Subgroups — #26121737

Order 12032.

1164 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689107	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689097	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688895	C₂	1	2	yes	maximal, complemented
4	#20243126	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#568	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689107	—	2	2	no	—
9	#15689107	—	2	2	no	—
10	C₂×#13093943	C₄	1	2	yes	complemented
11	C₂×#13093941	C₄	1	2	yes	complemented
12	#15689097	—	2	2	no	—
13	#15689097	—	2	2	no	—
14	C₂×#13093939	C₄	1	4	yes	—
15	#15688895	—	2	4	no	—
16	#15688891	—	2	4	no	—
17	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#568	—	2	4	no	—
19	C₄₇×#568	—	2	4	no	—
20	C₂×#131×C₄₇	—	2	2	no	—
21	C₂×#131×C₄₇	—	2	2	no	—
22	C₂²×M₁₆×C₄₇	C₄	1	4	yes	complemented
23	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	C₂×C₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	#13093983	—	2	2	no	—
33	#13093983	—	2	2	no	—
34	#13093983	—	2	2	no	—
35	#13093983	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	#13093943	—	2	4	no	—
40	#13093941	—	2	4	no	—
41	#13093939	—	2	8	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	D₄	1	2	yes	—
47	C₂×#41×C₄₇	D₄	1	2	yes	—
48	C₂×#41×C₄₇	D₄	1	2	yes	—
49	C₂×#41×C₄₇	Q₈	1	2	yes	—
50	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	#131×C₄₇	—	2	16	no	—
56	#131×C₄₇	—	2	16	no	—
57	C₂×M₁₆×C₄₇	—	2	4	no	—
58	C₂×M₁₆×C₄₇	—	2	1	no	—
59	C₂×M₁₆×C₄₇	—	2	1	no	—
60	C₂×M₁₆×C₄₇	—	2	2	no	—
61	C₂×M₁₆×C₄₇	—	2	2	no	—
62	C₂×M₁₆×C₄₇	—	2	8	no	—
63	C₂×M₁₆×C₄₇	—	2	8	no	—
64	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
67	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
68	C₂²×C₈×C₄₇	—	2	4	no	—
69	C₂²×C₈×C₄₇	—	2	1	no	—
70	C₂²×C₈×C₄₇	—	2	1	no	—
71	C₂⁴×C₄₇	C₄²	1	2	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	#41×C₄₇	—	2	4	no	—
74	#41×C₄₇	—	2	4	no	—
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
84	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
90	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×Dic₄₇	—	2	4	no	—
111	M₁₆×C₄₇	—	2	16	no	—
112	M₁₆×C₄₇	—	2	2	no	—
113	M₁₆×C₄₇	—	2	2	no	—
114	M₁₆×C₄₇	—	2	4	no	—
115	M₁₆×C₄₇	—	2	4	no	—
116	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
117	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
118	C₂×C₈×C₄₇	—	2	16	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	4	no	—
122	C₂×C₈×C₄₇	—	2	4	no	—
123	C₂²⋊Dic₄₇	—	2	4	no	—
124	C₂²⋊Dic₄₇	—	2	4	no	—
125	C₄⋊Dic₄₇	—	4	2	no	—
126	C₄⋊Dic₄₇	—	4	2	no	—
127	C₄×Dic₄₇	—	4	2	no	—
128	C₄×Dic₄₇	—	4	2	no	—
129	#10625329	—	2	4	no	—
130	#10625329	—	2	4	no	—
131	#10625329	—	4	2	no	—
132	#10625329	—	4	2	no	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂×C₄₇⋊C₈	—	4	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	8	1	no	—
139	C₂³×C₄₇	—	8	2	no	—
140	C₂³×C₄₇	#95	1	4	yes	—
141	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₇	C₄×D₄	1	2	yes	—
145	C₂³×C₄₇	C₄×D₄	1	2	yes	—
146	Q₈×C₄₇	—	2	4	no	—
147	Q₈×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	2	8	no	—
149	D₄×C₄₇	—	2	8	no	—
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	#95	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	#120	1	2	yes	—
170	C₂×C₄×C₄₇	#120	1	2	yes	—
171	C₂×C₄×C₄₇	#121	1	2	yes	—
172	C₂×C₄×C₄₇	#121	1	2	yes	—
173	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₄₇	#123	1	2	yes	—
176	C₂×C₄×C₄₇	#123	1	2	yes	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	8	4	no	—
179	C₈×C₄₇	—	2	4	no	—
180	C₈×C₄₇	—	2	4	no	—
181	C₄₇⋊C₈	—	4	4	no	—
182	#10771	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	1	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
193	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	#385	1	2	yes	—
196	C₂²×C₄₇	#386	1	2	yes	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	#379	1	1	yes	characteristic
199	C₄×C₄₇	#380	1	1	yes	characteristic
200	C₄×C₄₇	#380	1	1	yes	characteristic
201	C₄×C₄₇	#381	1	1	yes	characteristic
202	C₄×C₄₇	#385	1	2	yes	—
203	C₄×C₄₇	#386	1	2	yes	—
204	Dic₄₇	—	8	4	no	—
205	C₂×#568	D₄₇	1	1	yes	characteristic
206	C₂×#413	—	47	1	no	—
207	C₂×#410	—	47	1	no	—
208	C₂×#344	—	47	2	no	—
209	#1742	—	47	2	no	—
210	C₂×C₄₇	—	2	2	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	1	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	4	4	no	—
216	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
217	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
218	#568	—	2	4	no	—
219	#568	—	2	4	no	—
220	C₂×#131	—	2	2	no	—
221	C₂×#131	—	2	2	no	—
222	C₂²×M₁₆	—	47	2	no	—
223	C₂²×M₁₆	Dic₄₇	1	4	yes	complemented
224	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
225	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#117	—	47	2	no	—
227	#413	—	94	2	no	—
228	#413	—	94	2	no	—
229	C₂×#101	—	47	2	no	—
230	C₂×#100	—	47	2	no	—
231	#410	—	94	2	no	—
232	#410	—	94	2	no	—
233	C₂×#99	—	47	4	no	—
234	#344	—	94	4	no	—
235	#343	—	94	4	no	—
236	C₄₇	#10771	1	1	yes	characteristic, complemented, Sylow
