Subgroups — C₂×#19149289 #26004026

Order 11008.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149289	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583649	C₂	1	3	yes	maximal, complemented
3	C₂×#14583618	C₂	1	6	yes	maximal, complemented
4	C₂×#14583580	C₂	1	6	yes	maximal, complemented
5	C₂×#14583513	C₂	1	6	yes	maximal, complemented
6	C₂×#14583484	C₂	1	6	yes	maximal, complemented
7	C₂×#14583428	C₂	1	3	yes	maximal, complemented
8	C₂×C₄₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583649	C₂²	1	48	yes	complemented
10	#14583618	C₂²	1	96	yes	complemented
11	#14583580	C₂²	1	96	yes	complemented
12	#14583513	C₂²	1	96	yes	complemented
13	#14583484	C₂²	1	96	yes	complemented
14	C₂×#13063323	C₂²	1	6	yes	complemented
15	#14583428	C₂²	1	48	yes	complemented
16	C₂×#13063319	C₂²	1	2	yes	complemented
17	C₂×#13063318	C₂²	1	6	yes	complemented
18	C₂×#13063318	C₂²	1	6	yes	complemented
19	C₂×#13063318	C₂²	1	6	yes	complemented
20	C₂×#13063318	C₂²	1	6	yes	complemented
21	C₂×#13063317	C₂²	1	3	yes	complemented
22	C₂×#13063312	C₂²	1	6	yes	—
23	C₂×#13063311	C₂²	1	6	yes	complemented
24	C₂×#13063307	C₂²	1	6	yes	complemented
25	C₂×#13063306	C₂²	1	6	yes	—
26	C₂×#13063306	C₂²	1	6	yes	—
27	C₂×#13063302	C₂²	1	6	yes	complemented
28	C₂×#13063302	C₂²	1	6	yes	complemented
29	C₂×#13063302	C₂²	1	6	yes	complemented
30	C₂×#13063301	C₂²	1	3	yes	complemented
31	C₂×#13063297	C₂²	1	6	yes	—
32	C₂×#13063296	C₂²	1	3	yes	—
33	C₂×#13063294	C₂²	1	2	yes	complemented
34	C₂×Q₈×Dic₄₃	C₂²	1	3	yes	complemented
35	C₂×C₄×Dic₈₆	C₂²	1	6	yes	complemented
36	C₂×D₄×Dic₄₃	C₂²	1	3	yes	—
37	C₂×D₄×Dic₄₃	C₂²	1	6	yes	—
38	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	6	yes	complemented
39	C₂×#13063281	C₂²	1	6	yes	complemented
40	C₂×#13063281	C₂²	1	6	yes	complemented
41	C₂²×C₂²⋊Dic₄₃	C₂²	1	6	yes	complemented
42	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
43	C₄₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
44	C₂×#124×C₄₃	C₂²	1	3	yes	—
45	C₂×#124×C₄₃	C₂²	1	6	yes	—
46	C₂×#120×C₄₃	C₂²	1	6	yes	—
47	C₂²×Dic₈₆	C₂³	1	6	yes	—
48	C₂²×C₂²⋊D₄₃	C₂³	1	6	yes	—
49	C₂³×Dic₄₃	C₂³	1	6	yes	—
50	C₂³×Dic₄₃	C₂³	1	6	yes	—
51	C₂²×C₄×D₄₃	C₂³	1	3	yes	—
52	#13063323	C₂³	1	48	yes	complemented
53	#13063319	C₂³	1	16	yes	complemented
54	#13063318	C₂³	1	48	yes	complemented
55	#13063318	C₂³	1	48	yes	complemented
56	#13063318	C₂³	1	48	yes	complemented
57	#13063318	C₂³	1	48	yes	complemented
58	#13063317	C₂³	1	24	yes	complemented
59	#13063312	C₂³	1	48	yes	—
60	#13063311	C₂³	1	48	yes	complemented
61	#13063307	C₂³	1	48	yes	complemented
