Subgroups — #26122115

Order 12032.

898 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	4	yes	maximal
4	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
8	#15689147	—	2	2	no	—
9	#15689147	C₄	1	4	yes	complemented
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	—	2	1	no	—
13	C₄×C₄⋊Dic₄₇	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	—	2	1	no	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₂×C₄₇⋊#95	C₄	1	2	yes	—
17	#15688891	—	2	8	no	—
18	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#423	—	2	2	no	—
21	C₄₇×#423	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
23	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	4	no	—
27	C₂×#10625329	—	2	4	no	—
28	C₂×#10625329	C₂×C₄	1	4	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
35	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	4	4	no	—
39	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
41	C₄₇⋊#95	—	2	2	no	—
42	C₄₇⋊#95	—	2	2	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	—	2	4	no	—
48	C₂×M₁₆×C₄₇	—	2	4	no	—
49	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	D₄	1	2	yes	—
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
59	C₄⋊C₈×C₄₇	—	2	4	no	—
60	C₄⋊C₈×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	4	2	no	—
65	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
66	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×Dic₄₇	—	2	4	no	—
84	C₂²×Dic₄₇	—	2	4	no	—
85	C₂²×Dic₄₇	—	4	4	no	—
86	C₂²×Dic₄₇	—	4	4	no	—
87	C₂²×Dic₄₇	C₄⋊C₄	1	8	yes	—
88	M₁₆×C₄₇	—	2	8	no	—
89	M₁₆×C₄₇	—	4	2	no	—
90	M₁₆×C₄₇	—	4	2	no	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	4	4	no	—
93	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
98	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
99	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
100	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	2	4	no	—
103	C₄⋊Dic₄₇	—	2	4	no	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄×Dic₄₇	—	4	4	no	—
106	C₄×Dic₄₇	—	4	4	no	—
107	#10625329	—	2	8	no	—
108	#10625329	—	4	2	no	—
109	#10625329	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	4	4	no	—
112	C₂³×C₄₇	—	2	1	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
116	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	#117	1	2	yes	—
120	C₂×C₄×C₄₇	—	2	1	no	—
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	4	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	4	2	no	—
128	C₂×C₄×C₄₇	#95	1	2	yes	—
129	C₂×C₄×C₄₇	#95	1	2	yes	—
130	C₂×C₄×C₄₇	#95	1	2	yes	—
131	C₂×C₄×C₄₇	#95	1	2	yes	—
132	C₂×C₄×C₄₇	#100	1	2	yes	—
133	C₂×C₄×C₄₇	#101	1	2	yes	—
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	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₄₇	#121	1	2	yes	—
143	C₂×C₄×C₄₇	#121	1	2	yes	—
144	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#125	1	2	yes	—
149	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	4	8	no	—
154	C₂×Dic₄₇	—	4	4	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₂×Dic₄₇	—	4	8	no	—
157	C₈×C₄₇	—	4	4	no	—
158	C₄₇⋊C₈	—	4	4	no	—
159	#10847	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
169	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
170	C₂²×C₄₇	#380	1	2	yes	—
171	C₂²×C₄₇	#382	1	1	yes	characteristic
172	C₂²×C₄₇	#384	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
175	C₂²×C₄₇	#413	1	2	yes	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	#343	1	4	yes	complemented
180	C₄×C₄₇	#389	1	2	yes	—
181	C₄×C₄₇	#389	1	2	yes	—
182	C₄×C₄₇	#390	1	1	yes	characteristic
183	C₄×C₄₇	#390	1	1	yes	characteristic
184	C₄×C₄₇	#391	1	1	yes	characteristic
185	C₄×C₄₇	#391	1	1	yes	characteristic
186	Dic₄₇	—	4	8	no	—
187	C₂×#423	—	47	1	no	—
188	C₂×#423	D₄₇	1	1	yes	characteristic
189	C₂×C₄×C₄⋊C₄	—	47	1	no	—
190	C₂×#343	—	47	4	no	—
191	C₂×C₄₇	—	2	2	no	—
192	C₂×C₄₇	—	2	1	no	—
193	C₂×C₄₇	—	2	1	no	—
194	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
196	C₂×C₄₇	#1742	1	1	yes	characteristic
197	C₂×C₄₇	#1800	1	2	yes	—
198	C₂×C₄₇	#1801	1	2	yes	—
199	C₂²×M₁₆	—	47	2	no	—
200	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
201	C₂²×C₄⋊C₄	—	47	2	no	—
202	C₂²×C₄²	—	47	2	no	—
203	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
204	#423	—	2	2	no	—
205	#423	—	47	4	no	—
206	#423	—	94	2	no	—
207	#423	Dic₄₇	1	4	yes	complemented
208	C₂×C₄⋊C₈	—	2	1	no	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	—	94	1	no	—
211	C₂×C₄⋊C₈	—	94	1	no	—
212	C₄×C₄⋊C₄	—	94	1	no	—
213	C₄×C₄⋊C₄	—	94	1	no	—
214	C₄×C₄⋊C₄	—	94	1	no	—
215	C₄×C₄⋊C₄	—	94	1	no	—
216	C₂×#95	—	47	2	no	—
217	#343	—	94	8	no	—
218	C₄₇	#10847	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	47	4	no	—
