Subgroups — C₂×#19148469 #26004952

Order 11008.

8622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148469	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583635	C₂	1	4	yes	maximal, complemented
3	C₂×#14583569	C₂	1	4	yes	maximal, complemented
4	C₂×#14583543	C₂	1	8	yes	maximal, complemented
5	C₂×#14583503	C₂	1	4	yes	maximal, complemented
6	C₂×#14583466	C₂	1	2	yes	maximal, complemented
7	C₂×#14583456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14583447	C₂	1	4	yes	maximal, complemented
9	C₂×#14583374	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621898	C₂²	1	1	yes	characteristic
13	C₂²×#10621900	C₂²	1	8	yes	complemented
14	#14583635	C₂²	1	64	yes	complemented
15	#14583569	C₂²	1	64	yes	complemented
16	#14583543	C₂²	1	128	yes	complemented
17	#14583503	C₂²	1	64	yes	complemented
18	#14583466	C₂²	1	32	yes	complemented
19	#14583456	C₂²	1	16	yes	complemented
20	#14583447	C₂²	1	64	yes	complemented
21	C₂×#13063325	C₂²	1	2	yes	complemented
22	C₂×#13063321	C₂²	1	4	yes	complemented
23	C₂×#13063317	C₂²	1	2	yes	complemented
24	C₂×#13063312	C₂²	1	8	yes	complemented
25	C₂×#13063312	C₂²	1	4	yes	complemented
26	C₂×#13063306	C₂²	1	16	yes	complemented
27	C₂×#13063304	C₂²	1	4	yes	—
28	C₂×#13063297	C₂²	1	16	yes	complemented
29	C₂×#13063296	C₂²	1	8	yes	complemented
30	C₂×#13063296	C₂²	1	8	yes	complemented
31	C₂×#13063294	C₂²	1	8	yes	—
32	#14583374	C₂²	1	32	yes	complemented
33	C₄×#10621898	C₂²	1	16	yes	complemented
34	C₂×C₄×Dic₈₆	C₂²	1	4	yes	complemented
35	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
36	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
37	C₂×D₄×Dic₄₃	C₂²	1	8	yes	complemented
38	C₂×D₄×Dic₄₃	C₂²	1	8	yes	complemented
39	C₂×D₄×Dic₄₃	C₂²	1	8	yes	complemented
40	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
41	C₂×#13063284	C₂²	1	1	yes	characteristic
42	C₂×#13063284	C₂²	1	2	yes	—
43	C₂×#13063282	C₂²	1	2	yes	complemented
44	C₂²×C₂²⋊Dic₄₃	C₂²	1	8	yes	—
45	C₂×C₄²×D₄₃	C₂²	1	2	yes	complemented
46	C₂³×D₄×C₄₃	C₂²	1	2	yes	—
47	C₂³×D₄×C₄₃	C₂²	1	4	yes	—
48	C₂×#127×C₄₃	C₂²	1	4	yes	—
49	C₂×#127×C₄₃	C₂²	1	2	yes	—
50	C₂×#127×C₄₃	C₂²	1	2	yes	—
51	C₂×#127×C₄₃	C₂²	1	16	yes	complemented
52	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×#10621898	—	2	8	no	—
54	C₂×#10621898	C₂³	1	8	yes	—
55	C₂×#10621900	—	4	32	no	—
56	C₂×#10621900	C₂³	1	64	yes	complemented
57	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
58	C₂²×Dic₈₆	C₂³	1	4	yes	—
59	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
60	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
61	C₂²×C₂²⋊D₄₃	C₂³	1	16	yes	—
62	C₂³×Dic₄₃	C₂³	1	16	yes	—
