Finite Group Databasebeta

← C89×#60099 #36437947

Subgroups — C89×#60099 #36437947

Order 22784.

2738 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C89C212yesmaximal
2C2×C4×#41×C89C211yesmaximal, characteristic
3C89×#2906C2116yesmaximal, complemented
4C89×#2905C216yesmaximal, complemented
5C2×#423×C89C216yesmaximal, complemented
6C22×#41×C89C2211yescharacteristic
7#568×C89—216no—
8C2×#131×C89C22116yes—
9C22×M16×C89C22112yes—
10C4×#41×C89C414yes—
11C4×#41×C89C414yes—
12C4×#41×C89C2218yes—
13C2×C4×Q8×C89C412yes—
14C2×C4×D4×C89C416yes—
15C2×#117×C89C2213yes—
16C22×C42×C89C2213yes—
17#424×C89C22148yescomplemented
18#423×C89C2214yes—
19#423×C89C22112yes—
20#423×C89C22124yescomplemented
21C2×C4⋊C8×C89C22124yescomplemented
22C2×#41×C89C2×C414yes—
23C2×#41×C89D418yes—
24C2×#41×C89Q818yes—
25C2×#41×C89C2314yes—
26C22×Q8×C89C2×C411yescharacteristic
27C22×D4×C89C2×C413yes—
28C23×C4×C89C2×C416yes—
29C23×C4×C89C2313yes—
30#131×C89—264no—
31C2×M16×C89—248no—
32C2×M16×C89C2318yes—
33C2×M16×C89C23124yes—
34C22×C8×C89C23124yes—
35C4×Q8×C89C2×C418yes—
36C4×Q8×C89C2×C418yes—
37C4×D4×C89C2×C4124yes—
38C4×D4×C89C2×C4124yes—
39#117×C89C2×C4112yes—
40#117×C89C23112yes—
41C2×C4⋊C4×C89C2×C416yes—
42C2×C22⋊C4×C89C2×C416yes—
43C2×C42×C89C2×C416yes—
44C2×C42×C89C2×C416yes—
45C2×C42×C89C2×C416yes—
46C2×C42×C89C23112yes—
47C2×C42×C89C2311yescharacteristic
48C2×C42×C89C2313yes—
49C4⋊C8×C89C23116yes—
50C4⋊C8×C89C23148yes—
51C24×C89C22×C413yes—
52#41×C89C4⋊C4132yes—
53#41×C89C2×D4116yes—
54#41×C89C2×Q8116yes—
55C2×Q8×C89C4⋊C418yes—
56C2×Q8×C89C22×C414yes—
57C2×D4×C89C4⋊C4124yes—
58C2×D4×C89C22×C4112yes—
59C22×C4×C89—412no—
60C22×C4×C89C22×C412yes—
61C22×C4×C89C22×C4112yes—
62C22×C4×C89C22×C416yes—
63C22×C4×C89C22×C4112yes—
64C22×C4×C89C22×C413yes—
65C22×C4×C89C22×C416yes—
66C22×C4×C89C2×D4112yes—
67C22×C4×C89C2×Q8112yes—
68C22×C4×C89C2411yescharacteristic
69C22×C4×C89C2416yes—
70M16×C89—216no—
71M16×C89—248no—
72C2×C8×C89—248no—
73C2×C8×C89C24116yes—
74C4⋊C4×C89C22×C4124yes—
75C22⋊C4×C89C22×C4124yes—
76C42×C89C22×C411yescharacteristic
77C42×C89C22×C411yescharacteristic
78C42×C89C22×C416yes—
79C42×C89C22×C4112yes—
80C42×C89C22×C4112yes—
81C42×C89C2412yes—
82C42×C89C2416yes—
83C23×C89—46no—
84C23×C89C2×C4⋊C4112yes—
85C23×C89C23×C416yes—
86C23×C89C23×C411yescharacteristic
87Q8×C89C2×C4⋊C4116yes—
88D4×C89C2×C4⋊C4148yes—
89C2×C4×C89—24no—
