. #533	C₂×D₄₇	semidirect
476. #532	C₂×D₄₇	semidirect
477. #532	C₂×D₄₇	semidirect
485. #529	C₂×D₄₇	semidirect
494. C₄×#41	C₂×D₄₇	semidirect
529. C₄₇	#60782	semidirect
835. C₂×C₄	#13094044	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689673	2
#20254360	2
#20254349	2
#20254340	2
#20254333	2
#20254326	2
#20254317	2
#20254310	2
#20254303	2
#20253814	2
#20253713	2
#20252843	2
#20252604	2
C₂×#15689176	2
C₄₇×#3444	2
#60782	47