Subgroups — #26183389

Order 12032.

1128 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241887	C₂	1	2	yes	maximal, complemented
4	#20241883	C₂	1	2	yes	maximal, complemented
5	#20241879	C₂	1	4	yes	maximal, complemented
6	#20241874	C₂	1	4	yes	maximal, complemented
7	C₄₇×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂×#13093983	—	2	1	no	—
9	#15689176	—	2	1	no	—
10	#15689176	—	2	1	no	—
11	#15689176	C₂²	1	2	yes	—
12	#15689176	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	—	2	1	no	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
19	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
20	#15688969	C₂²	1	2	yes	—
21	C₄²×Dic₄₇	—	2	1	no	—
22	#15688860	C₂²	1	8	yes	—
23	#15688857	C₂²	1	8	yes	—
24	C₄₇×#533	C₄	1	1	yes	characteristic, complemented
25	C₄₇×#533	C₄	1	1	yes	characteristic, complemented
26	C₄₇×#533	C₂²	1	1	yes	characteristic
27	C₄₇×#532	C₄	1	1	yes	characteristic, complemented
28	C₄₇×#532	C₄	1	1	yes	characteristic, complemented
29	C₄₇×#532	C₂²	1	1	yes	characteristic
30	C₄₇×#529	—	2	1	no	—
31	C₄₇×#529	—	2	1	no	—
32	C₄₇×#529	—	2	1	no	—
33	C₄₇×#529	—	2	1	no	—
34	C₄₇×#529	C₄	1	2	yes	complemented
35	C₄₇×#529	C₂²	1	2	yes	—
36	C₄₇×#525	—	2	1	no	—
37	C₄₇×#525	—	2	1	no	—
38	C₄₇×#525	C₂²	1	2	yes	—
39	C₄×#41×C₄₇	—	2	1	no	—
40	C₄×#41×C₄₇	—	2	1	no	—
41	C₄×#41×C₄₇	C₄	1	2	yes	complemented
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	#13093983	—	2	8	no	—
45	C₂×C₄⋊Dic₄₇	—	2	2	no	—
46	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄×Dic₄₇	—	2	2	no	—
48	C₂×C₄×Dic₄₇	—	2	2	no	—
49	C₂×C₄×Dic₄₇	—	2	2	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
54	C₄×C₄₇⋊C₈	—	2	2	no	—
55	C₄×C₄₇⋊C₈	—	2	2	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	C₂³	1	4	yes	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
67	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
68	#126×C₄₇	—	2	2	no	—
69	#126×C₄₇	—	2	2	no	—
70	#125×C₄₇	—	2	1	no	—
71	#125×C₄₇	—	2	1	no	—
72	#125×C₄₇	C₂×C₄	1	2	yes	—
73	#124×C₄₇	—	2	1	no	—
74	#124×C₄₇	—	2	1	no	—
75	#124×C₄₇	C₂×C₄	1	2	yes	—
76	#123×C₄₇	—	2	2	no	—
77	#123×C₄₇	—	2	2	no	—
78	#123×C₄₇	—	2	2	no	—
79	C₂²⋊Q₈×C₄₇	—	2	1	no	—
80	C₂²⋊Q₈×C₄₇	—	2	1	no	—
81	C₂²⋊Q₈×C₄₇	—	2	1	no	—
82	C₂²⋊Q₈×C₄₇	—	2	1	no	—
83	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	#121×C₄₇	—	2	1	no	—
88	#121×C₄₇	—	2	1	no	—
89	#121×C₄₇	C₂×C₄	1	2	yes	—
90	#121×C₄₇	C₂³	1	2	yes	—
91	#120×C₄₇	—	2	2	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	—	2	1	no	—
96	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	2	no	—
100	C₄×D₄×C₄₇	—	2	2	no	—
101	C₄×D₄×C₄₇	—	2	2	no	—
102	C₄×D₄×C₄₇	—	2	2	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	—	2	1	no	—
107	C₄×D₄×C₄₇	—	2	1	no	—
108	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
110	#117×C₄₇	—	2	1	no	—
111	#117×C₄₇	—	2	1	no	—
112	#117×C₄₇	—	2	2	no	—
113	#117×C₄₇	—	2	2	no	—
114	#117×C₄₇	—	2	2	no	—
115	#117×C₄₇	C₂×C₄	1	2	yes	—
116	C₂×C₄²×C₄₇	—	2	2	no	—
117	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	4	no	—
132	#41×C₄₇	—	4	4	no	—
133	C₂×Q₈×C₄₇	—	2	1	no	—
134	C₂×Q₈×C₄₇	—	2	1	no	—
135	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	4	2	no	—
148	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
166	C₂²×Dic₄₇	—	2	4	no	—
167	C₄⋊C₄×C₄₇	—	2	1	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×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	C₂²×C₄	1	2	yes	—
178	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₂²⋊C₄×C₄₇	—	2	2	no	—
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₄²×C₄₇	—	2	2	no	—
189	C₄²×C₄₇	—	2	2	no	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
192	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
196	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²⋊Dic₄₇	—	2	8	no	—
208	C₄⋊Dic₄₇	—	2	8	no	—
209	C₄×Dic₄₇	—	2	8	no	—
210	C₄×Dic₄₇	—	4	4	no	—
211	C₄×Dic₄₇	—	4	4	no	—
212	C₂×C₄₇⋊C₈	—	2	4	no	—
213	C₂×C₄₇⋊C₈	—	4	4	no	—
214	C₂³×C₄₇	—	2	2	no	—
215	C₂³×C₄₇	—	2	2	no	—
216	C₂³×C₄₇	—	2	2	no	—
217	C₂³×C₄₇	—	4	1	no	—
218	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₄₇	—	4	2	no	—
222	Q₈×C₄₇	—	4	2	no	—
223	Q₈×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	4	no	—
226	D₄×C₄₇	—	4	4	no	—
227	D₄×C₄₇	—	4	4	no	—
228	D₄×C₄₇	—	4	2	no	—
229	D₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	4	1	no	—
