Subgroups — #26105808

Order 12032.

770 conjugacy classes of subgroups.

The subgroup lattice has 400 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×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093982	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×C₈×D₄₇	—	2	1	no	—
9	C₂×#13093982	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	#15689174	—	2	2	no	—
12	#15689174	C₄	1	4	yes	complemented
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	—	2	1	no	—
15	C₂×Dic₄₇⋊C₈	—	2	1	no	—
16	C₄⋊C₈×D₄₇	—	2	2	no	—
17	C₄⋊C₈×D₄₇	C₄	1	4	yes	complemented
18	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
23	#15688970	—	2	1	no	—
24	#15688968	—	2	1	no	—
25	C₄²×Dic₄₇	—	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	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	—	2	1	no	—
34	C₂×C₈×D₄₇	—	2	4	no	—
35	C₂×C₈×D₄₇	—	4	2	no	—
36	C₂×C₈×D₄₇	—	4	2	no	—
37	#13093982	—	2	4	no	—
38	#13093982	C₈	1	8	yes	complemented
39	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
40	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	2	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	C₂×C₄	1	2	yes	—
48	C₄²×D₄₇	C₂×C₄	1	2	yes	—
49	C₄²×D₄₇	D₄	1	2	yes	—
50	C₄²×D₄₇	Q₈	1	2	yes	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
53	Dic₄₇⋊C₈	—	2	4	no	—
54	Dic₄₇⋊C₈	—	2	4	no	—
55	(C₂×D₄₇)⋊C₈	—	2	4	no	—
56	C₄×C₄₇⋊C₈	—	2	1	no	—
57	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
58	C₄₇⋊#95	—	2	1	no	—
59	C₄₇⋊#95	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₇	—	2	1	no	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₄₇	—	2	1	no	—
66	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₄₇	—	2	1	no	—
68	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
69	#95×C₄₇	—	2	1	no	—
70	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₄₇	—	2	1	no	—
80	C₂×C₄×D₄₇	—	2	1	no	—
81	C₂×C₄×D₄₇	—	2	1	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	4	2	no	—
84	C₂×C₄×D₄₇	C₄²	1	2	yes	—
85	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
91	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	4	2	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	—	4	1	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
99	C₄²×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	—	4	1	no	—
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	(C₂×D₄₇)⋊C₄	—	2	8	no	—
106	C₄⋊Dic₄₇	—	2	2	no	—
107	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
108	C₄×Dic₄₇	—	2	8	no	—
109	C₄×Dic₄₇	—	4	4	no	—
110	C₄×Dic₄₇	—	4	1	no	—
111	C₄×Dic₄₇	—	4	1	no	—
112	C₄×Dic₄₇	C₄²	1	2	yes	—
113	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
114	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
115	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
116	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	4	1	no	—
122	C₂×C₄₇⋊C₈	—	4	1	no	—
123	C₈×D₄₇	—	4	8	no	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×D₄₇	—	2	1	no	—
126	C₂²×D₄₇	—	2	1	no	—
127	C₂²×D₄₇	—	2	2	no	—
128	C₂²×D₄₇	#95	1	2	yes	—
129	C₂²×D₄₇	C₂²⋊C₈	1	4	yes	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
142	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
146	C₂×Dic₄₇	—	2	1	no	—
147	C₂×Dic₄₇	—	2	1	no	—
148	C₂×Dic₄₇	—	2	2	no	—
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	4	2	no	—
151	C₂×Dic₄₇	—	4	2	no	—
152	C₂×Dic₄₇	#95	1	2	yes	—
153	C₂×Dic₄₇	#95	1	2	yes	—
