Subgroups — C₂²×C₁₁×#552 #14639897

Order 2816.

7934 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#552	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×#125	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×#123	C₂	1	2	yes	maximal
6	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×#117	C₂	1	2	yes	maximal, complemented
12	C₂³×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#552	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×#125	C₂²	1	24	yes	complemented
22	C₂×C₁₁×#123	C₂²	1	48	yes	—
23	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	24	yes	complemented
24	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	24	yes	complemented
25	C₂×C₄×Q₈×C₁₁	C₂²	1	24	yes	complemented
26	C₂×C₄×D₄×C₁₁	C₂²	1	24	yes	—
27	C₂×C₁₁×#117	C₂²	1	24	yes	complemented
28	C₂×C₁₁×#117	C₂²	1	48	yes	complemented
29	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
36	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₁₁×C₄⋊C₄	C₂²	1	24	yes	complemented
40	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
45	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
46	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
47	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
48	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
49	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₁	—	2	8	no	—
51	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
52	C₂²×D₄×C₁₁	—	2	8	no	—
53	C₂²×D₄×C₁₁	C₂³	1	12	yes	—
54	C₂³×C₄×C₁₁	—	2	16	no	—
55	C₂³×C₄×C₁₁	—	2	8	no	—
56	C₂³×C₄×C₁₁	—	2	8	no	—
57	C₂³×C₄×C₁₁	C₂³	1	24	yes	—
58	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
59	C₂³×C₄×C₁₁	C₂³	1	12	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	2	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
69	C₁₁×#126	C₂³	1	128	yes	complemented
70	C₁₁×#125	C₂³	1	128	yes	complemented
71	C₁₁×#125	C₂³	1	64	yes	complemented
72	C₁₁×#123	C₂³	1	128	yes	—
73	C₁₁×C₂²⋊Q₈	C₂³	1	64	yes	complemented
74	C₁₁×C₂²⋊Q₈	C₂³	1	64	yes	complemented
75	C₄×Q₈×C₁₁	C₂³	1	64	yes	complemented
76	C₄×D₄×C₁₁	C₂³	1	64	yes	—
77	C₁₁×#117	C₂³	1	64	yes	complemented
78	C₁₁×#117	C₂³	1	128	yes	complemented
79	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
80	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
81	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
82	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
83	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
84	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
85	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
86	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
87	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
88	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
89	C₂×C₁₁×C₄⋊C₄	C₂³	1	64	yes	complemented
90	C₂×C₁₁×C₂²⋊C₄	C₂³	1	12	yes	—
91	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
92	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
93	C₂×C₁₁×C₂²⋊C₄	C₂³	1	12	yes	—
94	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
95	C₂×C₄²×C₁₁	C₂³	1	24	yes	—
96	C₂×C₄²×C₁₁	C₂³	1	24	yes	—
97	C₂×C₄²×C₁₁	C₂³	1	12	yes	—
98	C₂²×#552	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₁	—	2	4	no	—
100	C₂⁴×C₁₁	—	2	4	no	—
101	C₂⁴×C₁₁	—	2	4	no	—
102	C₂⁴×C₁₁	—	2	4	no	—
103	C₂⁴×C₁₁	—	2	4	no	—
104	C₂⁴×C₁₁	#41	1	8	yes	—
105	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
106	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
