Subgroups — C₂×Q₈×Dic₂₉₂ #33966434

Order 18688.

1830 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₁₄₆	C₂	1	2	yes	maximal
2	Q₈×Dic₂₉₂	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988992	C₂	1	3	yes	maximal
4	C₂×#17988883	C₂	1	6	yes	maximal
5	C₂×C₄×Dic₂₉₂	C₂	1	3	yes	maximal
6	C₂×C₈×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic
8	Q₈×Dic₁₄₆	—	2	8	no	—
9	Q₈×Dic₁₄₆	C₂²	1	16	yes	—
10	C₂×#14556591	C₂²	1	6	yes	—
11	C₂×#14556590	—	2	6	no	—
12	C₂×Q₈×Dic₇₃	—	2	2	no	—
13	C₂×C₄×Dic₁₄₆	C₂²	1	6	yes	—
14	#17988992	C₂²	1	24	yes	—
15	#17988883	C₂²	1	48	yes	—
16	C₄×Dic₂₉₂	C₂²	1	24	yes	—
17	C₂×#14556525	C₂²	1	3	yes	—
18	C₂×#14556525	C₂²	1	6	yes	—
19	C₂×#14556516	C₂²	1	6	yes	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₈×Q₈×C₇₃	C₂²	1	8	yes	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	3	yes	—
23	C₂×C₄×C₈×C₇₃	C₂²	1	3	yes	—
24	C₂²×Dic₁₄₆	—	2	6	no	—
25	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
26	C₂×Dic₂₉₂	Q₈	1	8	yes	direct product factor
27	C₂×Dic₂₉₂	C₂³	1	4	yes	—
28	#14556591	—	2	12	no	—
29	#14556591	C₂³	1	24	yes	—
30	#14556590	—	2	48	no	—
31	Q₈×Dic₇₃	—	2	16	no	—
32	C₄×Dic₁₄₆	—	2	12	no	—
33	C₄×Dic₁₄₆	C₂³	1	24	yes	—
34	C₂×C₄⋊Dic₇₃	—	2	6	no	—
35	C₂×C₄⋊Dic₇₃	C₂³	1	6	yes	—
36	C₂×#11924007	—	2	6	no	—
37	C₂×C₄×Dic₇₃	—	2	6	no	—
38	#14556525	C₂³	1	24	yes	—
39	#14556525	C₂³	1	12	yes	—
40	#14556516	C₂³	1	24	yes	—
41	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₇₃	C₂³	1	3	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₇₃	D₄	1	4	yes	—
45	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₇₃	D₄	1	3	yes	—
47	C₂×C₄²×C₇₃	C₂³	1	3	yes	—
48	C₄⋊C₈×C₇₃	C₂³	1	12	yes	—
49	C₄×C₈×C₇₃	C₂³	1	12	yes	—
50	C₂×Dic₁₄₆	—	2	2	no	—
51	C₂×Dic₁₄₆	—	2	4	no	—
52	C₂×Dic₁₄₆	—	2	24	no	—
53	C₂×Dic₁₄₆	—	8	12	no	—
54	C₂×Dic₁₄₆	C₂×Q₈	1	8	yes	—
55	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
56	C₂²×Dic₇₃	—	2	2	no	—
57	C₂²×Dic₇₃	—	2	6	no	—
58	Dic₂₉₂	C₂×Q₈	1	16	yes	direct product factor
59	C₄⋊Dic₇₃	—	2	24	no	—
60	C₄⋊Dic₇₃	—	2	6	no	—
61	C₄⋊Dic₇₃	C₂⁴	1	12	yes	—
62	#11924007	—	2	24	no	—
63	C₄×Dic₇₃	—	2	24	no	—
64	C₂×Q₈×C₇₃	Q₁₆	1	8	yes	complemented
65	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
66	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
67	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
68	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
69	C₂×C₈×C₇₃	—	2	6	no	—
70	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	—
71	C₂×C₈×C₇₃	C₂⁴	1	6	yes	—
72	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
73	C₄⋊C₄×C₇₃	C₂×D₄	1	12	yes	—
74	C₄²×C₇₃	C₂×D₄	1	6	yes	—
75	C₄²×C₇₃	C₂⁴	1	6	yes	—
76	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
