Subgroups — D₄²×D₄₃ #19148030

Order 5504.

2536 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₄₃	C₂	1	4	yes	maximal, complemented
2	D₄×D₁₇₂	C₂	1	2	yes	maximal, complemented
3	#14583534	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583533	C₂	1	4	yes	maximal, complemented
5	D₄×C₂²⋊D₄₃	C₂	1	4	yes	maximal, complemented
6	#14583531	C₂	1	4	yes	maximal, complemented
7	#127×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#121×D₄₃	C₂	1	4	yes	maximal, complemented
9	#120×D₄₃	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₄₃	C₂	1	2	yes	maximal, complemented
11	D₄²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₄₃	C₂²	1	4	yes	complemented
13	C₂²×D₁₇₂	C₂²	1	4	yes	complemented
14	C₂²×C₂²⋊D₄₃	C₂²	1	8	yes	complemented
15	C₂×D₄×D₄₃	—	2	32	no	—
16	C₂×D₄×D₄₃	C₂²	1	2	yes	—
17	C₂×D₄×D₄₃	C₂²	1	8	yes	complemented
18	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
19	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
20	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
21	C₂×D₄×D₄₃	C₂²	1	8	yes	complemented
22	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₄₃	C₂²	1	4	yes	complemented
24	#13063322	C₂²	1	1	yes	characteristic, complemented
25	#13063321	C₂²	1	2	yes	complemented
26	#13063321	C₂²	1	4	yes	complemented
27	#13063300	C₂²	1	4	yes	complemented
28	#13063299	C₂²	1	4	yes	complemented
29	#13063298	C₂²	1	8	yes	complemented
30	#13063297	C₂²	1	8	yes	complemented
31	#13063296	C₂²	1	4	yes	complemented
32	#13063295	C₂²	1	8	yes	complemented
33	#13063295	C₂²	1	4	yes	complemented
34	#13063294	C₂²	1	4	yes	complemented
35	#13063293	C₂²	1	4	yes	complemented
36	#13063293	C₂²	1	8	yes	complemented
37	C₄×D₁₇₂	C₂²	1	2	yes	complemented
38	D₄×Dic₄₃	C₂²	1	2	yes	complemented
39	#13063287	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
41	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
42	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
44	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
45	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²×D₄×C₄₃	C₂²	1	4	yes	complemented
47	#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
48	#121×C₄₃	C₂²	1	4	yes	complemented
49	#120×C₄₃	C₂²	1	4	yes	complemented
50	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
51	C₂⁴×C₄₃	C₂³	1	4	yes	complemented
52	C₂³×D₄₃	—	2	32	no	—
53	C₂³×D₄₃	—	4	8	no	—
54	C₂³×D₄₃	C₂³	1	4	yes	—
