Subgroups — C₂×#19148953 #26004357

Order 11008.

7430 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148953	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583647	C₂	1	2	yes	maximal, complemented
3	C₂×#14583641	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14583615	C₂	1	2	yes	maximal, complemented
5	C₂×#14583577	C₂	1	2	yes	maximal, complemented
6	C₂×#14583574	C₂	1	4	yes	maximal, complemented
7	C₂×#14583540	C₂	1	4	yes	maximal, complemented
8	C₂×#14583519	C₂	1	4	yes	maximal, complemented
9	C₂×#14583488	C₂	1	4	yes	maximal, complemented
10	C₂×#14583474	C₂	1	2	yes	maximal, complemented
11	C₂×#14583460	C₂	1	2	yes	maximal, complemented
12	C₂×#14583434	C₂	1	2	yes	maximal, complemented
13	C₂×#124×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#10621902	C₂²	1	2	yes	—
16	C₂²×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₁₇₂	C₂²	1	2	yes	complemented
18	C₂²×D₄×D₄₃	C₂²	1	1	yes	characteristic
19	#14583647	C₂²	1	32	yes	complemented
20	#14583641	C₂²	1	16	yes	complemented
21	#14583615	C₂²	1	32	yes	complemented
22	#14583577	C₂²	1	32	yes	complemented
23	#14583574	C₂²	1	64	yes	complemented
24	#14583540	C₂²	1	64	yes	complemented
25	#14583519	C₂²	1	64	yes	complemented
26	#14583488	C₂²	1	64	yes	complemented
27	#14583474	C₂²	1	32	yes	complemented
28	#14583460	C₂²	1	32	yes	complemented
29	C₂×#13063323	C₂²	1	2	yes	complemented
30	#14583434	C₂²	1	32	yes	complemented
31	C₂×#13063320	C₂²	1	4	yes	complemented
32	C₂×#13063318	C₂²	1	4	yes	complemented
33	C₂×#13063314	C₂²	1	4	yes	complemented
34	C₂×#13063314	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13063314	C₂²	1	2	yes	complemented
36	C₂×#13063313	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13063313	C₂²	1	2	yes	complemented
38	C₂×#13063313	C₂²	1	2	yes	complemented
39	C₂×#13063312	C₂²	1	1	yes	characteristic
40	C₂×#13063311	C₂²	1	4	yes	complemented
41	C₂×#13063311	C₂²	1	4	yes	complemented
42	#124×D₄₃	C₂²	1	16	yes	complemented
43	C₂×#13063310	C₂²	1	4	yes	complemented
44	C₂×#13063310	C₂²	1	4	yes	complemented
45	C₂×#13063310	C₂²	1	4	yes	complemented
46	C₂×#13063310	C₂²	1	4	yes	complemented
47	C₂×#13063308	C₂²	1	2	yes	complemented
48	C₂×#13063307	C₂²	1	4	yes	complemented
49	C₂×#13063305	C₂²	1	2	yes	complemented
50	C₂×#13063303	C₂²	1	4	yes	complemented
51	C₂×#13063303	C₂²	1	4	yes	complemented
52	C₂×#13063303	C₂²	1	4	yes	complemented
53	C₂×#13063300	C₂²	1	2	yes	—
54	C₂×#13063300	C₂²	1	4	yes	complemented
55	C₂×#13063300	C₂²	1	4	yes	complemented
56	C₂×#13063300	C₂²	1	4	yes	complemented
57	C₂×#13063298	C₂²	1	4	yes	—
58	C₂×#13063295	C₂²	1	4	yes	—
59	C₂×#13063295	C₂²	1	4	yes	complemented
60	C₂×#13063295	C₂²	1	2	yes	complemented
61	C₂×#13063293	C₂²	1	2	yes	—
62	C₂×#13063290	C₂²	1	2	yes	complemented
63	C₂×C₄×D₁₇₂	C₂²	1	4	yes	complemented
64	C₂×#13063287	C₂²	1	4	yes	complemented
65	C₂×#13063287	C₂²	1	2	yes	complemented
66	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
67	C₂×#13063283	C₂²	1	4	yes	complemented
68	C₂×#13063283	C₂²	1	4	yes	complemented
69	C₂×#13063282	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊C₄×D₄₃	C₂²	1	2	yes	complemented
73	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
74	C₄₃×#563	C₂²	1	16	yes	complemented
75	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
76	C₂×#126×C₄₃	C₂²	1	4	yes	complemented
77	C₂×#125×C₄₃	C₂²	1	2	yes	complemented
78	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×#123×C₄₃	C₂²	1	2	yes	—
80	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	complemented
81	C₂⁴×D₄₃	C₂³	1	2	yes	—
82	C₂⁴×D₄₃	C₂³	1	2	yes	—
83	C₂×#10621902	—	4	8	no	—
84	C₂×#10621902	C₂³	1	16	yes	—
85	C₂²×Dic₈₆	C₂³	1	2	yes	—