247	C₂×C₄×C₄₇	—	4	1	no	—
248	C₂×C₄×C₄₇	—	4	1	no	—
249	C₂×C₄×C₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	4	4	no	—
251	C₂×C₄×C₄₇	—	4	4	no	—
252	C₂×C₄×C₄₇	#104	1	4	yes	—
253	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	#135	1	4	yes	—
264	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×Dic₄₇	—	2	8	no	—
267	C₂×Dic₄₇	—	4	4	no	—
268	C₂×Dic₄₇	—	4	4	no	—
269	C₄₇⋊C₈	—	4	4	no	—
270	#17533	—	47	1	no	maximal, Sylow
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	1	no	—
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	4	4	no	—
279	C₂²×C₄₇	—	4	2	no	—
280	C₂²×C₄₇	—	4	2	no	—
281	C₂²×C₄₇	—	4	2	no	—
282	C₂²×C₄₇	C₂×#104	1	2	yes	—
283	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄₇	C₂×#135	1	2	yes	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	1	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	4	2	no	—
293	C₄×C₄₇	—	4	2	no	—
294	C₄×C₄₇	—	4	2	no	—
295	C₄×C₄₇	#410	1	2	yes	—
296	C₄×C₄₇	#416	1	2	yes	—
297	C₄×C₄₇	#416	1	2	yes	—
298	C₄×C₄₇	C₂×#104	1	2	yes	—
299	C₄×C₄₇	C₂×#104	1	2	yes	—
300	Dic₄₇	—	4	8	no	—
301	#3444	D₄₇	1	1	yes	characteristic
302	C₂×#431	—	47	1	no	—
303	C₄×#117	—	47	1	no	—
304	#1503	—	47	2	no	—
305	#1502	—	47	2	no	—
306	#1501	—	47	4	no	—
307	#1500	—	47	4	no	—
308	C₂×C₄₇	—	2	2	no	—
309	C₂×C₄₇	—	2	2	no	—
310	C₂×C₄₇	—	4	1	no	—
311	C₂×C₄₇	—	8	2	no	—
312	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
313	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
314	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
315	#533	Dic₄₇	1	1	yes	characteristic, complemented
316	#533	Dic₄₇	1	1	yes	characteristic, complemented
317	#533	C₂×D₄₇	1	1	yes	characteristic
318	#532	Dic₄₇	1	1	yes	characteristic, complemented
319	#532	Dic₄₇	1	1	yes	characteristic, complemented
320	#532	C₂×D₄₇	1	1	yes	characteristic
321	#529	—	2	1	no	—
322	#529	—	2	1	no	—
323	#529	—	2	1	no	—
324	#529	—	2	1	no	—
325	#529	Dic₄₇	1	2	yes	complemented
326	#529	C₂×D₄₇	1	2	yes	—
327	#525	—	2	1	no	—
328	#525	—	2	1	no	—
329	#525	C₂×D₄₇	1	2	yes	—
330	C₄×#41	—	2	1	no	—
331	C₄×#41	—	2	1	no	—
332	C₄×#41	Dic₄₇	1	2	yes	complemented
333	C₂×#117	—	94	1	no	—
334	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
335	#431	—	47	2	no	—
336	#431	—	47	2	no	—
337	#431	—	94	1	no	—
338	#431	—	94	1	no	—
339	C₂×C₄⋊C₈	—	94	1	no	—
340	C₂×C₂²⋊C₈	—	47	2	no	—
341	C₂×C₄×C₈	—	94	1	no	—
342	C₄×C₄⋊C₄	—	47	2	no	—
343	C₄×C₄⋊C₄	—	94	1	no	—
344	C₄×C₂²⋊C₄	—	47	2	no	—
345	C₄×C₂²⋊C₄	—	94	1	no	—
346	#376	—	47	2	no	—
347	C₄³	—	94	1	no	—
348	#328	—	47	8	no	—
349	#327	—	47	8	no	—
350	C₄₇	#17533	1	1	yes	characteristic, complemented, Sylow
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	C₂×Dic₄₇	1	2	yes	—
354	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
355	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₂²×C₈	—	94	2	no	—
358	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
359	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
360	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
361	#127	C₂×Dic₄₇	1	1	yes	characteristic
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#125	—	2	1	no	—
365	#125	—	2	1	no	—
366	#125	C₂×Dic₄₇	1	2	yes	—
367	#124	—	2	1	no	—
368	#124	—	2	1	no	—
369	#124	C₂×Dic₄₇	1	2	yes	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	#123	—	2	2	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
378	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	C₂×Dic₄₇	1	2	yes	—
384	#121	C₂²×D₄₇	1	2	yes	—
385	#120	—	2	2	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
391	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
403	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	2	no	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	—	94	8	no	—
410	#117	C₂×Dic₄₇	1	2	yes	—
411	C₂×C₄⋊C₄	—	94	2	no	—
412	C₂×C₂²⋊C₄	—	94	2	no	—
413	C₂×C₄²	—	2	2	no	—
414	C₂×C₄²	—	94	2	no	—
415	C₂×C₄²	—	94	2	no	—
416	C₂×C₄²	—	94	2	no	—
417	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
418	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
419	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
420	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
423	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
424	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