55	C₂³×D₄₃	C₂³	1	4	yes	—
56	C₂³×D₄₃	C₂³	1	4	yes	complemented
57	C₂³×D₄₃	C₂³	1	8	yes	complemented
58	C₂×D₄×C₄₃	—	2	16	no	—
59	C₂×D₄×C₄₃	C₂³	1	2	yes	—
60	C₂×D₄×C₄₃	C₂³	1	8	yes	complemented
61	C₂×D₄×C₄₃	C₂³	1	4	yes	complemented
62	C₂×D₄×C₄₃	C₂³	1	2	yes	complemented
63	C₂²×C₄×C₄₃	C₂³	1	4	yes	complemented
64	C₂×C₂²⋊D₄₃	—	2	32	no	—
65	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₄₃	C₂³	1	8	yes	complemented
67	C₂×C₂²⋊D₄₃	C₂³	1	8	yes	complemented
68	C₂×C₂²⋊D₄₃	C₂³	1	8	yes	complemented
69	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	complemented
70	C₂²×Dic₄₃	C₂³	1	4	yes	complemented
71	D₄×D₄₃	—	2	16	no	—
72	D₄×D₄₃	—	2	32	no	—
73	D₄×D₄₃	—	2	16	no	—
74	D₄×D₄₃	—	2	16	no	—
75	D₄×D₄₃	—	2	32	no	—
76	D₄×D₄₃	—	4	4	no	—
77	D₄×D₄₃	D₄	1	16	yes	direct product factor
78	C₂×D₁₇₂	—	2	16	no	—
79	C₂×D₁₇₂	C₂³	1	2	yes	—
80	C₂×D₁₇₂	C₂³	1	8	yes	complemented
81	C₂×D₁₇₂	C₂³	1	4	yes	complemented
82	C₂×D₁₇₂	C₂³	1	2	yes	complemented
83	C₂×C₄×D₄₃	—	2	16	no	—
84	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₄₃	C₂³	1	4	yes	—
86	C₂×C₄×D₄₃	C₂³	1	2	yes	—
87	C₂×C₄×D₄₃	C₂³	1	4	yes	complemented
88	C₂×C₄×D₄₃	C₂³	1	4	yes	complemented
89	C₄⋊C₄×C₄₃	C₂³	1	2	yes	complemented
90	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	complemented
91	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	complemented
92	C₄²×C₄₃	C₂³	1	1	yes	characteristic, complemented
93	C₂²⋊Dic₄₃	C₂³	1	4	yes	complemented
94	C₂²⋊Dic₄₃	C₂³	1	4	yes	complemented
95	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
96	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	complemented
97	(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	complemented
98	C₄⋊Dic₄₃	C₂³	1	2	yes	complemented
99	Dic₄₃⋊C₄	C₂³	1	4	yes	complemented
100	C₄×Dic₄₃	C₂³	1	1	yes	characteristic, complemented
101	C₄×Dic₄₃	C₂³	1	2	yes	complemented
102	C₂³×C₄₃	—	2	16	no	—
103	C₂³×C₄₃	—	4	4	no	—
104	C₂³×C₄₃	C₂⁴	1	4	yes	—
105	C₂³×C₄₃	C₂⁴	1	4	yes	—
106	C₂²×D₄₃	—	2	8	no	—
107	C₂²×D₄₃	—	2	8	no	—
108	C₂²×D₄₃	—	2	16	no	—
109	C₂²×D₄₃	—	2	16	no	—
110	C₂²×D₄₃	—	2	16	no	—
111	C₂²×D₄₃	—	2	16	no	—
112	C₂²×D₄₃	—	2	8	no	—
113	C₂²×D₄₃	—	4	4	no	—
114	C₂²×D₄₃	—	4	8	no	—
115	C₂²×D₄₃	—	4	64	no	—
116	C₂²×D₄₃	C₂×D₄	1	16	yes	complemented
117	C₂²×D₄₃	C₂⁴	1	4	yes	—
118	C₂²×D₄₃	C₂⁴	1	4	yes	—
119	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
120	D₄×C₄₃	—	2	16	no	—
