Finite Group Databasebeta

← C2×C67×#2983 #30739494

Subgroups — C2×C67×#2983 #30739494

Order 17152.

1978 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C67C211yesmaximal, characteristic
2C67×#2983C2116yesmaximal, direct product factor
3C2×#446×C67C218yesmaximal, complemented
4C2×#432×C67C214yesmaximal
5C2×#431×C67C212yesmaximal
6C23×Q8×C67C411yescharacteristic
7C2×C4×Q8×C67C414yes—
8C2×C4×Q8×C67C418yes—
9C2×C4×Q8×C67C2214yes—
10C2×C4×Q8×C67C2218yes—
11C22×C4⋊C4×C67C412yes—
12C22×C4⋊C4×C67C411yescharacteristic
13C22×C42×C67C2211yescharacteristic
14C22×C42×C67C2212yes—
15#446×C67C22164yescomplemented
16#432×C67C22132yes—
17#431×C67C22116yes—
18C2×C4⋊C8×C67C2214yes—
19C2×C4⋊C8×C67C2218yes—
20C2×C22⋊C8×C67C2214yes—
21C2×#97×C67C2218yes—
22C2×C4×C8×C67C2214yes—
23C22×Q8×C67—28no—
24C22×Q8×C67C2×C414yes—
25C22×Q8×C67C2×C418yes—
26C23×C4×C67C2×C412yes—
27C23×C4×C67C2×C411yescharacteristic
28C23×C4×C67C2×C412yes—
29C23×C4×C67C2×C411yescharacteristic
30C23×C4×C67C2311yescharacteristic
31C22×C8×C67C2318yes—
32C4×Q8×C67C2×C4116yes—
33C4×Q8×C67C2×C4132yes—
34C4×Q8×C67C23116yes—
35C2×C4⋊C4×C67C2×C418yes—
36C2×C4⋊C4×C67C2×C414yes—
37C2×C4⋊C4×C67C2×C4116yes—
38C2×C4⋊C4×C67C2×C418yes—
39C2×C42×C67C2×C414yes—
40C2×C42×C67C2×C412yes—
41C2×C42×C67C2×C418yes—
42C2×C42×C67C2×C414yes—
43C2×C42×C67C2314yes—
44C2×C42×C67C2318yes—
45C2×C42×C67C2312yes—
46C2×C42×C67C2314yes—
47C4⋊C8×C67C23116yes—
48C4⋊C8×C67C23132yes—
49C22⋊C8×C67C23116yes—
50#97×C67C23132yes—
51C4×C8×C67C23116yes—
52C24×C67C22×C411yescharacteristic
53C2×Q8×C67—232no—
54C2×Q8×C67—216no—
55C2×Q8×C67C22×C4116yes—
56C22×C4×C67—28no—
57C22×C4×C67—24no—
58C22×C4×C67—42no—
59C22×C4×C67—44no—
60C22×C4×C67M1618yes—
61C22×C4×C67C22×C411yescharacteristic
62C22×C4×C67C22×C412yes—
63C22×C4×C67C22×C412yes—
64C22×C4×C67C22×C414yes—
65C22×C4×C67C22×C418yes—
66C22×C4×C67C22×C414yes—
67C22×C4×C67C22×C414yes—
68C22×C4×C67C22×C418yes—
69C22×C4×C67C22×C414yes—
70C22×C4×C67C22×C412yes—
71C22×C4×C67C2412yes—
72C22×C4×C67C2411yescharacteristic
73C2×C8×C67—216no—
74C2×C8×C67C24116yes—
75C4⋊C4×C67C22×C4132yes—
76C4⋊C4×C67C22×C4116yes—
77C42×C67C22×C4116yes—
78C42×C67C22×C418yes—
79C42×C67C22×C418yes—
80C42×C67C22×C414yes—
81C42×C67C2414yes—
82C42×C67C2418yes—
83C23×C67—22no—
84C23×C67—22no—
85C23×C67C2×M1614yes—
86C23×C67C23×C412yes—
87C23×C67C23×C411yescharacteristic
88Q8×C67—232no—
