Subgroups — #14772215

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622436	C₂	1	2	yes	maximal
2	C₄×#67003	C₂	1	1	yes	maximal, characteristic
3	#13077185	C₂	1	1	yes	maximal, characteristic, complemented
4	#13077184	C₂	1	1	yes	maximal, characteristic, complemented
5	#13069368	C₂	1	2	yes	maximal, complemented
6	#13068892	C₂	1	2	yes	maximal, complemented
7	#13068889	C₂	1	2	yes	maximal, complemented
8	#13068787	C₂	1	1	yes	maximal, characteristic, complemented
9	#13068637	C₂	1	1	yes	maximal, characteristic, complemented
10	#13068485	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×#67003	C₂²	1	1	yes	characteristic
14	C₂×#67001	C₂²	1	2	yes	—
15	C₂×#66960	C₂²	1	2	yes	—
16	C₄×#4339	C₂²	1	1	yes	characteristic
17	C₁₁×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#104	C₂²	1	2	yes	—
19	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	#10622846	C₂²	1	1	yes	characteristic
21	C₂×#66886	C₂²	1	2	yes	—
22	C₂×#66886	C₂²	1	2	yes	—
23	#10622732	C₂²	1	2	yes	—
24	C₄×#4326	C₄	1	1	yes	characteristic, complemented
25	C₄×#4326	C₄	1	1	yes	characteristic, complemented
26	C₄×#4325	C₄	1	1	yes	characteristic, complemented
27	C₄×#4325	C₄	1	1	yes	characteristic, complemented
28	C₄×#4324	C₄	1	1	yes	characteristic, complemented
29	C₄×#4324	C₄	1	1	yes	characteristic, complemented
30	C₄×#4323	C₄	1	1	yes	characteristic, complemented
31	C₄×#4323	C₄	1	1	yes	characteristic, complemented
32	#10622615	C₂²	1	1	yes	characteristic
33	#10622612	—	2	2	no	—
34	#10622612	C₂²	1	2	yes	—
35	#10622611	C₂²	1	1	yes	characteristic
36	C₂×#66869	C₂²	1	2	yes	—
37	#10622537	—	2	1	no	—
38	#10622537	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
40	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
41	C₂×#66867	C₂²	1	2	yes	—
42	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
43	#10622452	—	2	2	no	—
44	#10622450	—	2	1	no	—
45	D₁₁×C₄⋊C₈	—	2	1	no	—
46	#10622436	—	2	8	no	—
47	C₁₁×#339	C₂²	1	2	yes	—
48	#10622162	C₂²	1	2	yes	—
49	#10622161	C₂²	1	2	yes	—
50	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
51	C₂×#4339	C₂³	1	1	yes	characteristic
52	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
53	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₁	—	2	1	no	—
56	C₄×D₄×C₁₁	—	2	1	no	—
57	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₁₁×#117	—	2	1	no	—
60	C₁₁×#117	C₂³	1	1	yes	characteristic
61	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
62	C₂×C₄²×C₁₁	—	2	1	no	—
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	#67003	D₄	1	4	yes	—
66	#67003	Q₈	1	4	yes	—
67	#67001	—	2	4	no	—
68	#67001	—	4	2	no	—
69	C₂×#4326	C₂×C₄	1	1	yes	characteristic
70	C₂×#4325	C₂×C₄	1	1	yes	characteristic
71	C₂×#4324	C₂×C₄	1	1	yes	characteristic
72	C₂×#4323	C₂×C₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₁₁	—	2	1	no	—
