Subgroups — #26379088

Order 12032.

2954 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246545	C₂	1	4	yes	maximal, complemented
2	#20246430	C₂	1	4	yes	maximal, complemented
3	#20246257	C₂	1	2	yes	maximal, complemented
4	#20246237	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
6	#20246155	C₂	1	4	yes	maximal, complemented
7	#20246083	C₂	1	4	yes	maximal, complemented
8	#20245970	C₂	1	2	yes	maximal, complemented
9	#20245966	C₂	1	2	yes	maximal, complemented
10	#20245771	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂×D₄×Dic₄₇	C₂²	1	4	yes	complemented
14	C₂×#13093983	C₂²	1	4	yes	—
15	C₂×#13093983	C₂²	1	2	yes	complemented
16	C₂×#13093983	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
18	#15689026	C₂²	1	8	yes	complemented
19	#15689026	C₂²	1	8	yes	complemented
20	#15689026	C₂²	1	4	yes	complemented
21	#15689022	C₂²	1	4	yes	complemented
22	#15689016	C₂²	1	8	yes	complemented
23	#15689016	C₂²	1	8	yes	complemented
24	#15689009	C₂²	1	8	yes	complemented
25	#15689003	C₂²	1	8	yes	complemented
26	#15689003	C₂²	1	8	yes	complemented
27	#15689003	C₂²	1	8	yes	complemented
28	#15688998	C₂²	1	8	yes	complemented
29	#15688986	C₂²	1	4	yes	—
30	#15688986	C₂²	1	2	yes	complemented
31	#15688986	C₂²	1	2	yes	complemented
32	#15688983	C₂²	1	2	yes	—
33	#15688983	C₂²	1	2	yes	—
34	#15688983	C₂²	1	2	yes	complemented
35	#15688983	C₂²	1	2	yes	complemented
36	#15688979	C₂²	1	1	yes	characteristic
37	#15688979	C₂²	1	2	yes	—
38	#15688979	C₂²	1	1	yes	characteristic
39	#15688979	C₂²	1	4	yes	—
40	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	complemented
41	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
42	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
43	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
44	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
46	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
48	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#121×C₄₇	C₄	1	16	yes	complemented
50	C₂×#121×C₄₇	C₂²	1	2	yes	—
51	C₂×#121×C₄₇	C₂²	1	2	yes	—
52	C₂×#121×C₄₇	C₂²	1	2	yes	—
53	C₂×#121×C₄₇	C₂²	1	2	yes	—
54	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
56	C₂³×Dic₄₇	C₂³	1	8	yes	—
57	D₄×Dic₄₇	—	4	8	no	—
58	#13093983	—	4	4	no	—
59	#13093983	—	4	4	no	—
60	#13093983	—	4	8	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
63	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
64	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
65	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
70	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
71	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
74	C₂×C₂²⋊Dic₄₇	C₂³	1	2	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	4	yes	—
81	C₄₇⋊#95	C₂³	1	4	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	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
87	C₂⁵×C₄₇	C₂³	1	2	yes	—
88	C₂²×D₄×C₄₇	—	4	4	no	—
89	C₂²×D₄×C₄₇	—	4	8	no	—
90	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
91	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
92	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
95	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
96	C₂³×C₄×C₄₇	—	4	4	no	—
97	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
98	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
102	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
105	#121×C₄₇	C₂×C₄	1	16	yes	complemented
106	#121×C₄₇	C₂×C₄	1	16	yes	complemented
107	#121×C₄₇	C₂×C₄	1	16	yes	complemented
