Subgroups — #26376448

Order 12032.

2914 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246361	C₂	1	2	yes	maximal, complemented
2	#20246328	C₂	1	4	yes	maximal, complemented
3	#20246298	C₂	1	2	yes	maximal, complemented
4	#20246257	C₂	1	2	yes	maximal, complemented
5	#20246237	C₂	1	4	yes	maximal, complemented
6	D₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
7	#20246031	C₂	1	2	yes	maximal, complemented
8	#20246021	C₂	1	4	yes	maximal, complemented
9	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245771	C₂	1	2	yes	maximal, complemented
12	C₂×#15688986	C₂	1	2	yes	maximal, complemented
13	#20245749	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×#13093983	C₂²	1	4	yes	—
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
18	#15689026	C₂²	1	4	yes	—
19	#15689022	C₂²	1	4	yes	complemented
20	#15689016	C₂²	1	8	yes	complemented
21	#15689016	C₂²	1	8	yes	complemented
22	#15689009	C₂²	1	8	yes	complemented
23	#15689003	C₂²	1	8	yes	—
24	#15688998	C₂²	1	8	yes	complemented
25	#15688991	C₂²	1	2	yes	complemented
26	#15688991	C₂²	1	2	yes	complemented
27	#15688989	C₂²	1	2	yes	complemented
28	#15688989	C₂²	1	2	yes	complemented
29	#15688986	C₂²	1	1	yes	characteristic
30	#15688986	C₂²	1	2	yes	—
31	#15688986	C₂²	1	4	yes	—
32	#15688986	C₂²	1	1	yes	characteristic
33	#15688986	C₂²	1	4	yes	complemented
34	#15688986	C₂²	1	4	yes	complemented
35	#15688983	C₂²	1	2	yes	—
36	#15688983	C₂²	1	2	yes	—
37	#15688983	C₂²	1	4	yes	complemented
38	#15688983	C₂²	1	4	yes	complemented
39	#15688979	C₂²	1	4	yes	—
40	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	complemented
41	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
42	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
44	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
45	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
46	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
47	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	complemented
48	#15688969	C₂²	1	2	yes	complemented
49	#15688969	C₂²	1	2	yes	complemented
50	C₂×C₄₇⋊#95	C₂²	1	4	yes	complemented
51	C₂×C₄₇⋊#95	C₂²	1	4	yes	complemented
52	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
53	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
54	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
55	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
58	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
62	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
63	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
64	C₂³×Dic₄₇	C₂³	1	8	yes	—
65	D₄×Dic₄₇	—	2	16	no	—
66	#13093983	—	4	8	no	—
67	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
70	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
71	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
75	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
76	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
80	C₄₇⋊#95	C₂³	1	2	yes	—
81	C₄₇⋊#95	C₂³	1	2	yes	—
82	C₄₇⋊#95	C₂³	1	4	yes	—
83	C₄₇⋊#95	C₂³	1	4	yes	—
84	C₄₇⋊#95	C₂³	1	8	yes	—
85	C₄₇⋊#95	C₂³	1	8	yes	—
86	C₄₇⋊#95	C₂³	1	2	yes	—
87	C₄₇⋊#95	C₂³	1	4	yes	—
88	C₄₇⋊#95	C₂³	1	4	yes	—
89	C₄₇⋊#95	C₂³	1	4	yes	—
90	C₄₇⋊#95	C₂³	1	4	yes	—
91	C₄₇⋊#95	C₂³	1	2	yes	—
92	C₂⁵×C₄₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₇	—	2	8	no	—
94	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
95	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₇	—	4	8	no	—
99	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
103	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
104	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
108	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
109	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
110	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
111	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
112	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
