Subgroups — #27088365

Order 12032.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689680	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254563	C₂	1	4	yes	maximal, complemented
3	#20254552	C₂	1	4	yes	maximal, complemented
4	#20254543	C₂	1	2	yes	maximal, complemented
5	#20254536	C₂	1	1	yes	maximal, characteristic, complemented
6	#20254529	C₂	1	1	yes	maximal, characteristic, complemented
7	#20254520	C₂	1	2	yes	maximal, complemented
8	#20254513	C₂	1	1	yes	maximal, characteristic, complemented
9	#20254506	C₂	1	1	yes	maximal, characteristic, complemented
10	#20253898	C₂	1	2	yes	maximal, complemented
11	#20253710	C₂	1	2	yes	maximal, complemented
12	#20253297	C₂	1	4	yes	maximal, complemented
13	#20253176	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
16	#15689680	—	2	1	no	—
17	#15689680	—	2	1	no	—
18	#15689680	—	2	1	no	—
19	#15689680	—	2	1	no	—
20	#15689680	C₂²	1	2	yes	—
21	#15689680	C₂²	1	2	yes	—
22	#15689680	C₂²	1	2	yes	—
23	#15689680	C₂²	1	2	yes	—
24	C₂×#13094024	C₂²	1	1	yes	characteristic
25	C₂×#13094024	C₂²	1	1	yes	characteristic
26	C₂×#13094016	C₂²	1	2	yes	—
27	C₂×#13094003	—	2	1	no	—
28	C₂×#13094003	—	2	1	no	—
29	C₂×C₄×Dic₉₄	—	2	1	no	—
30	C₂×C₄×Dic₉₄	—	2	1	no	—
31	C₂×#13093983	C₂²	1	2	yes	—
32	#15689526	C₂²	1	2	yes	complemented
33	#15689526	C₂²	1	2	yes	complemented
34	#15689522	C₂²	1	8	yes	complemented
35	#15689519	C₂²	1	2	yes	complemented
36	#15689519	C₂²	1	2	yes	complemented
37	#15689477	C₂²	1	8	yes	complemented
38	#15689473	C₂²	1	2	yes	complemented
39	#15689473	C₂²	1	2	yes	complemented
40	#15689469	C₂²	1	2	yes	complemented
41	#15689469	C₂²	1	2	yes	complemented
42	#15689461	C₂²	1	8	yes	—
43	#15689456	C₂²	1	4	yes	—
44	#15689451	C₂²	1	4	yes	—
45	#15689444	C₂²	1	8	yes	—
46	#15689439	C₂²	1	4	yes	—
47	#15689434	C₂²	1	4	yes	—
48	#15689430	C₂²	1	8	yes	complemented
49	#15689423	C₂²	1	8	yes	complemented
50	#15689418	C₂²	1	4	yes	complemented
51	#15689413	C₂²	1	4	yes	complemented
52	#15689408	C₂²	1	4	yes	complemented
53	#15689403	C₂²	1	4	yes	complemented
54	#15689176	C₂²	1	1	yes	characteristic
55	#15689176	C₂²	1	1	yes	characteristic
56	#15689176	C₂²	1	2	yes	—
57	#15689176	C₂²	1	2	yes	—
58	#15689176	C₂²	1	2	yes	—
59	#15689159	C₂²	1	8	yes	—
60	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
61	#15689119	C₂²	1	8	yes	—
62	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
63	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
64	C₄₇×#533	C₂²	1	1	yes	characteristic
65	C₄₇×#533	C₂²	1	1	yes	characteristic
66	C₄₇×#533	C₂²	1	1	yes	characteristic
67	C₄₇×#532	C₂²	1	1	yes	characteristic
68	C₄₇×#532	C₂²	1	1	yes	characteristic
69	C₄₇×#532	C₂²	1	1	yes	characteristic
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	—
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	—
82	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
83	C₂²×Dic₉₄	—	2	1	no	—
84	C₂²×Dic₉₄	—	2	1	no	—