63	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
64	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
65	#13063325	C₂³	1	16	yes	complemented
66	#13063321	C₂³	1	32	yes	complemented
67	#13063317	C₂³	1	16	yes	complemented
68	#13063312	C₂³	1	32	yes	complemented
69	#13063312	C₂³	1	64	yes	complemented
70	#13063306	C₂³	1	128	yes	complemented
71	#13063304	C₂³	1	32	yes	—
72	#13063297	C₂³	1	128	yes	complemented
73	#13063296	C₂³	1	64	yes	complemented
74	#13063296	C₂³	1	64	yes	complemented
75	#13063294	C₂³	1	64	yes	—
76	C₄×Dic₈₆	C₂³	1	32	yes	complemented
77	C₄×Dic₈₆	C₂³	1	16	yes	complemented
78	C₄×D₁₇₂	C₂³	1	16	yes	complemented
79	D₄×Dic₄₃	C₂³	1	64	yes	complemented
80	D₄×Dic₄₃	C₂³	1	64	yes	complemented
81	D₄×Dic₄₃	C₂³	1	64	yes	complemented
82	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	—
83	#13063284	C₂³	1	8	yes	—
84	#13063284	C₂³	1	16	yes	—
85	#13063282	C₂³	1	16	yes	complemented
86	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
87	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
88	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
89	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
90	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
91	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊Dic₄₃	C₂³	1	16	yes	—
94	C₂×C₂²⋊Dic₄₃	C₂³	1	64	yes	—
95	C₂×C₂²⋊Dic₄₃	C₂³	1	16	yes	—
96	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
97	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
98	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
99	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
100	C₄²×D₄₃	C₂³	1	16	yes	complemented
101	C₂⁵×C₄₃	C₂³	1	4	yes	—
102	C₂²×D₄×C₄₃	—	2	16	no	—
103	C₂²×D₄×C₄₃	—	4	16	no	—
104	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
105	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
106	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
107	C₂²×D₄×C₄₃	C₂³	1	16	yes	—
108	C₂²×D₄×C₄₃	C₂³	1	8	yes	—
109	C₂²×D₄×C₄₃	C₂³	1	32	yes	—
110	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
112	#127×C₄₃	C₂³	1	32	yes	—
113	#127×C₄₃	C₂³	1	16	yes	—
114	#127×C₄₃	C₂³	1	16	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
119	C₂⁴×C₄₃	—	2	16	no	—
120	C₂⁴×C₄₃	—	4	16	no	—
121	C₂⁴×C₄₃	C₂⁴	1	8	yes	—
122	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₄₃	C₂⁴	1	16	yes	—
124	C₂³×D₄₃	C₂⁴	1	2	yes	—
125	C₂×D₄×C₄₃	—	2	16	no	—
126	C₂×D₄×C₄₃	—	2	16	no	—
127	C₂×D₄×C₄₃	—	2	64	no	—
128	C₂×D₄×C₄₃	—	2	32	no	—
129	C₂×D₄×C₄₃	—	4	16	no	—
130	C₂×D₄×C₄₃	—	4	64	no	—
131	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
132	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
133	C₂×D₄×C₄₃	C₂⁴	1	32	yes	—
