Subgroups — C₂×C₄×#13063373 #26003206

Order 11008.

11210 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063373	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063373	C₂	1	32	yes	maximal, direct product factor
3	C₂×#14583381	C₂	1	4	yes	maximal, complemented
4	C₂×#14583380	C₂	1	6	yes	maximal, complemented
5	C₂×#14583377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14583375	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×#10621902	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×#10621898	C₂	1	6	yes	maximal, complemented
9	C₂×C₄×Q₈×D₄₃	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#13063373	C₄	1	32	yes	direct product factor
12	C₂×#13063373	C₂²	1	16	yes	—
13	C₂²×#10621902	C₂²	1	4	yes	—
14	C₂²×#10621898	C₂²	1	6	yes	—
15	C₂²×Q₈×D₄₃	C₂²	1	4	yes	—
16	#14583381	C₂²	1	64	yes	complemented
17	#14583380	C₂²	1	96	yes	complemented
18	#14583377	C₂²	1	16	yes	complemented
19	#14583375	C₂²	1	64	yes	complemented
20	C₄×#10621902	C₂²	1	64	yes	complemented
21	C₄×#10621898	C₂²	1	96	yes	complemented
22	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
23	C₂×Q₈×Dic₄₃	C₂²	1	4	yes	—
24	C₂×C₄×Dic₈₆	C₂²	1	6	yes	—
25	C₂×C₄×Dic₈₆	C₂²	1	6	yes	—
26	C₂×#13063290	C₂²	1	12	yes	—
27	C₄×Q₈×D₄₃	C₂²	1	64	yes	complemented
28	C₂×C₄×D₁₇₂	C₂²	1	6	yes	—
29	C₂×C₄×D₁₇₂	C₂²	1	6	yes	—
30	C₂×#13063287	C₂²	1	12	yes	—
31	C₂×C₄×C₂²⋊D₄₃	C₂²	1	12	yes	—
32	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
33	C₂×#13063284	C₂²	1	6	yes	—
34	C₂×#13063283	C₂²	1	12	yes	—
35	C₂×#13063282	C₂²	1	12	yes	—
36	C₂×C₄⋊C₄×D₄₃	C₂²	1	12	yes	—
37	C₂×C₄²×D₄₃	C₂²	1	12	yes	—
38	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₄₃	C₂²	1	4	yes	—
40	C₂×C₄×Q₈×C₄₃	C₂²	1	4	yes	—
41	C₂×C₄×Q₈×C₄₃	C₂²	1	16	yes	complemented
42	C₂²×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
43	C₂²×C₄²×C₄₃	C₂²	1	3	yes	—
44	#13063373	C₂×C₄	1	256	yes	direct product factor
45	C₂×#10621902	C₂×C₄	1	64	yes	complemented
46	C₂×#10621902	C₂³	1	32	yes	—
47	C₂×#10621898	C₂×C₄	1	96	yes	complemented
48	C₂×#10621898	C₂³	1	48	yes	—
49	C₂²×Dic₈₆	C₂³	1	6	yes	—
50	C₂×Q₈×D₄₃	C₂×C₄	1	64	yes	complemented
51	C₂×Q₈×D₄₃	C₂³	1	32	yes	—
52	C₂²×D₁₇₂	C₂³	1	6	yes	—
53	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
54	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
55	C₂²×C₄×D₄₃	C₂³	1	12	yes	—
56	C₂²×C₄×D₄₃	C₂³	1	12	yes	—
57	Q₈×Dic₄₃	C₂³	1	32	yes	—
58	Q₈×Dic₄₃	C₂³	1	32	yes	—
59	C₄×Dic₈₆	C₂³	1	48	yes	—
60	C₄×Dic₈₆	C₂³	1	48	yes	—
61	#13063290	C₂³	1	96	yes	—
62	C₄×D₁₇₂	C₂³	1	48	yes	—
63	C₄×D₁₇₂	C₂³	1	48	yes	—
64	#13063287	C₂³	1	96	yes	—
65	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	—
66	C₄×C₂²⋊D₄₃	C₂³	1	96	yes	—
67	#13063284	C₂³	1	48	yes	—
68	#13063283	C₂³	1	96	yes	—
69	#13063282	C₂³	1	96	yes	—
70	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
71	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
72	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	—
73	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
74	C₄⋊C₄×D₄₃	C₂³	1	96	yes	—