108	#121×C₄₇	C₂×C₄	1	16	yes	complemented
109	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
113	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
115	C₂⁴×C₄₇	—	2	4	no	—
116	C₂⁴×C₄₇	—	2	8	no	—
117	C₂⁴×C₄₇	—	4	2	no	—
118	C₂⁴×C₄₇	—	4	2	no	—
119	C₂⁴×C₄₇	—	4	4	no	—
120	C₂⁴×C₄₇	—	4	4	no	—
121	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
122	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
124	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂×D₄×C₄₇	—	2	8	no	—
128	C₂×D₄×C₄₇	—	4	16	no	—
129	C₂×D₄×C₄₇	—	4	32	no	—
130	C₂×D₄×C₄₇	—	4	4	no	—
131	C₂×D₄×C₄₇	—	4	4	no	—
132	C₂×D₄×C₄₇	—	4	4	no	—
133	C₂×D₄×C₄₇	—	4	4	no	—
134	C₂×D₄×C₄₇	—	4	4	no	—
135	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
136	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
137	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
138	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
139	C₂²×C₄×C₄₇	—	2	8	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	4	16	no	—
144	C₂²×C₄×C₄₇	—	4	2	no	—
145	C₂²×C₄×C₄₇	—	4	2	no	—
146	C₂²×C₄×C₄₇	—	4	2	no	—
147	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
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	4	yes	—
154	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×Dic₄₇	—	4	8	no	—
160	C₂²×Dic₄₇	—	4	8	no	—
161	C₂²×Dic₄₇	—	4	8	no	—
162	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
163	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
164	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
165	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
166	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
167	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
168	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
169	C₂²⋊Dic₄₇	—	2	4	no	—
170	C₂²⋊Dic₄₇	—	2	8	no	—
171	C₂²⋊Dic₄₇	—	2	4	no	—
172	C₂²⋊Dic₄₇	—	4	8	no	—
173	C₂²⋊Dic₄₇	—	4	2	no	—
174	C₂²⋊Dic₄₇	—	4	8	no	—
175	C₂²⋊Dic₄₇	—	4	4	no	—
176	C₂²⋊Dic₄₇	—	4	2	no	—
177	C₂²⋊Dic₄₇	—	4	2	no	—
178	C₂²⋊Dic₄₇	—	4	2	no	—
179	C₂²⋊Dic₄₇	—	4	4	no	—
180	C₂²⋊Dic₄₇	—	4	8	no	—
181	C₄⋊Dic₄₇	—	2	8	no	—
182	C₄⋊Dic₄₇	—	4	4	no	—
183	C₄⋊Dic₄₇	—	4	8	no	—
184	C₄×Dic₄₇	—	2	8	no	—
185	C₄×Dic₄₇	—	4	8	no	—
186	C₄×Dic₄₇	—	4	4	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	—	2	2	no	—
189	C₂³×C₄₇	—	2	8	no	—
190	C₂³×C₄₇	—	2	2	no	—
191	C₂³×C₄₇	—	2	2	no	—
192	C₂³×C₄₇	—	2	4	no	—
193	C₂³×C₄₇	—	2	8	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	2	8	no	—
200	C₂³×C₄₇	—	2	16	no	—
201	C₂³×C₄₇	—	4	4	no	—
202	C₂³×C₄₇	—	4	4	no	—
203	C₂³×C₄₇	—	4	8	no	—
204	C₂³×C₄₇	—	4	8	no	—
205	C₂³×C₄₇	—	4	16	no	—
206	C₂³×C₄₇	—	8	16	no	—
207	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
208	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
209	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
210	C₂³×C₄₇	C₂³×C₄	1	2	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	—	4	8	no	—
215	D₄×C₄₇	—	4	16	no	—
216	D₄×C₄₇	—	4	16	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	2	no	—
221	C₂×C₄×C₄₇	—	2	4	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	8	no	—
224	C₂×C₄×C₄₇	—	2	8	no	—
225	C₂×C₄×C₄₇	—	2	8	no	—
226	C₂×C₄×C₄₇	—	4	4	no	—
227	C₂×C₄×C₄₇	—	4	4	no	—
228	C₂×C₄×C₄₇	—	4	4	no	—
229	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
230	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
233	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	2	4	no	—
237	C₂×Dic₄₇	—	2	4	no	—
238	C₂×Dic₄₇	—	2	8	no	—
239	C₂×Dic₄₇	—	2	8	no	—
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	—	8	16	no	—