220	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂×M₁₆	—	47	4	no	—
227	C₂×M₁₆	—	94	2	no	—
228	C₂×M₁₆	—	94	4	no	—
229	C₂×M₁₆	—	94	4	no	—
230	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₂×C₄⋊C₄	—	47	4	no	—
234	C₂×C₄⋊C₄	—	47	4	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₄⋊C₄	—	94	2	no	—
238	C₂×C₄⋊C₄	—	94	2	no	—
239	C₂×C₄²	—	94	2	no	—
240	C₂×C₄²	—	94	2	no	—
241	C₂×C₄²	—	188	4	no	—
242	C₂×C₄²	Dic₉₄	1	2	yes	—
243	C₂×C₄²	C₄×D₄₇	1	2	yes	—
244	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
245	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
247	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	94	4	no	—
253	C₄⋊C₈	—	94	4	no	—
254	#95	—	94	2	no	—
255	#95	—	94	2	no	—
256	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	47	8	no	—
261	C₂²×C₄	—	94	4	no	—
262	C₂²×C₄	—	94	4	no	—
263	C₂²×C₄	—	188	4	no	—
264	C₂²×C₄	—	188	4	no	—
265	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
266	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
267	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
268	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
269	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₄₇	1	2	yes	—
277	C₂²×C₄	#10625352	1	2	yes	—
278	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
279	C₂²×C₄	#10625354	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
283	M₁₆	—	2	8	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	94	8	no	—
287	M₁₆	—	188	2	no	—
288	M₁₆	—	188	2	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	—	94	4	no	—
292	C₂×C₈	—	188	4	no	—
293	C₄⋊C₄	—	94	4	no	—
294	C₄⋊C₄	—	94	4	no	—
295	C₄⋊C₄	—	94	4	no	—
296	C₄⋊C₄	—	94	4	no	—
297	C₄²	—	188	4	no	—
298	C₄²	—	188	4	no	—
299	C₄²	Dic₄₇⋊C₄	1	2	yes	—
300	C₄²	Dic₄₇⋊C₄	1	2	yes	—
301	C₄²	C₄⋊Dic₄₇	1	2	yes	—
302	C₄²	C₄⋊Dic₄₇	1	2	yes	—
303	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
304	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
305	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
306	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	2	no	—
310	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
311	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
312	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
313	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
314	C₂³	#13093982	1	2	yes	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	94	8	no	—
324	C₂×C₄	—	188	8	no	—
325	C₂×C₄	—	188	4	no	—
326	C₂×C₄	—	188	4	no	—
327	C₂×C₄	—	188	8	no	—
328	C₂×C₄	C₄₇⋊#95	1	2	yes	—
329	C₂×C₄	C₄₇⋊#95	1	2	yes	—
330	C₂×C₄	C₄₇⋊#95	1	2	yes	—
331	C₂×C₄	C₄₇⋊#95	1	2	yes	—
332	C₂×C₄	#13093940	1	2	yes	—
333	C₂×C₄	#13093942	1	2	yes	—
334	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
338	C₂×C₄	#13093986	1	2	yes	—
339	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
340	C₂×C₄	#13093989	1	2	yes	—
341	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
342	C₂×C₄	#13093995	1	2	yes	—
343	C₂×C₄	#13093999	1	2	yes	—
344	C₂×C₄	#13094000	1	2	yes	—
345	C₂×C₄	#13094004	1	2	yes	—
346	C₂×C₄	#13094011	1	1	yes	characteristic
347	C₂×C₄	#13094013	1	1	yes	characteristic
348	C₂×C₄	#13094015	1	2	yes	—
349	C₂×C₄	#13094020	1	1	yes	characteristic
350	C₂×C₄	#13094022	1	1	yes	characteristic
351	C₂×C₄	#13094023	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	188	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
363	C₂²	C₄⋊C₄×Dic₄₇	1	2	yes	—
364	C₂²	#15688980	1	2	yes	—
365	C₂²	#15688988	1	1	yes	characteristic
366	C₂²	#15688992	1	1	yes	characteristic
367	C₂²	C₂×#13093940	1	1	yes	characteristic
368	C₂²	C₂×#13093942	1	1	yes	characteristic
369	C₂²	#15689105	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	188	8	no	—
374	C₄	#15688891	1	4	yes	complemented
375	C₄	#15689019	1	2	yes	—
376	C₄	#15689022	1	2	yes	—
377	C₄	#15689024	1	1	yes	characteristic
378	C₄	#15689026	1	1	yes	characteristic
379	C₄	#15689028	1	1	yes	characteristic
380	C₄	#15689030	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	#20241617	1	1	yes	characteristic
385	C₂	C₂×#15688891	1	1	yes	characteristic
386	C₂	#20243126	1	1	yes	characteristic
387	C₂	#20243377	1	2	yes	—
388	C₂	#20243381	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#423	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	#10847
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
9. #15689147	C₄	semidirect
21. C₄₇×#423	C₄	semidirect
179. C₄×C₄₇	#343	semidirect
207. #423	Dic₄₇	semidirect
218. C₄₇	#10847	semidirect
374. C₄	#15688891	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688891	2
C₂×C₄₇×#423	2
#10847	47