Subgroups — #26105848

Order 12032.

818 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×#15689174	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241228	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	—	2	1	no	—
9	C₂×C₄⋊C₄×D₄₇	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	—	2	1	no	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689174	—	2	2	no	—
13	#15689174	C₄	1	4	yes	complemented
14	#15689145	—	2	2	no	—
15	#15689145	C₄	1	4	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	—	2	1	no	—
18	C₂×Dic₄₇⋊C₈	—	2	1	no	—
19	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
22	C₄×Dic₄₇⋊C₄	—	2	1	no	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	#15688974	—	2	1	no	—
25	#95×D₄₇	—	2	1	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	—	2	2	no	—
30	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
33	C₂×#10625324	—	2	4	no	—
34	C₂×#10625324	—	4	2	no	—
35	C₂×#10625324	—	4	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	1	no	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
39	C₂×Dic₄₇⋊C₄	—	2	2	no	—
40	C₄⋊C₄×D₄₇	—	2	4	no	—
41	C₄⋊C₄×D₄₇	—	2	4	no	—
42	C₂×C₄×Dic₄₇	—	2	1	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₄²×D₄₇	—	4	2	no	—
48	C₄²×D₄₇	—	4	2	no	—
49	C₄²×D₄₇	C₂×C₄	1	2	yes	—
50	C₄²×D₄₇	C₂×C₄	1	2	yes	—
51	C₄²×D₄₇	D₄	1	2	yes	—
52	C₄²×D₄₇	Q₈	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	complemented
55	Dic₄₇⋊C₈	—	2	4	no	—
56	Dic₄₇⋊C₈	—	2	4	no	—
57	(C₂×D₄₇)⋊C₈	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	1	no	—
59	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
60	C₄₇⋊#95	—	2	1	no	—
61	C₄₇⋊#95	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₄₇	—	2	1	no	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₇	—	2	1	no	—
68	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
69	C₄×C₈×C₄₇	—	2	1	no	—
70	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
71	#95×C₄₇	—	2	1	no	—
72	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₄₇	—	2	2	no	—
82	C₂×C₄×D₄₇	—	2	2	no	—
83	C₂×C₄×D₄₇	—	2	8	no	—
84	C₂×C₄×D₄₇	—	4	2	no	—
85	C₂×C₄×D₄₇	—	4	4	no	—
86	C₂×C₄×D₄₇	—	4	4	no	—
87	C₂×C₄×D₄₇	C₄²	1	2	yes	—
88	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
93	C₂×C₄×D₄₇	D₈	1	2	yes	—
94	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
95	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
96	C₂×C₄×D₄₇	Q₁₆	1	2	yes	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	4	2	no	—
100	C₂×C₈×C₄₇	—	4	1	no	—
101	C₂×C₈×C₄₇	—	4	1	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
104	C₄²×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	—	4	1	no	—
106	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	M₁₆	1	4	yes	complemented
112	Dic₄₇⋊C₄	—	2	8	no	—
113	C₄×Dic₄₇	—	4	1	no	—
114	C₄×Dic₄₇	—	4	1	no	—
115	C₄×Dic₄₇	—	4	4	no	—
116	C₄×Dic₄₇	C₄²	1	2	yes	—
117	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
118	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
119	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
120	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
121	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂×C₄₇⋊C₈	—	4	1	no	—
126	C₂×C₄₇⋊C₈	—	4	1	no	—
127	#10625324	—	4	8	no	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	2	no	—
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	#95	1	2	yes	—
132	C₂²×D₄₇	#102	1	2	yes	—
