Subgroups — C₂×#13070737 #14908331

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10622514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10622510	C₂	1	2	yes	maximal, complemented
4	#13070737	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10622133	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66961	—	2	2	no	—
8	C₂²×D₈₈	C₂²	1	2	yes	—
9	C₂×#66954	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#108	C₂²	1	2	yes	—
12	C₂×#66887	—	2	2	no	—
13	C₂×#66876	C₂²	1	1	yes	characteristic
14	C₂×D₁₇₆	—	2	1	no	—
15	C₂×D₁₇₆	—	2	1	no	—
16	C₂×D₁₇₆	—	2	2	no	—
17	C₂×D₁₇₆	C₂²	1	4	yes	complemented
18	#10622514	—	2	2	no	—
19	#10622514	C₂²	1	4	yes	complemented
20	C₂×#66862	—	2	1	no	—
21	C₂×C₁₆×D₁₁	—	2	1	no	—
22	#10622510	—	2	4	no	—
23	#10622510	C₂²	1	8	yes	complemented
24	C₁₁×#368	C₂²	1	4	yes	complemented
25	#10622133	C₂²	1	8	yes	complemented
26	C₂×#4339	D₄	1	1	yes	characteristic
27	C₂²×D₄₄	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
30	C₂×#4318	D₄	1	1	yes	characteristic
31	#66961	—	2	8	no	—
32	#66961	—	4	4	no	—
33	C₂×D₈₈	—	2	2	no	—
34	C₂×D₈₈	—	2	2	no	—
35	C₂×D₈₈	—	2	2	no	—
36	C₂×D₈₈	—	2	2	no	—
37	C₂×D₈₈	—	2	2	no	—
38	C₂×D₈₈	—	4	2	no	—
39	C₂×D₈₈	C₂³	1	4	yes	—
40	C₂×#4314	—	4	2	no	—
41	#66954	—	2	1	no	—
42	#66954	—	2	1	no	—
43	#66954	D₄	1	2	yes	—
44	#66954	C₂³	1	2	yes	—
45	C₂×#4313	—	2	1	no	—
46	C₂×C₈×D₁₁	—	2	1	no	—
47	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
48	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
49	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
50	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
51	C₁₁×#108	—	2	2	no	—
52	C₁₁×#108	C₂³	1	4	yes	—
53	#66887	—	2	8	no	—
54	#66876	—	2	1	no	—
55	#66876	C₂³	1	2	yes	—
56	C₂×C₁₁⋊C₁₆	—	2	1	no	—
57	D₁₇₆	—	2	4	no	—
58	D₁₇₆	—	2	4	no	—
59	#66862	—	2	4	no	—
60	C₁₆×D₁₁	—	2	4	no	—
61	C₂×#2221	—	11	1	no	maximal, Sylow
62	C₂³×D₁₁	—	4	2	no	—
63	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₁	—	2	1	no	—
65	#4339	—	2	1	no	—
66	#4339	—	2	1	no	—
67	#4339	D₈	1	2	yes	—
68	#4339	C₂×D₄	1	2	yes	—
69	C₂×D₄₄	—	2	4	no	—
70	C₂×D₄₄	—	4	2	no	—
71	C₂×D₄₄	—	4	2	no	—
72	C₂×D₄₄	—	4	2	no	—
73	C₂×D₄₄	—	4	2	no	—
74	C₂×D₄₄	—	4	2	no	—
75	C₂×D₄₄	D₈	1	1	yes	characteristic
76	C₂×C₄×D₁₁	—	2	1	no	—
77	C₂×Dic₂₂	D₈	1	1	yes	characteristic
78	C₁₁×M₁₆	—	2	4	no	—
79	C₁₁×M₁₆	—	4	2	no	—
80	C₂×C₈×C₁₁	—	4	2	no	—
81	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
85	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
87	#4318	—	2	1	no	—
88	#4318	C₂×D₄	1	2	yes	—
89	C₂×C₁₁⋊C₈	—	2	1	no	—
90	D₈₈	—	2	4	no	—
91	D₈₈	—	2	4	no	—
92	D₈₈	—	4	8	no	—
93	D₈₈	—	4	2	no	—
94	D₈₈	—	4	2	no	—
95	#4314	—	4	8	no	—
96	#4313	—	2	2	no	—
97	#4313	—	2	2	no	—
98	C₈×D₁₁	—	2	2	no	—
99	C₈×D₁₁	—	2	2	no	—
100	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
101	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
102	C₁₁⋊C₁₆	—	2	2	no	—
103	C₂²×D₁₆	—	11	1	no	—
104	C₂×#504	—	11	1	no	—
105	C₂×#472	—	11	2	no	—
106	#2221	—	11	8	no	—
107	C₂×#368	D₁₁	1	1	yes	characteristic, complemented
108	C₂×#361	—	11	2	no	—
109	C₂³×C₁₁	#135	1	1	yes	characteristic
110	C₂²×D₁₁	—	2	1	no	—
111	C₂²×D₁₁	—	4	4	no	—
112	C₂²×D₁₁	—	8	2	no	—
113	C₂²×D₁₁	—	8	2	no	—
114	C₂²×D₁₁	—	16	4	no	—
