Subgroups — #14767706

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077533	C₂	1	1	yes	maximal, characteristic, complemented
2	#13077468	C₂	1	1	yes	maximal, characteristic, complemented
3	#13069527	C₂	1	1	yes	maximal, characteristic, complemented
4	#13069515	C₂	1	1	yes	maximal, characteristic, complemented
5	#13069149	C₂	1	2	yes	maximal, complemented
6	#13069144	C₂	1	2	yes	maximal, complemented
7	#13069105	C₂	1	2	yes	maximal, complemented
8	#13069098	C₂	1	2	yes	maximal, complemented
9	#13068740	C₂	1	1	yes	maximal, characteristic, complemented
10	#13068371	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3155	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₁₁×#535	C₂²	1	2	yes	—
16	#10623350	C₂²	1	2	yes	—
17	#10623329	C₂²	1	2	yes	—
18	C₁₁×#496	C₄	1	4	yes	complemented
19	C₁₁×#495	C₄	1	2	yes	complemented
20	C₁₁×#493	C₄	1	2	yes	complemented
21	C₁₁×#405	C₂²	1	1	yes	characteristic
22	#10622853	C₂²	1	2	yes	—
23	#10622849	C₂²	1	2	yes	—
24	#10622849	C₂²	1	2	yes	—
25	C₂×#66897	C₂²	1	2	yes	—
26	#10622828	C₂²	1	2	yes	—
27	#10622828	C₂²	1	2	yes	—
28	#10622810	—	2	2	no	—
29	#10622809	—	2	2	no	—
30	#10622765	—	2	2	no	—
31	D₈×Dic₁₁	—	2	2	no	—
32	C₂×#66883	C₂²	1	1	yes	characteristic
33	#10622719	C₂²	1	1	yes	characteristic
34	#10622714	C₂²	1	1	yes	characteristic
35	#10622714	C₂²	1	1	yes	characteristic
36	C₁₁⋊#338	C₂²	1	1	yes	characteristic
37	#10622195	C₂²	1	1	yes	characteristic
38	#10622194	C₂²	1	2	yes	—
39	#10622169	C₂²	1	1	yes	characteristic
40	#10622169	C₂²	1	1	yes	characteristic
41	#10622169	C₂²	1	2	yes	—
42	C₂×C₁₁×#41	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₁₁×AGL(1,ℤ/8)	—	4	2	no	—
45	C₁₁×AGL(1,ℤ/8)	—	4	2	no	—
46	C₁₁×#135	—	2	1	no	—
47	C₁₁×#135	—	2	1	no	—
48	C₁₁×#135	—	2	1	no	—
49	C₁₁×#135	—	2	1	no	—
50	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	complemented
52	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₁₁×D₈	—	2	1	no	—
54	C₂×C₁₁×D₈	—	2	1	no	—
55	C₂×C₁₁×D₈	—	2	1	no	—
56	C₂×C₁₁×D₈	—	2	1	no	—
57	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
61	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₁₁×#127	C₂×C₄	1	4	yes	complemented
64	C₁₁×#124	C₂×C₄	1	4	yes	complemented
65	C₁₁×#121	—	4	2	no	—
66	C₁₁×#120	—	4	2	no	—
67	C₁₁×#117	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊Dic₁₁	—	4	2	no	—
69	#67001	—	2	4	no	—
70	#67001	—	4	2	no	—
71	D₄×Dic₁₁	—	2	4	no	—
72	D₄×Dic₁₁	—	4	2	no	—
73	#66979	C₂³	1	2	yes	—
74	#66979	C₂³	1	1	yes	characteristic
75	#66979	C₂³	1	1	yes	characteristic
76	C₂×#4318	—	4	2	no	—
77	C₂×#4318	C₂³	1	2	yes	—
78	C₂×#4318	C₂³	1	1	yes	characteristic
79	C₂×#4318	C₂³	1	1	yes	characteristic
80	C₁₁×#97	C₂×C₄	1	2	yes	complemented
81	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	complemented
82	#66901	—	2	4	no	—
83	#66901	—	4	2	no	—
84	#66898	—	4	2	no	—
85	#66897	—	4	2	no	—
86	#66896	—	2	4	no	—
87	#66896	—	4	2	no	—
88	#66883	—	2	1	no	—
89	#66883	—	2	1	no	—
90	#66882	—	2	1	no	—
91	#66881	—	2	1	no	—
92	#66879	—	2	1	no	—
93	#66879	D₄	1	2	yes	complemented
94	C₈×Dic₁₁	—	2	1	no	—
95	C₈×Dic₁₁	D₄	1	2	yes	complemented
96	#22286	—	11	1	no	maximal, Sylow
97	C₂⁴×C₁₁	—	2	2	no	—
98	C₁₁×#41	—	2	2	no	—
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	2	2	no	—