85	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
86	#13094024	—	2	1	no	—
87	#13094024	—	2	1	no	—
88	#13094024	—	2	1	no	—
89	#13094024	—	2	1	no	—
90	#13094024	C₂³	1	2	yes	—
91	#13094024	C₂³	1	2	yes	—
92	#13094024	C₂³	1	2	yes	—
93	#13094024	C₂³	1	2	yes	—
94	#13094016	—	2	2	no	—
95	#13094016	—	2	2	no	—
96	#13094016	C₂³	1	4	yes	—
97	#13094016	C₂³	1	4	yes	—
98	#13094003	—	2	2	no	—
99	#13094003	—	2	2	no	—
100	#13094003	—	2	2	no	—
101	#13094003	—	2	2	no	—
102	#13094003	—	2	2	no	—
103	#13094003	—	2	2	no	—
104	#13094003	—	2	2	no	—
105	#13094003	—	2	2	no	—
106	C₄×Dic₉₄	—	2	2	no	—
107	C₄×Dic₉₄	—	2	2	no	—
108	C₄×Dic₉₄	—	2	2	no	—
109	C₄×Dic₉₄	—	2	2	no	—
110	C₄×Dic₉₄	—	2	2	no	—
111	C₄×Dic₉₄	—	2	2	no	—
112	C₄×Dic₉₄	—	2	2	no	—
113	C₄×Dic₉₄	—	2	2	no	—
114	#13093983	—	2	2	no	—
115	#13093983	—	2	2	no	—
116	#13093983	C₂³	1	4	yes	—
117	#13093983	C₂³	1	4	yes	—
118	C₂×C₄⋊Dic₄₇	—	2	1	no	—
119	C₂×C₄⋊Dic₄₇	—	2	1	no	—
120	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
121	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
122	C₂×Dic₄₇⋊C₄	—	2	2	no	—
123	C₂×Dic₄₇⋊C₄	—	2	2	no	—
124	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
125	C₂×C₄×Dic₄₇	—	2	2	no	—
126	#13093957	C₂³	1	8	yes	—
127	#13093957	C₂³	1	8	yes	—
128	#13093955	C₂³	1	8	yes	—
129	#13093955	C₂³	1	8	yes	—
130	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
131	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
132	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
133	#13093948	C₂³	1	8	yes	—
134	#13093948	C₂³	1	8	yes	—
135	#13093945	C₂³	1	8	yes	—
136	#13093945	C₂³	1	8	yes	—
137	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
138	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
139	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
140	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
141	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
142	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
143	C₂×#41×C₄₇	—	2	1	no	—
144	C₂×#41×C₄₇	—	2	1	no	—
145	C₂×#41×C₄₇	C₂³	1	2	yes	—
146	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
147	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
148	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
149	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
150	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
152	#127×C₄₇	C₂³	1	1	yes	characteristic
153	#126×C₄₇	—	2	2	no	—
154	#126×C₄₇	—	2	2	no	—
155	#125×C₄₇	—	2	1	no	—
156	#125×C₄₇	—	2	1	no	—
157	#125×C₄₇	C₂³	1	2	yes	—
158	#124×C₄₇	—	2	1	no	—
159	#124×C₄₇	—	2	1	no	—
160	#124×C₄₇	C₂³	1	2	yes	—
161	#123×C₄₇	—	2	2	no	—
162	#123×C₄₇	—	2	2	no	—
163	#123×C₄₇	—	2	2	no	—
164	C₂²⋊Q₈×C₄₇	—	2	1	no	—
165	C₂²⋊Q₈×C₄₇	—	2	1	no	—
166	C₂²⋊Q₈×C₄₇	—	2	1	no	—
167	C₂²⋊Q₈×C₄₇	—	2	1	no	—
168	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
169	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
170	#121×C₄₇	—	2	1	no	—
171	#121×C₄₇	—	2	1	no	—
172	#121×C₄₇	—	2	1	no	—