62	#13063306	C₂³	1	48	yes	—
63	#13063306	C₂³	1	48	yes	—
64	#13063302	C₂³	1	48	yes	complemented
65	#13063302	C₂³	1	48	yes	complemented
66	#13063302	C₂³	1	48	yes	complemented
67	#13063301	C₂³	1	24	yes	complemented
68	#13063297	C₂³	1	48	yes	—
69	#13063296	C₂³	1	24	yes	—
70	#13063294	C₂³	1	16	yes	complemented
71	Q₈×Dic₄₃	C₂³	1	24	yes	complemented
72	C₄×Dic₈₆	C₂³	1	48	yes	complemented
73	D₄×Dic₄₃	C₂³	1	24	yes	—
74	D₄×Dic₄₃	C₂³	1	48	yes	—
75	(C₂²⋊D₄₃)⋊C₄	C₂³	1	48	yes	complemented
76	#13063281	C₂³	1	48	yes	complemented
77	#13063281	C₂³	1	48	yes	complemented
78	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
79	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
80	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
81	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
82	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
83	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
84	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
85	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
86	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
87	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
88	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
89	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
90	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
91	C₂×C₂²⋊Dic₄₃	C₂³	1	48	yes	complemented
92	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
93	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
94	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
95	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
96	C₄²×D₄₃	C₂³	1	8	yes	complemented
97	C₂⁵×C₄₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₄₃	C₂³	1	3	yes	—
99	C₂²×D₄×C₄₃	C₂³	1	3	yes	—
100	C₂²×D₄×C₄₃	C₂³	1	6	yes	—
101	#124×C₄₃	C₂³	1	48	yes	—
102	#124×C₄₃	C₂³	1	24	yes	—
103	#120×C₄₃	C₂³	1	48	yes	—
104	C₂×C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
105	C₂×C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
106	C₂×C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
109	C₂⁴×C₄₃	—	4	12	no	—
110	C₂⁴×C₄₃	C₂⁴	1	6	yes	—
111	C₂⁴×C₄₃	C₂⁴	1	8	yes	—
112	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
113	C₂×Q₈×C₄₃	—	4	6	no	—
114	C₂×Q₈×C₄₃	C₂⁴	1	12	yes	—
115	C₂×D₄×C₄₃	—	4	6	no	—
116	C₂×D₄×C₄₃	—	4	12	no	—
117	C₂×D₄×C₄₃	C₂⁴	1	12	yes	—
118	C₂×D₄×C₄₃	C₂⁴	1	24	yes	—
119	C₂²×C₄×C₄₃	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
121	C₂×C₂²⋊D₄₃	—	4	12	no	—
122	C₂×C₂²⋊D₄₃	C₂⁴	1	24	yes	—
123	C₂²×Dic₄₃	—	4	12	no	—
124	C₂²×Dic₄₃	—	4	12	no	—
