Subgroups — #26122131

Order 12032.

978 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	#20245795	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688884	C₂	1	4	yes	maximal
4	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093983	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
7	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
8	#15688993	C₄	1	2	yes	complemented
9	#15688989	C₄	1	2	yes	complemented
10	#15688983	—	2	1	no	—
11	#15688983	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	—	2	1	no	—
13	C₄×C₄⋊Dic₄₇	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	—	2	2	no	—
15	C₄×C₄⋊Dic₄₇	C₄	1	4	yes	complemented
16	C₂×C₄₇⋊#95	—	2	1	no	—
17	#15688884	—	2	8	no	—
18	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₄₇	—	2	2	no	—
21	C₄×M₁₆×C₄₇	C₄	1	4	yes	complemented
22	C₂×#97×C₄₇	—	2	1	no	—
23	C₂×C₄×C₈×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	#13093983	—	2	4	no	—
26	#13093983	—	2	4	no	—
27	C₂×C₄⋊Dic₄₇	—	2	8	no	—
28	C₂×C₄⋊Dic₄₇	—	2	4	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
32	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	4	no	—
34	C₂×C₄×Dic₄₇	—	2	4	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
38	C₄₇⋊#95	—	2	4	no	—
39	C₄₇⋊#95	—	2	2	no	—
40	C₄₇⋊#95	—	2	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₇	—	2	2	no	—
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
48	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
49	C₂×M₁₆×C₄₇	Q₈	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	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	C₂×C₄	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	2	yes	—
58	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
59	#97×C₄₇	—	2	4	no	—
60	C₄×C₈×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
78	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₄₇	#41	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×Dic₄₇	—	2	8	no	—
83	C₂²×Dic₄₇	—	2	4	no	—
84	C₂²×Dic₄₇	—	2	4	no	—
85	C₂²×Dic₄₇	—	4	4	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂²×Dic₄₇	—	4	2	no	—
88	M₁₆×C₄₇	—	2	4	no	—
89	M₁₆×C₄₇	—	2	4	no	—
90	M₁₆×C₄₇	—	2	4	no	—
91	M₁₆×C₄₇	C₄⋊C₄	1	8	yes	complemented
92	C₂×C₈×C₄₇	—	2	4	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	4	no	—
95	C₄²×C₄₇	C₄²	1	2	yes	—
96	C₄²×C₄₇	C₄²	1	2	yes	—
97	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
100	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
103	C₂²⋊Dic₄₇	—	4	2	no	—
104	C₂²⋊Dic₄₇	—	4	2	no	—
105	C₄⋊Dic₄₇	—	2	16	no	—
106	C₄⋊Dic₄₇	—	2	8	no	—
107	C₄⋊Dic₄₇	—	4	4	no	—
108	C₄⋊Dic₄₇	—	4	4	no	—
109	C₄×Dic₄₇	—	2	8	no	—
110	C₄×Dic₄₇	—	4	4	no	—
111	C₄×Dic₄₇	—	4	4	no	—
112	C₂³×C₄₇	—	2	2	no	—
113	C₂³×C₄₇	—	2	2	no	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₇	#124	1	1	yes	characteristic
118	C₂³×C₄₇	#124	1	1	yes	characteristic
119	C₂³×C₄₇	#127	1	1	yes	characteristic
120	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	2	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	#104	1	4	yes	—
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×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	#117	1	2	yes	—
139	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	#121	1	2	yes	—
144	C₂×C₄×C₄₇	#121	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	#125	1	2	yes	—