134	C₂×D₄×C₄₃	C₂⁴	1	32	yes	—
135	C₂²×C₄×C₄₃	—	2	8	no	—
136	C₂²×C₄×C₄₃	#41	1	8	yes	complemented
137	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
143	C₂×C₂²⋊D₄₃	—	2	8	no	—
144	C₂×C₂²⋊D₄₃	—	4	32	no	—
145	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
146	C₂×C₂²⋊D₄₃	C₂⁴	1	64	yes	—
147	C₂²×Dic₄₃	—	4	32	no	—
148	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
149	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
150	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
151	C₂²×Dic₄₃	C₂⁴	1	64	yes	—
152	#10621900	—	4	128	no	—
153	#10621898	—	2	32	no	—
154	C₂×D₁₇₂	—	2	4	no	—
155	C₂×D₁₇₂	C₂⁴	1	4	yes	—
156	C₂×C₄×D₄₃	—	2	8	no	—
157	C₂×C₄×D₄₃	—	2	16	no	—
158	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
159	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
160	C₂×Dic₈₆	—	2	4	no	—
161	C₂×Dic₈₆	—	2	16	no	—
162	C₂×Dic₈₆	C₂⁴	1	4	yes	—
163	C₂×Dic₈₆	C₂⁴	1	16	yes	—
164	C₄²×C₄₃	C₂⁴	1	4	yes	—
165	C₄²×C₄₃	C₂⁴	1	4	yes	—
166	C₄²×C₄₃	C₂⁴	1	8	yes	—
167	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
168	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
169	C₂²⋊Dic₄₃	C₂⁴	1	64	yes	—
170	C₂²⋊Dic₄₃	C₂⁴	1	64	yes	—
171	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
172	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
173	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
174	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
175	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
176	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
177	C₄×Dic₄₃	C₂⁴	1	8	yes	—
178	C₄×Dic₄₃	C₂⁴	1	16	yes	—
179	C₄×Dic₄₃	C₂⁴	1	16	yes	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	2	16	no	—
182	C₂³×C₄₃	—	2	32	no	—
183	C₂³×C₄₃	—	2	32	no	—
184	C₂³×C₄₃	—	4	32	no	—
185	C₂³×C₄₃	—	8	32	no	—
186	C₂³×C₄₃	C₂×#41	1	4	yes	—
187	C₂³×C₄₃	C₂⁵	1	16	yes	—
188	C₂³×C₄₃	C₂⁵	1	2	yes	—
189	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
190	C₂²×D₄₃	—	2	4	no	—
191	C₂²×D₄₃	—	2	8	no	—
192	C₂²×D₄₃	C₂⁵	1	4	yes	—
193	D₄×C₄₃	—	2	32	no	—
194	D₄×C₄₃	—	2	32	no	—
195	D₄×C₄₃	—	2	64	no	—
196	D₄×C₄₃	—	4	32	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	16	no	—
199	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
200	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
201	C₂×C₄×C₄₃	C₂×#41	1	16	yes	complemented
202	C₂×C₄×C₄₃	H(5,𝔽₂)	1	8	yes	—
203	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
204	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
205	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
206	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
207	C₂²⋊D₄₃	—	2	16	no	—
208	C₂²⋊D₄₃	—	4	64	no	—