86	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
87	C₂²×Dic₈₆	C₂³	1	2	yes	—
88	C₂×Q₈×D₄₃	—	4	4	no	—
89	C₂×Q₈×D₄₃	C₂³	1	8	yes	complemented
90	C₂²×D₁₇₂	—	4	8	no	—
91	C₂²×D₁₇₂	C₂³	1	4	yes	—
92	C₂²×D₁₇₂	C₂³	1	2	yes	—
93	C₂²×D₁₇₂	C₂³	1	4	yes	—
94	C₂²×D₁₇₂	C₂³	1	2	yes	—
95	C₂²×D₁₇₂	C₂³	1	4	yes	—
96	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
97	C₂²×D₁₇₂	C₂³	1	16	yes	complemented
98	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
99	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
100	C₂×D₄×D₄₃	—	4	4	no	—
101	C₂×D₄×D₄₃	C₂³	1	8	yes	—
102	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
104	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
105	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
106	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
107	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
108	#13063323	C₂³	1	16	yes	complemented
109	#13063320	C₂³	1	32	yes	complemented
110	#13063318	C₂³	1	32	yes	complemented
111	#13063314	C₂³	1	8	yes	complemented
112	#13063314	C₂³	1	16	yes	complemented
113	#13063314	C₂³	1	32	yes	complemented
114	#13063313	C₂³	1	16	yes	complemented
115	#13063313	C₂³	1	8	yes	complemented
116	#13063313	C₂³	1	16	yes	complemented
117	#13063312	C₂³	1	8	yes	—
118	#13063311	C₂³	1	32	yes	complemented
119	#13063311	C₂³	1	32	yes	complemented
120	#13063310	C₂³	1	32	yes	complemented
121	#13063310	C₂³	1	32	yes	complemented
122	#13063310	C₂³	1	32	yes	complemented
123	#13063310	C₂³	1	32	yes	complemented
124	#13063308	C₂³	1	16	yes	complemented
125	#13063307	C₂³	1	32	yes	complemented
126	#13063305	C₂³	1	16	yes	complemented
127	#13063303	C₂³	1	32	yes	complemented
128	#13063303	C₂³	1	32	yes	complemented
129	#13063303	C₂³	1	32	yes	complemented
130	#13063300	C₂³	1	16	yes	—
131	#13063300	C₂³	1	32	yes	complemented
132	#13063300	C₂³	1	32	yes	complemented
133	#13063300	C₂³	1	32	yes	complemented
134	#13063298	C₂³	1	32	yes	—
135	#13063295	C₂³	1	32	yes	—
136	#13063295	C₂³	1	32	yes	complemented
137	#13063295	C₂³	1	16	yes	complemented
138	#13063293	C₂³	1	16	yes	—
139	#13063290	C₂³	1	16	yes	complemented
140	C₄×D₁₇₂	C₂³	1	32	yes	complemented
141	#13063287	C₂³	1	32	yes	complemented
142	#13063287	C₂³	1	16	yes	complemented
143	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
144	#13063283	C₂³	1	32	yes	complemented
145	#13063283	C₂³	1	32	yes	complemented
146	#13063282	C₂³	1	16	yes	complemented
147	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
148	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
149	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
150	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
151	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
152	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
153	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
154	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
155	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
156	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
157	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
159	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
160	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
161	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
162	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
163	C₂²⋊C₄×D₄₃	C₂³	1	16	yes	complemented
164	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	complemented
165	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	complemented
166	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
168	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
