Subgroups — C₂²×C₁₁×#539 #14639865

Order 2816.

8062 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#539	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₁×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₁×#125	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₁×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₁×#123	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₁×#121	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×D₄×C₁₁	C₂	1	2	yes	maximal, complemented
10	C₂³×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#539	C₂²	1	256	yes	direct product factor
19	C₂×C₁₁×#126	C₂²	1	48	yes	complemented
20	C₂×C₁₁×#125	C₂²	1	48	yes	complemented
21	C₂×C₁₁×#123	C₂²	1	48	yes	complemented
22	C₂×C₁₁×#123	C₂²	1	48	yes	complemented
23	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	24	yes	complemented
24	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	48	yes	complemented
25	C₂×C₁₁×#121	C₂²	1	24	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	48	yes	complemented
27	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₁×C₄⋊C₄	C₂²	1	24	yes	complemented
36	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
42	C₂⁵×C₁₁	C₂³	1	2	yes	—
43	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₁	—	4	4	no	—
45	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
46	C₂²×D₄×C₁₁	—	2	16	no	—
47	C₂²×D₄×C₁₁	—	4	4	no	—
48	C₂²×D₄×C₁₁	C₂³	1	24	yes	—
49	C₂²×D₄×C₁₁	C₂³	1	12	yes	—
50	C₂³×C₄×C₁₁	—	2	8	no	—
51	C₂³×C₄×C₁₁	—	4	4	no	—
52	C₂³×C₄×C₁₁	—	4	8	no	—
53	C₂³×C₄×C₁₁	—	4	4	no	—
54	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
55	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
64	C₂³×C₄×C₁₁	C₂³	1	24	yes	—
65	C₁₁×#126	C₂³	1	128	yes	complemented
66	C₁₁×#125	C₂³	1	128	yes	complemented
67	C₁₁×#123	C₂³	1	128	yes	complemented
68	C₁₁×#123	C₂³	1	128	yes	complemented
69	C₁₁×C₂²⋊Q₈	C₂³	1	64	yes	complemented
70	C₁₁×C₂²⋊Q₈	C₂³	1	128	yes	complemented
71	C₁₁×#121	C₂³	1	64	yes	—
72	C₄×D₄×C₁₁	C₂³	1	128	yes	complemented
73	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
79	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
80	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
81	C₂×C₁₁×C₄⋊C₄	C₂³	1	64	yes	complemented
82	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
83	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
84	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
85	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
86	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
87	C₂×C₄²×C₁₁	C₂³	1	24	yes	—
88	C₂²×#539	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₁	—	2	4	no	—
90	C₂⁴×C₁₁	—	2	4	no	—
91	C₂⁴×C₁₁	—	2	8	no	—
92	C₂⁴×C₁₁	—	2	8	no	—
93	C₂⁴×C₁₁	—	2	8	no	—
94	C₂⁴×C₁₁	#41	1	8	yes	—
95	C₂⁴×C₁₁	C₂⁴	1	12	yes	—
96	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
97	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
98	C₂×Q₈×C₁₁	—	4	24	no	—
99	C₂×Q₈×C₁₁	C₂⁴	1	16	yes	—
100	C₂×D₄×C₁₁	—	2	96	no	—
101	C₂×D₄×C₁₁	—	4	24	no	—
102	C₂×D₄×C₁₁	C₂⁴	1	32	yes	—
103	C₂×D₄×C₁₁	C₂⁴	1	16	yes	—
104	C₂²×C₄×C₁₁	—	2	48	no	—
105	C₂²×C₄×C₁₁	—	2	8	no	—
106	C₂²×C₄×C₁₁	—	2	8	no	—
107	C₂²×C₄×C₁₁	—	2	8	no	—
108	C₂²×C₄×C₁₁	—	2	4	no	—
109	C₂²×C₄×C₁₁	—	2	8	no	—
110	C₂²×C₄×C₁₁	—	2	4	no	—
111	C₂²×C₄×C₁₁	—	2	8	no	—
112	C₂²×C₄×C₁₁	—	4	24	no	—
113	C₂²×C₄×C₁₁	—	4	48	no	—
114	C₂²×C₄×C₁₁	—	4	24	no	—
115	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
116	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
117	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
118	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
123	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
124	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	32	yes	—
126	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
127	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
128	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
