Subgroups — C₂×#19148217 #26003695

Order 11008.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148217	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583628	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583619	C₂	1	3	yes	maximal, complemented
4	C₂×#14583588	C₂	1	6	yes	maximal, complemented
5	C₂×Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14583556	C₂	1	2	yes	maximal, complemented
7	C₂×#14583554	C₂	1	3	yes	maximal, complemented
8	C₂×#14583456	C₂	1	3	yes	maximal, complemented
9	C₂×#14583431	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#10621898	C₂	1	3	yes	maximal, complemented
11	C₂×C₄×Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#10621898	C₂²	1	3	yes	—
14	C₂²×Q₈×D₄₃	C₂²	1	2	yes	—
15	#14583628	C₂²	1	16	yes	complemented
16	#14583619	C₂²	1	48	yes	complemented
17	#14583588	C₂²	1	96	yes	complemented
18	Q₈×D₁₇₂	C₂²	1	16	yes	complemented
19	#14583556	C₂²	1	32	yes	complemented
20	#14583554	C₂²	1	48	yes	complemented
21	#14583456	C₂²	1	48	yes	complemented
22	C₂×#13063325	C₂²	1	3	yes	—
23	C₂×#13063325	C₂²	1	3	yes	—
24	#14583431	C₂²	1	96	yes	complemented
25	C₂×#13063318	C₂²	1	12	yes	—
26	C₂×#13063317	C₂²	1	6	yes	—
27	C₂×#13063316	C₂²	1	6	yes	—
28	C₂×#13063312	C₂²	1	6	yes	—
29	C₂×#13063307	C₂²	1	12	yes	—
30	C₂×#13063305	C₂²	1	6	yes	—
31	C₂×#13063304	C₂²	1	6	yes	—
32	C₂×#13063304	C₂²	1	6	yes	—
33	C₂×#13063296	C₂²	1	6	yes	—
34	C₄×#10621898	C₂²	1	48	yes	complemented
35	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
36	C₂×C₄×Dic₈₆	C₂²	1	6	yes	—
37	C₂×C₄×Dic₈₆	C₂²	1	3	yes	—
38	C₂×C₄×Dic₈₆	C₂²	1	3	yes	—
39	C₂×#13063290	C₂²	1	6	yes	—
40	C₄×Q₈×D₄₃	C₂²	1	32	yes	complemented
41	C₂×C₄×D₁₇₂	C₂²	1	3	yes	—
42	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₂²⋊D₄₃	C₂²	1	6	yes	—
44	C₂×C₄×C₂²⋊D₄₃	C₂²	1	6	yes	—
45	C₂×#13063284	C₂²	1	6	yes	—
46	C₂×#13063284	C₂²	1	3	yes	—
47	C₂×#13063282	C₂²	1	6	yes	—
48	C₂×C₄⋊C₄×D₄₃	C₂²	1	6	yes	—
49	C₂×C₄²×D₄₃	C₂²	1	6	yes	—
50	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
51	C₄×#41×C₄₃	C₂²	1	16	yes	complemented
52	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₄₃	C₂²	1	3	yes	—
55	C₂×C₄×D₄×C₄₃	C₂²	1	3	yes	—
56	C₂×#117×C₄₃	C₂²	1	3	yes	—
57	C₂²×C₄²×C₄₃	C₂²	1	3	yes	—
58	C₂×#10621898	—	2	24	no	—
59	C₂×#10621898	C₂³	1	24	yes	—
60	C₂²×Dic₈₆	C₂³	1	6	yes	—
61	C₂²×Dic₈₆	C₂³	1	3	yes	—
62	C₂×Q₈×D₄₃	—	2	16	no	—
63	C₂×Q₈×D₄₃	C₂³	1	16	yes	—
64	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
65	C₂²×C₂²⋊D₄₃	C₂³	1	6	yes	—
66	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
67	C₂²×C₄×D₄₃	C₂³	1	6	yes	—