169	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
170	C₄²×D₄₃	C₂³	1	8	yes	complemented
171	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
172	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
175	C₄⋊Q₈×C₄₃	C₂³	1	16	yes	complemented
176	#126×C₄₃	C₂³	1	32	yes	complemented
177	#125×C₄₃	C₂³	1	16	yes	complemented
178	#124×C₄₃	C₂³	1	8	yes	—
179	#123×C₄₃	C₂³	1	16	yes	—
180	C₂²⋊Q₈×C₄₃	C₂³	1	32	yes	complemented
181	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
187	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
188	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
191	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
192	C₂³×D₄₃	—	2	8	no	—
193	C₂³×D₄₃	—	4	4	no	—
194	C₂³×D₄₃	—	4	8	no	—
195	C₂³×D₄₃	—	4	8	no	—
196	C₂³×D₄₃	C₂⁴	1	4	yes	—
197	C₂³×D₄₃	C₂⁴	1	2	yes	—
198	C₂³×D₄₃	C₂⁴	1	1	yes	characteristic
199	C₂³×D₄₃	C₂⁴	1	8	yes	—
200	C₂³×D₄₃	C₂⁴	1	8	yes	—
201	C₂×Q₈×C₄₃	—	4	2	no	—
202	C₂×Q₈×C₄₃	—	4	4	no	—
203	C₂×Q₈×C₄₃	C₂⁴	1	8	yes	—
204	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₄₃	—	4	2	no	—
206	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₄₃	—	4	4	no	—
208	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
214	C₂×C₂²⋊D₄₃	—	4	4	no	—
215	C₂×C₂²⋊D₄₃	—	4	8	no	—
216	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
217	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
218	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
219	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
220	C₂²×Dic₄₃	C₂⁴	1	1	yes	characteristic
221	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
222	#10621902	—	4	32	no	—
223	Q₈×D₄₃	—	4	16	no	—
224	D₄×D₄₃	—	4	16	no	—
225	C₂×D₁₇₂	—	2	16	no	—
226	C₂×D₁₇₂	—	4	2	no	—
227	C₂×D₁₇₂	—	4	8	no	—
228	C₂×D₁₇₂	—	4	8	no	—
229	C₂×D₁₇₂	—	4	4	no	—
230	C₂×D₁₇₂	—	4	4	no	—
231	C₂×D₁₇₂	—	4	32	no	—
232	C₂×D₁₇₂	C₂⁴	1	16	yes	—
233	C₂×D₁₇₂	C₂⁴	1	8	yes	—
234	C₂×D₁₇₂	C₂⁴	1	16	yes	—
235	C₂×D₁₇₂	C₂⁴	1	8	yes	—
236	C₂×D₁₇₂	C₂⁴	1	16	yes	—
237	C₂×D₁₇₂	C₂⁴	1	4	yes	—
238	C₂×C₄×D₄₃	—	2	4	no	—
239	C₂×C₄×D₄₃	—	2	8	no	—
240	C₂×C₄×D₄₃	—	4	4	no	—
241	C₂×C₄×D₄₃	—	4	8	no	—
242	C₂×C₄×D₄₃	—	4	8	no	—
243	C₂×C₄×D₄₃	—	4	8	no	—
244	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
245	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
246	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
247	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
248	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
249	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
250	C₂×Dic₈₆	—	4	2	no	—
251	C₂×Dic₈₆	—	4	4	no	—
252	C₂×Dic₈₆	—	4	4	no	—
253	C₂×Dic₈₆	C₂⁴	1	8	yes	—
254	C₂×Dic₈₆	C₂⁴	1	4	yes	—
255	C₂×Dic₈₆	C₂⁴	1	8	yes	—
256	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
257	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
258	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
259	C₄⋊C₄×C₄₃	C₂⁴	1	16	yes	—
260	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
261	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
262	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
263	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
264	C₄²×C₄₃	C₂⁴	1	4	yes	—
265	C₄²×C₄₃	C₂⁴	1	8	yes	—
266	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
267	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
268	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
269	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
270	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
271	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
272	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
273	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
274	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
