Subgroups — #26105804

Order 12032.

830 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689175	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	#15689175	—	2	2	no	—
12	#15689175	C₄	1	4	yes	complemented
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₈×Dic₄₇	—	2	1	no	—
17	C₂×C₈×Dic₄₇	—	2	1	no	—
18	C₄×C₈×D₄₇	—	2	2	no	—
19	C₄×C₈×D₄₇	C₄	1	4	yes	complemented
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	8	no	—
35	C₂×C₈×D₄₇	—	2	4	no	—
36	#13093982	—	2	4	no	—
37	#13093982	C₈	1	8	yes	complemented
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
39	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	2	2	no	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
46	C₄²×D₄₇	C₂×C₄	1	2	yes	—
47	C₄²×D₄₇	C₂×C₄	1	2	yes	—
48	C₄²×D₄₇	D₄	1	2	yes	—
49	C₄²×D₄₇	Q₈	1	2	yes	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
52	(C₂×D₄₇)⋊C₈	—	2	4	no	—
53	C₄×C₄₇⋊C₈	—	2	1	no	—
54	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
55	C₈×Dic₄₇	—	2	4	no	—
56	C₈×Dic₄₇	—	2	4	no	—
57	C₄₇⋊#95	—	2	1	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₄₇	—	2	1	no	—
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₄₇	—	2	1	no	—
67	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
68	#95×C₄₇	—	2	1	no	—
69	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₄₇	—	2	1	no	—
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	4	no	—
83	C₂×C₄×D₄₇	C₄²	1	2	yes	—
84	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₇	C₄⋊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	C₂×C₈	1	4	yes	—
90	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
98	C₄²×C₄₇	—	4	1	no	—
99	C₄²×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	(C₂×D₄₇)⋊C₄	—	2	8	no	—
105	C₄⋊Dic₄₇	—	2	2	no	—
106	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
107	C₄×Dic₄₇	—	2	8	no	—
108	C₄×Dic₄₇	—	4	1	no	—
109	C₄×Dic₄₇	—	4	1	no	—
110	C₄×Dic₄₇	—	4	4	no	—
111	C₄×Dic₄₇	C₄²	1	2	yes	—
112	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
113	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
114	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
115	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
116	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	4	1	no	—
121	C₂×C₄₇⋊C₈	—	4	1	no	—
122	C₈×D₄₇	—	2	16	no	—
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×D₄₇	—	2	1	no	—
125	C₂²×D₄₇	—	2	1	no	—
126	C₂²×D₄₇	—	2	2	no	—
127	C₂²×D₄₇	#95	1	2	yes	—
128	C₂²×D₄₇	C₂²⋊C₈	1	4	yes	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₄⋊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	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
141	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
145	C₂×Dic₄₇	—	2	1	no	—
146	C₂×Dic₄₇	—	2	1	no	—
147	C₂×Dic₄₇	—	2	4	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	#95	1	2	yes	—
151	C₂×Dic₄₇	#95	1	2	yes	—
152	C₂×Dic₄₇	#95	1	2	yes	—
153	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
154	C₂×Dic₄₇	#104	1	4	yes	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	2	2	no	—
158	C₄×D₄₇	—	2	2	no	—
159	C₄×D₄₇	—	2	4	no	—
160	C₄×D₄₇	—	2	4	no	—
161	C₄×D₄₇	C₄×C₈	1	4	yes	—