113	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
114	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
123	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
124	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂⁴×C₄₇	—	2	8	no	—
129	C₂⁴×C₄₇	—	2	8	no	—
130	C₂⁴×C₄₇	—	4	4	no	—
131	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
132	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
133	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
134	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₄₇	—	2	8	no	—
136	C₂×D₄×C₄₇	—	2	32	no	—
137	C₂×D₄×C₄₇	—	2	4	no	—
138	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
139	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
140	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
141	C₂×D₄×C₄₇	#41	1	8	yes	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	8	no	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	4	32	no	—
146	C₂²×C₄×C₄₇	—	4	4	no	—
147	C₂²×C₄×C₄₇	—	4	4	no	—
148	C₂²×C₄×C₄₇	—	4	4	no	—
149	C₂²×C₄×C₄₇	—	4	4	no	—
150	C₂²×C₄×C₄₇	—	4	2	no	—
151	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
153	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
154	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
157	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
159	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂²×Dic₄₇	—	2	16	no	—
168	C₂²×Dic₄₇	—	4	8	no	—
169	C₂²×Dic₄₇	—	4	8	no	—
170	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
171	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
172	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
173	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
174	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
175	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
176	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
177	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
178	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
179	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
180	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
181	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
182	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
183	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
184	C₂²⋊Dic₄₇	—	2	16	no	—
185	C₂²⋊Dic₄₇	—	2	4	no	—
186	C₂²⋊Dic₄₇	—	2	8	no	—
187	C₂²⋊Dic₄₇	—	2	4	no	—
188	C₂²⋊Dic₄₇	—	4	8	no	—
189	C₂²⋊Dic₄₇	—	4	8	no	—
190	C₄⋊Dic₄₇	—	2	8	no	—
191	C₄⋊Dic₄₇	—	4	4	no	—
192	C₄⋊Dic₄₇	—	4	8	no	—
193	C₄×Dic₄₇	—	2	8	no	—
194	C₄×Dic₄₇	—	4	4	no	—
195	C₄×Dic₄₇	—	4	8	no	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	4	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	16	no	—
201	C₂³×C₄₇	—	2	16	no	—
202	C₂³×C₄₇	—	2	4	no	—
203	C₂³×C₄₇	—	2	4	no	—
204	C₂³×C₄₇	—	2	4	no	—
205	C₂³×C₄₇	—	4	8	no	—
206	C₂³×C₄₇	—	4	32	no	—
207	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
208	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
209	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
210	C₂³×C₄₇	C₂×#41	1	8	yes	—
211	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
212	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
213	D₄×C₄₇	—	2	16	no	—
214	D₄×C₄₇	—	2	8	no	—
215	D₄×C₄₇	#117	1	16	yes	complemented
216	C₂×C₄×C₄₇	—	2	8	no	—
217	C₂×C₄×C₄₇	—	2	16	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	4	no	—
220	C₂×C₄×C₄₇	—	2	4	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	8	no	—
226	C₂×C₄×C₄₇	—	4	8	no	—
227	C₂×C₄×C₄₇	—	4	8	no	—
228	C₂×C₄×C₄₇	—	4	8	no	—
229	C₂×C₄×C₄₇	—	4	8	no	—
230	C₂×C₄×C₄₇	—	4	4	no	—
231	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
233	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
235	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
236	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
237	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
238	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