125	C₂²×Dic₄₃	C₂⁴	1	3	yes	—
126	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
127	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
128	C₂²×Dic₄₃	C₂⁴	1	24	yes	—
129	C₂²×Dic₄₃	C₂⁴	1	24	yes	—
130	C₂×C₄×D₄₃	—	4	6	no	—
131	C₂×C₄×D₄₃	C₂⁴	1	12	yes	—
132	C₂×Dic₈₆	—	4	12	no	—
133	C₂×Dic₈₆	C₂⁴	1	24	yes	—
134	C₂²⋊C₄×C₄₃	C₂⁴	1	24	yes	—
135	C₂²⋊C₄×C₄₃	C₂⁴	1	24	yes	—
136	C₂²⋊C₄×C₄₃	C₂⁴	1	24	yes	—
137	C₄²×C₄₃	C₂⁴	1	4	yes	—
138	C₄²×C₄₃	C₂⁴	1	8	yes	—
139	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
140	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
141	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
142	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
143	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
144	(C₂×D₄₃)⋊C₄	C₂⁴	1	24	yes	—
145	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
146	C₄⋊Dic₄₃	C₂⁴	1	12	yes	—
147	C₄⋊Dic₄₃	C₂⁴	1	12	yes	—
148	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
149	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
150	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
151	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
152	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
153	C₄×Dic₄₃	C₂⁴	1	12	yes	—
154	C₄×Dic₄₃	C₂⁴	1	24	yes	—
155	C₄×Dic₄₃	C₂⁴	1	24	yes	—
156	C₂³×C₄₃	—	2	12	no	—
157	C₂³×C₄₃	—	2	12	no	—
158	C₂³×C₄₃	—	2	12	no	—
159	C₂³×C₄₃	—	4	24	no	—
160	C₂³×C₄₃	—	8	16	no	—
161	C₂³×C₄₃	C₂⁵	1	12	yes	—
162	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
163	C₂²×D₄₃	—	2	6	no	—
164	C₂²×D₄₃	C₂⁵	1	2	yes	—
165	Q₈×C₄₃	—	4	12	no	—
166	D₄×C₄₃	—	4	24	no	—
167	D₄×C₄₃	—	4	12	no	—
168	C₂×C₄×C₄₃	—	2	12	no	—
169	C₂×C₄×C₄₃	—	2	6	no	—
170	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
171	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
172	C₂²⋊D₄₃	—	4	24	no	—
173	C₂×Dic₄₃	—	2	12	no	—
174	C₂×Dic₄₃	—	2	12	no	—
175	C₂×Dic₄₃	—	2	6	no	—
176	C₂×Dic₄₃	—	4	24	no	—
177	C₂×Dic₄₃	—	4	24	no	—
178	C₂×Dic₄₃	C₂⁵	1	6	yes	—
179	C₂×Dic₄₃	C₂⁵	1	12	yes	—
180	C₂×Dic₄₃	C₂⁵	1	12	yes	—
181	C₄×D₄₃	—	4	12	no	—
182	Dic₈₆	—	4	24	no	—
183	C₂×#3568	—	43	1	no	maximal, Sylow
184	C₂²×C₄₃	—	2	12	no	—
185	C₂²×C₄₃	—	2	12	no	—
186	C₂²×C₄₃	—	2	12	no	—
187	C₂²×C₄₃	—	4	24	no	—
188	C₂²×C₄₃	—	8	16	no	—
189	C₂²×C₄₃	#585	1	6	yes	—
190	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
191	C₂×D₄₃	—	2	6	no	—
192	C₂×D₄₃	—	4	4	no	—
193	C₄×C₄₃	—	2	12	no	—
194	C₄×C₄₃	—	2	6	no	—
195	Dic₄₃	—	2	12	no	—
196	Dic₄₃	—	2	12	no	—
197	Dic₄₃	—	2	6	no	—
198	#3568	—	43	32	no	—
199	C₂×#563	—	43	3	no	—
200	C₂×H(3,𝔽₄)	D₄₃	1	1	yes	characteristic, complemented
