Subgroups — C₂×#19148293 #26004651

Order 11008.

7390 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148293	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583582	C₂	1	8	yes	maximal, complemented
3	C₂×#14583573	C₂	1	8	yes	maximal, complemented
4	C₂×#14583525	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14583496	C₂	1	4	yes	maximal, complemented
6	C₂×#14583461	C₂	1	1	yes	maximal, characteristic
7	C₂×#14583433	C₂	1	4	yes	maximal, complemented
8	C₂²×#13063308	C₂	1	2	yes	maximal, complemented
9	C₂×#14583372	C₂	1	2	yes	maximal, complemented
10	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₂²⋊D₄₃	C₂²	1	2	yes	—
12	#14583582	C₂²	1	128	yes	complemented
13	#14583573	C₂²	1	128	yes	complemented
14	#14583525	C₂²	1	16	yes	complemented
15	#14583496	C₂²	1	64	yes	complemented
16	#14583461	C₂²	1	16	yes	—
17	#14583433	C₂²	1	64	yes	complemented
18	C₂×#13063320	C₂²	1	8	yes	complemented
19	C₂×#13063319	C₂²	1	8	yes	complemented
20	C₂×#13063317	C₂²	1	4	yes	complemented
21	C₂×#13063315	C₂²	1	8	yes	complemented
22	C₂×#13063313	C₂²	1	4	yes	complemented
23	C₂×#13063310	C₂²	1	8	yes	complemented
24	C₂×#13063309	C₂²	1	4	yes	—
25	C₂×#13063308	C₂²	1	8	yes	—
26	C₂×#13063308	C₂²	1	4	yes	complemented
27	C₂×#13063308	C₂²	1	4	yes	complemented
28	C₂×#13063308	C₂²	1	32	yes	complemented
29	C₂×#13063304	C₂²	1	4	yes	complemented
30	C₂×#13063303	C₂²	1	8	yes	complemented
31	C₂×#13063302	C₂²	1	8	yes	complemented
32	C₂×#13063299	C₂²	1	4	yes	—
33	C₂×#13063295	C₂²	1	4	yes	—
34	#14583372	C₂²	1	32	yes	complemented
35	C₂×C₄×Dic₈₆	C₂²	1	4	yes	complemented
36	C₂×C₄×D₁₇₂	C₂²	1	4	yes	complemented
37	C₂×C₄×C₂²⋊D₄₃	C₂²	1	8	yes	complemented
38	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	8	yes	—
39	C₂×#13063282	C₂²	1	8	yes	complemented
40	C₂×#13063281	C₂²	1	4	yes	complemented
41	C₂²×Dic₄₃⋊C₄	C₂²	1	4	yes	complemented
42	C₂²×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
43	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	complemented
44	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
45	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#117×C₄₃	C₂²	1	8	yes	complemented
47	C₂×#117×C₄₃	C₂²	1	16	yes	complemented
48	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₄₃	C₂²	1	2	yes	complemented
52	C₂⁴×D₄₃	C₂³	1	2	yes	—
53	C₂²×Dic₈₆	C₂³	1	4	yes	—
54	C₂²×D₁₇₂	C₂³	1	4	yes	—
55	C₂²×C₂²⋊D₄₃	—	2	16	no	—
56	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
57	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
58	C₂²×C₂²⋊D₄₃	C₂³	1	16	yes	—
59	C₂³×Dic₄₃	C₂³	1	2	yes	—
60	C₂³×Dic₄₃	C₂³	1	4	yes	—
61	C₂²×C₄×D₄₃	C₂³	1	8	yes	—
62	#13063320	C₂³	1	64	yes	complemented
63	#13063319	C₂³	1	64	yes	complemented
64	#13063317	C₂³	1	32	yes	complemented
65	#13063315	C₂³	1	64	yes	complemented
66	#13063313	C₂³	1	32	yes	complemented
67	#13063310	C₂³	1	64	yes	complemented
68	#13063309	C₂³	1	32	yes	—
69	#13063308	C₂³	1	64	yes	—
70	#13063308	C₂³	1	32	yes	complemented
71	#13063308	C₂³	1	32	yes	complemented
72	#13063304	C₂³	1	32	yes	complemented
73	#13063303	C₂³	1	64	yes	complemented
74	#13063302	C₂³	1	64	yes	complemented