209	C₂×Dic₄₃	—	2	4	no	—
210	C₂×Dic₄₃	—	2	16	no	—
211	C₂×Dic₄₃	—	2	8	no	—
212	C₂×Dic₄₃	—	4	64	no	—
213	C₂×Dic₄₃	C₂⁵	1	4	yes	—
214	C₂×Dic₄₃	C₂⁵	1	8	yes	—
215	C₂×Dic₄₃	C₂⁵	1	16	yes	—
216	D₁₇₂	—	2	8	no	—
217	C₄×D₄₃	—	2	16	no	—
218	C₄×D₄₃	—	2	32	no	—
219	Dic₈₆	—	2	8	no	—
220	Dic₈₆	—	2	32	no	—
221	C₂×#3508	—	43	1	no	maximal, Sylow
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	2	8	no	—
224	C₂²×C₄₃	—	2	16	no	—
225	C₂²×C₄₃	—	2	32	no	—
226	C₂²×C₄₃	—	4	32	no	—
227	C₂²×C₄₃	—	8	32	no	—
228	C₂²×C₄₃	C₂²×#41	1	4	yes	—
229	C₂²×C₄₃	C₂²×#41	1	2	yes	—
230	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
231	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
232	C₂×D₄₃	—	2	4	no	—
233	C₂×D₄₃	—	2	8	no	—
234	C₂×D₄₃	—	4	8	no	—
235	C₄×C₄₃	—	2	4	no	—
236	C₄×C₄₃	C₂²×#41	1	4	yes	—
237	C₄×C₄₃	C₂²×#41	1	4	yes	—
238	C₄×C₄₃	C₂×H(5,𝔽₂)	1	8	yes	—
239	Dic₄₃	—	2	4	no	—
240	Dic₄₃	—	2	16	no	—
241	Dic₄₃	—	2	8	no	—
242	#3508	—	43	32	no	—
243	C₂×#559	—	43	4	no	—
244	C₂×#550	—	43	4	no	—
245	C₂×#546	—	43	8	no	—
246	C₂×#540	—	43	4	no	—
247	C₂×#535	—	43	2	no	—
248	C₂×#533	—	43	1	no	—
249	C₂×#532	—	43	4	no	—
250	C₂²×#127	D₄₃	1	1	yes	characteristic, complemented
251	C₂×#518	—	43	2	no	—
252	C₂×C₄×#41	—	43	1	no	—
253	C₂×C₄₃	—	2	4	no	—
254	C₂×C₄₃	—	4	16	no	—
255	C₂×C₄₃	#3508	1	4	yes	complemented
256	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
257	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	2	yes	—
258	D₄₃	—	4	4	no	—
259	C₂²×#41	—	43	8	no	—
260	C₂²×#41	—	43	1	no	—
261	C₂³×D₄	C₂×D₄₃	1	2	yes	—
262	C₂³×D₄	C₂×D₄₃	1	4	yes	—
263	#559	—	43	64	no	—
264	#550	—	43	64	no	—
265	#546	—	43	128	no	—
266	#540	—	43	64	no	—
267	#535	—	43	32	no	—
268	#533	—	43	16	no	—
269	#532	—	43	64	no	—
270	C₂×C₄⋊Q₈	—	43	2	no	—
271	C₂×#127	—	43	4	no	—
272	C₂×#127	C₂×D₄₃	1	2	yes	—
273	C₂×#127	C₂×D₄₃	1	2	yes	—
274	C₂×#127	C₂×D₄₃	1	4	yes	—
275	C₂×#127	C₂×D₄₃	1	16	yes	complemented
276	C₂×#125	—	43	2	no	—
277	C₂×#124	—	43	8	no	—
278	C₂×#124	—	43	4	no	—
279	C₂×#123	—	43	16	no	—
280	C₂×C₂²⋊Q₈	—	43	4	no	—
281	C₂×#121	—	43	8	no	—
282	C₂×#121	—	43	8	no	—
283	C₂×#121	—	43	16	no	—
284	C₂×#120	—	43	8	no	—
285	#518	—	43	32	no	—
286	C₄×#41	—	43	16	no	—
287	C₂×C₄×Q₈	—	43	2	no	—
288	C₂×C₄×Q₈	—	43	4	no	—
289	C₂×C₄×D₄	—	43	8	no	—
290	C₂×C₄×D₄	—	43	8	no	—
291	C₂×C₄×D₄	—	43	8	no	—
292	C₂×C₄×D₄	—	43	4	no	—
293	C₂×C₄×D₄	—	43	2	no	—
294	C₂×#117	—	43	1	no	—
295	C₂×#117	—	43	2	no	—
296	C₂×#117	—	43	2	no	—
297	C₂²×C₂²⋊C₄	—	43	8	no	—
298	C₂²×C₄²	—	43	2	no	—
299	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
300	C₄₃	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
301	C₂⁵	C₂²×D₄₃	1	4	yes	—
302	C₂×#41	—	43	64	no	—
