Subgroups — #26217184

Order 12032.

1312 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689171	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689141	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689141	C₂	1	1	yes	maximal, characteristic
6	#20243629	C₂	1	8	yes	maximal, complemented
7	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	—	2	2	no	—
13	#15689889	C₂²	1	4	yes	—
14	C₂×#13094032	—	2	2	no	—
15	C₂×#13094030	—	2	2	no	—
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×D₄₇	—	2	2	no	—
20	#15689171	—	2	2	no	—
21	#15689171	C₂²	1	4	yes	complemented
22	C₂×#13093959	—	2	2	no	—
23	#15689150	—	2	2	no	—
24	#15689150	—	2	2	no	—
25	#15689147	C₂²	1	4	yes	complemented
26	#15689141	—	2	2	no	—
27	#15689141	C₄	1	4	yes	complemented
28	#15689141	C₄	1	4	yes	complemented
29	#15689141	C₂²	1	4	yes	—
30	C₂×#13093952	—	2	2	no	—
31	C₂×#13093952	C₂²	1	4	yes	—
32	#15688893	C₂²	1	4	yes	complemented
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#339	C₂²	1	4	yes	complemented
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	C₂×C₄	1	2	yes	—
44	C₂×#10625350	C₂×C₄	1	2	yes	—
45	C₂×#10625350	D₄	1	2	yes	—
46	C₂×#10625350	D₄	1	2	yes	—
47	C₂×#10625350	Q₈	1	2	yes	—
48	C₂×#10625350	C₂³	1	2	yes	—
49	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
50	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
51	C₂²×C₂²⋊D₄₇	—	2	1	no	—
52	C₂²×C₄×D₄₇	—	2	1	no	—
53	#13094032	—	2	8	no	—
54	#13094032	—	2	8	no	—
55	#13094030	—	2	8	no	—
56	#13094030	—	2	8	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	—	2	1	no	—
62	C₂×#10625329	—	2	1	no	—
63	C₂×#10625329	—	2	1	no	—
64	C₂×#10625329	—	2	1	no	—
65	C₂×#10625329	—	2	1	no	—
66	C₂×#10625329	—	2	1	no	—
67	C₂×#10625329	—	2	1	no	—
68	C₂×#10625329	—	2	1	no	—
69	C₂×#10625329	C₂×C₄	1	2	yes	—
70	C₂×#10625329	C₂×C₄	1	2	yes	—
71	C₂×#10625329	D₄	1	2	yes	—
72	C₂×#10625329	C₂³	1	2	yes	—
73	C₂×#10625329	C₂³	1	2	yes	—
74	C₂×#10625329	C₂³	1	2	yes	—
75	C₂×#10625324	—	2	4	no	—
76	M₁₆×D₄₇	—	2	8	no	—
77	M₁₆×D₄₇	—	2	8	no	—
78	C₂²×C₄₇⋊C₈	—	2	1	no	—
79	C₂²×C₄₇⋊C₈	—	2	1	no	—
80	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
81	C₂×C₈×D₄₇	—	2	4	no	—
82	#13093959	—	2	8	no	—
83	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
84	#13093952	—	2	8	no	—
85	#13093952	C₂×C₄	1	16	yes	complemented
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
91	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
92	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
93	C₂²×C₈×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	C₂×C₄	1	2	yes	—
100	#117×C₄₇	C₂×C₄	1	2	yes	—
101	#117×C₄₇	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
106	C₂×C₄²×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
108	C₂⁴×C₄₇	#41	1	1	yes	characteristic
109	C₂³×D₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	4	1	no	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₇	—	2	2	no	—
127	C₂×C₂²⋊D₄₇	—	2	2	no	—
128	C₂×C₂²⋊D₄₇	—	2	2	no	—
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	C₂×C₂²⋊D₄₇	—	2	2	no	—
131	C₂×C₂²⋊D₄₇	—	2	2	no	—
132	C₂²×Dic₄₇	—	2	1	no	—
133	#10625350	—	2	2	no	—
134	#10625350	—	2	2	no	—
135	#10625350	—	2	2	no	—