68	C₂²×C₄×D₄₃	C₂³	1	6	yes	—
69	#13063325	C₂³	1	24	yes	—
70	#13063325	C₂³	1	24	yes	—
71	#13063318	C₂³	1	96	yes	—
72	#13063317	C₂³	1	48	yes	—
73	#13063316	C₂³	1	48	yes	—
74	#13063312	C₂³	1	48	yes	—
75	#13063307	C₂³	1	96	yes	—
76	#13063305	C₂³	1	48	yes	—
77	#13063304	C₂³	1	48	yes	—
78	#13063304	C₂³	1	48	yes	—
79	#13063296	C₂³	1	48	yes	—
80	Q₈×Dic₄₃	C₂³	1	16	yes	—
81	C₄×Dic₈₆	C₂³	1	48	yes	—
82	C₄×Dic₈₆	C₂³	1	24	yes	—
83	C₄×Dic₈₆	C₂³	1	24	yes	—
84	#13063290	C₂³	1	48	yes	—
85	C₄×D₁₇₂	C₂³	1	24	yes	—
86	C₄×D₁₇₂	C₂³	1	8	yes	—
87	C₄×C₂²⋊D₄₃	C₂³	1	48	yes	—
88	C₄×C₂²⋊D₄₃	C₂³	1	48	yes	—
89	#13063284	C₂³	1	24	yes	—
90	#13063284	C₂³	1	48	yes	—
91	#13063282	C₂³	1	48	yes	—
92	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
93	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
95	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
96	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
97	C₂×Dic₄₃⋊C₄	C₂³	1	12	yes	—
98	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
99	C₂×Dic₄₃⋊C₄	C₂³	1	6	yes	—
100	C₄⋊C₄×D₄₃	C₂³	1	48	yes	—
101	C₂×C₂²⋊Dic₄₃	C₂³	1	6	yes	—
102	C₂×C₂²⋊Dic₄₃	C₂³	1	12	yes	—
103	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
104	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
105	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
106	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
107	C₂×C₄×Dic₄₃	C₂³	1	6	yes	—
108	C₄²×D₄₃	C₂³	1	48	yes	—
109	C₂×#41×C₄₃	—	2	8	no	—
110	C₂×#41×C₄₃	C₂³	1	8	yes	—
111	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₄₃	C₂³	1	3	yes	—
113	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
114	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
115	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
116	C₄×Q₈×C₄₃	C₂³	1	8	yes	—
117	C₄×Q₈×C₄₃	C₂³	1	8	yes	—
118	C₄×D₄×C₄₃	C₂³	1	24	yes	—
119	C₄×D₄×C₄₃	C₂³	1	24	yes	—
120	#117×C₄₃	C₂³	1	24	yes	—
121	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
122	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
123	C₂×C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
124	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
126	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
127	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
128	C₂×C₄²×C₄₃	C₂³	1	24	yes	—
129	C₂⁴×C₄₃	C₂⁴	1	3	yes	—
130	C₂³×D₄₃	C₂⁴	1	2	yes	—
131	#41×C₄₃	—	2	32	no	—
132	C₂×Q₈×C₄₃	#41	1	8	yes	complemented
133	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
134	C₂×D₄×C₄₃	—	2	12	no	—
135	C₂×D₄×C₄₃	C₂⁴	1	12	yes	—
136	C₂²×C₄×C₄₃	—	2	12	no	—
137	C₂²×C₄×C₄₃	—	2	12	no	—
138	C₂²×C₄×C₄₃	—	2	12	no	—
