Subgroups — #25002451

Order 11008.

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	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic
2	#19137002	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582659	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10621877	C₂²	1	2	yes	—
6	C₂×#13063284	C₂²	1	2	yes	—
7	C₄×#10621877	—	2	2	no	—
8	C₄×#10621877	C₄	1	4	yes	complemented
9	C₂×#13063236	—	2	1	no	—
10	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
11	#14582769	C₄	1	2	yes	complemented
12	#14582765	C₄	1	2	yes	complemented
13	#14582759	—	2	1	no	—
14	#14582759	—	2	1	no	—
15	C₄×C₄⋊Dic₄₃	—	2	1	no	—
16	C₄×C₄⋊Dic₄₃	—	2	1	no	—
17	#14582659	—	2	8	no	—
18	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
19	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄×C₄⋊C₄×C₄₃	C₄	1	4	yes	complemented
23	C₂×#95×C₄₃	—	2	1	no	—
24	C₂×#10621877	—	2	2	no	—
25	C₂×#10621877	—	2	2	no	—
26	C₂×#10621877	—	2	2	no	—
27	C₂×#10621877	C₂×C₄	1	4	yes	—
28	C₂×#10621877	D₄	1	4	yes	—
29	C₂×#10621877	Q₈	1	4	yes	—
30	C₂²×C₄₃⋊C₈	—	2	2	no	—
31	#13063284	—	2	4	no	—
32	#13063284	—	2	4	no	—
33	C₂×C₄⋊Dic₄₃	—	2	2	no	—
34	C₂×C₄⋊Dic₄₃	—	2	2	no	—
35	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
36	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
37	C₂×C₄×Dic₄₃	—	2	2	no	—
38	#13063236	—	2	4	no	—
39	C₄×C₄₃⋊C₈	—	2	4	no	—
40	C₄₃⋊#95	—	2	2	no	—
41	C₄₃⋊#95	—	2	2	no	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
48	C₂×C₄²×C₄₃	—	2	4	no	—
49	C₂×C₄²×C₄₃	—	2	4	no	—
50	C₂×C₄²×C₄₃	—	2	2	no	—
51	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	D₄	1	2	yes	—
59	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
60	#95×C₄₃	—	2	4	no	—
61	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	8	no	—
64	C₂²×C₄×C₄₃	—	2	4	no	—
65	C₂²×C₄×C₄₃	—	4	2	no	—
66	C₂²×C₄×C₄₃	—	4	4	no	—
67	C₂²×C₄×C₄₃	—	4	2	no	—
68	C₂²×C₄×C₄₃	—	4	2	no	—
69	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₄₃	#41	1	2	yes	—
86	C₂²×C₄×C₄₃	#41	1	2	yes	—
87	C₂²×Dic₄₃	—	2	4	no	—
88	C₄⋊C₄×C₄₃	—	2	16	no	—
89	C₄²×C₄₃	—	2	8	no	—
90	C₄²×C₄₃	—	4	4	no	—
91	C₄²×C₄₃	C₄²	1	2	yes	—
92	C₄²×C₄₃	C₄²	1	2	yes	—
93	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
96	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
97	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
98	C₄²×C₄₃	C₄⋊C₄	1	2	yes	—
99	C₂²⋊Dic₄₃	—	4	2	no	—
100	C₂²⋊Dic₄₃	—	4	2	no	—
101	C₄⋊Dic₄₃	—	2	8	no	—
102	C₄⋊Dic₄₃	—	4	4	no	—
103	C₄⋊Dic₄₃	—	4	4	no	—
104	C₄×Dic₄₃	—	4	4	no	—
105	#10621877	—	2	4	no	—
106	#10621877	—	2	4	no	—
107	#10621877	—	2	4	no	—
108	#10621877	C₄⋊C₄	1	8	yes	complemented
109	C₂×C₄₃⋊C₈	—	2	4	no	—
110	C₂×C₄₃⋊C₈	—	2	4	no	—
111	C₂×C₄₃⋊C₈	—	2	4	no	—
112	C₂³×C₄₃	—	2	2	no	—
113	C₂³×C₄₃	—	2	2	no	—
114	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₄₃	#124	1	1	yes	characteristic
118	C₂³×C₄₃	#124	1	1	yes	characteristic
119	C₂³×C₄₃	#127	1	1	yes	characteristic
120	C₂³×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
121	C₂×C₄×C₄₃	—	2	2	no	—
122	C₂×C₄×C₄₃	—	2	2	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	4	no	—
125	C₂×C₄×C₄₃	—	2	4	no	—
126	C₂×C₄×C₄₃	—	2	8	no	—
127	C₂×C₄×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	—	4	2	no	—
129	C₂×C₄×C₄₃	—	4	8	no	—
130	C₂×C₄×C₄₃	—	4	8	no	—
131	C₂×C₄×C₄₃	—	4	4	no	—
132	C₂×C₄×C₄₃	—	4	4	no	—
133	C₂×C₄×C₄₃	#95	1	2	yes	—
134	C₂×C₄×C₄₃	#95	1	2	yes	—
135	C₂×C₄×C₄₃	#95	1	2	yes	—
136	C₂×C₄×C₄₃	#95	1	2	yes	—
137	C₂×C₄×C₄₃	#104	1	4	yes	—
138	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#117	1	2	yes	—