303	C₂×#41	—	43	8	no	—
304	C₂×#41	—	86	8	no	—
305	C₂×#41	—	172	32	no	—
306	C₂²×Q₈	—	43	1	no	—
307	C₂²×Q₈	—	43	4	no	—
308	C₂²×D₄	—	2	16	no	—
309	C₂²×D₄	—	4	16	no	—
310	C₂²×D₄	—	43	2	no	—
311	C₂²×D₄	—	43	16	no	—
312	C₂²×D₄	—	43	1	no	—
313	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
314	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
315	C₂²×D₄	C₂²×D₄₃	1	8	yes	—
316	C₂²×D₄	C₂²×D₄₃	1	16	yes	—
317	C₂²×D₄	C₂²×D₄₃	1	8	yes	—
318	C₂²×D₄	C₂²×D₄₃	1	32	yes	—
319	C₂³×C₄	—	43	16	no	—
320	C₂³×C₄	—	43	2	no	—
321	C₂³×C₄	—	43	4	no	—
322	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
323	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
324	C₄⋊Q₈	—	43	16	no	—
325	#127	—	43	32	no	—
326	#127	C₂²×D₄₃	1	16	yes	—
327	#127	C₂²×D₄₃	1	16	yes	—
328	#127	C₂²×D₄₃	1	32	yes	—
329	#125	—	43	16	no	—
330	#124	—	43	64	no	—
331	#124	—	43	32	no	—
332	#123	—	43	128	no	—
333	C₂²⋊Q₈	—	43	32	no	—
334	#121	—	43	64	no	—
335	#121	—	43	64	no	—
336	#121	—	43	128	no	—
337	#120	—	43	64	no	—
338	C₄×Q₈	—	43	16	no	—
339	C₄×Q₈	—	43	32	no	—
340	C₄×D₄	—	43	64	no	—
341	C₄×D₄	—	43	64	no	—
342	C₄×D₄	—	43	64	no	—
343	C₄×D₄	—	43	32	no	—
344	C₄×D₄	—	43	16	no	—
345	#117	—	43	8	no	—
346	#117	—	43	16	no	—
347	#117	—	43	16	no	—
348	C₂×C₄⋊C₄	—	43	2	no	—
349	C₂×C₄⋊C₄	—	43	4	no	—
350	C₂×C₄⋊C₄	—	43	4	no	—
351	C₂×C₄⋊C₄	—	43	4	no	—
352	C₂×C₄⋊C₄	—	43	8	no	—
353	C₂×C₂²⋊C₄	—	43	2	no	—
354	C₂×C₂²⋊C₄	—	43	4	no	—
355	C₂×C₂²⋊C₄	—	43	16	no	—
356	C₂×C₂²⋊C₄	—	43	64	no	—
357	C₂×C₂²⋊C₄	—	43	16	no	—
358	C₂×C₂²⋊C₄	—	43	4	no	—
359	C₂×C₄²	—	43	2	no	—
360	C₂×C₄²	—	43	4	no	—
361	C₂×C₄²	—	43	4	no	—
362	C₂×C₄²	—	43	16	no	—
363	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
365	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
366	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
367	C₂⁴	—	2	16	no	—
368	C₂⁴	—	4	16	no	—
369	C₂⁴	—	43	2	no	—
370	C₂⁴	C₂³×D₄₃	1	8	yes	—
371	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
372	C₂⁴	C₂³×D₄₃	1	16	yes	—
373	#41	—	86	32	no	—
374	#41	—	172	128	no	—
375	C₂×Q₈	—	43	4	no	—
376	C₂×Q₈	—	43	16	no	—
377	C₂×Q₈	—	86	4	no	—
378	C₂×Q₈	—	86	16	no	—
379	C₂×D₄	—	2	16	no	—
380	C₂×D₄	—	2	16	no	—
381	C₂×D₄	—	2	64	no	—
382	C₂×D₄	—	2	32	no	—
383	C₂×D₄	—	4	64	no	—
384	C₂×D₄	—	4	16	no	—
385	C₂×D₄	—	43	8	no	—
386	C₂×D₄	—	43	64	no	—
387	C₂×D₄	—	43	4	no	—
388	C₂×D₄	—	86	8	no	—
389	C₂×D₄	—	86	4	no	—
390	C₂×D₄	—	172	32	no	—
391	C₂×D₄	C₂³×D₄₃	1	16	yes	—
392	C₂×D₄	C₂³×D₄₃	1	16	yes	—
393	C₂×D₄	C₂³×D₄₃	1	32	yes	—
394	C₂×D₄	C₂³×D₄₃	1	32	yes	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	43	2	no	—
397	C₂²×C₄	—	43	4	no	—
398	C₂²×C₄	—	43	8	no	—
399	C₂²×C₄	—	43	64	no	—
