Subgroups — C₂×C₄×#67042 #15660376

Order 2816.

12378 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67042	C₂	1	1	yes	maximal, characteristic
2	C₄×#67042	C₂	1	32	yes	maximal, direct product factor
3	C₂×#10623358	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10623105	C₂	1	2	yes	maximal, complemented
5	C₂×#10623054	C₂	1	3	yes	maximal, complemented
6	C₂×#10623052	C₂	1	3	yes	maximal, complemented
7	C₂×#10623076	C₂	1	6	yes	maximal, complemented
8	C₂×C₄×#4343	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#4339	C₂	1	3	yes	maximal, complemented
10	C₂²×C₄×D₄₄	C₂	1	3	yes	maximal, complemented
11	C₂×C₄×D₄×D₁₁	C₂	1	6	yes	maximal, complemented
12	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂×#67042	C₄	1	32	yes	direct product factor
15	C₂×#67042	C₂²	1	16	yes	—
16	C₂²×#4343	C₂²	1	2	yes	—
17	C₂²×D₄×D₁₁	C₂²	1	6	yes	—
18	C₂²×#4339	C₂²	1	3	yes	—
19	C₂³×D₄₄	C₂²	1	3	yes	—
20	C₂³×C₄×D₁₁	C₂²	1	6	yes	complemented
21	C₄×C₁₁×#41	C₂²	1	16	yes	complemented
22	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄×D₄×C₁₁	C₂²	1	3	yes	complemented
25	C₂×C₄×D₄×C₁₁	C₂²	1	3	yes	complemented
26	C₂×C₁₁×#117	C₂²	1	3	yes	complemented
27	C₂²×C₄²×C₁₁	C₂²	1	3	yes	complemented
28	#10623358	C₂²	1	16	yes	complemented
29	C₂×Q₈×Dic₁₁	C₂²	1	2	yes	complemented
30	C₂×D₄×Dic₁₁	C₂²	1	6	yes	complemented
31	C₂×C₄×C₂²⋊D₁₁	C₂²	1	6	yes	complemented
32	C₂×C₄×C₂²⋊D₁₁	C₂²	1	6	yes	complemented
33	C₂²×(C₂×D₁₁)⋊C₄	C₂²	1	6	yes	complemented
34	C₂×#66979	C₂²	1	3	yes	complemented
35	C₂²×C₄⋊Dic₁₁	C₂²	1	3	yes	complemented
36	#10623105	C₂²	1	32	yes	complemented
37	C₄×#4343	C₂²	1	32	yes	complemented
38	#10623076	C₂²	1	96	yes	complemented
39	C₄×D₄×D₁₁	C₂²	1	96	yes	complemented
40	#10623054	C₂²	1	48	yes	complemented
41	#10623052	C₂²	1	48	yes	complemented
42	C₂×#66946	C₂²	1	6	yes	complemented
43	C₂×#66946	C₂²	1	6	yes	complemented
44	C₂×#66945	C₂²	1	6	yes	complemented
45	C₂×C₄⋊C₄×D₁₁	C₂²	1	6	yes	complemented
46	C₂×(C₂²⋊D₁₁)⋊C₄	C₂²	1	12	yes	complemented
47	C₂×C₂²⋊C₄×D₁₁	C₂²	1	12	yes	complemented
48	C₄×#4339	C₂²	1	48	yes	complemented
49	C₂×C₄×D₄₄	C₂²	1	6	yes	complemented
50	C₂×C₄×D₄₄	C₂²	1	3	yes	complemented
51	C₂×C₄×D₄₄	C₂²	1	6	yes	complemented
52	C₂×C₄×D₄₄	C₂²	1	6	yes	complemented
53	C₂×C₄×D₄₄	C₂²	1	3	yes	complemented
54	C₂×C₄×D₄₄	C₂²	1	48	yes	complemented
55	C₂×#66925	C₂²	1	6	yes	complemented
56	C₂×C₄²×D₁₁	C₂²	1	6	yes	complemented
57	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₂₂	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₁	C₂³	1	6	yes	—
60	C₂×C₁₁×#41	C₂×C₄	1	16	yes	complemented
61	C₂×C₁₁×#41	C₂³	1	8	yes	—
62	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₁	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
65	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
66	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
