Subgroups — #26215821

Order 12032.

1482 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689140	C₂	1	2	yes	maximal
3	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243408	C₂	1	8	yes	maximal, complemented
5	#20243097	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂×#13093983	C₂²	1	2	yes	—
9	#15689147	—	2	1	no	—
10	#15689147	—	2	1	no	—
11	#15689147	C₂²	1	4	yes	complemented
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
13	#15689140	—	2	8	no	—
14	C₂×#13093951	C₂²	1	8	yes	—
15	#15688993	—	2	1	no	—
16	#15688989	—	2	1	no	—
17	#15688983	—	2	2	no	—
18	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
19	#15688882	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₄×#41×C₄₇	—	2	1	no	—
22	C₄×#41×C₄₇	—	2	1	no	—
23	C₄×#41×C₄₇	—	2	2	no	—
24	C₄×#41×C₄₇	C₄	1	2	yes	complemented
25	C₄×#41×C₄₇	C₄	1	2	yes	complemented
26	C₄×#41×C₄₇	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	complemented
28	C₂×C₄×D₄×C₄₇	—	2	2	no	—
29	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
30	C₂×#117×C₄₇	—	2	1	no	—
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	—	2	1	no	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	4	no	—
36	C₂×#10625329	—	2	4	no	—
37	C₂×#10625329	C₂³	1	4	yes	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	#13093983	—	2	4	no	—
40	#13093983	—	2	4	no	—
41	C₂×C₄⋊Dic₄₇	—	2	4	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
45	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
47	#13093951	—	2	16	no	—
48	C₄₇⋊#95	—	2	4	no	—
49	C₂×#41×C₄₇	—	2	1	no	—
50	C₂×#41×C₄₇	—	2	1	no	—
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×#41×C₄₇	D₄	1	4	yes	—
55	C₂×#41×C₄₇	Q₈	1	4	yes	—
56	C₂×#41×C₄₇	C₂³	1	2	yes	—
57	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₇	—	2	1	no	—
59	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	—	2	1	no	—
61	C₂³×C₄×C₄₇	—	2	2	no	—
62	C₂³×C₄×C₄₇	D₄	1	2	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₄₇	—	2	2	no	—
65	C₄×Q₈×C₄₇	—	2	2	no	—
66	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
68	C₄×D₄×C₄₇	—	2	4	no	—
69	C₄×D₄×C₄₇	—	2	4	no	—
70	C₄×D₄×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
76	#117×C₄₇	—	2	1	no	—
77	#117×C₄₇	—	2	1	no	—
78	#117×C₄₇	—	2	2	no	—
79	#117×C₄₇	—	2	2	no	—
80	#117×C₄₇	—	2	4	no	—
81	#117×C₄₇	C₂×C₄	1	2	yes	—
82	#117×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	—	2	4	no	—
92	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	2	yes	—
100	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
103	#41×C₄₇	—	2	4	no	—
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	2	4	no	—
106	#41×C₄₇	—	2	4	no	—
107	#41×C₄₇	—	2	4	no	—
108	#41×C₄₇	—	2	2	no	—
109	#41×C₄₇	—	2	2	no	—
110	#41×C₄₇	C₄⋊C₄	1	8	yes	complemented
111	#41×C₄₇	C₂×D₄	1	4	yes	—
112	#41×C₄₇	C₂×Q₈	1	4	yes	—
113	C₂×Q₈×C₄₇	—	2	1	no	—
114	C₂×Q₈×C₄₇	—	2	2	no	—
115	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
116	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	—	2	4	no	—
119	C₂×D₄×C₄₇	—	2	4	no	—
120	C₂×D₄×C₄₇	—	2	2	no	—
121	C₂×D₄×C₄₇	—	2	1	no	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	complemented
124	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	4	4	no	—
134	C₂²×C₄×C₄₇	—	4	8	no	—
135	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
138	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
148	C₂²×C₄×C₄₇	#41	1	2	yes	—
149	C₂²×C₄×C₄₇	#41	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₄₇	—	2	4	no	—
152	C₄⋊C₄×C₄₇	—	2	4	no	—
153	C₄⋊C₄×C₄₇	—	2	4	no	—
154	C₄⋊C₄×C₄₇	—	2	2	no	—
155	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
156	C₂²⋊C₄×C₄₇	—	2	2	no	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₂²⋊C₄×C₄₇	—	2	4	no	—
159	C₂²⋊C₄×C₄₇	—	2	4	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	2	4	no	—
162	C₄²×C₄₇	—	2	4	no	—
163	C₄²×C₄₇	—	2	2	no	—
164	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
169	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
170	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
171	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
172	C₄²×C₄₇	C₂×D₄	1	2	yes	—
173	C₄²×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²⋊Dic₄₇	—	4	4	no	—
175	C₄⋊Dic₄₇	—	4	8	no	—
176	C₄⋊Dic₄₇	—	4	4	no	—
177	C₄×Dic₄₇	—	2	4	no	—
178	C₄×Dic₄₇	—	2	4	no	—
179	#10625329	—	2	4	no	—
180	#10625329	—	2	4	no	—
181	#10625329	—	4	4	no	—
182	C₂×C₄₇⋊C₈	—	2	4	no	—
183	C₂×C₄₇⋊C₈	—	4	4	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	4	no	—
186	C₂³×C₄₇	—	4	2	no	—
187	C₂³×C₄₇	—	4	4	no	—
188	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₄₇	#121	1	2	yes	—
191	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₄₇	—	2	2	no	—
194	Q₈×C₄₇	—	2	4	no	—
195	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