115	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
119	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
121	C₂²⋊D₁₁	—	2	2	no	—
122	C₂²⋊D₁₁	—	2	2	no	—
123	C₂×Dic₁₁	—	2	1	no	—
124	D₄₄	—	2	1	no	—
125	D₄₄	—	4	4	no	—
126	D₄₄	—	4	4	no	—
127	D₄₄	—	8	2	no	—
128	D₄₄	—	8	2	no	—
129	D₄₄	C₂×D₈	1	2	yes	—
130	C₄×D₁₁	—	2	2	no	—
131	C₄×D₁₁	—	2	2	no	—
132	Dic₂₂	—	2	1	no	—
133	Dic₂₂	C₂×D₈	1	2	yes	—
134	C₈×C₁₁	—	4	4	no	—
135	C₈×C₁₁	#121	1	1	yes	characteristic
136	C₈×C₁₁	#121	1	1	yes	characteristic
137	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
138	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
139	C₁₁⋊C₈	—	2	2	no	—
140	C₂×AGL(1,ℤ/8)	—	22	2	no	—
141	C₂²×D₈	—	11	2	no	—
142	C₂×#131	—	11	1	no	—
143	C₂×D₁₆	—	11	4	no	—
144	C₂×D₁₆	—	22	1	no	—
145	C₂×D₁₆	—	22	1	no	—
146	C₂×D₁₆	—	22	2	no	—
147	#504	—	11	4	no	—
148	#504	—	22	2	no	—
149	C₂×M₃₂	—	11	1	no	—
150	C₂×M₃₂	—	22	1	no	—
151	C₂²×C₁₆	—	22	1	no	—
152	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
153	#472	—	11	8	no	—
154	#472	—	22	4	no	—
155	C₂×#108	C₂×D₁₁	1	2	yes	—
156	C₂×#100	—	22	2	no	—
157	#368	C₂×D₁₁	1	4	yes	complemented
158	#361	—	11	8	no	—
159	C₂²×C₁₁	—	2	2	no	—
160	C₂²×C₁₁	#466	1	1	yes	characteristic
161	C₂²×C₁₁	#466	1	1	yes	characteristic
162	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
163	C₂×D₁₁	—	2	2	no	—
164	C₂×D₁₁	—	4	2	no	—
165	C₂×D₁₁	—	8	4	no	—
166	C₂×D₁₁	—	16	4	no	—
167	C₂×D₁₁	—	16	4	no	—
168	C₂×D₁₁	—	16	4	no	—
169	C₄×C₁₁	#466	1	1	yes	characteristic
170	C₄×C₁₁	#466	1	1	yes	characteristic
171	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
172	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
173	Dic₁₁	—	2	2	no	—
174	C₂×#41	—	11	1	no	—
175	C₂²×D₄	—	22	2	no	—
176	AGL(1,ℤ/8)	—	22	8	no	—
177	AGL(1,ℤ/8)	—	44	4	no	—
178	C₂×SD₁₆	—	44	2	no	—
179	C₂×D₈	—	11	4	no	—
180	C₂×D₈	—	22	2	no	—
181	C₂×D₈	—	22	2	no	—
182	C₂×D₈	—	22	2	no	—
183	C₂×D₈	—	22	2	no	—
184	C₂×D₈	—	22	2	no	—
185	C₂×D₈	—	44	2	no	—
186	#131	—	11	2	no	—
187	#131	—	11	2	no	—
188	#131	—	22	1	no	—
189	#131	—	22	1	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	11	1	no	—
192	C₂×M₁₆	—	22	1	no	—
193	C₂²×C₈	—	22	1	no	—
194	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
195	D₁₆	—	22	4	no	—
196	D₁₆	—	22	4	no	—
197	M₃₂	—	11	2	no	—
198	M₃₂	—	22	1	no	—
199	M₃₂	—	22	4	no	—
200	C₂×C₁₆	—	22	1	no	—
201	C₂×C₁₆	—	22	4	no	—
202	C₂×C₁₆	D₄₄	1	1	yes	characteristic
203	C₂×C₁₆	D₄₄	1	1	yes	characteristic
204	C₂×C₁₆	D₄₄	1	2	yes	—
205	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
206	#108	—	2	2	no	—
207	#108	C₂²×D₁₁	1	4	yes	—
208	#100	—	22	8	no	—
209	C₂×C₁₁	—	2	1	no	—
210	C₂×C₁₁	—	2	1	no	—
211	C₂×C₁₁	#2221	1	2	yes	complemented
212	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
213	D₁₁	—	4	2	no	—
214	D₁₁	—	16	4	no	—
215	C₂⁴	—	44	2	no	—
216	#41	—	11	2	no	—
217	#41	—	11	2	no	—
218	#41	—	22	1	no	—
219	#41	—	22	1	no	—
220	C₂×Q₈	—	11	1	no	—
221	C₂×D₄	—	11	1	no	—
222	C₂×D₄	—	22	1	no	—
223	C₂×D₄	—	22	4	no	—
224	C₂×D₄	—	44	2	no	—
225	C₂×D₄	—	44	2	no	—
226	C₂×D₄	—	44	2	no	—
227	C₂×D₄	—	44	2	no	—
228	C₂×D₄	—	44	2	no	—
229	C₂²×C₄	—	22	1	no	—
230	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
231	SD₁₆	—	44	8	no	—
232	D₈	—	22	4	no	—