75	#13063299	C₂³	1	32	yes	—
76	#13063295	C₂³	1	32	yes	—
77	C₄×Dic₈₆	C₂³	1	32	yes	complemented
78	C₄×D₁₇₂	C₂³	1	32	yes	complemented
79	C₄×C₂²⋊D₄₃	C₂³	1	64	yes	complemented
80	(C₂²⋊D₄₃)⋊C₄	C₂³	1	64	yes	—
81	#13063282	C₂³	1	64	yes	complemented
82	#13063281	C₂³	1	32	yes	complemented
83	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
84	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
85	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
86	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
87	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
88	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
89	C₂×Dic₄₃⋊C₄	C₂³	1	32	yes	complemented
90	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊Dic₄₃	C₂³	1	16	yes	—
93	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
94	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
95	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
96	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	8	yes	—
97	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	32	yes	complemented
98	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	complemented
99	C₂×C₄×Dic₄₃	C₂³	1	8	yes	—
100	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₄₃	—	2	8	no	—
102	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
105	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
106	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
107	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
108	#117×C₄₃	C₂³	1	64	yes	complemented
109	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	—
110	C₂×C₄⋊C₄×C₄₃	C₂³	1	16	yes	complemented
111	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
116	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₄₃	C₂³	1	16	yes	complemented
118	C₂⁴×C₄₃	—	4	4	no	—
119	C₂⁴×C₄₃	#41	1	8	yes	—
120	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
121	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
123	C₂³×D₄₃	—	2	8	no	—
124	C₂³×D₄₃	—	4	8	no	—
125	C₂³×D₄₃	C₂⁴	1	4	yes	—
126	C₂³×D₄₃	C₂⁴	1	8	yes	—
127	C₂²×C₄×C₄₃	—	2	16	no	—
128	C₂²×C₄×C₄₃	—	2	4	no	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	32	no	—
131	C₂²×C₄×C₄₃	—	4	4	no	—
132	C₂²×C₄×C₄₃	—	4	4	no	—
133	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂⁴	1	16	yes	—
140	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
142	C₂×C₂²⋊D₄₃	—	2	16	no	—
143	C₂×C₂²⋊D₄₃	—	2	16	no	—
144	C₂×C₂²⋊D₄₃	—	2	64	no	—
145	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
146	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
147	C₂²×Dic₄₃	—	2	8	no	—
148	C₂²×Dic₄₃	—	4	8	no	—
149	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
150	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
151	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
152	C₂²×Dic₄₃	C₂⁴	1	16	yes	—
153	C₂×D₁₇₂	—	4	8	no	—
154	C₂×D₁₇₂	C₂⁴	1	16	yes	—
155	C₂×C₄×D₄₃	—	4	16	no	—
156	C₂×C₄×D₄₃	C₂⁴	1	32	yes	—
157	C₂×Dic₈₆	—	4	8	no	—
158	C₂×Dic₈₆	C₂⁴	1	16	yes	—
159	C₄⋊C₄×C₄₃	C₂⁴	1	32	yes	—
160	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
161	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