75	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
76	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
77	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
78	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
80	C₂×C₄×Dic₄₃	C₂³	1	12	yes	—
81	C₄²×D₄₃	C₂³	1	96	yes	—
82	C₂²×Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
83	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
84	C₂²×Q₈×C₄₃	C₂³	1	8	yes	—
85	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
87	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
88	C₄×Q₈×C₄₃	C₂³	1	32	yes	—
89	C₄×Q₈×C₄₃	C₂³	1	32	yes	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	12	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	24	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	6	yes	—
94	C₂×C₄²×C₄₃	C₂³	1	24	yes	—
95	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂³×D₄₃	C₂⁴	1	4	yes	—
97	C₂×Q₈×C₄₃	C₂²×C₄	1	32	yes	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	64	yes	complemented
99	C₂×Q₈×C₄₃	C₂⁴	1	16	yes	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	4	6	no	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	24	yes	—
103	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
106	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
107	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
108	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₂²⋊D₄₃	C₂²×C₄	1	32	yes	—
111	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
112	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
113	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
114	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
115	#10621902	C₂²×C₄	1	256	yes	complemented
116	Q₈×D₄₃	C₂²×C₄	1	256	yes	complemented
117	#10621898	C₂²×C₄	1	384	yes	complemented
118	C₂×D₁₇₂	C₂²×C₄	1	48	yes	—
119	C₂×D₁₇₂	C₂⁴	1	24	yes	—
120	C₂×C₄×D₄₃	—	2	16	no	—
121	C₂×C₄×D₄₃	—	4	24	no	—
122	C₂×C₄×D₄₃	C₂²×C₄	1	96	yes	—
123	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
124	C₂×C₄×D₄₃	C₂⁴	1	48	yes	—
125	C₂×C₄×D₄₃	C₂⁴	1	48	yes	—
126	C₂×Dic₈₆	C₂²×C₄	1	48	yes	—
127	C₂×Dic₈₆	C₂⁴	1	24	yes	—
128	C₄⋊C₄×C₄₃	C₂⁴	1	48	yes	—
129	C₄²×C₄₃	C₂⁴	1	24	yes	—
130	C₄²×C₄₃	C₂⁴	1	24	yes	—
131	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
132	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
133	(C₂×D₄₃)⋊C₄	C₂⁴	1	48	yes	—
134	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
135	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
136	Dic₄₃⋊C₄	C₂⁴	1	48	yes	—
137	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
138	C₄×Dic₄₃	C₂⁴	1	16	yes	—
139	C₄×Dic₄₃	C₂⁴	1	48	yes	—
140	C₄×Dic₄₃	C₂⁴	1	48	yes	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
144	C₂³×C₄₃	C₂⁵	1	2	yes	—
145	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
146	C₂²×D₄₃	—	2	8	no	—
147	C₂²×D₄₃	—	2	8	no	—
148	C₂²×D₄₃	C₂³×C₄	1	16	yes	—
149	C₂²×D₄₃	C₂⁵	1	8	yes	—
150	Q₈×C₄₃	C₂³×C₄	1	64	yes	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	12	no	—
153	C₂×C₄×C₄₃	—	2	8	no	—
154	C₂×C₄×C₄₃	—	4	12	no	—
