Subgroups — #26220802

Order 12032.

1250 conjugacy classes of subgroups.

The subgroup lattice has 392 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	#20244346	C₂	1	4	yes	maximal, complemented
4	#20244341	C₂	1	2	yes	maximal, complemented
5	#20244337	C₂	1	2	yes	maximal, complemented
6	#20243109	C₂	1	4	yes	maximal
7	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	2	yes	—
9	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂²×C₄×Dic₄₇	—	2	1	no	—
11	#15689147	—	2	4	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₄×C₄⋊Dic₄₇	—	2	1	no	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	C₂×C₄₇⋊#95	—	2	1	no	—
19	#15688885	C₂²	1	8	yes	—
20	#15688885	C₂²	1	8	yes	—
21	C₄₇×#533	—	2	4	no	—
22	C₄₇×#533	C₄	1	8	yes	complemented
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₄₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
30	C₂×#117×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	—	2	8	no	—
35	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄⋊Dic₄₇	Q₈	1	8	yes	complemented
39	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	2	no	—
42	C₂×C₄×Dic₄₇	—	4	4	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	C₄₇⋊#95	—	2	2	no	—
46	C₄₇⋊#95	—	2	2	no	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
55	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
56	#125×C₄₇	—	2	4	no	—
57	#125×C₄₇	C₂×C₄	1	8	yes	complemented
58	C₂²⋊Q₈×C₄₇	—	2	8	no	—
59	C₂²⋊Q₈×C₄₇	—	2	8	no	—
60	C₄×Q₈×C₄₇	—	2	8	no	—
61	C₄×Q₈×C₄₇	—	2	8	no	—
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	C₂×C₄	1	8	yes	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	D₄	1	4	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	4	4	no	—
82	C₂×Q₈×C₄₇	—	4	2	no	—
83	C₂×Q₈×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₇	#41	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	—	2	8	no	—
102	C₂²×Dic₄₇	—	2	4	no	—
103	C₂²×Dic₄₇	—	4	4	no	—
104	C₂²×Dic₄₇	—	4	4	no	—
105	C₄⋊C₄×C₄₇	—	2	8	no	—
106	C₄⋊C₄×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂²⋊C₄×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	—	2	8	no	—
115	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
116	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂×D₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄⋊Dic₄₇	—	2	8	no	—
122	C₄⋊Dic₄₇	—	2	4	no	—
123	C₄⋊Dic₄₇	C₂×Q₈	1	8	yes	—
124	C₄×Dic₄₇	—	4	4	no	—
125	C₄×Dic₄₇	—	4	4	no	—
126	#10625329	—	4	8	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	C₂×C₄₇⋊C₈	—	2	8	no	—
129	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	4	8	no	—
136	Q₈×C₄₇	—	4	8	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	8	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₇	#124	1	4	yes	—
156	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₇	#137	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
163	C₂×Dic₄₇	—	2	8	no	—
164	C₂×Dic₄₇	—	4	16	no	—
165	C₂×Dic₄₇	—	4	4	no	—
166	C₂×Dic₄₇	—	4	4	no	—
167	C₄₇⋊C₈	—	4	4	no	—
168	#21312	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	#391	1	4	yes	—
174	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
176	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
178	C₂²×C₄₇	#575	1	2	yes	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	4	4	no	—
183	C₄×C₄₇	—	4	4	no	—
184	C₄×C₄₇	#391	1	4	yes	—
185	C₄×C₄₇	#417	1	4	yes	—
186	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
187	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	Dic₄₇	—	4	8	no	—
190	C₂×#533	D₄₇	1	1	yes	characteristic
191	C₂×#423	—	47	1	no	—
192	C₂×C₄×C₄⋊C₄	—	47	1	no	—
193	#1989	—	47	4	no	—
194	#1988	—	47	2	no	—
195	#1987	—	47	2	no	—
196	#1736	—	47	4	no	—
197	C₂×C₄₇	—	2	4	no	—
198	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
200	C₂×C₄₇	#2896	1	1	yes	characteristic
201	C₂×C₄₇	#3077	1	2	yes	—
202	C₂×C₄₇	#3078	1	2	yes	—
203	C₂²×M₁₆	—	47	2	no	—
204	#533	—	2	4	no	—
205	#533	Dic₄₇	1	8	yes	complemented
206	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
208	C₂×#125	C₂×D₄₇	1	2	yes	—
209	C₂×C₂²⋊Q₈	—	2	1	no	—
210	C₂×C₂²⋊Q₈	—	2	1	no	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	—	2	1	no	—
213	C₂×#117	C₂×D₄₇	1	2	yes	—
214	C₂²×C₄⋊C₄	—	47	2	no	—
215	C₂²×C₄²	—	94	1	no	—
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#423	—	94	4	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	47	2	no	—
220	C₄×C₄⋊C₄	—	47	2	no	—
221	C₄×C₄⋊C₄	—	47	2	no	—