101	C₁₁×#41	—	2	2	no	—
102	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	4	4	no	—
110	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₁₁	—	4	4	no	—
115	C₁₁×Q₁₆	—	2	1	no	—
116	C₁₁×Q₁₆	—	2	1	no	—
117	C₁₁×SD₁₆	—	2	2	no	—
118	C₁₁×SD₁₆	—	2	2	no	—
119	C₁₁×SD₁₆	—	4	4	no	—
120	C₁₁×D₈	—	2	2	no	—
121	C₁₁×D₈	—	2	2	no	—
122	C₁₁×D₈	—	2	2	no	—
123	C₁₁×D₈	—	2	2	no	—
124	C₁₁×D₈	—	2	1	no	—
125	C₁₁×D₈	—	2	1	no	—
126	C₁₁×D₈	—	4	4	no	—
127	C₁₁×M₁₆	—	2	1	no	—
128	C₁₁×M₁₆	—	2	1	no	—
129	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
135	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
136	C₁₁×C₄⋊C₄	—	2	1	no	—
137	C₁₁×C₂²⋊C₄	—	2	1	no	—
138	C₁₁×C₂²⋊C₄	—	4	4	no	—
139	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
140	C₂²⋊Dic₁₁	—	2	1	no	—
141	C₂²⋊Dic₁₁	—	2	1	no	—
142	C₂²⋊Dic₁₁	—	2	2	no	—
143	C₂²⋊Dic₁₁	—	4	4	no	—
144	C₄⋊Dic₁₁	—	2	2	no	—
145	C₄⋊Dic₁₁	—	2	1	no	—
146	C₄⋊Dic₁₁	—	2	1	no	—
147	C₄×Dic₁₁	—	2	1	no	—
148	C₄×Dic₁₁	—	2	2	no	—
149	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
150	#4318	—	2	2	no	—
151	#4318	—	2	1	no	—
152	#4318	—	2	1	no	—
153	#4318	—	2	1	no	—
154	#4318	—	2	2	no	—
155	#4318	—	2	1	no	—
156	#4318	—	4	4	no	—
157	C₂×C₁₁⋊C₈	—	2	1	no	—
158	C₂×C₁₁⋊C₈	—	2	2	no	—
159	C₂×C₁₁⋊C₈	—	4	4	no	—
160	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
161	#3155	D₁₁	1	1	yes	characteristic
162	#2957	—	11	1	no	—
163	#2948	—	11	1	no	—
164	#1978	—	11	1	no	—
165	#1976	—	11	1	no	—
166	#1911	—	11	2	no	—
167	#1910	—	11	2	no	—
168	#1904	—	11	2	no	—
169	#1903	—	11	2	no	—
170	#1833	—	11	1	no	—
171	#1747	—	11	1	no	—
172	C₂³×C₁₁	—	2	4	no	—
173	C₂³×C₁₁	—	2	2	no	—
174	C₂³×C₁₁	—	4	2	no	—
175	C₂³×C₁₁	—	4	2	no	—
176	C₂³×C₁₁	—	16	2	no	—
177	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
178	Q₈×C₁₁	—	2	2	no	—
179	Q₈×C₁₁	—	2	2	no	—
180	D₄×C₁₁	—	2	4	no	—
181	D₄×C₁₁	—	2	2	no	—
182	D₄×C₁₁	—	2	2	no	—
183	D₄×C₁₁	—	2	4	no	—
184	D₄×C₁₁	—	4	2	no	—
185	D₄×C₁₁	—	4	2	no	—
186	D₄×C₁₁	—	4	2	no	—
187	D₄×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	16	4	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	4	2	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×Dic₁₁	—	2	2	no	—
200	C₂×Dic₁₁	—	4	2	no	—
201	C₂×Dic₁₁	—	4	1	no	—
202	C₂×Dic₁₁	—	16	4	no	—
203	C₈×C₁₁	—	2	2	no	—
204	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
205	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
206	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₁₁⋊C₈	—	2	2	no	—
209	C₁₁⋊C₈	—	4	2	no	—
210	C₁₁⋊C₈	—	4	1	no	—
211	C₂×AGL(1,ℤ/8)	C₂×D₁₁	1	2	yes	—
212	C₂×#135	C₂×D₁₁	1	1	yes	characteristic
213	C₂²×D₈	C₂×D₁₁	1	1	yes	characteristic
214	#568	—	11	2	no	—
215	#535	C₂×D₁₁	1	2	yes	—
216	#518	—	11	2	no	—
217	#496	Dic₁₁	1	4	yes	complemented
218	#495	Dic₁₁	1	2	yes	complemented
219	#493	Dic₁₁	1	2	yes	complemented
220	#444	—	22	2	no	—
221	#443	—	22	2	no	—
222	#442	—	22	2	no	—
223	C₄×D₈	—	22	2	no	—
224	C₂×#108	—	11	1	no	—
225	#427	—	11	1	no	—
226	#421	—	11	2	no	—
227	#421	—	11	2	no	—
228	#418	—	11	2	no	—
229	#418	—	11	2	no	—
230	C₂×#100	—	11	2	no	—
231	#410	—	11	2	no	—
232	#405	—	11	1	no	—
233	#405	—	11	1	no	—
234	#405	C₂×D₁₁	1	1	yes	characteristic
235	#344	—	11	2	no	—
236	#338	—	11	1	no	—
237	H(3,ℤ/4)	—	11	1	no	—
