Subgroups — #26214454

Order 12032.

950 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689184	C₂	1	2	yes	maximal
2	#20243245	C₂	1	2	yes	maximal, complemented
3	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243154	C₂	1	2	yes	maximal
6	#20243150	C₂	1	1	yes	maximal, characteristic
7	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	#20243137	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243134	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243075	C₂	1	2	yes	maximal, complemented
11	C₄×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689184	C₄	1	16	yes	complemented
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
23	#15688878	C₂²	1	1	yes	characteristic
24	#15688878	C₂²	1	1	yes	characteristic
25	#15688878	C₂²	1	1	yes	characteristic
26	#15688878	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
34	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
35	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
36	C₄₇×#376	C₂²	1	1	yes	characteristic
37	C₄₇×#376	C₂²	1	1	yes	characteristic
38	C₄³×C₄₇	C₂²	1	1	yes	characteristic
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
45	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
46	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
47	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
48	#13093935	—	2	4	no	—
49	#13093935	—	2	4	no	—
50	#13093935	C₂×C₄	1	8	yes	complemented
51	C₄×C₄₇⋊C₈	—	2	4	no	—
52	C₄×C₄₇⋊C₈	—	2	4	no	—
53	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	#117×C₄₇	—	2	2	no	—
57	#117×C₄₇	—	2	2	no	—
58	#117×C₄₇	C₂×C₄	1	8	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	—	2	4	no	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	#95×C₄₇	C₂×C₄	1	2	yes	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	#95×C₄₇	C₂×C₄	1	2	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
101	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
102	C₂²⋊C₄×C₄₇	—	2	4	no	—
103	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
104	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
105	C₄²×C₄₇	—	2	4	no	—
106	C₄²×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	4	2	no	—
112	C₄²×C₄₇	—	4	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
115	C₄²×C₄₇	#41	1	4	yes	—
116	C₄²×C₄₇	#41	1	2	yes	—
117	C₄²×C₄₇	#41	1	2	yes	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
135	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	4	8	no	—
154	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
159	C₂×C₄×C₄₇	#117	1	4	yes	—
160	C₂×C₄×C₄₇	#117	1	4	yes	—
161	C₂×C₄×C₄₇	#131	1	4	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₄₇⋊C₈	—	2	4	no	—
167	C₄₇⋊C₈	—	2	4	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	—	2	4	no	—
170	#20468	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#131	1	2	yes	—
180	C₂²×C₄₇	#568	1	2	yes	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	2	2	no	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	2	2	no	—
185	C₄×C₄₇	—	2	4	no	—
186	C₄×C₄₇	—	2	4	no	—
187	C₄×C₄₇	—	2	4	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	C₄×#41	1	2	yes	—
191	C₄×C₄₇	C₄×#41	1	2	yes	—
192	C₂×#433	—	47	2	no	—
193	C₄×#117	D₄₇	1	1	yes	characteristic
194	#1768	—	47	2	no	—
195	#1767	—	47	1	no	—
196	C₄×C₄⋊C₈	—	47	1	no	—
197	#1750	—	47	2	no	—
198	#1749	—	47	1	no	—
199	C₄×C₂²⋊C₈	—	47	1	no	—
200	#1745	—	47	1	no	—
201	#1744	—	47	1	no	—
202	#1726	—	47	2	no	—
203	C₂×C₄₇	—	4	2	no	—
204	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
205	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
206	C₂×C₄₇	#2875	1	1	yes	characteristic
207	C₂×C₄₇	#2924	1	2	yes	—
208	C₂×C₄₇	#2925	1	2	yes	—
209	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
210	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
211	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
212	#433	—	47	16	no	—
213	C₂×C₄⋊C₈	—	47	2	no	—
214	C₂×C₄⋊C₈	—	47	2	no	—
215	C₂×C₂²⋊C₈	—	47	2	no	—
216	C₂×C₂²⋊C₈	—	47	2	no	—
217	C₂×#97	—	47	2	no	—
218	C₂×#97	—	47	2	no	—
219	C₂×#97	—	47	2	no	—
220	C₂×C₄×C₈	—	47	2	no	—
221	C₂×C₄×C₈	—	47	2	no	—
222	C₂×C₄×C₈	—	47	2	no	—
223	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
224	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