155	C₂×C₄×C₄₃	C₂³×C₄	1	24	yes	—
156	C₂×C₄×C₄₃	C₂³×C₄	1	48	yes	—
157	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	complemented
158	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
159	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
160	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
161	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
162	C₂²⋊D₄₃	C₂³×C₄	1	64	yes	—
163	C₂×Dic₄₃	—	2	8	no	—
164	C₂×Dic₄₃	—	2	8	no	—
165	C₂×Dic₄₃	C₂³×C₄	1	16	yes	—
166	C₂×Dic₄₃	C₂⁵	1	8	yes	—
167	C₂×Dic₄₃	C₂⁵	1	8	yes	—
168	C₂×Dic₄₃	C₂⁵	1	8	yes	—
169	D₁₇₂	C₂³×C₄	1	96	yes	—
170	C₄×D₄₃	—	2	32	no	—
171	C₄×D₄₃	—	4	48	no	—
172	C₄×D₄₃	C₂³×C₄	1	192	yes	—
173	Dic₈₆	C₂³×C₄	1	96	yes	—
174	C₂×C₄×2₋¹⁺⁴	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	8	no	—
178	C₂²×C₄₃	C₂⁴×C₄	1	4	yes	—
179	C₂²×C₄₃	C₂⁴×C₄	1	2	yes	—
180	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
181	C₂²×C₄₃	#585	1	2	yes	—
182	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
183	C₂×D₄₃	—	2	8	no	—
184	C₂×D₄₃	—	2	8	no	—
185	C₂×D₄₃	—	2	32	no	—
186	C₂×D₄₃	C₂⁴×C₄	1	16	yes	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	2	12	no	—
189	C₄×C₄₃	C₂⁴×C₄	1	24	yes	—
190	C₄×C₄₃	C₂×2₋¹⁺⁴	1	4	yes	complemented
191	Dic₄₃	—	2	8	no	—
192	Dic₄₃	—	2	8	no	—
193	Dic₄₃	C₂⁴×C₄	1	16	yes	—
194	C₂²×2₋¹⁺⁴	—	43	1	no	—
195	C₄×2₋¹⁺⁴	—	43	32	no	—
196	C₂×#520	—	43	4	no	—
197	C₂×#520	—	43	6	no	—
198	C₂×#519	—	43	1	no	—
199	C₂×#519	—	43	4	no	—
200	C₂×C₄×#41	—	43	6	no	—
201	C₂×C₄×#41	—	43	4	no	—
202	C₂²×C₄×Q₈	—	43	4	no	—
203	C₂²×C₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
204	C₂×C₄₃	—	2	4	no	—
205	C₂×C₄₃	C₄×2₋¹⁺⁴	1	4	yes	complemented
206	C₂×C₄₃	C₂⁵×C₄	1	1	yes	characteristic
207	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₄₃	C₂×#585	1	1	yes	characteristic
209	D₄₃	—	2	16	no	—
210	C₂×2₋¹⁺⁴	—	43	16	no	—
211	C₂×2₋¹⁺⁴	—	43	32	no	—
212	C₂²×#41	—	43	4	no	—
213	C₂²×#41	—	43	6	no	—
214	C₂³×Q₈	—	43	4	no	—
215	C₂³×Q₈	C₂×D₄₃	1	1	yes	characteristic
216	#520	—	43	64	no	—
217	#520	—	43	96	no	—
218	#519	—	43	16	no	—
219	#519	—	43	64	no	—
220	C₄×#41	—	43	64	no	—
221	C₄×#41	—	43	96	no	—
222	C₂×C₄×Q₈	—	43	4	no	—
223	C₂×C₄×Q₈	—	43	4	no	—
224	C₂×C₄×Q₈	—	43	64	no	—
225	C₂×C₄×Q₈	—	43	12	no	—
226	C₂×C₄×Q₈	—	43	6	no	—
227	C₂×C₄×Q₈	—	43	6	no	—
228	C₂×C₄×Q₈	C₂×D₄₃	1	4	yes	—
229	C₂×C₄×Q₈	C₂×D₄₃	1	4	yes	—
230	C₂×C₄×Q₈	C₂×D₄₃	1	16	yes	complemented
231	C₂×C₄×D₄	—	43	4	no	—
232	C₂×C₄×D₄	—	43	12	no	—
233	C₂×C₄×D₄	—	43	12	no	—
234	C₂×C₄×D₄	—	43	6	no	—
235	C₂×C₄×D₄	—	43	6	no	—
236	C₂×#117	—	43	6	no	—
237	C₂×#117	—	43	12	no	—
238	C₂×#117	—	43	12	no	—
239	C₂²×C₄⋊C₄	—	43	12	no	—
240	C₂²×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
241	C₂²×C₄²	—	43	12	no	—
242	C₂²×C₄²	C₂×D₄₃	1	3	yes	—
243	C₄₃	C₂×C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
244	2₋¹⁺⁴	—	43	256	no	—
245	C₂×#41	—	43	64	no	—
246	C₂×#41	—	43	32	no	—
247	C₂×#41	—	43	96	no	—
248	C₂×#41	—	43	48	no	—
249	C₂²×Q₈	—	43	64	no	—
250	C₂²×Q₈	—	43	32	no	—
251	C₂²×Q₈	—	43	6	no	—
252	C₂²×Q₈	C₄×D₄₃	1	16	yes	complemented