238	H(3,ℤ/4)	—	11	2	no	—
239	H(3,ℤ/4)	—	11	1	no	—
240	H(3,ℤ/4)	—	11	1	no	—
241	C₂²×C₁₁	—	4	1	no	—
242	C₂²×C₁₁	—	4	2	no	—
243	C₂²×C₁₁	—	4	4	no	—
244	C₂²×C₁₁	—	8	2	no	—
245	C₂²×C₁₁	—	8	4	no	—
246	C₂²×C₁₁	—	8	4	no	—
247	C₂²×C₁₁	—	16	2	no	—
248	C₂²×C₁₁	#518	1	1	yes	characteristic
249	C₂²×C₁₁	#535	1	1	yes	characteristic
250	C₂²×C₁₁	#540	1	1	yes	characteristic
251	C₄×C₁₁	—	4	2	no	—
252	C₄×C₁₁	—	4	2	no	—
253	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₁₁	#518	1	1	yes	characteristic
255	C₄×C₁₁	#535	1	1	yes	characteristic
256	C₄×C₁₁	#540	1	1	yes	characteristic
257	Dic₁₁	—	4	2	no	—
258	Dic₁₁	—	8	1	no	—
259	Dic₁₁	—	8	2	no	—
260	C₂×#41	C₂²×D₁₁	1	2	yes	—
261	C₂²×D₄	C₂²×D₁₁	1	2	yes	—
262	AGL(1,ℤ/8)	—	4	2	no	—
263	AGL(1,ℤ/8)	—	4	2	no	—
264	#135	—	2	1	no	—
265	#135	—	2	1	no	—
266	#135	—	2	1	no	—
267	#135	—	2	1	no	—
268	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	C₂×Dic₁₁	1	2	yes	complemented
270	C₂×SD₁₆	C₂×Dic₁₁	1	4	yes	complemented
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	C₂×Dic₁₁	1	2	yes	—
276	C₂×D₈	C₂×Dic₁₁	1	2	yes	—
277	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic, complemented
278	C₂×D₈	C₂×Dic₁₁	1	4	yes	complemented
279	#131	—	22	4	no	—
280	#131	—	44	2	no	—
281	C₂×M₁₆	—	11	1	no	—
282	C₂×M₁₆	—	11	2	no	—
283	C₂×M₁₆	—	11	1	no	—
284	C₂×M₁₆	—	44	2	no	—
285	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
287	#127	C₂×Dic₁₁	1	4	yes	complemented
288	#124	C₂×Dic₁₁	1	4	yes	complemented
289	#121	—	4	2	no	—
290	#120	—	4	2	no	—
291	C₄×D₄	—	22	4	no	—
292	C₄×D₄	—	44	2	no	—
293	#117	—	11	1	no	—
294	#117	—	11	2	no	—
295	#117	—	11	1	no	—
296	#117	C₂²×D₁₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	44	2	no	—
298	#108	—	22	1	no	—
299	#108	—	22	1	no	—
300	#107	—	22	1	no	—
301	#106	—	22	1	no	—
302	#104	—	22	4	no	—
303	#104	—	44	2	no	—
304	#102	—	22	4	no	—
305	#102	—	44	2	no	—
306	#100	—	44	2	no	—
307	#99	—	44	2	no	—
308	#97	—	11	2	no	—
309	#97	—	22	1	no	—
310	#97	C₂×Dic₁₁	1	2	yes	complemented
311	C₄×C₈	—	11	2	no	—
312	C₄×C₈	—	22	1	no	—
313	C₄×C₈	C₂×Dic₁₁	1	2	yes	complemented
314	C₂×C₁₁	—	2	1	no	—
315	C₂×C₁₁	—	2	1	no	—
316	C₂×C₁₁	—	2	1	no	—
317	C₂×C₁₁	—	8	2	no	—
318	C₂×C₁₁	—	8	4	no	—
319	C₂×C₁₁	#2328	1	1	yes	characteristic
320	C₂⁴	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	C₂×Q₈	C₂²×Dic₁₁	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	C₂²×Dic₁₁	1	4	yes	—
334	C₂×D₄	C₂²×Dic₁₁	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	44	4	no	—
337	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	2	1	no	—
340	SD₁₆	—	2	2	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	4	4	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	1	no	—
349	D₈	—	4	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	22	1	no	—
353	M₁₆	—	22	1	no	—
354	M₁₆	—	22	2	no	—
355	M₁₆	—	22	1	no	—
356	M₁₆	—	22	2	no	—
357	M₁₆	—	22	1	no	—
358	M₁₆	—	44	4	no	—
359	C₂×C₈	—	11	2	no	—
360	C₂×C₈	—	22	1	no	—
361	C₂×C₈	—	22	2	no	—
362	C₂×C₈	—	44	4	no	—
363	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
364	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
365	C₂×C₈	#4341	1	1	yes	characteristic
366	C₂×C₈	#4341	1	1	yes	characteristic
367	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