162	C₄×D₄₇	#97	1	4	yes	—
163	C₄×D₄₇	C₄⋊C₈	1	8	yes	—
164	C₈×C₄₇	—	2	4	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₄₇⋊C₈	—	2	4	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	#7890	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
171	C₂²×C₄₇	#416	1	1	yes	characteristic
172	C₂²×C₄₇	#416	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#104	1	2	yes	—
174	C₂×D₄₇	—	2	4	no	—
175	C₂×D₄₇	—	2	4	no	—
176	C₂×D₄₇	—	2	2	no	—
177	C₂×D₄₇	—	2	2	no	—
178	C₂×D₄₇	#336	1	4	yes	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
183	C₄×C₄₇	C₂×#97	1	1	yes	characteristic
184	C₄×C₄₇	#416	1	1	yes	characteristic
185	C₄×C₄₇	#416	1	1	yes	characteristic
186	C₄×C₄₇	C₂×C₄⋊C₈	1	2	yes	—
187	C₄×C₄₇	#427	1	1	yes	characteristic
188	C₄×C₄₇	#427	1	1	yes	characteristic
189	Dic₄₇	—	2	2	no	—
190	Dic₄₇	—	4	4	no	—
191	Dic₄₇	#336	1	4	yes	—
192	Dic₄₇	#339	1	4	yes	—
193	C₂×#431	—	47	1	no	—
194	C₂²×C₄×C₈	—	47	1	no	—
195	C₄×#117	—	47	1	no	—
196	#1279	—	47	1	no	—
197	#1279	—	47	1	no	—
198	#1279	—	47	1	no	—
199	#1279	D₄₇	1	1	yes	characteristic, complemented
200	C₂×C₄₇	#1476	1	2	yes	—
201	C₂×C₄₇	#1476	1	2	yes	—
202	C₂×C₄₇	C₂×#336	1	1	yes	characteristic
203	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
204	C₂×C₄₇	#1735	1	1	yes	characteristic
205	D₄₇	—	2	4	no	—
206	C₂³×C₈	—	94	1	no	—
207	C₂×#117	—	47	2	no	—
208	C₂²×C₄²	—	47	1	no	—
209	#431	—	47	4	no	—
210	#431	—	94	2	no	—
211	C₂×C₄⋊C₈	—	47	1	no	—
212	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
213	C₂×C₂²⋊C₈	—	94	1	no	—
214	C₂×C₄×C₈	—	47	1	no	—
215	C₂×C₄×C₈	—	47	4	no	—
216	C₂×C₄×C₈	—	94	2	no	—
217	C₂×C₄×C₈	—	94	1	no	—
218	C₂×C₄×C₈	—	94	1	no	—
219	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₄×C₄⋊C₄	—	47	2	no	—
221	C₄×C₄⋊C₄	—	47	1	no	—
222	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
223	C₄×C₂²⋊C₄	—	94	1	no	—
224	C₄×C₂²⋊C₄	—	94	1	no	—
225	#376	—	94	1	no	—
226	C₄³	—	94	1	no	—
227	C₄₇	#7890	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₄	—	47	1	no	—
229	C₂³×C₄	—	47	1	no	—
230	C₂³×C₄	—	47	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	94	4	no	—
234	C₂²×C₈	—	94	8	no	—
235	C₂²×C₈	—	94	1	no	—
236	C₂²×C₈	—	94	1	no	—
237	#117	—	47	8	no	—
238	#117	—	94	4	no	—
239	C₂×C₄⋊C₄	—	47	2	no	—
240	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
241	C₂×C₂²⋊C₄	—	94	2	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	47	1	no	—
244	C₂×C₄²	—	47	1	no	—
245	C₂×C₄²	—	47	1	no	—
246	C₂×C₄²	—	47	2	no	—
247	C₂×C₄²	—	47	2	no	—
248	C₂×C₄²	—	47	2	no	—
249	C₂×C₄²	—	47	2	no	—
250	C₂×C₄²	—	94	2	no	—
251	C₂×C₄²	—	94	2	no	—
252	C₂×C₄²	—	94	1	no	—
253	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	47	2	no	—
256	C₄⋊C₈	—	94	1	no	—
257	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
258	C₂²⋊C₈	—	94	4	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	—	47	2	no	—
261	C₄×C₈	—	94	4	no	—
262	C₄×C₈	—	94	4	no	—
263	C₄×C₈	—	94	1	no	—
264	C₄×C₈	C₄×D₄₇	1	2	yes	—
265	#95	—	2	1	no	—
266	#95	—	94	2	no	—
267	#95	—	94	1	no	—
268	C₂⁴	—	47	1	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	47	1	no	—