136	#10625350	—	2	2	no	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	C₄⋊C₄	1	4	yes	—
146	#10625350	C₄⋊C₄	1	4	yes	—
147	#10625350	C₂²×C₄	1	4	yes	—
148	#10625350	C₂×D₄	1	4	yes	—
149	C₂×D₁₈₈	—	2	1	no	—
150	C₂×D₁₈₈	—	2	1	no	—
151	C₂×D₁₈₈	—	2	1	no	—
152	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
153	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
154	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
155	C₂×C₄×D₄₇	—	2	2	no	—
156	C₂×C₄×D₄₇	—	2	2	no	—
157	C₂×C₄×D₄₇	—	2	2	no	—
158	C₂×C₄×D₄₇	—	2	2	no	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×Dic₉₄	—	2	1	no	—
162	C₂×Dic₉₄	—	2	1	no	—
163	C₂×Dic₉₄	—	2	1	no	—
164	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
165	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
166	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
167	M₁₆×C₄₇	—	2	2	no	—
168	M₁₆×C₄₇	—	2	2	no	—
169	M₁₆×C₄₇	—	2	2	no	—
170	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	—	2	2	no	—
175	C₄⋊C₄×C₄₇	—	2	2	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	—	4	1	no	—
178	C₂²⋊C₄×C₄₇	—	2	2	no	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₂²⋊C₄×C₄₇	—	2	2	no	—
181	C₂²⋊C₄×C₄₇	—	4	1	no	—
182	C₄²×C₄₇	—	2	2	no	—
183	C₄²×C₄₇	—	2	2	no	—
184	C₄²×C₄₇	—	4	1	no	—
185	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
186	#10625329	—	2	2	no	—
187	#10625329	—	2	2	no	—
188	#10625329	—	2	2	no	—
189	#10625329	—	2	2	no	—
190	#10625329	—	2	2	no	—
191	#10625329	—	2	2	no	—
192	#10625329	—	2	2	no	—
193	#10625329	—	2	2	no	—
194	#10625329	—	2	2	no	—
195	#10625329	—	4	1	no	—
196	#10625329	—	4	1	no	—
197	#10625329	C₂²×C₄	1	4	yes	—
198	C₂×C₄₇⋊C₈	—	2	2	no	—
199	C₂×C₄₇⋊C₈	—	2	2	no	—
200	C₂×C₄₇⋊C₈	—	2	2	no	—
201	C₂×C₄₇⋊C₈	—	2	2	no	—
202	C₂×C₄₇⋊C₈	—	2	2	no	—
203	C₂×C₄₇⋊C₈	—	2	2	no	—
204	C₂×C₄₇⋊C₈	—	4	1	no	—
205	C₂×C₄₇⋊C₈	—	4	1	no	—
206	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
207	#10625324	—	2	16	no	—
208	C₈×D₄₇	—	2	16	no	—
209	C₂³×C₄₇	—	8	1	no	—
210	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
211	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
213	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
214	C₂³×C₄₇	#123	1	1	yes	characteristic
215	C₂³×C₄₇	#123	1	1	yes	characteristic
216	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
217	C₂²×D₄₇	—	2	2	no	—
218	C₂²×D₄₇	—	2	2	no	—
219	C₂²×D₄₇	—	2	2	no	—
220	C₂²×D₄₇	—	8	2	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	4	2	no	—
223	C₂×C₄×C₄₇	—	8	2	no	—
224	C₂×C₄×C₄₇	—	8	2	no	—
225	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂²⋊D₄₇	—	2	4	no	—
254	C₂²⋊D₄₇	—	2	4	no	—
255	C₂²⋊D₄₇	—	2	4	no	—
256	C₂²⋊D₄₇	—	2	4	no	—
257	C₂×Dic₄₇	—	2	2	no	—
258	C₂×Dic₄₇	—	2	2	no	—
259	C₂×Dic₄₇	—	2	2	no	—
260	D₁₈₈	—	2	2	no	—
261	D₁₈₈	—	2	2	no	—
262	D₁₈₈	—	2	2	no	—
263	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
264	C₄×D₄₇	—	2	4	no	—
265	C₄×D₄₇	—	2	4	no	—
266	C₄×D₄₇	—	2	4	no	—
267	C₄×D₄₇	—	2	4	no	—
268	Dic₉₄	—	2	2	no	—
269	Dic₉₄	—	2	2	no	—
270	Dic₉₄	—	2	2	no	—
271	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
272	C₈×C₄₇	—	2	4	no	—
273	C₄₇⋊C₈	—	2	4	no	—
274	C₄₇⋊C₈	—	2	4	no	—
275	C₄₇⋊C₈	—	4	2	no	—
276	#20867	—	47	1	no	maximal, Sylow
277	C₂²×C₄₇	—	4	1	no	—