129	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
130	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
131	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
132	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
133	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
134	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
135	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
136	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
137	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
138	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
139	C₄²×C₁₁	C₂⁴	1	32	yes	—
140	C₂×#539	C₂×C₁₁	1	48	yes	direct product factor
141	C₂²×#126	C₂×C₁₁	1	2	yes	complemented
142	C₂²×#125	C₂×C₁₁	1	2	yes	complemented
143	C₂²×#123	C₂×C₁₁	1	2	yes	complemented
144	C₂²×#123	C₂×C₁₁	1	2	yes	complemented
145	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	2	yes	complemented
147	C₂²×#121	C₂×C₁₁	1	1	yes	characteristic
148	C₂²×C₄×D₄	C₂×C₁₁	1	2	yes	complemented
149	C₂³×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
150	C₂³×C₁₁	—	2	32	no	—
151	C₂³×C₁₁	—	2	12	no	—
152	C₂³×C₁₁	—	2	12	no	—
153	C₂³×C₁₁	—	2	24	no	—
154	C₂³×C₁₁	—	2	24	no	—
155	C₂³×C₁₁	—	2	24	no	—
156	C₂³×C₁₁	—	4	32	no	—
157	C₂³×C₁₁	C₂×#41	1	24	yes	—
158	C₂³×C₁₁	C₂×#41	1	4	yes	—
159	C₂³×C₁₁	H(5,𝔽₂)	1	4	yes	—
160	C₂³×C₁₁	2₋¹⁺⁴	1	4	yes	—
161	C₂³×C₁₁	C₂⁵	1	8	yes	—
162	C₂³×C₁₁	C₂⁵	1	4	yes	—
163	C₂³×C₁₁	C₂⁵	1	3	yes	—
164	Q₈×C₁₁	—	4	16	no	—
165	D₄×C₁₁	—	2	64	no	—
166	D₄×C₁₁	—	4	16	no	—
167	C₂×C₄×C₁₁	—	2	32	no	—
168	C₂×C₄×C₁₁	—	2	24	no	—
169	C₂×C₄×C₁₁	—	2	24	no	—
170	C₂×C₄×C₁₁	—	2	24	no	—
171	C₂×C₄×C₁₁	—	2	12	no	—
172	C₂×C₄×C₁₁	—	2	24	no	—
173	C₂×C₄×C₁₁	—	2	12	no	—
174	C₂×C₄×C₁₁	—	2	24	no	—
175	C₂×C₄×C₁₁	—	4	16	no	—
176	C₂×C₄×C₁₁	—	4	32	no	—
177	C₂×C₄×C₁₁	—	4	16	no	—
178	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
179	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
180	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
181	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
182	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
183	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
184	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
185	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
186	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
187	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
188	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
189	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
190	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
191	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
192	#539	C₂²×C₁₁	1	256	yes	direct product factor
193	C₂×#126	C₂²×C₁₁	1	48	yes	complemented
194	C₂×#125	C₂²×C₁₁	1	48	yes	complemented
195	C₂×#123	C₂²×C₁₁	1	48	yes	complemented
196	C₂×#123	C₂²×C₁₁	1	48	yes	complemented
197	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	24	yes	complemented
198	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	48	yes	complemented
199	C₂×#121	C₂²×C₁₁	1	24	yes	—
200	C₂×C₄×D₄	C₂²×C₁₁	1	48	yes	complemented
201	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
207	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₁₁	1	24	yes	complemented
210	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
215	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
216	C₂²×C₁₁	—	2	4	no	—
217	C₂²×C₁₁	—	2	4	no	—
218	C₂²×C₁₁	—	2	48	no	—
219	C₂²×C₁₁	—	2	8	no	—
220	C₂²×C₁₁	—	2	8	no	—
221	C₂²×C₁₁	—	2	8	no	—
222	C₂²×C₁₁	—	4	48	no	—
223	C₂²×C₁₁	#539	1	16	yes	direct product factor
224	C₂²×C₁₁	C₂²×#41	1	8	yes	—
225	C₂²×C₁₁	C₂²×#41	1	6	yes	—
226	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	6	yes	—
227	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	6	yes	—
228	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
229	C₄×C₁₁	—	2	8	no	—
230	C₄×C₁₁	—	2	8	no	—
231	C₄×C₁₁	—	2	8	no	—