201	C₂×#556	—	43	6	no	—
202	C₂×#551	—	43	6	no	—
203	C₂×#542	—	43	6	no	—
204	C₂×#538	—	43	6	no	—
205	C₂×#529	—	43	3	no	—
206	C₂×C₄₃	—	4	12	no	—
207	C₂×C₄₃	#3568	1	4	yes	complemented
208	C₂×C₄₃	C₂×#585	1	3	yes	—
209	D₄₃	—	4	2	no	—
210	#563	—	43	48	no	—
211	H(3,𝔽₄)	C₂×D₄₃	1	16	yes	complemented
212	#556	—	43	96	no	—
213	#551	—	43	96	no	—
214	#542	—	43	96	no	—
215	#538	—	43	96	no	—
216	C₂×C₄⋊Q₈	—	43	6	no	—
217	#529	—	43	48	no	—
218	C₂×#126	—	43	6	no	—
219	C₂×#126	—	43	6	no	—
220	C₂×#126	—	43	6	no	—
221	C₂×#126	—	43	6	no	—
222	C₂×#126	—	43	2	no	—
223	C₂×#125	—	43	3	no	—
224	C₂×#124	—	43	6	no	—
225	C₂×#124	—	43	6	no	—
226	C₂×#124	C₂×D₄₃	1	3	yes	—
227	C₂×#124	C₂×D₄₃	1	6	yes	—
228	C₂×#123	—	43	6	no	—
229	C₂×#123	—	43	6	no	—
230	C₂×#123	—	43	6	no	—
231	C₂×C₂²⋊Q₈	—	43	3	no	—
232	C₂×C₂²⋊Q₈	—	43	6	no	—
233	C₂×C₂²⋊Q₈	—	43	6	no	—
234	C₂×C₂²⋊Q₈	—	43	6	no	—
235	C₂×#121	—	43	3	no	—
236	C₂×#121	—	43	6	no	—
237	C₂×#120	—	43	2	no	—
238	C₂×#120	C₂×D₄₃	1	6	yes	—
239	C₂×C₄×Q₈	—	43	3	no	—
240	C₂×C₄×Q₈	—	43	6	no	—
241	C₂×C₄×D₄	—	43	3	no	—
242	C₂×C₄×D₄	—	43	6	no	—
243	C₂×C₄×D₄	—	43	6	no	—
244	C₂×#117	—	43	6	no	—
245	C₂×#117	—	43	6	no	—
246	C₂²×C₂²⋊C₄	—	43	6	no	—
247	C₂²×C₄²	—	43	1	no	—
248	C₄₃	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
249	C₂⁵	C₂²×D₄₃	1	2	yes	—
250	C₂²×Q₈	—	43	6	no	—
251	C₂²×Q₈	C₂²×D₄₃	1	3	yes	—
252	C₂²×D₄	—	43	6	no	—
253	C₂²×D₄	C₂²×D₄₃	1	3	yes	—
254	C₂²×D₄	C₂²×D₄₃	1	6	yes	—
255	C₂³×C₄	—	43	6	no	—
256	C₂³×C₄	—	43	6	no	—
257	C₂³×C₄	—	43	3	no	—
258	C₄⋊Q₈	—	43	48	no	—
259	#126	—	43	48	no	—
260	#126	—	43	48	no	—
261	#126	—	43	48	no	—
262	#126	—	43	48	no	—
263	#126	—	43	16	no	—
264	#125	—	43	24	no	—
265	#124	—	43	48	no	—
266	#124	—	43	48	no	—
267	#124	C₂²×D₄₃	1	24	yes	—
268	#124	C₂²×D₄₃	1	48	yes	—
269	#123	—	43	48	no	—
270	#123	—	43	48	no	—
271	#123	—	43	48	no	—
272	C₂²⋊Q₈	—	43	24	no	—
273	C₂²⋊Q₈	—	43	48	no	—
274	C₂²⋊Q₈	—	43	48	no	—
275	C₂²⋊Q₈	—	43	48	no	—
276	#121	—	43	24	no	—
277	#121	—	43	48	no	—
278	#120	—	43	16	no	—
279	#120	C₂²×D₄₃	1	48	yes	—
280	C₄×Q₈	—	43	24	no	—
281	C₄×Q₈	—	43	48	no	—
282	C₄×D₄	—	43	24	no	—
283	C₄×D₄	—	43	48	no	—
284	C₄×D₄	—	43	48	no	—
285	#117	—	43	48	no	—
286	#117	—	43	48	no	—
287	C₂×C₄⋊C₄	—	43	6	no	—
288	C₂×C₄⋊C₄	—	43	6	no	—
289	C₂×C₄⋊C₄	—	43	6	no	—
290	C₂×C₄⋊C₄	—	43	6	no	—
291	C₂×C₄⋊C₄	—	43	3	no	—
292	C₂×C₄⋊C₄	—	43	6	no	—
293	C₂×C₄⋊C₄	—	43	3	no	—
294	C₂×C₄⋊C₄	—	43	6	no	—
295	C₂×C₂²⋊C₄	—	43	6	no	—
296	C₂×C₂²⋊C₄	—	43	6	no	—
297	C₂×C₂²⋊C₄	—	43	6	no	—
298	C₂×C₂²⋊C₄	—	43	6	no	—
299	C₂×C₂²⋊C₄	—	43	48	no	—