239	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
240	C₂×Dic₄₇	—	2	4	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	2	8	no	—
243	C₂×Dic₄₇	—	2	4	no	—
244	C₂×Dic₄₇	—	2	8	no	—
245	C₂×Dic₄₇	—	2	4	no	—
246	C₂×Dic₄₇	—	2	8	no	—
247	C₂×Dic₄₇	—	2	4	no	—
248	C₂×Dic₄₇	—	2	4	no	—
249	C₂×Dic₄₇	—	8	16	no	—
250	#34190	—	47	1	no	maximal, Sylow
251	C₂²×C₄₇	—	2	2	no	—
252	C₂²×C₄₇	—	2	4	no	—
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	4	no	—
255	C₂²×C₄₇	—	2	16	no	—
256	C₂²×C₄₇	—	2	8	no	—
257	C₂²×C₄₇	—	2	4	no	—
258	C₂²×C₄₇	—	2	4	no	—
259	C₂²×C₄₇	—	2	4	no	—
260	C₂²×C₄₇	—	4	32	no	—
261	C₂²×C₄₇	—	4	8	no	—
262	C₂²×C₄₇	C₂×#117	1	8	yes	—
263	C₂²×C₄₇	#518	1	4	yes	—
264	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
265	C₂²×C₄₇	C₂²×#41	1	2	yes	—
266	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
267	C₂²×C₄₇	#585	1	2	yes	—
268	C₄×C₄₇	—	2	2	no	—
269	C₄×C₄₇	—	2	2	no	—
270	C₄×C₄₇	—	2	2	no	—
271	C₄×C₄₇	—	2	4	no	—
272	C₄×C₄₇	—	2	4	no	—
273	C₄×C₄₇	—	2	2	no	—
274	C₄×C₄₇	—	2	2	no	—
275	C₄×C₄₇	C₂×#117	1	4	yes	—
276	Dic₄₇	—	4	4	no	—
277	Dic₄₇	—	4	8	no	—
278	Dic₄₇	—	4	4	no	—
279	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
280	#2357	—	47	2	no	—
281	#2353	—	47	4	no	—
282	#2349	—	47	2	no	—
283	#2344	—	47	2	no	—
284	#2342	—	47	4	no	—
285	D₄×C₂²⋊C₄	—	47	2	no	—
286	#2319	—	47	2	no	—
287	#2318	—	47	4	no	—
288	#2283	—	47	1	no	—
289	#2283	—	47	1	no	—
290	#2280	—	47	2	no	—
291	C₂×#381	—	47	2	no	—
292	#2275	—	47	2	no	—
293	C₂×C₄₇	—	2	4	no	—
294	C₂×C₄₇	—	2	8	no	—
295	C₂×C₄₇	—	4	4	no	—
296	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
297	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
298	C₂×C₄₇	#3428	1	1	yes	characteristic
299	C₂×C₄₇	#3513	1	4	yes	—
300	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
301	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
302	C₂×C₄×D₄	—	47	4	no	—
303	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
304	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
307	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
309	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
310	C₂×#117	—	47	4	no	—
311	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	—	47	4	no	—
313	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
314	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
315	#390	—	47	4	no	—
316	#389	—	47	4	no	—
317	#388	—	47	8	no	—
318	#388	—	47	8	no	—
319	#387	—	47	8	no	—
320	#386	—	47	8	no	—
321	#385	—	47	8	no	—
322	#383	—	47	2	no	—
323	#383	—	47	2	no	—
324	#382	—	47	2	no	—
325	#382	—	47	2	no	—
326	#381	—	47	4	no	—
327	#381	—	47	4	no	—
328	#381	—	47	1	no	—
329	#381	—	47	2	no	—
330	#381	—	47	1	no	—
331	#381	—	47	4	no	—
332	#380	—	47	4	no	—
333	#380	—	47	2	no	—
334	#380	—	47	2	no	—
335	#380	—	47	4	no	—
336	#379	—	47	4	no	—
337	C₄×C₄⋊C₄	—	47	4	no	—
338	C₄×C₄⋊C₄	—	47	2	no	—
339	C₄×C₄⋊C₄	—	47	2	no	—
340	C₄×C₂²⋊C₄	—	47	2	no	—
341	C₄×C₂²⋊C₄	—	47	2	no	—
342	C₄×C₂²⋊C₄	—	47	4	no	—
343	C₄×C₂²⋊C₄	—	47	4	no	—
344	C₄×C₂²⋊C₄	—	47	8	no	—
345	#376	—	47	2	no	—
346	#376	—	47	2	no	—
347	C₂×#95	—	47	4	no	—
348	C₂×#95	—	47	4	no	—
349	C₄₇	#34190	1	1	yes	characteristic, complemented, Sylow
350	C₂⁵	C₂²×D₄₇	1	2	yes	—
351	C₂²×D₄	—	2	8	no	—
352	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
353	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
354	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂³×C₄	—	4	8	no	—
357	C₂³×C₄	—	47	8	no	—
358	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
359	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
360	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
361	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
362	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
363	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
364	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
365	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