245	#34363	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	8	no	—
249	C₂²×C₄₇	—	2	2	no	—
250	C₂²×C₄₇	—	2	2	no	—
251	C₂²×C₄₇	—	2	8	no	—
252	C₂²×C₄₇	—	2	2	no	—
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	8	no	—
255	C₂²×C₄₇	—	2	2	no	—
256	C₂²×C₄₇	—	2	2	no	—
257	C₂²×C₄₇	—	2	8	no	—
258	C₂²×C₄₇	—	4	16	no	—
259	C₂²×C₄₇	—	4	8	no	—
260	C₂²×C₄₇	—	4	4	no	—
261	C₂²×C₄₇	—	4	4	no	—
262	C₂²×C₄₇	—	4	8	no	—
263	C₂²×C₄₇	—	8	16	no	—
264	C₂²×C₄₇	#518	1	4	yes	—
265	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
266	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
267	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
268	C₂²×C₄₇	#585	1	2	yes	—
269	C₄×C₄₇	—	2	2	no	—
270	C₄×C₄₇	—	2	2	no	—
271	C₄×C₄₇	—	2	2	no	—
272	C₄×C₄₇	—	2	8	no	—
273	C₄×C₄₇	#518	1	4	yes	—
274	Dic₄₇	—	4	4	no	—
275	Dic₄₇	—	4	8	no	—
276	Dic₄₇	—	4	4	no	—
277	C₂²×#121	D₄₇	1	1	yes	characteristic
278	#2377	—	47	4	no	—
279	#2363	—	47	4	no	—
280	#2344	—	47	2	no	—
281	#2342	—	47	4	no	—
282	D₄×C₂²⋊C₄	—	47	2	no	—
283	#2333	—	47	4	no	—
284	#2324	—	47	4	no	—
285	#2309	—	47	2	no	—
286	#2308	—	47	2	no	—
287	#2280	—	47	1	no	—
288	#2280	—	47	1	no	—
289	C₂×C₄₇	—	2	4	no	—
290	C₂×C₄₇	—	4	2	no	—
291	C₂×C₄₇	—	4	2	no	—
292	C₂×C₄₇	—	4	8	no	—
293	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
294	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
295	C₂×C₄₇	#3428	1	1	yes	characteristic
296	C₂×C₄₇	#3542	1	4	yes	—
297	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
298	C₂³×D₄	C₂×D₄₇	1	2	yes	—
299	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
300	C₂×#121	Dic₄₇	1	16	yes	complemented
301	C₂×#121	C₂×D₄₇	1	2	yes	—
302	C₂×#121	C₂×D₄₇	1	2	yes	—
303	C₂×#121	C₂×D₄₇	1	2	yes	—
304	C₂×#121	C₂×D₄₇	1	2	yes	—
305	C₂×C₄×D₄	—	47	4	no	—
306	C₂×#117	—	47	4	no	—
307	C₂×#117	—	47	2	no	—
308	C₂×#117	—	47	2	no	—
309	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	—	47	4	no	—
311	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
312	#390	—	47	8	no	—
313	#390	—	47	8	no	—
314	#390	—	47	4	no	—
315	#389	—	47	4	no	—
316	#388	—	47	8	no	—
317	#388	—	47	8	no	—
318	#387	—	47	8	no	—
319	#386	—	47	8	no	—
320	#386	—	47	8	no	—
321	#386	—	47	8	no	—
322	#385	—	47	8	no	—
323	#381	—	47	4	no	—
324	#381	—	47	2	no	—
325	#381	—	47	2	no	—
326	#380	—	47	2	no	—
327	#380	—	47	2	no	—
328	#380	—	47	2	no	—
329	#380	—	47	2	no	—
330	#379	—	47	1	no	—
331	#379	—	47	2	no	—
332	#379	—	47	1	no	—
333	#379	—	47	4	no	—
334	C₄×C₄⋊C₄	—	47	4	no	—
335	C₄×C₂²⋊C₄	—	47	2	no	—
336	C₄×C₂²⋊C₄	—	47	2	no	—
337	C₄×C₂²⋊C₄	—	47	2	no	—
338	C₄×C₂²⋊C₄	—	47	2	no	—
339	C₄×C₂²⋊C₄	—	47	8	no	—
340	C₄₇	#34363	1	1	yes	characteristic, complemented, Sylow
341	C₂⁵	C₂²×D₄₇	1	2	yes	—
342	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
343	C₂²×D₄	—	4	4	no	—
344	C₂²×D₄	—	4	8	no	—
345	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
346	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
347	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
348	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
349	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
350	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
351	C₂³×C₄	—	4	4	no	—
352	C₂³×C₄	—	47	8	no	—
353	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
354	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
358	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
359	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
360	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
