Subgroups — #26226638

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689181	C₂	1	2	yes	maximal
2	#20245871	C₂	1	1	yes	maximal, characteristic
3	#20244110	C₂	1	2	yes	maximal, complemented
4	#20244108	C₂	1	2	yes	maximal, complemented
5	#20244105	C₂	1	2	yes	maximal, complemented
6	#20244103	C₂	1	2	yes	maximal, complemented
7	#20243370	C₂	1	2	yes	maximal
8	#20243368	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689181	—	2	8	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×#13093934	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	#15689021	C₄	1	1	yes	characteristic
23	#15689021	C₄	1	1	yes	characteristic
24	#15689021	C₄	1	1	yes	characteristic
25	#15689021	C₄	1	1	yes	characteristic
26	#15688996	C₄	1	2	yes	—
27	#15688996	C₄	1	2	yes	—
28	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
29	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#336	C₂²	1	2	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	#13093983	—	4	1	no	—
41	#13093983	—	4	1	no	—
42	#13093983	D₄	1	4	yes	—
43	#13093983	Q₈	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
58	Dic₄₇⋊C₈	—	2	4	no	—
59	Dic₄₇⋊C₈	—	2	4	no	—
60	Dic₄₇⋊C₈	—	4	2	no	—
61	Dic₄₇⋊C₈	—	4	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
63	#13093934	—	2	4	no	—
64	C₈×Dic₄₇	—	2	4	no	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	—	4	1	no	—
75	C₂×C₄²×C₄₇	—	4	1	no	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	4	1	no	—
81	C₄⋊C₈×C₄₇	—	4	1	no	—
82	C₂²⋊C₈×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	1	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	4	1	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	1	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	4	1	no	—
117	C₄²×C₄₇	—	4	1	no	—
118	C₂²⋊Dic₄₇	—	4	2	no	—
119	C₂²⋊Dic₄₇	C₄⋊C₄	1	8	yes	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	—	4	1	no	—
122	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
123	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
124	Dic₄₇⋊C₄	—	2	4	no	—
125	Dic₄₇⋊C₄	—	2	4	no	—
126	Dic₄₇⋊C₄	—	4	2	no	—
127	Dic₄₇⋊C₄	—	4	2	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
131	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	—	2	1	no	—
143	C₂³×C₄₇	—	2	1	no	—
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	#131	1	2	yes	—
166	C₂×C₄×C₄₇	#131	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
184	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
185	C₈×C₄₇	—	4	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	#21957	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	1	no	—
195	C₂²×C₄₇	—	4	1	no	—
196	C₂²×C₄₇	—	4	1	no	—
197	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	#518	1	1	yes	characteristic
199	C₂²×C₄₇	#519	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
202	C₂²×C₄₇	#568	1	1	yes	characteristic
203	C₂²×C₄₇	#568	1	1	yes	characteristic
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	#537	1	1	yes	characteristic
210	C₄×C₄₇	#537	1	1	yes	characteristic
211	C₄×C₄₇	#544	1	1	yes	characteristic
212	C₄×C₄₇	#544	1	1	yes	characteristic
213	Dic₄₇	—	2	4	no	—
214	Dic₄₇	—	2	4	no	—
215	Dic₄₇	—	4	2	no	—
216	Dic₄₇	—	4	2	no	—
217	C₂×#433	—	47	2	no	—
218	#2296	—	47	1	no	—
219	#1940	—	47	2	no	—
220	#1940	—	47	2	no	—
221	#1939	—	47	2	no	—
222	#1939	—	47	2	no	—
223	#1798	—	47	2	no	—
224	#1797	—	47	1	no	—
225	#1797	D₄₇	1	1	yes	characteristic
226	C₂×C₄₇	—	4	2	no	—
227	C₂×C₄₇	#2316	1	1	yes	characteristic
228	C₂×C₄₇	#2906	1	1	yes	characteristic
229	C₂×C₄₇	#2906	1	1	yes	characteristic
230	C₂×C₄₇	#2976	1	1	yes	characteristic
231	C₂×C₄₇	#2976	1	1	yes	characteristic
232	C₂×C₄₇	#2986	1	1	yes	characteristic
233	C₂×C₄₇	#2987	1	1	yes	characteristic
234	C₂×#117	—	47	1	no	—
235	C₂×#117	—	47	1	no	—
236	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
237	#433	—	94	8	no	—
238	C₂×C₄⋊C₈	—	47	2	no	—
239	C₂×C₄⋊C₈	—	47	2	no	—
240	C₂×C₄⋊C₈	—	47	2	no	—
241	C₂×C₄⋊C₈	—	47	2	no	—
242	C₂×C₄⋊C₈	—	47	1	no	—
243	C₂×C₄⋊C₈	—	47	1	no	—
244	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	—	47	2	no	—
247	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
248	C₂×#97	—	47	2	no	—
249	C₂×C₄×C₈	—	47	2	no	—
250	#389	—	47	1	no	—
251	#389	—	47	1	no	—
252	#389	—	47	1	no	—