74	C₄×C₂²⋊D₁₁	—	2	1	no	—
75	#66979	C₂³	1	1	yes	characteristic
76	C₂×#4318	—	2	2	no	—
77	C₂×#4318	C₂³	1	2	yes	—
78	C₂²×C₁₁⋊C₈	—	2	2	no	—
79	C₂²×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₁₁⋊C₈	C₂³	1	2	yes	—
81	C₂²×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
82	#66960	—	2	4	no	—
83	#66960	—	4	2	no	—
84	C₂×#4313	—	2	2	no	—
85	C₂×C₈×D₁₁	—	2	2	no	—
86	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
88	#66925	—	2	1	no	—
89	C₄²×D₁₁	—	2	1	no	—
90	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
91	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
92	C₁₁×C₄⋊C₈	—	2	1	no	—
93	C₁₁×C₄⋊C₈	—	2	1	no	—
94	C₁₁×#104	—	2	4	no	—
95	C₁₁×#95	—	2	1	no	—
96	#66899	C₂×C₄	1	1	yes	characteristic
97	#66899	C₂×C₄	1	1	yes	characteristic
98	#66896	C₂×C₄	1	1	yes	characteristic
99	#66896	C₂×C₄	1	1	yes	characteristic
100	#66886	—	2	4	no	—
101	#66886	—	4	2	no	—
102	Dic₁₁⋊C₈	—	2	2	no	—
103	Dic₁₁⋊C₈	—	2	2	no	—
104	#66874	C₂×C₄	1	1	yes	characteristic
105	#66874	C₂×C₄	1	1	yes	characteristic
106	#66873	C₂×C₄	1	1	yes	characteristic
107	#66873	C₂×C₄	1	1	yes	characteristic
108	#66872	C₂×C₄	1	1	yes	characteristic
109	#66872	C₂×C₄	1	1	yes	characteristic
110	#66871	C₂×C₄	1	1	yes	characteristic
111	#66871	C₂×C₄	1	1	yes	characteristic
112	#66869	—	2	4	no	—
113	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
114	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
115	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
116	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
117	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
118	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
119	C₄⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
120	#66867	—	2	4	no	—
121	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
125	#22686	—	11	1	no	maximal, Sylow
126	C₁₁×#41	—	2	1	no	—
127	C₁₁×#41	—	2	1	no	—
128	C₁₁×#41	C₂×D₄	1	2	yes	—
129	C₁₁×#41	C₂×Q₈	1	2	yes	—
130	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₄×C₁₁	—	2	1	no	—
132	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	—	2	1	no	—
135	C₂²×C₄×C₁₁	—	2	1	no	—
136	C₂²×C₄×C₁₁	—	2	2	no	—
137	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁	—	2	1	no	—
141	#4339	—	2	1	no	—
142	#4339	—	2	1	no	—
143	#4339	C₂×D₄	1	2	yes	—
144	#4339	C₂×Q₈	1	2	yes	—
145	C₂×D₄₄	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₁₁	—	2	1	no	—
147	C₂×C₄×D₁₁	—	2	1	no	—
148	C₂×C₄×D₁₁	—	2	1	no	—
149	C₂×Dic₂₂	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×M₁₆	—	2	2	no	—
151	C₁₁×M₁₆	—	2	2	no	—
152	C₂×C₈×C₁₁	—	2	2	no	—
153	C₁₁×C₄⋊C₄	—	2	1	no	—
154	C₁₁×C₄⋊C₄	—	2	1	no	—
155	C₁₁×C₄⋊C₄	—	4	2	no	—
156	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₁₁×C₂²⋊C₄	—	2	1	no	—
159	C₁₁×C₂²⋊C₄	—	2	1	no	—