67	C₂²×C₂²⋊D₁₁	C₂³	1	6	yes	—
68	C₂³×Dic₁₁	C₂³	1	6	yes	—
69	#67042	C₂×C₄	1	256	yes	direct product factor
70	C₂×#4343	C₂×C₄	1	32	yes	complemented
71	C₂×#4343	C₂³	1	16	yes	—
72	C₂×D₄×D₁₁	C₂×C₄	1	96	yes	complemented
73	C₂×D₄×D₁₁	C₂³	1	48	yes	—
74	C₂×#4339	C₂×C₄	1	48	yes	complemented
75	C₂×#4339	C₂³	1	24	yes	—
76	C₂²×D₄₄	C₂×C₄	1	48	yes	complemented
77	C₂²×D₄₄	C₂³	1	3	yes	—
78	C₂²×D₄₄	C₂³	1	6	yes	—
79	C₂²×D₄₄	C₂³	1	24	yes	—
80	C₂²×C₄×D₁₁	—	4	24	no	—
81	C₂²×C₄×D₁₁	C₂³	1	6	yes	—
82	C₂²×C₄×D₁₁	C₂³	1	6	yes	—
83	C₂²×C₄×D₁₁	C₂³	1	12	yes	—
84	C₂²×C₄×D₁₁	C₂³	1	6	yes	—
85	C₂²×C₄×D₁₁	C₂³	1	48	yes	complemented
86	C₂²×Dic₂₂	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₁₁	C₂³	1	8	yes	complemented
88	C₄×Q₈×C₁₁	C₂³	1	8	yes	complemented
89	C₄×D₄×C₁₁	C₂³	1	24	yes	complemented
90	C₄×D₄×C₁₁	C₂³	1	24	yes	complemented
91	C₁₁×#117	C₂³	1	24	yes	complemented
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
94	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
95	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
97	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
98	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
99	C₂×C₄²×C₁₁	C₂³	1	24	yes	complemented
100	C₂×C₂²⋊Dic₁₁	C₂³	1	6	yes	—
101	Q₈×Dic₁₁	C₂³	1	16	yes	complemented
102	D₄×Dic₁₁	C₂³	1	48	yes	complemented
103	C₄×C₂²⋊D₁₁	C₂³	1	48	yes	complemented
104	C₄×C₂²⋊D₁₁	C₂³	1	48	yes	complemented
105	C₂×(C₂×D₁₁)⋊C₄	C₂³	1	6	yes	—
106	C₂×(C₂×D₁₁)⋊C₄	C₂³	1	6	yes	—
107	C₂×(C₂×D₁₁)⋊C₄	C₂³	1	12	yes	—
108	C₂×(C₂×D₁₁)⋊C₄	C₂³	1	48	yes	complemented
109	#66979	C₂³	1	24	yes	complemented
110	C₂×C₄⋊Dic₁₁	C₂³	1	3	yes	—
111	C₂×C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊Dic₁₁	C₂³	1	6	yes	—
113	C₂×C₄⋊Dic₁₁	C₂³	1	24	yes	complemented
114	C₂×Dic₁₁⋊C₄	C₂³	1	2	yes	—
115	C₂×Dic₁₁⋊C₄	C₂³	1	6	yes	—
116	C₂×C₄×Dic₁₁	C₂³	1	2	yes	—
117	C₂×C₄×Dic₁₁	C₂³	1	6	yes	—
118	C₂×C₄×Dic₁₁	C₂³	1	6	yes	—
119	#66946	C₂³	1	48	yes	complemented
120	#66946	C₂³	1	48	yes	complemented
121	#66945	C₂³	1	48	yes	complemented
122	C₄⋊C₄×D₁₁	C₂³	1	48	yes	complemented
123	(C₂²⋊D₁₁)⋊C₄	C₂³	1	96	yes	complemented
124	C₂²⋊C₄×D₁₁	C₂³	1	96	yes	complemented
125	C₄×D₄₄	C₂³	1	24	yes	complemented
126	C₄×D₄₄	C₂³	1	48	yes	complemented
127	C₄×D₄₄	C₂³	1	48	yes	complemented
128	C₄×D₄₄	C₂³	1	48	yes	complemented
129	C₄×D₄₄	C₂³	1	24	yes	complemented
130	#66925	C₂³	1	48	yes	complemented
131	C₄²×D₁₁	C₂³	1	48	yes	complemented
132	C₄×Dic₂₂	C₂³	1	8	yes	complemented
133	C₄×Dic₂₂	C₂³	1	24	yes	complemented
134	C₂×C₄×H(5,𝔽₂)	—	11	1	no	maximal, Sylow
135	C₂⁴×C₁₁	C₂⁴	1	3	yes	—
136	C₂³×D₁₁	—	4	12	no	—
137	C₂³×D₁₁	—	4	12	no	—
138	C₂³×D₁₁	C₂²×C₄	1	48	yes	complemented
139	C₂³×D₁₁	C₂⁴	1	6	yes	—
140	C₂³×D₁₁	C₂⁴	1	24	yes	—
141	C₁₁×#41	C₂²×C₄	1	64	yes	complemented
142	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	complemented