173	#121×C₄₇	—	2	1	no	—
174	#121×C₄₇	C₂³	1	2	yes	—
175	#121×C₄₇	C₂³	1	2	yes	—
176	#120×C₄₇	—	2	2	no	—
177	C₄×Q₈×C₄₇	—	2	1	no	—
178	C₄×Q₈×C₄₇	—	2	1	no	—
179	C₄×Q₈×C₄₇	—	2	1	no	—
180	C₄×Q₈×C₄₇	—	2	1	no	—
181	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
182	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
183	C₄×D₄×C₄₇	—	2	2	no	—
184	C₄×D₄×C₄₇	—	2	2	no	—
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	1	no	—
190	C₄×D₄×C₄₇	—	2	1	no	—
191	C₄×D₄×C₄₇	—	2	1	no	—
192	C₄×D₄×C₄₇	—	2	1	no	—
193	C₄×D₄×C₄₇	C₂³	1	2	yes	—
194	C₄×D₄×C₄₇	C₂³	1	2	yes	—
195	#117×C₄₇	—	2	1	no	—
196	#117×C₄₇	—	2	1	no	—
197	#117×C₄₇	—	2	2	no	—
198	#117×C₄₇	—	2	2	no	—
199	#117×C₄₇	—	2	2	no	—
200	#117×C₄₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₄₇	—	2	2	no	—
202	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
203	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₇	C₂³	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	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
215	#41×C₄₇	—	2	8	no	—
216	#41×C₄₇	—	4	4	no	—
217	#41×C₄₇	—	4	4	no	—
218	C₂×Q₈×C₄₇	—	2	1	no	—
219	C₂×Q₈×C₄₇	—	2	1	no	—
220	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
221	C₂×D₄×C₄₇	—	2	2	no	—
222	C₂×D₄×C₄₇	—	2	2	no	—
223	C₂×D₄×C₄₇	—	2	2	no	—
224	C₂×D₄×C₄₇	—	2	1	no	—
225	C₂×D₄×C₄₇	—	2	1	no	—
226	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₄₇	—	2	4	no	—
228	C₂²×C₄×C₄₇	—	2	4	no	—
229	C₂²×C₄×C₄₇	—	2	2	no	—
230	C₂²×C₄×C₄₇	—	2	2	no	—
231	C₂²×C₄×C₄₇	—	2	2	no	—
232	C₂²×C₄×C₄₇	—	4	2	no	—
233	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²×Dic₄₇	—	2	2	no	—
252	C₂²×Dic₄₇	—	2	2	no	—
253	C₂×Dic₉₄	—	2	2	no	—
254	C₂×Dic₉₄	—	2	2	no	—
255	C₂×Dic₉₄	—	2	2	no	—
256	C₂×Dic₉₄	—	2	2	no	—
257	C₂×Dic₉₄	—	4	4	no	—
258	C₂×Dic₉₄	—	4	4	no	—
259	C₄⋊C₄×C₄₇	—	2	1	no	—
260	C₄⋊C₄×C₄₇	—	2	1	no	—
261	C₄⋊C₄×C₄₇	—	2	1	no	—
262	C₄⋊C₄×C₄₇	—	2	1	no	—
263	C₄⋊C₄×C₄₇	—	2	2	no	—
264	C₄⋊C₄×C₄₇	—	2	2	no	—
265	C₄⋊C₄×C₄₇	—	2	2	no	—
266	C₄⋊C₄×C₄₇	—	2	2	no	—
267	C₄⋊C₄×C₄₇	—	2	2	no	—
268	C₄⋊C₄×C₄₇	—	2	2	no	—
269	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₄₇	—	2	2	no	—
272	C₂²⋊C₄×C₄₇	—	2	2	no	—
273	C₂²⋊C₄×C₄₇	—	2	2	no	—
274	C₂²⋊C₄×C₄₇	—	2	2	no	—
275	C₂²⋊C₄×C₄₇	—	2	2	no	—
276	C₂²⋊C₄×C₄₇	—	2	2	no	—
277	C₂²⋊C₄×C₄₇	—	2	2	no	—
278	C₂²⋊C₄×C₄₇	—	2	2	no	—
279	C₂²⋊C₄×C₄₇	—	2	2	no	—
280	C₄²×C₄₇	—	2	2	no	—
281	C₄²×C₄₇	—	2	2	no	—
282	C₄²×C₄₇	—	2	2	no	—
283	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
291	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
292	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
293	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
294	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
295	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
296	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
297	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
298	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