148	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
149	C₂×Dic₄₇	—	2	8	no	—
150	C₂×Dic₄₇	—	4	8	no	—
151	C₂×Dic₄₇	—	4	8	no	—
152	C₂×Dic₄₇	—	4	4	no	—
153	C₂×Dic₄₇	—	4	4	no	—
154	C₂×Dic₄₇	—	4	4	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₂×Dic₄₇	—	4	4	no	—
157	C₈×C₄₇	—	2	8	no	—
158	#10851	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
168	C₂²×C₄₇	#382	1	1	yes	characteristic
169	C₂²×C₄₇	#384	1	1	yes	characteristic
170	C₂²×C₄₇	#390	1	1	yes	characteristic
171	C₂²×C₄₇	#390	1	1	yes	characteristic
172	C₂²×C₄₇	#391	1	1	yes	characteristic
173	C₂²×C₄₇	#391	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#104	1	2	yes	—
175	C₂²×C₄₇	#421	1	2	yes	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	#339	1	4	yes	complemented
180	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
181	C₄×C₄₇	#380	1	2	yes	—
182	C₄×C₄₇	#389	1	2	yes	—
183	C₄×C₄₇	#389	1	2	yes	—
184	Dic₄₇	—	4	8	no	—
185	Dic₄₇	—	8	4	no	—
186	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
187	#2285	—	47	1	no	—
188	C₂×C₄×C₄⋊C₄	—	47	1	no	—
189	C₂×#339	—	47	4	no	—
190	C₂×C₄₇	—	2	1	no	—
191	C₂×C₄₇	—	2	1	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×#339	1	1	yes	characteristic
196	C₂×C₄₇	#1733	1	1	yes	characteristic
197	C₂×C₄₇	#1980	1	2	yes	—
198	C₂×C₄₇	#1986	1	2	yes	—
199	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
200	C₂×#117	—	47	2	no	—
201	C₂²×C₄⋊C₄	—	94	1	no	—
202	C₂²×C₄²	—	47	2	no	—
203	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
204	C₄×M₁₆	—	2	2	no	—
205	C₄×M₁₆	Dic₄₇	1	4	yes	complemented
206	C₂×#97	—	2	1	no	—
207	C₂×C₄×C₈	—	2	1	no	—
208	#384	—	47	2	no	—
209	#382	—	47	2	no	—
210	#380	—	94	1	no	—
211	#380	—	94	1	no	—
212	C₄×C₄⋊C₄	—	47	4	no	—
213	C₄×C₄⋊C₄	—	94	2	no	—
214	C₄×C₄⋊C₄	—	94	1	no	—
215	C₄×C₄⋊C₄	—	94	1	no	—
216	C₂×#95	—	94	1	no	—
217	#339	—	94	8	no	—
218	C₄₇	#10851	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	94	2	no	—
220	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
221	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	Dic₉₄	1	4	yes	—
227	C₂×M₁₆	D₁₈₈	1	4	yes	—
228	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
229	C₂²×C₈	—	2	2	no	—
230	#117	—	94	4	no	—
231	#117	—	94	4	no	—
232	C₂×C₄⋊C₄	—	47	4	no	—
233	C₂×C₄⋊C₄	—	94	8	no	—
234	C₂×C₄⋊C₄	—	94	4	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₂²⋊C₄	—	94	2	no	—
238	C₂×C₄²	—	47	4	no	—
239	C₂×C₄²	—	94	4	no	—
240	C₂×C₄²	—	94	4	no	—
241	C₂×C₄²	—	94	2	no	—
242	C₂×C₄²	—	94	2	no	—
243	C₂×C₄²	Dic₉₄	1	2	yes	—
244	C₂×C₄²	C₄×D₄₇	1	2	yes	—
245	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
248	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
249	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
251	#97	—	2	4	no	—
252	C₄×C₈	—	2	4	no	—
253	#95	—	94	4	no	—
254	#95	—	94	2	no	—
255	#95	—	94	2	no	—
256	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	94	8	no	—
260	C₂²×C₄	—	94	4	no	—
261	C₂²×C₄	—	94	4	no	—
262	C₂²×C₄	—	188	4	no	—
263	C₂²×C₄	—	188	2	no	—
264	C₂²×C₄	—	188	2	no	—
265	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
266	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
267	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
271	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