154	C₂×Dic₄₇	#95	1	2	yes	—
155	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	2	2	no	—
158	C₄×D₄₇	—	2	2	no	—
159	C₄×D₄₇	—	2	2	no	—
160	C₄×D₄₇	—	4	2	no	—
161	C₄×D₄₇	—	4	2	no	—
162	C₄×D₄₇	C₄×C₈	1	4	yes	—
163	C₄×D₄₇	#97	1	4	yes	—
164	C₄×D₄₇	C₄⋊C₈	1	8	yes	—
165	C₈×C₄₇	—	4	2	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	C₄₇⋊C₈	—	4	2	no	—
169	#7891	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
172	C₂²×C₄₇	#417	1	1	yes	characteristic
173	C₂²×C₄₇	#417	1	1	yes	characteristic
174	C₂²×C₄₇	#421	1	2	yes	—
175	C₂×D₄₇	—	2	4	no	—
176	C₂×D₄₇	—	2	4	no	—
177	C₂×D₄₇	—	2	2	no	—
178	C₂×D₄₇	—	2	2	no	—
179	C₂×D₄₇	#336	1	4	yes	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	4	no	—
183	C₄×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#97	1	1	yes	characteristic
185	C₄×C₄₇	#418	1	1	yes	characteristic
186	C₄×C₄₇	#419	1	1	yes	characteristic
187	C₄×C₄₇	C₂×C₄⋊C₈	1	2	yes	—
188	C₄×C₄₇	#428	1	1	yes	characteristic
189	C₄×C₄₇	#428	1	1	yes	characteristic
190	Dic₄₇	—	2	2	no	—
191	Dic₄₇	—	2	2	no	—
192	Dic₄₇	—	4	4	no	—
193	Dic₄₇	#336	1	4	yes	—
194	C₂×#431	—	47	1	no	—
195	C₂²×C₄⋊C₈	—	47	1	no	—
196	C₄×#117	—	47	1	no	—
197	#1279	—	47	1	no	—
198	#1279	—	47	1	no	—
199	#1279	—	47	1	no	—
200	#1279	D₄₇	1	1	yes	characteristic, complemented
201	C₂×C₄₇	#1477	1	2	yes	—
202	C₂×C₄₇	#1477	1	2	yes	—
203	C₂×C₄₇	C₂×#336	1	1	yes	characteristic
204	C₂×C₄₇	#1733	1	1	yes	characteristic
205	C₂×C₄₇	#1736	1	1	yes	characteristic
206	D₄₇	—	2	4	no	—
207	C₂³×C₈	—	94	1	no	—
208	C₂×#117	—	47	2	no	—
209	C₂²×C₄²	—	47	1	no	—
210	#431	—	47	4	no	—
211	#431	—	94	2	no	—
212	C₂×C₄⋊C₈	—	47	1	no	—
213	C₂×C₄⋊C₈	—	47	4	no	—
214	C₂×C₄⋊C₈	—	94	2	no	—
215	C₂×C₄⋊C₈	—	94	1	no	—
216	C₂×C₄⋊C₈	—	94	1	no	—
217	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	—	94	1	no	—
219	C₂×C₄×C₈	—	47	1	no	—
220	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	47	2	no	—
222	C₄×C₄⋊C₄	—	47	1	no	—
223	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	—	94	1	no	—
225	C₄×C₂²⋊C₄	—	94	1	no	—
226	#376	—	94	1	no	—
227	C₄³	—	94	1	no	—
228	C₄₇	#7891	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₄	—	47	1	no	—
230	C₂³×C₄	—	47	1	no	—
231	C₂³×C₄	—	47	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	94	4	no	—
235	C₂²×C₈	—	94	1	no	—
236	C₂²×C₈	—	94	1	no	—
237	C₂²×C₈	—	188	2	no	—
238	C₂²×C₈	—	188	2	no	—
239	#117	—	47	8	no	—
240	#117	—	94	4	no	—
241	C₂×C₄⋊C₄	—	47	2	no	—
242	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
243	C₂×C₂²⋊C₄	—	94	2	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	47	1	no	—
246	C₂×C₄²	—	47	1	no	—
247	C₂×C₄²	—	47	1	no	—
248	C₂×C₄²	—	47	2	no	—
249	C₂×C₄²	—	47	2	no	—
250	C₂×C₄²	—	47	2	no	—
251	C₂×C₄²	—	47	2	no	—
252	C₂×C₄²	—	94	2	no	—
253	C₂×C₄²	—	94	2	no	—
254	C₂×C₄²	—	94	1	no	—
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	47	2	no	—
258	C₄⋊C₈	—	94	4	no	—
259	C₄⋊C₈	—	94	4	no	—
260	C₄⋊C₈	—	94	1	no	—
261	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
262	C₂²⋊C₈	—	94	4	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	47	2	no	—
265	C₄×C₈	—	94	1	no	—
266	C₄×C₈	C₄×D₄₇	1	2	yes	—
267	#95	—	2	1	no	—
268	#95	—	94	2	no	—
269	#95	—	94	1	no	—
270	C₂⁴	—	47	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	47	1	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	47	2	no	—
275	C₂²×C₄	—	47	4	no	—
276	C₂²×C₄	—	47	4	no	—