90C2×C4×C89—224no—
91C2×C4×C89—412no—
92C2×C4×C89—46no—
93C2×C4×C89C2×C4⋊C4112yes—
94C2×C4×C89C2×C4⋊C4124yes—
95C2×C4×C89C23×C412yes—
96C2×C4×C89C23×C4112yes—
97C2×C4×C89C23×C411yescharacteristic
98C2×C4×C89C23×C416yes—
99C2×C4×C89C23×C412yes—
100C2×C4×C89C22×D4112yes—
101C2×C4×C89C22×D412yes—
102C2×C4×C89C22×Q812yes—
103C2×C4×C89C22×Q8112yes—
104C2×C4×C89C2511yescharacteristic
105C8×C89—216no—
106C22×C89—22no—
107C22×C89—212no—
108C22×C89—412no—
109C22×C89C22×C4⋊C412yes—
110C22×C89C22×C4⋊C4112yes—
111C22×C89C24×C411yescharacteristic
112C4×C89—22no—
113C4×C89—212no—
114C4×C89C22×C4⋊C412yes—
115C4×C89C22×C4⋊C4112yes—
116C4×C89#56814yescomplemented
117C4×C89C23×D411yescharacteristic
118C4×C89C23×Q811yescharacteristic
119#60099C8911yesmaximal, characteristic, direct product factor, Sylow
120C2×C89—22no—
121C2×C89—212no—
122C2×C89C23×C4⋊C411yescharacteristic
123C2×C89C2×#56812yes—
124C2×#568C2×C8912yes—
125C2×C4×#41C2×C8911yescharacteristic
126#2906C2×C89116yescomplemented
127#2905C2×C8916yescomplemented
128C2×#423C2×C8916yescomplemented
129C89#6009911yescharacteristic, direct product factor, Sylow
130C22×#41C22×C8911yescharacteristic
131#568—216no—
132C2×#131C22×C89116yes—
133C22×M16C22×C89112yes—
134C4×#41C4×C8914yes—
135C4×#41C4×C8914yes—
136C4×#41C22×C8918yes—
137C2×C4×Q8C4×C8912yes—
138C2×C4×D4C4×C8916yes—
139C2×#117C22×C8913yes—
140C22×C42C22×C8913yes—
141#424C22×C89148yescomplemented
142#423C22×C8914yes—
143#423C22×C89112yes—
144#423C22×C89124yescomplemented
145C2×C4⋊C8C22×C89124yescomplemented
146C2×#41C2×C4×C8914yes—
147C2×#41D4×C8918yes—
148C2×#41Q8×C8918yes—
149C2×#41C23×C8914yes—
150C22×Q8C2×C4×C8911yescharacteristic
151C22×D4C2×C4×C8913yes—
152C23×C4C2×C4×C8916yes—
153C23×C4C23×C8913yes—
154#131—264no—
155C2×M16—248no—
156C2×M16C23×C8918yes—
157C2×M16C23×C89124yes—
158C22×C8C23×C89124yes—
159C4×Q8C2×C4×C8918yes—
160C4×Q8C2×C4×C8918yes—
161C4×D4C2×C4×C89124yes—
162C4×D4C2×C4×C89124yes—
163#117C2×C4×C89112yes—
164#117C23×C89112yes—
165C2×C4⋊C4C2×C4×C8916yes—
166C2×C22⋊C4C2×C4×C8916yes—
167C2×C42C2×C4×C8916yes—
168C2×C42C2×C4×C8916yes—
169C2×C42C2×C4×C8916yes—
170C2×C42C23×C8913yes—
171C2×C42C23×C89112yes—
172C2×C42C23×C8911yescharacteristic
173C4⋊C8C23×C89116yes—
174C4⋊C8C23×C89148yes—
175C24C22×C4×C8913yes—
176#41C4⋊C4×C89132yes—
177#41C2×D4×C89116yes—
178#41C2×Q8×C89116yes—
179C2×Q8C4⋊C4×C8918yes—