139	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
142	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
143	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
144	C₂²×C₄×C₄₃	C₂⁴	1	12	yes	—
145	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₂²⋊D₄₃	—	2	24	no	—
149	C₂×C₂²⋊D₄₃	C₂⁴	1	24	yes	—
150	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
151	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
152	C₂²×Dic₄₃	C₂⁴	1	6	yes	—
153	Q₈×D₄₃	—	2	64	no	—
154	#10621898	—	2	96	no	—
155	C₂×D₁₇₂	#41	1	8	yes	complemented
156	C₂×D₁₇₂	C₂⁴	1	4	yes	—
157	C₂×C₄×D₄₃	—	2	24	no	—
158	C₂×C₄×D₄₃	—	2	8	no	—
159	C₂×C₄×D₄₃	—	2	24	no	—
160	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
161	C₂×C₄×D₄₃	C₂⁴	1	24	yes	—
162	C₂×C₄×D₄₃	C₂⁴	1	24	yes	—
163	C₂×Dic₈₆	—	2	24	no	—
164	C₂×Dic₈₆	—	2	12	no	—
165	C₂×Dic₈₆	C₂⁴	1	24	yes	—
166	C₂×Dic₈₆	C₂⁴	1	12	yes	—
167	C₄⋊C₄×C₄₃	C₂⁴	1	12	yes	—
168	C₄⋊C₄×C₄₃	C₂⁴	1	12	yes	—
169	C₂²⋊C₄×C₄₃	C₂⁴	1	24	yes	—
170	C₄²×C₄₃	C₂⁴	1	4	yes	—
171	C₄²×C₄₃	C₂⁴	1	12	yes	—
172	C₄²×C₄₃	C₂⁴	1	12	yes	—
173	C₄²×C₄₃	C₂⁴	1	12	yes	—
174	C₂²⋊Dic₄₃	C₂⁴	1	24	yes	—
175	C₂²⋊Dic₄₃	C₂⁴	1	48	yes	—
176	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
177	(C₂×D₄₃)⋊C₄	C₂⁴	1	24	yes	—
178	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
179	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
180	C₄⋊Dic₄₃	C₂⁴	1	12	yes	—
181	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
182	C₄⋊Dic₄₃	C₂⁴	1	24	yes	—
183	Dic₄₃⋊C₄	C₂⁴	1	48	yes	—
184	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
185	Dic₄₃⋊C₄	C₂⁴	1	24	yes	—
186	C₄×Dic₄₃	C₂⁴	1	24	yes	—
187	C₄×Dic₄₃	C₂⁴	1	24	yes	—
188	C₄×Dic₄₃	C₂⁴	1	24	yes	—
189	C₂³×C₄₃	—	2	6	no	—
190	C₂³×C₄₃	—	2	6	no	—
191	C₂³×C₄₃	—	2	6	no	—
192	C₂³×C₄₃	C₂⁵	1	6	yes	—
193	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	4	no	—
195	C₂²×D₄₃	—	2	4	no	—
196	C₂²×D₄₃	C₂×#41	1	8	yes	—
197	C₂²×D₄₃	C₂⁵	1	4	yes	—
198	Q₈×C₄₃	C₂×#41	1	16	yes	complemented
199	D₄×C₄₃	—	2	24	no	—
200	C₂×C₄×C₄₃	—	2	6	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	6	no	—
203	C₂×C₄×C₄₃	—	2	24	no	—
204	C₂×C₄×C₄₃	—	2	24	no	—
205	C₂×C₄×C₄₃	—	2	24	no	—
206	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
207	C₂×C₄×C₄₃	C₂×#41	1	12	yes	—
208	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
209	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
210	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
211	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
212	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