278	C₂²×C₄₇	—	4	1	no	—
279	C₂²×C₄₇	—	4	1	no	—
280	C₂²×C₄₇	—	4	1	no	—
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	#385	1	1	yes	characteristic
285	C₂²×C₄₇	#385	1	1	yes	characteristic
286	C₂²×C₄₇	#385	1	1	yes	characteristic
287	C₂²×C₄₇	#385	1	1	yes	characteristic
288	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
290	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
291	C₂×D₄₇	—	2	4	no	—
292	C₂×D₄₇	—	4	4	no	—
293	C₂×D₄₇	—	8	2	no	—
294	C₂×D₄₇	—	8	2	no	—
295	C₄×C₄₇	—	4	4	no	—
296	C₄×C₄₇	—	8	2	no	—
297	C₄×C₄₇	#385	1	1	yes	characteristic
298	C₄×C₄₇	#385	1	1	yes	characteristic
299	C₄×C₄₇	#385	1	1	yes	characteristic
300	C₄×C₄₇	#385	1	1	yes	characteristic
301	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
302	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
304	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	Dic₄₇	—	2	4	no	—
306	C₂×#568	—	47	1	no	—
307	C₂×#430	—	47	1	no	—
308	#2905	—	47	1	no	—
309	C₂×#421	—	47	1	no	—
310	C₂×#421	—	47	1	no	—
311	#1861	—	47	8	no	—
312	C₂×#344	—	47	1	no	—
313	#1733	D₄₇	1	1	yes	characteristic, complemented
314	C₂×C₄₇	—	2	1	no	—
315	C₂×C₄₇	—	2	1	no	—
316	C₂×C₄₇	—	2	1	no	—
317	C₂×C₄₇	—	2	1	no	—
318	C₂×C₄₇	—	2	1	no	—
319	C₂×C₄₇	—	2	1	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
322	D₄₇	—	4	4	no	—
323	C₂²×#41	—	47	1	no	—
324	#568	—	47	4	no	—
325	#568	—	94	2	no	—
326	#568	—	94	2	no	—
327	#568	—	94	2	no	—
328	C₂×#131	—	94	2	no	—
329	C₂×#131	—	94	2	no	—
330	C₂²×M₁₆	—	47	1	no	—
331	C₂²×M₁₆	—	47	1	no	—
332	C₂²×M₁₆	—	47	1	no	—
333	C₂²×M₁₆	—	94	2	no	—
334	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
335	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
336	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
337	#430	—	47	4	no	—
338	#430	—	94	2	no	—
339	C₂×#108	—	94	2	no	—
340	#424	—	94	2	no	—
341	#424	—	94	2	no	—
342	#423	—	47	4	no	—
343	#421	—	47	4	no	—
344	#421	—	47	4	no	—
345	#421	—	47	4	no	—
346	#421	—	94	2	no	—
347	C₂×#104	—	47	4	no	—
348	C₂×#104	—	94	2	no	—
349	#344	—	47	4	no	—
350	#339	C₂×D₄₇	1	4	yes	complemented
351	C₄₇	#20867	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	47	2	no	—
353	C₂×#41	—	47	2	no	—
354	C₂×#41	—	47	2	no	—
355	C₂×#41	—	47	2	no	—
356	C₂×#41	—	47	2	no	—
357	C₂×#41	—	47	2	no	—
358	C₂×#41	—	94	1	no	—
359	C₂×#41	—	94	1	no	—
360	C₂×#41	—	94	1	no	—
361	C₂×#41	—	94	1	no	—
362	C₂×#41	—	94	1	no	—
363	C₂×#41	—	94	1	no	—
364	C₂²×Q₈	—	47	1	no	—
365	C₂²×D₄	—	47	1	no	—
366	C₂²×D₄	—	94	1	no	—
367	C₂³×C₄	—	94	1	no	—
368	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
369	#131	—	94	8	no	—
370	#131	—	94	8	no	—
371	#131	—	94	8	no	—
372	#131	—	94	8	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	47	2	no	—
377	C₂×M₁₆	—	47	2	no	—
378	C₂×M₁₆	—	47	2	no	—
379	C₂×M₁₆	—	47	2	no	—
380	C₂×M₁₆	—	47	2	no	—
381	C₂×M₁₆	—	47	2	no	—
382	C₂×M₁₆	—	94	4	no	—
383	C₂×M₁₆	—	94	8	no	—
384	C₂×M₁₆	—	94	1	no	—
385	C₂×M₁₆	—	94	1	no	—
386	C₂×M₁₆	—	94	1	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂×M₁₆	—	94	1	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	—	94	8	no	—
392	C₂×M₁₆	—	94	1	no	—
393	C₂×M₁₆	—	94	1	no	—
394	C₂×M₁₆	—	94	1	no	—
395	C₂×M₁₆	—	94	1	no	—
396	C₂×M₁₆	—	94	1	no	—