272	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
275	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
278	C₂²×C₄	#10625350	1	2	yes	—
279	C₂²×C₄	#10625350	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	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	C₄⋊Dic₄₇	1	8	yes	complemented
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₄⋊C₄	—	94	16	no	—
291	C₄⋊C₄	—	94	8	no	—
292	C₄⋊C₄	—	188	4	no	—
293	C₄⋊C₄	—	188	4	no	—
294	C₂²⋊C₄	—	188	2	no	—
295	C₂²⋊C₄	—	188	2	no	—
296	C₄²	—	94	8	no	—
297	C₄²	—	188	4	no	—
298	C₄²	—	188	4	no	—
299	C₄²	C₄×Dic₄₇	1	2	yes	—
300	C₄²	C₄×Dic₄₇	1	2	yes	—
301	C₄²	Dic₄₇⋊C₄	1	2	yes	—
302	C₄²	Dic₄₇⋊C₄	1	2	yes	—
303	C₄²	Dic₄₇⋊C₄	1	2	yes	—
304	C₄²	Dic₄₇⋊C₄	1	2	yes	—
305	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
306	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
312	C₂³	#13094012	1	1	yes	characteristic
313	C₂³	#13094012	1	1	yes	characteristic
314	C₂³	#13094021	1	1	yes	characteristic
315	C₂³	#13094024	1	1	yes	characteristic
316	C₂×C₄	—	2	2	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	4	no	—
325	C₂×C₄	—	188	4	no	—
326	C₂×C₄	—	188	4	no	—
327	C₂×C₄	—	188	8	no	—
328	C₂×C₄	—	188	8	no	—
329	C₂×C₄	—	188	4	no	—
330	C₂×C₄	—	188	4	no	—
331	C₂×C₄	C₄₇⋊#95	1	2	yes	—
332	C₂×C₄	C₄₇⋊#95	1	2	yes	—
333	C₂×C₄	C₄₇⋊#95	1	2	yes	—
334	C₂×C₄	C₄₇⋊#95	1	2	yes	—
335	C₂×C₄	#13093950	1	4	yes	—
336	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
341	C₂×C₄	#13093983	1	2	yes	—
342	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
343	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
344	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
345	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
346	C₂×C₄	#13093998	1	2	yes	—
347	C₂×C₄	#13093998	1	2	yes	—
348	C₂×C₄	#13094003	1	2	yes	—
349	C₂×C₄	#13094003	1	2	yes	—
350	C₂×C₄	#13094016	1	2	yes	—
351	C₂×C₄	#13094024	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
362	C₂²	#15688989	1	1	yes	characteristic
363	C₂²	#15688993	1	1	yes	characteristic
364	C₂²	#15689025	1	1	yes	characteristic
365	C₂²	#15689025	1	1	yes	characteristic
366	C₂²	#15689029	1	1	yes	characteristic
367	C₂²	#15689029	1	1	yes	characteristic
368	C₂²	C₂×#13093950	1	2	yes	—
369	C₂²	#15689139	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	376	4	no	—
374	C₄	—	188	8	no	—
375	C₄	#15688884	1	4	yes	complemented
376	C₄	C₄×C₄⋊Dic₄₇	1	2	yes	—
377	C₄	#15688983	1	2	yes	—
378	C₄	#15689021	1	2	yes	—
379	C₄	#15689021	1	2	yes	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	#20241618	1	1	yes	characteristic
385	C₂	C₂×#15688884	1	1	yes	characteristic
386	C₂	#20243099	1	1	yes	characteristic
387	C₂	#20244307	1	2	yes	—
388	C₂	#20244332	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	#10851
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
8. #15688993	C₄	semidirect
9. #15688989	C₄	semidirect
15. C₄×C₄⋊Dic₄₇	C₄	semidirect
21. C₄×M₁₆×C₄₇	C₄	semidirect
91. M₁₆×C₄₇	C₄⋊C₄	semidirect
179. C₄×C₄₇	#339	semidirect
205. C₄×M₁₆	Dic₄₇	semidirect
218. C₄₇	#10851	semidirect
286. M₁₆	C₄⋊Dic₄₇	semidirect
375. C₄	#15688884	semidirect

Maximal subgroups

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

subgroup	index
#20245795	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688884	2
C₂×C₄×M₁₆×C₄₇	2
#10851	47