143	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	complemented
145	C₂×D₄×C₁₁	C₂⁴	1	12	yes	—
146	C₂²×C₄×C₁₁	—	2	12	no	—
147	C₂²×C₄×C₁₁	—	4	6	no	—
148	C₂²×C₄×C₁₁	C₂²×C₄	1	24	yes	complemented
149	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
150	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
152	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
153	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
155	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
158	C₂×C₂²⋊D₁₁	C₂²×C₄	1	48	yes	complemented
159	C₂×C₂²⋊D₁₁	C₂⁴	1	24	yes	—
160	C₂²×Dic₁₁	—	4	12	no	—
161	C₂²×Dic₁₁	C₂⁴	1	2	yes	—
162	C₂²×Dic₁₁	C₂⁴	1	6	yes	—
163	C₂²×Dic₁₁	C₂⁴	1	24	yes	—
164	C₂²×Dic₁₁	C₂⁴	1	2	yes	—
165	#4343	C₂²×C₄	1	128	yes	complemented
166	D₄×D₁₁	C₂²×C₄	1	384	yes	complemented
167	#4339	C₂²×C₄	1	192	yes	complemented
168	C₂×D₄₄	C₂²×C₄	1	24	yes	complemented
169	C₂×D₄₄	C₂²×C₄	1	48	yes	complemented
170	C₂×D₄₄	C₂²×C₄	1	192	yes	complemented
171	C₂×D₄₄	C₂⁴	1	12	yes	—
172	C₂×D₄₄	C₂⁴	1	24	yes	—
173	C₂×C₄×D₁₁	—	2	24	no	—
174	C₂×C₄×D₁₁	—	4	24	no	—
175	C₂×C₄×D₁₁	—	4	12	no	—
176	C₂×C₄×D₁₁	—	4	96	no	—
177	C₂×C₄×D₁₁	C₂²×C₄	1	48	yes	complemented
178	C₂×C₄×D₁₁	C₂⁴	1	24	yes	—
179	C₂×C₄×D₁₁	C₂⁴	1	24	yes	—
180	C₂×C₄×D₁₁	C₂⁴	1	48	yes	—
181	C₂×C₄×D₁₁	C₂⁴	1	24	yes	—
182	C₂×Dic₂₂	C₂²×C₄	1	8	yes	complemented
183	C₂×Dic₂₂	C₂⁴	1	4	yes	—
184	C₁₁×C₄⋊C₄	C₂⁴	1	12	yes	—
185	C₁₁×C₄⋊C₄	C₂⁴	1	12	yes	—
186	C₁₁×C₂²⋊C₄	C₂⁴	1	24	yes	—
187	C₄²×C₁₁	C₂⁴	1	4	yes	—
188	C₄²×C₁₁	C₂⁴	1	12	yes	—
189	C₄²×C₁₁	C₂⁴	1	12	yes	—
190	C₄²×C₁₁	C₂⁴	1	12	yes	—
191	C₂²⋊Dic₁₁	C₂⁴	1	24	yes	—
192	(C₂×D₁₁)⋊C₄	C₂⁴	1	24	yes	—
193	(C₂×D₁₁)⋊C₄	C₂⁴	1	24	yes	—
194	(C₂×D₁₁)⋊C₄	C₂⁴	1	48	yes	—
195	C₄⋊Dic₁₁	C₂⁴	1	12	yes	—
196	C₄⋊Dic₁₁	C₂⁴	1	4	yes	—
197	C₄⋊Dic₁₁	C₂⁴	1	24	yes	—
198	Dic₁₁⋊C₄	C₂⁴	1	8	yes	—
199	Dic₁₁⋊C₄	C₂⁴	1	24	yes	—
200	C₄×Dic₁₁	C₂⁴	1	8	yes	—
201	C₄×Dic₁₁	C₂⁴	1	24	yes	—
202	C₄×Dic₁₁	C₂⁴	1	24	yes	—
203	C₂²×H(5,𝔽₂)	—	11	1	no	—
204	C₄×H(5,𝔽₂)	—	11	32	no	—
205	C₂×#520	—	11	1	no	—
206	C₂×#520	—	11	2	no	—
207	C₂×#520	—	11	3	no	—
208	C₂×#518	—	11	6	no	—
209	C₂×#518	—	11	3	no	—
210	C₂×C₄×#41	—	11	3	no	—
211	C₂×C₄×#41	—	11	2	no	—
212	C₂×C₄×#41	D₁₁	1	1	yes	characteristic, complemented
213	C₂²×C₄×D₄	—	11	3	no	—
214	C₂²×C₄×D₄	—	11	6	no	—
215	C₂³×C₁₁	—	2	6	no	—
216	C₂³×C₁₁	—	2	6	no	—
217	C₂³×C₁₁	C₂³×C₄	1	12	yes	—
218	C₂³×C₁₁	C₂⁵	1	6	yes	—
219	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
220	C₂²×D₁₁	—	2	12	no	—
221	C₂²×D₁₁	—	2	12	no	—
222	C₂²×D₁₁	—	4	24	no	—
223	C₂²×D₁₁	—	4	96	no	—
224	C₂²×D₁₁	—	4	24	no	—
225	C₂²×D₁₁	C₂³×C₄	1	24	yes	—
226	C₂²×D₁₁	C₂³×C₄	1	96	yes	complemented
227	C₂²×D₁₁	C₂⁵	1	12	yes	—
228	Q₈×C₁₁	C₂³×C₄	1	16	yes	complemented
229	D₄×C₁₁	C₂³×C₄	1	48	yes	complemented
230	C₂×C₄×C₁₁	—	2	6	no	—
231	C₂×C₄×C₁₁	—	2	6	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	24	no	—