89C2×C4×C67—22no—
90C2×C4×C67—216no—
91C2×C4×C67—28no—
92C2×C4×C67—24no—
93C2×C4×C67—28no—
94C2×C4×C67—24no—
95C2×C4×C67—24no—
96C2×C4×C67—44no—
97C2×C4×C67—48no—
98C2×C4×C67C2×M16116yes—
99C2×C4×C67C2×M1618yes—
100C2×C4×C67C23×C412yes—
101C2×C4×C67C23×C414yes—
102C2×C4×C67C23×C418yes—
103C2×C4×C67C23×C418yes—
104C2×C4×C67C23×C411yescharacteristic
105C2×C4×C67C23×C414yes—
106C2×C4×C672−1+414yes—
107C2×C4×C67C2511yescharacteristic
108C8×C67—216no—
109C22×C67—22no—
110C22×C67—28no—
111C22×C67—22no—
112C22×C67#51912yes—
113C22×C67C22×M1614yes—
114C22×C67C22×M1612yes—
115C22×C67#56812yes—
116C22×C67C24×C411yescharacteristic
117C4×C67—22no—
118C4×C67—28no—
119C4×C67—24no—
120C4×C67—28no—
121C4×C67#51912yes—
122C4×C67C22×M1618yes—
123C4×C67C2×2−1+412yes—
124C2×#2983C6711yesmaximal, characteristic, direct product factor, Sylow
125C2×C67—24no—
126C2×C67#298314yesdirect product factor
127C2×C67C2×#51911yescharacteristic
128C2×C67C23×M1611yescharacteristic
129C2×C67C2×#56811yescharacteristic
130C22×C4×Q8C2×C6711yescharacteristic
131#2983C2×C67116yesdirect product factor
132C2×#446C2×C6718yescomplemented
133C2×#432C2×C6714yes—
134C2×#431C2×C6712yes—
135C67C2×#298311yescharacteristic, direct product factor, Sylow
136C23×Q8C4×C6711yescharacteristic
137C2×C4×Q8C4×C6714yes—
138C2×C4×Q8C4×C6718yes—
139C2×C4×Q8C22×C6714yes—
140C2×C4×Q8C22×C6718yes—
141C22×C4⋊C4C4×C6712yes—
142C22×C4⋊C4C4×C6711yescharacteristic
143C22×C42C22×C6711yescharacteristic
144C22×C42C22×C6712yes—
145#446C22×C67164yescomplemented
146#432C22×C67132yes—
147#431C22×C67116yes—
148C2×C4⋊C8C22×C6714yes—
149C2×C4⋊C8C22×C6718yes—
150C2×C22⋊C8C22×C6714yes—
151C2×#97C22×C6718yes—
152C2×C4×C8C22×C6714yes—
153C22×Q8—28no—
154C22×Q8C2×C4×C6714yes—
155C22×Q8C2×C4×C6718yes—
156C23×C4C2×C4×C6712yes—
157C23×C4C2×C4×C6711yescharacteristic
158C23×C4C2×C4×C6712yes—
159C23×C4C2×C4×C6711yescharacteristic
160C23×C4C23×C6711yescharacteristic
161C22×C8C23×C6718yes—
162C4×Q8C2×C4×C67116yes—
163C4×Q8C2×C4×C67132yes—
164C4×Q8C23×C67116yes—
165C2×C4⋊C4C2×C4×C6718yes—
166C2×C4⋊C4C2×C4×C6714yes—
167C2×C4⋊C4C2×C4×C67116yes—
168C2×C4⋊C4C2×C4×C6718yes—
169C2×C42C2×C4×C6714yes—
170C2×C42C2×C4×C6712yes—
171C2×C42C2×C4×C6718yes—
172C2×C42C2×C4×C6714yes—
173C2×C42C23×C6712yes—
174C2×C42C23×C6714yes—
175C2×C42C23×C6714yes—
176C2×C42C23×C6718yes—
177C4⋊C8C23×C67116yes—
178C4⋊C8C23×C67132yes—