225	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
226	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
227	#376	C₂×D₄₇	1	1	yes	characteristic
228	#376	C₂×D₄₇	1	1	yes	characteristic
229	C₄³	C₂×D₄₇	1	1	yes	characteristic
230	C₄³	C₂×D₄₇	1	1	yes	characteristic
231	#336	—	47	1	no	—
232	#336	—	47	1	no	—
233	#336	—	47	2	no	—
234	#336	—	47	1	no	—
235	#336	—	47	1	no	—
236	#336	—	47	2	no	—
237	C₄₇	#20468	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₂²×C₈	—	47	2	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	2	no	—
243	C₂²×C₈	—	47	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	C₄×D₄₇	1	8	yes	—
247	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
253	C₂×C₄²	—	2	4	no	—
254	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
255	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
256	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
257	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
258	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
265	C₄⋊C₈	—	47	8	no	—
266	C₄⋊C₈	—	47	8	no	—
267	C₂²⋊C₈	—	47	8	no	—
268	C₂²⋊C₈	—	47	8	no	—
269	#97	—	47	8	no	—
270	#97	—	94	4	no	—
271	#97	—	94	4	no	—
272	C₄×C₈	—	47	8	no	—
273	C₄×C₈	—	94	4	no	—
274	C₄×C₈	—	94	4	no	—
275	#95	C₂×Dic₄₇	1	2	yes	—
276	#95	C₂×Dic₄₇	1	2	yes	—
277	#95	C₂×Dic₄₇	1	2	yes	—
278	#95	C₂×Dic₄₇	1	2	yes	—
279	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
294	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
296	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
297	C₂×C₈	—	47	4	no	—
298	C₂×C₈	—	47	4	no	—
299	C₂×C₈	—	47	4	no	—
300	C₂×C₈	—	47	4	no	—
301	C₂×C₈	—	94	2	no	—
302	C₂×C₈	—	94	2	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
311	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
314	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	C₂×C₄×D₄₇	1	4	yes	—
324	C₄²	C₂×C₄×D₄₇	1	4	yes	—
325	C₄²	#10625350	1	2	yes	—
326	C₄²	#10625350	1	4	yes	—
327	C₄²	#10625350	1	2	yes	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
333	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
353	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
354	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
355	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
356	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
357	C₂×C₄	#13093983	1	4	yes	—
358	C₂×C₄	#13093983	1	4	yes	—
359	C₂×C₄	#13094031	1	4	yes	—
360	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
361	C₂×C₄	C₂×#10625350	1	2	yes	—
362	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
363	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
364	C₈	—	94	4	no	—
365	C₈	—	94	4	no	—
366	C₈	—	94	4	no	—
367	C₈	—	94	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
374	C₂²	C₂×#13093983	1	1	yes	characteristic
375	C₂²	C₂×#13093983	1	1	yes	characteristic
376	C₂²	C₂×#13094031	1	2	yes	—
377	C₂²	#15689890	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	2	4	no	—
380	C₄	—	2	4	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	C₄×#10625350	1	2	yes	—
388	C₄	C₄×#10625350	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₄×#13093983	1	1	yes	characteristic
391	C₂	C₄×#13094031	1	1	yes	characteristic
392	C₂	#20251816	1	1	yes	characteristic
393	C₂	#20252046	1	2	yes	—
394	C₂	#20252054	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄×#117×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#117	D₄₇
hypocenter	C₄₇	#20468
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
2. #20243245	C₂	semidirect
3. #20243241	C₂	semidirect
4. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
8. #20243137	C₂	semidirect
9. #20243134	C₂	semidirect
10. #20243075	C₂	semidirect
12. #15689184	C₄	semidirect
44. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
45. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
50. #13093935	C₂×C₄	semidirect
53. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
237. C₄₇	#20468	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689184	2
#20243245	2
#20243241	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243154	2
#20243150	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
#20243137	2
#20243134	2
#20243075	2
C₄×#117×C₄₇	2
#20468	47