160	C₁₁×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
170	C₂²⋊Dic₁₁	—	2	1	no	—
171	#4326	C₄⋊C₄	1	4	yes	complemented
172	#4325	C₄⋊C₄	1	4	yes	complemented
173	#4324	C₄⋊C₄	1	4	yes	complemented
174	#4323	C₄⋊C₄	1	4	yes	complemented
175	(C₂×D₁₁)⋊C₄	—	2	1	no	—
176	(C₂×D₁₁)⋊C₄	—	2	1	no	—
177	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
179	Dic₁₁⋊C₄	—	2	1	no	—
180	Dic₁₁⋊C₄	—	2	1	no	—
181	C₄×Dic₁₁	—	2	1	no	—
182	C₄×Dic₁₁	—	2	1	no	—
183	C₄×Dic₁₁	—	2	1	no	—
184	#4318	—	2	2	no	—
185	#4318	—	2	2	no	—
186	#4318	—	4	4	no	—
187	C₂×C₁₁⋊C₈	—	2	2	no	—
188	C₂×C₁₁⋊C₈	—	2	2	no	—
189	C₂×C₁₁⋊C₈	—	2	1	no	—
190	C₂×C₁₁⋊C₈	—	2	2	no	—
191	C₂×C₁₁⋊C₈	—	2	1	no	—
192	C₂×C₁₁⋊C₈	—	4	4	no	—
193	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
194	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
198	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
199	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
200	C₂×C₁₁⋊C₈	C₂×Q₈	1	2	yes	—
201	#4313	—	4	4	no	—
202	C₈×D₁₁	—	4	4	no	—
203	C₂×#444	—	11	2	no	—
204	C₄×#135	—	11	1	no	—
205	#2906	—	11	1	no	—
206	#2906	—	11	1	no	—
207	#1946	—	11	2	no	—
208	#1866	—	11	2	no	—
209	#1866	—	11	2	no	—
210	#1848	—	11	1	no	—
211	#1806	—	11	1	no	—
212	#1806	D₁₁	1	1	yes	characteristic, complemented
213	#1770	—	11	1	no	—
214	C₂³×C₁₁	—	2	1	no	—
215	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
216	C₂²×D₁₁	—	2	1	no	—
217	Q₈×C₁₁	—	2	1	no	—
218	Q₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
219	D₄×C₁₁	—	2	2	no	—
220	D₄×C₁₁	—	2	2	no	—
221	D₄×C₁₁	—	2	1	no	—
222	D₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	2	2	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	2	1	no	—
229	C₂×C₄×C₁₁	—	4	1	no	—
230	C₂×C₄×C₁₁	—	4	2	no	—
231	C₂×C₄×C₁₁	—	4	2	no	—
232	C₂×C₄×C₁₁	—	4	2	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	8	1	no	—
235	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
245	C₂²⋊D₁₁	—	2	2	no	—
246	C₂²⋊D₁₁	—	2	2	no	—
247	C₂×Dic₁₁	—	2	1	no	—
248	C₂×Dic₁₁	—	2	1	no	—
249	C₂×Dic₁₁	—	2	1	no	—
250	D₄₄	—	2	1	no	—
251	D₄₄	C₂×C₄⋊C₄	1	2	yes	—
252	C₄×D₁₁	—	2	2	no	—
253	C₄×D₁₁	—	2	2	no	—
254	C₄×D₁₁	—	4	2	no	—
255	C₄×D₁₁	—	8	1	no	—
256	Dic₂₂	—	2	1	no	—
257	Dic₂₂	C₂×C₄⋊C₄	1	2	yes	—
258	C₈×C₁₁	—	4	2	no	—
259	C₁₁⋊C₈	—	2	1	no	—
260	C₁₁⋊C₈	—	2	1	no	—
261	C₁₁⋊C₈	—	2	2	no	—
262	C₁₁⋊C₈	—	2	2	no	—
263	C₁₁⋊C₈	—	4	2	no	—
264	C₁₁⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
265	C₁₁⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
266	C₂×#135	—	11	1	no	—
267	C₂×#131	—	11	2	no	—
268	C₂×#131	—	11	2	no	—
269	C₄×#41	—	11	1	no	—
270	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
271	#444	—	22	8	no	—
272	C₄×Q₁₆	—	11	1	no	—
273	C₄×Q₁₆	—	11	1	no	—
274	C₄×SD₁₆	—	11	1	no	—
275	C₄×SD₁₆	—	11	1	no	—
276	C₄×SD₁₆	—	11	1	no	—
277	C₄×SD₁₆	—	11	1	no	—
278	C₄×D₈	—	11	1	no	—