107	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₁	—	2	48	no	—
109	C₂×Q₈×C₁₁	C₂⁴	1	16	yes	—
110	C₂×D₄×C₁₁	—	2	48	no	—
111	C₂×D₄×C₁₁	C₂⁴	1	16	yes	—
112	C₂²×C₄×C₁₁	—	2	96	no	—
113	C₂²×C₄×C₁₁	—	2	8	no	—
114	C₂²×C₄×C₁₁	—	2	8	no	—
115	C₂²×C₄×C₁₁	—	2	4	no	—
116	C₂²×C₄×C₁₁	—	2	4	no	—
117	C₂²×C₄×C₁₁	—	2	4	no	—
118	C₂²×C₄×C₁₁	—	2	8	no	—
119	C₂²×C₄×C₁₁	—	2	4	no	—
120	C₂²×C₄×C₁₁	—	2	8	no	—
121	C₂²×C₄×C₁₁	—	2	48	no	—
122	C₂²×C₄×C₁₁	—	2	48	no	—
123	C₂²×C₄×C₁₁	#41	1	8	yes	—
124	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
127	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
128	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
129	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
132	C₂²×C₄×C₁₁	C₂⁴	1	32	yes	—
133	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
134	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
135	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
136	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
137	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
138	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
139	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
140	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
141	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
142	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
143	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
144	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
145	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	—
146	C₁₁×C₂²⋊C₄	C₂⁴	1	16	yes	—
147	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
148	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
149	C₁₁×C₂²⋊C₄	C₂⁴	1	16	yes	—
150	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
151	C₄²×C₁₁	C₂⁴	1	32	yes	—
152	C₄²×C₁₁	C₂⁴	1	32	yes	—
153	C₄²×C₁₁	C₂⁴	1	16	yes	—
154	C₂×#552	C₂×C₁₁	1	48	yes	direct product factor
155	C₂²×#126	C₂×C₁₁	1	2	yes	complemented
156	C₂²×#125	C₂×C₁₁	1	1	yes	characteristic, complemented
157	C₂²×#125	C₂×C₁₁	1	2	yes	complemented
158	C₂²×#123	C₂×C₁₁	1	2	yes	—
159	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
161	C₂²×C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
162	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
163	C₂²×#117	C₂×C₁₁	1	2	yes	complemented
164	C₂²×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
165	C₂³×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₂³×C₁₁	—	2	32	no	—
167	C₂³×C₁₁	—	2	12	no	—
168	C₂³×C₁₁	—	2	12	no	—
169	C₂³×C₁₁	—	2	12	no	—
170	C₂³×C₁₁	—	2	12	no	—
171	C₂³×C₁₁	—	2	12	no	—
172	C₂³×C₁₁	—	4	16	no	—
173	C₂³×C₁₁	C₂×#41	1	24	yes	—
174	C₂³×C₁₁	C₂×#41	1	4	yes	—
175	C₂³×C₁₁	C₂×#41	1	4	yes	—
176	C₂³×C₁₁	2₋¹⁺⁴	1	4	yes	—
177	C₂³×C₁₁	C₂⁵	1	4	yes	—
178	C₂³×C₁₁	C₂⁵	1	4	yes	—
179	C₂³×C₁₁	C₂⁵	1	3	yes	—
180	Q₈×C₁₁	—	2	32	no	—
181	D₄×C₁₁	—	2	32	no	—
182	C₂×C₄×C₁₁	—	2	64	no	—
183	C₂×C₄×C₁₁	—	2	24	no	—
184	C₂×C₄×C₁₁	—	2	24	no	—
185	C₂×C₄×C₁₁	—	2	12	no	—
186	C₂×C₄×C₁₁	—	2	12	no	—
187	C₂×C₄×C₁₁	—	2	12	no	—
188	C₂×C₄×C₁₁	—	2	24	no	—
189	C₂×C₄×C₁₁	—	2	12	no	—
190	C₂×C₄×C₁₁	—	2	24	no	—
191	C₂×C₄×C₁₁	—	2	32	no	—
192	C₂×C₄×C₁₁	—	2	32	no	—
193	C₂×C₄×C₁₁	C₂×#41	1	24	yes	—
194	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
195	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
196	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
197	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
198	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