300	C₂×C₂²⋊C₄	—	43	6	no	—
301	C₂×C₂²⋊C₄	—	43	6	no	—
302	C₂×C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
304	C₂×C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
305	C₂×C₄²	—	43	6	no	—
306	C₂×C₄²	—	43	3	no	—
307	C₂×C₄²	—	43	6	no	—
308	C₂×C₄²	—	43	8	no	—
309	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	C₂⁴	—	4	12	no	—
312	C₂⁴	—	43	1	no	—
313	C₂⁴	C₂³×D₄₃	1	6	yes	—
314	C₂⁴	C₂³×D₄₃	1	8	yes	—
315	C₂×Q₈	—	4	6	no	—
316	C₂×Q₈	—	43	24	no	—
317	C₂×Q₈	—	172	12	no	—
318	C₂×Q₈	C₂³×D₄₃	1	12	yes	—
319	C₂×D₄	—	4	6	no	—
320	C₂×D₄	—	4	12	no	—
321	C₂×D₄	—	43	24	no	—
322	C₂×D₄	—	172	12	no	—
323	C₂×D₄	C₂³×D₄₃	1	12	yes	—
324	C₂×D₄	C₂³×D₄₃	1	24	yes	—
325	C₂²×C₄	—	43	3	no	—
326	C₂²×C₄	—	43	6	no	—
327	C₂²×C₄	—	43	6	no	—
328	C₂²×C₄	—	43	24	no	—
329	C₂²×C₄	—	43	24	no	—
330	C₂²×C₄	—	43	12	no	—
331	C₂²×C₄	—	172	6	no	—
332	C₂²×C₄	—	172	12	no	—
333	C₂²×C₄	—	172	12	no	—
334	C₂²×C₄	C₂³×D₄₃	1	6	yes	—
335	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
336	C₄⋊C₄	—	43	24	no	—
337	C₄⋊C₄	—	43	24	no	—
338	C₄⋊C₄	—	43	24	no	—
339	C₄⋊C₄	—	43	24	no	—
340	C₄⋊C₄	—	43	12	no	—
341	C₄⋊C₄	—	43	24	no	—
342	C₄⋊C₄	—	43	12	no	—
343	C₄⋊C₄	—	43	24	no	—
344	C₂²⋊C₄	—	43	24	no	—
345	C₂²⋊C₄	—	43	24	no	—
346	C₂²⋊C₄	—	43	24	no	—
347	C₂²⋊C₄	—	43	24	no	—
348	C₂²⋊C₄	—	43	24	no	—
349	C₂²⋊C₄	—	43	24	no	—
350	C₂²⋊C₄	C₂³×D₄₃	1	24	yes	—
351	C₂²⋊C₄	C₂³×D₄₃	1	24	yes	—
352	C₂²⋊C₄	C₂³×D₄₃	1	24	yes	—
353	C₄²	—	43	12	no	—
354	C₄²	—	43	24	no	—
355	C₄²	—	43	24	no	—
356	C₄²	C₂³×D₄₃	1	4	yes	—
357	C₄²	C₂³×D₄₃	1	8	yes	—
358	C₂³	—	2	12	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	4	24	no	—
362	C₂³	—	8	16	no	—
363	C₂³	—	43	2	no	—
364	C₂³	—	86	6	no	—
365	C₂³	C₂⁴×D₄₃	1	12	yes	—
366	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
367	Q₈	—	4	12	no	—
368	Q₈	—	172	24	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	24	no	—
371	D₄	—	172	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	43	6	no	—
375	C₂×C₄	—	43	12	no	—
376	C₂×C₄	—	43	12	no	—
377	C₂×C₄	—	86	6	no	—
378	C₂×C₄	—	86	12	no	—
379	C₂×C₄	—	86	12	no	—
380	C₂×C₄	—	172	12	no	—
381	C₂×C₄	—	172	24	no	—
382	C₂×C₄	—	172	24	no	—
383	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
384	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
385	C₂²	—	2	12	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	86	6	no	—
391	C₂²	—	172	4	no	—
392	C₂²	#14583734	1	6	yes	—
393	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	86	6	no	—
397	C₄	—	86	12	no	—
398	C₄	—	86	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	172	2	no	—
