Subgroups — C₂×#117×Dic₄₃ #25254784

Order 11008.

4462 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063284	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₄₃	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×Dic₄₃	C₂	1	4	yes	maximal, complemented
5	C₂×C₂²⋊C₄×Dic₄₃	C₂	1	4	yes	maximal
6	C₂×#14582745	C₂	1	2	yes	maximal, complemented
7	C₂×C₄²×Dic₄₃	C₂	1	2	yes	maximal, complemented
8	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂⁴×Dic₄₃	C₂²	1	2	yes	—
10	C₂×#13063284	C₄	1	16	yes	complemented
11	C₂×#13063284	C₂²	1	8	yes	—
12	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂²×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₃	C₄	1	16	yes	complemented
15	C₂²×C₄×Dic₄₃	C₂²	1	8	yes	—
16	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
19	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
20	C₂²×C₄×Dic₄₃	C₂²	1	8	yes	—
21	C₄⋊C₄×Dic₄₃	C₂²	1	32	yes	complemented
22	C₂²⋊C₄×Dic₄₃	C₂²	1	32	yes	—
23	#14582745	C₂²	1	16	yes	complemented
24	C₂×C₄₃⋊#95	C₂²	1	8	yes	—
25	C₄²×Dic₄₃	C₂²	1	16	yes	complemented
26	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₄	1	16	yes	complemented
28	C₂×#117×C₄₃	C₂²	1	8	yes	—
29	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
32	C₂³×Dic₄₃	—	2	16	no	—
33	C₂³×Dic₄₃	C₂×C₄	1	16	yes	—
34	C₂³×Dic₄₃	C₂³	1	4	yes	—
35	C₂³×Dic₄₃	C₂³	1	2	yes	—
36	C₂³×Dic₄₃	C₂³	1	8	yes	—
37	C₂³×Dic₄₃	C₂³	1	2	yes	—
38	#13063284	C₂×C₄	1	64	yes	complemented
39	C₂×C₄⋊Dic₄₃	C₂×C₄	1	16	yes	complemented
40	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
41	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	16	yes	—
42	C₂×C₂²⋊Dic₄₃	C₂³	1	8	yes	—
43	C₂×C₄×Dic₄₃	—	2	32	no	—
44	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
45	C₂×C₄×Dic₄₃	C₂×C₄	1	16	yes	—
46	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
47	C₂×C₄×Dic₄₃	C₂×C₄	1	64	yes	complemented
48	C₂×C₄×Dic₄₃	C₂×C₄	1	16	yes	complemented
49	C₂×C₄×Dic₄₃	C₂³	1	32	yes	—
50	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
51	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
52	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
53	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
54	C₄₃⋊#95	C₂³	1	32	yes	—
55	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
58	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
59	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	#117×C₄₃	C₂×C₄	1	64	yes	complemented
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	complemented
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
67	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
68	C₂×C₄²×C₄₃	C₂×C₄	1	16	yes	complemented
69	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
70	C₂⁴×C₄₃	—	2	8	no	—
71	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
72	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
75	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	—	2	16	no	—
77	C₂²×C₄×C₄₃	C₄²	1	64	yes	complemented
78	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₄₃	C₂²×C₄	1	16	yes	—
83	C₂²×C₄×C₄₃	C₂²×C₄	1	16	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	16	yes	—
85	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	16	yes	—
88	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
91	C₂²×Dic₄₃	—	2	64	no	—
92	C₂²×Dic₄₃	—	2	32	no	—
93	C₂²×Dic₄₃	—	2	16	no	—
94	C₂²×Dic₄₃	—	2	8	no	—
95	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
96	C₂²×Dic₄₃	C₂²×C₄	1	32	yes	—
97	C₂²×Dic₄₃	C₂²×C₄	1	16	yes	—