366	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
367	C₄×D₄	—	94	16	no	—
368	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
369	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
370	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
371	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
372	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
373	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
374	#117	—	188	8	no	—
375	C₂×C₄⋊C₄	—	47	4	no	—
376	C₂×C₄⋊C₄	—	47	8	no	—
377	C₂×C₄⋊C₄	—	47	4	no	—
378	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
379	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
381	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	47	2	no	—
383	C₂×C₂²⋊C₄	—	47	4	no	—
384	C₂×C₂²⋊C₄	—	47	2	no	—
385	C₂×C₂²⋊C₄	—	47	8	no	—
386	C₂×C₂²⋊C₄	—	47	8	no	—
387	C₂×C₂²⋊C₄	—	47	8	no	—
388	C₂×C₂²⋊C₄	—	188	8	no	—
389	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
390	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
394	C₂×C₄²	—	47	4	no	—
395	C₂×C₄²	—	47	8	no	—
396	C₂×C₄²	—	47	4	no	—
397	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
398	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
399	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
402	#95	—	47	2	no	—
403	#95	—	47	2	no	—
404	#95	—	47	4	no	—
405	#95	—	47	4	no	—
406	#95	—	47	8	no	—
407	#95	—	47	8	no	—
408	#95	—	47	2	no	—
409	#95	—	47	4	no	—
410	#95	—	47	4	no	—
411	#95	—	47	2	no	—
412	#95	—	47	4	no	—
413	#95	—	47	4	no	—
414	C₂⁴	—	2	8	no	—
415	C₂⁴	—	2	8	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
418	C₂⁴	C₂³×D₄₇	1	2	yes	—
419	C₂⁴	C₂³×D₄₇	1	2	yes	—
420	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	32	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	#10625350	1	8	yes	—
425	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
426	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
427	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	4	32	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	47	4	no	—
438	C₂²×C₄	—	47	8	no	—
439	C₂²×C₄	—	47	4	no	—
440	C₂²×C₄	—	94	16	no	—
441	C₂²×C₄	—	188	8	no	—
442	C₂²×C₄	—	188	8	no	—
443	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
444	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
445	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
446	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
447	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
448	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
449	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
450	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
451	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
456	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
458	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
459	C₄⋊C₄	—	94	8	no	—
460	C₄⋊C₄	—	188	4	no	—
461	C₄⋊C₄	—	188	8	no	—
462	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
463	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
464	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
465	C₂²⋊C₄	—	94	16	no	—
466	C₂²⋊C₄	—	94	4	no	—
467	C₂²⋊C₄	—	94	8	no	—
468	C₂²⋊C₄	—	94	4	no	—
469	C₂²⋊C₄	—	188	8	no	—
470	C₂²⋊C₄	—	188	8	no	—
471	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
472	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
473	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
474	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
475	C₄²	—	94	8	no	—
476	C₄²	—	188	4	no	—
477	C₄²	—	188	8	no	—
478	C₄²	C₂²×Dic₄₇	1	4	yes	—
479	C₄²	C₂²×Dic₄₇	1	4	yes	—
480	C₄²	C₂²×Dic₄₇	1	4	yes	—
481	C₄²	C₂²×Dic₄₇	1	4	yes	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	16	no	—
487	C₂³	—	2	16	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	4	8	no	—
492	C₂³	—	4	32	no	—
493	C₂³	C₂³×Dic₄₇	1	4	yes	—
494	C₂³	C₂³×Dic₄₇	1	4	yes	—
495	C₂³	C₂³×Dic₄₇	1	2	yes	—
496	C₂³	C₂×#10625350	1	8	yes	—
497	C₂³	#13094069	1	4	yes	—