271	C₂²×C₄	—	47	1	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	47	4	no	—
275	C₂²×C₄	—	47	4	no	—
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	94	4	no	—
282	C₂²×C₄	—	94	1	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	1	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	94	16	no	—
296	C₂×C₈	—	94	4	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	94	2	no	—
299	C₂×C₈	—	188	1	no	—
300	C₂×C₈	—	188	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	47	4	no	—
303	C₄⋊C₄	—	94	2	no	—
304	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
305	C₂²⋊C₄	—	94	8	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	47	2	no	—
309	C₄²	—	47	2	no	—
310	C₄²	—	47	2	no	—
311	C₄²	—	47	2	no	—
312	C₄²	—	47	2	no	—
313	C₄²	—	47	2	no	—
314	C₄²	—	94	8	no	—
315	C₄²	—	188	4	no	—
316	C₄²	—	188	1	no	—
317	C₄²	—	188	1	no	—
318	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₄²	D₄×D₄₇	1	1	yes	characteristic
321	C₄²	Q₈×D₄₇	1	1	yes	characteristic
322	C₂³	—	47	2	no	—
323	C₂³	—	47	4	no	—
324	C₂³	—	94	1	no	—
325	C₂³	—	94	1	no	—
326	C₂³	—	94	2	no	—
327	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	47	2	no	—
333	C₂×C₄	—	47	2	no	—
334	C₂×C₄	—	47	4	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	—	94	4	no	—
341	C₂×C₄	—	94	4	no	—
342	C₂×C₄	—	94	1	no	—
343	C₂×C₄	—	94	1	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	C₄²×D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
358	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
359	C₂×C₄	#13094043	1	1	yes	characteristic
360	C₂×C₄	#13094045	1	1	yes	characteristic
361	C₂×C₄	#13094045	1	1	yes	characteristic
362	C₂×C₄	#13094047	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₈	—	4	2	no	—
365	C₈	—	94	4	no	—
366	C₈	—	188	2	no	—
367	C₂²	—	47	4	no	—
368	C₂²	—	94	4	no	—
369	C₂²	—	94	4	no	—
370	C₂²	—	94	2	no	—
371	C₂²	—	94	2	no	—
372	C₂²	#95×D₄₇	1	1	yes	characteristic
373	C₂²	C₂²⋊C₈×D₄₇	1	2	yes	—
374	C₂²	#15689116	1	1	yes	characteristic
375	C₂²	#15689118	1	1	yes	characteristic
376	C₂²	#104×D₄₇	1	2	yes	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	4	no	—
380	C₄	—	47	4	no	—
381	C₄	—	47	4	no	—
382	C₄	—	94	2	no	—
383	C₄	—	188	4	no	—
384	C₄	C₄×C₈×D₄₇	1	1	yes	characteristic
385	C₄	#97×D₄₇	1	1	yes	characteristic
386	C₄	#15689116	1	1	yes	characteristic
387	C₄	#15689118	1	1	yes	characteristic
388	C₄	C₄⋊C₈×D₄₇	1	2	yes	—
389	C₄	#15689158	1	1	yes	characteristic
390	C₄	#15689160	1	1	yes	characteristic
391	C₂	—	94	4	no	—
392	C₂	#20241767	1	2	yes	—
393	C₂	#20241769	1	2	yes	—
394	C₂	#336×D₄₇	1	1	yes	characteristic
395	C₂	#339×D₄₇	1	1	yes	characteristic
396	C₂	#20243103	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	#7890
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. #15689175	C₄	semidirect
19. C₄×C₈×D₄₇	C₄	semidirect
37. #13093982	C₈	semidirect
97. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
106. C₄⋊Dic₄₇	C₂×C₈	semidirect
199. #1279	D₄₇	semidirect
227. C₄₇	#7890	semidirect
304. 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×#15689175	2
C₂×C₄×C₈×D₄₇	2
C₄×#13093982	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7890	47