Subgroups — C₄₇×#22803 #26062501

Order 12032.

710 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2925	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1975	C₂	1	2	yes	maximal
4	C₄₇×#1929	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1806	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1773	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
10	C₄×#41×C₄₇	C₂²	1	2	yes	—
11	C₄×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
12	C₄×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
13	C₄×SD₁₆×C₄₇	C₄	1	2	yes	complemented
14	C₄×SD₁₆×C₄₇	C₄	1	2	yes	complemented
15	C₄×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
16	C₄×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
17	C₄₇×#433	—	2	4	no	—
18	C₄₇×#432	—	2	2	no	—
19	C₄₇×#431	—	2	2	no	—
20	C₂×#108×C₄₇	C₂²	1	2	yes	—
21	C₂×#108×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#427	C₂²	1	1	yes	characteristic
23	C₄₇×#423	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#104×C₄₇	C₂²	1	4	yes	—
26	C₄₇×#416	C₂²	1	2	yes	—
27	C₄₇×#408	C₂²	1	4	yes	—
28	C₄₇×#405	C₂²	1	4	yes	—
29	C₂×#97×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#339	C₂²	1	4	yes	—
33	C₄₇×#336	C₂²	1	2	yes	—
34	C₂×#41×C₄₇	C₂³	1	2	yes	—
35	#135×C₄₇	—	2	2	no	—
36	#135×C₄₇	—	2	2	no	—
37	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
41	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₄₇	—	2	2	no	—
47	C₄×D₄×C₄₇	—	2	2	no	—
48	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
50	#117×C₄₇	—	2	2	no	—
51	#117×C₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
55	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
56	#108×C₄₇	—	2	4	no	—
57	#108×C₄₇	—	4	2	no	—
58	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
59	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
60	#106×C₄₇	C₂×C₄	1	2	yes	—
61	C₄⋊C₈×C₄₇	—	2	2	no	—
62	C₄⋊C₈×C₄₇	—	2	2	no	—
63	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
64	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
65	#104×C₄₇	—	4	4	no	—
66	#103×C₄₇	C₂×C₄	1	2	yes	—
67	#103×C₄₇	C₂×C₄	1	2	yes	—
68	#102×C₄₇	C₂×C₄	1	2	yes	—
69	#102×C₄₇	C₂×C₄	1	2	yes	—
70	C₂²⋊C₈×C₄₇	—	2	4	no	—
71	C₂²⋊C₈×C₄₇	—	2	4	no	—
72	#97×C₄₇	—	2	4	no	—
73	#97×C₄₇	—	2	4	no	—
74	C₄×C₈×C₄₇	—	2	4	no	—
75	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#95×C₄₇	—	2	1	no	—
80	#41×C₄₇	—	2	2	no	—
81	#41×C₄₇	—	2	2	no	—
82	#41×C₄₇	—	2	2	no	—
83	#41×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	Q₁₆×C₄₇	—	2	2	no	—
95	SD₁₆×C₄₇	—	2	4	no	—
96	D₈×C₄₇	—	2	2	no	—
97	M₁₆×C₄₇	—	2	4	no	—
98	M₁₆×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	4	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₄₇	#41	1	2	yes	—
110	C₂×C₈×C₄₇	#41	1	2	yes	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	4	2	no	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
130	Q₈×C₄₇	—	2	2	no	—
131	Q₈×C₄₇	—	2	2	no	—
132	D₄×C₄₇	—	2	2	no	—
133	D₄×C₄₇	—	2	2	no	—
134	D₄×C₄₇	—	4	2	no	—
135	D₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	8	2	no	—
148	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₈×C₄₇	—	2	1	no	—
159	C₈×C₄₇	—	2	1	no	—
160	C₈×C₄₇	—	2	4	no	—
161	C₈×C₄₇	—	4	4	no	—
162	C₈×C₄₇	#117	1	2	yes	—
163	C₈×C₄₇	#117	1	2	yes	—
164	#22803	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	4	2	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	—	4	2	no	—
170	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₄₇	#555	1	1	yes	characteristic
172	C₂²×C₄₇	#556	1	1	yes	characteristic
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	1	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	—	4	2	no	—
178	C₄×C₄₇	—	4	2	no	—
179	C₄×C₄₇	—	8	2	no	—
180	C₄×C₄₇	#444	1	2	yes	—
181	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
182	C₄×C₄₇	#520	1	1	yes	characteristic
183	C₄×C₄₇	#547	1	1	yes	characteristic
184	C₄×C₄₇	#550	1	1	yes	characteristic
185	C₄×#135	C₂×C₄₇	1	1	yes	characteristic
186	#2925	C₂×C₄₇	1	2	yes	complemented
187	#1975	C₂×C₄₇	1	2	yes	—
188	#1929	C₂×C₄₇	1	4	yes	complemented
189	#1848	C₂×C₄₇	1	1	yes	characteristic, complemented
190	#1806	C₂×C₄₇	1	2	yes	complemented
191	#1773	C₂×C₄₇	1	2	yes	complemented
192	#1770	C₂×C₄₇	1	1	yes	characteristic, complemented
193	C₂×C₄₇	—	2	1	no	—
194	C₂×C₄₇	—	2	1	no	—
195	C₂×C₄₇	—	8	2	no	—
196	C₂×C₄₇	#2354	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
198	C₂×C₄₇	#2957	1	1	yes	characteristic
199	C₂×#135	C₂²×C₄₇	1	1	yes	characteristic
200	C₄×#41	C₂²×C₄₇	1	2	yes	—
201	C₄×Q₁₆	C₄×C₄₇	1	1	yes	characteristic, complemented
202	C₄×Q₁₆	C₄×C₄₇	1	1	yes	characteristic, complemented
203	C₄×SD₁₆	C₄×C₄₇	1	2	yes	complemented