361	#121	C₂×Dic₄₇	1	16	yes	complemented
362	#121	C₂×Dic₄₇	1	16	yes	complemented
363	#121	C₂×Dic₄₇	1	16	yes	complemented
364	#121	C₂×Dic₄₇	1	16	yes	complemented
365	C₄×D₄	—	188	8	no	—
366	#117	—	188	4	no	—
367	#117	—	188	8	no	—
368	#117	—	188	4	no	—
369	C₂×C₄⋊C₄	—	47	4	no	—
370	C₂×C₄⋊C₄	—	47	4	no	—
371	C₂×C₄⋊C₄	—	47	8	no	—
372	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
373	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
374	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
375	C₂×C₂²⋊C₄	—	47	2	no	—
376	C₂×C₂²⋊C₄	—	47	4	no	—
377	C₂×C₂²⋊C₄	—	47	2	no	—
378	C₂×C₂²⋊C₄	—	47	8	no	—
379	C₂×C₂²⋊C₄	—	47	2	no	—
380	C₂×C₂²⋊C₄	—	47	4	no	—
381	C₂×C₂²⋊C₄	—	47	2	no	—
382	C₂×C₂²⋊C₄	—	47	8	no	—
383	C₂×C₂²⋊C₄	—	47	2	no	—
384	C₂×C₂²⋊C₄	—	47	4	no	—
385	C₂×C₂²⋊C₄	—	47	2	no	—
386	C₂×C₂²⋊C₄	—	47	8	no	—
387	C₂×C₂²⋊C₄	—	188	8	no	—
388	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
389	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
391	C₂×C₄²	—	47	4	no	—
392	C₂×C₄²	—	47	4	no	—
393	C₂×C₄²	—	47	8	no	—
394	#95	—	47	4	no	—
395	#95	—	47	4	no	—
396	#95	—	47	4	no	—
397	#95	—	47	4	no	—
398	#95	—	47	8	no	—
399	#95	—	47	8	no	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	4	4	no	—
405	C₂⁴	—	4	4	no	—
406	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
407	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
408	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
409	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
410	C₂⁴	C₂³×D₄₇	1	4	yes	—
411	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	4	16	no	—
414	C₂×D₄	—	4	32	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
421	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
422	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
423	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	4	16	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	47	4	no	—
433	C₂²×C₄	—	47	8	no	—
434	C₂²×C₄	—	47	4	no	—
435	C₂²×C₄	—	188	8	no	—
436	C₂²×C₄	—	188	8	no	—
437	C₂²×C₄	—	188	8	no	—
438	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
439	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
440	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
441	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
442	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
443	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
444	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
445	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
448	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
450	C₄⋊C₄	—	94	8	no	—
451	C₄⋊C₄	—	188	4	no	—
452	C₄⋊C₄	—	188	8	no	—
453	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
454	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
455	C₂²⋊C₄	—	94	4	no	—
456	C₂²⋊C₄	—	94	8	no	—
457	C₂²⋊C₄	—	94	4	no	—
458	C₂²⋊C₄	—	188	2	no	—
459	C₂²⋊C₄	—	188	8	no	—
460	C₂²⋊C₄	—	188	4	no	—
461	C₂²⋊C₄	—	188	2	no	—
462	C₂²⋊C₄	—	188	8	no	—
463	C₂²⋊C₄	—	188	2	no	—
464	C₂²⋊C₄	—	188	2	no	—
465	C₂²⋊C₄	—	188	4	no	—
466	C₂²⋊C₄	—	188	8	no	—
467	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
468	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
469	C₄²	—	94	8	no	—
470	C₄²	—	188	4	no	—
471	C₄²	—	188	8	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	16	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	8	no	—
490	C₂³	—	4	16	no	—
491	C₂³	—	8	16	no	—
492	C₂³	C₂³×Dic₄₇	1	8	yes	—
493	C₂³	C₂³×Dic₄₇	1	2	yes	—
494	C₂³	C₂³×Dic₄₇	1	2	yes	—
495	C₂³	C₂³×Dic₄₇	1	2	yes	—