277	C₂²×C₄	—	47	1	no	—
278	C₂²×C₄	—	47	1	no	—
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	1	no	—
286	C₂²×C₄	—	94	1	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	188	2	no	—
289	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	94	2	no	—
299	C₂×C₈	—	188	8	no	—
300	C₂×C₈	—	188	2	no	—
301	C₂×C₈	—	188	1	no	—
302	C₂×C₈	—	188	1	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	47	4	no	—
305	C₄⋊C₄	—	94	2	no	—
306	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
307	C₂²⋊C₄	—	94	8	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	1	no	—
310	C₄²	—	47	2	no	—
311	C₄²	—	47	2	no	—
312	C₄²	—	47	2	no	—
313	C₄²	—	47	2	no	—
314	C₄²	—	47	2	no	—
315	C₄²	—	47	2	no	—
316	C₄²	—	94	8	no	—
317	C₄²	—	188	4	no	—
318	C₄²	—	188	1	no	—
319	C₄²	—	188	1	no	—
320	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₄²	D₄×D₄₇	1	1	yes	characteristic
323	C₄²	Q₈×D₄₇	1	1	yes	characteristic
324	C₂³	—	47	2	no	—
325	C₂³	—	47	4	no	—
326	C₂³	—	94	1	no	—
327	C₂³	—	94	1	no	—
328	C₂³	—	94	2	no	—
329	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	47	2	no	—
335	C₂×C₄	—	47	4	no	—
336	C₂×C₄	—	47	4	no	—
337	C₂×C₄	—	47	4	no	—
338	C₂×C₄	—	47	8	no	—
339	C₂×C₄	—	47	2	no	—
340	C₂×C₄	—	47	2	no	—
341	C₂×C₄	—	94	1	no	—
342	C₂×C₄	—	94	1	no	—
343	C₂×C₄	—	94	2	no	—
344	C₂×C₄	—	94	2	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	4	no	—
349	C₂×C₄	—	188	2	no	—
350	C₂×C₄	—	188	2	no	—
351	C₂×C₄	—	188	2	no	—
352	C₂×C₄	—	188	2	no	—
353	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
358	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
360	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
361	C₂×C₄	#13094048	1	1	yes	characteristic
362	C₂×C₄	#13094051	1	1	yes	characteristic
363	C₂×C₄	#13094053	1	1	yes	characteristic
364	C₂×C₄	#13094056	1	1	yes	characteristic
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₈	—	188	2	no	—
368	C₈	—	188	2	no	—
369	C₂²	—	47	4	no	—
370	C₂²	—	94	4	no	—
371	C₂²	—	94	4	no	—
372	C₂²	—	94	2	no	—
373	C₂²	—	94	2	no	—
374	C₂²	#95×D₄₇	1	1	yes	characteristic
375	C₂²	C₂²⋊C₈×D₄₇	1	2	yes	—
376	C₂²	#15689121	1	1	yes	characteristic
377	C₂²	#15689123	1	1	yes	characteristic
378	C₂²	#15689138	1	2	yes	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	4	no	—
382	C₄	—	47	4	no	—
383	C₄	—	94	2	no	—
384	C₄	—	94	2	no	—
385	C₄	—	188	4	no	—
386	C₄	C₄×C₈×D₄₇	1	1	yes	characteristic
387	C₄	#97×D₄₇	1	1	yes	characteristic
388	C₄	#15689126	1	1	yes	characteristic
389	C₄	#15689130	1	1	yes	characteristic
390	C₄	C₄⋊C₈×D₄₇	1	2	yes	—
391	C₄	#15689162	1	1	yes	characteristic
392	C₄	#15689164	1	1	yes	characteristic
393	C₂	—	94	4	no	—
394	C₂	#20241772	1	2	yes	—
395	C₂	#20241774	1	2	yes	—
396	C₂	#336×D₄₇	1	1	yes	characteristic
397	C₂	#20243096	1	1	yes	characteristic
398	C₂	#20243106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂×C₄×C₈
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	#7891
LCS	G ▷ 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
12. #15689174	C₄	semidirect
17. C₄⋊C₈×D₄₇	C₄	semidirect
38. #13093982	C₈	semidirect
98. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
107. C₄⋊Dic₄₇	C₂×C₈	semidirect
200. #1279	D₄₇	semidirect
228. C₄₇	#7891	semidirect
306. C₄⋊C₄	C₈×D₄₇	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×C₄⋊C₈×D₄₇	2
C₄×#13093982	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7891	47