180C2×Q8C22×C4×C8914yes—
181C2×D4C4⋊C4×C89124yes—
182C2×D4C22×C4×C89112yes—
183C22×C4—412no—
184C22×C4C22×C4×C8912yes—
185C22×C4C22×C4×C89112yes—
186C22×C4C22×C4×C8916yes—
187C22×C4C22×C4×C89112yes—
188C22×C4C22×C4×C8913yes—
189C22×C4C22×C4×C8916yes—
190C22×C4C2×D4×C89112yes—
191C22×C4C2×Q8×C89112yes—
192C22×C4C24×C8911yescharacteristic
193C22×C4C24×C8916yes—
194M16—216no—
195M16—248no—
196C2×C8—248no—
197C2×C8C24×C89116yes—
198C4⋊C4C22×C4×C89124yes—
199C22⋊C4C22×C4×C89124yes—
200C42C22×C4×C8911yescharacteristic
201C42C22×C4×C8911yescharacteristic
202C42C22×C4×C8916yes—
203C42C22×C4×C89112yes—
204C42C22×C4×C89112yes—
205C42C24×C8912yes—
206C42C24×C8916yes—
207C23—46no—
208C23C2×C4⋊C4×C89112yes—
209C23C23×C4×C8916yes—
210C23C23×C4×C8911yescharacteristic
211Q8C2×C4⋊C4×C89116yes—
212D4C2×C4⋊C4×C89148yes—
213C2×C4—24no—
214C2×C4—224no—
215C2×C4—412no—
216C2×C4—46no—
217C2×C4C2×C4⋊C4×C89112yes—
218C2×C4C2×C4⋊C4×C89124yes—
219C2×C4C23×C4×C8912yes—
220C2×C4C23×C4×C89112yes—
221C2×C4C23×C4×C8911yescharacteristic
222C2×C4C23×C4×C8916yes—
223C2×C4C23×C4×C8912yes—
224C2×C4C22×D4×C89112yes—
225C2×C4C22×D4×C8912yes—
226C2×C4C22×Q8×C8912yes—
227C2×C4C22×Q8×C89112yes—
228C2×C4C25×C8911yescharacteristic
229C8—216no—
230C22—22no—
231C22—212no—
232C22—412no—
233C22C22×C4⋊C4×C8912yes—
234C22C22×C4⋊C4×C89112yes—
235C22C24×C4×C8911yescharacteristic
236C4—22no—
237C4—212no—
238C4C22×C4⋊C4×C8912yes—
239C4C22×C4⋊C4×C89112yes—
240C4#568×C8914yescomplemented
241C4C23×D4×C8911yescharacteristic
242C4C23×Q8×C8911yescharacteristic
243C2—22no—
244C2—212no—
245C2C23×C4⋊C4×C8911yescharacteristic
246C2C2×#568×C8912yes—
subgroupG/H
centerC2×C4×C89C25
commutatorC22C24×C4×C89
Frattini, cosocleC2×C4C25×C89
socleC22×C89C24×C4
prime radicalC22×#41×C89C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
3. C89×#2906C2semidirect
4. C89×#2905C2semidirect
5. C2×#423×C89C2semidirect
17. #424×C89C22semidirect
20. #423×C89C22semidirect
21. C2×C4⋊C8×C89C22semidirect
116. C4×C89#568semidirect
119. #60099C89direct (N × H)
126. #2906C2×C89semidirect
127. #2905C2×C89semidirect
128. C2×#423C2×C89semidirect
129. C89#60099direct (N × H)
141. #424C22×C89semidirect
144. #423C22×C89semidirect
145. C2×C4⋊C8C22×C89semidirect
240. C4#568×C89semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C892
C2×C4×#41×C892
C89×#29062
C89×#29052
C2×#423×C892
#6009989