196	D₄×C₄₇	—	2	4	no	—
197	D₄×C₄₇	—	2	4	no	—
198	D₄×C₄₇	—	2	8	no	—
199	D₄×C₄₇	—	2	2	no	—
200	D₄×C₄₇	—	2	4	no	—
201	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	8	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	8	no	—
215	C₂×C₄×C₄₇	—	4	4	no	—
216	C₂×C₄×C₄₇	—	4	8	no	—
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
225	C₂×C₄×C₄₇	#117	1	2	yes	—
226	C₂×C₄×C₄₇	#117	1	2	yes	—
227	C₂×C₄×C₄₇	#121	1	2	yes	—
228	C₂×C₄×C₄₇	#121	1	2	yes	—
229	C₂×C₄×C₄₇	#121	1	2	yes	—
230	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
232	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
233	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
239	C₂×Dic₄₇	—	4	8	no	—
240	C₂×Dic₄₇	—	4	4	no	—
241	C₄₇⋊C₈	—	4	4	no	—
242	#20654	—	47	1	no	maximal, Sylow
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	2	2	no	—
245	C₂²×C₄₇	—	2	2	no	—
246	C₂²×C₄₇	—	2	4	no	—
247	C₂²×C₄₇	—	4	2	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	4	8	no	—
250	C₂²×C₄₇	—	4	4	no	—
251	C₂²×C₄₇	#380	1	2	yes	—
252	C₂²×C₄₇	#380	1	2	yes	—
253	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
255	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	—	2	2	no	—
258	C₄×C₄₇	—	2	2	no	—
259	C₄×C₄₇	—	2	4	no	—
260	C₄×C₄₇	—	4	4	no	—
261	C₄×C₄₇	#380	1	2	yes	—
262	C₄×C₄₇	#380	1	2	yes	—
263	C₄×C₄₇	#421	1	4	yes	complemented
264	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
265	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
266	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
267	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
268	Dic₄₇	—	8	4	no	—
269	C₂×C₄×#41	D₄₇	1	1	yes	characteristic
270	C₂×#423	—	47	1	no	—
271	C₂×#421	—	47	2	no	—
272	#2285	—	47	1	no	—
273	#1806	—	47	8	no	—
274	#1733	—	47	2	no	—
275	C₂×C₄₇	—	2	1	no	—
276	C₂×C₄₇	—	2	2	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#421	1	2	yes	—
282	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
283	C₂²×M₁₆	—	47	2	no	—
284	C₄×#41	—	2	1	no	—
285	C₄×#41	—	2	1	no	—
286	C₄×#41	—	2	2	no	—
287	C₄×#41	Dic₄₇	1	2	yes	complemented
288	C₄×#41	Dic₄₇	1	2	yes	complemented
289	C₄×#41	C₂×D₄₇	1	4	yes	—
290	C₂×C₄×Q₈	Dic₄₇	1	2	yes	complemented
291	C₂×C₄×D₄	—	2	2	no	—
292	C₂×C₄×D₄	Dic₄₇	1	2	yes	complemented
293	C₂×#117	—	2	1	no	—
294	C₂×#117	—	47	2	no	—
295	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
296	C₂²×C₄²	—	2	1	no	—
297	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
298	#423	—	47	4	no	—
299	#423	—	94	1	no	—
300	#423	—	94	1	no	—
301	C₂×C₄⋊C₈	—	94	2	no	—
302	#421	—	94	8	no	—
303	C₂×#104	—	47	8	no	—
304	#384	—	94	1	no	—
305	#382	—	94	1	no	—
306	#380	—	94	2	no	—
307	C₄×C₄⋊C₄	—	47	4	no	—
308	#339	—	47	8	no	—
309	C₄₇	#20654	1	1	yes	characteristic, complemented, Sylow
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	Dic₉₄	1	4	yes	—
315	C₂×#41	D₁₈₈	1	4	yes	—
316	C₂×#41	C₂×Dic₄₇	1	2	yes	—
317	C₂×#41	C₂²×D₄₇	1	2	yes	—
318	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
319	C₂²×D₄	—	2	1	no	—
320	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
324	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×M₁₆	—	47	4	no	—
326	C₂×M₁₆	—	94	2	no	—
327	C₂×M₁₆	—	94	4	no	—
328	C₂×M₁₆	—	94	4	no	—
329	C₂²×C₈	—	94	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
333	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
341	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	—	2	4	no	—
347	#117	—	94	4	no	—
348	#117	—	94	4	no	—
349	#117	C₂×Dic₄₇	1	2	yes	—
350	#117	C₂²×D₄₇	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	94	2	no	—
353	C₂×C₄⋊C₄	—	94	4	no	—
354	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	94	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	4	no	—
363	C₂×C₄²	—	47	4	no	—
364	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
365	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
366	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
367	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
368	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
369	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
371	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
372	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
373	C₄⋊C₈	—	94	4	no	—
374	C₄⋊C₈	—	94	4	no	—
375	#104	—	94	16	no	—
376	#95	—	94	4	no	—
377	C₂⁴	—	2	1	no	—
378	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	4	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	C₄⋊Dic₄₇	1	8	yes	complemented
387	#41	C₂×Dic₉₄	1	4	yes	—
388	#41	C₂×D₁₈₈	1	4	yes	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	complemented
392	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	complemented
400	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	94	4	no	—
412	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