299	C₂²⋊Dic₄₇	—	2	4	no	—
300	C₂²⋊Dic₄₇	—	2	4	no	—
301	C₄⋊Dic₄₇	—	2	2	no	—
302	C₄⋊Dic₄₇	—	2	2	no	—
303	C₄⋊Dic₄₇	—	2	2	no	—
304	C₄⋊Dic₄₇	—	2	2	no	—
305	C₄⋊Dic₄₇	—	2	2	no	—
306	C₄⋊Dic₄₇	—	2	2	no	—
307	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
308	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
309	Dic₄₇⋊C₄	—	2	4	no	—
310	Dic₄₇⋊C₄	—	2	4	no	—
311	Dic₄₇⋊C₄	—	2	4	no	—
312	Dic₄₇⋊C₄	—	2	4	no	—
313	C₄×Dic₄₇	—	2	4	no	—
314	C₄×Dic₄₇	—	2	4	no	—
315	C₂×C₄₇⋊C₈	—	2	8	no	—
316	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
317	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
318	C₂³×C₄₇	—	2	2	no	—
319	C₂³×C₄₇	—	2	2	no	—
320	C₂³×C₄₇	—	2	2	no	—
321	C₂³×C₄₇	—	4	1	no	—
322	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
324	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₄₇	—	2	4	no	—
326	Q₈×C₄₇	—	4	2	no	—
327	Q₈×C₄₇	—	4	2	no	—
328	D₄×C₄₇	—	2	4	no	—
329	D₄×C₄₇	—	4	4	no	—
330	D₄×C₄₇	—	4	4	no	—
331	D₄×C₄₇	—	4	4	no	—
332	D₄×C₄₇	—	4	2	no	—
333	D₄×C₄₇	—	4	2	no	—
334	C₂×C₄×C₄₇	—	2	2	no	—
335	C₂×C₄×C₄₇	—	2	2	no	—
336	C₂×C₄×C₄₇	—	2	2	no	—
337	C₂×C₄×C₄₇	—	2	2	no	—
338	C₂×C₄×C₄₇	—	2	2	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	2	no	—
341	C₂×C₄×C₄₇	—	2	2	no	—
342	C₂×C₄×C₄₇	—	2	2	no	—
343	C₂×C₄×C₄₇	—	2	2	no	—
344	C₂×C₄×C₄₇	—	2	2	no	—
345	C₂×C₄×C₄₇	—	2	2	no	—
346	C₂×C₄×C₄₇	—	2	2	no	—
347	C₂×C₄×C₄₇	—	2	2	no	—
348	C₂×C₄×C₄₇	—	2	2	no	—
349	C₂×C₄×C₄₇	—	2	2	no	—
350	C₂×C₄×C₄₇	—	4	1	no	—
351	C₂×C₄×C₄₇	—	4	1	no	—
352	C₂×C₄×C₄₇	—	4	1	no	—
353	C₂×C₄×C₄₇	—	4	4	no	—
354	C₂×C₄×C₄₇	—	4	4	no	—
355	C₂×C₄×C₄₇	—	4	4	no	—
356	C₂×C₄×C₄₇	#135	1	4	yes	—
357	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₇	2₋¹⁺⁴	1	4	yes	—
369	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
370	C₂×Dic₄₇	—	2	4	no	—
371	C₂×Dic₄₇	—	2	4	no	—
372	C₂×Dic₄₇	—	4	4	no	—
373	C₂×Dic₄₇	—	4	4	no	—
374	Dic₉₄	—	4	4	no	—
375	Dic₉₄	—	4	4	no	—
376	Dic₉₄	—	4	4	no	—
377	Dic₉₄	—	4	4	no	—
378	C₄₇⋊C₈	—	2	4	no	—
379	C₄₇⋊C₈	—	2	4	no	—
380	#60846	—	47	1	no	maximal, Sylow
381	C₂²×C₄₇	—	2	1	no	—
382	C₂²×C₄₇	—	2	1	no	—
383	C₂²×C₄₇	—	2	1	no	—
384	C₂²×C₄₇	—	2	1	no	—
385	C₂²×C₄₇	—	2	1	no	—
386	C₂²×C₄₇	—	2	1	no	—
387	C₂²×C₄₇	—	2	1	no	—
388	C₂²×C₄₇	—	4	4	no	—
389	C₂²×C₄₇	—	4	2	no	—
390	C₂²×C₄₇	—	4	2	no	—
391	C₂²×C₄₇	—	4	2	no	—
392	C₂²×C₄₇	#536	1	2	yes	—
393	C₂²×C₄₇	C₂×#135	1	2	yes	—
394	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₄₇	—	2	1	no	—
396	C₄×C₄₇	—	2	1	no	—
397	C₄×C₄₇	—	2	1	no	—
398	C₄×C₄₇	—	2	1	no	—
399	C₄×C₄₇	—	2	1	no	—
400	C₄×C₄₇	—	2	1	no	—
401	C₄×C₄₇	—	2	1	no	—
402	C₄×C₄₇	—	4	2	no	—
403	C₄×C₄₇	—	4	2	no	—
404	C₄×C₄₇	—	4	2	no	—
405	C₄×C₄₇	#536	1	2	yes	—
406	C₄×C₄₇	C₂×#135	1	2	yes	—
407	C₄×C₄₇	C₂×#135	1	2	yes	—
408	C₄×C₄₇	#575	1	2	yes	—
409	C₄×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
410	Dic₄₇	—	4	4	no	—
411	Dic₄₇	—	4	4	no	—
412	#3444	D₄₇	1	1	yes	characteristic
413	C₂×#533	—	47	1	no	—
414	#3233	—	47	4	no	—
415	#3232	—	47	4	no	—