121	D₄×C₄₃	—	2	8	no	—
122	D₄×C₄₃	—	4	2	no	—
123	D₄×C₄₃	C₂×D₄	1	8	yes	complemented
124	C₂×C₄×C₄₃	—	2	8	no	—
125	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
128	C₂²⋊D₄₃	—	2	16	no	—
129	C₂²⋊D₄₃	—	2	16	no	—
130	C₂²⋊D₄₃	—	2	16	no	—
131	C₂²⋊D₄₃	—	4	4	no	—
132	C₂²⋊D₄₃	C₂×D₄	1	16	yes	complemented
133	C₂×Dic₄₃	—	2	8	no	—
134	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
135	C₂×Dic₄₃	C₂⁴	1	4	yes	—
136	C₂×Dic₄₃	C₂⁴	1	2	yes	—
137	D₁₇₂	—	2	16	no	—
138	D₁₇₂	—	2	8	no	—
139	D₁₇₂	—	4	2	no	—
140	D₁₇₂	C₂×D₄	1	8	yes	complemented
141	C₄×D₄₃	—	2	8	no	—
142	C₄×D₄₃	—	2	2	no	—
143	C₄×D₄₃	—	2	8	no	—
144	C₄×D₄₃	—	2	8	no	—
145	C₄×D₄₃	C₂×D₄	1	8	yes	complemented
146	C₂²×C₄₃	—	2	4	no	—
147	C₂²×C₄₃	—	2	4	no	—
148	C₂²×C₄₃	—	2	8	no	—
149	C₂²×C₄₃	—	2	4	no	—
150	C₂²×C₄₃	—	4	16	no	—
151	C₂²×C₄₃	C₂²×D₄	1	8	yes	complemented
152	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
153	C₂×D₄₃	—	2	4	no	—
154	C₂×D₄₃	—	2	4	no	—
155	C₂×D₄₃	—	2	32	no	—
156	C₂×D₄₃	—	2	8	no	—
157	C₂×D₄₃	—	2	4	no	—
158	C₂×D₄₃	—	4	16	no	—
159	C₂×D₄₃	—	4	32	no	—
160	C₂×D₄₃	—	4	16	no	—
161	C₂×D₄₃	C₂²×D₄	1	4	yes	—
162	C₂×D₄₃	C₂²×D₄	1	8	yes	complemented
163	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
164	C₄×C₄₃	—	2	4	no	—
165	C₄×C₄₃	—	2	1	no	—
166	C₄×C₄₃	C₂²×D₄	1	4	yes	complemented
167	Dic₄₃	—	2	4	no	—
168	Dic₄₃	—	2	1	no	—
169	Dic₄₃	C₂²×D₄	1	4	yes	complemented
170	C₂×D₄²	—	43	1	no	maximal, Sylow
171	C₂×C₄₃	—	2	8	no	—
172	C₂×C₄₃	—	4	4	no	—
173	C₂×C₄₃	C₂³×D₄	1	2	yes	—
174	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
175	D₄₃	—	2	8	no	—
176	D₄₃	—	4	4	no	—
177	D₄₃	D₄²	1	4	yes	direct product factor
178	C₂³×D₄	—	43	4	no	—
179	D₄²	—	43	4	no	—
180	D₄²	—	43	1	no	—
181	D₄²	—	43	4	no	—
182	D₄²	—	43	4	no	—
183	D₄²	—	43	2	no	—
184	D₄²	D₄₃	1	1	yes	characteristic, direct product factor
185	C₂×#127	—	43	1	no	—
186	C₂×#121	—	43	4	no	—
187	C₂×#120	—	43	4	no	—
188	C₂×C₄×D₄	—	43	2	no	—
189	C₄₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
190	C₂⁵	—	43	4	no	—
191	C₂²×D₄	—	43	2	no	—
192	C₂²×D₄	—	43	8	no	—
193	C₂²×D₄	—	43	4	no	—
194	C₂²×D₄	—	43	8	no	—
195	C₂²×D₄	—	43	4	no	—
196	C₂²×D₄	—	43	8	no	—
197	C₂²×D₄	—	43	4	no	—
198	C₂²×D₄	—	43	2	no	—
199	C₂²×D₄	—	43	4	no	—
200	C₂²×D₄	—	86	32	no	—
201	C₂²×D₄	C₂×D₄₃	1	4	yes	complemented
202	C₂³×C₄	—	43	4	no	—
203	#127	—	43	2	no	—
204	#127	—	43	4	no	—
205	#127	—	43	1	no	—
206	#127	C₂×D₄₃	1	1	yes	characteristic, complemented