213	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
214	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
215	C₂²⋊D₄₃	—	2	48	no	—
216	C₂×Dic₄₃	—	2	12	no	—
217	C₂×Dic₄₃	—	2	12	no	—
218	C₂×Dic₄₃	—	2	4	no	—
219	C₂×Dic₄₃	C₂⁵	1	4	yes	—
220	C₂×Dic₄₃	C₂⁵	1	12	yes	—
221	C₂×Dic₄₃	C₂⁵	1	12	yes	—
222	D₁₇₂	C₂×#41	1	16	yes	complemented
223	C₄×D₄₃	—	2	48	no	—
224	C₄×D₄₃	—	2	48	no	—
225	C₄×D₄₃	—	2	16	no	—
226	Dic₈₆	—	2	24	no	—
227	Dic₈₆	—	2	48	no	—
228	C₂×#3482	—	43	1	no	maximal, Sylow
229	C₂²×C₄₃	—	2	6	no	—
230	C₂²×C₄₃	—	2	6	no	—
231	C₂²×C₄₃	—	2	6	no	—
232	C₂²×C₄₃	—	4	12	no	—
233	C₂²×C₄₃	C₂²×#41	1	2	yes	—
234	C₂²×C₄₃	C₂²×#41	1	2	yes	—
235	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
236	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
237	C₂×D₄₃	—	2	4	no	—
238	C₂×D₄₃	—	2	4	no	—
239	C₂×D₄₃	—	2	16	no	—
240	C₂×D₄₃	C₂²×#41	1	8	yes	—
241	C₄×C₄₃	—	2	6	no	—
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	2	6	no	—
244	C₄×C₄₃	C₂²×#41	1	4	yes	—
245	C₄×C₄₃	C₂²×#41	1	12	yes	—
246	C₄×C₄₃	C₂×2₋¹⁺⁴	1	4	yes	—
247	Dic₄₃	—	2	12	no	—
248	Dic₄₃	—	2	12	no	—
249	Dic₄₃	—	2	4	no	—
250	#3482	—	43	32	no	—
251	C₂×#557	—	43	1	no	—
252	C₂×#556	—	43	3	no	—
253	C₂×#552	—	43	6	no	—
254	C₂×D₄×Q₈	—	43	1	no	—
255	C₂×#548	—	43	2	no	—
256	C₂×#547	—	43	3	no	—
257	C₂×#533	—	43	3	no	—
258	C₂×#529	—	43	6	no	—
259	C₂×C₄×#41	—	43	3	no	—
260	C₂×C₄×#41	D₄₃	1	1	yes	characteristic, complemented
261	C₂²×C₄×Q₈	—	43	2	no	—
262	C₂×C₄₃	—	4	6	no	—
263	C₂×C₄₃	#3482	1	4	yes	complemented
264	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
265	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
266	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
267	D₄₃	—	2	8	no	—
268	C₂²×#41	—	43	3	no	—
269	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
270	C₂³×Q₈	—	43	2	no	—
271	#557	—	43	16	no	—
272	#556	—	43	48	no	—
273	#552	—	43	96	no	—
274	D₄×Q₈	—	43	16	no	—
275	#548	—	43	32	no	—
276	#547	—	43	48	no	—
277	#533	—	43	48	no	—
278	C₂×C₄⋊Q₈	—	43	3	no	—
279	C₂×C₄⋊Q₈	—	43	3	no	—
280	#529	—	43	96	no	—
281	C₂×#126	—	43	12	no	—
282	C₂×#125	—	43	6	no	—
283	C₂×#125	—	43	6	no	—
284	C₂×#124	—	43	6	no	—
285	C₂×#123	—	43	12	no	—
286	C₂×C₂²⋊Q₈	—	43	6	no	—
287	C₂×C₂²⋊Q₈	—	43	6	no	—
288	C₂×C₂²⋊Q₈	—	43	6	no	—
289	C₂×#121	—	43	6	no	—
290	C₄×#41	—	43	48	no	—
291	C₄×#41	C₂×D₄₃	1	16	yes	complemented
292	C₂×C₄×Q₈	—	43	2	no	—
293	C₂×C₄×Q₈	—	43	32	no	—
294	C₂×C₄×Q₈	—	43	6	no	—
295	C₂×C₄×Q₈	—	43	6	no	—
296	C₂×C₄×Q₈	—	43	3	no	—
297	C₂×C₄×Q₈	—	43	3	no	—
298	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
300	C₂×C₄×D₄	—	43	6	no	—