413	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
414	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
415	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
416	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
417	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
418	C₂²×C₄	#10625350	1	2	yes	—
419	C₂²×C₄	#10625350	1	2	yes	—
420	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
421	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
423	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
424	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
428	M₁₆	—	94	4	no	—
429	M₁₆	—	94	4	no	—
430	M₁₆	—	188	4	no	—
431	C₂×C₈	—	94	4	no	—
432	C₂×C₈	—	188	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	188	8	no	—
437	C₄⋊C₄	—	188	4	no	—
438	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	188	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	94	4	no	—
449	C₄²	—	94	4	no	—
450	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
451	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
452	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
453	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
454	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
455	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
456	C₄²	C₂²×Dic₄₇	1	2	yes	—
457	C₄²	C₂²×Dic₄₇	1	2	yes	—
458	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
459	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	4	no	—
464	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
465	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
466	C₂³	#13093998	1	2	yes	—
467	C₂³	#13094003	1	2	yes	—
468	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
469	Q₈	—	2	4	no	—
470	Q₈	—	2	2	no	—
471	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	—
472	D₄	—	2	8	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	2	no	—
477	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	188	8	no	—
494	C₂×C₄	—	188	4	no	—
495	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
496	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
497	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
498	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
499	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
500	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
501	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
502	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
503	C₂×C₄	#13093983	1	2	yes	—
504	C₂×C₄	#13093983	1	2	yes	—
505	C₂×C₄	#13093998	1	2	yes	—
506	C₂×C₄	#13093998	1	2	yes	—
507	C₂×C₄	#13093998	1	2	yes	—
508	C₂×C₄	#13094003	1	2	yes	—
509	C₂×C₄	#13094003	1	2	yes	—
510	C₂×C₄	#13094003	1	2	yes	—
511	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
514	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
515	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
516	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
517	C₈	—	188	4	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	8	no	—
525	C₂²	—	4	4	no	—
526	C₂²	#15688983	1	2	yes	—
527	C₂²	#15688983	1	2	yes	—
528	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
529	C₂²	C₂×#13093998	1	1	yes	characteristic
530	C₂²	C₂×#13094003	1	1	yes	characteristic
531	C₄	—	2	4	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	376	4	no	—
537	C₄	#15688983	1	2	yes	—
538	C₄	#15688983	1	2	yes	—
539	C₄	#15689140	1	4	yes	complemented
540	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
541	C₄	C₂×#13093983	1	1	yes	characteristic
542	C₄	C₂×#13093998	1	1	yes	characteristic
543	C₄	C₂×#13094003	1	1	yes	characteristic
544	C₂	—	2	1	no	—
545	C₂	—	2	2	no	—
546	C₂	—	2	2	no	—
547	C₂	—	2	1	no	—
548	C₂	—	4	4	no	—
549	C₂	C₂×#15688983	1	1	yes	characteristic
550	C₂	C₂×#15689140	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	#20654
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#15689147	C₂	semidirect
3. #20245795	C₂	semidirect
4. #20243408	C₂	semidirect
5. #20243097	C₂	semidirect
11. #15689147	C₂²	semidirect
18. C₄×C₄⋊Dic₄₇	C₂²	semidirect
19. #15688882	C₂²	semidirect
24. C₄×#41×C₄₇	C₄	semidirect
25. C₄×#41×C₄₇	C₄	semidirect
27. C₂×C₄×Q₈×C₄₇	C₄	semidirect
29. C₂×C₄×D₄×C₄₇	C₄	semidirect
110. #41×C₄₇	C₄⋊C₄	semidirect
115. C₂×Q₈×C₄₇	C₄⋊C₄	semidirect
123. C₂×D₄×C₄₇	C₄⋊C₄	semidirect
263. C₄×C₄₇	#421	semidirect
287. C₄×#41	Dic₄₇	semidirect
288. C₄×#41	Dic₄₇	semidirect
290. C₂×C₄×Q₈	Dic₄₇	semidirect
292. C₂×C₄×D₄	Dic₄₇	semidirect
309. C₄₇	#20654	semidirect
386. #41	C₄⋊Dic₄₇	semidirect
391. C₂×Q₈	C₄⋊Dic₄₇	semidirect
399. C₂×D₄	C₄⋊Dic₄₇	semidirect
539. C₄	#15689140	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×#15689140	2
#20245795	2
#20243408	2
#20243097	2
C₂×C₄×#41×C₄₇	2
#20654	47