416	#3231	—	47	2	no	—
417	#3230	—	47	1	no	—
418	#3229	—	47	1	no	—
419	#3228	—	47	2	no	—
420	#3227	—	47	1	no	—
421	#3226	—	47	1	no	—
422	#3160	—	47	2	no	—
423	#3131	—	47	2	no	—
424	#3091	—	47	4	no	—
425	#3076	—	47	4	no	—
426	C₂×#431	—	47	1	no	—
427	C₂×C₄₇	—	2	2	no	—
428	C₂×C₄₇	—	2	2	no	—
429	C₂×C₄₇	—	4	1	no	—
430	C₂×C₄₇	—	8	2	no	—
431	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
432	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
433	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
434	#533	—	47	2	no	—
435	#533	—	47	2	no	—
436	#533	—	47	2	no	—
437	#533	—	47	2	no	—
438	#533	—	94	1	no	—
439	#533	—	94	1	no	—
440	#533	—	94	1	no	—
441	#533	—	94	1	no	—
442	#533	C₂×D₄₇	1	1	yes	characteristic
443	#533	C₂×D₄₇	1	1	yes	characteristic
444	#533	C₂×D₄₇	1	1	yes	characteristic
445	#532	C₂×D₄₇	1	1	yes	characteristic
446	#532	C₂×D₄₇	1	1	yes	characteristic
447	#532	C₂×D₄₇	1	1	yes	characteristic
448	C₂×C₄⋊Q₈	—	47	1	no	—
449	C₂×C₄⋊Q₈	—	47	1	no	—
450	#529	—	2	1	no	—
451	#529	—	2	1	no	—
452	#529	—	2	1	no	—
453	#529	—	2	1	no	—
454	#529	C₂×D₄₇	1	2	yes	—
455	#529	C₂×D₄₇	1	2	yes	—
456	C₂×#125	—	47	2	no	—
457	#525	—	2	1	no	—
458	#525	—	2	1	no	—
459	#525	C₂×D₄₇	1	2	yes	—
460	C₂×C₂²⋊Q₈	—	94	1	no	—
461	C₂×C₂²⋊Q₈	—	94	1	no	—
462	C₄×#41	—	2	1	no	—
463	C₄×#41	—	2	1	no	—
464	C₄×#41	C₂×D₄₇	1	2	yes	—
465	C₂×C₄×Q₈	—	94	1	no	—
466	C₂×C₄×Q₈	—	94	1	no	—
467	C₂×#117	—	47	2	no	—
468	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
469	#500	—	47	2	no	—
470	#500	—	47	2	no	—
471	#499	—	47	8	no	—
472	#498	—	47	2	no	—
473	#498	—	47	2	no	—
474	#488	—	47	8	no	—
475	#487	—	47	2	no	—
476	#487	—	47	2	no	—
477	#486	—	47	2	no	—
478	#486	—	47	2	no	—
479	#485	—	47	8	no	—
480	#484	—	47	4	no	—
481	#483	—	47	4	no	—
482	#482	—	47	8	no	—
483	#481	—	47	4	no	—
484	#480	—	47	4	no	—
485	#479	—	47	8	no	—
486	#478	—	47	8	no	—
487	#477	—	47	4	no	—
488	#476	—	47	4	no	—
489	#475	—	47	4	no	—
490	#474	—	47	4	no	—
491	#431	—	47	1	no	—
492	#431	—	47	1	no	—
493	#431	—	47	2	no	—
494	#431	—	47	2	no	—
495	#431	—	47	2	no	—
496	#427	—	47	8	no	—
497	C₂×C₄⋊C₈	—	47	2	no	—
498	#416	—	47	8	no	—
499	C₂×C₂²⋊C₈	—	47	2	no	—
500	C₂×C₄×C₈	—	47	2	no	—
501	C₄₇	#60846	1	1	yes	characteristic, complemented, Sylow
502	C₂×#41	—	2	1	no	—
503	C₂×#41	—	2	1	no	—
504	C₂×#41	C₂²×D₄₇	1	2	yes	—
505	C₂²×Q₈	—	94	1	no	—
506	C₂²×Q₈	—	94	1	no	—
507	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
508	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
509	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
510	C₂²×C₈	—	47	4	no	—
511	C₄⋊Q₈	—	47	2	no	—
512	C₄⋊Q₈	—	47	2	no	—
513	C₄⋊Q₈	—	47	2	no	—
514	C₄⋊Q₈	—	47	2	no	—
515	C₄⋊Q₈	—	94	1	no	—
516	C₄⋊Q₈	—	94	1	no	—
517	C₄⋊Q₈	—	94	1	no	—
518	C₄⋊Q₈	—	94	1	no	—
519	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
520	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
521	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