234	C₂×C₄×C₁₁	—	4	12	no	—
235	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
236	C₂×C₄×C₁₁	C₂³×C₄	1	12	yes	—
237	C₂×C₄×C₁₁	C₂³×C₄	1	48	yes	complemented
238	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	complemented
239	C₂×C₄×C₁₁	C₂⁵	1	6	yes	—
240	C₂×C₄×C₁₁	C₂⁵	1	2	yes	—
241	C₂×C₄×C₁₁	C₂⁵	1	6	yes	—
242	C₂×C₄×C₁₁	C₂⁵	1	6	yes	—
243	C₂×C₄×C₁₁	C₂⁵	1	2	yes	—
244	C₂×C₄×C₁₁	C₂⁵	1	2	yes	—
245	C₂²⋊D₁₁	C₂³×C₄	1	96	yes	complemented
246	C₂×Dic₁₁	—	2	12	no	—
247	C₂×Dic₁₁	—	2	4	no	—
248	C₂×Dic₁₁	—	4	24	no	—
249	C₂×Dic₁₁	C₂³×C₄	1	8	yes	—
250	C₂×Dic₁₁	C₂⁵	1	4	yes	—
251	C₂×Dic₁₁	C₂⁵	1	12	yes	—
252	C₂×Dic₁₁	C₂⁵	1	4	yes	—
253	D₄₄	C₂³×C₄	1	48	yes	complemented
254	D₄₄	C₂³×C₄	1	96	yes	complemented
255	C₄×D₁₁	—	2	48	no	—
256	C₄×D₁₁	—	4	48	no	—
257	C₄×D₁₁	—	4	24	no	—
258	C₄×D₁₁	C₂³×C₄	1	96	yes	complemented
259	Dic₂₂	C₂³×C₄	1	16	yes	complemented
260	C₂×H(5,𝔽₂)	—	11	16	no	—
261	C₂×H(5,𝔽₂)	—	11	32	no	—
262	C₂²×#41	—	11	2	no	—
263	C₂²×#41	—	11	3	no	—
264	C₂²×#41	C₂×D₁₁	1	1	yes	characteristic
265	C₂³×D₄	—	11	6	no	—
266	C₂³×D₄	—	11	3	no	—
267	C₂⁴×C₄	—	11	6	no	—
268	#520	—	11	16	no	—
269	#520	—	11	32	no	—
270	#520	—	11	48	no	—
271	#518	—	11	96	no	—
272	#518	—	11	48	no	—
273	C₄×#41	—	11	32	no	—
274	C₄×#41	—	11	48	no	—
275	C₄×#41	C₂×D₁₁	1	16	yes	complemented
276	C₂×C₄×Q₈	—	11	2	no	—
277	C₂×C₄×Q₈	—	11	1	no	—
278	C₂×C₄×Q₈	—	11	3	no	—
279	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
280	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
281	C₂×C₄×D₄	—	11	6	no	—
282	C₂×C₄×D₄	—	11	6	no	—
283	C₂×C₄×D₄	—	11	6	no	—
284	C₂×C₄×D₄	—	11	96	no	—
285	C₂×C₄×D₄	—	11	6	no	—
286	C₂×C₄×D₄	—	11	6	no	—
287	C₂×C₄×D₄	—	11	12	no	—
288	C₂×C₄×D₄	—	11	3	no	—
289	C₂×C₄×D₄	—	11	6	no	—
290	C₂×C₄×D₄	—	11	6	no	—
291	C₂×C₄×D₄	—	11	6	no	—
292	C₂×C₄×D₄	—	11	3	no	—
293	C₂×C₄×D₄	—	11	48	no	—
294	C₂×C₄×D₄	C₂×D₁₁	1	3	yes	complemented
295	C₂×C₄×D₄	C₂×D₁₁	1	3	yes	complemented
296	C₂×#117	—	11	3	no	—
297	C₂×#117	—	11	6	no	—
298	C₂×#117	—	11	6	no	—
299	C₂×#117	C₂×D₁₁	1	3	yes	complemented
300	C₂²×C₄⋊C₄	—	11	3	no	—
301	C₂²×C₄⋊C₄	—	11	6	no	—
302	C₂²×C₂²⋊C₄	—	11	6	no	—
303	C₂²×C₂²⋊C₄	—	11	12	no	—
304	C₂²×C₄²	—	11	6	no	—
305	C₂²×C₄²	C₂×D₁₁	1	3	yes	complemented
306	C₂²×C₁₁	—	2	6	no	—
307	C₂²×C₁₁	—	2	6	no	—
308	C₂²×C₁₁	—	2	24	no	—
309	C₂²×C₁₁	C₂⁴×C₄	1	12	yes	—
310	C₂²×C₁₁	C₂⁴×C₄	1	2	yes	—
311	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₁₁	#585	1	2	yes	—
313	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
314	C₂×D₁₁	—	2	12	no	—
315	C₂×D₁₁	—	2	12	no	—
316	C₂×D₁₁	—	2	48	no	—
317	C₂×D₁₁	—	4	96	no	—
318	C₂×D₁₁	C₂⁴×C₄	1	24	yes	—
319	C₄×C₁₁	—	2	6	no	—
320	C₄×C₁₁	—	2	2	no	—
321	C₄×C₁₁	—	2	6	no	—
322	C₄×C₁₁	C₂⁴×C₄	1	4	yes	—
323	C₄×C₁₁	C₂⁴×C₄	1	12	yes	—
324	C₄×C₁₁	C₂×H(5,𝔽₂)	1	4	yes	complemented
325	Dic₁₁	—	2	12	no	—
326	Dic₁₁	—	2	4	no	—