233	D₈	—	22	4	no	—
234	D₈	—	44	8	no	—
235	D₈	—	44	2	no	—
236	D₈	—	44	2	no	—
237	M₁₆	—	2	4	no	—
238	M₁₆	—	4	2	no	—
239	M₁₆	—	11	2	no	—
240	M₁₆	—	22	1	no	—
241	M₁₆	—	22	2	no	—
242	M₁₆	—	22	2	no	—
243	C₂×C₈	—	4	2	no	—
244	C₂×C₈	—	22	1	no	—
245	C₂×C₈	—	22	2	no	—
246	C₂×C₈	—	22	2	no	—
247	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
248	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
249	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
250	C₂×C₈	#4343	1	1	yes	characteristic
251	C₂×C₈	#4343	1	1	yes	characteristic
252	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
253	C₁₆	—	22	2	no	—
254	C₁₆	C₂×D₄₄	1	2	yes	—
255	C₁₆	C₂×D₄₄	1	2	yes	—
256	C₁₁	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
257	C₂³	—	22	1	no	—
258	C₂³	—	44	4	no	—
259	C₂³	—	88	2	no	—
260	C₂³	—	88	2	no	—
261	C₂³	—	176	4	no	—
262	C₂³	#66972	1	1	yes	characteristic
263	Q₈	—	11	2	no	—
264	Q₈	—	22	1	no	—
265	D₄	—	11	2	no	—
266	D₄	—	22	2	no	—
267	D₄	—	22	2	no	—
268	D₄	—	22	1	no	—
269	D₄	—	44	4	no	—
270	D₄	—	44	4	no	—
271	D₄	—	88	2	no	—
272	D₄	—	88	2	no	—
273	C₂×C₄	—	22	1	no	—
274	C₂×C₄	—	22	2	no	—
275	C₂×C₄	—	22	2	no	—
276	C₂×C₄	#66948	1	1	yes	characteristic
277	C₂×C₄	#66948	1	1	yes	characteristic
278	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
279	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
280	C₂×C₄	#66972	1	1	yes	characteristic
281	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
282	C₈	—	4	4	no	—
283	C₈	—	22	2	no	—
284	C₈	#66948	1	1	yes	characteristic
285	C₈	#66948	1	1	yes	characteristic
286	C₈	C₂²×D₄₄	1	1	yes	characteristic
287	C₈	C₂×#4343	1	1	yes	characteristic
288	C₂²	—	2	2	no	—
289	C₂²	—	22	2	no	—
290	C₂²	—	44	2	no	—
291	C₂²	—	88	4	no	—
292	C₂²	—	176	4	no	—
293	C₂²	—	176	4	no	—
294	C₂²	—	176	4	no	—
295	C₂²	#10622496	1	1	yes	characteristic
296	C₂²	#10622496	1	1	yes	characteristic
297	C₂²	C₂×#66972	1	1	yes	characteristic
298	C₄	—	22	2	no	—
299	C₄	#10622496	1	1	yes	characteristic
300	C₄	#10622496	1	1	yes	characteristic
301	C₄	C₂×#66948	1	1	yes	characteristic
302	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
303	C₂	—	2	1	no	—
304	C₂	—	2	1	no	—
305	C₂	—	44	2	no	—
306	C₂	—	176	4	no	—
307	C₂	#13070737	1	2	yes	direct product factor
308	C₂	C₂×#10622496	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622496
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#368	C₂
socle	C₂²×C₁₁	#466
hypercenter	C₂×#368	D₁₁
hypocenter	C₁₁	C₂×#2221
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₇₆	C₂	semidirect
2. C₂×#10622514	C₂	semidirect
3. C₂×#10622510	C₂	semidirect
4. #13070737	C₂	direct (N × H)
5. C₂×#10622133	C₂	semidirect
6. C₂×C₁₁×#368	C₂	semidirect
17. C₂×D₁₇₆	C₂²	semidirect
19. #10622514	C₂²	semidirect
23. #10622510	C₂²	semidirect
24. C₁₁×#368	C₂²	semidirect
25. #10622133	C₂²	semidirect
107. C₂×#368	D₁₁	semidirect
157. #368	C₂×D₁₁	semidirect
211. C₂×C₁₁	#2221	semidirect
256. C₁₁	C₂×#2221	semidirect
307. C₂	#13070737	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₇₆	2
C₂×#10622514	2
C₂×#10622510	2
#13070737	2
C₂×#10622133	2
C₂×C₁₁×#368	2
C₂×#2221	11

Subgroups — C2×#13070737 #14908331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070737 #14908331