301	C₂×C₄×D₄	—	43	6	no	—
302	C₂×C₄×D₄	—	43	1	no	—
303	C₂×C₄×D₄	—	43	3	no	—
304	C₂×C₄×D₄	C₂×D₄₃	1	3	yes	—
305	C₂×C₄×D₄	C₂×D₄₃	1	3	yes	—
306	C₂×#117	—	43	3	no	—
307	C₂×#117	—	43	6	no	—
308	C₂×#117	—	43	6	no	—
309	C₂×#117	C₂×D₄₃	1	3	yes	—
310	C₂²×C₄⋊C₄	—	43	6	no	—
311	C₂²×C₄²	—	43	6	no	—
312	C₂²×C₄²	C₂×D₄₃	1	3	yes	—
313	C₄₃	C₂×#3482	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	43	24	no	—
316	C₂×#41	—	86	24	no	—
317	C₂×#41	C₂²×D₄₃	1	8	yes	—
318	C₂²×Q₈	—	43	16	no	—
319	C₂²×Q₈	—	43	6	no	—
320	C₂²×Q₈	—	43	3	no	—
321	C₂²×Q₈	—	86	16	no	—
322	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
323	C₂²×D₄	—	43	6	no	—
324	C₂²×D₄	—	43	1	no	—
325	C₂²×D₄	C₂²×D₄₃	1	3	yes	—
326	C₂³×C₄	—	43	6	no	—
327	C₂³×C₄	—	43	6	no	—
328	C₂³×C₄	—	43	2	no	—
329	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
330	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
331	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
332	C₄⋊Q₈	—	43	24	no	—
333	C₄⋊Q₈	—	43	24	no	—
334	#126	—	43	96	no	—
335	#125	—	43	48	no	—
336	#125	—	43	48	no	—
337	#124	—	43	48	no	—
338	#123	—	43	96	no	—
339	C₂²⋊Q₈	—	43	48	no	—
340	C₂²⋊Q₈	—	43	48	no	—
341	C₂²⋊Q₈	—	43	48	no	—
342	#121	—	43	48	no	—
343	C₄×Q₈	—	43	16	no	—
344	C₄×Q₈	—	43	48	no	—
345	C₄×Q₈	—	43	48	no	—
346	C₄×Q₈	—	43	24	no	—
347	C₄×Q₈	—	43	24	no	—
348	C₄×Q₈	C₂²×D₄₃	1	8	yes	—
349	C₄×Q₈	C₂²×D₄₃	1	8	yes	—
350	C₄×D₄	—	43	48	no	—
351	C₄×D₄	—	43	48	no	—
352	C₄×D₄	—	43	8	no	—
353	C₄×D₄	—	43	24	no	—
354	C₄×D₄	C₂²×D₄₃	1	24	yes	—
355	C₄×D₄	C₂²×D₄₃	1	24	yes	—
356	#117	—	43	24	no	—
357	#117	—	43	48	no	—
358	#117	—	43	48	no	—
359	#117	C₂²×D₄₃	1	24	yes	—
360	C₂×C₄⋊C₄	—	43	6	no	—
361	C₂×C₄⋊C₄	—	43	12	no	—
362	C₂×C₄⋊C₄	—	43	1	no	—
363	C₂×C₄⋊C₄	—	43	6	no	—
364	C₂×C₄⋊C₄	—	43	3	no	—
365	C₂×C₄⋊C₄	—	43	6	no	—
366	C₂×C₄⋊C₄	—	43	6	no	—
367	C₂×C₄⋊C₄	—	43	6	no	—
368	C₂×C₄⋊C₄	—	43	48	no	—
369	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
370	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
371	C₂×C₂²⋊C₄	—	43	6	no	—
372	C₂×C₂²⋊C₄	—	43	12	no	—
373	C₂×C₂²⋊C₄	—	43	2	no	—
374	C₂×C₂²⋊C₄	—	43	6	no	—
375	C₂×C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
376	C₂×C₄²	—	43	6	no	—
377	C₂×C₄²	—	43	6	no	—
378	C₂×C₄²	—	43	6	no	—
379	C₂×C₄²	—	43	48	no	—
380	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
381	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
382	C₂×C₄²	C₂²×D₄₃	1	24	yes	—
383	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
384	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
385	C₂⁴	—	43	2	no	—
386	C₂⁴	C₂³×D₄₃	1	3	yes	—
387	#41	—	2	32	no	—