162	C₄²×C₄₃	C₂⁴	1	16	yes	—
163	C₄²×C₄₃	C₂⁴	1	16	yes	—
164	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
165	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
166	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
167	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
168	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
169	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
170	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
171	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
172	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
173	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
174	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
175	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
176	C₄×Dic₄₃	C₂⁴	1	32	yes	—
177	C₂³×C₄₃	—	2	8	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	4	16	no	—
180	C₂³×C₄₃	—	4	8	no	—
181	C₂³×C₄₃	C₂×#41	1	8	yes	—
182	C₂³×C₄₃	C₂×#41	1	4	yes	—
183	C₂³×C₄₃	C₂×#41	1	16	yes	—
184	C₂³×C₄₃	C₂⁵	1	2	yes	—
185	C₂³×C₄₃	C₂⁵	1	4	yes	—
186	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
187	C₂²×D₄₃	—	2	8	no	—
188	C₂²×D₄₃	—	2	16	no	—
189	C₂²×D₄₃	—	2	16	no	—
190	C₂²×D₄₃	—	4	16	no	—
191	C₂²×D₄₃	—	8	16	no	—
192	C₂²×D₄₃	C₂⁵	1	8	yes	—
193	C₂×C₄×C₄₃	—	2	32	no	—
194	C₂×C₄×C₄₃	—	2	8	no	—
195	C₂×C₄×C₄₃	—	2	8	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	8	no	—
199	C₂×C₄×C₄₃	—	2	8	no	—
200	C₂×C₄×C₄₃	—	4	8	no	—
201	C₂×C₄×C₄₃	—	4	8	no	—
202	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
203	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
204	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
205	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
206	C₂²⋊D₄₃	—	2	32	no	—
207	C₂²⋊D₄₃	—	2	32	no	—
208	C₂×Dic₄₃	—	2	16	no	—
209	C₂×Dic₄₃	—	2	8	no	—
210	C₂×Dic₄₃	—	2	16	no	—
211	C₂×Dic₄₃	—	4	16	no	—
212	C₂×Dic₄₃	C₂⁵	1	8	yes	—
213	C₂×Dic₄₃	C₂⁵	1	16	yes	—
214	D₁₇₂	—	4	16	no	—
215	C₄×D₄₃	—	4	32	no	—
216	Dic₈₆	—	4	16	no	—
217	C₂×#3491	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	8	no	—
219	C₂²×C₄₃	—	2	4	no	—
220	C₂²×C₄₃	—	2	16	no	—
221	C₂²×C₄₃	—	2	8	no	—
222	C₂²×C₄₃	—	4	16	no	—
223	C₂²×C₄₃	C₂²×#41	1	8	yes	—
224	C₂²×C₄₃	C₂²×#41	1	4	yes	—
225	C₂²×C₄₃	C₂²×#41	1	2	yes	—
226	C₂²×C₄₃	#585	1	4	yes	—
227	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
228	C₂×D₄₃	—	2	8	no	—
229	C₂×D₄₃	—	2	16	no	—
230	C₂×D₄₃	—	4	16	no	—
231	C₂×D₄₃	—	8	16	no	—
232	C₄×C₄₃	—	2	4	no	—
233	C₄×C₄₃	—	2	4	no	—
234	C₄×C₄₃	—	2	8	no	—
235	C₄×C₄₃	—	2	8	no	—
236	Dic₄₃	—	2	8	no	—
237	Dic₄₃	—	2	16	no	—
238	#3491	—	43	32	no	—
239	C₂×#552	—	43	8	no	—
240	C₂×#551	—	43	8	no	—
241	C₂×#543	—	43	1	no	—
242	C₂×#539	—	43	4	no	—
243	C₂×#534	—	43	1	no	—
244	C₂×#529	—	43	4	no	—
245	C₂²×#123	—	43	2	no	—
246	C₂×#518	—	43	2	no	—
247	C₂²×#117	D₄₃	1	1	yes	characteristic, complemented
248	C₂×C₄₃	—	2	8	no	—
249	C₂×C₄₃	—	2	4	no	—
250	C₂×C₄₃	#3491	1	4	yes	complemented
251	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
252	C₂×C₄₃	C₂×#585	1	2	yes	—
253	D₄₃	—	4	8	no	—
254	C₂³×D₄	—	43	2	no	—
255	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
256	#552	—	43	128	no	—