253	C₂²×Q₈	C₂²×D₄₃	1	4	yes	—
254	C₂²×Q₈	C₂²×D₄₃	1	8	yes	—
255	C₂²×D₄	—	43	4	no	—
256	C₂²×D₄	—	43	6	no	—
257	C₂³×C₄	—	43	12	no	—
258	C₂³×C₄	—	43	4	no	—
259	C₂³×C₄	—	43	12	no	—
260	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
262	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
263	C₄×Q₈	—	43	32	no	—
264	C₄×Q₈	—	43	32	no	—
265	C₄×Q₈	—	43	96	no	—
266	C₄×Q₈	—	43	48	no	—
267	C₄×Q₈	—	43	48	no	—
268	C₄×Q₈	C₂²×D₄₃	1	32	yes	—
269	C₄×Q₈	C₂²×D₄₃	1	32	yes	—
270	C₄×D₄	—	43	32	no	—
271	C₄×D₄	—	43	96	no	—
272	C₄×D₄	—	43	96	no	—
273	C₄×D₄	—	43	48	no	—
274	C₄×D₄	—	43	48	no	—
275	#117	—	43	48	no	—
276	#117	—	43	96	no	—
277	#117	—	43	96	no	—
278	C₂×C₄⋊C₄	—	43	12	no	—
279	C₂×C₄⋊C₄	—	43	6	no	—
280	C₂×C₄⋊C₄	—	43	4	no	—
281	C₂×C₄⋊C₄	—	43	6	no	—
282	C₂×C₄⋊C₄	—	43	96	no	—
283	C₂×C₄⋊C₄	C₂²×D₄₃	1	12	yes	—
284	C₂×C₄⋊C₄	C₂²×D₄₃	1	24	yes	—
285	C₂×C₂²⋊C₄	—	43	4	no	—
286	C₂×C₂²⋊C₄	—	43	12	no	—
287	C₂×C₂²⋊C₄	—	43	4	no	—
288	C₂×C₄²	—	43	12	no	—
289	C₂×C₄²	—	43	12	no	—
290	C₂×C₄²	—	43	4	no	—
291	C₂×C₄²	—	43	96	no	—
292	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
293	C₂×C₄²	C₂²×D₄₃	1	24	yes	—
294	C₂×C₄²	C₂²×D₄₃	1	6	yes	—
295	C₂⁴	—	43	4	no	—
296	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
297	#41	—	43	256	no	—
298	#41	—	43	384	no	—
299	C₂×Q₈	—	43	256	no	—
300	C₂×Q₈	—	43	48	no	—
301	C₂×Q₈	—	43	24	no	—
302	C₂×Q₈	C₂×C₄×D₄₃	1	32	yes	—
303	C₂×Q₈	C₂×C₄×D₄₃	1	64	yes	complemented
304	C₂×Q₈	C₂³×D₄₃	1	16	yes	—
305	C₂×D₄	—	43	32	no	—
306	C₂×D₄	—	43	16	no	—
307	C₂×D₄	—	43	48	no	—
308	C₂×D₄	—	43	24	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	4	6	no	—
311	C₂²×C₄	—	43	4	no	—
312	C₂²×C₄	—	43	96	no	—
313	C₂²×C₄	—	43	48	no	—
314	C₂²×C₄	—	43	4	no	—
315	C₂²×C₄	—	43	4	no	—
316	C₂²×C₄	—	43	16	no	—
317	C₂²×C₄	—	43	48	no	—
318	C₂²×C₄	—	86	16	no	—
319	C₂²×C₄	—	172	24	no	—
320	C₂²×C₄	C₂×C₄×D₄₃	1	24	yes	—
321	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
322	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
324	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
325	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
326	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
327	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
328	C₄⋊C₄	—	43	48	no	—
329	C₄⋊C₄	—	43	24	no	—
330	C₄⋊C₄	—	43	16	no	—
331	C₄⋊C₄	—	43	24	no	—
332	C₄⋊C₄	C₂³×D₄₃	1	48	yes	—
333	C₂²⋊C₄	—	43	16	no	—
334	C₂²⋊C₄	—	43	48	no	—
335	C₂²⋊C₄	—	43	16	no	—
336	C₄²	—	43	16	no	—
337	C₄²	—	43	48	no	—
338	C₄²	—	43	48	no	—
339	C₄²	C₂³×D₄₃	1	24	yes	—
340	C₄²	C₂³×D₄₃	1	24	yes	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	43	16	no	—
344	C₂³	—	43	8	no	—
345	C₂³	—	86	8	no	—
346	C₂³	—	86	8	no	—
347	C₂³	C₂²×C₄×D₄₃	1	4	yes	—
348	C₂³	C₂⁴×D₄₃	1	2	yes	—
349	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
350	Q₈	—	43	96	no	—
351	Q₈	C₂²×C₄×D₄₃	1	64	yes	—
352	D₄	—	43	64	no	—
353	D₄	—	43	96	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	12	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	4	12	no	—
358	C₂×C₄	—	43	16	no	—
359	C₂×C₄	—	43	8	no	—