496	C₂³	#13094069	1	4	yes	—
497	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
498	D₄	—	2	16	no	—
499	D₄	—	4	8	no	—
500	D₄	—	4	16	no	—
501	D₄	—	4	16	no	—
502	C₂×C₄	—	2	16	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	94	4	no	—
515	C₂×C₄	—	94	4	no	—
516	C₂×C₄	—	94	4	no	—
517	C₂×C₄	—	94	8	no	—
518	C₂×C₄	—	94	8	no	—
519	C₂×C₄	—	94	4	no	—
520	C₂×C₄	—	94	4	no	—
521	C₂×C₄	—	94	8	no	—
522	C₂×C₄	—	94	4	no	—
523	C₂×C₄	—	376	16	no	—
524	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
525	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
526	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
527	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
528	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
529	C₂×C₄	#13094069	1	4	yes	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	8	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	8	no	—
547	C₂²	—	8	16	no	—
548	C₂²	#15689598	1	4	yes	—
549	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
550	C₂²	C₂×#13094069	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	8	no	—
557	C₄	—	188	4	no	—
558	C₄	—	188	8	no	—
559	C₄	—	188	4	no	—
560	C₄	#15689598	1	4	yes	—
561	C₂	—	2	4	no	—
562	C₂	—	4	2	no	—
563	C₂	—	4	2	no	—
564	C₂	—	4	8	no	—
565	C₂	C₂×#15689598	1	1	yes	characteristic
566	C₂	C₂×#15689598	1	1	yes	characteristic
567	C₂	#20256591	1	1	yes	characteristic
568	C₂	#20257708	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂²×#121×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#121	D₄₇
hypocenter	C₄₇	#34363
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. #20246545	C₂	semidirect
2. #20246430	C₂	semidirect
3. #20246257	C₂	semidirect
4. #20246237	C₂	semidirect
5. D₄×C₂²⋊Dic₄₇	C₂	semidirect
6. #20246155	C₂	semidirect
7. #20246083	C₂	semidirect
8. #20245970	C₂	semidirect
9. #20245966	C₂	semidirect
10. #20245771	C₂	semidirect
11. #20245771	C₂	semidirect
13. C₂×D₄×Dic₄₇	C₂²	semidirect
15. C₂×#13093983	C₂²	semidirect
16. C₂×#13093983	C₂²	semidirect
18. #15689026	C₂²	semidirect
19. #15689026	C₂²	semidirect
20. #15689026	C₂²	semidirect
21. #15689022	C₂²	semidirect
22. #15689016	C₂²	semidirect
23. #15689016	C₂²	semidirect
24. #15689009	C₂²	semidirect
25. #15689003	C₂²	semidirect
26. #15689003	C₂²	semidirect
27. #15689003	C₂²	semidirect
28. #15688998	C₂²	semidirect
30. #15688986	C₂²	semidirect
31. #15688986	C₂²	semidirect
34. #15688983	C₂²	semidirect
35. #15688983	C₂²	semidirect
40. C₄⋊C₄×Dic₄₇	C₂²	semidirect
41. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
44. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
45. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
49. C₂×#121×C₄₇	C₄	semidirect
91. C₂²×D₄×C₄₇	C₂×C₄	semidirect
97. C₂³×C₄×C₄₇	C₂×C₄	semidirect
105. #121×C₄₇	C₂×C₄	semidirect
106. #121×C₄₇	C₂×C₄	semidirect
107. #121×C₄₇	C₂×C₄	semidirect
108. #121×C₄₇	C₂×C₄	semidirect
109. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
112. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
300. C₂×#121	Dic₄₇	semidirect
340. C₄₇	#34363	semidirect
346. C₂²×D₄	C₂×Dic₄₇	semidirect
353. C₂³×C₄	C₂×Dic₄₇	semidirect
361. #121	C₂×Dic₄₇	semidirect
362. #121	C₂×Dic₄₇	semidirect
363. #121	C₂×Dic₄₇	semidirect
364. #121	C₂×Dic₄₇	semidirect
372. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
388. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246545	2
#20246430	2
#20246257	2
#20246237	2
D₄×C₂²⋊Dic₄₇	2
#20246155	2
#20246083	2
#20245970	2
#20245966	2
#20245771	2
C₂²×#121×C₄₇	2
#34363	47