98	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
99	C₂²×Dic₄₃	#41	1	16	yes	—
100	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
101	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
102	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
103	C₄⋊C₄×C₄₃	C₂²×C₄	1	32	yes	complemented
104	C₂²⋊C₄×C₄₃	C₂²×C₄	1	32	yes	—
105	C₄²×C₄₃	C₂²×C₄	1	32	yes	complemented
106	C₂²⋊Dic₄₃	C₂²×C₄	1	32	yes	—
107	C₄⋊Dic₄₃	C₂²×C₄	1	32	yes	complemented
108	C₄×Dic₄₃	—	2	64	no	—
109	C₄×Dic₄₃	C₂²×C₄	1	16	yes	—
110	C₄×Dic₄₃	C₂²×C₄	1	32	yes	—
111	C₄×Dic₄₃	C₂²×C₄	1	16	yes	—
112	C₄×Dic₄₃	C₂²×C₄	1	32	yes	complemented
113	C₂³×C₄₃	—	2	16	no	—
114	C₂³×C₄₃	—	2	16	no	—
115	C₂³×C₄₃	—	2	16	no	—
116	C₂³×C₄₃	—	2	8	no	—
117	C₂³×C₄₃	C₂×C₄²	1	16	yes	—
118	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
119	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
120	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
121	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
122	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
123	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
124	C₂³×C₄₃	C₂×#41	1	8	yes	—
125	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
126	C₂×C₄×C₄₃	—	2	32	no	—
127	C₂×C₄×C₄₃	—	2	16	no	—
128	C₂×C₄×C₄₃	C₂×C₄²	1	16	yes	—
129	C₂×C₄×C₄₃	C₂×C₄²	1	16	yes	—
130	C₂×C₄×C₄₃	C₂×C₄²	1	64	yes	complemented
131	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
132	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
133	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
134	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
135	C₂×C₄×C₄₃	C₂³×C₄	1	16	yes	—
136	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
137	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
138	C₂×Dic₄₃	—	2	16	no	—
139	C₂×Dic₄₃	—	2	32	no	—
140	C₂×Dic₄₃	—	2	16	no	—
141	C₂×Dic₄₃	—	2	8	no	—
142	C₂×Dic₄₃	—	2	64	no	—
143	C₂×Dic₄₃	#117	1	32	yes	direct product factor
144	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
145	C₂×Dic₄₃	C₂³×C₄	1	16	yes	—
146	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
147	C₂×Dic₄₃	C₂×#41	1	16	yes	—
148	C₂×C₄×#117	—	43	1	no	maximal, Sylow
149	C₂²×C₄₃	—	2	8	no	—
150	C₂²×C₄₃	—	2	8	no	—
151	C₂²×C₄₃	—	2	8	no	—
152	C₂²×C₄₃	—	2	32	no	—
153	C₂²×C₄₃	C₂²×C₄²	1	8	yes	—
154	C₂²×C₄₃	C₂²×C₄²	1	4	yes	—
155	C₂²×C₄₃	C₂×#117	1	8	yes	—
156	C₂²×C₄₃	C₄×#41	1	8	yes	—
157	C₂²×C₄₃	C₄×#41	1	8	yes	—
158	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
159	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
160	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
161	C₂²×C₄₃	C₂²×#41	1	4	yes	—
162	C₄×C₄₃	—	2	16	no	—
163	C₄×C₄₃	C₂²×C₄²	1	8	yes	—
164	C₄×C₄₃	C₂²×C₄²	1	8	yes	—
165	Dic₄₃	—	2	8	no	—
166	Dic₄₃	—	2	16	no	—
167	Dic₄₃	C₂×#117	1	16	yes	direct product factor
168	C₂²×#117	—	43	1	no	—
169	C₂²×#117	D₄₃	1	1	yes	characteristic
170	C₂³×C₄²	—	43	1	no	—
171	C₄×#117	—	43	16	no	—
172	C₂×C₄×C₄⋊C₄	—	43	4	no	—
173	C₂×C₄×C₂²⋊C₄	—	43	4	no	—
174	C₂×#376	—	43	2	no	—
175	C₂×C₄³	—	43	2	no	—
176	C₂×C₄₃	—	2	8	no	—
177	C₂×C₄₃	C₄×#117	1	8	yes	complemented
178	C₂×C₄₃	C₂³×C₄²	1	1	yes	characteristic
179	C₂×C₄₃	C₂²×#117	1	2	yes	—
180	C₂×C₄₃	C₂×C₄×#41	1	2	yes	—
181	C₂×C₄₃	C₂×C₄×#41	1	2	yes	—
182	C₂⁴×C₄	—	43	2	no	—
183	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
184	C₂×#117	—	43	8	no	—
185	C₂×#117	—	43	16	no	—
186	C₂×#117	Dic₄₃	1	16	yes	direct product factor
187	C₂×#117	C₂×D₄₃	1	8	yes	—
188	C₂²×C₄⋊C₄	—	43	2	no	—
189	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	—	43	2	no	—