368	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
369	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	22	1	no	—
372	C₄⋊C₄	—	22	2	no	—
373	C₄⋊C₄	—	22	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	22	1	no	—
377	C₂²⋊C₄	—	22	1	no	—
378	C₂²⋊C₄	—	22	2	no	—
379	C₂²⋊C₄	—	44	4	no	—
380	C₄²	—	11	2	no	—
381	C₄²	—	22	1	no	—
382	C₄²	—	22	2	no	—
383	C₄²	C₂²×Dic₁₁	1	2	yes	—
384	C₁₁	#22286	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	#67037	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	22	2	no	—
407	C₂×C₄	—	44	2	no	—
408	C₂×C₄	—	44	1	no	—
409	C₂×C₄	—	176	4	no	—
410	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#4341	1	1	yes	characteristic
412	C₂×C₄	#67037	1	1	yes	characteristic
413	C₂×C₄	#67037	1	1	yes	characteristic
414	C₂×C₄	#67037	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	22	2	no	—
418	C₈	—	44	2	no	—
419	C₈	—	44	1	no	—
420	C₈	D₄×Dic₁₁	1	1	yes	characteristic
421	C₈	D₄×Dic₁₁	1	1	yes	characteristic
422	C₈	D₄×Dic₁₁	1	1	yes	characteristic
423	C₈	D₄×Dic₁₁	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	#10623246	1	1	yes	characteristic
432	C₂²	#10623250	1	1	yes	characteristic
433	C₂²	#10623329	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	44	2	no	—
437	C₄	—	88	2	no	—
438	C₄	—	88	1	no	—
439	C₄	#10623246	1	1	yes	characteristic
440	C₄	#10623250	1	1	yes	characteristic
441	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
442	C₄	#10623329	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	#13071342	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13071342
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting, prime radical	C₁₁×#3155	C₂
socle	C₂×C₁₁	#2328
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#3155	D₁₁
hypocenter	C₁₁	#22286
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #13077533	C₂	semidirect
2. #13077468	C₂	semidirect
3. #13069527	C₂	semidirect
4. #13069515	C₂	semidirect
5. #13069149	C₂	semidirect
6. #13069144	C₂	semidirect
7. #13069105	C₂	semidirect
8. #13069098	C₂	semidirect
9. #13068740	C₂	semidirect
10. #13068371	C₂	semidirect
18. C₁₁×#496	C₄	semidirect
19. C₁₁×#495	C₄	semidirect
20. C₁₁×#493	C₄	semidirect
50. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
51. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
52. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
59. C₂×C₁₁×D₈	C₂×C₄	semidirect
60. C₂×C₁₁×D₈	C₂×C₄	semidirect
63. C₁₁×#127	C₂×C₄	semidirect
64. C₁₁×#124	C₂×C₄	semidirect
80. C₁₁×#97	C₂×C₄	semidirect
81. C₄×C₈×C₁₁	C₂×C₄	semidirect
93. #66879	D₄	semidirect
95. C₈×Dic₁₁	D₄	semidirect
217. #496	Dic₁₁	semidirect
218. #495	Dic₁₁	semidirect
219. #493	Dic₁₁	semidirect
268. C₂×Q₁₆	C₂×Dic₁₁	semidirect
269. C₂×SD₁₆	C₂×Dic₁₁	semidirect
270. C₂×SD₁₆	C₂×Dic₁₁	semidirect
277. C₂×D₈	C₂×Dic₁₁	semidirect
278. C₂×D₈	C₂×Dic₁₁	semidirect
287. #127	C₂×Dic₁₁	semidirect
288. #124	C₂×Dic₁₁	semidirect
310. #97	C₂×Dic₁₁	semidirect
313. C₄×C₈	C₂×Dic₁₁	semidirect
384. C₁₁	#22286	semidirect

Maximal subgroups

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

subgroup	index
#13077533	2
#13077468	2
#13069527	2
#13069515	2
#13069149	2
#13069144	2
#13069105	2
#13069098	2
#13068740	2
#13068371	2
C₁₁×#3155	2
#22286	11