Subgroups — C₂×Q₈⋊#6092 #16787350

Order 3328.

382 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6092	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6092	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#6092	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₈×#1055	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×#6092	—	2	1	no	—
7	C₂²×#6092	—	2	1	no	—
8	Q₈×#1055	—	2	1	no	—
9	Q₈×#1055	—	2	1	no	—
10	Q₈×#1055	C₄	1	2	yes	—
11	Q₈×#1055	C₂²	1	2	yes	—
12	C₂×C₄⋊#1055	—	2	1	no	—
13	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic
14	C₂×C₄×#1055	—	2	1	no	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₄⋊#6092	—	2	1	no	—
17	C₄⋊#6092	C₂²	1	2	yes	—
18	C₄×#6092	—	2	1	no	—
19	C₄×#6092	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
21	C₄×Q₈×C₁₃	—	2	1	no	—
22	C₄×Q₈×C₁₃	—	2	1	no	—
23	C₄×Q₈×C₁₃	C₈	1	2	yes	—
24	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	—	2	1	no	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	—	2	1	no	—
30	C₂²×#1055	D₄	1	1	yes	characteristic
31	C₂²×#1055	D₄	1	1	yes	characteristic
32	C₂×#6092	—	2	4	no	—
33	C₂×#6092	—	2	2	no	—
34	C₂×#6092	—	2	2	no	—
35	C₂×#6092	—	4	2	no	—
36	C₄⋊#1055	—	2	1	no	—
37	C₄⋊#1055	—	2	2	no	—
38	C₄⋊#1055	—	2	2	no	—
39	C₄⋊#1055	C₂×C₄	1	2	yes	—
40	C₄×#1055	—	2	2	no	—
41	C₄×#1055	—	2	2	no	—
42	C₄×#1055	C₂×C₄	1	1	yes	characteristic
43	C₄×#1055	D₄	1	1	yes	characteristic
44	C₄×#1055	D₄	1	1	yes	characteristic
45	C₄×#1055	C₂³	1	1	yes	characteristic
46	C₂×Q₈⋊C₁₆	—	13	1	no	maximal, Sylow
47	C₂×Q₈×C₁₃	—	2	1	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂×Q₈×C₁₃	C₁₆	1	4	yes	complemented
50	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
51	C₂²×C₄×C₁₃	—	2	1	no	—
52	C₂²×C₄×C₁₃	—	2	1	no	—
53	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
56	C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
60	C₄²×C₁₃	—	2	2	no	—
61	C₄²×C₁₃	—	2	2	no	—
62	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
64	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂×#1055	—	2	2	no	—
67	C₂×#1055	—	2	2	no	—
68	C₂×#1055	—	4	2	no	—
69	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×#1055	SD₁₆	1	2	yes	—
72	C₂×#1055	Q₁₆	1	2	yes	—
73	C₂×#1055	C₂×D₄	1	1	yes	characteristic
74	C₂×#1055	C₂×D₄	1	1	yes	characteristic
75	#6092	—	2	4	no	—
76	#6092	—	4	2	no	—
77	C₂×C₈×Q₈	—	13	1	no	—
78	C₂×C₄⋊C₁₆	—	13	1	no	—
79	C₂×C₄×C₁₆	—	13	1	no	—
80	Q₈⋊C₁₆	—	13	4	no	—
81	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
82	Q₈×C₁₃	—	2	4	no	—
83	Q₈×C₁₃	—	2	2	no	—
84	Q₈×C₁₃	C₂×C₁₆	1	4	yes	complemented
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	4	2	no	—
90	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#103	1	2	yes	—
94	C₂×C₄×C₁₃	#104	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
96	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
100	#1055	—	2	1	no	—
101	#1055	—	2	1	no	—
102	#1055	—	4	2	no	—
103	#1055	#103	1	2	yes	—
104	#1055	C₂×SD₁₆	1	1	yes	characteristic
105	#1055	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×Q₈	#261	1	1	yes	characteristic
107	C₂²×C₁₆	—	26	1	no	—
108	C₂²×C₁₆	—	26	1	no	—
109	C₈×Q₈	—	13	2	no	—
110	C₈×Q₈	—	13	2	no	—
111	C₈×Q₈	—	26	1	no	—
112	C₈×Q₈	—	26	1	no	—
113	C₂×C₄⋊C₈	—	13	1	no	—
114	C₂×C₄⋊C₈	—	26	1	no	—
115	C₂×C₄×C₈	—	13	1	no	—
116	C₂×C₄×C₈	—	26	1	no	—
117	C₄⋊C₁₆	—	13	2	no	—
118	C₄⋊C₁₆	—	26	1	no	—
119	C₄×C₁₆	—	13	2	no	—
120	C₄×C₁₆	—	26	1	no	—
121	C₂²×C₁₃	Q₈⋊C₈	1	2	yes	—
122	C₂²×C₁₃	C₂²⋊C₁₆	1	2	yes	—
123	C₂²×C₁₃	#350	1	2	yes	—
124	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₄×C₁₃	—	2	4	no	—
126	C₄×C₁₃	—	2	1	no	—
127	C₄×C₁₃	—	2	1	no	—
128	C₄×C₁₃	—	4	2	no	—
129	C₄×C₁₃	Q₈⋊C₈	1	2	yes	—
130	C₄×C₁₃	C₂²⋊C₁₆	1	2	yes	—
131	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
132	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