397	C₂×M₁₆	D₁₈₈	1	2	yes	—
398	C₂×M₁₆	D₁₈₈	1	2	yes	—
399	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	47	2	no	—
402	C₂²×C₈	—	94	4	no	—
403	C₂²×C₈	—	94	1	no	—
404	C₂²×C₈	—	94	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	C₄×D₄₇	1	2	yes	—
411	#117	C₄×D₄₇	1	2	yes	—
412	#117	C₂²×D₄₇	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
419	#108	—	94	8	no	—
420	C₄⋊C₈	—	94	8	no	—
421	#104	—	47	16	no	—
422	#104	—	94	8	no	—
423	C₂⁴	—	94	1	no	—
424	C₂⁴	#10625352	1	1	yes	characteristic
425	#41	—	47	4	no	—
426	#41	—	47	4	no	—
427	#41	—	47	4	no	—
428	#41	—	47	4	no	—
429	#41	—	94	2	no	—
430	#41	—	94	2	no	—
431	#41	—	94	2	no	—
432	#41	—	94	2	no	—
433	#41	—	94	2	no	—
434	#41	—	94	2	no	—
435	#41	—	94	2	no	—
436	#41	—	94	2	no	—
437	#41	—	94	2	no	—
438	#41	—	94	2	no	—
439	#41	—	94	2	no	—
440	#41	—	94	2	no	—
441	C₂×Q₈	—	47	2	no	—
442	C₂×Q₈	—	47	2	no	—
443	C₂×Q₈	—	47	2	no	—
444	C₂×Q₈	—	94	1	no	—
445	C₂×Q₈	—	94	1	no	—
446	C₂×Q₈	—	94	1	no	—
447	C₂×D₄	—	47	2	no	—
448	C₂×D₄	—	47	2	no	—
449	C₂×D₄	—	47	2	no	—
450	C₂×D₄	—	94	2	no	—
451	C₂×D₄	—	94	2	no	—
452	C₂×D₄	—	94	2	no	—
453	C₂×D₄	—	94	2	no	—
454	C₂×D₄	—	94	2	no	—
455	C₂×D₄	—	94	2	no	—
456	C₂×D₄	—	94	1	no	—
457	C₂×D₄	—	94	1	no	—
458	C₂×D₄	—	94	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	94	1	no	—
462	C₂²×C₄	—	94	2	no	—
463	C₂²×C₄	—	94	2	no	—
464	C₂²×C₄	—	94	2	no	—
465	C₂²×C₄	—	94	2	no	—
466	C₂²×C₄	—	94	2	no	—
467	C₂²×C₄	—	94	2	no	—
468	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
472	C₂²×C₄	#10625350	1	1	yes	characteristic
473	C₂²×C₄	#10625350	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	#10625352	1	1	yes	characteristic
479	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	47	4	no	—
486	M₁₆	—	94	16	no	—
487	M₁₆	—	94	2	no	—
488	M₁₆	—	94	2	no	—
489	M₁₆	—	94	2	no	—
490	M₁₆	—	94	2	no	—
491	M₁₆	—	94	2	no	—
492	M₁₆	—	94	2	no	—
493	M₁₆	—	94	2	no	—
494	M₁₆	—	94	2	no	—
495	M₁₆	—	94	2	no	—
496	M₁₆	—	188	1	no	—
497	M₁₆	—	188	1	no	—
498	M₁₆	C₂×D₁₈₈	1	4	yes	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	47	4	no	—
503	C₂×C₈	—	94	16	no	—
504	C₂×C₈	—	94	2	no	—
505	C₂×C₈	—	94	2	no	—
506	C₂×C₈	—	94	2	no	—
507	C₂×C₈	—	94	2	no	—
508	C₂×C₈	—	94	2	no	—
509	C₂×C₈	—	94	2	no	—
510	C₂×C₈	—	188	1	no	—
511	C₂×C₈	—	188	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	4	1	no	—
523	C₄²	C₂×C₄×D₄₇	1	4	yes	—
524	C₂³	—	8	1	no	—
525	C₂³	—	94	2	no	—
526	C₂³	—	94	2	no	—
527	C₂³	—	94	2	no	—
528	C₂³	—	376	2	no	—
529	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
530	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
531	C₂³	#13094004	1	1	yes	characteristic
532	C₂³	#13094004	1	1	yes	characteristic
533	C₂³	#13094006	1	1	yes	characteristic
534	C₂³	#13094006	1	1	yes	characteristic
535	C₂³	C₂×#10625352	1	1	yes	characteristic
536	Q₈	—	47	4	no	—
537	Q₈	—	94	2	no	—
538	Q₈	—	94	2	no	—
539	Q₈	—	94	2	no	—
540	D₄	—	47	4	no	—
541	D₄	—	94	4	no	—
542	D₄	—	94	4	no	—
543	D₄	—	94	4	no	—
544	D₄	—	94	4	no	—
545	D₄	—	94	2	no	—
546	D₄	—	94	2	no	—
547	D₄	—	94	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	94	2	no	—
553	C₂×C₄	—	94	2	no	—
554	C₂×C₄	—	94	2	no	—
555	C₂×C₄	—	94	4	no	—
556	C₂×C₄	—	94	4	no	—
557	C₂×C₄	—	94	4	no	—