327	Dic₁₁	C₂⁴×C₄	1	8	yes	—
328	C₂⁵	—	11	6	no	—
329	H(5,𝔽₂)	—	11	256	no	—
330	C₂×#41	—	11	32	no	—
331	C₂×#41	—	11	16	no	—
332	C₂×#41	—	11	48	no	—
333	C₂×#41	—	11	24	no	—
334	C₂×#41	C₄×D₁₁	1	16	yes	complemented
335	C₂×#41	C₂²×D₁₁	1	8	yes	—
336	C₂²×Q₈	—	11	1	no	—
337	C₂²×Q₈	C₂²×D₁₁	1	1	yes	characteristic
338	C₂²×D₄	—	11	6	no	—
339	C₂²×D₄	—	11	96	no	—
340	C₂²×D₄	—	11	48	no	—
341	C₂²×D₄	—	11	48	no	—
342	C₂²×D₄	—	11	6	no	—
343	C₂²×D₄	—	11	3	no	—
344	C₂²×D₄	—	11	24	no	—
345	C₂²×D₄	C₂²×D₁₁	1	3	yes	—
346	C₂³×C₄	—	11	6	no	—
347	C₂³×C₄	—	11	6	no	—
348	C₂³×C₄	—	11	6	no	—
349	C₂³×C₄	—	11	6	no	—
350	C₂³×C₄	—	11	12	no	—
351	C₂³×C₄	—	11	48	no	—
352	C₂³×C₄	—	44	24	no	—
353	C₂³×C₄	C₂²×D₁₁	1	3	yes	—
354	C₂³×C₄	C₂²×D₁₁	1	3	yes	—
355	C₂³×C₄	C₂²×D₁₁	1	3	yes	—
356	C₄×Q₈	—	11	16	no	—
357	C₄×Q₈	—	11	8	no	—
358	C₄×Q₈	—	11	24	no	—
359	C₄×Q₈	C₂²×D₁₁	1	8	yes	complemented
360	C₄×Q₈	C₂²×D₁₁	1	8	yes	complemented
361	C₄×D₄	—	11	48	no	—
362	C₄×D₄	—	11	48	no	—
363	C₄×D₄	—	11	48	no	—
364	C₄×D₄	—	11	48	no	—
365	C₄×D₄	—	11	48	no	—
366	C₄×D₄	—	11	96	no	—
367	C₄×D₄	—	11	48	no	—
368	C₄×D₄	—	11	24	no	—
369	C₄×D₄	—	11	48	no	—
370	C₄×D₄	—	11	48	no	—
371	C₄×D₄	—	11	24	no	—
372	C₄×D₄	C₂²×D₁₁	1	24	yes	complemented
373	C₄×D₄	C₂²×D₁₁	1	24	yes	complemented
374	#117	—	11	24	no	—
375	#117	—	11	48	no	—
376	#117	—	11	48	no	—
377	#117	C₂²×D₁₁	1	24	yes	complemented
378	C₂×C₄⋊C₄	—	11	6	no	—
379	C₂×C₄⋊C₄	—	11	6	no	—
380	C₂×C₄⋊C₄	—	11	3	no	—
381	C₂×C₄⋊C₄	—	11	24	no	—
382	C₂×C₄⋊C₄	—	11	2	no	—
383	C₂×C₄⋊C₄	—	11	1	no	—
384	C₂×C₄⋊C₄	—	11	48	no	—
385	C₂×C₄⋊C₄	C₂²×D₁₁	1	3	yes	—
386	C₂×C₄⋊C₄	C₂²×D₁₁	1	3	yes	—
387	C₂×C₂²⋊C₄	—	11	6	no	—
388	C₂×C₂²⋊C₄	—	11	6	no	—
389	C₂×C₂²⋊C₄	—	11	12	no	—
390	C₂×C₂²⋊C₄	—	11	6	no	—
391	C₂×C₂²⋊C₄	—	11	48	no	—
392	C₂×C₂²⋊C₄	—	11	96	no	—
393	C₂×C₂²⋊C₄	C₂²×D₁₁	1	6	yes	—
394	C₂×C₄²	—	11	6	no	—
395	C₂×C₄²	—	11	6	no	—
396	C₂×C₄²	—	11	2	no	—
397	C₂×C₄²	—	11	48	no	—
398	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
399	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
400	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
402	C₂×C₄²	C₂²×D₁₁	1	24	yes	complemented
403	C₂×C₁₁	—	2	12	no	—
404	C₂×C₁₁	C₄×H(5,𝔽₂)	1	4	yes	complemented
405	C₂×C₁₁	C₂⁵×C₄	1	1	yes	characteristic
406	C₂×C₁₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₁₁	C₂×#585	1	1	yes	characteristic
408	D₁₁	—	2	24	no	—
409	C₂⁴	—	11	6	no	—
410	C₂⁴	—	11	48	no	—
411	C₂⁴	—	11	24	no	—
412	C₂⁴	—	44	12	no	—
413	C₂⁴	—	44	12	no	—
414	C₂⁴	C₂³×D₁₁	1	3	yes	—
415	#41	—	11	128	no	—
416	#41	—	11	192	no	—
417	#41	C₂×C₄×D₁₁	1	64	yes	complemented
418	C₂×Q₈	—	11	8	no	—
419	C₂×Q₈	—	11	4	no	—
420	C₂×Q₈	C₂×C₄×D₁₁	1	8	yes	complemented
421	C₂×Q₈	C₂³×D₁₁	1	4	yes	—
422	C₂×D₄	—	11	48	no	—
423	C₂×D₄	—	11	24	no	—
424	C₂×D₄	—	11	384	no	—
425	C₂×D₄	—	11	48	no	—
426	C₂×D₄	—	11	24	no	—