400	C₂²×C₄	—	43	8	no	—
401	C₂²×C₄	—	43	16	no	—
402	C₂²×C₄	—	86	8	no	—
403	C₂²×C₄	—	86	16	no	—
404	C₂²×C₄	—	172	32	no	—
405	C₂²×C₄	#10621900	1	8	yes	complemented
406	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
407	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
408	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
409	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
411	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
412	C₄⋊C₄	—	43	8	no	—
413	C₄⋊C₄	—	43	16	no	—
414	C₄⋊C₄	—	43	16	no	—
415	C₄⋊C₄	—	43	16	no	—
416	C₄⋊C₄	—	43	32	no	—
417	C₂²⋊C₄	—	43	8	no	—
418	C₂²⋊C₄	—	43	16	no	—
419	C₂²⋊C₄	—	43	64	no	—
420	C₂²⋊C₄	—	43	64	no	—
421	C₂²⋊C₄	—	43	16	no	—
422	C₄²	—	43	8	no	—
423	C₄²	—	43	16	no	—
424	C₄²	—	43	16	no	—
425	C₄²	C₂³×D₄₃	1	4	yes	—
426	C₄²	C₂³×D₄₃	1	4	yes	—
427	C₄²	C₂³×D₄₃	1	8	yes	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	16	no	—
430	C₂³	—	2	32	no	—
431	C₂³	—	2	32	no	—
432	C₂³	—	4	32	no	—
433	C₂³	—	8	32	no	—
434	C₂³	—	43	4	no	—
435	C₂³	—	86	4	no	—
436	C₂³	—	86	8	no	—
437	C₂³	C₂×#10621900	1	4	yes	—
438	C₂³	C₂⁴×D₄₃	1	16	yes	—
439	C₂³	C₂⁴×D₄₃	1	2	yes	—
440	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
441	Q₈	—	86	8	no	—
442	Q₈	—	86	32	no	—
443	D₄	—	2	32	no	—
444	D₄	—	2	32	no	—
445	D₄	—	2	64	no	—
446	D₄	—	4	32	no	—
447	D₄	—	86	16	no	—
448	D₄	—	86	8	no	—
449	D₄	—	172	64	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	16	no	—
452	C₂×C₄	—	43	4	no	—
453	C₂×C₄	—	43	8	no	—
454	C₂×C₄	—	43	16	no	—
455	C₂×C₄	—	86	4	no	—
456	C₂×C₄	—	86	8	no	—
457	C₂×C₄	—	86	16	no	—
458	C₂×C₄	—	86	16	no	—
459	C₂×C₄	—	86	32	no	—
460	C₂×C₄	—	172	64	no	—
461	C₂×C₄	C₂×#10621900	1	4	yes	—
462	C₂×C₄	C₂×#10621900	1	4	yes	—
463	C₂×C₄	C₂×#10621900	1	16	yes	complemented
464	C₂×C₄	#13063370	1	8	yes	—
465	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
466	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
467	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
468	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	16	no	—
472	C₂²	—	2	32	no	—
473	C₂²	—	4	32	no	—
474	C₂²	—	8	32	no	—
475	C₂²	—	86	4	no	—
476	C₂²	—	86	8	no	—
477	C₂²	—	172	8	no	—
478	C₂²	C₂²×#10621900	1	4	yes	—
479	C₂²	C₂²×#10621900	1	2	yes	—
480	C₂²	C₂×#13063370	1	4	yes	—
481	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	86	4	no	—
484	C₄	—	86	8	no	—
485	C₄	—	86	16	no	—
486	C₄	C₂²×#10621900	1	4	yes	—
487	C₄	C₂²×#10621900	1	4	yes	—
488	C₄	C₂×#13063370	1	8	yes	—
489	C₂	—	2	4	no	—
490	C₂	—	4	16	no	—
491	C₂	—	172	4	no	—
492	C₂	#19148469	1	4	yes	direct product factor
493	C₂	C₂³×#10621900	1	1	yes	characteristic
