Subgroups — #26121763

Order 12032.

1394 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689597	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689129	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689127	C₂	1	1	yes	maximal, characteristic
4	#20243126	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243120	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243097	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	#15689597	—	2	2	no	—
11	#15689597	—	2	2	no	—
12	#15689597	—	2	2	no	—
13	#15689597	—	2	2	no	—
14	C₂×C₄×D₁₈₈	—	2	2	no	—
15	C₂×#13093986	C₄	1	4	yes	complemented
16	C₂×#13093983	C₂²	1	1	yes	characteristic
17	C₂×#13093983	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×D₄₇	—	2	2	no	—
19	#15689129	—	2	2	no	—
20	#15689129	C₄	1	4	yes	complemented
21	#15689127	—	2	2	no	—
22	#15689127	C₄	1	4	yes	complemented
23	C₂×#13093946	—	2	2	no	—
24	C₂×#13093944	—	2	2	no	—
25	#15688891	—	2	2	no	—
26	#15688889	—	2	2	no	—
27	#15688882	—	2	2	no	—
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#339	—	2	2	no	—
32	C₂⁴×D₄₇	—	2	1	no	—
33	C₂²×D₁₈₈	—	2	1	no	—
34	C₂²×D₁₈₈	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
41	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
42	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	D₄	1	2	yes	—
44	C₂²×D₁₈₈	D₄	1	2	yes	—
45	C₂²×D₁₈₈	D₄	1	2	yes	—
46	C₂²×D₁₈₈	Q₈	1	2	yes	—
47	C₂²×C₄×D₄₇	—	2	4	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	C₂×C₄	1	2	yes	complemented
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₄×D₁₈₈	—	2	8	no	—
56	C₄×D₁₈₈	—	2	8	no	—
57	#13093986	—	2	8	no	—
58	#13093986	—	2	8	no	—
59	#13093983	—	2	1	no	—
60	#13093983	—	2	1	no	—
61	#13093983	—	2	1	no	—
62	#13093983	—	2	1	no	—
63	#13093983	—	2	1	no	—
64	#13093983	—	2	1	no	—
65	#13093983	—	2	1	no	—
66	#13093983	C₂×C₄	1	2	yes	complemented
67	C₂×C₄⋊Dic₄₇	—	2	1	no	—
68	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
69	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
70	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
71	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
72	C₂²⋊C₄×D₄₇	—	2	8	no	—
73	C₂²⋊C₄×D₄₇	—	2	8	no	—
74	C₂×C₄×Dic₄₇	—	2	1	no	—
75	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
76	#13093946	—	2	8	no	—
77	#13093944	—	2	8	no	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₄₇	—	2	1	no	—
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
85	C₂²×C₈×C₄₇	—	2	1	no	—
86	#117×C₄₇	—	2	1	no	—
87	#117×C₄₇	—	2	1	no	—
88	#117×C₄₇	—	2	1	no	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	—	2	1	no	—
91	#117×C₄₇	C₂×C₄	1	2	yes	complemented
92	#117×C₄₇	D₄	1	2	yes	—
93	#117×C₄₇	D₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	—	2	1	no	—
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂³×D₄₇	—	2	2	no	—
102	C₂³×D₄₇	—	2	2	no	—
103	C₂³×D₄₇	—	2	2	no	—
104	C₂³×D₄₇	—	2	2	no	—
105	C₂³×D₄₇	—	2	2	no	—
106	C₂³×D₄₇	—	2	2	no	—
107	C₂³×D₄₇	—	2	2	no	—
108	C₂³×D₄₇	—	8	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	4	1	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	#41	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×Dic₄₇	—	4	1	no	—
126	C₂²×Dic₄₇	C₂²⋊C₄	1	4	yes	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	—	2	2	no	—