257	#551	—	43	128	no	—
258	#543	—	43	16	no	—
259	#539	—	43	64	no	—
260	#534	—	43	16	no	—
261	#529	—	43	64	no	—
262	C₂×#126	—	43	8	no	—
263	C₂×#126	—	43	8	no	—
264	C₂×#125	—	43	8	no	—
265	C₂×#125	—	43	4	no	—
266	C₂×#124	—	43	4	no	—
267	C₂×#123	—	43	8	no	—
268	C₂×#123	—	43	4	no	—
269	C₂×#123	—	43	4	no	—
270	C₂×#123	—	43	32	no	—
271	C₂×#123	—	43	8	no	—
272	C₂×#123	—	43	4	no	—
273	C₂×C₂²⋊Q₈	—	43	4	no	—
274	C₂×C₂²⋊Q₈	—	43	8	no	—
275	C₂×C₂²⋊Q₈	—	43	8	no	—
276	C₂×#121	—	43	4	no	—
277	C₂×#120	—	43	4	no	—
278	#518	—	43	32	no	—
279	C₂×C₄×Q₈	—	43	4	no	—
280	C₂×C₄×D₄	—	43	8	no	—
281	C₂×C₄×D₄	—	43	8	no	—
282	C₂×C₄×D₄	—	43	4	no	—
283	C₂×#117	—	43	4	no	—
284	C₂×#117	—	43	8	no	—
285	C₂×#117	C₂×D₄₃	1	8	yes	complemented
286	C₂×#117	C₂×D₄₃	1	16	yes	complemented
287	C₂²×C₄⋊C₄	—	43	4	no	—
288	C₂²×C₄⋊C₄	C₂×D₄₃	1	2	yes	complemented
289	C₂²×C₂²⋊C₄	—	43	2	no	—
290	C₂²×C₂²⋊C₄	—	43	4	no	—
291	C₂²×C₂²⋊C₄	—	43	4	no	—
292	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
294	C₂²×C₄²	C₂×D₄₃	1	2	yes	complemented
295	C₄₃	C₂×#3491	1	1	yes	characteristic, complemented, Sylow
296	C₂⁵	—	43	2	no	—
297	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
298	C₂²×Q₈	—	43	4	no	—
299	C₂²×D₄	—	43	4	no	—
300	C₂²×D₄	—	43	4	no	—
301	C₂²×D₄	—	43	16	no	—
302	C₂²×D₄	—	43	4	no	—
303	C₂²×D₄	—	86	16	no	—
304	C₂³×C₄	—	2	8	no	—
305	C₂³×C₄	—	43	2	no	—
306	C₂³×C₄	—	43	4	no	—
307	C₂³×C₄	—	43	8	no	—
308	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
309	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
310	C₂³×C₄	C₂²×D₄₃	1	8	yes	—
311	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
312	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
313	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
314	#126	—	43	64	no	—
315	#126	—	43	64	no	—
316	#125	—	43	64	no	—
317	#125	—	43	32	no	—
318	#124	—	43	32	no	—
319	#123	—	43	32	no	—
320	#123	—	43	32	no	—
321	#123	—	43	64	no	—
322	#123	—	43	64	no	—
323	#123	—	43	32	no	—
324	C₂²⋊Q₈	—	43	32	no	—
325	C₂²⋊Q₈	—	43	64	no	—
326	C₂²⋊Q₈	—	43	64	no	—
327	#121	—	43	32	no	—
328	#120	—	43	32	no	—
329	C₄×Q₈	—	43	32	no	—
330	C₄×D₄	—	43	64	no	—
331	C₄×D₄	—	43	64	no	—
332	C₄×D₄	—	43	32	no	—
333	#117	—	43	32	no	—
334	#117	—	43	64	no	—
335	#117	C₂²×D₄₃	1	64	yes	complemented
336	C₂×C₄⋊C₄	—	43	8	no	—
337	C₂×C₄⋊C₄	—	43	8	no	—
338	C₂×C₄⋊C₄	—	43	32	no	—
339	C₂×C₄⋊C₄	—	43	8	no	—
340	C₂×C₄⋊C₄	—	43	8	no	—
341	C₂×C₄⋊C₄	—	43	4	no	—
342	C₂×C₄⋊C₄	—	43	4	no	—
343	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	—
344	C₂×C₄⋊C₄	C₂²×D₄₃	1	16	yes	complemented
345	C₂×C₂²⋊C₄	—	43	4	no	—
346	C₂×C₂²⋊C₄	—	43	4	no	—
347	C₂×C₂²⋊C₄	—	43	16	no	—
348	C₂×C₂²⋊C₄	—	43	8	no	—
349	C₂×C₂²⋊C₄	—	43	8	no	—
350	C₂×C₂²⋊C₄	—	43	8	no	—
351	C₂×C₂²⋊C₄	—	43	32	no	—
352	C₂×C₂²⋊C₄	—	43	8	no	—
353	C₂×C₂²⋊C₄	—	43	32	no	—
354	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
358	C₂×C₄²	—	43	8	no	—
359	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
360	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
361	C₂×C₄²	C₂²×D₄₃	1	16	yes	complemented
362	C₂⁴	—	4	4	no	—
363	C₂⁴	—	43	4	no	—
364	C₂⁴	—	43	8	no	—
365	C₂⁴	—	86	8	no	—
366	C₂⁴	—	172	8	no	—