427	C₂×D₄	—	11	192	no	—
428	C₂×D₄	—	11	24	no	—
429	C₂×D₄	—	11	12	no	—
430	C₂×D₄	C₂×C₄×D₁₁	1	24	yes	complemented
431	C₂×D₄	C₂³×D₁₁	1	12	yes	—
432	C₂²×C₄	—	2	12	no	—
433	C₂²×C₄	—	4	6	no	—
434	C₂²×C₄	—	11	2	no	—
435	C₂²×C₄	—	11	48	no	—
436	C₂²×C₄	—	11	24	no	—
437	C₂²×C₄	—	11	2	no	—
438	C₂²×C₄	—	11	6	no	—
439	C₂²×C₄	—	11	24	no	—
440	C₂²×C₄	—	11	24	no	—
441	C₂²×C₄	—	11	24	no	—
442	C₂²×C₄	—	11	48	no	—
443	C₂²×C₄	—	22	24	no	—
444	C₂²×C₄	—	44	96	no	—
445	C₂²×C₄	—	44	24	no	—
446	C₂²×C₄	—	44	12	no	—
447	C₂²×C₄	—	44	12	no	—
448	C₂²×C₄	C₂×C₄×D₁₁	1	24	yes	complemented
449	C₂²×C₄	C₂³×D₁₁	1	3	yes	—
450	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
451	C₂²×C₄	C₂³×D₁₁	1	3	yes	—
452	C₂²×C₄	C₂³×D₁₁	1	12	yes	—
453	C₂²×C₄	C₂³×D₁₁	1	12	yes	—
454	C₂²×C₄	C₂³×D₁₁	1	3	yes	—
455	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
456	C₂²×C₄	C₂³×D₁₁	1	12	yes	—
457	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
458	C₄⋊C₄	—	11	24	no	—
459	C₄⋊C₄	—	11	24	no	—
460	C₄⋊C₄	—	11	12	no	—
461	C₄⋊C₄	—	11	8	no	—
462	C₄⋊C₄	—	11	4	no	—
463	C₄⋊C₄	C₂³×D₁₁	1	12	yes	—
464	C₄⋊C₄	C₂³×D₁₁	1	12	yes	—
465	C₂²⋊C₄	—	11	24	no	—
466	C₂²⋊C₄	—	11	24	no	—
467	C₂²⋊C₄	—	11	48	no	—
468	C₂²⋊C₄	—	11	24	no	—
469	C₂²⋊C₄	C₂³×D₁₁	1	24	yes	—
470	C₄²	—	11	8	no	—
471	C₄²	—	11	24	no	—
472	C₄²	—	11	24	no	—
473	C₄²	C₂³×D₁₁	1	12	yes	—
474	C₄²	C₂³×D₁₁	1	4	yes	—
475	C₄²	C₂³×D₁₁	1	12	yes	—
476	C₄²	C₂³×D₁₁	1	12	yes	—
477	C₁₁	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
478	C₂³	—	2	6	no	—
479	C₂³	—	2	6	no	—
480	C₂³	—	11	24	no	—
481	C₂³	—	11	12	no	—
482	C₂³	—	11	96	no	—
483	C₂³	—	22	12	no	—
484	C₂³	—	22	12	no	—
485	C₂³	—	44	24	no	—
486	C₂³	—	44	24	no	—
487	C₂³	—	44	96	no	—
488	C₂³	C₂²×C₄×D₁₁	1	12	yes	—
489	C₂³	C₂⁴×D₁₁	1	6	yes	—
490	C₂³	C₂⁴×D₁₁	1	1	yes	characteristic
491	Q₈	—	11	16	no	—
492	Q₈	C₂²×C₄×D₁₁	1	16	yes	complemented
493	D₄	—	11	96	no	—
494	D₄	—	11	96	no	—
495	D₄	—	11	48	no	—
496	D₄	C₂²×C₄×D₁₁	1	48	yes	complemented
497	C₂×C₄	—	2	6	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	6	no	—
500	C₂×C₄	—	2	24	no	—
501	C₂×C₄	—	4	12	no	—
502	C₂×C₄	—	11	8	no	—
503	C₂×C₄	—	11	4	no	—
504	C₂×C₄	—	11	96	no	—
505	C₂×C₄	—	11	4	no	—
506	C₂×C₄	—	11	12	no	—
507	C₂×C₄	—	22	12	no	—
508	C₂×C₄	—	22	4	no	—
509	C₂×C₄	—	22	48	no	—
510	C₂×C₄	—	44	48	no	—
511	C₂×C₄	—	44	24	no	—
512	C₂×C₄	—	44	24	no	—
513	C₂×C₄	C₂²×C₄×D₁₁	1	12	yes	—
514	C₂×C₄	C₂²×C₄×D₁₁	1	4	yes	—
515	C₂×C₄	C₂²×C₄×D₁₁	1	48	yes	complemented
516	C₂×C₄	#67042	1	4	yes	direct product factor
517	C₂×C₄	C₂⁴×D₁₁	1	6	yes	—
518	C₂×C₄	C₂⁴×D₁₁	1	2	yes	—
519	C₂×C₄	C₂⁴×D₁₁	1	6	yes	—
520	C₂×C₄	C₂⁴×D₁₁	1	6	yes	—
521	C₂×C₄	C₂⁴×D₁₁	1	2	yes	—
522	C₂×C₄	C₂⁴×D₁₁	1	2	yes	—
523	C₂²	—	2	6	no	—
524	C₂²	—	2	6	no	—
525	C₂²	—	2	24	no	—
526	C₂²	—	11	24	no	—
527	C₂²	—	22	12	no	—
528	C₂²	—	22	12	no	—
529	C₂²	—	22	48	no	—
530	C₂²	—	44	96	no	—