232	C₄×C₁₁	—	2	4	no	—
233	C₄×C₁₁	—	2	8	no	—
234	C₄×C₁₁	—	2	4	no	—
235	C₄×C₁₁	—	2	8	no	—
236	C₂⁵	C₂³×C₁₁	1	2	yes	—
237	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
238	C₂²×Q₈	—	4	4	no	—
239	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
240	C₂²×D₄	—	2	16	no	—
241	C₂²×D₄	—	4	4	no	—
242	C₂²×D₄	C₂³×C₁₁	1	24	yes	—
243	C₂²×D₄	C₂³×C₁₁	1	12	yes	—
244	C₂³×C₄	—	2	8	no	—
245	C₂³×C₄	—	4	4	no	—
246	C₂³×C₄	—	4	8	no	—
247	C₂³×C₄	—	4	4	no	—
248	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
250	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
256	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
257	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
258	C₂³×C₄	C₂³×C₁₁	1	24	yes	—
259	#126	C₂³×C₁₁	1	128	yes	complemented
260	#125	C₂³×C₁₁	1	128	yes	complemented
261	#123	C₂³×C₁₁	1	128	yes	complemented
262	#123	C₂³×C₁₁	1	128	yes	complemented
263	C₂²⋊Q₈	C₂³×C₁₁	1	64	yes	complemented
264	C₂²⋊Q₈	C₂³×C₁₁	1	128	yes	complemented
265	#121	C₂³×C₁₁	1	64	yes	—
266	C₄×D₄	C₂³×C₁₁	1	128	yes	complemented
267	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₁	1	64	yes	complemented
276	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
281	C₂×C₄²	C₂³×C₁₁	1	24	yes	—
282	C₂×C₁₁	—	2	8	no	—
283	C₂×C₁₁	—	4	8	no	—
284	C₂×C₁₁	C₂×#539	1	12	yes	direct product factor
285	C₂×C₁₁	C₂³×#41	1	1	yes	characteristic
286	C₂×C₁₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₁₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	8	no	—
291	C₂⁴	—	2	8	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	C₁₁×#41	1	8	yes	—
294	C₂⁴	C₂⁴×C₁₁	1	12	yes	—
295	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
296	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
297	C₂×Q₈	—	4	24	no	—
298	C₂×Q₈	C₂⁴×C₁₁	1	16	yes	—
299	C₂×D₄	—	2	96	no	—
300	C₂×D₄	—	4	24	no	—
301	C₂×D₄	C₂⁴×C₁₁	1	32	yes	—
302	C₂×D₄	C₂⁴×C₁₁	1	16	yes	—
303	C₂²×C₄	—	2	48	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	4	24	no	—
312	C₂²×C₄	—	4	48	no	—
313	C₂²×C₄	—	4	24	no	—
314	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
315	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
316	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
317	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
318	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
319	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
320	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
321	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
322	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
323	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
324	C₂²×C₄	C₂⁴×C₁₁	1	32	yes	—
325	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
326	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
327	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
328	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
329	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
330	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
331	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
332	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
333	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
334	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
335	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
336	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
337	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
338	C₄²	C₂⁴×C₁₁	1	32	yes	—
339	C₁₁	C₂²×#539	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	2	32	no	—
341	C₂³	—	2	12	no	—
342	C₂³	—	2	12	no	—
343	C₂³	—	2	24	no	—
344	C₂³	—	2	24	no	—
345	C₂³	—	2	24	no	—
346	C₂³	—	4	32	no	—
347	C₂³	C₂×C₁₁×#41	1	24	yes	—
348	C₂³	C₂×C₁₁×#41	1	4	yes	—
349	C₂³	C₁₁×H(5,𝔽₂)	1	4	yes	—
350	C₂³	C₁₁×2₋¹⁺⁴	1	4	yes	—
351	C₂³	C₂⁵×C₁₁	1	8	yes	—
352	C₂³	C₂⁵×C₁₁	1	4	yes	—
353	C₂³	C₂⁵×C₁₁	1	3	yes	—
354	Q₈	—	4	16	no	—
355	D₄	—	2	64	no	—
356	D₄	—	4	16	no	—