522	#127	C₂²×D₄₇	1	1	yes	characteristic
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#125	—	2	1	no	—
526	#125	—	2	1	no	—
527	#125	—	47	4	no	—
528	#125	—	47	4	no	—
529	#125	—	94	2	no	—
530	#125	—	94	2	no	—
531	#125	C₂²×D₄₇	1	2	yes	—
532	#124	—	2	1	no	—
533	#124	—	2	1	no	—
534	#124	C₂²×D₄₇	1	2	yes	—
535	#123	—	2	2	no	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	94	2	no	—
543	C₂²⋊Q₈	—	94	2	no	—
544	C₂²⋊Q₈	—	94	2	no	—
545	C₂²⋊Q₈	—	94	2	no	—
546	C₂²⋊Q₈	—	94	2	no	—
547	C₂²⋊Q₈	—	94	2	no	—
548	C₂²⋊Q₈	—	94	2	no	—
549	C₂²⋊Q₈	—	94	2	no	—
550	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
551	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
552	#121	—	2	1	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	C₂²×D₄₇	1	2	yes	—
557	#121	C₂²×D₄₇	1	2	yes	—
558	#120	—	2	2	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	—	2	1	no	—
563	C₄×Q₈	—	94	2	no	—
564	C₄×Q₈	—	94	2	no	—
565	C₄×Q₈	—	94	2	no	—
566	C₄×Q₈	—	94	2	no	—
567	C₄×Q₈	—	94	2	no	—
568	C₄×Q₈	—	94	2	no	—
569	C₄×Q₈	—	94	2	no	—
570	C₄×Q₈	—	94	2	no	—
571	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
572	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	C₂²×D₄₇	1	2	yes	—
584	C₄×D₄	C₂²×D₄₇	1	2	yes	—
585	#117	—	2	1	no	—
586	#117	—	2	1	no	—
587	#117	—	2	2	no	—
588	#117	—	2	2	no	—
589	#117	—	2	2	no	—
590	#117	—	47	4	no	—
591	#117	—	47	4	no	—
592	#117	—	94	2	no	—
593	#117	—	94	2	no	—
594	#117	C₂²×D₄₇	1	2	yes	—
595	C₂×C₄⋊C₄	—	47	2	no	—
596	C₂×C₄⋊C₄	—	47	2	no	—
597	C₂×C₄⋊C₄	—	94	2	no	—
598	C₂×C₄⋊C₄	—	94	2	no	—
599	C₂×C₄⋊C₄	—	94	1	no	—
600	C₂×C₄⋊C₄	—	94	1	no	—
601	C₂×C₂²⋊C₄	—	94	2	no	—
602	C₂×C₄²	—	2	2	no	—
603	C₂×C₄²	—	94	2	no	—
604	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
605	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
606	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
607	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
608	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
609	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
610	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
611	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
612	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
613	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
614	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
615	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
616	#107	—	47	8	no	—
617	#107	—	47	8	no	—
618	#106	—	47	8	no	—
619	#106	—	47	8	no	—
620	C₄⋊C₈	—	47	2	no	—
621	C₄⋊C₈	—	47	2	no	—
622	C₄⋊C₈	—	47	4	no	—
623	#103	—	47	8	no	—
624	#103	—	47	8	no	—
625	#102	—	47	8	no	—
626	#102	—	47	8	no	—
627	C₂²⋊C₈	—	47	2	no	—
628	C₂²⋊C₈	—	47	2	no	—
629	C₂²⋊C₈	—	47	4	no	—
630	C₄×C₈	—	47	2	no	—
631	C₄×C₈	—	47	2	no	—
632	C₄×C₈	—	47	4	no	—
633	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
634	#41	—	2	8	no	—
635	#41	—	4	4	no	—
636	#41	—	4	4	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	1	no	—