275	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
276	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
277	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
278	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
279	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
280	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
281	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
282	C₄×Dic₄₃	C₂⁴	1	4	yes	—
283	C₄×Dic₄₃	C₂⁴	1	8	yes	—
284	C₄×Dic₄₃	C₂⁴	1	8	yes	—
285	C₄×Dic₄₃	C₂⁴	1	16	yes	—
286	C₂³×C₄₃	—	2	4	no	—
287	C₂³×C₄₃	—	2	8	no	—
288	C₂³×C₄₃	C₂⁵	1	4	yes	—
289	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
290	C₂²×D₄₃	—	2	4	no	—
291	C₂²×D₄₃	—	2	8	no	—
292	C₂²×D₄₃	—	2	4	no	—
293	C₂²×D₄₃	—	2	8	no	—
294	C₂²×D₄₃	—	2	8	no	—
295	C₂²×D₄₃	—	2	8	no	—
296	C₂²×D₄₃	—	2	16	no	—
297	C₂²×D₄₃	—	4	8	no	—
298	C₂²×D₄₃	—	4	16	no	—
299	C₂²×D₄₃	—	4	16	no	—
300	C₂²×D₄₃	—	8	16	no	—
301	C₂²×D₄₃	—	8	16	no	—
302	C₂²×D₄₃	H(5,𝔽₂)	1	4	yes	—
303	C₂²×D₄₃	C₂⁵	1	4	yes	—
304	C₂²×D₄₃	C₂⁵	1	8	yes	—
305	C₂²×D₄₃	C₂⁵	1	2	yes	—
306	Q₈×C₄₃	—	4	4	no	—
307	Q₈×C₄₃	—	4	8	no	—
308	D₄×C₄₃	—	4	4	no	—
309	C₂×C₄×C₄₃	—	2	2	no	—
310	C₂×C₄×C₄₃	—	2	4	no	—
311	C₂×C₄×C₄₃	—	2	8	no	—
312	C₂×C₄×C₄₃	—	2	4	no	—
313	C₂×C₄×C₄₃	—	2	8	no	—
314	C₂×C₄×C₄₃	—	4	8	no	—
315	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
316	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
317	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
318	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
319	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
320	C₂²⋊D₄₃	—	4	8	no	—
321	C₂²⋊D₄₃	—	4	16	no	—
322	C₂×Dic₄₃	—	2	4	no	—
323	C₂×Dic₄₃	—	2	2	no	—
324	C₂×Dic₄₃	—	2	8	no	—
325	C₂×Dic₄₃	—	2	4	no	—
326	C₂×Dic₄₃	C₂⁵	1	4	yes	—
327	C₂×Dic₄₃	C₂⁵	1	2	yes	—
328	C₂×Dic₄₃	C₂⁵	1	8	yes	—
329	C₂×Dic₄₃	C₂⁵	1	4	yes	—
330	D₁₇₂	—	2	32	no	—
331	D₁₇₂	—	4	16	no	—
332	D₁₇₂	—	4	8	no	—
333	D₁₇₂	—	4	16	no	—
334	D₁₇₂	—	4	4	no	—
335	D₁₇₂	—	4	8	no	—
336	C₄×D₄₃	—	2	8	no	—
337	C₄×D₄₃	—	2	16	no	—
338	C₄×D₄₃	—	4	16	no	—
339	C₄×D₄₃	—	4	8	no	—
340	C₄×D₄₃	—	4	16	no	—
341	C₄×D₄₃	—	4	16	no	—
342	Dic₈₆	—	4	8	no	—
343	Dic₈₆	—	4	4	no	—
344	Dic₈₆	—	4	8	no	—
345	C₂×#3545	—	43	1	no	maximal, Sylow
346	C₂²×C₄₃	—	2	4	no	—
347	C₂²×C₄₃	—	2	8	no	—
348	C₂²×C₄₃	—	4	8	no	—
349	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
350	C₂²×C₄₃	#585	1	4	yes	—
351	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
352	C₂×D₄₃	—	2	4	no	—
353	C₂×D₄₃	—	2	8	no	—
354	C₂×D₄₃	—	2	4	no	—
355	C₂×D₄₃	—	2	8	no	—
356	C₂×D₄₃	—	2	8	no	—
357	C₂×D₄₃	—	2	8	no	—
358	C₂×D₄₃	—	2	8	no	—
359	C₂×D₄₃	—	4	16	no	—
360	C₂×D₄₃	—	4	8	no	—
361	C₂×D₄₃	—	8	16	no	—
362	C₂×D₄₃	—	8	16	no	—
363	C₂×D₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
364	C₄×C₄₃	—	2	2	no	—
365	C₄×C₄₃	—	2	4	no	—
366	C₄×C₄₃	—	2	8	no	—
367	C₄×C₄₃	—	2	4	no	—
368	C₄×C₄₃	—	2	8	no	—
369	Dic₄₃	—	2	4	no	—
370	Dic₄₃	—	2	2	no	—
371	Dic₄₃	—	2	8	no	—
372	Dic₄₃	—	2	4	no	—
373	#3545	—	43	32	no	—
374	C₂×#563	D₄₃	1	1	yes	characteristic, complemented
375	C₂×#562	—	43	2	no	—
376	C₂×H(3,𝔽₄)	—	43	1	no	—
377	C₂×#555	—	43	2	no	—
378	C₂×#551	—	43	4	no	—
379	C₂×#551	—	43	2	no	—
380	C₂×#546	—	43	4	no	—
381	C₂×#542	—	43	4	no	—
382	C₂×#538	—	43	4	no	—
383	C₂×#536	—	43	2	no	—
384	C₂×#534	—	43	2	no	—
385	C₂×#529	—	43	2	no	—
386	C₂²×#124	—	43	1	no	—
387	C₂×C₄₃	—	4	4	no	—
388	C₂×C₄₃	#3545	1	4	yes	complemented
389	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄₃	C₂×#585	1	2	yes	—
391	D₄₃	—	2	4	no	—
392	D₄₃	—	4	4	no	—
393	D₄₃	—	4	8	no	—
394	C₂²×#41	—	43	2	no	—
395	C₂³×Q₈	—	43	1	no	—
396	C₂³×D₄	—	43	1	no	—
397	C₂³×D₄	—	43	2	no	—
398	#563	C₂×D₄₃	1	16	yes	complemented