144	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
145	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
147	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
148	C₂×C₄×C₄₃	#121	1	2	yes	—
149	C₂×C₄×C₄₃	#121	1	2	yes	—
150	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
152	C₂×C₄×C₄₃	#125	1	2	yes	—
153	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
154	C₂×Dic₄₃	—	4	4	no	—
155	C₂×Dic₄₃	—	4	4	no	—
156	C₂×Dic₄₃	—	4	4	no	—
157	C₄₃⋊C₈	—	2	8	no	—
158	#10851	—	43	1	no	maximal, Sylow
159	C₂²×C₄₃	—	2	2	no	—
160	C₂²×C₄₃	—	2	2	no	—
161	C₂²×C₄₃	—	2	2	no	—
162	C₂²×C₄₃	—	2	2	no	—
163	C₂²×C₄₃	—	2	1	no	—
164	C₂²×C₄₃	—	2	1	no	—
165	C₂²×C₄₃	—	2	1	no	—
166	C₂²×C₄₃	—	2	1	no	—
167	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
168	C₂²×C₄₃	#382	1	1	yes	characteristic
169	C₂²×C₄₃	#384	1	1	yes	characteristic
170	C₂²×C₄₃	#390	1	1	yes	characteristic
171	C₂²×C₄₃	#390	1	1	yes	characteristic
172	C₂²×C₄₃	#391	1	1	yes	characteristic
173	C₂²×C₄₃	#391	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#104	1	2	yes	—
175	C₂²×C₄₃	#421	1	2	yes	—
176	C₄×C₄₃	—	2	2	no	—
177	C₄×C₄₃	—	2	2	no	—
178	C₄×C₄₃	—	2	2	no	—
179	C₄×C₄₃	—	4	8	no	—
180	C₄×C₄₃	#339	1	4	yes	complemented
181	C₄×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
182	C₄×C₄₃	#380	1	2	yes	—
183	C₄×C₄₃	#389	1	2	yes	—
184	C₄×C₄₃	#389	1	2	yes	—
185	Dic₄₃	—	8	4	no	—
186	C₂×C₄×M₁₆	—	43	1	no	—
187	#2285	—	43	1	no	—
188	C₂×C₄×C₄⋊C₄	D₄₃	1	1	yes	characteristic
189	C₂×#339	—	43	4	no	—
190	C₂×C₄₃	—	2	1	no	—
191	C₂×C₄₃	—	2	1	no	—
192	C₂×C₄₃	—	2	1	no	—
193	C₂×C₄₃	—	2	1	no	—
194	C₂×C₄₃	C₄⋊#95	1	1	yes	characteristic
195	C₂×C₄₃	C₂×#339	1	1	yes	characteristic
196	C₂×C₄₃	#1733	1	1	yes	characteristic
197	C₂×C₄₃	#1980	1	2	yes	—
198	C₂×C₄₃	#1986	1	2	yes	—
199	C₂²×M₁₆	—	43	2	no	—
200	C₂×#117	—	43	2	no	—
201	C₂²×C₄⋊C₄	—	2	1	no	—
202	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
203	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
204	C₄×M₁₆	—	43	4	no	—
205	C₄×M₁₆	—	86	2	no	—
206	C₂×#97	—	86	1	no	—
207	C₂×C₄×C₈	—	86	1	no	—
208	#384	—	43	2	no	—
209	#382	—	43	2	no	—
210	#380	—	86	1	no	—
211	#380	—	86	1	no	—
212	C₄×C₄⋊C₄	—	2	2	no	—
213	C₄×C₄⋊C₄	—	86	1	no	—
214	C₄×C₄⋊C₄	—	86	1	no	—
215	C₄×C₄⋊C₄	Dic₄₃	1	4	yes	complemented
216	C₂×#95	—	2	1	no	—
217	#339	—	86	8	no	—
218	C₄₃	#10851	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
221	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
223	C₂×M₁₆	—	43	4	no	—
224	C₂×M₁₆	—	43	4	no	—
225	C₂×M₁₆	—	43	4	no	—
226	C₂×M₁₆	—	86	2	no	—
227	C₂×M₁₆	—	86	2	no	—
228	C₂×M₁₆	—	86	2	no	—
229	C₂²×C₈	—	86	2	no	—
230	#117	—	86	4	no	—
231	#117	—	86	4	no	—
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	—	43	4	no	—
235	C₂×C₄⋊C₄	—	86	2	no	—
236	C₂×C₄⋊C₄	—	86	2	no	—
237	C₂×C₂²⋊C₄	—	86	2	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	2	4	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	86	2	no	—
242	C₂×C₄²	Dic₈₆	1	2	yes	—
243	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₄₃	1	2	yes	—
246	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
247	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
248	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
249	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
250	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
251	#97	—	86	4	no	—
252	C₄×C₈	—	86	4	no	—
253	#95	—	2	4	no	—
254	#95	—	86	2	no	—
255	#95	—	86	2	no	—
256	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	86	4	no	—
265	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
266	C₂²×C₄	Dic₄₃⋊C₄	1	2	yes	—