639	C₂×Q₈	—	94	2	no	—
640	C₂×Q₈	—	94	2	no	—
641	C₂×Q₈	—	94	2	no	—
642	C₂×Q₈	—	94	2	no	—
643	C₂×Q₈	—	188	4	no	—
644	C₂×Q₈	—	188	4	no	—
645	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	C₂³×D₄₇	1	2	yes	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	94	2	no	—
659	C₂²×C₄	—	94	2	no	—
660	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
661	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
662	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
663	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
664	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
666	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
667	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
668	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
669	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
670	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
671	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
672	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
673	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
674	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
675	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
676	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
677	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
678	C₂×C₈	—	47	4	no	—
679	C₂×C₈	—	47	4	no	—
680	C₂×C₈	—	94	8	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	47	4	no	—
692	C₄⋊C₄	—	47	4	no	—
693	C₄⋊C₄	—	94	4	no	—
694	C₄⋊C₄	—	94	4	no	—
695	C₄⋊C₄	—	94	4	no	—
696	C₄⋊C₄	—	94	4	no	—
697	C₄⋊C₄	—	94	2	no	—
698	C₄⋊C₄	—	94	2	no	—
699	C₄⋊C₄	—	94	2	no	—
700	C₄⋊C₄	—	94	2	no	—
701	C₄⋊C₄	—	94	2	no	—
702	C₄⋊C₄	—	94	2	no	—
703	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
704	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	94	4	no	—
715	C₂²⋊C₄	—	94	4	no	—
716	C₄²	—	2	2	no	—
717	C₄²	—	2	2	no	—
718	C₄²	—	2	2	no	—
719	C₄²	—	94	4	no	—
720	C₄²	—	94	4	no	—
721	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
722	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
723	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
724	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
725	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
726	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
727	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
728	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
729	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
730	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
731	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
732	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
733	C₄²	C₂³×D₄₇	1	1	yes	characteristic
734	C₄²	C₂³×D₄₇	1	1	yes	characteristic
735	C₄²	C₂³×D₄₇	1	1	yes	characteristic
736	C₄²	C₂³×D₄₇	1	1	yes	characteristic
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	1	no	—
741	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