133	C₂²×D₄₇	#103	1	2	yes	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	4	no	—
153	C₂×Dic₄₇	—	4	2	no	—
154	C₂×Dic₄₇	—	4	2	no	—
155	C₂×Dic₄₇	#95	1	2	yes	—
156	C₂×Dic₄₇	#95	1	2	yes	—
157	C₂×Dic₄₇	#95	1	2	yes	—
158	C₂×Dic₄₇	#102	1	2	yes	—
159	C₂×Dic₄₇	#103	1	2	yes	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	4	no	—
163	C₄×D₄₇	—	4	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	C₄×D₄₇	—	4	16	no	—
166	C₄×D₄₇	#102	1	4	yes	—
167	C₄×D₄₇	#103	1	4	yes	—
168	C₄×D₄₇	#106	1	4	yes	—
169	C₄×D₄₇	#107	1	4	yes	—
170	C₈×C₄₇	—	4	2	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	#7901	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
176	C₂²×C₄₇	#407	1	2	yes	—
177	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
179	C₂²×C₄₇	#421	1	2	yes	—
180	C₂×D₄₇	—	2	2	no	—
181	C₂×D₄₇	—	2	2	no	—
182	C₂×D₄₇	—	2	4	no	—
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	#340	1	4	yes	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
189	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
191	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
192	C₄×C₄₇	#423	1	2	yes	—
193	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
195	Dic₄₇	—	2	2	no	—
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	4	4	no	—
198	Dic₄₇	#340	1	4	yes	—
199	C₂×#431	—	47	1	no	—
200	C₂×#423	—	47	1	no	—
201	C₂×C₄×C₄⋊C₄	—	47	1	no	—
202	#1279	—	47	1	no	—
203	#1279	—	47	1	no	—
204	#1279	—	47	1	no	—
205	#1279	D₄₇	1	1	yes	characteristic, complemented
206	C₂×C₄₇	#1486	1	2	yes	—
207	C₂×C₄₇	#1487	1	2	yes	—
208	C₂×C₄₇	#1728	1	1	yes	characteristic
209	C₂×C₄₇	#1733	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
211	D₄₇	—	2	4	no	—
212	C₂²×M₁₆	—	94	1	no	—
213	C₂²×C₄⋊C₄	—	47	2	no	—
214	C₂²×C₄²	—	47	1	no	—
215	C₂²×C₄²	—	94	1	no	—
216	#431	—	47	4	no	—
217	#431	—	94	2	no	—
218	#423	—	47	4	no	—
219	#423	—	94	2	no	—
220	C₂×C₄⋊C₈	—	47	1	no	—
221	C₂×C₄⋊C₈	—	94	1	no	—
222	C₂×C₄⋊C₈	—	94	1	no	—
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	—	94	1	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
227	C₄×C₄⋊C₄	—	47	2	no	—
228	C₄×C₄⋊C₄	—	47	1	no	—
229	C₄×C₄⋊C₄	—	94	1	no	—
230	C₄×C₄⋊C₄	—	94	1	no	—
231	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
232	C₂×#95	—	94	1	no	—
233	C₄₇	#7901	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	—	47	1	no	—
235	C₂³×C₄	—	47	1	no	—
236	C₂³×C₄	—	47	1	no	—
237	C₂³×C₄	—	94	2	no	—
238	C₂×M₁₆	—	94	4	no	—
239	C₂×M₁₆	—	188	2	no	—
240	C₂×M₁₆	—	188	2	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	94	1	no	—
244	C₂²×C₈	—	94	1	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	—	94	4	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	—	94	4	no	—
249	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	47	1	no	—
252	C₂×C₄²	—	47	1	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	47	2	no	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	—	47	2	no	—
257	C₂×C₄²	—	47	2	no	—
258	C₂×C₄²	—	94	2	no	—
259	C₂×C₄²	—	94	1	no	—
260	C₂×C₄²	—	188	2	no	—
261	C₂×C₄²	—	188	2	no	—
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	47	2	no	—
265	C₄⋊C₈	—	94	4	no	—
266	C₄⋊C₈	—	94	4	no	—
267	C₄⋊C₈	—	94	1	no	—
268	C₄⋊C₈	C₄×D₄₇	1	2	yes	complemented
269	C₂²⋊C₈	—	94	4	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	47	2	no	—
272	C₄×C₈	—	94	1	no	—
273	C₄×C₈	C₄×D₄₇	1	2	yes	complemented
274	#95	—	2	1	no	—
275	#95	—	94	2	no	—
276	#95	—	94	1	no	—
