Subgroups — #2449×C₂₁₁ #41010069

Order 27008.

648 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊Q₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Q₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊C₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#399×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#398×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#396×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#395×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#389×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#387×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#386×C₂₁₁	C₂	1	1	yes	maximal, characteristic
12	#386×C₂₁₁	C₂	1	1	yes	maximal, characteristic
13	#385×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#385×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#385×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₂₁₁	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₂₁₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
22	C₂²⋊Q₈×C₂₁₁	—	2	4	no	—
23	C₂²⋊Q₈×C₂₁₁	—	2	4	no	—
24	C₄×D₄×C₂₁₁	—	2	4	no	—
25	C₂×C₄⋊C₄×C₂₁₁	—	2	4	no	—
26	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
47	#95×C₂₁₁	C₂²	1	1	yes	characteristic
48	#95×C₂₁₁	C₂²	1	1	yes	characteristic
49	#95×C₂₁₁	C₂²	1	1	yes	characteristic
50	#95×C₂₁₁	C₂²	1	1	yes	characteristic
51	#95×C₂₁₁	C₂²	1	1	yes	characteristic
52	#95×C₂₁₁	C₂²	1	1	yes	characteristic
53	#95×C₂₁₁	C₂²	1	1	yes	characteristic
54	#95×C₂₁₁	C₂²	1	1	yes	characteristic
55	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
56	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
57	C₂×Q₈×C₂₁₁	—	2	2	no	—
58	C₂×Q₈×C₂₁₁	—	2	2	no	—
59	C₂×Q₈×C₂₁₁	—	4	1	no	—
60	C₂×D₄×C₂₁₁	—	2	2	no	—
61	C₂×D₄×C₂₁₁	—	2	2	no	—
62	C₂×D₄×C₂₁₁	Q₈	1	4	yes	complemented
63	C₂²×C₄×C₂₁₁	—	2	2	no	—
64	C₂²×C₄×C₂₁₁	—	2	2	no	—
65	C₂²×C₄×C₂₁₁	—	2	2	no	—
66	C₂²×C₄×C₂₁₁	—	2	2	no	—
67	C₂²×C₄×C₂₁₁	—	2	2	no	—
68	C₂²×C₄×C₂₁₁	—	2	2	no	—
69	C₂²×C₄×C₂₁₁	—	2	2	no	—
70	C₂²×C₄×C₂₁₁	—	2	2	no	—
71	C₂²×C₄×C₂₁₁	—	2	2	no	—
72	C₂²×C₄×C₂₁₁	—	4	1	no	—
73	C₂²×C₄×C₂₁₁	—	4	1	no	—
74	C₂²×C₄×C₂₁₁	—	4	1	no	—
75	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₂₁₁	—	2	2	no	—
89	C₄⋊C₄×C₂₁₁	—	2	2	no	—
90	C₄⋊C₄×C₂₁₁	—	2	2	no	—
91	C₄⋊C₄×C₂₁₁	—	2	2	no	—
92	C₄⋊C₄×C₂₁₁	—	2	2	no	—
93	C₄⋊C₄×C₂₁₁	—	2	2	no	—
94	C₄⋊C₄×C₂₁₁	—	2	2	no	—
95	C₄⋊C₄×C₂₁₁	—	2	2	no	—
96	C₄⋊C₄×C₂₁₁	—	2	2	no	—
97	C₄⋊C₄×C₂₁₁	—	2	2	no	—
98	C₄⋊C₄×C₂₁₁	—	4	1	no	—
99	C₄⋊C₄×C₂₁₁	D₄	1	4	yes	complemented
100	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
101	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
102	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