191	C₂²×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
192	C₂²×C₄²	—	43	2	no	—
193	C₂²×C₄²	—	43	8	no	—
194	C₂²×C₄²	—	43	1	no	—
195	C₂²×C₄²	—	43	1	no	—
196	C₂²×C₄²	—	43	2	no	—
197	C₂²×C₄²	—	43	16	no	—
198	C₂²×C₄²	—	43	8	no	—
199	C₂²×C₄²	C₂×D₄₃	1	2	yes	—
200	C₄×C₄⋊C₄	—	43	32	no	—
201	C₄×C₂²⋊C₄	—	43	32	no	—
202	#376	—	43	16	no	—
203	C₂×#95	—	43	8	no	—
204	C₄³	—	43	16	no	—
205	C₄₃	C₂×C₄×#117	1	1	yes	characteristic, complemented, Sylow
206	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
207	C₂³×C₄	—	43	2	no	—
208	C₂³×C₄	—	43	16	no	—
209	C₂³×C₄	—	43	4	no	—
210	C₂³×C₄	—	43	2	no	—
211	C₂³×C₄	—	43	8	no	—
212	C₂³×C₄	—	86	16	no	—
213	C₂³×C₄	C₄×D₄₃	1	8	yes	—
214	C₂³×C₄	C₄×D₄₃	1	8	yes	—
215	C₂³×C₄	C₂×Dic₄₃	1	8	yes	—
216	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
217	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
218	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
219	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
220	#117	—	43	64	no	—
221	#117	C₂×Dic₄₃	1	64	yes	direct product factor
222	C₂×C₄⋊C₄	—	43	16	no	—
223	C₂×C₄⋊C₄	—	43	8	no	—
224	C₂×C₄⋊C₄	C₂×Dic₄₃	1	16	yes	complemented
225	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
226	C₂×C₂²⋊C₄	—	43	16	no	—
227	C₂×C₂²⋊C₄	—	43	8	no	—
228	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	16	yes	—
229	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
230	C₂×C₄²	—	43	16	no	—
231	C₂×C₄²	—	43	8	no	—
232	C₂×C₄²	—	43	16	no	—
233	C₂×C₄²	—	43	8	no	—
234	C₂×C₄²	—	43	64	no	—
235	C₂×C₄²	—	43	8	no	—
236	C₂×C₄²	—	43	4	no	—
237	C₂×C₄²	—	43	4	no	—
238	C₂×C₄²	—	43	8	no	—
239	C₂×C₄²	—	43	32	no	—
240	C₂×C₄²	—	86	32	no	—
241	C₂×C₄²	C₂×Dic₄₃	1	16	yes	complemented
242	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
243	#95	—	43	32	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	C₂×C₄×D₄₃	1	4	yes	—
246	C₂⁴	C₂×C₄×D₄₃	1	4	yes	—
247	C₂⁴	C₂²×Dic₄₃	1	4	yes	—
248	C₂⁴	C₂³×D₄₃	1	2	yes	—
249	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	43	8	no	—
252	C₂²×C₄	—	43	16	no	—
253	C₂²×C₄	—	43	4	no	—
254	C₂²×C₄	—	43	32	no	—
255	C₂²×C₄	—	43	8	no	—
256	C₂²×C₄	—	43	16	no	—
257	C₂²×C₄	—	43	4	no	—
258	C₂²×C₄	—	43	8	no	—
259	C₂²×C₄	—	86	64	no	—
260	C₂²×C₄	—	86	32	no	—
261	C₂²×C₄	—	86	16	no	—
262	C₂²×C₄	—	86	8	no	—
263	C₂²×C₄	C₄×Dic₄₃	1	64	yes	complemented
264	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
265	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
266	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
267	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
268	C₂²×C₄	C₂×C₄×D₄₃	1	16	yes	—
269	C₂²×C₄	C₂×C₄×D₄₃	1	16	yes	—
270	C₂²×C₄	C₂²×Dic₄₃	1	16	yes	—
271	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
272	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₄₃	1	16	yes	—
274	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
275	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
276	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
277	C₄⋊C₄	—	43	32	no	—
278	C₄⋊C₄	C₂²×Dic₄₃	1	32	yes	complemented
279	C₂²⋊C₄	—	43	32	no	—
280	C₂²⋊C₄	C₂²×Dic₄₃	1	32	yes	—
281	C₄²	—	43	16	no	—
282	C₄²	—	43	32	no	—
283	C₄²	—	43	16	no	—
284	C₄²	—	43	32	no	—
285	C₄²	—	86	64	no	—
286	C₄²	C₂²×Dic₄₃	1	32	yes	complemented
287	C₂³	—	2	16	no	—
288	C₂³	—	2	16	no	—
289	C₂³	—	2	16	no	—
290	C₂³	—	2	8	no	—
291	C₂³	C₂×C₄×Dic₄₃	1	16	yes	—
292	C₂³	C₂²×C₄×D₄₃	1	4	yes	—
293	C₂³	C₂²×C₄×D₄₃	1	4	yes	—
294	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
295	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