277	C₂⁴	—	47	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	47	2	no	—
285	C₂²×C₄	—	47	2	no	—
286	C₂²×C₄	—	47	1	no	—
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	47	2	no	—
289	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	94	8	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	—	94	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	4	no	—
298	C₂²×C₄	—	188	4	no	—
299	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
302	M₁₆	—	188	8	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	188	2	no	—
311	C₂×C₈	—	188	1	no	—
312	C₂×C₈	—	188	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	47	4	no	—
315	C₄⋊C₄	—	94	8	no	—
316	C₄⋊C₄	—	94	2	no	—
317	C₄⋊C₄	#10625324	1	4	yes	complemented
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	47	2	no	—
321	C₄²	—	47	2	no	—
322	C₄²	—	47	2	no	—
323	C₄²	—	47	2	no	—
324	C₄²	—	47	2	no	—
325	C₄²	—	47	2	no	—
326	C₄²	—	188	4	no	—
327	C₄²	—	188	1	no	—
328	C₄²	—	188	1	no	—
329	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₄²	D₄×D₄₇	1	1	yes	characteristic
332	C₄²	Q₈×D₄₇	1	1	yes	characteristic
333	C₂³	—	47	2	no	—
334	C₂³	—	47	2	no	—
335	C₂³	—	47	2	no	—
336	C₂³	—	94	2	no	—
337	C₂³	—	94	2	no	—
338	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	47	2	no	—
344	C₂×C₄	—	47	2	no	—
345	C₂×C₄	—	47	2	no	—
346	C₂×C₄	—	47	4	no	—
347	C₂×C₄	—	47	4	no	—
348	C₂×C₄	—	47	4	no	—
349	C₂×C₄	—	47	4	no	—
350	C₂×C₄	—	47	2	no	—
351	C₂×C₄	—	47	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	16	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
370	C₂×C₄	C₂×#10625324	1	2	yes	—
371	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
374	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	188	2	no	—
378	C₈	—	188	2	no	—
379	C₂²	—	47	4	no	—
380	C₂²	—	94	2	no	—
381	C₂²	—	94	4	no	—
382	C₂²	—	94	4	no	—
383	C₂²	—	94	2	no	—
384	C₂²	#95×D₄₇	1	1	yes	characteristic
385	C₂²	#15689085	1	2	yes	—
386	C₂²	#102×D₄₇	1	1	yes	characteristic
387	C₂²	#103×D₄₇	1	1	yes	characteristic
388	C₂²	#15689138	1	2	yes	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	4	no	—
392	C₄	—	47	4	no	—
393	C₄	—	94	2	no	—
394	C₄	—	94	2	no	—
395	C₄	—	188	4	no	—
396	C₄	C₄×#10625324	1	1	yes	characteristic
397	C₄	#15689075	1	1	yes	characteristic
398	C₄	#102×D₄₇	1	1	yes	characteristic
399	C₄	#103×D₄₇	1	1	yes	characteristic
400	C₄	#15689145	1	2	yes	—
401	C₄	#106×D₄₇	1	1	yes	characteristic
402	C₄	#107×D₄₇	1	1	yes	characteristic
403	C₂	—	94	4	no	—
404	C₂	#20241811	1	2	yes	—
405	C₂	#20241815	1	2	yes	—
406	C₂	#20243080	1	1	yes	characteristic
407	C₂	#20243096	1	1	yes	characteristic
408	C₂	#340×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#7901
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #20241229	C₂	semidirect
5. #20241228	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
13. #15689174	C₄	semidirect
15. #15689145	C₄	semidirect
54. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
59. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
68. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
70. C₄×C₈×C₄₇	C₂×C₄	semidirect
103. C₄⋊C₄×C₄₇	M₁₆	semidirect
111. C₄⋊Dic₄₇	M₁₆	semidirect
205. #1279	D₄₇	semidirect
233. C₄₇	#7901	semidirect
268. C₄⋊C₈	C₄×D₄₇	semidirect
273. C₄×C₈	C₄×D₄₇	semidirect
317. C₄⋊C₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689174	2
C₂×#15689145	2
C₄×C₄⋊C₄×D₄₇	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7901	47