207	#121	—	43	4	no	—
208	#121	—	43	8	no	—
209	#121	—	43	4	no	—
210	#121	—	43	4	no	—
211	#121	—	43	8	no	—
212	#121	C₂×D₄₃	1	4	yes	complemented
213	#120	—	43	4	no	—
214	#120	—	43	8	no	—
215	#120	—	43	4	no	—
216	#120	—	43	4	no	—
217	#120	—	43	8	no	—
218	#120	C₂×D₄₃	1	4	yes	complemented
219	C₄×D₄	—	43	2	no	—
220	C₄×D₄	—	43	4	no	—
221	C₄×D₄	—	43	2	no	—
222	C₄×D₄	—	43	4	no	—
223	C₄×D₄	—	43	2	no	—
224	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
225	C₂×C₄⋊C₄	—	43	2	no	—
226	C₂×C₂²⋊C₄	—	43	4	no	—
227	C₂×C₂²⋊C₄	—	43	4	no	—
228	C₂×C₄²	—	43	1	no	—
229	C₂⁴	—	43	4	no	—
230	C₂⁴	—	43	4	no	—
231	C₂⁴	—	43	4	no	—
232	C₂⁴	—	43	8	no	—
233	C₂⁴	—	86	32	no	—
234	C₂⁴	—	172	8	no	—
235	C₂⁴	C₂²×D₄₃	1	4	yes	complemented
236	C₂×D₄	—	2	16	no	—
237	C₂×D₄	—	43	4	no	—
238	C₂×D₄	—	43	16	no	—
239	C₂×D₄	—	43	8	no	—
240	C₂×D₄	—	43	8	no	—
241	C₂×D₄	—	43	8	no	—
242	C₂×D₄	—	43	4	no	—
243	C₂×D₄	—	43	2	no	—
244	C₂×D₄	—	43	8	no	—
245	C₂×D₄	—	43	4	no	—
246	C₂×D₄	—	43	2	no	—
247	C₂×D₄	—	86	16	no	—
248	C₂×D₄	—	86	16	no	—
249	C₂×D₄	—	86	32	no	—
250	C₂×D₄	—	86	16	no	—
251	C₂×D₄	—	86	32	no	—
252	C₂×D₄	—	86	32	no	—
253	C₂×D₄	—	86	16	no	—
254	C₂×D₄	—	172	4	no	—
255	C₂×D₄	C₂²×D₄₃	1	2	yes	—
256	C₂×D₄	C₂²×D₄₃	1	8	yes	complemented
257	C₂×D₄	C₂²×D₄₃	1	4	yes	complemented
258	C₂×D₄	C₂²×D₄₃	1	2	yes	complemented
259	C₂²×C₄	—	43	2	no	—
260	C₂²×C₄	—	43	4	no	—
261	C₂²×C₄	—	43	1	no	—
262	C₂²×C₄	—	43	4	no	—
263	C₂²×C₄	—	43	4	no	—
264	C₂²×C₄	—	43	4	no	—
265	C₂²×C₄	—	86	16	no	—
266	C₂²×C₄	C₂²×D₄₃	1	4	yes	complemented
267	C₄⋊C₄	—	43	4	no	—
268	C₄⋊C₄	—	43	2	no	—
269	C₄⋊C₄	C₂²×D₄₃	1	2	yes	complemented
270	C₂²⋊C₄	—	43	4	no	—
271	C₂²⋊C₄	—	43	4	no	—
272	C₂²⋊C₄	—	43	4	no	—
273	C₂²⋊C₄	—	43	4	no	—
274	C₂²⋊C₄	—	43	8	no	—
275	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	complemented
276	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	complemented
277	C₄²	—	43	1	no	—
278	C₄²	—	43	2	no	—
279	C₄²	C₂²×D₄₃	1	1	yes	characteristic, complemented
280	C₂³	—	2	16	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	43	1	no	—
283	C₂³	—	43	16	no	—
284	C₂³	—	43	4	no	—
285	C₂³	—	43	4	no	—
286	C₂³	—	86	8	no	—
287	C₂³	—	86	8	no	—
288	C₂³	—	86	16	no	—
289	C₂³	—	86	16	no	—
290	C₂³	—	86	16	no	—
291	C₂³	—	86	8	no	—
292	C₂³	—	86	16	no	—
293	C₂³	—	172	8	no	—
294	C₂³	—	172	4	no	—
295	C₂³	—	172	64	no	—
296	C₂³	C₂³×D₄₃	1	4	yes	—
297	C₂³	C₂³×D₄₃	1	4	yes	—