296	C₂³	C₂³×Dic₄₃	1	4	yes	—
297	C₂³	C₂³×Dic₄₃	1	2	yes	—
298	C₂³	#41×D₄₃	1	8	yes	—
299	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
300	C₂×C₄	—	2	32	no	—
301	C₂×C₄	—	2	16	no	—
302	C₂×C₄	—	43	32	no	—
303	C₂×C₄	—	43	8	no	—
304	C₂×C₄	—	43	16	no	—
305	C₂×C₄	—	43	8	no	—
306	C₂×C₄	—	43	16	no	—
307	C₂×C₄	—	86	64	no	—
308	C₂×C₄	—	86	16	no	—
309	C₂×C₄	—	86	32	no	—
310	C₂×C₄	—	86	16	no	—
311	C₂×C₄	—	86	8	no	—
312	C₂×C₄	C₂×C₄×Dic₄₃	1	16	yes	—
313	C₂×C₄	C₂×C₄×Dic₄₃	1	16	yes	—
314	C₂×C₄	C₂×C₄×Dic₄₃	1	64	yes	complemented
315	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
316	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
317	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
318	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
319	C₂×C₄	C₂³×Dic₄₃	1	16	yes	—
320	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
321	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	32	no	—
324	C₂²	—	2	8	no	—
325	C₂²	—	2	8	no	—
326	C₂²	C₂²×C₄×Dic₄₃	1	8	yes	—
327	C₂²	C₂²×C₄×Dic₄₃	1	4	yes	—
328	C₂²	#117×D₄₃	1	8	yes	—
329	C₂²	#14583367	1	8	yes	—
330	C₂²	#41×Dic₄₃	1	8	yes	—
331	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
332	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
333	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
334	C₂²	C₂×#41×D₄₃	1	4	yes	—
335	C₄	—	2	16	no	—
336	C₄	—	43	16	no	—
337	C₄	—	86	8	no	—
338	C₄	—	86	16	no	—
339	C₄	C₂²×C₄×Dic₄₃	1	8	yes	—
340	C₄	C₂²×C₄×Dic₄₃	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	#117×Dic₄₃	1	8	yes	direct product factor
343	C₂	C₂³×C₄×Dic₄₃	1	1	yes	characteristic
344	C₂	C₂×#117×D₄₃	1	2	yes	—
345	C₂	C₂×#14583367	1	2	yes	—
346	C₂	C₂×#41×Dic₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂²×#117×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂⁴
prime radical	C₂⁵×C₄₃	C₂³
cosocle	C₂³×C₄₃	C₂⁵
hypercenter	C₂²×#117	D₄₃
hypocenter	C₄₃	C₂×C₄×#117
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
3. #117×Dic₄₃	C₂	direct (N × H)
4. C₂×C₄⋊C₄×Dic₄₃	C₂	semidirect
6. C₂×#14582745	C₂	semidirect
7. C₂×C₄²×Dic₄₃	C₂	semidirect
10. C₂×#13063284	C₄	semidirect
14. C₂²×C₄×Dic₄₃	C₄	semidirect
21. C₄⋊C₄×Dic₄₃	C₂²	semidirect
23. #14582745	C₂²	semidirect
25. C₄²×Dic₄₃	C₂²	semidirect
27. C₂×#117×C₄₃	C₄	semidirect
38. #13063284	C₂×C₄	semidirect
39. C₂×C₄⋊Dic₄₃	C₂×C₄	semidirect
47. C₂×C₄×Dic₄₃	C₂×C₄	semidirect
48. C₂×C₄×Dic₄₃	C₂×C₄	semidirect
63. #117×C₄₃	C₂×C₄	semidirect
64. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
68. C₂×C₄²×C₄₃	C₂×C₄	semidirect
77. C₂²×C₄×C₄₃	C₄²	semidirect
103. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
105. C₄²×C₄₃	C₂²×C₄	semidirect
107. C₄⋊Dic₄₃	C₂²×C₄	semidirect
112. C₄×Dic₄₃	C₂²×C₄	semidirect
130. C₂×C₄×C₄₃	C₂×C₄²	semidirect
143. C₂×Dic₄₃	#117	direct (N × H)
167. Dic₄₃	C₂×#117	direct (N × H)
177. C₂×C₄₃	C₄×#117	semidirect
186. C₂×#117	Dic₄₃	direct (N × H)
205. C₄₃	C₂×C₄×#117	semidirect
221. #117	C₂×Dic₄₃	direct (N × H)
224. C₂×C₄⋊C₄	C₂×Dic₄₃	semidirect
241. C₂×C₄²	C₂×Dic₄₃	semidirect
263. C₂²×C₄	C₄×Dic₄₃	semidirect
278. C₄⋊C₄	C₂²×Dic₄₃	semidirect
286. C₄²	C₂²×Dic₄₃	semidirect
314. C₂×C₄	C₂×C₄×Dic₄₃	semidirect
342. C₂	#117×Dic₄₃	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×#13063284	2
C₂³×C₄×Dic₄₃	2
#117×Dic₄₃	2
C₂×C₄⋊C₄×Dic₄₃	2
C₂×C₂²⋊C₄×Dic₄₃	2
C₂×#14582745	2
C₂×C₄²×Dic₄₃	2
C₂²×#117×C₄₃	2
C₂×C₄×#117	43

Subgroups — C2×#117×Dic43 #25254784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#117×Dic₄₃ #25254784