103	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
104	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
105	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
106	C₂²⋊C₄×C₂₁₁	—	4	1	no	—
107	C₂²⋊C₄×C₂₁₁	D₄	1	4	yes	—
108	C₄²×C₂₁₁	—	2	2	no	—
109	C₂³×C₂₁₁	—	2	1	no	—
110	C₂³×C₂₁₁	—	2	1	no	—
111	C₂³×C₂₁₁	—	2	1	no	—
112	C₂³×C₂₁₁	—	2	1	no	—
113	C₂³×C₂₁₁	—	2	1	no	—
114	C₂³×C₂₁₁	—	2	1	no	—
115	C₂³×C₂₁₁	—	2	1	no	—
116	C₂³×C₂₁₁	—	2	1	no	—
117	C₂³×C₂₁₁	—	2	1	no	—
118	C₂³×C₂₁₁	—	2	1	no	—
119	C₂³×C₂₁₁	C₂×D₄	1	2	yes	—
120	C₂³×C₂₁₁	C₂×Q₈	1	2	yes	—
121	C₂³×C₂₁₁	C₂×Q₈	1	2	yes	—
122	C₂³×C₂₁₁	#41	1	2	yes	—
123	C₂³×C₂₁₁	C₂⁴	1	1	yes	characteristic
124	Q₈×C₂₁₁	—	4	4	no	—
125	D₄×C₂₁₁	—	2	8	no	—
126	C₂×C₄×C₂₁₁	—	2	8	no	—
127	C₂×C₄×C₂₁₁	—	2	1	no	—
128	C₂×C₄×C₂₁₁	—	2	1	no	—
129	C₂×C₄×C₂₁₁	—	2	1	no	—
130	C₂×C₄×C₂₁₁	—	2	1	no	—
131	C₂×C₄×C₂₁₁	—	2	1	no	—
132	C₂×C₄×C₂₁₁	—	2	1	no	—
133	C₂×C₄×C₂₁₁	—	2	1	no	—
134	C₂×C₄×C₂₁₁	—	2	1	no	—
135	C₂×C₄×C₂₁₁	—	2	1	no	—
136	C₂×C₄×C₂₁₁	—	2	1	no	—
137	C₂×C₄×C₂₁₁	—	2	1	no	—
138	C₂×C₄×C₂₁₁	—	2	1	no	—
139	C₂×C₄×C₂₁₁	—	2	1	no	—
140	C₂×C₄×C₂₁₁	—	2	1	no	—
141	C₂×C₄×C₂₁₁	—	2	1	no	—
142	C₂×C₄×C₂₁₁	—	2	1	no	—
143	C₂×C₄×C₂₁₁	—	2	1	no	—
144	C₂×C₄×C₂₁₁	—	2	1	no	—
145	C₂×C₄×C₂₁₁	—	2	1	no	—
146	C₂×C₄×C₂₁₁	—	2	1	no	—
147	C₂×C₄×C₂₁₁	—	2	1	no	—
148	C₂×C₄×C₂₁₁	—	2	1	no	—
149	C₂×C₄×C₂₁₁	—	2	1	no	—
150	C₂×C₄×C₂₁₁	—	2	1	no	—
151	C₂×C₄×C₂₁₁	—	2	1	no	—
152	C₂×C₄×C₂₁₁	—	2	1	no	—
153	C₂×C₄×C₂₁₁	—	2	1	no	—
154	C₂×C₄×C₂₁₁	—	2	1	no	—
155	C₂×C₄×C₂₁₁	—	2	1	no	—
156	C₂×C₄×C₂₁₁	—	2	1	no	—
157	C₂×C₄×C₂₁₁	—	2	1	no	—
158	C₂×C₄×C₂₁₁	—	2	1	no	—
159	C₂×C₄×C₂₁₁	—	4	4	no	—
160	C₂×C₄×C₂₁₁	—	4	4	no	—
161	C₂×C₄×C₂₁₁	—	4	4	no	—
162	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
164	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
165	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
166	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
167	C₂×C₄×C₂₁₁	C₂×Q₈	1	2	yes	—
168	C₂×C₄×C₂₁₁	#41	1	2	yes	—
169	C₂²×C₂₁₁	—	2	2	no	—
170	C₂²×C₂₁₁	—	2	2	no	—
171	C₂²×C₂₁₁	—	2	2	no	—
172	C₂²×C₂₁₁	—	2	2	no	—
173	C₂²×C₂₁₁	—	2	2	no	—
174	C₂²×C₂₁₁	—	2	2	no	—
175	C₂²×C₂₁₁	—	2	2	no	—
176	C₂²×C₂₁₁	—	2	2	no	—
177	C₂²×C₂₁₁	—	2	2	no	—
178	C₂²×C₂₁₁	—	4	1	no	—
179	C₂²×C₂₁₁	—	4	1	no	—
180	C₂²×C₂₁₁	—	4	1	no	—
181	C₂²×C₂₁₁	—	4	1	no	—
182	C₂²×C₂₁₁	C₂²⋊Q₈	1	4	yes	complemented
183	C₂²×C₂₁₁	C₂²×D₄	1	1	yes	characteristic
184	C₂²×C₂₁₁	C₂²×D₄	1	1	yes	characteristic
185	C₂²×C₂₁₁	C₂²×Q₈	1	1	yes	characteristic
186	C₂²×C₂₁₁	C₂×#41	1	1	yes	characteristic
187	C₂²×C₂₁₁	C₂×#41	1	1	yes	characteristic
188	C₂²×C₂₁₁	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂²×C₂₁₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₄×C₂₁₁	—	2	2	no	—