131	C₂×D₁₈₈	—	2	2	no	—
132	C₂×D₁₈₈	—	2	2	no	—
133	C₂×D₁₈₈	—	2	2	no	—
134	C₂×D₁₈₈	—	2	2	no	—
135	C₂×D₁₈₈	—	2	2	no	—
136	C₂×D₁₈₈	—	2	2	no	—
137	C₂×D₁₈₈	—	2	2	no	—
138	C₂×D₁₈₈	—	2	2	no	—
139	C₂×D₁₈₈	—	2	2	no	—
140	C₂×D₁₈₈	—	2	2	no	—
141	C₂×D₁₈₈	—	2	2	no	—
142	C₂×D₁₈₈	—	2	2	no	—
143	C₂×D₁₈₈	—	2	2	no	—
144	C₂×D₁₈₈	—	2	2	no	—
145	C₂×D₁₈₈	—	2	2	no	—
146	C₂×D₁₈₈	—	2	2	no	—
147	C₂×D₁₈₈	—	2	2	no	—
148	C₂×D₁₈₈	C₄²	1	4	yes	—
149	C₂×D₁₈₈	C₂²⋊C₄	1	4	yes	—
150	C₂×D₁₈₈	C₂²⋊C₄	1	4	yes	—
151	C₂×D₁₈₈	C₂²⋊C₄	1	4	yes	—
152	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
153	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
154	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
155	C₂×C₄×D₄₇	—	2	16	no	—
156	C₂×C₄×D₄₇	—	8	8	no	—
157	M₁₆×C₄₇	—	2	2	no	—
158	M₁₆×C₄₇	—	2	2	no	—
159	M₁₆×C₄₇	—	4	1	no	—
160	M₁₆×C₄₇	—	4	1	no	—
161	C₂×C₈×C₄₇	—	2	2	no	—
162	C₂×C₈×C₄₇	—	4	1	no	—
163	C₂×C₈×C₄₇	—	4	1	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	4	1	no	—
167	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
168	C₂²⋊C₄×C₄₇	—	2	2	no	—
169	C₂²⋊C₄×C₄₇	—	2	2	no	—
170	C₂²⋊C₄×C₄₇	—	2	2	no	—
171	C₂²⋊C₄×C₄₇	—	4	1	no	—
172	C₄²×C₄₇	—	2	2	no	—
173	C₄²×C₄₇	—	2	2	no	—
174	C₄²×C₄₇	—	2	2	no	—
175	C₄²×C₄₇	—	4	1	no	—
176	C₂²⋊Dic₄₇	—	2	2	no	—
177	C₂²⋊Dic₄₇	—	2	2	no	—
178	C₂²⋊Dic₄₇	—	2	2	no	—
179	C₂²⋊Dic₄₇	—	4	1	no	—
180	(C₂×D₄₇)⋊C₄	—	2	16	no	—
181	C₄⋊Dic₄₇	—	2	2	no	—
182	C₄⋊Dic₄₇	—	2	2	no	—
183	C₄⋊Dic₄₇	—	2	2	no	—
184	C₄⋊Dic₄₇	—	4	1	no	—
185	C₄×Dic₄₇	—	2	2	no	—
186	C₄×Dic₄₇	—	2	2	no	—
187	C₄×Dic₄₇	—	2	2	no	—
188	C₄×Dic₄₇	—	4	1	no	—
189	#10625329	—	2	2	no	—
190	#10625329	—	2	2	no	—
191	#10625329	—	4	1	no	—
192	#10625329	—	4	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	C₂×C₄₇⋊C₈	—	4	1	no	—
195	C₂×C₄₇⋊C₈	—	4	1	no	—
196	C₂³×C₄₇	—	4	2	no	—
197	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₄₇	#120	1	1	yes	characteristic
201	C₂³×C₄₇	#120	1	1	yes	characteristic
202	C₂³×C₄₇	#121	1	1	yes	characteristic
203	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂²×D₄₇	—	2	4	no	—
205	C₂²×D₄₇	—	2	4	no	—
206	C₂²×D₄₇	—	2	4	no	—
207	C₂²×D₄₇	—	2	4	no	—
208	C₂²×D₄₇	—	2	4	no	—
209	C₂²×D₄₇	—	2	4	no	—
210	C₂²×D₄₇	—	2	4	no	—
211	C₂²×D₄₇	—	4	8	no	—
212	C₂²×D₄₇	—	8	4	no	—
213	C₂²×D₄₇	—	8	4	no	—
214	C₂²×D₄₇	—	8	4	no	—
215	C₂²×D₄₇	—	8	4	no	—
216	C₂²×D₄₇	—	8	4	no	—
217	C₂²×D₄₇	—	8	4	no	—
218	C₂×C₄×C₄₇	—	2	4	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	4	2	no	—
221	C₂×C₄×C₄₇	—	8	2	no	—
222	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₂²⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#117	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	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
249	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
250	C₂×Dic₄₇	—	2	4	no	—
251	C₂×Dic₄₇	—	4	4	no	—
252	C₂×Dic₄₇	—	4	2	no	—
253	C₂×Dic₄₇	—	8	2	no	—
254	D₁₈₈	—	2	4	no	—
255	D₁₈₈	—	2	4	no	—
256	D₁₈₈	—	2	4	no	—
257	D₁₈₈	—	2	4	no	—
258	D₁₈₈	—	2	4	no	—
259	D₁₈₈	—	2	4	no	—
260	D₁₈₈	—	2	4	no	—
261	D₁₈₈	#95	1	8	yes	—
262	C₄×D₄₇	—	8	16	no	—
263	C₈×C₄₇	—	4	2	no	—
264	C₄₇⋊C₈	—	4	2	no	—
265	#10776	—	47	1	no	maximal, Sylow
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	—	4	1	no	—