425	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
427	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
428	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
429	C₄⋊C₈	—	94	2	no	—
430	C₄⋊C₈	—	94	2	no	—
431	C₂²⋊C₈	—	47	4	no	—
432	C₂²⋊C₈	—	94	2	no	—
433	C₄×C₈	—	94	2	no	—
434	C₄×C₈	—	94	2	no	—
435	#95	—	47	4	no	—
436	#95	—	94	2	no	—
437	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
438	#41	—	4	4	no	—
439	#41	—	4	4	no	—
440	#41	—	4	4	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	94	4	no	—
457	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
461	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
462	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
475	C₂×C₈	—	94	4	no	—
476	C₂×C₈	—	188	4	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	94	8	no	—
488	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
489	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	94	8	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	94	8	no	—
504	C₄²	—	188	4	no	—
505	C₄²	—	188	4	no	—
506	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
507	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
508	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
509	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
510	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
511	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
512	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
513	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
514	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
515	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
516	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
517	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
518	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
519	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
520	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
521	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	4	1	no	—
526	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
527	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
528	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
529	Q₈	—	4	2	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	94	8	no	—
561	C₂×C₄	—	188	4	no	—
562	C₂×C₄	—	188	4	no	—
563	C₂×C₄	#13093951	1	4	yes	—
564	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
565	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
566	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
567	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
571	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
573	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
574	C₂×C₄	#13094044	1	4	yes	—
575	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
576	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
577	C₈	—	188	4	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	C₂×#13093951	1	2	yes	—
590	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
591	C₂²	C₂×#13094044	1	2	yes	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	188	8	no	—
603	C₄	#15689097	1	2	yes	—
604	C₄	#15689119	1	2	yes	—
605	C₄	#15689119	1	2	yes	—
606	C₄	C₂×#13093951	1	2	yes	—
607	C₄	C₂×#13093951	1	2	yes	—
608	C₂	—	2	2	no	—
609	C₂	—	2	2	no	—
610	C₂	—	4	1	no	—
611	C₂	—	8	2	no	—
612	C₂	C₂×#15689097	1	1	yes	characteristic
613	C₂	C₂×#15689119	1	1	yes	characteristic
614	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3444	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#17533
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂×#15689176	C₂	semidirect
2. C₄×#13093983	C₂	semidirect
3. #20241887	C₂	semidirect
4. #20241883	C₂	semidirect
5. #20241879	C₂	semidirect
6. #20241874	C₂	semidirect
24. C₄₇×#533	C₄	semidirect
25. C₄₇×#533	C₄	semidirect
27. C₄₇×#532	C₄	semidirect
28. C₄₇×#532	C₄	semidirect
34. C₄₇×#529	C₄	semidirect
41. C₄×#41×C₄₇	C₄	semidirect
315. #533	Dic₄₇	semidirect
316. #533	Dic₄₇	semidirect
318. #532	Dic₄₇	semidirect
319. #532	Dic₄₇	semidirect
325. #529	Dic₄₇	semidirect
332. C₄×#41	Dic₄₇	semidirect
350. C₄₇	#17533	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
C₄×#13093983	2
#20241887	2
#20241883	2
#20241879	2
#20241874	2
C₄₇×#3444	2
#17533	47