742	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
743	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
744	Q₈	—	2	4	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	4	2	no	—
747	Q₈	—	188	4	no	—
748	Q₈	—	188	4	no	—
749	Q₈	—	188	4	no	—
750	Q₈	—	188	4	no	—
751	D₄	—	2	4	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	4	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	94	4	no	—
780	C₂×C₄	—	94	4	no	—
781	C₂×C₄	—	188	4	no	—
782	C₂×C₄	—	188	4	no	—
783	C₂×C₄	#13094044	1	4	yes	—
784	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
788	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
789	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
790	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
791	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
792	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
793	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
794	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
795	C₂×C₄	#13094071	1	4	yes	—
796	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
797	C₈	—	94	4	no	—
798	C₈	—	94	4	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	#15689694	1	2	yes	—
811	C₂²	C₂×#13094044	1	2	yes	—
812	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	188	4	no	—
824	C₄	—	188	4	no	—
825	C₄	#15689694	1	2	yes	—
826	C₄	C₂×#13094044	1	2	yes	—
827	C₄	C₂×#13094044	1	2	yes	—
828	C₄	#15689921	1	2	yes	—
829	C₄	C₂×#13094071	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×#15689694	1	1	yes	characteristic
835	C₂	C₂²×#13094044	1	1	yes	characteristic
836	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, prime radical	C₄₇×#3444	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#60846
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×#15689680	C₂	semidirect
2. #20254563	C₂	semidirect
3. #20254552	C₂	semidirect
4. #20254543	C₂	semidirect
5. #20254536	C₂	semidirect
6. #20254529	C₂	semidirect
7. #20254520	C₂	semidirect
8. #20254513	C₂	semidirect
9. #20254506	C₂	semidirect
10. #20253898	C₂	semidirect
11. #20253710	C₂	semidirect
12. #20253297	C₂	semidirect
13. #20253176	C₂	semidirect
14. C₂×#15689176	C₂	semidirect
32. #15689526	C₂²	semidirect
33. #15689526	C₂²	semidirect
34. #15689522	C₂²	semidirect
35. #15689519	C₂²	semidirect
36. #15689519	C₂²	semidirect
37. #15689477	C₂²	semidirect
38. #15689473	C₂²	semidirect
39. #15689473	C₂²	semidirect
40. #15689469	C₂²	semidirect
41. #15689469	C₂²	semidirect
48. #15689430	C₂²	semidirect
49. #15689423	C₂²	semidirect
50. #15689418	C₂²	semidirect
51. #15689413	C₂²	semidirect
52. #15689408	C₂²	semidirect
53. #15689403	C₂²	semidirect
501. C₄₇	#60846	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689680	2
#20254563	2
#20254552	2
#20254543	2
#20254536	2
#20254529	2
#20254520	2
#20254513	2
#20254506	2
#20253898	2
#20253710	2
#20253297	2
#20253176	2
C₂×#15689176	2
C₄₇×#3444	2
#60846	47