273	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₄₇	#379	1	1	yes	characteristic
275	C₂²×C₄₇	#380	1	1	yes	characteristic
276	C₂²×C₄₇	#385	1	1	yes	characteristic
277	C₂²×C₄₇	#385	1	1	yes	characteristic
278	C₂²×C₄₇	#386	1	1	yes	characteristic
279	C₂²×C₄₇	#386	1	1	yes	characteristic
280	C₂×D₄₇	—	2	8	no	—
281	C₂×D₄₇	—	4	8	no	—
282	C₂×D₄₇	—	4	8	no	—
283	C₂×D₄₇	—	4	8	no	—
284	C₂×D₄₇	—	8	4	no	—
285	C₂×D₄₇	—	8	4	no	—
286	C₂×D₄₇	—	8	4	no	—
287	C₂×D₄₇	—	8	4	no	—
288	C₄×C₄₇	—	4	4	no	—
289	C₄×C₄₇	—	8	2	no	—
290	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
291	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
292	C₄×C₄₇	#380	1	1	yes	characteristic
293	C₄×C₄₇	#381	1	1	yes	characteristic
294	C₄×C₄₇	#385	1	1	yes	characteristic
295	C₄×C₄₇	#385	1	1	yes	characteristic
296	C₄×C₄₇	#386	1	1	yes	characteristic
297	C₄×C₄₇	#386	1	1	yes	characteristic
298	Dic₄₇	—	4	4	no	—
299	Dic₄₇	—	8	2	no	—
300	C₂×#518	—	47	1	no	—
301	C₂×#418	—	47	1	no	—
302	C₂×#418	—	47	1	no	—
303	#1742	—	47	1	no	—
304	#1740	—	47	1	no	—
305	#1733	—	47	1	no	—
306	#1733	D₄₇	1	1	yes	characteristic, complemented
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	1	no	—
313	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
314	C₂×C₄₇	#1795	1	2	yes	—
315	D₄₇	—	4	8	no	—
316	C₂³×D₄	—	47	1	no	—
317	C₂²×M₁₆	—	47	1	no	—
318	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
319	#518	—	94	2	no	—
320	#518	—	94	2	no	—
321	#518	—	94	2	no	—
322	#518	—	94	2	no	—
323	C₂×C₄×D₄	—	47	4	no	—
324	C₂×C₄×D₄	—	94	2	no	—
325	C₂×#117	—	47	1	no	—
326	C₂×#117	—	47	1	no	—
327	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
328	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	—	94	2	no	—
330	#418	—	47	4	no	—
331	#418	—	47	4	no	—
332	#418	—	94	2	no	—
333	#418	—	94	2	no	—
334	C₂×#102	—	94	2	no	—
335	C₂×#102	—	94	2	no	—
336	#343	—	94	2	no	—
337	#342	—	94	2	no	—
338	#339	—	2	2	no	—
339	#339	—	94	2	no	—
340	C₄₇	#10776	1	1	yes	characteristic, complemented, Sylow
341	C₂⁵	—	94	1	no	—
342	C₂²×D₄	—	47	2	no	—
343	C₂²×D₄	—	47	2	no	—
344	C₂²×D₄	—	47	2	no	—
345	C₂²×D₄	—	47	2	no	—
346	C₂²×D₄	—	47	2	no	—
347	C₂²×D₄	—	47	2	no	—
348	C₂²×D₄	—	47	2	no	—
349	C₂²×D₄	—	94	1	no	—
350	C₂²×D₄	—	94	1	no	—
351	C₂²×D₄	—	94	1	no	—
352	C₂²×D₄	—	94	1	no	—
353	C₂²×D₄	—	94	1	no	—
354	C₂²×D₄	—	94	1	no	—
355	C₂²×D₄	—	94	1	no	—
356	C₂³×C₄	—	94	4	no	—
357	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	47	2	no	—
364	C₂×M₁₆	—	94	1	no	—
365	C₂×M₁₆	—	94	1	no	—
366	C₂×M₁₆	—	94	1	no	—
367	C₂×M₁₆	—	94	1	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂×M₁₆	C₄×D₄₇	1	2	yes	complemented
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	94	1	no	—
372	C₄×D₄	—	94	8	no	—
373	C₄×D₄	—	94	8	no	—
374	C₄×D₄	—	94	8	no	—
375	C₄×D₄	—	94	8	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	47	2	no	—
382	#117	—	94	1	no	—
383	#117	—	94	1	no	—
384	#117	—	94	1	no	—
385	#117	—	94	1	no	—
386	#117	—	94	1	no	—
387	#117	—	94	1	no	—
388	#117	—	94	1	no	—
389	#117	C₄×D₄₇	1	2	yes	complemented
390	#117	D₁₈₈	1	2	yes	—
391	#117	C₂²⋊D₄₇	1	2	yes	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	47	2	no	—
394	C₂×C₄⋊C₄	—	94	1	no	—