388	#41	—	86	96	no	—
389	C₂×Q₈	—	43	24	no	—
390	C₂×Q₈	—	43	12	no	—
391	C₂×Q₈	—	86	64	no	—
392	C₂×Q₈	—	86	12	no	—
393	C₂×Q₈	—	86	24	no	—
394	C₂×Q₈	#10621898	1	8	yes	complemented
395	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
396	C₂×D₄	—	2	12	no	—
397	C₂×D₄	—	43	24	no	—
398	C₂×D₄	—	43	8	no	—
399	C₂×D₄	—	43	4	no	—
400	C₂×D₄	—	86	24	no	—
401	C₂×D₄	C₂³×D₄₃	1	12	yes	—
402	C₂²×C₄	—	2	12	no	—
403	C₂²×C₄	—	2	12	no	—
404	C₂²×C₄	—	2	12	no	—
405	C₂²×C₄	—	43	2	no	—
406	C₂²×C₄	—	43	6	no	—
407	C₂²×C₄	—	43	6	no	—
408	C₂²×C₄	—	43	8	no	—
409	C₂²×C₄	—	43	24	no	—
410	C₂²×C₄	—	43	24	no	—
411	C₂²×C₄	—	86	24	no	—
412	C₂²×C₄	—	86	24	no	—
413	C₂²×C₄	—	86	8	no	—
414	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
415	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
417	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
418	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
419	C₂²×C₄	C₂³×D₄₃	1	12	yes	—
420	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
421	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
422	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
423	C₄⋊C₄	—	43	24	no	—
424	C₄⋊C₄	—	43	48	no	—
425	C₄⋊C₄	—	43	4	no	—
426	C₄⋊C₄	—	43	24	no	—
427	C₄⋊C₄	—	43	12	no	—
428	C₄⋊C₄	—	43	24	no	—
429	C₄⋊C₄	—	43	24	no	—
430	C₄⋊C₄	—	43	24	no	—
431	C₄⋊C₄	C₂³×D₄₃	1	12	yes	—
432	C₄⋊C₄	C₂³×D₄₃	1	12	yes	—
433	C₂²⋊C₄	—	43	24	no	—
434	C₂²⋊C₄	—	43	48	no	—
435	C₂²⋊C₄	—	43	8	no	—
436	C₂²⋊C₄	—	43	24	no	—
437	C₂²⋊C₄	C₂³×D₄₃	1	24	yes	—
438	C₄²	—	43	24	no	—
439	C₄²	—	43	24	no	—
440	C₄²	—	43	24	no	—
441	C₄²	C₂³×D₄₃	1	12	yes	—
442	C₄²	C₂³×D₄₃	1	4	yes	—
443	C₄²	C₂³×D₄₃	1	12	yes	—
444	C₄²	C₂³×D₄₃	1	12	yes	—
445	C₂³	—	2	6	no	—
446	C₂³	—	2	6	no	—
447	C₂³	—	2	6	no	—
448	C₂³	—	43	8	no	—
449	C₂³	—	43	4	no	—
450	C₂³	—	86	4	no	—
451	C₂³	—	86	4	no	—
452	C₂³	C₂⁴×D₄₃	1	6	yes	—
453	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
454	Q₈	—	86	24	no	—
455	Q₈	—	86	48	no	—
456	Q₈	C₂×#10621898	1	16	yes	complemented
457	D₄	—	2	24	no	—
458	D₄	—	43	16	no	—
459	D₄	—	86	48	no	—
460	C₂×C₄	—	2	6	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	2	24	no	—
464	C₂×C₄	—	2	24	no	—
465	C₂×C₄	—	2	24	no	—
466	C₂×C₄	—	43	4	no	—
467	C₂×C₄	—	43	12	no	—
468	C₂×C₄	—	43	12	no	—
469	C₂×C₄	—	86	48	no	—
470	C₂×C₄	—	86	12	no	—
471	C₂×C₄	—	86	12	no	—
472	C₂×C₄	—	86	4	no	—
473	C₂×C₄	—	86	48	no	—
474	C₂×C₄	—	86	16	no	—
475	C₂×C₄	#41×D₄₃	1	4	yes	—
476	C₂×C₄	C₂×#10621898	1	12	yes	—
477	C₂×C₄	#13063372	1	4	yes	—
478	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
479	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