357	C₂×C₄	—	2	32	no	—
358	C₂×C₄	—	2	24	no	—
359	C₂×C₄	—	2	24	no	—
360	C₂×C₄	—	2	24	no	—
361	C₂×C₄	—	2	12	no	—
362	C₂×C₄	—	2	24	no	—
363	C₂×C₄	—	2	12	no	—
364	C₂×C₄	—	2	24	no	—
365	C₂×C₄	—	4	16	no	—
366	C₂×C₄	—	4	32	no	—
367	C₂×C₄	—	4	16	no	—
368	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
369	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
370	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
371	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
372	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
373	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
374	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
375	C₂²	—	2	48	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	4	48	no	—
382	C₂²	C₁₁×#539	1	16	yes	direct product factor
383	C₂²	C₂²×C₁₁×#41	1	8	yes	—
384	C₂²	C₂²×C₁₁×#41	1	6	yes	—
385	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	6	yes	—
386	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	6	yes	—
387	C₂²	C₂⁶×C₁₁	1	1	yes	characteristic
388	C₄	—	2	8	no	—
389	C₄	—	2	8	no	—
390	C₄	—	2	8	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	8	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	8	no	—
395	C₂	—	2	8	no	—
396	C₂	—	4	8	no	—
397	C₂	C₂×C₁₁×#539	1	12	yes	direct product factor
398	C₂	C₂³×C₁₁×#41	1	1	yes	characteristic
399	C₂	C₂²×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂	C₂²×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
prime radical	C₂²×C₁₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#539	C₂	direct (N × H)
2. C₂²×C₁₁×#126	C₂	semidirect
3. C₂²×C₁₁×#125	C₂	semidirect
4. C₂²×C₁₁×#123	C₂	semidirect
5. C₂²×C₁₁×#123	C₂	semidirect
6. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
7. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
9. C₂²×C₄×D₄×C₁₁	C₂	semidirect
10. C₂³×C₁₁×C₄⋊C₄	C₂	semidirect
18. C₁₁×#539	C₂²	direct (N × H)
19. C₂×C₁₁×#126	C₂²	semidirect
20. C₂×C₁₁×#125	C₂²	semidirect
21. C₂×C₁₁×#123	C₂²	semidirect
22. C₂×C₁₁×#123	C₂²	semidirect
23. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×D₄×C₁₁	C₂²	semidirect
35. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
65. C₁₁×#126	C₂³	semidirect
66. C₁₁×#125	C₂³	semidirect
67. C₁₁×#123	C₂³	semidirect
68. C₁₁×#123	C₂³	semidirect
69. C₁₁×C₂²⋊Q₈	C₂³	semidirect
70. C₁₁×C₂²⋊Q₈	C₂³	semidirect
72. C₄×D₄×C₁₁	C₂³	semidirect
81. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
88. C₂²×#539	C₁₁	direct (N × H)
140. C₂×#539	C₂×C₁₁	direct (N × H)
141. C₂²×#126	C₂×C₁₁	semidirect
142. C₂²×#125	C₂×C₁₁	semidirect
143. C₂²×#123	C₂×C₁₁	semidirect
144. C₂²×#123	C₂×C₁₁	semidirect
145. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
146. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
148. C₂²×C₄×D₄	C₂×C₁₁	semidirect
149. C₂³×C₄⋊C₄	C₂×C₁₁	semidirect
192. #539	C₂²×C₁₁	direct (N × H)
193. C₂×#126	C₂²×C₁₁	semidirect
194. C₂×#125	C₂²×C₁₁	semidirect
195. C₂×#123	C₂²×C₁₁	semidirect
196. C₂×#123	C₂²×C₁₁	semidirect
197. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
198. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
200. C₂×C₄×D₄	C₂²×C₁₁	semidirect
209. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
223. C₂²×C₁₁	#539	direct (N × H)
259. #126	C₂³×C₁₁	semidirect
260. #125	C₂³×C₁₁	semidirect
261. #123	C₂³×C₁₁	semidirect
262. #123	C₂³×C₁₁	semidirect
263. C₂²⋊Q₈	C₂³×C₁₁	semidirect
264. C₂²⋊Q₈	C₂³×C₁₁	semidirect
266. C₄×D₄	C₂³×C₁₁	semidirect
275. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
284. C₂×C₁₁	C₂×#539	direct (N × H)
339. C₁₁	C₂²×#539	direct (N × H)
382. C₂²	C₁₁×#539	direct (N × H)
397. C₂	C₂×C₁₁×#539	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×C₁₁×#539	2
C₂²×C₁₁×#126	2
C₂²×C₁₁×#125	2
C₂²×C₁₁×#123	2
C₂²×C₁₁×C₂²⋊Q₈	2
C₂²×C₁₁×#121	2
C₂²×C₄×D₄×C₁₁	2
C₂³×C₁₁×C₄⋊C₄	2
C₂²×#539	11

Subgroups — C22×C11×#539 #14639865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#539 #14639865