399	#562	—	43	32	no	—
400	H(3,𝔽₄)	—	43	16	no	—
401	#555	—	43	32	no	—
402	#551	—	43	64	no	—
403	#551	—	43	32	no	—
404	#546	—	43	64	no	—
405	#542	—	43	64	no	—
406	#538	—	43	64	no	—
407	#536	—	43	32	no	—
408	#534	—	43	32	no	—
409	C₂×C₄⋊Q₈	—	43	2	no	—
410	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	complemented
411	#529	—	43	32	no	—
412	C₂×#126	—	43	4	no	—
413	C₂×#126	—	43	4	no	—
414	C₂×#126	C₂×D₄₃	1	4	yes	complemented
415	C₂×#125	C₂×D₄₃	1	2	yes	complemented
416	C₂×#124	—	43	1	no	—
417	C₂×#124	—	43	2	no	—
418	C₂×#124	—	43	4	no	—
419	C₂×#124	—	43	1	no	—
420	C₂×#124	—	43	16	no	—
421	C₂×#124	—	43	4	no	—
422	C₂×#124	—	43	4	no	—
423	C₂×#124	—	43	1	no	—
424	C₂×#124	—	43	2	no	—
425	C₂×#124	—	43	2	no	—
426	C₂×#124	C₂×D₄₃	1	1	yes	characteristic
427	C₂×#123	—	43	2	no	—
428	C₂×#123	—	43	4	no	—
429	C₂×#123	—	43	4	no	—
430	C₂×#123	—	43	4	no	—
431	C₂×#123	—	43	4	no	—
432	C₂×#123	—	43	4	no	—
433	C₂×#123	C₂×D₄₃	1	2	yes	—
434	C₂×C₂²⋊Q₈	—	43	4	no	—
435	C₂×C₂²⋊Q₈	—	43	4	no	—
436	C₂×C₂²⋊Q₈	—	43	4	no	—
437	C₂×C₂²⋊Q₈	—	43	2	no	—
438	C₂×C₂²⋊Q₈	C₂×D₄₃	1	4	yes	complemented
439	C₂×#121	—	43	2	no	—
440	C₂×#121	—	43	4	no	—
441	C₂×#121	—	43	4	no	—
442	C₂×#121	—	43	4	no	—
443	C₂×#121	—	43	4	no	—
444	C₂×#120	—	43	2	no	—
445	C₂×#120	—	43	4	no	—
446	C₂×#120	—	43	2	no	—
447	C₂×#120	—	43	4	no	—
448	C₂×C₄×Q₈	—	43	2	no	—
449	C₂×C₄×D₄	—	43	4	no	—
450	C₂×C₄×D₄	—	43	2	no	—
451	C₂×C₄×D₄	—	43	4	no	—
452	C₂×C₄×D₄	—	43	4	no	—
453	C₂×#117	—	43	4	no	—
454	C₂×#117	—	43	4	no	—
455	C₂×#117	—	43	2	no	—
456	C₂²×C₂²⋊C₄	—	43	4	no	—
457	C₂²×C₂²⋊C₄	—	43	2	no	—
458	C₂²×C₂²⋊C₄	—	43	4	no	—
459	C₂²×C₄²	—	43	1	no	—
460	C₄₃	C₂×#3545	1	1	yes	characteristic, complemented, Sylow
461	C₂⁵	—	43	2	no	—
462	C₂⁵	—	43	2	no	—
463	C₂×#41	—	43	16	no	—
464	C₂×#41	—	172	8	no	—
465	C₂²×Q₈	—	43	8	no	—
466	C₂²×Q₈	—	43	2	no	—
467	C₂²×Q₈	—	43	1	no	—
468	C₂²×Q₈	—	43	2	no	—
469	C₂²×Q₈	—	172	4	no	—
470	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
471	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
472	C₂²×D₄	—	43	4	no	—
473	C₂²×D₄	—	43	2	no	—
474	C₂²×D₄	—	43	8	no	—
475	C₂²×D₄	—	43	4	no	—
476	C₂²×D₄	—	43	4	no	—
477	C₂²×D₄	—	43	2	no	—
478	C₂²×D₄	—	43	2	no	—
479	C₂²×D₄	—	43	4	no	—
480	C₂²×D₄	—	43	1	no	—
481	C₂²×D₄	—	43	16	no	—
482	C₂²×D₄	—	172	8	no	—
483	C₂²×D₄	—	172	4	no	—
484	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
485	C₂³×C₄	—	43	2	no	—
486	C₂³×C₄	—	43	1	no	—
487	C₂³×C₄	—	43	2	no	—
488	C₂³×C₄	—	43	4	no	—
489	C₂³×C₄	—	43	4	no	—
490	C₂³×C₄	—	43	4	no	—
491	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
492	C₄⋊Q₈	—	43	16	no	—
493	C₄⋊Q₈	C₂²×D₄₃	1	16	yes	complemented
494	#126	—	43	32	no	—
495	#126	—	43	32	no	—
496	#126	C₂²×D₄₃	1	32	yes	complemented
497	#125	C₂²×D₄₃	1	16	yes	complemented
498	#124	—	43	8	no	—
499	#124	—	43	16	no	—
500	#124	—	43	32	no	—
501	#124	—	43	8	no	—
502	#124	—	43	32	no	—
503	#124	—	43	32	no	—
504	#124	—	43	8	no	—
505	#124	—	43	16	no	—
506	#124	—	43	16	no	—
507	#124	C₂²×D₄₃	1	8	yes	—
508	#123	—	43	16	no	—
509	#123	—	43	32	no	—
510	#123	—	43	32	no	—
511	#123	—	43	32	no	—
512	#123	—	43	32	no	—
513	#123	—	43	32	no	—
514	#123	C₂²×D₄₃	1	16	yes	—
515	C₂²⋊Q₈	—	43	16	no	—
516	C₂²⋊Q₈	—	43	32	no	—
517	C₂²⋊Q₈	—	43	32	no	—
518	C₂²⋊Q₈	—	43	32	no	—
519	C₂²⋊Q₈	C₂²×D₄₃	1	32	yes	complemented
520	#121	—	43	16	no	—
521	#121	—	43	32	no	—
522	#121	—	43	32	no	—
523	#121	—	43	32	no	—
524	#121	—	43	32	no	—
525	#120	—	43	16	no	—
526	#120	—	43	16	no	—
527	#120	—	43	32	no	—
528	#120	—	43	32	no	—
529	C₄×Q₈	—	43	16	no	—
530	C₄×D₄	—	43	32	no	—
531	C₄×D₄	—	43	16	no	—
532	C₄×D₄	—	43	32	no	—
533	C₄×D₄	—	43	32	no	—
534	#117	—	43	32	no	—
535	#117	—	43	32	no	—
536	#117	—	43	16	no	—