191	C₄×C₂₁₁	—	2	2	no	—
192	C₄×C₂₁₁	—	2	2	no	—
193	C₄×C₂₁₁	—	2	2	no	—
194	C₄×C₂₁₁	—	2	2	no	—
195	C₄×C₂₁₁	—	2	2	no	—
196	C₄×C₂₁₁	—	2	2	no	—
197	C₄×C₂₁₁	—	4	1	no	—
198	C₄×C₂₁₁	—	4	1	no	—
199	C₄×C₂₁₁	—	4	1	no	—
200	C₄×C₂₁₁	—	4	1	no	—
201	C₄×C₂₁₁	—	4	1	no	—
202	C₄×C₂₁₁	—	4	1	no	—
203	C₂×C₂₁₁	—	2	4	no	—
204	C₂×C₂₁₁	—	4	2	no	—
205	C₂×C₂₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₂₁₁	#525	1	1	yes	characteristic
207	C₂×C₂₁₁	#539	1	1	yes	characteristic
208	C₂×C₂₁₁	D₄²	1	1	yes	characteristic
209	C₂×C₂₁₁	#547	1	1	yes	characteristic
210	C₂×C₂₁₁	D₄×Q₈	1	1	yes	characteristic
211	C₂×C₂₁₁	#554	1	1	yes	characteristic
212	C₂₁₁	#2449	1	1	yes	characteristic, direct product factor, Sylow
213	#2449	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₂²⋊Q₈	C₂×C₂₁₁	1	1	yes	characteristic, complemented
215	C₂×C₂²⋊Q₈	C₂×C₂₁₁	1	1	yes	characteristic, complemented
216	C₂×C₄×D₄	C₂×C₂₁₁	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	C₂×C₂₁₁	1	1	yes	characteristic, complemented
218	#399	C₂×C₂₁₁	1	1	yes	characteristic, complemented
219	#398	C₂×C₂₁₁	1	1	yes	characteristic, complemented
220	#396	C₂×C₂₁₁	1	1	yes	characteristic, complemented
221	#395	C₂×C₂₁₁	1	1	yes	characteristic, complemented
222	#389	C₂×C₂₁₁	1	1	yes	characteristic, complemented
223	#387	C₂×C₂₁₁	1	1	yes	characteristic, complemented
224	#386	C₂×C₂₁₁	1	1	yes	characteristic
225	#386	C₂×C₂₁₁	1	1	yes	characteristic
226	#385	C₂×C₂₁₁	1	1	yes	characteristic, complemented
227	#385	C₂×C₂₁₁	1	1	yes	characteristic, complemented
228	#385	C₂×C₂₁₁	1	1	yes	characteristic, complemented
229	C₂²×Q₈	C₂²×C₂₁₁	1	1	yes	characteristic
230	C₂²×D₄	C₂²×C₂₁₁	1	1	yes	characteristic
231	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
232	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
233	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
234	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
259	C₂×C₄²	C₂²×C₂₁₁	1	1	yes	characteristic
260	#95	C₂²×C₂₁₁	1	1	yes	characteristic
261	#95	C₂²×C₂₁₁	1	1	yes	characteristic
262	#95	C₂²×C₂₁₁	1	1	yes	characteristic
263	#95	C₂²×C₂₁₁	1	1	yes	characteristic
264	#95	C₂²×C₂₁₁	1	1	yes	characteristic
265	#95	C₂²×C₂₁₁	1	1	yes	characteristic
266	#95	C₂²×C₂₁₁	1	1	yes	characteristic
267	#95	C₂²×C₂₁₁	1	1	yes	characteristic
268	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
269	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	Q₈×C₂₁₁	1	4	yes	complemented
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	D₄×C₂₁₁	1	4	yes	complemented
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	D₄×C₂₁₁	1	4	yes	—