77	Q₈×C₇₃	C₂×Q₁₆	1	16	yes	complemented
78	C₂×C₄×C₇₃	—	2	6	no	—
79	C₂×C₄×C₇₃	C₂×Q₁₆	1	12	yes	—
80	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
81	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
82	C₂×C₄×C₇₃	C₂²×D₄	1	6	yes	—
83	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
84	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
85	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
86	C₂×Dic₇₃	—	2	8	no	—
87	C₂×Dic₇₃	—	2	4	no	—
88	C₂×Dic₇₃	—	2	12	no	—
89	C₂×Dic₇₃	—	4	12	no	—
90	Dic₁₄₆	—	2	8	no	—
91	Dic₁₄₆	—	2	4	no	—
92	Dic₁₄₆	—	8	24	no	—
93	Dic₁₄₆	C₂²×Q₈	1	8	yes	—
94	C₈×C₇₃	—	2	6	no	—
95	C₈×C₇₃	C₂²×Q₈	1	4	yes	—
96	C₂²×C₇₃	D₄×Q₈	1	2	yes	—
97	C₂²×C₇₃	C₂²×Q₁₆	1	2	yes	—
98	C₂²×C₇₃	#576	1	2	yes	—
99	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
100	C₄×C₇₃	—	2	6	no	—
101	C₄×C₇₃	D₄×Q₈	1	2	yes	—
102	C₄×C₇₃	C₂²×Q₁₆	1	12	yes	—
103	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
104	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
105	Dic₇₃	—	2	8	no	—
106	Dic₇₃	—	4	12	no	—
107	C₂×Q₈×Q₁₆	—	73	1	no	maximal, Sylow
108	C₂×C₇₃	Q₈×Q₁₆	1	4	yes	complemented
109	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
110	C₂×C₇₃	C₂³×Q₁₆	1	1	yes	characteristic
111	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
112	C₂×Q₈²	—	73	2	no	—
113	Q₈×Q₁₆	—	73	16	no	—
114	C₂×#500	—	73	3	no	—
115	C₂×#477	—	73	6	no	—
116	C₂×C₈×Q₈	D₇₃	1	1	yes	characteristic
117	C₂×C₄×Q₁₆	—	73	3	no	—
118	C₇₃	C₂×Q₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	—	73	1	no	—
120	Q₈²	—	73	16	no	—
121	Q₈²	—	146	8	no	—
122	C₂×C₄⋊Q₈	—	73	6	no	—
123	C₂×C₄⋊Q₈	—	146	6	no	—
124	C₂×C₄×Q₈	—	73	6	no	—
125	C₂×C₄×Q₈	—	146	2	no	—
126	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
127	#500	—	73	24	no	—
128	#477	—	73	48	no	—
129	C₈×Q₈	C₂×D₇₃	1	8	yes	—
130	C₄×Q₁₆	—	73	24	no	—
131	C₂×#107	—	73	6	no	—
132	C₂×#107	—	73	3	no	—
133	C₂×C₄⋊C₈	C₂×D₇₃	1	3	yes	—
134	C₂×#103	—	73	6	no	—
135	C₂×C₄×C₈	C₂×D₇₃	1	3	yes	—
136	C₂²×Q₈	—	73	2	no	—
137	C₂²×Q₈	—	146	6	no	—
138	C₂²×Q₈	D₂₉₂	1	1	yes	characteristic
139	C₂×Q₁₆	—	73	8	no	—
140	C₂×Q₁₆	—	73	4	no	—
141	C₂²×C₈	C₂²×D₇₃	1	3	yes	—
142	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
143	C₄⋊Q₈	—	73	24	no	—
144	C₄⋊Q₈	—	146	48	no	—
145	C₄⋊Q₈	—	146	12	no	—
146	C₄×Q₈	—	73	24	no	—
147	C₄×Q₈	—	146	16	no	—
148	C₄×Q₈	—	146	12	no	—
149	C₄×Q₈	D₂₉₂	1	4	yes	—
150	C₄×Q₈	C₂²×D₇₃	1	4	yes	—
151	C₂×C₄⋊C₄	—	73	6	no	—
152	C₂×C₄⋊C₄	—	146	6	no	—
153	C₂×C₄⋊C₄	—	146	6	no	—
154	C₂×C₄⋊C₄	D₂₉₂	1	3	yes	—
155	C₂×C₄²	—	146	6	no	—
156	C₂×C₄²	C₂²×D₇₃	1	3	yes	—
157	#107	—	73	12	no	—
158	#107	—	73	24	no	—
159	C₄⋊C₈	C₂²×D₇₃	1	12	yes	—
160	#103	—	73	24	no	—
161	C₄×C₈	C₂²×D₇₃	1	12	yes	—
162	C₂×Q₈	—	584	12	no	—