199	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
200	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
201	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
202	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
203	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
205	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
206	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
207	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
208	#552	C₂²×C₁₁	1	256	yes	direct product factor
209	C₂×#126	C₂²×C₁₁	1	48	yes	complemented
210	C₂×#125	C₂²×C₁₁	1	48	yes	complemented
211	C₂×#125	C₂²×C₁₁	1	24	yes	complemented
212	C₂×#123	C₂²×C₁₁	1	48	yes	—
213	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	24	yes	complemented
214	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	24	yes	complemented
215	C₂×C₄×Q₈	C₂²×C₁₁	1	24	yes	complemented
216	C₂×C₄×D₄	C₂²×C₁₁	1	24	yes	—
217	C₂×#117	C₂²×C₁₁	1	24	yes	complemented
218	C₂×#117	C₂²×C₁₁	1	48	yes	complemented
219	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₁	1	24	yes	complemented
230	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
231	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
234	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
235	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
236	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
237	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
238	C₂²×C₁₁	—	2	4	no	—
239	C₂²×C₁₁	—	2	4	no	—
240	C₂²×C₁₁	—	2	48	no	—
241	C₂²×C₁₁	—	2	4	no	—
242	C₂²×C₁₁	—	2	4	no	—
243	C₂²×C₁₁	—	2	4	no	—
244	C₂²×C₁₁	—	4	24	no	—
245	C₂²×C₁₁	#552	1	16	yes	direct product factor
246	C₂²×C₁₁	C₂²×#41	1	8	yes	—
247	C₂²×C₁₁	C₂²×#41	1	6	yes	—
248	C₂²×C₁₁	C₂²×#41	1	6	yes	—
249	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	6	yes	—
250	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
251	C₄×C₁₁	—	2	8	no	—
252	C₄×C₁₁	—	2	8	no	—
253	C₄×C₁₁	—	2	4	no	—
254	C₄×C₁₁	—	2	4	no	—
255	C₄×C₁₁	—	2	4	no	—
256	C₄×C₁₁	—	2	8	no	—
257	C₄×C₁₁	—	2	4	no	—
258	C₄×C₁₁	—	2	8	no	—
259	C₄×C₁₁	C₂²×#41	1	8	yes	—
260	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
261	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
262	C₂²×Q₈	—	2	8	no	—
263	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	C₂³×C₁₁	1	12	yes	—
266	C₂³×C₄	—	2	16	no	—
267	C₂³×C₄	—	2	8	no	—
268	C₂³×C₄	—	2	8	no	—
269	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
276	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₁₁	1	24	yes	—
278	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
279	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
280	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
281	#126	C₂³×C₁₁	1	128	yes	complemented
282	#125	C₂³×C₁₁	1	128	yes	complemented
283	#125	C₂³×C₁₁	1	64	yes	complemented
284	#123	C₂³×C₁₁	1	128	yes	—
285	C₂²⋊Q₈	C₂³×C₁₁	1	64	yes	complemented
286	C₂²⋊Q₈	C₂³×C₁₁	1	64	yes	complemented
287	C₄×Q₈	C₂³×C₁₁	1	64	yes	complemented
288	C₄×D₄	C₂³×C₁₁	1	64	yes	—
289	#117	C₂³×C₁₁	1	64	yes	complemented
290	#117	C₂³×C₁₁	1	128	yes	complemented
291	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₁	1	64	yes	complemented
302	C₂×C₂²⋊C₄	C₂³×C₁₁	1	12	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₁	1	12	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
307	C₂×C₄²	C₂³×C₁₁	1	24	yes	—
308	C₂×C₄²	C₂³×C₁₁	1	24	yes	—
309	C₂×C₄²	C₂³×C₁₁	1	12	yes	—
310	C₂×C₁₁	—	2	8	no	—
311	C₂×C₁₁	—	4	4	no	—