298	D₄	—	2	16	no	—
299	D₄	—	2	8	no	—
300	D₄	—	4	2	no	—
301	D₄	—	43	16	no	—
302	D₄	—	43	8	no	—
303	D₄	—	86	16	no	—
304	D₄	—	86	16	no	—
305	D₄	—	86	16	no	—
306	D₄	—	86	16	no	—
307	D₄	—	86	8	no	—
308	D₄	—	172	2	no	—
309	D₄	—	172	4	no	—
310	D₄	D₄×D₄₃	1	8	yes	direct product factor
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	43	2	no	—
313	C₂×C₄	—	43	8	no	—
314	C₂×C₄	—	43	1	no	—
315	C₂×C₄	—	43	4	no	—
316	C₂×C₄	—	86	8	no	—
317	C₂×C₄	—	86	8	no	—
318	C₂×C₄	—	86	2	no	—
319	C₂×C₄	—	86	8	no	—
320	C₂×C₄	—	86	8	no	—
321	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
322	C₂×C₄	C₂³×D₄₃	1	4	yes	—
323	C₂×C₄	C₂³×D₄₃	1	2	yes	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	4	16	no	—
329	C₂²	—	43	4	no	—
330	C₂²	—	43	2	no	—
331	C₂²	—	43	8	no	—
332	C₂²	—	86	32	no	—
333	C₂²	—	86	4	no	—
334	C₂²	—	86	4	no	—
335	C₂²	—	86	8	no	—
336	C₂²	—	86	4	no	—
337	C₂²	—	172	32	no	—
338	C₂²	—	172	16	no	—
339	C₂²	—	172	16	no	—
340	C₂²	C₂×D₄×D₄₃	1	8	yes	complemented
341	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	2	1	no	—
344	C₄	—	43	4	no	—
345	C₄	—	86	4	no	—
346	C₄	—	86	1	no	—
347	C₄	C₂×D₄×D₄₃	1	4	yes	complemented
348	C₂	—	2	8	no	—
349	C₂	—	4	4	no	—
350	C₂	—	43	4	no	—
351	C₂	—	86	8	no	—
352	C₂	—	172	4	no	—
353	C₂	C₂²×D₄×D₄₃	1	2	yes	—
354	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	D₄²×C₄₃	C₂
hypercenter	D₄²	D₄₃
hypocenter	C₄₃	C₂×D₄²
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₄₃	C₂	semidirect
2. D₄×D₁₇₂	C₂	semidirect
3. #14583534	C₂	semidirect
4. #14583533	C₂	semidirect
5. D₄×C₂²⋊D₄₃	C₂	semidirect
6. #14583531	C₂	semidirect
7. #127×D₄₃	C₂	semidirect
8. #121×D₄₃	C₂	semidirect
9. #120×D₄₃	C₂	semidirect
10. C₄×D₄×D₄₃	C₂	semidirect
11. D₄²×C₄₃	C₂	semidirect
12. C₂⁴×D₄₃	C₂²	semidirect
13. C₂²×D₁₇₂	C₂²	semidirect
14. C₂²×C₂²⋊D₄₃	C₂²	semidirect
17. C₂×D₄×D₄₃	C₂²	semidirect
18. C₂×D₄×D₄₃	C₂²	semidirect
19. C₂×D₄×D₄₃	C₂²	semidirect
20. C₂×D₄×D₄₃	C₂²	semidirect
21. C₂×D₄×D₄₃	C₂²	semidirect
22. C₂×D₄×D₄₃	C₂²	semidirect
23. C₂²×C₄×D₄₃	C₂²	semidirect
24. #13063322	C₂²	semidirect
25. #13063321	C₂²	semidirect
26. #13063321	C₂²	semidirect
27. #13063300	C₂²	semidirect
28. #13063299	C₂²	semidirect
29. #13063298	C₂²	semidirect
30. #13063297	C₂²	semidirect
31. #13063296	C₂²	semidirect
32. #13063295	C₂²	semidirect
33. #13063295	C₂²	semidirect
34. #13063294	C₂²	semidirect