279	C₄×D₈	—	11	1	no	—
280	C₂×#108	—	11	2	no	—
281	C₂×#108	—	11	2	no	—
282	#427	—	11	1	no	—
283	#424	—	11	2	no	—
284	#424	—	11	2	no	—
285	#424	—	22	2	no	—
286	#424	—	22	2	no	—
287	#423	—	11	1	no	—
288	#423	—	22	1	no	—
289	#423	—	22	1	no	—
290	#423	C₂×D₁₁	1	1	yes	characteristic
291	C₂×C₄⋊C₈	—	11	1	no	—
292	C₂×C₄⋊C₈	—	22	1	no	—
293	C₂×C₄⋊C₈	—	22	1	no	—
294	C₂×#104	—	11	2	no	—
295	C₂×#104	C₂×D₁₁	1	2	yes	—
296	#416	—	11	1	no	—
297	#416	—	11	1	no	—
298	C₂×#97	—	11	2	no	—
299	C₂×C₄×C₈	—	11	1	no	—
300	C₄×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
301	#339	—	11	2	no	—
302	#339	C₂×D₁₁	1	2	yes	—
303	#336	—	11	2	no	—
304	C₂²×C₁₁	—	2	1	no	—
305	C₂²×C₁₁	—	2	1	no	—
306	C₂²×C₁₁	—	2	2	no	—
307	C₂²×C₁₁	—	4	1	no	—
308	C₂²×C₁₁	—	4	1	no	—
309	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₁₁	#547	1	1	yes	characteristic
311	C₂²×C₁₁	#554	1	1	yes	characteristic
312	C₂×D₁₁	—	2	2	no	—
313	C₂×D₁₁	—	4	1	no	—
314	C₂×D₁₁	—	4	1	no	—
315	C₄×C₁₁	—	2	2	no	—
316	C₄×C₁₁	—	2	1	no	—
317	C₄×C₁₁	—	2	1	no	—
318	C₄×C₁₁	—	2	1	no	—
319	C₄×C₁₁	—	4	1	no	—
320	C₄×C₁₁	—	4	1	no	—
321	C₄×C₁₁	—	8	2	no	—
322	C₄×C₁₁	#444	1	2	yes	complemented
323	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
324	C₄×C₁₁	#520	1	1	yes	characteristic
325	C₄×C₁₁	D₄²	1	1	yes	characteristic
326	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
327	Dic₁₁	—	2	2	no	—
328	Dic₁₁	—	4	1	no	—
329	Dic₁₁	—	4	1	no	—
330	C₂×#41	—	11	1	no	—
331	C₂×#41	C₂²×D₁₁	1	1	yes	characteristic
332	#135	—	11	4	no	—
333	#135	—	11	4	no	—
334	C₂×Q₁₆	—	11	1	no	—
335	C₂×SD₁₆	—	11	1	no	—
336	C₂×SD₁₆	—	11	1	no	—
337	C₂×D₈	—	11	1	no	—
338	#131	—	22	4	no	—
339	#131	—	22	4	no	—
340	#131	—	44	2	no	—
341	#131	—	44	2	no	—
342	C₂×M₁₆	—	11	2	no	—
343	C₂×M₁₆	—	22	2	no	—
344	C₂×M₁₆	—	22	2	no	—
345	C₂×M₁₆	C₂²×D₁₁	1	2	yes	—
346	C₂²×C₈	—	11	1	no	—
347	C₂²×C₈	—	11	2	no	—
348	C₂²×C₈	—	11	1	no	—
349	C₂²×C₈	—	22	2	no	—
350	C₂²×C₈	—	22	2	no	—
351	C₄×Q₈	—	11	1	no	—
352	C₄×Q₈	—	11	1	no	—
353	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
354	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
355	C₄×D₄	—	2	1	no	—
356	C₄×D₄	—	2	1	no	—
357	C₄×D₄	—	11	1	no	—
358	C₄×D₄	—	11	1	no	—
359	C₄×D₄	—	22	1	no	—
360	C₄×D₄	—	22	1	no	—
361	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
362	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
363	#117	—	2	1	no	—
364	#117	—	11	1	no	—
365	#117	—	22	1	no	—
366	#117	C₂²×D₁₁	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	22	1	no	—
370	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
371	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
372	#108	—	22	4	no	—
373	#108	—	44	2	no	—
374	#107	—	11	1	no	—
375	#107	—	11	1	no	—
376	#106	—	11	1	no	—
377	#106	—	11	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	11	1	no	—