222	C₄×C₄⋊C₄	—	94	1	no	—
223	C₄×C₄⋊C₄	—	94	1	no	—
224	C₂×#95	—	94	1	no	—
225	#340	—	47	8	no	—
226	#340	—	47	8	no	—
227	C₄₇	#21312	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂³×C₄	—	94	2	no	—
231	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
234	C₂×M₁₆	—	94	8	no	—
235	C₂×M₁₆	—	94	4	no	—
236	C₂²×C₈	—	47	4	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
240	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
241	#125	—	2	4	no	—
242	#125	C₂×Dic₄₇	1	8	yes	complemented
243	C₂²⋊Q₈	—	2	8	no	—
244	C₂²⋊Q₈	—	2	8	no	—
245	C₄×Q₈	—	2	8	no	—
246	C₄×Q₈	—	2	8	no	—
247	#117	—	2	4	no	—
248	#117	C₂×Dic₄₇	1	8	yes	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	47	8	no	—
254	C₂×C₄⋊C₄	—	47	4	no	—
255	C₂×C₄⋊C₄	—	94	4	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	94	2	no	—
262	C₂×C₄²	—	94	2	no	—
263	C₂×C₄²	—	188	4	no	—
264	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
265	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₄⋊C₈	—	94	4	no	—
271	C₄⋊C₈	—	94	4	no	—
272	#95	—	94	2	no	—
273	#95	—	94	2	no	—
274	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	94	8	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	—	188	4	no	—
288	C₂²×C₄	—	188	4	no	—
289	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
290	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
291	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
292	C₂²×C₄	#10625354	1	4	yes	—
293	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
294	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
300	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
301	M₁₆	—	188	8	no	—
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	94	8	no	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	47	8	no	—
311	C₄⋊C₄	—	94	8	no	—
312	C₄⋊C₄	—	94	4	no	—
313	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
314	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₄²	—	2	8	no	—
317	C₄²	—	188	4	no	—
318	C₄²	—	188	4	no	—
319	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
320	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
321	C₄²	C₂²×Dic₄₇	1	2	yes	—
322	C₄²	C₂²×Dic₄₇	1	2	yes	—
323	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
324	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
329	C₂³	#13094000	1	4	yes	—
330	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
331	Q₈	—	4	8	no	—
332	Q₈	—	4	8	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	94	8	no	—
345	C₂×C₄	—	188	16	no	—
346	C₂×C₄	—	188	4	no	—
347	C₂×C₄	—	188	4	no	—
348	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
349	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
350	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
353	C₂×C₄	Q₈×Dic₄₇	1	8	yes	—
354	C₂×C₄	#13094000	1	4	yes	—
355	C₂×C₄	#13094013	1	4	yes	—
356	C₂×C₄	#13094022	1	4	yes	—
357	C₂×C₄	#13094049	1	2	yes	—
358	C₂×C₄	#13094054	1	2	yes	—
359	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
362	C₂×C₄	C₂×#10625354	1	2	yes	—
363	C₈	—	188	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	#15689030	1	4	yes	—
369	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
370	C₂²	C₂×#13094000	1	2	yes	—
371	C₂²	C₂×#13094049	1	1	yes	characteristic
372	C₂²	C₂×#13094054	1	1	yes	characteristic
373	C₂²	#15689921	1	2	yes	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	188	8	no	—
380	C₄	#15689030	1	4	yes	—
381	C₄	#15689124	1	4	yes	—
382	C₄	C₂×Q₈×Dic₄₇	1	2	yes	—
383	C₄	C₂×#13094013	1	1	yes	characteristic
384	C₄	C₂×#13094022	1	1	yes	characteristic
385	C₂	—	2	4	no	—
386	C₂	C₂×#15689030	1	1	yes	characteristic
387	C₂	C₂×#15689124	1	1	yes	characteristic
388	C₂	#20251907	1	1	yes	characteristic
389	C₂	#20253181	1	2	yes	—
390	C₂	#20253189	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21312
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244346	C₂	semidirect
4. #20244341	C₂	semidirect
5. #20244337	C₂	semidirect
22. C₄₇×#533	C₄	semidirect
38. C₂×C₄⋊Dic₄₇	Q₈	semidirect
54. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
55. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
57. #125×C₄₇	C₂×C₄	semidirect
205. #533	Dic₄₇	semidirect
227. C₄₇	#21312	semidirect
239. C₄⋊Q₈	C₂×Dic₄₇	semidirect
240. C₄⋊Q₈	C₂×Dic₄₇	semidirect
242. #125	C₂×Dic₄₇	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
#20244346	2
#20244341	2
#20244337	2
#20243109	2
C₂×C₄₇×#533	2
#21312	47