531	C₂²	C₂³×C₄×D₁₁	1	12	yes	—
532	C₂²	C₂³×C₄×D₁₁	1	2	yes	—
533	C₂²	C₂×#67042	1	2	yes	—
534	C₂²	#10623453	1	2	yes	—
535	C₂²	C₂⁵×D₁₁	1	1	yes	characteristic
536	C₄	—	2	6	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	6	no	—
539	C₄	—	11	8	no	—
540	C₄	—	22	12	no	—
541	C₄	—	22	4	no	—
542	C₄	C₂³×C₄×D₁₁	1	12	yes	—
543	C₄	C₂³×C₄×D₁₁	1	4	yes	—
544	C₄	C₂×#67042	1	4	yes	direct product factor
545	C₂	—	2	12	no	—
546	C₂	—	22	24	no	—
547	C₂	C₄×#67042	1	4	yes	direct product factor
548	C₂	C₂⁴×C₄×D₁₁	1	1	yes	characteristic
549	C₂	C₂²×#67042	1	1	yes	characteristic
550	C₂	C₂×#10623453	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₁
commutator	C₂×C₁₁	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₁
Fitting	C₂×C₄×C₁₁×#41	C₂
socle	C₂³×C₁₁	C₂⁵
prime radical	C₂²×#67042	C₂
cosocle	C₂²×C₁₁	C₂⁶
hypercenter	C₂×C₄×#41	D₁₁
hypocenter	C₁₁	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×#67042	C₂	direct (N × H)
3. C₂×#10623358	C₂	semidirect
4. C₂×#10623105	C₂	semidirect
5. C₂×#10623054	C₂	semidirect
6. C₂×#10623052	C₂	semidirect
7. C₂×#10623076	C₂	semidirect
8. C₂×C₄×#4343	C₂	semidirect
9. C₂×C₄×#4339	C₂	semidirect
10. C₂²×C₄×D₄₄	C₂	semidirect
11. C₂×C₄×D₄×D₁₁	C₂	semidirect
12. C₂×C₄×C₁₁×#41	C₂	semidirect
14. C₂×#67042	C₄	direct (N × H)
20. C₂³×C₄×D₁₁	C₂²	semidirect
21. C₄×C₁₁×#41	C₂²	semidirect
22. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
23. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
24. C₂×C₄×D₄×C₁₁	C₂²	semidirect
25. C₂×C₄×D₄×C₁₁	C₂²	semidirect
26. C₂×C₁₁×#117	C₂²	semidirect
27. C₂²×C₄²×C₁₁	C₂²	semidirect
28. #10623358	C₂²	semidirect
29. C₂×Q₈×Dic₁₁	C₂²	semidirect
30. C₂×D₄×Dic₁₁	C₂²	semidirect
31. C₂×C₄×C₂²⋊D₁₁	C₂²	semidirect
32. C₂×C₄×C₂²⋊D₁₁	C₂²	semidirect
33. C₂²×(C₂×D₁₁)⋊C₄	C₂²	semidirect
34. C₂×#66979	C₂²	semidirect
35. C₂²×C₄⋊Dic₁₁	C₂²	semidirect
36. #10623105	C₂²	semidirect
37. C₄×#4343	C₂²	semidirect
38. #10623076	C₂²	semidirect
39. C₄×D₄×D₁₁	C₂²	semidirect
40. #10623054	C₂²	semidirect
41. #10623052	C₂²	semidirect
42. C₂×#66946	C₂²	semidirect
43. C₂×#66946	C₂²	semidirect
44. C₂×#66945	C₂²	semidirect
45. C₂×C₄⋊C₄×D₁₁	C₂²	semidirect
46. C₂×(C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
47. C₂×C₂²⋊C₄×D₁₁	C₂²	semidirect
48. C₄×#4339	C₂²	semidirect
49. C₂×C₄×D₄₄	C₂²	semidirect
50. C₂×C₄×D₄₄	C₂²	semidirect
51. C₂×C₄×D₄₄	C₂²	semidirect
52. C₂×C₄×D₄₄	C₂²	semidirect
53. C₂×C₄×D₄₄	C₂²	semidirect
54. C₂×C₄×D₄₄	C₂²	semidirect
55. C₂×#66925	C₂²	semidirect
56. C₂×C₄²×D₁₁	C₂²	semidirect
57. C₂×C₄×Dic₂₂	C₂²	semidirect
58. C₂×C₄×Dic₂₂	C₂²	semidirect
60. C₂×C₁₁×#41	C₂×C₄	semidirect
69. #67042	C₂×C₄	direct (N × H)
70. C₂×#4343	C₂×C₄	semidirect
72. C₂×D₄×D₁₁	C₂×C₄	semidirect
74. C₂×#4339	C₂×C₄	semidirect
76. C₂²×D₄₄	C₂×C₄	semidirect
85. C₂²×C₄×D₁₁	C₂³	semidirect
