Subgroups — #26213775

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689081	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243138	C₂	1	2	yes	maximal, complemented
5	#20243138	C₂	1	2	yes	maximal, complemented
6	#20243135	C₂	1	2	yes	maximal, complemented
7	#20243132	C₂	1	2	yes	maximal, complemented
8	#20243085	C₂	1	1	yes	maximal, characteristic
9	#20243081	C₂	1	1	yes	maximal, characteristic
10	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	#15689081	C₄	1	8	yes	complemented
17	#15689078	C₄	1	8	yes	complemented
18	C₂×#13093934	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
23	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
24	C₂²⋊C₄×Dic₄₇	C₄	1	4	yes	—
25	#15688969	C₂²	1	2	yes	—
26	C₄²×Dic₄₇	C₂²	1	2	yes	—
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688877	C₂²	1	1	yes	characteristic
30	#15688877	C₂²	1	1	yes	characteristic
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#336	C₂²	1	2	yes	—
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	C₂×C₄	1	4	yes	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	#13093983	C₂×C₄	1	4	yes	—
51	#13093983	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	#13093934	C₂×C₄	1	8	yes	complemented
64	#13093934	C₂×C₄	1	8	yes	complemented
65	C₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
66	C₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
67	C₄₇⋊#95	C₂×C₄	1	4	yes	—
68	C₄₇⋊#95	C₂×C₄	1	4	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	—	2	2	no	—
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	#117×C₄₇	—	2	2	no	—
80	#117×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	#41	1	2	yes	—
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
101	M₁₆×C₄₇	—	2	8	no	—
102	C₂×C₈×C₄₇	—	2	8	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₂²⋊C₄×C₄₇	—	2	4	no	—
114	C₄²×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₂²⋊Dic₄₇	C₄²	1	8	yes	—
117	C₄⋊Dic₄₇	C₄²	1	4	yes	—
118	C₄⋊Dic₄₇	C₄²	1	4	yes	—
119	C₄×Dic₄₇	—	2	4	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	8	no	—
125	C₄×Dic₄₇	—	4	4	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
127	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
128	#10625329	—	2	8	no	—
129	C₂×C₄₇⋊C₈	—	2	8	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
142	C₂³×C₄₇	#117	1	2	yes	—
143	C₂³×C₄₇	#117	1	2	yes	—
144	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₄₇	#117	1	4	yes	—
150	C₂×C₄×C₄₇	#117	1	4	yes	—
151	C₂×C₄×C₄₇	#117	1	2	yes	—
152	C₂×C₄×C₄₇	#117	1	4	yes	—
153	C₂×C₄×C₄₇	#117	1	4	yes	—
154	C₂×C₄×C₄₇	#117	1	2	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	4	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	4	8	no	—
169	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
170	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
171	C₂×Dic₄₇	#131	1	4	yes	—
172	C₈×C₄₇	—	2	2	no	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	—	2	4	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	2	4	no	—
178	#20368	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	4	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	#376	1	4	yes	—
184	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#131	1	2	yes	—
188	C₂²×C₄₇	#568	1	2	yes	—
189	C₄×C₄₇	—	4	4	no	—
190	C₄×C₄₇	#376	1	4	yes	—
191	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
192	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	4	2	no	—
199	C₂×#405	—	47	1	no	—
200	C₂×#405	—	47	1	no	—
201	C₄×#117	—	47	1	no	—
202	#1746	—	47	2	no	—
203	#1746	—	47	2	no	—
204	#1745	—	47	2	no	—
205	#1744	—	47	2	no	—
206	#1729	—	47	1	no	—
207	#1729	D₄₇	1	1	yes	characteristic
208	#1728	—	47	1	no	—
209	C₂×#336	—	47	1	no	—
210	C₂×C₄₇	—	2	4	no	—
211	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
212	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
213	C₂×C₄₇	#2875	1	1	yes	characteristic
214	C₂×C₄₇	#2924	1	2	yes	—
215	C₂×C₄₇	#2925	1	2	yes	—
216	C₂²×M₁₆	—	47	1	no	—
217	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
218	C₂³×C₈	—	47	1	no	—
219	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×#117	—	47	1	no	—
221	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
222	C₂²×C₄²	—	47	1	no	—
223	#405	—	47	8	no	—
224	#405	—	47	8	no	—
225	C₂×#97	—	47	2	no	—
226	C₂×#97	—	47	2	no	—
227	C₂×C₄×C₈	—	47	2	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₄×C₄⋊C₄	—	47	2	no	—