537	C₂×C₄⋊C₄	—	43	4	no	—
538	C₂×C₄⋊C₄	—	43	4	no	—
539	C₂×C₄⋊C₄	—	43	4	no	—
540	C₂×C₄⋊C₄	—	43	4	no	—
541	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
542	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
543	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
544	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
545	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
546	C₂×C₂²⋊C₄	—	43	4	no	—
547	C₂×C₂²⋊C₄	—	43	2	no	—
548	C₂×C₂²⋊C₄	—	43	4	no	—
549	C₂×C₂²⋊C₄	—	43	4	no	—
550	C₂×C₂²⋊C₄	—	43	4	no	—
551	C₂×C₂²⋊C₄	—	43	4	no	—
552	C₂×C₂²⋊C₄	—	43	4	no	—
553	C₂×C₂²⋊C₄	—	43	4	no	—
554	C₂×C₂²⋊C₄	—	43	4	no	—
555	C₂×C₂²⋊C₄	—	43	4	no	—
556	C₂×C₂²⋊C₄	—	43	4	no	—
557	C₂×C₂²⋊C₄	—	43	4	no	—
558	C₂×C₂²⋊C₄	—	43	32	no	—
559	C₂×C₂²⋊C₄	—	43	16	no	—
560	C₂×C₂²⋊C₄	—	43	32	no	—
561	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
562	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
563	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
564	C₂×C₄²	—	43	1	no	—
565	C₂×C₄²	—	43	2	no	—
566	C₂×C₄²	—	43	4	no	—
567	C₂×C₄²	—	43	2	no	—
568	C₂×C₄²	—	43	8	no	—
569	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
570	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
571	C₂⁴	—	43	1	no	—
572	C₂⁴	—	43	4	no	—
573	C₂⁴	—	43	2	no	—
574	C₂⁴	—	43	8	no	—
575	C₂⁴	—	43	8	no	—
576	C₂⁴	—	86	8	no	—
577	C₂⁴	—	172	4	no	—
578	C₂⁴	—	172	8	no	—
579	C₂⁴	—	172	8	no	—
580	C₂⁴	C₂³×D₄₃	1	2	yes	—
581	#41	—	172	32	no	—
582	C₂×Q₈	—	4	2	no	—
583	C₂×Q₈	—	4	4	no	—
584	C₂×Q₈	—	43	8	no	—
585	C₂×Q₈	—	43	4	no	—
586	C₂×Q₈	—	43	8	no	—
587	C₂×Q₈	—	172	2	no	—
588	C₂×Q₈	—	172	4	no	—
589	C₂×Q₈	—	172	4	no	—
590	C₂×Q₈	—	172	16	no	—
591	C₂×Q₈	C₂³×D₄₃	1	8	yes	—
592	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
593	C₂×D₄	—	4	2	no	—
594	C₂×D₄	—	43	16	no	—
595	C₂×D₄	—	43	8	no	—
596	C₂×D₄	—	43	16	no	—
597	C₂×D₄	—	43	16	no	—
598	C₂×D₄	—	43	8	no	—
599	C₂×D₄	—	43	8	no	—
600	C₂×D₄	—	43	16	no	—
601	C₂×D₄	—	43	4	no	—
602	C₂×D₄	—	86	16	no	—
603	C₂×D₄	—	172	8	no	—
604	C₂×D₄	—	172	2	no	—
605	C₂×D₄	—	172	4	no	—
606	C₂×D₄	—	172	8	no	—
607	C₂×D₄	—	172	4	no	—
608	C₂×D₄	—	172	32	no	—
609	C₂×D₄	—	172	16	no	—
610	C₂×D₄	—	172	4	no	—
611	C₂×D₄	—	172	8	no	—
612	C₂×D₄	C₂³×D₄₃	1	4	yes	—
613	C₂²×C₄	—	4	4	no	—
614	C₂²×C₄	—	43	2	no	—
615	C₂²×C₄	—	43	4	no	—
616	C₂²×C₄	—	43	1	no	—
617	C₂²×C₄	—	43	2	no	—
618	C₂²×C₄	—	43	4	no	—
619	C₂²×C₄	—	43	8	no	—
620	C₂²×C₄	—	43	8	no	—
621	C₂²×C₄	—	43	16	no	—
622	C₂²×C₄	—	43	16	no	—
623	C₂²×C₄	—	43	16	no	—
624	C₂²×C₄	—	86	4	no	—
625	C₂²×C₄	—	86	8	no	—
626	C₂²×C₄	—	172	8	no	—
627	C₂²×C₄	—	172	8	no	—
628	C₂²×C₄	—	172	8	no	—
629	C₂²×C₄	—	172	4	no	—
630	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
631	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
632	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
633	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
634	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
635	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
636	C₄⋊C₄	—	43	16	no	—
637	C₄⋊C₄	—	43	16	no	—
638	C₄⋊C₄	—	43	16	no	—
639	C₄⋊C₄	—	43	16	no	—
640	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
641	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
642	C₄⋊C₄	C₂³×D₄₃	1	16	yes	—
643	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
644	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
645	C₂²⋊C₄	—	43	16	no	—
646	C₂²⋊C₄	—	43	8	no	—
647	C₂²⋊C₄	—	43	16	no	—
648	C₂²⋊C₄	—	43	16	no	—
649	C₂²⋊C₄	—	43	16	no	—
650	C₂²⋊C₄	—	43	16	no	—
651	C₂²⋊C₄	—	43	16	no	—
652	C₂²⋊C₄	—	43	16	no	—
653	C₂²⋊C₄	—	43	16	no	—
654	C₂²⋊C₄	—	43	16	no	—
655	C₂²⋊C₄	—	43	16	no	—
656	C₂²⋊C₄	—	43	16	no	—