381	C₄⋊C₈	—	11	1	no	—
382	C₄⋊C₈	—	11	2	no	—
383	C₄⋊C₈	—	22	2	no	—
384	C₄⋊C₈	—	22	2	no	—
385	C₄⋊C₈	—	22	2	no	—
386	C₄⋊C₈	—	22	2	no	—
387	C₄⋊C₈	—	22	1	no	—
388	C₄⋊C₈	—	22	1	no	—
389	#104	—	2	4	no	—
390	#104	—	22	4	no	—
391	#103	—	11	1	no	—
392	#103	—	11	1	no	—
393	#103	—	11	1	no	—
394	#103	—	11	1	no	—
395	#102	—	11	1	no	—
396	#102	—	11	1	no	—
397	#102	—	11	1	no	—
398	#102	—	11	1	no	—
399	#97	—	22	4	no	—
400	C₄×C₈	—	11	1	no	—
401	C₄×C₈	—	11	1	no	—
402	C₄×C₈	—	11	1	no	—
403	C₄×C₈	—	11	1	no	—
404	#95	—	2	1	no	—
405	C₂×C₁₁	—	2	1	no	—
406	C₂×C₁₁	—	2	1	no	—
407	C₂×C₁₁	—	4	2	no	—
408	C₂×C₁₁	D₄×C₄⋊C₄	1	1	yes	characteristic
409	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
410	C₂×C₁₁	#2957	1	1	yes	characteristic
411	D₁₁	—	4	2	no	—
412	#41	—	2	1	no	—
413	#41	—	2	1	no	—
414	#41	—	11	2	no	—
415	#41	—	11	2	no	—
416	#41	—	22	1	no	—
417	#41	—	22	1	no	—
418	#41	D₄×D₁₁	1	2	yes	—
419	#41	Q₈×D₁₁	1	2	yes	—
420	C₂×Q₈	—	11	1	no	—
421	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	11	1	no	—
424	C₂×D₄	—	22	1	no	—
425	C₂×D₄	C₂×C₄×D₁₁	1	1	yes	characteristic
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	22	1	no	—
431	C₂²×C₄	—	22	1	no	—
432	C₂²×C₄	—	22	1	no	—
433	C₂²×C₄	#4341	1	1	yes	characteristic
434	C₂²×C₄	#4341	1	1	yes	characteristic
435	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
436	Q₁₆	—	11	4	no	—
437	SD₁₆	—	11	4	no	—
438	SD₁₆	—	11	4	no	—
439	D₈	—	11	4	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	22	2	no	—
443	M₁₆	—	22	2	no	—
444	M₁₆	—	44	4	no	—
445	M₁₆	—	44	4	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	11	1	no	—
448	C₂×C₈	—	11	1	no	—
449	C₂×C₈	—	11	2	no	—
450	C₂×C₈	—	11	2	no	—
451	C₂×C₈	—	11	1	no	—
452	C₂×C₈	—	11	1	no	—
453	C₂×C₈	—	11	2	no	—
454	C₂×C₈	—	11	2	no	—
455	C₂×C₈	—	22	2	no	—
456	C₂×C₈	—	22	1	no	—
457	C₂×C₈	—	22	2	no	—
458	C₂×C₈	—	22	1	no	—
459	C₂×C₈	—	22	2	no	—
460	C₂×C₈	—	44	4	no	—
461	C₂×C₈	—	44	4	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	11	1	no	—
466	C₄⋊C₄	—	11	1	no	—
467	C₄⋊C₄	—	22	1	no	—
468	C₄⋊C₄	—	22	1	no	—
469	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
470	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	22	1	no	—
475	C₂²⋊C₄	—	22	1	no	—
476	C₂²⋊C₄	—	22	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	22	1	no	—
483	C₄²	—	22	1	no	—
484	C₄²	—	22	1	no	—
485	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
486	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
487	C₄²	D₄×D₁₁	1	1	yes	characteristic
488	C₄²	D₄×D₁₁	1	1	yes	characteristic
489	C₁₁	#22686	1	1	yes	characteristic, complemented, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	—	22	1	no	—
492	C₂³	C₂×#4341	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	11	2	no	—
495	Q₈	—	22	1	no	—
496	Q₈	C₄⋊C₄×D₁₁	1	2	yes	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	1	no	—