230	C₄×C₄⋊C₄	—	47	2	no	—
231	C₄×C₂²⋊C₄	—	47	4	no	—
232	#376	—	47	2	no	—
233	C₄³	—	47	2	no	—
234	#336	—	47	1	no	—
235	#336	—	47	1	no	—
236	#336	—	47	1	no	—
237	#336	—	47	1	no	—
238	#336	—	47	2	no	—
239	#336	—	47	2	no	—
240	#336	—	47	2	no	—
241	#336	—	47	2	no	—
242	#336	C₂×D₄₇	1	2	yes	—
243	#336	C₂×D₄₇	1	2	yes	—
244	C₄₇	#20368	1	1	yes	characteristic, complemented, Sylow
245	C₂³×C₄	—	47	2	no	—
246	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	47	4	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	47	4	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	47	2	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	C₄×D₄₇	1	4	yes	—
262	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	#117	—	47	4	no	—
268	#117	—	47	4	no	—
269	C₂×C₄⋊C₄	—	47	1	no	—
270	C₂×C₄⋊C₄	—	47	1	no	—
271	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	47	2	no	—
273	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
274	C₂×C₄²	—	47	2	no	—
275	C₂×C₄²	—	47	4	no	—
276	C₂×C₄²	—	47	2	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	4	no	—
280	C₂×C₄²	—	94	2	no	—
281	C₂×C₄²	—	94	2	no	—
282	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
283	#97	—	47	8	no	—
284	#97	—	47	8	no	—
285	C₄×C₈	—	47	8	no	—
286	C₄×C₈	—	47	8	no	—
287	#95	—	47	4	no	—
288	#95	—	47	4	no	—
289	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	94	4	no	—
295	C₂²×C₄	—	94	4	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
301	C₂²×C₄	#10625352	1	2	yes	—
302	C₂²×C₄	#10625352	1	2	yes	—
303	C₂²×C₄	#10625352	1	2	yes	—
304	C₂²×C₄	#10625354	1	2	yes	—
305	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
306	M₁₆	—	2	8	no	—
307	M₁₆	—	94	8	no	—
308	C₂×C₈	—	2	8	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	—	47	4	no	—
317	C₂×C₈	—	47	2	no	—
318	C₂×C₈	—	94	8	no	—
319	C₂×C₈	—	94	1	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	2	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
326	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
327	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	47	4	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	47	8	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	47	4	no	—
336	C₄²	—	47	4	no	—
337	C₄²	—	94	8	no	—
338	C₄²	—	94	4	no	—
339	C₄²	—	94	1	no	—
340	C₄²	—	94	1	no	—
341	C₄²	—	94	1	no	—
342	C₄²	—	94	1	no	—
343	C₄²	—	188	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	C₄²×D₄₇	1	2	yes	—
347	C₂³	#13093980	1	2	yes	—
348	C₂³	#13093982	1	2	yes	—
349	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	188	8	no	—
364	C₂×C₄	C₄²×D₄₇	1	2	yes	—
365	C₂×C₄	#13093980	1	2	yes	—
366	C₂×C₄	#13093980	1	4	yes	—
367	C₂×C₄	#13093980	1	4	yes	—
368	C₂×C₄	#13093982	1	2	yes	—
369	C₂×C₄	#13093982	1	4	yes	—
370	C₂×C₄	#13093982	1	4	yes	—
371	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	4	no	—
380	C₈	—	94	2	no	—
381	C₈	—	94	2	no	—
382	C₈	—	94	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#15688968	1	4	yes	—
388	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
389	C₂²	C₂×#13093980	1	1	yes	characteristic
390	C₂²	C₂×#13093982	1	1	yes	characteristic
391	C₂²	#131×D₄₇	1	2	yes	—
392	C₂²	#15689888	1	2	yes	—
393	C₄	—	4	4	no	—
394	C₄	—	94	4	no	—
395	C₄	—	94	4	no	—
396	C₄	—	94	4	no	—
397	C₄	—	188	2	no	—
398	C₄	#15688968	1	4	yes	—
399	C₄	C₂×#13093980	1	1	yes	characteristic
400	C₄	C₂×#13093980	1	1	yes	characteristic
401	C₄	C₂×#13093982	1	1	yes	characteristic
402	C₄	C₂×#13093982	1	1	yes	characteristic
403	C₂	—	2	4	no	—
404	C₂	C₂×#15688968	1	1	yes	characteristic
405	C₂	#20251810	1	1	yes	characteristic
406	C₂	#20251815	1	1	yes	characteristic
407	C₂	#20252045	1	2	yes	—
408	C₂	#20252050	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1729	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1729	D₄₇
hypocenter	C₄₇	#20368
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. #20243138	C₂	semidirect
5. #20243138	C₂	semidirect
6. #20243135	C₂	semidirect
7. #20243132	C₂	semidirect
16. #15689081	C₄	semidirect
17. #15689078	C₄	semidirect
63. #13093934	C₂×C₄	semidirect
64. #13093934	C₂×C₄	semidirect
65. C₈×Dic₄₇	C₂×C₄	semidirect
66. C₈×Dic₄₇	C₂×C₄	semidirect
244. C₄₇	#20368	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689081	2
C₂×#15689078	2
#117×Dic₄₇	2
#20243138	2
#20243135	2
#20243132	2
#20243085	2
#20243081	2
C₂×#15688877	2
C₄₇×#1729	2
#20368	47