657	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
658	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
659	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
660	C₄²	—	43	4	no	—
661	C₄²	—	43	8	no	—
662	C₄²	—	43	8	no	—
663	C₄²	—	43	16	no	—
664	C₄²	C₂³×D₄₃	1	4	yes	—
665	C₄²	C₂³×D₄₃	1	8	yes	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	8	no	—
668	C₂³	—	43	4	no	—
669	C₂³	—	43	2	no	—
670	C₂³	—	43	8	no	—
671	C₂³	—	43	4	no	—
672	C₂³	—	86	16	no	—
673	C₂³	—	86	4	no	—
674	C₂³	—	86	8	no	—
675	C₂³	—	86	4	no	—
676	C₂³	—	86	8	no	—
677	C₂³	—	86	8	no	—
678	C₂³	—	86	8	no	—
679	C₂³	—	344	16	no	—
680	C₂³	—	344	16	no	—
681	C₂³	—	172	8	no	—
682	C₂³	—	172	16	no	—
683	C₂³	—	172	16	no	—
684	C₂³	C₂⁴×D₄₃	1	4	yes	—
685	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
686	Q₈	—	4	4	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	172	4	no	—
689	Q₈	—	172	8	no	—
690	Q₈	—	172	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	86	32	no	—
693	D₄	—	172	16	no	—
694	D₄	—	172	4	no	—
695	D₄	—	172	8	no	—
696	D₄	—	172	16	no	—
697	D₄	—	172	8	no	—
698	D₄	—	172	8	no	—
699	D₄	—	172	16	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	43	4	no	—
707	C₂×C₄	—	43	8	no	—
708	C₂×C₄	—	43	2	no	—
709	C₂×C₄	—	43	4	no	—
710	C₂×C₄	—	86	8	no	—
711	C₂×C₄	—	86	16	no	—
712	C₂×C₄	—	86	4	no	—
713	C₂×C₄	—	86	2	no	—
714	C₂×C₄	—	86	4	no	—
715	C₂×C₄	—	86	8	no	—
716	C₂×C₄	—	172	16	no	—
717	C₂×C₄	—	172	16	no	—
718	C₂×C₄	—	172	16	no	—
719	C₂×C₄	—	172	8	no	—
720	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
721	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
722	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
723	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
724	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
725	C₂²	—	2	4	no	—
726	C₂²	—	2	8	no	—
727	C₂²	—	4	8	no	—
728	C₂²	—	43	4	no	—
729	C₂²	—	86	4	no	—
730	C₂²	—	86	8	no	—
731	C₂²	—	86	8	no	—
732	C₂²	—	86	4	no	—
733	C₂²	—	86	8	no	—
734	C₂²	—	86	8	no	—
735	C₂²	—	86	8	no	—
736	C₂²	—	344	16	no	—
737	C₂²	—	344	16	no	—
738	C₂²	—	172	16	no	—
739	C₂²	—	172	8	no	—
740	C₂²	H(5,𝔽₂)×D₄₃	1	2	yes	—
741	C₂²	#14583736	1	4	yes	—
742	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
743	C₄	—	2	8	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	8	no	—
747	C₄	—	2	4	no	—
748	C₄	—	86	4	no	—
749	C₄	—	86	2	no	—
750	C₄	—	86	4	no	—
751	C₄	—	86	8	no	—
752	C₂	—	4	4	no	—
753	C₂	—	86	4	no	—
754	C₂	—	172	8	no	—
755	C₂	—	172	4	no	—
756	C₂	#19148953	1	4	yes	direct product factor
757	C₂	C₂×H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
758	C₂	C₂×#14583736	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#563	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#563	D₄₃
hypocenter	C₄₃	C₂×#3545
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#563

Complements

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

N	H ≅ G/N	type
1. #19148953	C₂	direct (N × H)
2. C₂×#14583647	C₂	semidirect
3. C₂×#14583641	C₂	semidirect
4. C₂×#14583615	C₂	semidirect
5. C₂×#14583577	C₂	semidirect
6. C₂×#14583574	C₂	semidirect
7. C₂×#14583540	C₂	semidirect
8. C₂×#14583519	C₂	semidirect
9. C₂×#14583488	C₂	semidirect
10. C₂×#14583474	C₂	semidirect
11. C₂×#14583460	C₂	semidirect
12. C₂×#14583434	C₂	semidirect
13. C₂×#124×D₄₃	C₂	semidirect
14. C₂×C₄₃×#563	C₂	semidirect
16. C₂²×Q₈×D₄₃	C₂²	semidirect
17. C₂³×D₁₇₂	C₂²	semidirect
19. #14583647	C₂²	semidirect
20. #14583641	C₂²	semidirect
21. #14583615	C₂²	semidirect
22. #14583577	C₂²	semidirect
23. #14583574	C₂²	semidirect
24. #14583540	C₂²	semidirect
25. #14583519	C₂²	semidirect
26. #14583488	C₂²	semidirect
27. #14583474	C₂²	semidirect
28. #14583460	C₂²	semidirect
