Subgroups — C₂²×#14583433 #26003278

Order 11008.

8670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂³×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂⁴
prime radical	C₂²×#13063299	C₂
hypercenter	C₂³×C₄²	D₄₃
hypocenter	C₄₃	C₂²×#529
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#14583433	C₂	direct (N × H)
2. C₂²×#13063319	C₂	semidirect
3. C₂²×#13063317	C₂	semidirect
4. C₂²×#13063313	C₂	semidirect
5. C₂²×#13063308	C₂	semidirect
6. C₂²×#13063304	C₂	semidirect
8. C₂²×C₄×Dic₈₆	C₂	semidirect
9. C₂²×C₄×D₁₇₂	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₄₃	C₂	semidirect
11. C₂²×#13063282	C₂	semidirect
12. C₂³×C₄²×C₄₃	C₂	semidirect
17. #14583433	C₂²	direct (N × H)
18. C₂×#13063319	C₂²	semidirect
19. C₂×#13063317	C₂²	semidirect
20. C₂×#13063313	C₂²	semidirect
21. C₂×#13063308	C₂²	semidirect
22. C₂×#13063304	C₂²	semidirect
24. C₂×C₄×Dic₈₆	C₂²	semidirect
25. C₂×C₄×D₁₇₂	C₂²	semidirect
26. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
27. C₂×#13063282	C₂²	semidirect
47. C₂²×C₄²×C₄₃	C₂²	semidirect
60. #13063319	C₂³	semidirect
61. #13063317	C₂³	semidirect
62. #13063313	C₂³	semidirect
63. #13063308	C₂³	semidirect
64. #13063304	C₂³	semidirect
66. C₄×Dic₈₆	C₂³	semidirect
67. C₄×D₁₇₂	C₂³	semidirect
68. C₄×C₂²⋊D₄₃	C₂³	semidirect
69. #13063282	C₂³	semidirect
99. C₂×C₄²×C₄₃	C₂³	semidirect
200. C₂²×C₄₃	#529	semidirect
230. C₂³×C₄²	D₄₃	semidirect
232. C₂×C₄₃	C₂×#529	semidirect
271. C₂²×C₄²	C₂×D₄₃	semidirect
272. C₄₃	C₂²×#529	semidirect
324. C₂×C₄²	C₂²×D₄₃	semidirect
428. C₂²	#14583433	direct (N × H)
445. C₂	C₂×#14583433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#14583433	2
C₂²×#13063319	2
C₂²×#13063317	2
C₂²×#13063313	2
C₂²×#13063308	2
C₂²×#13063304	2
C₂²×#13063299	2
C₂²×C₄×Dic₈₆	2
C₂²×C₄×D₁₇₂	2
C₂²×C₄×C₂²⋊D₄₃	2
C₂²×#13063282	2
C₂³×C₄²×C₄₃	2
C₂²×#529	43

Subgroups — C22×#14583433 #26003278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583433 #26003278