558	C₂×C₄	—	94	4	no	—
559	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
560	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
561	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
562	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
563	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
564	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
566	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
567	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
568	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
569	C₂×C₄	#13093994	1	1	yes	characteristic
570	C₂×C₄	#13093994	1	1	yes	characteristic
571	C₂×C₄	#13093994	1	1	yes	characteristic
572	C₂×C₄	#13093994	1	1	yes	characteristic
573	C₂×C₄	#13094002	1	1	yes	characteristic
574	C₂×C₄	#13094002	1	1	yes	characteristic
575	C₂×C₄	#13094002	1	1	yes	characteristic
576	C₂×C₄	#13094002	1	1	yes	characteristic
577	C₂×C₄	#13094004	1	1	yes	characteristic
578	C₂×C₄	#13094004	1	1	yes	characteristic
579	C₂×C₄	#13094006	1	1	yes	characteristic
580	C₂×C₄	#13094006	1	1	yes	characteristic
581	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
582	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
585	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
586	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
587	C₈	—	2	4	no	—
588	C₈	—	94	4	no	—
589	C₈	—	94	4	no	—
590	C₈	—	188	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	94	4	no	—
599	C₂²	—	376	2	no	—
600	C₂²	—	376	2	no	—
601	C₂²	—	188	4	no	—
602	C₂²	#15688997	1	1	yes	characteristic
603	C₂²	#15688997	1	1	yes	characteristic
604	C₂²	#15688997	1	1	yes	characteristic
605	C₂²	#15688997	1	1	yes	characteristic
606	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
607	C₂²	C₂×#13094004	1	1	yes	characteristic
608	C₂²	C₂×#13094006	1	1	yes	characteristic
609	C₄	—	4	4	no	—
610	C₄	—	8	2	no	—
611	C₄	—	94	4	no	—
612	C₄	#15688997	1	1	yes	characteristic
613	C₄	#15688997	1	1	yes	characteristic
614	C₄	#15688997	1	1	yes	characteristic
615	C₄	#15688997	1	1	yes	characteristic
616	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
617	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
618	C₄	C₂×#13093994	1	1	yes	characteristic
619	C₄	C₂×#13094002	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	188	4	no	—
628	C₂	C₂×#15688997	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093994
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1733	C₂
socle	C₂×C₄₇	C₂×#385
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1733	D₄₇
hypocenter	C₄₇	#20867
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
2. C₂×#15689171	C₂	semidirect
3. #20251952	C₂	semidirect
6. #20243629	C₂	semidirect
7. C₂×#15688893	C₂	semidirect
8. C₄₇×#1733	C₂	semidirect
21. #15689171	C₂²	semidirect
25. #15689147	C₂²	semidirect
27. #15689141	C₄	semidirect
28. #15689141	C₄	semidirect
32. #15688893	C₂²	semidirect
36. C₄₇×#339	C₂²	semidirect
85. #13093952	C₂×C₄	semidirect
313. #1733	D₄₇	semidirect
350. #339	C₂×D₄₇	semidirect
351. C₄₇	#20867	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
C₂×#15689171	2
#20251952	2
C₂×#15689141	2
#20243629	2
C₂×#15688893	2
C₄₇×#1733	2
#20867	47