237	C₂×#41	—	2	2	no	—
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	2	2	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	Dic₉₄	1	2	yes	—
242	C₂×#41	D₁₈₈	1	2	yes	—
243	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
244	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
245	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
246	C₂²×D₄	C₄×D₄₇	1	2	yes	—
247	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
248	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
249	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
250	#131	—	2	16	no	—
251	#131	—	2	16	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	8	no	—
258	C₂×M₁₆	—	2	8	no	—
259	C₂×M₁₆	—	47	4	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	—	94	2	no	—
264	C₂×M₁₆	—	94	2	no	—
265	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
266	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
267	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
268	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
269	C₂²×C₈	—	2	4	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	94	2	no	—
273	#117	—	94	2	no	—
274	#117	—	94	2	no	—
275	#117	—	94	2	no	—
276	#117	—	94	2	no	—
277	C₂×C₄⋊C₄	—	94	2	no	—
278	C₂×C₂²⋊C₄	—	47	4	no	—
279	C₂×C₄²	—	94	2	no	—
280	#101	—	94	4	no	—
281	#100	—	94	4	no	—
282	#99	—	94	8	no	—
283	C₂⁴	C₄×Dic₄₇	1	2	yes	—
284	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	#41	—	2	4	no	—
290	#41	—	2	4	no	—
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
296	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
302	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
303	C₂×D₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
304	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	94	4	no	—
310	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
311	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
312	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
313	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
316	C₂²×C₄	#10625350	1	2	yes	—
317	C₂²×C₄	#10625350	1	2	yes	—
318	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
323	M₁₆	—	2	16	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	94	4	no	—
329	M₁₆	—	94	4	no	—
330	M₁₆	—	188	2	no	—
331	M₁₆	—	188	2	no	—
332	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
333	M₁₆	C₂²⋊Dic₄₇	1	4	yes	—
334	C₂×C₈	—	2	16	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	4	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	94	4	no	—
340	C₂×C₈	—	188	2	no	—
341	C₂×C₈	—	188	2	no	—
342	C₄⋊C₄	—	188	2	no	—
343	C₄⋊C₄	—	188	2	no	—
344	C₂²⋊C₄	—	94	4	no	—
345	C₂²⋊C₄	—	94	4	no	—
346	C₄²	—	188	2	no	—
347	C₄²	—	188	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	2	no	—
352	C₂³	C₄₇⋊#95	1	4	yes	—
353	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
354	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
355	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
356	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
357	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
358	Q₈	—	2	4	no	—
359	Q₈	—	2	4	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	376	4	no	—
371	C₂×C₄	—	188	4	no	—
372	C₂×C₄	C₄₇⋊#95	1	4	yes	—
373	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	#13093983	1	1	yes	characteristic
380	C₂×C₄	#13093983	1	1	yes	characteristic
381	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
382	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
383	C₂×C₄	#13093993	1	2	yes	—
384	C₂×C₄	#13093993	1	2	yes	—
385	C₂×C₄	#13093998	1	2	yes	—
386	C₂×C₄	#13093998	1	2	yes	—
387	C₂×C₄	#13094003	1	2	yes	—
388	C₂×C₄	#13094003	1	2	yes	—
389	C₂×C₄	#13094007	1	2	yes	—
390	C₂×C₄	#13094007	1	2	yes	—
391	C₈	—	2	4	no	—
392	C₈	—	2	4	no	—
393	C₈	—	188	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
404	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
405	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
406	C₂²	#15688996	1	2	yes	—
407	C₂²	#15689002	1	2	yes	—
408	C₄	—	2	4	no	—
409	C₄	—	376	4	no	—
410	C₄	#15688979	1	1	yes	characteristic
411	C₄	#15688983	1	1	yes	characteristic
412	C₄	#15688983	1	1	yes	characteristic
413	C₄	#15688986	1	1	yes	characteristic
414	C₄	#15688996	1	2	yes	—
415	C₄	#15689002	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	2	no	—
421	C₂	—	4	4	no	—
422	C₂	#20241611	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15688986
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#568	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#568	D₄₇
hypocenter	C₄₇	#10771
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
3. C₂×#15688895	C₂	semidirect
4. #20243126	C₂	semidirect
10. C₂×#13093943	C₄	semidirect
11. C₂×#13093941	C₄	semidirect
22. C₂²×M₁₆×C₄₇	C₄	semidirect
223. C₂²×M₁₆	Dic₄₇	semidirect
236. C₄₇	#10771	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689107	2
C₂×#15689097	2
C₂×#15688895	2
#20243126	2
C₂×C₄₇×#568	2
#10771	47