133	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
134	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
135	C₂²×Q₈	#1057	1	1	yes	characteristic
136	C₂²×C₈	—	13	1	no	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	26	1	no	—
139	C₄×Q₈	—	2	1	no	—
140	C₄×Q₈	—	2	1	no	—
141	C₄×Q₈	#1057	1	2	yes	—
142	C₄×Q₈	C₂×#261	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	#1057	1	1	yes	characteristic
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	C₂×#261	1	1	yes	characteristic
147	C₂×C₁₆	—	26	2	no	—
148	C₂×C₁₆	—	26	4	no	—
149	C₂×C₁₆	—	26	2	no	—
150	C₂×C₁₆	—	52	2	no	—
151	C₄⋊C₈	—	13	2	no	—
152	C₄⋊C₈	—	26	2	no	—
153	C₄⋊C₈	—	26	2	no	—
154	C₄⋊C₈	—	26	1	no	—
155	C₄×C₈	—	13	1	no	—
156	C₄×C₈	—	13	1	no	—
157	C₄×C₈	—	13	1	no	—
158	C₄×C₈	—	13	1	no	—
159	C₄×C₈	—	26	2	no	—
160	C₄×C₈	—	26	2	no	—
161	C₂×C₁₃	Q₈⋊C₁₆	1	4	yes	complemented
162	C₂×C₁₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
163	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
164	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	#6092	1	4	yes	complemented
168	C₂×Q₈	C₂×#1057	1	2	yes	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
172	C₂²×C₄	#6122	1	1	yes	characteristic
173	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
174	C₂×C₈	—	13	2	no	—
175	C₂×C₈	—	13	2	no	—
176	C₂×C₈	—	13	1	no	—
177	C₂×C₈	—	13	1	no	—
178	C₂×C₈	—	13	1	no	—
179	C₂×C₈	—	13	1	no	—
180	C₂×C₈	—	26	2	no	—
181	C₂×C₈	—	26	2	no	—
182	C₂×C₈	—	52	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	C₂×#1057	1	2	yes	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	C₂×#1057	1	1	yes	characteristic
190	C₄²	#6122	1	1	yes	characteristic
191	C₄²	C₂²⋊#261	1	1	yes	characteristic
192	C₄²	C₂²×#261	1	1	yes	characteristic
193	C₁₆	—	26	4	no	—
194	C₁₆	—	52	2	no	—
195	C₁₃	C₂×Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂³	C₂²⋊#1057	1	1	yes	characteristic
197	Q₈	—	2	4	no	—
198	Q₈	—	2	2	no	—
199	Q₈	C₂×#6092	1	4	yes	complemented
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	C₂×#6092	1	2	yes	—
206	C₂×C₄	#88106	1	2	yes	—
207	C₂×C₄	#88117	1	2	yes	—
208	C₂×C₄	#88118	1	2	yes	—
209	C₂×C₄	C₂²⋊#1057	1	1	yes	characteristic
210	C₂×C₄	C₂²⋊#1057	1	1	yes	characteristic
211	C₂×C₄	C₂²⋊#1057	1	1	yes	characteristic
212	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
213	C₂×C₄	C₂×#6122	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
215	C₈	—	13	1	no	—
216	C₈	—	13	2	no	—
217	C₈	—	13	1	no	—
218	C₈	—	26	1	no	—
219	C₈	—	26	1	no	—
220	C₈	—	52	2	no	—
221	C₂²	C₂²⋊#6092	1	2	yes	—
222	C₂²	Q₈⋊#1057	1	2	yes	—
223	C₂²	#11718304	1	2	yes	—
224	C₂²	C₂×C₂²⋊#1057	1	1	yes	characteristic
225	C₄	—	2	4	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	2	no	—
229	C₄	C₂²⋊#6092	1	2	yes	—
230	C₄	Q₈⋊#1057	1	2	yes	—
231	C₄	C₂²×#6092	1	1	yes	characteristic
232	C₄	C₂×#88106	1	1	yes	characteristic
233	C₄	C₂×#88117	1	1	yes	characteristic
234	C₄	C₂×#88118	1	1	yes	characteristic
235	C₂	Q₈⋊#6092	1	4	yes	direct product factor
236	C₂	C₂×Q₈⋊#1057	1	1	yes	characteristic
237	C₂	C₂×C₂²⋊#6092	1	1	yes	characteristic
238	C₂	C₂×#11718304	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₄×Q₈×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²⋊C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₂×C₄×Q₈	#261
hypocenter	C₁₃	C₂×Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. Q₈⋊#6092	C₂	direct (N × H)
49. C₂×Q₈×C₁₃	C₁₆	semidirect
84. Q₈×C₁₃	C₂×C₁₆	semidirect
161. C₂×C₁₃	Q₈⋊C₁₆	semidirect
167. C₂×Q₈	#6092	semidirect
195. C₁₃	C₂×Q₈⋊C₁₆	semidirect
199. Q₈	C₂×#6092	semidirect
235. C₂	Q₈⋊#6092	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×C₄⋊#6092	2
C₂×C₄×#6092	2
Q₈⋊#6092	2
C₂×Q₈×#1055	2
C₂×Q₈⋊C₁₆	13

Subgroups — C2×Q8⋊#6092 #16787350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈⋊#6092 #16787350