312	C₂×C₁₁	C₂×#552	1	12	yes	direct product factor
313	C₂×C₁₁	C₂³×#41	1	1	yes	characteristic
314	C₂×C₁₁	C₂³×#41	1	1	yes	characteristic
315	C₂×C₁₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	C₁₁×#41	1	8	yes	—
322	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
323	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
324	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
325	C₂×Q₈	—	2	48	no	—
326	C₂×Q₈	C₂⁴×C₁₁	1	16	yes	—
327	C₂×D₄	—	2	48	no	—
328	C₂×D₄	C₂⁴×C₁₁	1	16	yes	—
329	C₂²×C₄	—	2	96	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	48	no	—
339	C₂²×C₄	—	2	48	no	—
340	C₂²×C₄	C₁₁×#41	1	8	yes	—
341	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
342	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
343	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
344	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
345	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
346	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
347	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
348	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
349	C₂²×C₄	C₂⁴×C₁₁	1	32	yes	—
350	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
351	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
352	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
353	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
354	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
355	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
356	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
357	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
358	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
359	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
360	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
361	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
362	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	—
363	C₂²⋊C₄	C₂⁴×C₁₁	1	16	yes	—
364	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
365	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
366	C₂²⋊C₄	C₂⁴×C₁₁	1	16	yes	—
367	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
368	C₄²	C₂⁴×C₁₁	1	32	yes	—
369	C₄²	C₂⁴×C₁₁	1	32	yes	—
370	C₄²	C₂⁴×C₁₁	1	16	yes	—
371	C₁₁	C₂²×#552	1	1	yes	characteristic, direct product factor, Sylow
372	C₂³	—	2	32	no	—
373	C₂³	—	2	12	no	—
374	C₂³	—	2	12	no	—
375	C₂³	—	2	12	no	—
376	C₂³	—	2	12	no	—
377	C₂³	—	2	12	no	—
378	C₂³	—	4	16	no	—
379	C₂³	C₂×C₁₁×#41	1	24	yes	—
380	C₂³	C₂×C₁₁×#41	1	4	yes	—
381	C₂³	C₂×C₁₁×#41	1	4	yes	—
382	C₂³	C₁₁×2₋¹⁺⁴	1	4	yes	—
383	C₂³	C₂⁵×C₁₁	1	4	yes	—
384	C₂³	C₂⁵×C₁₁	1	4	yes	—
385	C₂³	C₂⁵×C₁₁	1	3	yes	—
386	Q₈	—	2	32	no	—
387	D₄	—	2	32	no	—
388	C₂×C₄	—	2	64	no	—
389	C₂×C₄	—	2	24	no	—
390	C₂×C₄	—	2	24	no	—
391	C₂×C₄	—	2	12	no	—
392	C₂×C₄	—	2	12	no	—
393	C₂×C₄	—	2	12	no	—
394	C₂×C₄	—	2	24	no	—
395	C₂×C₄	—	2	12	no	—
396	C₂×C₄	—	2	24	no	—
397	C₂×C₄	—	2	32	no	—
398	C₂×C₄	—	2	32	no	—
399	C₂×C₄	C₂×C₁₁×#41	1	24	yes	—
400	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
401	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
402	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
403	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
404	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
405	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
406	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
407	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