179C22⋊C8C23×C67116yes—
180#97C23×C67132yes—
181C4×C8C23×C67116yes—
182C24C22×C4×C6711yescharacteristic
183C2×Q8—232no—
184C2×Q8—216no—
185C2×Q8C22×C4×C67116yes—
186C22×C4—28no—
187C22×C4—24no—
188C22×C4—42no—
189C22×C4—44no—
190C22×C4M16×C6718yes—
191C22×C4C22×C4×C6711yescharacteristic
192C22×C4C22×C4×C6712yes—
193C22×C4C22×C4×C6712yes—
194C22×C4C22×C4×C6714yes—
195C22×C4C22×C4×C6718yes—
196C22×C4C22×C4×C6714yes—
197C22×C4C22×C4×C6714yes—
198C22×C4C22×C4×C6718yes—
199C22×C4C22×C4×C6714yes—
200C22×C4C22×C4×C6712yes—
201C22×C4C24×C6712yes—
202C22×C4C24×C6711yescharacteristic
203C2×C8—216no—
204C2×C8C24×C67116yes—
205C4⋊C4C22×C4×C67132yes—
206C4⋊C4C22×C4×C67116yes—
207C42C22×C4×C67116yes—
208C42C22×C4×C6718yes—
209C42C22×C4×C6718yes—
210C42C22×C4×C6714yes—
211C42C24×C6714yes—
212C42C24×C6718yes—
213C23—22no—
214C23—22no—
215C23C2×M16×C6714yes—
216C23C23×C4×C6712yes—
217C23C23×C4×C6711yescharacteristic
218Q8—232no—
219C2×C4—22no—
220C2×C4—216no—
221C2×C4—28no—
222C2×C4—24no—
223C2×C4—28no—
224C2×C4—24no—
225C2×C4—24no—
226C2×C4—44no—
227C2×C4—48no—
228C2×C4C2×M16×C67116yes—
229C2×C4C2×M16×C6718yes—
230C2×C4C23×C4×C6712yes—
231C2×C4C23×C4×C6714yes—
232C2×C4C23×C4×C6718yes—
233C2×C4C23×C4×C6718yes—
234C2×C4C23×C4×C6711yescharacteristic
235C2×C4C23×C4×C6714yes—
236C2×C42−1+4×C6714yes—
237C2×C4C25×C6711yescharacteristic
238C8—216no—
239C22—22no—
240C22—22no—
241C22—28no—
242C22#519×C6712yes—
243C22C22×M16×C6714yes—
244C22C22×M16×C6712yes—
245C22#568×C6712yes—
246C22C24×C4×C6711yescharacteristic
247C4—28no—
248C4—24no—
249C4—28no—
250C4—22no—
251C4#519×C6712yes—
252C4C22×M16×C6718yes—
253C4C2×2−1+4×C6712yes—
254C2—24no—
255C2C67×#298314yesdirect product factor
256C2C2×#519×C6711yescharacteristic
257C2C23×M16×C6711yescharacteristic
258C2C2×#568×C6711yescharacteristic
subgroupG/H
centerC22×C4×C67C24
commutatorC22C24×C4×C67
Frattini, cosocleC2×C4C25×C67
socleC23×C67C23×C4
prime radicalC24×C67C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C67×#2983C2direct (N × H)
3. C2×#446×C67C2semidirect
15. #446×C67C22semidirect
124. C2×#2983C67direct (N × H)
126. C2×C67#2983direct (N × H)
131. #2983C2×C67direct (N × H)
132. C2×#446C2×C67semidirect
135. C67C2×#2983direct (N × H)
145. #446C22×C67semidirect
255. C2C67×#2983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C672
C67×#29832
C2×#446×C672
C2×#432×C672
C2×#431×C672
C2×#298367