401	C₂	#19149289	1	4	yes	direct product factor
402	C₂	C₂×#14583734	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×H(3,𝔽₄)	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₄₃
hypocenter	C₄₃	C₂×#3568
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #19149289	C₂	direct (N × H)
2. C₂×#14583649	C₂	semidirect
3. C₂×#14583618	C₂	semidirect
4. C₂×#14583580	C₂	semidirect
5. C₂×#14583513	C₂	semidirect
6. C₂×#14583484	C₂	semidirect
7. C₂×#14583428	C₂	semidirect
8. C₂×C₄₃×H(3,𝔽₄)	C₂	semidirect
9. #14583649	C₂²	semidirect
10. #14583618	C₂²	semidirect
11. #14583580	C₂²	semidirect
12. #14583513	C₂²	semidirect
13. #14583484	C₂²	semidirect
14. C₂×#13063323	C₂²	semidirect
15. #14583428	C₂²	semidirect
16. C₂×#13063319	C₂²	semidirect
17. C₂×#13063318	C₂²	semidirect
18. C₂×#13063318	C₂²	semidirect
19. C₂×#13063318	C₂²	semidirect
20. C₂×#13063318	C₂²	semidirect
21. C₂×#13063317	C₂²	semidirect
23. C₂×#13063311	C₂²	semidirect
24. C₂×#13063307	C₂²	semidirect
27. C₂×#13063302	C₂²	semidirect
28. C₂×#13063302	C₂²	semidirect
29. C₂×#13063302	C₂²	semidirect
30. C₂×#13063301	C₂²	semidirect
33. C₂×#13063294	C₂²	semidirect
34. C₂×Q₈×Dic₄₃	C₂²	semidirect
35. C₂×C₄×Dic₈₆	C₂²	semidirect
38. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
39. C₂×#13063281	C₂²	semidirect
40. C₂×#13063281	C₂²	semidirect
41. C₂²×C₂²⋊Dic₄₃	C₂²	semidirect
42. C₂×C₄²×D₄₃	C₂²	semidirect
43. C₄₃×H(3,𝔽₄)	C₂²	semidirect
52. #13063323	C₂³	semidirect
53. #13063319	C₂³	semidirect
54. #13063318	C₂³	semidirect
55. #13063318	C₂³	semidirect
56. #13063318	C₂³	semidirect
57. #13063318	C₂³	semidirect
58. #13063317	C₂³	semidirect
60. #13063311	C₂³	semidirect
61. #13063307	C₂³	semidirect
64. #13063302	C₂³	semidirect
65. #13063302	C₂³	semidirect
66. #13063302	C₂³	semidirect
67. #13063301	C₂³	semidirect
70. #13063294	C₂³	semidirect
71. Q₈×Dic₄₃	C₂³	semidirect
72. C₄×Dic₈₆	C₂³	semidirect
75. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
76. #13063281	C₂³	semidirect
77. #13063281	C₂³	semidirect
91. C₂×C₂²⋊Dic₄₃	C₂³	semidirect
96. C₄²×D₄₃	C₂³	semidirect
200. C₂×H(3,𝔽₄)	D₄₃	semidirect
207. C₂×C₄₃	#3568	semidirect
211. H(3,𝔽₄)	C₂×D₄₃	semidirect
248. C₄₃	C₂×#3568	semidirect
401. C₂	#19149289	direct (N × H)

Maximal subgroups

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

subgroup	index
#19149289	2
C₂×#14583649	2
C₂×#14583618	2
C₂×#14583580	2
C₂×#14583513	2
C₂×#14583484	2
C₂×#14583428	2
C₂×C₄₃×H(3,𝔽₄)	2
C₂×#3568	43

Subgroups — C2×#19149289 #26004026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19149289 #26004026