395	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	47	2	no	—
399	C₂×C₂²⋊C₄	—	94	8	no	—
400	C₂×C₂²⋊C₄	—	94	8	no	—
401	C₂×C₂²⋊C₄	—	94	4	no	—
402	C₂×C₂²⋊C₄	—	94	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	47	2	no	—
406	C₂×C₄²	—	94	1	no	—
407	#102	—	94	8	no	—
408	#102	—	94	8	no	—
409	C₂⁴	—	94	2	no	—
410	C₂⁴	—	94	2	no	—
411	C₂⁴	—	94	2	no	—
412	C₂⁴	—	94	2	no	—
413	C₂⁴	—	94	2	no	—
414	C₂⁴	—	94	2	no	—
415	C₂⁴	—	94	2	no	—
416	C₂⁴	—	376	4	no	—
417	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
418	C₂×D₄	—	47	4	no	—
419	C₂×D₄	—	47	4	no	—
420	C₂×D₄	—	47	4	no	—
421	C₂×D₄	—	47	4	no	—
422	C₂×D₄	—	47	4	no	—
423	C₂×D₄	—	47	4	no	—
424	C₂×D₄	—	47	4	no	—
425	C₂×D₄	—	94	2	no	—
426	C₂×D₄	—	94	2	no	—
427	C₂×D₄	—	94	2	no	—
428	C₂×D₄	—	94	2	no	—
429	C₂×D₄	—	94	2	no	—
430	C₂×D₄	—	94	2	no	—
431	C₂×D₄	—	94	2	no	—
432	C₂×D₄	—	94	2	no	—
433	C₂×D₄	—	94	2	no	—
434	C₂×D₄	—	94	2	no	—
435	C₂×D₄	—	94	2	no	—
436	C₂×D₄	—	94	2	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	2	no	—
439	C₂×D₄	—	94	2	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	2	no	—
442	C₂×D₄	—	94	2	no	—
443	C₂×D₄	—	94	2	no	—
444	C₂×D₄	—	94	2	no	—
445	C₂×D₄	—	94	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	47	4	no	—
449	C₂²×C₄	—	94	16	no	—
450	C₂²×C₄	—	376	8	no	—
451	C₂²×C₄	—	188	1	no	—
452	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
456	C₂²×C₄	#10625350	1	1	yes	characteristic
457	C₂²×C₄	#10625350	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	#10625352	1	1	yes	characteristic
463	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
464	C₂²×C₄	#10625354	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	94	2	no	—
471	M₁₆	—	94	2	no	—
472	M₁₆	—	188	1	no	—
473	M₁₆	—	188	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	94	2	no	—
478	C₂×C₈	—	188	1	no	—
479	C₂×C₈	—	188	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	94	2	no	—
484	C₄⋊C₄	—	94	2	no	—
485	C₄⋊C₄	—	94	2	no	—
486	C₄⋊C₄	—	188	1	no	—
487	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	94	16	no	—
493	C₂²⋊C₄	—	94	2	no	—
494	C₂²⋊C₄	—	94	2	no	—
495	C₂²⋊C₄	—	94	2	no	—
496	C₂²⋊C₄	—	188	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	94	2	no	—
502	C₄²	—	94	2	no	—
503	C₄²	—	94	2	no	—
504	C₄²	—	188	1	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	94	4	no	—
507	C₂³	—	94	4	no	—
508	C₂³	—	94	4	no	—
509	C₂³	—	94	4	no	—
510	C₂³	—	94	4	no	—
511	C₂³	—	94	4	no	—
512	C₂³	—	94	4	no	—
513	C₂³	—	376	4	no	—
514	C₂³	—	376	4	no	—
515	C₂³	—	376	4	no	—
516	C₂³	—	376	4	no	—
517	C₂³	—	376	4	no	—
518	C₂³	—	376	4	no	—
519	C₂³	—	188	8	no	—
520	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
521	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
522	C₂³	#13093986	1	1	yes	characteristic
523	C₂³	#13093992	1	1	yes	characteristic
524	C₂³	#13093994	1	1	yes	characteristic
525	C₂³	#13093997	1	1	yes	characteristic
526	C₂³	#13094002	1	1	yes	characteristic
527	D₄	—	47	8	no	—
528	D₄	—	94	4	no	—
529	D₄	—	94	4	no	—
530	D₄	—	94	4	no	—
531	D₄	—	94	4	no	—
532	D₄	—	94	4	no	—
533	D₄	—	94	4	no	—
534	D₄	—	94	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	94	4	no	—
540	C₂×C₄	—	376	16	no	—
541	C₂×C₄	—	376	2	no	—
542	C₂×C₄	—	188	2	no	—
543	C₂×C₄	—	188	4	no	—