267	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
272	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
273	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
277	C₂²×C₄	D₄×D₄₃	1	2	yes	—
278	C₂²×C₄	#10621900	1	2	yes	—
279	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
280	C₂²×C₄	#10621902	1	2	yes	—
281	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
283	M₁₆	—	43	8	no	—
284	M₁₆	—	86	4	no	—
285	M₁₆	—	86	4	no	—
286	M₁₆	—	86	4	no	—
287	C₂×C₈	—	86	4	no	—
288	C₂×C₈	—	86	4	no	—
289	C₂×C₈	—	86	4	no	—
290	C₄⋊C₄	—	2	16	no	—
291	C₄⋊C₄	—	86	8	no	—
292	C₄⋊C₄	—	172	4	no	—
293	C₄⋊C₄	—	172	4	no	—
294	C₂²⋊C₄	—	172	2	no	—
295	C₂²⋊C₄	—	172	2	no	—
296	C₄²	—	2	8	no	—
297	C₄²	—	4	4	no	—
298	C₄²	—	172	4	no	—
299	C₄²	C₄×Dic₄₃	1	2	yes	—
300	C₄²	C₄×Dic₄₃	1	2	yes	—
301	C₄²	Dic₄₃⋊C₄	1	2	yes	—
302	C₄²	Dic₄₃⋊C₄	1	2	yes	—
303	C₄²	C₄⋊Dic₄₃	1	2	yes	—
304	C₄²	C₄⋊Dic₄₃	1	2	yes	—
305	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
306	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
311	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
312	C₂³	#13063312	1	1	yes	characteristic
313	C₂³	#13063314	1	1	yes	characteristic
314	C₂³	#13063321	1	1	yes	characteristic
315	C₂³	#13063323	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	—	2	8	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	8	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	172	4	no	—
329	C₂×C₄	—	172	4	no	—
330	C₂×C₄	—	172	4	no	—
331	C₂×C₄	C₄₃⋊#95	1	2	yes	—
332	C₂×C₄	C₄₃⋊#95	1	2	yes	—
333	C₂×C₄	C₄₃⋊#95	1	2	yes	—
334	C₂×C₄	C₄₃⋊#95	1	2	yes	—
335	C₂×C₄	#13063253	1	4	yes	—
336	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
337	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
339	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
341	C₂×C₄	#13063283	1	2	yes	—
342	C₂×C₄	#13063287	1	2	yes	—
343	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
344	C₂×C₄	#13063290	1	2	yes	—
345	C₂×C₄	Q₈×Dic₄₃	1	2	yes	—
346	C₂×C₄	#13063296	1	2	yes	—
347	C₂×C₄	#13063300	1	2	yes	—
348	C₂×C₄	#13063301	1	2	yes	—
349	C₂×C₄	#13063305	1	2	yes	—
350	C₂×C₄	#13063316	1	2	yes	—
351	C₂×C₄	#13063324	1	2	yes	—
352	C₈	—	86	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×C₄₃⋊#95	1	1	yes	characteristic
362	C₂²	#14582764	1	1	yes	characteristic
363	C₂²	#14582768	1	1	yes	characteristic
364	C₂²	#14582800	1	1	yes	characteristic
365	C₂²	#14582802	1	1	yes	characteristic
366	C₂²	#14582804	1	1	yes	characteristic
367	C₂²	#14582806	1	1	yes	characteristic
368	C₂²	C₂×#13063253	1	2	yes	—
369	C₂²	#14582917	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	8	no	—
374	C₄	—	344	4	no	—
375	C₄	#14582659	1	4	yes	complemented
376	C₄	C₄⋊C₄×Dic₄₃	1	2	yes	—
377	C₄	#14582756	1	2	yes	—
378	C₄	#14582795	1	2	yes	—
379	C₄	#14582798	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	#19132824	1	1	yes	characteristic
385	C₂	C₂×#14582659	1	1	yes	characteristic
386	C₂	#19134305	1	1	yes	characteristic
387	C₂	#19135513	1	2	yes	—
388	C₂	#19135538	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₄⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#10851
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. C₄×#10621877	C₄	semidirect
11. #14582769	C₄	semidirect
12. #14582765	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
108. #10621877	C₄⋊C₄	semidirect
180. C₄×C₄₃	#339	semidirect
215. C₄×C₄⋊C₄	Dic₄₃	semidirect
218. C₄₃	#10851	semidirect
375. C₄	#14582659	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621877	2
#19137002	2
C₂×#14582659	2
C₂×C₄×C₄⋊C₄×C₄₃	2
#10851	43