408	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
409	C₂²	—	2	48	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	4	24	no	—
416	C₂²	C₁₁×#552	1	16	yes	direct product factor
417	C₂²	C₂²×C₁₁×#41	1	8	yes	—
418	C₂²	C₂²×C₁₁×#41	1	6	yes	—
419	C₂²	C₂²×C₁₁×#41	1	6	yes	—
420	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	6	yes	—
421	C₂²	C₂⁶×C₁₁	1	1	yes	characteristic
422	C₄	—	2	8	no	—
423	C₄	—	2	8	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	4	no	—
427	C₄	—	2	8	no	—
428	C₄	—	2	4	no	—
429	C₄	—	2	8	no	—
430	C₄	C₂²×C₁₁×#41	1	8	yes	—
431	C₂	—	2	8	no	—
432	C₂	—	4	4	no	—
433	C₂	C₂×C₁₁×#552	1	12	yes	direct product factor
434	C₂	C₂³×C₁₁×#41	1	1	yes	characteristic
435	C₂	C₂³×C₁₁×#41	1	1	yes	characteristic
436	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	C₂³×D₄×C₁₁	C₂²
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×#552	C₂	direct (N × H)
2. C₂²×C₁₁×#126	C₂	semidirect
3. C₂²×C₁₁×#125	C₂	semidirect
4. C₂²×C₁₁×#125	C₂	semidirect
6. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
7. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₄×Q₈×C₁₁	C₂	semidirect
10. C₂²×C₁₁×#117	C₂	semidirect
11. C₂²×C₁₁×#117	C₂	semidirect
12. C₂³×C₁₁×C₄⋊C₄	C₂	semidirect
18. C₁₁×#552	C₂²	direct (N × H)
19. C₂×C₁₁×#126	C₂²	semidirect
20. C₂×C₁₁×#125	C₂²	semidirect
21. C₂×C₁₁×#125	C₂²	semidirect
23. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
27. C₂×C₁₁×#117	C₂²	semidirect
28. C₂×C₁₁×#117	C₂²	semidirect
39. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
69. C₁₁×#126	C₂³	semidirect
70. C₁₁×#125	C₂³	semidirect
71. C₁₁×#125	C₂³	semidirect
73. C₁₁×C₂²⋊Q₈	C₂³	semidirect
74. C₁₁×C₂²⋊Q₈	C₂³	semidirect
75. C₄×Q₈×C₁₁	C₂³	semidirect
77. C₁₁×#117	C₂³	semidirect
78. C₁₁×#117	C₂³	semidirect
89. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
98. C₂²×#552	C₁₁	direct (N × H)
154. C₂×#552	C₂×C₁₁	direct (N × H)
155. C₂²×#126	C₂×C₁₁	semidirect
156. C₂²×#125	C₂×C₁₁	semidirect
157. C₂²×#125	C₂×C₁₁	semidirect
159. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
160. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
161. C₂²×C₄×Q₈	C₂×C₁₁	semidirect
163. C₂²×#117	C₂×C₁₁	semidirect
164. C₂²×#117	C₂×C₁₁	semidirect
165. C₂³×C₄⋊C₄	C₂×C₁₁	semidirect
208. #552	C₂²×C₁₁	direct (N × H)
209. C₂×#126	C₂²×C₁₁	semidirect
210. C₂×#125	C₂²×C₁₁	semidirect
211. C₂×#125	C₂²×C₁₁	semidirect
213. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
214. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
215. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
217. C₂×#117	C₂²×C₁₁	semidirect
218. C₂×#117	C₂²×C₁₁	semidirect
229. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
245. C₂²×C₁₁	#552	direct (N × H)
281. #126	C₂³×C₁₁	semidirect
282. #125	C₂³×C₁₁	semidirect
283. #125	C₂³×C₁₁	semidirect
285. C₂²⋊Q₈	C₂³×C₁₁	semidirect
286. C₂²⋊Q₈	C₂³×C₁₁	semidirect
287. C₄×Q₈	C₂³×C₁₁	semidirect
289. #117	C₂³×C₁₁	semidirect
290. #117	C₂³×C₁₁	semidirect
301. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
312. C₂×C₁₁	C₂×#552	direct (N × H)
371. C₁₁	C₂²×#552	direct (N × H)
416. C₂²	C₁₁×#552	direct (N × H)
433. C₂	C₂×C₁₁×#552	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×#552	2
C₂²×C₁₁×#126	2
C₂²×C₁₁×#125	2
C₂²×C₁₁×#123	2
C₂²×C₁₁×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₁	2
C₂²×C₄×D₄×C₁₁	2
C₂²×C₁₁×#117	2
C₂³×C₁₁×C₄⋊C₄	2
C₂²×#552	11

Subgroups — C22×C11×#552 #14639897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#552 #14639897