253	#389	—	47	1	no	—
254	#385	—	47	2	no	—
255	#385	—	47	2	no	—
256	C₄×C₄⋊C₄	—	47	2	no	—
257	C₄×C₄⋊C₄	—	47	2	no	—
258	#336	—	47	2	no	—
259	#336	—	47	2	no	—
260	#336	—	47	2	no	—
261	#336	C₂×D₄₇	1	2	yes	—
262	C₄₇	#21957	1	1	yes	characteristic, complemented, Sylow
263	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
264	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	—	47	2	no	—
267	C₂²×C₈	—	47	2	no	—
268	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
269	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
270	#117	—	47	4	no	—
271	#117	—	47	4	no	—
272	#117	—	188	1	no	—
273	#117	—	188	1	no	—
274	C₂×C₄⋊C₄	—	47	1	no	—
275	C₂×C₄⋊C₄	—	47	1	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₄⋊C₄	—	47	1	no	—
279	C₂×C₄⋊C₄	—	47	1	no	—
280	C₂×C₄⋊C₄	—	47	2	no	—
281	C₂×C₄⋊C₄	—	47	2	no	—
282	C₂×C₂²⋊C₄	—	47	2	no	—
283	C₂×C₂²⋊C₄	—	47	2	no	—
284	C₂×C₄²	—	4	1	no	—
285	C₂×C₄²	—	4	1	no	—
286	C₂×C₄²	—	47	2	no	—
287	C₂×C₄²	—	47	2	no	—
288	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
289	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
292	C₄⋊C₈	—	4	1	no	—
293	C₄⋊C₈	—	4	1	no	—
294	C₄⋊C₈	—	94	4	no	—
295	C₄⋊C₈	—	94	4	no	—
296	C₄⋊C₈	—	188	1	no	—
297	C₄⋊C₈	—	188	1	no	—
298	C₄⋊C₈	—	188	2	no	—
299	C₄⋊C₈	—	188	2	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₂²⋊C₈	—	94	4	no	—
302	#97	—	94	4	no	—
303	C₄×C₈	—	94	4	no	—
304	#95	—	47	2	no	—
305	#95	—	47	2	no	—
306	#95	—	47	2	no	—
307	#95	—	47	2	no	—
308	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	47	2	no	—
320	C₂²×C₄	—	47	2	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	2	no	—
323	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₇	1	2	yes	—
329	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
330	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₄⋊C₄	—	47	4	no	—
344	C₄⋊C₄	—	47	4	no	—
345	C₄⋊C₄	—	94	4	no	—
346	C₄⋊C₄	—	94	4	no	—
347	C₄⋊C₄	—	188	2	no	—
348	C₄⋊C₄	—	188	2	no	—
349	C₄⋊C₄	—	188	1	no	—
350	C₄⋊C₄	—	188	1	no	—
351	C₂²⋊C₄	—	47	8	no	—
352	C₂²⋊C₄	—	188	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	47	4	no	—
360	C₄²	—	47	4	no	—
361	C₄²	—	94	2	no	—
362	C₄²	—	94	2	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
370	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	47	4	no	—
390	C₂×C₄	—	47	4	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	2	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
402	C₂×C₄	#13094030	1	2	yes	—
403	C₂×C₄	#13094032	1	2	yes	—
404	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
406	C₂×C₄	#13094069	1	1	yes	characteristic
407	C₂×C₄	#13094069	1	1	yes	characteristic
408	C₂×C₄	#13094071	1	1	yes	characteristic
409	C₂×C₄	#13094071	1	1	yes	characteristic
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	188	2	no	—
413	C₈	—	188	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
422	C₂²	#15689596	1	1	yes	characteristic
423	C₂²	#15689600	1	1	yes	characteristic
424	C₂²	C₂×#13094030	1	1	yes	characteristic
425	C₂²	C₂×#13094032	1	1	yes	characteristic
426	C₂²	#15689889	1	1	yes	characteristic
427	C₂²	#15689889	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	94	4	no	—
434	C₄	—	94	4	no	—
435	C₄	—	188	2	no	—
436	C₄	—	188	2	no	—
437	C₄	#15689700	1	1	yes	characteristic
438	C₄	#15689700	1	1	yes	characteristic
439	C₄	#15689752	1	1	yes	characteristic
440	C₄	#15689752	1	1	yes	characteristic
441	C₂	—	4	2	no	—
442	C₂	#20246005	1	1	yes	characteristic
443	C₂	#20251953	1	1	yes	characteristic
444	C₂	#20251957	1	1	yes	characteristic
445	C₂	#20252433	1	1	yes	characteristic
446	C₂	#20252438	1	1	yes	characteristic
447	C₂	#20252489	1	1	yes	characteristic
448	C₂	#20252493	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1797	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1797	D₄₇
hypocenter	C₄₇	#21957
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1797

Complements

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

N	H ≅ G/N	type
3. #20244110	C₂	semidirect
4. #20244108	C₂	semidirect
5. #20244105	C₂	semidirect
6. #20244103	C₂	semidirect
262. C₄₇	#21957	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689181	2
#20245871	2
#20244110	2
#20244108	2
#20244105	2
#20244103	2
#20243370	2
#20243368	2
C₄₇×#1797	2
#21957	47