494	C₂	C₂²×#13063370	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×#127×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂²×#127	D₄₃
hypocenter	C₄₃	C₂×#3508
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#127

Complements

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

N	H ≅ G/N	type
1. #19148469	C₂	direct (N × H)
2. C₂×#14583635	C₂	semidirect
3. C₂×#14583569	C₂	semidirect
4. C₂×#14583543	C₂	semidirect
5. C₂×#14583503	C₂	semidirect
6. C₂×#14583466	C₂	semidirect
7. C₂×#14583456	C₂	semidirect
8. C₂×#14583447	C₂	semidirect
9. C₂×#14583374	C₂	semidirect
10. C₂×C₄×#10621898	C₂	semidirect
11. C₂²×#127×C₄₃	C₂	semidirect
13. C₂²×#10621900	C₂²	semidirect
14. #14583635	C₂²	semidirect
15. #14583569	C₂²	semidirect
16. #14583543	C₂²	semidirect
17. #14583503	C₂²	semidirect
18. #14583466	C₂²	semidirect
19. #14583456	C₂²	semidirect
20. #14583447	C₂²	semidirect
21. C₂×#13063325	C₂²	semidirect
22. C₂×#13063321	C₂²	semidirect
23. C₂×#13063317	C₂²	semidirect
24. C₂×#13063312	C₂²	semidirect
25. C₂×#13063312	C₂²	semidirect
26. C₂×#13063306	C₂²	semidirect
28. C₂×#13063297	C₂²	semidirect
29. C₂×#13063296	C₂²	semidirect
30. C₂×#13063296	C₂²	semidirect
32. #14583374	C₂²	semidirect
33. C₄×#10621898	C₂²	semidirect
34. C₂×C₄×Dic₈₆	C₂²	semidirect
35. C₂×C₄×Dic₈₆	C₂²	semidirect
36. C₂×C₄×D₁₇₂	C₂²	semidirect
37. C₂×D₄×Dic₄₃	C₂²	semidirect
38. C₂×D₄×Dic₄₃	C₂²	semidirect
39. C₂×D₄×Dic₄₃	C₂²	semidirect
43. C₂×#13063282	C₂²	semidirect
45. C₂×C₄²×D₄₃	C₂²	semidirect
51. C₂×#127×C₄₃	C₂²	semidirect
56. C₂×#10621900	C₂³	semidirect
65. #13063325	C₂³	semidirect
66. #13063321	C₂³	semidirect
67. #13063317	C₂³	semidirect
68. #13063312	C₂³	semidirect
69. #13063312	C₂³	semidirect
70. #13063306	C₂³	semidirect
72. #13063297	C₂³	semidirect
73. #13063296	C₂³	semidirect
74. #13063296	C₂³	semidirect
76. C₄×Dic₈₆	C₂³	semidirect
77. C₄×Dic₈₆	C₂³	semidirect
78. C₄×D₁₇₂	C₂³	semidirect
79. D₄×Dic₄₃	C₂³	semidirect
80. D₄×Dic₄₃	C₂³	semidirect
81. D₄×Dic₄₃	C₂³	semidirect
85. #13063282	C₂³	semidirect
100. C₄²×D₄₃	C₂³	semidirect
136. C₂²×C₄×C₄₃	#41	semidirect
201. C₂×C₄×C₄₃	C₂×#41	semidirect
250. C₂²×#127	D₄₃	semidirect
255. C₂×C₄₃	#3508	semidirect
275. C₂×#127	C₂×D₄₃	semidirect
300. C₄₃	C₂×#3508	semidirect
405. C₂²×C₄	#10621900	semidirect
463. C₂×C₄	C₂×#10621900	semidirect
492. C₂	#19148469	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148469	2
C₂×#14583635	2
C₂×#14583569	2
C₂×#14583543	2
C₂×#14583503	2
C₂×#14583466	2
C₂×#14583456	2
C₂×#14583447	2
C₂×#14583374	2
C₂×C₄×#10621898	2
C₂²×#127×C₄₃	2
C₂×#3508	43

Subgroups — C2×#19148469 #26004952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148469 #26004952