367	C₂⁴	#10621898	1	8	yes	—
368	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
369	C₂⁴	C₂³×D₄₃	1	2	yes	—
370	C₂⁴	C₂³×D₄₃	1	4	yes	—
371	C₂×Q₈	—	43	16	no	—
372	C₂×Q₈	—	172	8	no	—
373	C₂×D₄	—	43	16	no	—
374	C₂×D₄	—	43	16	no	—
375	C₂×D₄	—	43	16	no	—
376	C₂×D₄	—	86	64	no	—
377	C₂×D₄	—	86	16	no	—
378	C₂×D₄	—	86	16	no	—
379	C₂×D₄	—	172	8	no	—
380	C₂²×C₄	—	2	16	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	32	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	43	8	no	—
387	C₂²×C₄	—	43	4	no	—
388	C₂²×C₄	—	43	8	no	—
389	C₂²×C₄	—	43	16	no	—
390	C₂²×C₄	—	43	32	no	—
391	C₂²×C₄	—	86	8	no	—
392	C₂²×C₄	—	172	16	no	—
393	C₂²×C₄	—	172	8	no	—
394	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
395	C₂²×C₄	C₂³×D₄₃	1	16	yes	—
396	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
397	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
398	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
399	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
400	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
401	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
402	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
403	C₄⋊C₄	—	43	32	no	—
404	C₄⋊C₄	—	43	32	no	—
405	C₄⋊C₄	—	43	32	no	—
406	C₄⋊C₄	—	43	32	no	—
407	C₄⋊C₄	—	43	16	no	—
408	C₄⋊C₄	—	43	16	no	—
409	C₄⋊C₄	C₂³×D₄₃	1	32	yes	—
410	C₂²⋊C₄	—	43	16	no	—
411	C₂²⋊C₄	—	43	16	no	—
412	C₂²⋊C₄	—	43	32	no	—
413	C₂²⋊C₄	—	43	32	no	—
414	C₂²⋊C₄	—	43	32	no	—
415	C₂²⋊C₄	—	43	32	no	—
416	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
417	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
418	C₄²	—	43	32	no	—
419	C₄²	C₂³×D₄₃	1	16	yes	—
420	C₄²	C₂³×D₄₃	1	16	yes	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	4	16	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	43	8	no	—
426	C₂³	—	86	16	no	—
427	C₂³	—	86	8	no	—
428	C₂³	—	86	16	no	—
429	C₂³	—	344	16	no	—
430	C₂³	—	172	16	no	—
431	C₂³	C₂×#10621898	1	8	yes	—
432	C₂³	C₂×#10621898	1	4	yes	—
433	C₂³	C₂×#10621898	1	16	yes	—
434	C₂³	C₂⁴×D₄₃	1	2	yes	—
435	C₂³	C₂⁴×D₄₃	1	4	yes	—
436	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
437	Q₈	—	172	16	no	—
438	D₄	—	86	32	no	—
439	D₄	—	86	32	no	—
440	D₄	—	172	16	no	—
441	C₂×C₄	—	2	32	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	43	8	no	—
451	C₂×C₄	—	43	16	no	—
452	C₂×C₄	—	86	16	no	—
453	C₂×C₄	—	86	8	no	—
454	C₂×C₄	—	86	16	no	—
455	C₂×C₄	—	172	32	no	—
456	C₂×C₄	—	172	16	no	—
457	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
458	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
459	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
460	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
461	C₂²	—	2	16	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	4	16	no	—
466	C₂²	—	86	8	no	—
467	C₂²	—	86	16	no	—
468	C₂²	—	344	16	no	—
469	C₂²	—	172	16	no	—
470	C₂²	C₂²×#10621898	1	8	yes	—
471	C₂²	C₂²×#10621898	1	4	yes	—
472	C₂²	C₂²×#10621898	1	2	yes	—
473	C₂²	#14583735	1	4	yes	—
474	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	8	no	—
478	C₄	—	2	8	no	—
479	C₄	—	86	8	no	—
480	C₄	—	86	16	no	—
481	C₂	—	2	8	no	—