35. #13063293	C₂²	semidirect
36. #13063293	C₂²	semidirect
37. C₄×D₁₇₂	C₂²	semidirect
38. D₄×Dic₄₃	C₂²	semidirect
39. #13063287	C₂²	semidirect
40. C₄×C₂²⋊D₄₃	C₂²	semidirect
41. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
42. C₄⋊C₄×D₄₃	C₂²	semidirect
43. C₂²⋊C₄×D₄₃	C₂²	semidirect
44. C₂²⋊C₄×D₄₃	C₂²	semidirect
45. C₄²×D₄₃	C₂²	semidirect
46. C₂²×D₄×C₄₃	C₂²	semidirect
47. #127×C₄₃	C₂²	semidirect
48. #121×C₄₃	C₂²	semidirect
49. #120×C₄₃	C₂²	semidirect
50. C₄×D₄×C₄₃	C₂²	semidirect
51. C₂⁴×C₄₃	C₂³	semidirect
56. C₂³×D₄₃	C₂³	semidirect
57. C₂³×D₄₃	C₂³	semidirect
60. C₂×D₄×C₄₃	C₂³	semidirect
61. C₂×D₄×C₄₃	C₂³	semidirect
62. C₂×D₄×C₄₃	C₂³	semidirect
63. C₂²×C₄×C₄₃	C₂³	semidirect
66. C₂×C₂²⋊D₄₃	C₂³	semidirect
67. C₂×C₂²⋊D₄₃	C₂³	semidirect
68. C₂×C₂²⋊D₄₃	C₂³	semidirect
69. C₂×C₂²⋊D₄₃	C₂³	semidirect
70. C₂²×Dic₄₃	C₂³	semidirect
77. D₄×D₄₃	D₄	direct (N × H)
80. C₂×D₁₇₂	C₂³	semidirect
81. C₂×D₁₇₂	C₂³	semidirect
82. C₂×D₁₇₂	C₂³	semidirect
87. C₂×C₄×D₄₃	C₂³	semidirect
88. C₂×C₄×D₄₃	C₂³	semidirect
89. C₄⋊C₄×C₄₃	C₂³	semidirect
90. C₂²⋊C₄×C₄₃	C₂³	semidirect
91. C₂²⋊C₄×C₄₃	C₂³	semidirect
92. C₄²×C₄₃	C₂³	semidirect
93. C₂²⋊Dic₄₃	C₂³	semidirect
94. C₂²⋊Dic₄₃	C₂³	semidirect
95. (C₂×D₄₃)⋊C₄	C₂³	semidirect
96. (C₂×D₄₃)⋊C₄	C₂³	semidirect
97. (C₂×D₄₃)⋊C₄	C₂³	semidirect
98. C₄⋊Dic₄₃	C₂³	semidirect
99. Dic₄₃⋊C₄	C₂³	semidirect
100. C₄×Dic₄₃	C₂³	semidirect
101. C₄×Dic₄₃	C₂³	semidirect
116. C₂²×D₄₃	C₂×D₄	semidirect
123. D₄×C₄₃	C₂×D₄	semidirect
132. C₂²⋊D₄₃	C₂×D₄	semidirect
140. D₁₇₂	C₂×D₄	semidirect
145. C₄×D₄₃	C₂×D₄	semidirect
151. C₂²×C₄₃	C₂²×D₄	semidirect
162. C₂×D₄₃	C₂²×D₄	semidirect
166. C₄×C₄₃	C₂²×D₄	semidirect
169. Dic₄₃	C₂²×D₄	semidirect
177. D₄₃	D₄²	direct (N × H)
184. D₄²	D₄₃	direct (N × H)
189. C₄₃	C₂×D₄²	semidirect
201. C₂²×D₄	C₂×D₄₃	semidirect
206. #127	C₂×D₄₃	semidirect
212. #121	C₂×D₄₃	semidirect
218. #120	C₂×D₄₃	semidirect
224. C₄×D₄	C₂×D₄₃	semidirect
235. C₂⁴	C₂²×D₄₃	semidirect
256. C₂×D₄	C₂²×D₄₃	semidirect
257. C₂×D₄	C₂²×D₄₃	semidirect
258. C₂×D₄	C₂²×D₄₃	semidirect
266. C₂²×C₄	C₂²×D₄₃	semidirect
269. C₄⋊C₄	C₂²×D₄₃	semidirect
275. C₂²⋊C₄	C₂²×D₄₃	semidirect
276. C₂²⋊C₄	C₂²×D₄₃	semidirect
279. C₄²	C₂²×D₄₃	semidirect
310. D₄	D₄×D₄₃	direct (N × H)
340. C₂²	C₂×D₄×D₄₃	semidirect
347. C₄	C₂×D₄×D₄₃	semidirect

Subgroups — D42×D43 #19148030

Conjugacy classes of subgroups

Complements

Subgroups — D₄²×D₄₃ #19148030