204	C₄×SD₁₆	C₄×C₄₇	1	2	yes	complemented
205	C₄×D₈	C₄×C₄₇	1	1	yes	characteristic, complemented
206	C₄×D₈	C₄×C₄₇	1	1	yes	characteristic, complemented
207	#433	—	2	4	no	—
208	#432	—	2	2	no	—
209	#431	—	2	2	no	—
210	C₂×#108	C₂²×C₄₇	1	2	yes	—
211	C₂×#108	C₂²×C₄₇	1	2	yes	—
212	#427	C₂²×C₄₇	1	1	yes	characteristic
213	#423	C₂²×C₄₇	1	2	yes	—
214	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×#104	C₂²×C₄₇	1	4	yes	—
216	#416	C₂²×C₄₇	1	2	yes	—
217	#408	C₂²×C₄₇	1	4	yes	—
218	#405	C₂²×C₄₇	1	4	yes	—
219	C₂×#97	C₂²×C₄₇	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
221	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
222	#339	C₂²×C₄₇	1	4	yes	—
223	#336	C₂²×C₄₇	1	2	yes	—
224	C₄₇	#22803	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#41	C₂³×C₄₇	1	2	yes	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	C₂×Q₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
230	C₂×D₈	C₂×C₄×C₄₇	1	1	yes	characteristic
231	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
232	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
234	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
235	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
236	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
240	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
241	#117	—	2	2	no	—
242	#117	C₂³×C₄₇	1	2	yes	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
246	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
247	#108	—	2	4	no	—
248	#108	—	4	2	no	—
249	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
250	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
251	#106	C₂×C₄×C₄₇	1	2	yes	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	2	no	—
254	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
255	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
256	#104	—	4	4	no	—
257	#103	C₂×C₄×C₄₇	1	2	yes	—
258	#103	C₂×C₄×C₄₇	1	2	yes	—
259	#102	C₂×C₄×C₄₇	1	2	yes	—
260	#102	C₂×C₄×C₄₇	1	2	yes	—
261	C₂²⋊C₈	—	2	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	#97	—	2	4	no	—
265	C₄×C₈	—	2	4	no	—
266	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
267	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
268	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
269	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
270	#95	—	2	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
283	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	2	4	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
298	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
300	C₂×C₈	#41×C₄₇	1	2	yes	—
301	C₂×C₈	#41×C₄₇	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
306	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
316	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
347	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
348	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	4	no	—
353	C₈	#117×C₄₇	1	2	yes	—
354	C₈	#117×C₄₇	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
361	C₂²	C₄₇×#555	1	1	yes	characteristic
362	C₂²	C₄₇×#556	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	C₄₇×#444	1	2	yes	—
371	C₄	C₂×#117×C₄₇	1	1	yes	characteristic
372	C₄	C₄₇×#520	1	1	yes	characteristic
373	C₄	C₄₇×#547	1	1	yes	characteristic
374	C₄	C₄₇×#550	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₄₇×#2354	1	1	yes	characteristic
379	C₂	C₂×C₄₇×#444	1	1	yes	characteristic
380	C₂	C₄₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#135×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂×C₄⋊C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2925	C₂	semidirect
4. C₄₇×#1929	C₂	semidirect
5. C₄₇×#1848	C₂	semidirect
6. C₄₇×#1806	C₂	semidirect
7. C₄₇×#1773	C₂	semidirect
8. C₄₇×#1770	C₂	semidirect
11. C₄×Q₁₆×C₄₇	C₄	semidirect
12. C₄×Q₁₆×C₄₇	C₄	semidirect
13. C₄×SD₁₆×C₄₇	C₄	semidirect
14. C₄×SD₁₆×C₄₇	C₄	semidirect
15. C₄×D₈×C₄₇	C₄	semidirect
16. C₄×D₈×C₄₇	C₄	semidirect
164. #22803	C₄₇	direct (N × H)
186. #2925	C₂×C₄₇	semidirect
188. #1929	C₂×C₄₇	semidirect
189. #1848	C₂×C₄₇	semidirect
190. #1806	C₂×C₄₇	semidirect
191. #1773	C₂×C₄₇	semidirect
192. #1770	C₂×C₄₇	semidirect
201. C₄×Q₁₆	C₄×C₄₇	semidirect
202. C₄×Q₁₆	C₄×C₄₇	semidirect
203. C₄×SD₁₆	C₄×C₄₇	semidirect
204. C₄×SD₁₆	C₄×C₄₇	semidirect
205. C₄×D₈	C₄×C₄₇	semidirect
206. C₄×D₈	C₄×C₄₇	semidirect
224. C₄₇	#22803	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#135×C₄₇	2
C₄₇×#2925	2
C₄₇×#1975	2
C₄₇×#1929	2
C₄₇×#1848	2
C₄₇×#1806	2
C₄₇×#1773	2
C₄₇×#1770	2
#22803	47

Subgroups — C47×#22803 #26062501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22803 #26062501