482	C₂	—	2	4	no	—
483	C₂	—	172	8	no	—
484	C₂	#19148293	1	4	yes	direct product factor
485	C₂	C₂³×#10621898	1	1	yes	characteristic
486	C₂	C₂×#14583735	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×#117×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
prime radical	C₂×#14583461	C₂
hypercenter	C₂²×#117	D₄₃
hypocenter	C₄₃	C₂×#3491
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #19148293	C₂	direct (N × H)
2. C₂×#14583582	C₂	semidirect
3. C₂×#14583573	C₂	semidirect
4. C₂×#14583525	C₂	semidirect
5. C₂×#14583496	C₂	semidirect
7. C₂×#14583433	C₂	semidirect
8. C₂²×#13063308	C₂	semidirect
9. C₂×#14583372	C₂	semidirect
10. C₂²×#117×C₄₃	C₂	semidirect
12. #14583582	C₂²	semidirect
13. #14583573	C₂²	semidirect
14. #14583525	C₂²	semidirect
15. #14583496	C₂²	semidirect
17. #14583433	C₂²	semidirect
18. C₂×#13063320	C₂²	semidirect
19. C₂×#13063319	C₂²	semidirect
20. C₂×#13063317	C₂²	semidirect
21. C₂×#13063315	C₂²	semidirect
22. C₂×#13063313	C₂²	semidirect
23. C₂×#13063310	C₂²	semidirect
26. C₂×#13063308	C₂²	semidirect
27. C₂×#13063308	C₂²	semidirect
28. C₂×#13063308	C₂²	semidirect
29. C₂×#13063304	C₂²	semidirect
30. C₂×#13063303	C₂²	semidirect
31. C₂×#13063302	C₂²	semidirect
34. #14583372	C₂²	semidirect
35. C₂×C₄×Dic₈₆	C₂²	semidirect
36. C₂×C₄×D₁₇₂	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
39. C₂×#13063282	C₂²	semidirect
40. C₂×#13063281	C₂²	semidirect
41. C₂²×Dic₄₃⋊C₄	C₂²	semidirect
43. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
44. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
46. C₂×#117×C₄₃	C₂²	semidirect
47. C₂×#117×C₄₃	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
51. C₂²×C₄²×C₄₃	C₂²	semidirect
62. #13063320	C₂³	semidirect
63. #13063319	C₂³	semidirect
64. #13063317	C₂³	semidirect
65. #13063315	C₂³	semidirect
66. #13063313	C₂³	semidirect
67. #13063310	C₂³	semidirect
70. #13063308	C₂³	semidirect
71. #13063308	C₂³	semidirect
72. #13063304	C₂³	semidirect
73. #13063303	C₂³	semidirect
74. #13063302	C₂³	semidirect
77. C₄×Dic₈₆	C₂³	semidirect
78. C₄×D₁₇₂	C₂³	semidirect
79. C₄×C₂²⋊D₄₃	C₂³	semidirect
81. #13063282	C₂³	semidirect
82. #13063281	C₂³	semidirect
89. C₂×Dic₄₃⋊C₄	C₂³	semidirect
97. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
98. C₂²⋊C₄×D₄₃	C₂³	semidirect
108. #117×C₄₃	C₂³	semidirect
110. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
117. C₂×C₄²×C₄₃	C₂³	semidirect
247. C₂²×#117	D₄₃	semidirect
250. C₂×C₄₃	#3491	semidirect
285. C₂×#117	C₂×D₄₃	semidirect
286. C₂×#117	C₂×D₄₃	semidirect
288. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
294. C₂²×C₄²	C₂×D₄₃	semidirect
295. C₄₃	C₂×#3491	semidirect
335. #117	C₂²×D₄₃	semidirect
344. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
361. C₂×C₄²	C₂²×D₄₃	semidirect
484. C₂	#19148293	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148293	2
C₂×#14583582	2
C₂×#14583573	2
C₂×#14583525	2
C₂×#14583496	2
C₂×#14583461	2
C₂×#14583433	2
C₂²×#13063308	2
C₂×#14583372	2
C₂²×#117×C₄₃	2
C₂×#3491	43

Subgroups — C2×#19148293 #26004651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148293 #26004651