360	C₂×C₄	—	43	192	no	—
361	C₂×C₄	—	43	8	no	—
362	C₂×C₄	—	43	8	no	—
363	C₂×C₄	—	86	8	no	—
364	C₂×C₄	—	86	8	no	—
365	C₂×C₄	—	86	32	no	—
366	C₂×C₄	—	172	48	no	—
367	C₂×C₄	C₂²×C₄×D₄₃	1	24	yes	—
368	C₂×C₄	C₂²×C₄×D₄₃	1	48	yes	—
369	C₂×C₄	#13063373	1	4	yes	direct product factor
370	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
371	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
372	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
373	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	43	16	no	—
378	C₂²	—	86	32	no	—
379	C₂²	—	86	8	no	—
380	C₂²	—	86	8	no	—
381	C₂²	C₂³×C₄×D₄₃	1	4	yes	—
382	C₂²	C₂³×C₄×D₄₃	1	2	yes	—
383	C₂²	C₂×#13063373	1	2	yes	—
384	C₂²	#14583735	1	2	yes	—
385	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	12	no	—
388	C₄	—	43	16	no	—
389	C₄	—	86	8	no	—
390	C₄	—	86	8	no	—
391	C₄	C₂³×C₄×D₄₃	1	24	yes	—
392	C₄	C₂×#13063373	1	4	yes	direct product factor
393	C₂	—	2	4	no	—
394	C₂	—	86	16	no	—
395	C₂	C₄×#13063373	1	4	yes	direct product factor
396	C₂	C₂⁴×C₄×D₄₃	1	1	yes	characteristic
397	C₂	C₂²×#13063373	1	1	yes	characteristic
398	C₂	C₂×#14583735	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×C₄×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
prime radical	C₂²×#13063373	C₂
cosocle	C₂²×C₄₃	C₂⁶
hypercenter	C₂²×C₄×Q₈	D₄₃
hypocenter	C₄₃	C₂×C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄×#13063373	C₂	direct (N × H)
3. C₂×#14583381	C₂	semidirect
4. C₂×#14583380	C₂	semidirect
5. C₂×#14583377	C₂	semidirect
6. C₂×#14583375	C₂	semidirect
7. C₂×C₄×#10621902	C₂	semidirect
8. C₂×C₄×#10621898	C₂	semidirect
9. C₂×C₄×Q₈×D₄₃	C₂	semidirect
10. C₂²×C₄×Q₈×C₄₃	C₂	semidirect
11. C₂×#13063373	C₄	direct (N × H)
16. #14583381	C₂²	semidirect
17. #14583380	C₂²	semidirect
18. #14583377	C₂²	semidirect
19. #14583375	C₂²	semidirect
20. C₄×#10621902	C₂²	semidirect
21. C₄×#10621898	C₂²	semidirect
27. C₄×Q₈×D₄₃	C₂²	semidirect
41. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
44. #13063373	C₂×C₄	direct (N × H)
45. C₂×#10621902	C₂×C₄	semidirect
47. C₂×#10621898	C₂×C₄	semidirect
50. C₂×Q₈×D₄₃	C₂×C₄	semidirect
82. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
98. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
115. #10621902	C₂²×C₄	semidirect
116. Q₈×D₄₃	C₂²×C₄	semidirect
117. #10621898	C₂²×C₄	semidirect
157. C₂×C₄×C₄₃	2₋¹⁺⁴	semidirect
190. C₄×C₄₃	C₂×2₋¹⁺⁴	semidirect
203. C₂²×C₄×Q₈	D₄₃	semidirect
205. C₂×C₄₃	C₄×2₋¹⁺⁴	semidirect
230. C₂×C₄×Q₈	C₂×D₄₃	semidirect
243. C₄₃	C₂×C₄×2₋¹⁺⁴	semidirect
252. C₂²×Q₈	C₄×D₄₃	semidirect
303. C₂×Q₈	C₂×C₄×D₄₃	semidirect
369. C₂×C₄	#13063373	direct (N × H)
392. C₄	C₂×#13063373	direct (N × H)
395. C₂	C₄×#13063373	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063373	2
C₄×#13063373	2
C₂×#14583381	2
C₂×#14583380	2
C₂×#14583377	2
C₂×#14583375	2
C₂×C₄×#10621902	2
C₂×C₄×#10621898	2
C₂×C₄×Q₈×D₄₃	2
C₂²×C₄×Q₈×C₄₃	2
C₂×C₄×2₋¹⁺⁴	43

Subgroups — C2×C4×#13063373 #26003206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13063373 #26003206