544	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
546	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
549	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
551	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	#13093981	1	1	yes	characteristic
553	C₂×C₄	#13093982	1	1	yes	characteristic
554	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
555	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
556	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
557	C₂×C₄	#13093986	1	1	yes	characteristic
558	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
559	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
560	C₂×C₄	#13093992	1	1	yes	characteristic
561	C₂×C₄	#13093994	1	1	yes	characteristic
562	C₂×C₄	#13093995	1	1	yes	characteristic
563	C₂×C₄	#13093997	1	1	yes	characteristic
564	C₂×C₄	#13093999	1	1	yes	characteristic
565	C₂×C₄	#13094000	1	1	yes	characteristic
566	C₂×C₄	#13094002	1	1	yes	characteristic
567	C₂×C₄	#13094004	1	1	yes	characteristic
568	C₂×C₄	#13094006	1	1	yes	characteristic
569	C₂×C₄	#13094006	1	1	yes	characteristic
570	C₂×C₄	#13094009	1	1	yes	characteristic
571	C₂×C₄	#13094009	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	188	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	94	8	no	—
582	C₂²	—	376	4	no	—
583	C₂²	—	376	4	no	—
584	C₂²	—	376	4	no	—
585	C₂²	—	376	4	no	—
586	C₂²	—	188	8	no	—
587	C₂²	—	188	8	no	—
588	C₂²	—	188	8	no	—
589	C₂²	#15688970	1	1	yes	characteristic
590	C₂²	#15688978	1	1	yes	characteristic
591	C₂²	#15688982	1	1	yes	characteristic
592	C₂²	#15688994	1	1	yes	characteristic
593	C₂²	#15688997	1	1	yes	characteristic
594	C₂²	#15688999	1	1	yes	characteristic
595	C₂²	#15689001	1	1	yes	characteristic
596	C₄	—	4	4	no	—
597	C₄	—	8	2	no	—
598	C₄	—	376	2	no	—
599	C₄	—	188	4	no	—
600	C₄	#95×D₄₇	1	1	yes	characteristic
601	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
602	C₄	#15688980	1	1	yes	characteristic
603	C₄	#15688985	1	1	yes	characteristic
604	C₄	#15688994	1	1	yes	characteristic
605	C₄	#15688997	1	1	yes	characteristic
606	C₄	#15688999	1	1	yes	characteristic
607	C₄	#15689001	1	1	yes	characteristic
608	C₂	—	2	1	no	—
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	188	8	no	—
615	C₂	(C₂×D₄₇)⋊#95	1	1	yes	characteristic
616	C₂	#20243357	1	2	yes	—

	subgroup	G/H
center	C₂²	#15688978
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#1733	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂³×D₁₈₈	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#1733	D₄₇
hypocenter	C₄₇	#10776
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
4. #20243126	C₂	semidirect
5. #20243120	C₂	semidirect
6. #20243097	C₂	semidirect
7. C₄₇×#1733	C₂	semidirect
15. C₂×#13093986	C₄	semidirect
20. #15689129	C₄	semidirect
22. #15689127	C₄	semidirect
53. C₂×#10625329	C₂×C₄	semidirect
66. #13093983	C₂×C₄	semidirect
84. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
91. #117×C₄₇	C₂×C₄	semidirect
306. #1733	D₄₇	semidirect
340. C₄₇	#10776	semidirect
369. C₂×M₁₆	C₄×D₄₇	semidirect
389. #117	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689597	2
C₂×#15689129	2
C₂×#15689127	2
#20243126	2
#20243120	2
#20243097	2
C₄₇×#1733	2
#10776	47