29. C₂×#13063323	C₂²	semidirect
30. #14583434	C₂²	semidirect
31. C₂×#13063320	C₂²	semidirect
32. C₂×#13063318	C₂²	semidirect
33. C₂×#13063314	C₂²	semidirect
34. C₂×#13063314	C₂²	semidirect
35. C₂×#13063314	C₂²	semidirect
36. C₂×#13063313	C₂²	semidirect
37. C₂×#13063313	C₂²	semidirect
38. C₂×#13063313	C₂²	semidirect
40. C₂×#13063311	C₂²	semidirect
41. C₂×#13063311	C₂²	semidirect
42. #124×D₄₃	C₂²	semidirect
43. C₂×#13063310	C₂²	semidirect
44. C₂×#13063310	C₂²	semidirect
45. C₂×#13063310	C₂²	semidirect
46. C₂×#13063310	C₂²	semidirect
47. C₂×#13063308	C₂²	semidirect
48. C₂×#13063307	C₂²	semidirect
49. C₂×#13063305	C₂²	semidirect
50. C₂×#13063303	C₂²	semidirect
51. C₂×#13063303	C₂²	semidirect
52. C₂×#13063303	C₂²	semidirect
54. C₂×#13063300	C₂²	semidirect
55. C₂×#13063300	C₂²	semidirect
56. C₂×#13063300	C₂²	semidirect
59. C₂×#13063295	C₂²	semidirect
60. C₂×#13063295	C₂²	semidirect
62. C₂×#13063290	C₂²	semidirect
63. C₂×C₄×D₁₇₂	C₂²	semidirect
64. C₂×#13063287	C₂²	semidirect
65. C₂×#13063287	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
67. C₂×#13063283	C₂²	semidirect
68. C₂×#13063283	C₂²	semidirect
69. C₂×#13063282	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
72. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
73. C₂×C₄²×D₄₃	C₂²	semidirect
74. C₄₃×#563	C₂²	semidirect
75. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
76. C₂×#126×C₄₃	C₂²	semidirect
77. C₂×#125×C₄₃	C₂²	semidirect
80. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
89. C₂×Q₈×D₄₃	C₂³	semidirect
97. C₂²×D₁₇₂	C₂³	semidirect
108. #13063323	C₂³	semidirect
109. #13063320	C₂³	semidirect
110. #13063318	C₂³	semidirect
111. #13063314	C₂³	semidirect
112. #13063314	C₂³	semidirect
113. #13063314	C₂³	semidirect
114. #13063313	C₂³	semidirect
115. #13063313	C₂³	semidirect
116. #13063313	C₂³	semidirect
118. #13063311	C₂³	semidirect
119. #13063311	C₂³	semidirect
120. #13063310	C₂³	semidirect
121. #13063310	C₂³	semidirect
122. #13063310	C₂³	semidirect
123. #13063310	C₂³	semidirect
124. #13063308	C₂³	semidirect
125. #13063307	C₂³	semidirect
126. #13063305	C₂³	semidirect
127. #13063303	C₂³	semidirect
128. #13063303	C₂³	semidirect
129. #13063303	C₂³	semidirect
131. #13063300	C₂³	semidirect
132. #13063300	C₂³	semidirect
133. #13063300	C₂³	semidirect
136. #13063295	C₂³	semidirect
137. #13063295	C₂³	semidirect
139. #13063290	C₂³	semidirect
140. C₄×D₁₇₂	C₂³	semidirect
141. #13063287	C₂³	semidirect
142. #13063287	C₂³	semidirect
143. C₄×C₂²⋊D₄₃	C₂³	semidirect
144. #13063283	C₂³	semidirect
145. #13063283	C₂³	semidirect
146. #13063282	C₂³	semidirect
163. C₂²⋊C₄×D₄₃	C₂³	semidirect
164. C₂²⋊C₄×D₄₃	C₂³	semidirect
165. C₂²⋊C₄×D₄₃	C₂³	semidirect
170. C₄²×D₄₃	C₂³	semidirect
175. C₄⋊Q₈×C₄₃	C₂³	semidirect
176. #126×C₄₃	C₂³	semidirect
177. #125×C₄₃	C₂³	semidirect
180. C₂²⋊Q₈×C₄₃	C₂³	semidirect
374. C₂×#563	D₄₃	semidirect
388. C₂×C₄₃	#3545	semidirect
398. #563	C₂×D₄₃	semidirect
410. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
414. C₂×#126	C₂×D₄₃	semidirect
415. C₂×#125	C₂×D₄₃	semidirect
438. C₂×C₂²⋊Q₈	C₂×D₄₃	semidirect
460. C₄₃	C₂×#3545	semidirect
493. C₄⋊Q₈	C₂²×D₄₃	semidirect
496. #126	C₂²×D₄₃	semidirect
497. #125	C₂²×D₄₃	semidirect
519. C₂²⋊Q₈	C₂²×D₄₃	semidirect
756. C₂	#19148953	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148953	2
C₂×#14583647	2
C₂×#14583641	2
C₂×#14583615	2
C₂×#14583577	2
C₂×#14583574	2
C₂×#14583540	2
C₂×#14583519	2
C₂×#14583488	2
C₂×#14583474	2
C₂×#14583460	2
C₂×#14583434	2
C₂×#124×D₄₃	2
C₂×C₄₃×#563	2
C₂×#3545	43

Subgroups — C2×#19148953 #26004357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148953 #26004357