163	C₂×Q₈	—	73	8	no	—
164	C₂×Q₈	—	73	4	no	—
165	C₂×Q₈	—	146	24	no	—
166	C₂×Q₈	—	146	2	no	—
167	C₂×Q₈	—	146	4	no	—
168	C₂×Q₈	Dic₂₉₂	1	8	yes	direct product factor
169	C₂×Q₈	C₂×D₂₉₂	1	4	yes	—
170	C₂²×C₄	—	146	6	no	—
171	C₂²×C₄	—	146	2	no	—
172	C₂²×C₄	C₂×D₂₉₂	1	3	yes	—
173	C₂²×C₄	C₂×D₂₉₂	1	3	yes	—
174	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
175	Q₁₆	—	73	16	no	—
176	C₂×C₈	—	2	6	no	—
177	C₂×C₈	Q₈×D₇₃	1	4	yes	—
178	C₂×C₈	C₂³×D₇₃	1	6	yes	—
179	C₂×C₈	C₂³×D₇₃	1	2	yes	—
180	C₄⋊C₄	—	73	12	no	—
181	C₄⋊C₄	—	146	24	no	—
182	C₄⋊C₄	—	146	6	no	—
183	C₄⋊C₄	—	146	24	no	—
184	C₄⋊C₄	C₂×D₂₉₂	1	12	yes	—
185	C₄²	—	146	24	no	—
186	C₄²	C₂×D₂₉₂	1	6	yes	—
187	C₄²	C₂³×D₇₃	1	6	yes	—
188	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
189	Q₈	—	584	24	no	—
190	Q₈	—	73	8	no	—
191	Q₈	—	146	4	no	—
192	Q₈	—	146	8	no	—
193	Q₈	C₂×Dic₂₉₂	1	16	yes	direct product factor
194	C₂×C₄	—	2	6	no	—
195	C₂×C₄	—	292	12	no	—
196	C₂×C₄	—	146	12	no	—
197	C₂×C₄	—	146	4	no	—
198	C₂×C₄	—	146	8	no	—
199	C₂×C₄	C₂×Dic₂₉₂	1	12	yes	—
200	C₂×C₄	C₂²×D₂₉₂	1	6	yes	—
201	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
202	C₂×C₄	C₂²×D₂₉₂	1	6	yes	—
203	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
204	C₂×C₄	#14556638	1	2	yes	—
205	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
206	C₈	—	2	6	no	—
207	C₈	C₂×Q₈×D₇₃	1	4	yes	—
208	C₂²	Q₈×D₂₉₂	1	2	yes	—
209	C₂²	C₂²×Dic₂₉₂	1	2	yes	—
210	C₂²	#17989392	1	2	yes	—
211	C₂²	C₂³×D₂₉₂	1	1	yes	characteristic
212	C₄	—	2	6	no	—
213	C₄	—	292	12	no	—
214	C₄	—	146	8	no	—
215	C₄	Q₈×D₂₉₂	1	2	yes	—
216	C₄	C₂²×Dic₂₉₂	1	12	yes	—
217	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
218	C₄	C₂×#14556638	1	1	yes	characteristic
219	C₂	Q₈×Dic₂₉₂	1	4	yes	direct product factor
220	C₂	C₂×Q₈×D₂₉₂	1	1	yes	characteristic
221	C₂	C₂³×Dic₂₉₂	1	1	yes	characteristic
222	C₂	C₂×#17989392	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₂₉₂
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×C₈×Q₈×C₇₃	C₂
socle, prime radical	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂×C₈×Q₈	D₇₃
hypocenter	C₇₃	C₂×Q₈×Q₁₆
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×Dic₂₉₂	C₂	direct (N × H)
26. C₂×Dic₂₉₂	Q₈	direct (N × H)
58. Dic₂₉₂	C₂×Q₈	direct (N × H)
64. C₂×Q₈×C₇₃	Q₁₆	semidirect
77. Q₈×C₇₃	C₂×Q₁₆	semidirect
108. C₂×C₇₃	Q₈×Q₁₆	semidirect
118. C₇₃	C₂×Q₈×Q₁₆	semidirect
168. C₂×Q₈	Dic₂₉₂	direct (N × H)
193. Q₈	C₂×Dic₂₉₂	direct (N × H)
219. C₂	Q₈×Dic₂₉₂	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×Q₈×Dic₁₄₆	2
Q₈×Dic₂₉₂	2
C₂×#17988992	2
C₂×#17988883	2
C₂×C₄×Dic₂₉₂	2
C₂×C₈×Q₈×C₇₃	2
C₂×Q₈×Q₁₆	73

Subgroups — C2×Q8×Dic292 #33966434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×Dic₂₉₂ #33966434