480	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
481	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
482	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
483	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
484	C₂²	—	2	6	no	—
485	C₂²	—	2	6	no	—
486	C₂²	—	2	6	no	—
487	C₂²	—	4	12	no	—
488	C₂²	—	43	8	no	—
489	C₂²	—	86	4	no	—
490	C₂²	—	86	4	no	—
491	C₂²	—	86	16	no	—
492	C₂²	C₂×#41×D₄₃	1	2	yes	—
493	C₂²	C₂²×#10621898	1	2	yes	—
494	C₂²	C₂×#13063372	1	2	yes	—
495	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
496	C₄	—	2	6	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	6	no	—
499	C₄	—	86	12	no	—
500	C₄	—	86	12	no	—
501	C₄	—	86	4	no	—
502	C₄	C₂×#41×D₄₃	1	4	yes	—
503	C₄	C₂²×#10621898	1	12	yes	—
504	C₄	C₂×#13063372	1	4	yes	—
505	C₂	—	4	6	no	—
506	C₂	—	86	8	no	—
507	C₂	#19148217	1	4	yes	direct product factor
508	C₂	C₂²×#41×D₄₃	1	1	yes	characteristic
509	C₂	C₂³×#10621898	1	1	yes	characteristic
510	C₂	C₂²×#13063372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄×#41×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×C₄×#41	D₄₃
hypocenter	C₄₃	C₂×#3482
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #19148217	C₂	direct (N × H)
2. C₂×#14583628	C₂	semidirect
3. C₂×#14583619	C₂	semidirect
4. C₂×#14583588	C₂	semidirect
5. C₂×Q₈×D₁₇₂	C₂	semidirect
6. C₂×#14583556	C₂	semidirect
7. C₂×#14583554	C₂	semidirect
8. C₂×#14583456	C₂	semidirect
9. C₂×#14583431	C₂	semidirect
10. C₂×C₄×#10621898	C₂	semidirect
11. C₂×C₄×Q₈×D₄₃	C₂	semidirect
12. C₂×C₄×#41×C₄₃	C₂	semidirect
15. #14583628	C₂²	semidirect
16. #14583619	C₂²	semidirect
17. #14583588	C₂²	semidirect
18. Q₈×D₁₇₂	C₂²	semidirect
19. #14583556	C₂²	semidirect
20. #14583554	C₂²	semidirect
21. #14583456	C₂²	semidirect
24. #14583431	C₂²	semidirect
34. C₄×#10621898	C₂²	semidirect
40. C₄×Q₈×D₄₃	C₂²	semidirect
51. C₄×#41×C₄₃	C₂²	semidirect
132. C₂×Q₈×C₄₃	#41	semidirect
155. C₂×D₁₇₂	#41	semidirect
198. Q₈×C₄₃	C₂×#41	semidirect
222. D₁₇₂	C₂×#41	semidirect
260. C₂×C₄×#41	D₄₃	semidirect
263. C₂×C₄₃	#3482	semidirect
291. C₄×#41	C₂×D₄₃	semidirect
313. C₄₃	C₂×#3482	semidirect
394. C₂×Q₈	#10621898	semidirect
456. Q₈	C₂×#10621898	semidirect
507. C₂	#19148217	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148217	2
C₂×#14583628	2
C₂×#14583619	2
C₂×#14583588	2
C₂×Q₈×D₁₇₂	2
C₂×#14583556	2
C₂×#14583554	2
C₂×#14583456	2
C₂×#14583431	2
C₂×C₄×#10621898	2
C₂×C₄×Q₈×D₄₃	2
C₂×C₄×#41×C₄₃	2
C₂×#3482	43

Subgroups — C2×#19148217 #26003695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148217 #26003695