321	C₄²	—	2	2	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	C₂×D₄×C₂₁₁	1	2	yes	—
333	C₂³	C₂×Q₈×C₂₁₁	1	2	yes	—
334	C₂³	C₂×Q₈×C₂₁₁	1	2	yes	—
335	C₂³	#41×C₂₁₁	1	2	yes	—
336	C₂³	C₂⁴×C₂₁₁	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
376	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
377	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
378	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
379	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
380	C₂×C₄	C₂×Q₈×C₂₁₁	1	2	yes	—
381	C₂×C₄	#41×C₂₁₁	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	C₂²⋊Q₈×C₂₁₁	1	4	yes	complemented
396	C₂²	C₂²×D₄×C₂₁₁	1	1	yes	characteristic
397	C₂²	C₂²×D₄×C₂₁₁	1	1	yes	characteristic
398	C₂²	C₂²×Q₈×C₂₁₁	1	1	yes	characteristic
399	C₂²	C₂×#41×C₂₁₁	1	1	yes	characteristic
400	C₂²	C₂×#41×C₂₁₁	1	1	yes	characteristic
401	C₂²	H(5,𝔽₂)×C₂₁₁	1	1	yes	characteristic
402	C₂²	2₋¹⁺⁴×C₂₁₁	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₂	—	2	4	no	—
417	C₂	—	4	2	no	—
418	C₂	C₂×C₂²⋊Q₈×C₂₁₁	1	1	yes	characteristic
419	C₂	#525×C₂₁₁	1	1	yes	characteristic
420	C₂	#539×C₂₁₁	1	1	yes	characteristic
421	C₂	D₄²×C₂₁₁	1	1	yes	characteristic
422	C₂	#547×C₂₁₁	1	1	yes	characteristic
423	C₂	D₄×Q₈×C₂₁₁	1	1	yes	characteristic
424	C₂	#554×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₁₁
prime radical	C₂²×D₄×C₂₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂²⋊Q₈×C₂₁₁	C₂	semidirect
2. C₂×C₂²⋊Q₈×C₂₁₁	C₂	semidirect
4. C₂²×C₄⋊C₄×C₂₁₁	C₂	semidirect
5. #399×C₂₁₁	C₂	semidirect
6. #398×C₂₁₁	C₂	semidirect
7. #396×C₂₁₁	C₂	semidirect
8. #395×C₂₁₁	C₂	semidirect
9. #389×C₂₁₁	C₂	semidirect
10. #387×C₂₁₁	C₂	semidirect
13. #385×C₂₁₁	C₂	semidirect
14. #385×C₂₁₁	C₂	semidirect
15. #385×C₂₁₁	C₂	semidirect
62. C₂×D₄×C₂₁₁	Q₈	semidirect
99. C₄⋊C₄×C₂₁₁	D₄	semidirect
182. C₂²×C₂₁₁	C₂²⋊Q₈	semidirect
212. C₂₁₁	#2449	direct (N × H)
213. #2449	C₂₁₁	direct (N × H)
214. C₂×C₂²⋊Q₈	C₂×C₂₁₁	semidirect
215. C₂×C₂²⋊Q₈	C₂×C₂₁₁	semidirect
217. C₂²×C₄⋊C₄	C₂×C₂₁₁	semidirect
218. #399	C₂×C₂₁₁	semidirect
219. #398	C₂×C₂₁₁	semidirect
220. #396	C₂×C₂₁₁	semidirect
221. #395	C₂×C₂₁₁	semidirect
222. #389	C₂×C₂₁₁	semidirect
223. #387	C₂×C₂₁₁	semidirect
226. #385	C₂×C₂₁₁	semidirect
227. #385	C₂×C₂₁₁	semidirect
228. #385	C₂×C₂₁₁	semidirect
275. C₂×D₄	Q₈×C₂₁₁	semidirect
312. C₄⋊C₄	D₄×C₂₁₁	semidirect
395. C₂²	C₂²⋊Q₈×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊Q₈×C₂₁₁	2
C₂×C₄×D₄×C₂₁₁	2
C₂²×C₄⋊C₄×C₂₁₁	2
#399×C₂₁₁	2
#398×C₂₁₁	2
#396×C₂₁₁	2
#395×C₂₁₁	2
#389×C₂₁₁	2
#387×C₂₁₁	2
#386×C₂₁₁	2
#385×C₂₁₁	2
#2449	211

Subgroups — #2449×C211 #41010069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2449×C₂₁₁ #41010069