498	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
499	D₄	—	2	16	no	—
500	D₄	—	2	8	no	—
501	D₄	#13093983	1	16	yes	complemented
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	16	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	94	4	no	—
518	C₂×C₄	—	94	4	no	—
519	C₂×C₄	—	94	8	no	—
520	C₂×C₄	—	94	4	no	—
521	C₂×C₄	—	94	8	no	—
522	C₂×C₄	—	94	4	no	—
523	C₂×C₄	—	94	8	no	—
524	C₂×C₄	—	94	4	no	—
525	C₂×C₄	—	94	4	no	—
526	C₂×C₄	—	376	16	no	—
527	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
528	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
529	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
530	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
531	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
532	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
533	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
534	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
535	C₂×C₄	C₂×#10625350	1	4	yes	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	16	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	4	32	no	—
546	C₂²	—	4	8	no	—
547	C₂²	C₂×#13093983	1	8	yes	—
548	C₂²	#15689598	1	4	yes	—
549	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
550	C₂²	C₂²×#10625350	1	2	yes	—
551	C₂²	C₂×#13094069	1	2	yes	—
552	C₂²	#15689959	1	2	yes	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	188	4	no	—
561	C₄	—	188	8	no	—
562	C₄	—	188	4	no	—
563	C₄	C₂×#13093983	1	4	yes	—
564	C₂	—	2	4	no	—
565	C₂	—	2	8	no	—
566	C₂	—	4	4	no	—
567	C₂	C₂²×#13093983	1	1	yes	characteristic
568	C₂	C₂×#15689598	1	1	yes	characteristic
569	C₂	#20256591	1	1	yes	characteristic
570	C₂	#20257328	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	#34190
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20246361	C₂	semidirect
2. #20246328	C₂	semidirect
3. #20246298	C₂	semidirect
4. #20246257	C₂	semidirect
5. #20246237	C₂	semidirect
7. #20246031	C₂	semidirect
8. #20246021	C₂	semidirect
9. #20245786	C₂	semidirect
10. #20245786	C₂	semidirect
11. #20245771	C₂	semidirect
12. C₂×#15688986	C₂	semidirect
13. #20245749	C₂	semidirect
19. #15689022	C₂²	semidirect
20. #15689016	C₂²	semidirect
21. #15689016	C₂²	semidirect
22. #15689009	C₂²	semidirect
24. #15688998	C₂²	semidirect
25. #15688991	C₂²	semidirect
26. #15688991	C₂²	semidirect
27. #15688989	C₂²	semidirect
28. #15688989	C₂²	semidirect
33. #15688986	C₂²	semidirect
34. #15688986	C₂²	semidirect
37. #15688983	C₂²	semidirect
38. #15688983	C₂²	semidirect
40. C₄⋊C₄×Dic₄₇	C₂²	semidirect
41. C₄×C₄⋊Dic₄₇	C₂²	semidirect
42. C₄×C₄⋊Dic₄₇	C₂²	semidirect
43. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
46. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
47. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
48. #15688969	C₂²	semidirect
49. #15688969	C₂²	semidirect
50. C₂×C₄₇⋊#95	C₂²	semidirect
51. C₂×C₄₇⋊#95	C₂²	semidirect
54. C₂×C₄×D₄×C₄₇	C₄	semidirect
99. C₂³×C₄×C₄₇	C₂×C₄	semidirect
110. C₄×D₄×C₄₇	C₂×C₄	semidirect
111. C₄×D₄×C₄₇	C₂×C₄	semidirect
112. C₄×D₄×C₄₇	C₂×C₄	semidirect
113. C₄×D₄×C₄₇	C₂×C₄	semidirect
114. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
118. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
123. C₂×C₄²×C₄₇	C₂×C₄	semidirect
215. D₄×C₄₇	#117	semidirect
303. C₂×C₄×D₄	Dic₄₇	semidirect
349. C₄₇	#34190	semidirect
358. C₂³×C₄	C₂×Dic₄₇	semidirect
370. C₄×D₄	C₂×Dic₄₇	semidirect
371. C₄×D₄	C₂×Dic₄₇	semidirect
372. C₄×D₄	C₂×Dic₄₇	semidirect
373. C₄×D₄	C₂×Dic₄₇	semidirect
378. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
389. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
397. C₂×C₄²	C₂×Dic₄₇	semidirect
501. D₄	#13093983	semidirect

Maximal subgroups

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

subgroup	index
#20246361	2
#20246328	2
#20246298	2
#20246257	2
#20246237	2
D₄×C₂²⋊Dic₄₇	2
#20246031	2
#20246021	2
#20245786	2
#20245771	2
C₂×#15688986	2
#20245749	2
C₂²×C₄×D₄×C₄₇	2
#34190	47