87. C₄×Q₈×C₁₁	C₂³	semidirect
88. C₄×Q₈×C₁₁	C₂³	semidirect
89. C₄×D₄×C₁₁	C₂³	semidirect
90. C₄×D₄×C₁₁	C₂³	semidirect
91. C₁₁×#117	C₂³	semidirect
99. C₂×C₄²×C₁₁	C₂³	semidirect
101. Q₈×Dic₁₁	C₂³	semidirect
102. D₄×Dic₁₁	C₂³	semidirect
103. C₄×C₂²⋊D₁₁	C₂³	semidirect
104. C₄×C₂²⋊D₁₁	C₂³	semidirect
108. C₂×(C₂×D₁₁)⋊C₄	C₂³	semidirect
109. #66979	C₂³	semidirect
113. C₂×C₄⋊Dic₁₁	C₂³	semidirect
119. #66946	C₂³	semidirect
120. #66946	C₂³	semidirect
121. #66945	C₂³	semidirect
122. C₄⋊C₄×D₁₁	C₂³	semidirect
123. (C₂²⋊D₁₁)⋊C₄	C₂³	semidirect
124. C₂²⋊C₄×D₁₁	C₂³	semidirect
125. C₄×D₄₄	C₂³	semidirect
126. C₄×D₄₄	C₂³	semidirect
127. C₄×D₄₄	C₂³	semidirect
128. C₄×D₄₄	C₂³	semidirect
129. C₄×D₄₄	C₂³	semidirect
130. #66925	C₂³	semidirect
131. C₄²×D₁₁	C₂³	semidirect
132. C₄×Dic₂₂	C₂³	semidirect
133. C₄×Dic₂₂	C₂³	semidirect
138. C₂³×D₁₁	C₂²×C₄	semidirect
141. C₁₁×#41	C₂²×C₄	semidirect
142. C₂×Q₈×C₁₁	C₂²×C₄	semidirect
144. C₂×D₄×C₁₁	C₂²×C₄	semidirect
148. C₂²×C₄×C₁₁	C₂²×C₄	semidirect
158. C₂×C₂²⋊D₁₁	C₂²×C₄	semidirect
165. #4343	C₂²×C₄	semidirect
166. D₄×D₁₁	C₂²×C₄	semidirect
167. #4339	C₂²×C₄	semidirect
168. C₂×D₄₄	C₂²×C₄	semidirect
169. C₂×D₄₄	C₂²×C₄	semidirect
170. C₂×D₄₄	C₂²×C₄	semidirect
177. C₂×C₄×D₁₁	C₂²×C₄	semidirect
182. C₂×Dic₂₂	C₂²×C₄	semidirect
212. C₂×C₄×#41	D₁₁	semidirect
226. C₂²×D₁₁	C₂³×C₄	semidirect
228. Q₈×C₁₁	C₂³×C₄	semidirect
229. D₄×C₁₁	C₂³×C₄	semidirect
237. C₂×C₄×C₁₁	C₂³×C₄	semidirect
238. C₂×C₄×C₁₁	H(5,𝔽₂)	semidirect
245. C₂²⋊D₁₁	C₂³×C₄	semidirect
253. D₄₄	C₂³×C₄	semidirect
254. D₄₄	C₂³×C₄	semidirect
258. C₄×D₁₁	C₂³×C₄	semidirect
259. Dic₂₂	C₂³×C₄	semidirect
275. C₄×#41	C₂×D₁₁	semidirect
279. C₂×C₄×Q₈	C₂×D₁₁	semidirect
280. C₂×C₄×Q₈	C₂×D₁₁	semidirect
294. C₂×C₄×D₄	C₂×D₁₁	semidirect
295. C₂×C₄×D₄	C₂×D₁₁	semidirect
299. C₂×#117	C₂×D₁₁	semidirect
305. C₂²×C₄²	C₂×D₁₁	semidirect
324. C₄×C₁₁	C₂×H(5,𝔽₂)	semidirect
334. C₂×#41	C₄×D₁₁	semidirect
359. C₄×Q₈	C₂²×D₁₁	semidirect
360. C₄×Q₈	C₂²×D₁₁	semidirect
372. C₄×D₄	C₂²×D₁₁	semidirect
373. C₄×D₄	C₂²×D₁₁	semidirect
377. #117	C₂²×D₁₁	semidirect
402. C₂×C₄²	C₂²×D₁₁	semidirect
404. C₂×C₁₁	C₄×H(5,𝔽₂)	semidirect
417. #41	C₂×C₄×D₁₁	semidirect
420. C₂×Q₈	C₂×C₄×D₁₁	semidirect
430. C₂×D₄	C₂×C₄×D₁₁	semidirect
448. C₂²×C₄	C₂×C₄×D₁₁	semidirect
477. C₁₁	C₂×C₄×H(5,𝔽₂)	semidirect
492. Q₈	C₂²×C₄×D₁₁	semidirect
496. D₄	C₂²×C₄×D₁₁	semidirect
515. C₂×C₄	C₂²×C₄×D₁₁	semidirect
516. C₂×C₄	#67042	direct (N × H)
544. C₄	C₂×#67042	direct (N × H)
547. C₂	C₄×#67042	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#67042	2
C₄×#67042	2
C₂×#10623358	2
C₂×#10623105	2
C₂×#10623054	2
C₂×#10623052	2
C₂×#10623076	2
C₂×C₄×#4343	2
C₂×C₄×#4339	2
C₂²×C₄×D₄₄	2
C₂×C₄×D₄×D₁₁	2
C₂×C₄×C₁₁×#41	2
C₂×C₄×H(5,𝔽₂)	11

Subgroups — C2×C4×#67042 #15660376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#67042 #15660376