500	D₄	—	11	2	no	—
501	D₄	—	22	2	no	—
502	D₄	—	22	2	no	—
503	D₄	—	22	1	no	—
504	D₄	C₄⋊C₄×D₁₁	1	2	yes	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	22	1	no	—
518	C₂×C₄	—	22	2	no	—
519	C₂×C₄	—	22	2	no	—
520	C₂×C₄	—	22	1	no	—
521	C₂×C₄	—	22	1	no	—
522	C₂×C₄	—	44	2	no	—
523	C₂×C₄	—	88	1	no	—
524	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
525	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
526	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
527	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
530	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
531	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
532	C₂×C₄	#67042	1	1	yes	characteristic
533	C₂×C₄	#67043	1	1	yes	characteristic
534	C₈	—	4	2	no	—
535	C₈	—	11	2	no	—
536	C₈	—	11	2	no	—
537	C₈	—	22	1	no	—
538	C₈	—	22	1	no	—
539	C₈	—	22	2	no	—
540	C₈	—	22	2	no	—
541	C₈	—	44	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	22	2	no	—
548	C₂²	—	44	1	no	—
549	C₂²	—	44	1	no	—
550	C₂²	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
551	C₂²	#10623142	1	1	yes	characteristic
552	C₂²	#10623166	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	8	2	no	—
560	C₄	—	22	2	no	—
561	C₄	—	44	1	no	—
562	C₄	—	44	1	no	—
563	C₄	#10622436	1	2	yes	complemented
564	C₄	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
565	C₄	#10623054	1	1	yes	characteristic
566	C₄	#10623140	1	1	yes	characteristic
567	C₄	#10623163	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	44	2	no	—
572	C₂	#13071512	1	1	yes	characteristic
573	C₂	C₂×#10622436	1	1	yes	characteristic
574	C₂	#13077529	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#1806	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#67003	C₂²
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#1806	D₁₁
hypocenter	C₁₁	#22686
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
3. #13077185	C₂	semidirect
4. #13077184	C₂	semidirect
5. #13069368	C₂	semidirect
6. #13068892	C₂	semidirect
7. #13068889	C₂	semidirect
8. #13068787	C₂	semidirect
9. #13068637	C₂	semidirect
10. #13068485	C₂	semidirect
11. C₁₁×#1806	C₂	semidirect
24. C₄×#4326	C₄	semidirect
25. C₄×#4326	C₄	semidirect
26. C₄×#4325	C₄	semidirect
27. C₄×#4325	C₄	semidirect
28. C₄×#4324	C₄	semidirect
29. C₄×#4324	C₄	semidirect
30. C₄×#4323	C₄	semidirect
31. C₄×#4323	C₄	semidirect
171. #4326	C₄⋊C₄	semidirect
172. #4325	C₄⋊C₄	semidirect
173. #4324	C₄⋊C₄	semidirect
174. #4323	C₄⋊C₄	semidirect
212. #1806	D₁₁	semidirect
322. C₄×C₁₁	#444	semidirect
489. C₁₁	#22686	semidirect
563. C₄	#10622436	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622436	2
C₄×#67003	2
#13077185	2
#13077184	2
#13069368	2
#13068892	2
#13068889	2
#13068787	2
#13068637	2
#13068485	2
C₁₁×#1806	2
#22686	11