Finite Group Databasebeta

← C89×#7554 #36385402

Subgroups — C89×#7554 #36385402

Order 22784.

3158 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C89C211yesmaximal, characteristic
2C22×#95×C89C216yesmaximal
3C24×C4×C89C2214yes—
4C24×C4×C89C2213yes—
5C22×C42×C89—212no—
6C22×C42×C89C414yescomplemented
7C2×#95×C89—212no—
8C2×#95×C89—212no—
9C2×#95×C89C4124yescomplemented
10C25×C89C2311yescharacteristic
11C23×C4×C89—212no—
12C23×C4×C89—212no—
13C23×C4×C89—212no—
14C23×C4×C89—212no—
15C23×C4×C89—224no—
16C23×C4×C89C2×C4124yes—
17C23×C4×C89C2×C4112yes—
18C23×C4×C89C2×C416yes—
19C23×C4×C89D416yes—
20C23×C4×C89D4112yes—
21C23×C4×C89Q816yes—
22C2×C42×C89—232no—
23C2×C42×C89—224no—
24#95×C89—248no—
25C24×C89C22×C411yescharacteristic
26C24×C89C22×C416yes—
27C24×C89C2×D416yes—
28C24×C89C2×D413yes—
29C24×C89C2×Q813yes—
30C24×C89#41112yes—
31C22×C4×C89—212no—
32C22×C4×C89—212no—
33C22×C4×C89—248no—
34C22×C4×C89—224no—
35C22×C4×C89—224no—
36C22×C4×C89—224no—
37C22×C4×C89—224no—
38C22×C4×C89—224no—
39C22×C4×C89—224no—
40C22×C4×C89—248no—
41C22×C4×C89—248no—
42C22×C4×C89—44no—
43C22×C4×C89—424no—
44C22×C4×C89—412no—
45C22×C4×C89—412no—
46C22×C4×C89—48no—
47C22×C4×C89—44no—
48C22×C4×C89C42112yes—
49C22×C4×C89C42116yescomplemented
50C22×C4×C89C22⋊C4124yes—
51C22×C4×C89C22⋊C4112yes—
52C22×C4×C89C4⋊C4112yes—
53C22×C4×C89C4⋊C4124yes—
54C42×C89—232no—
55C23×C89C2×C4213yes—
56C23×C89C2×C4214yes—
57C23×C89C2×C22⋊C413yes—
58C23×C89C2×C22⋊C416yes—
59C23×C89C2×C4⋊C413yes—
60C23×C89C2×C4⋊C416yes—
61C23×C89#11716yes—
62C23×C89#117112yes—
63C23×C89C4×D4124yes—
64C23×C89C4×D4112yes—
65C23×C89C4×Q8112yes—
66C23×C89#12014yes—
67C23×C89#121112yes—
68C23×C89C22⋊Q8112yes—
69C23×C89#123112yes—
70C23×C89#12416yes—
71C23×C89#12516yes—
72C23×C89#12618yes—
73C23×C89#12711yescharacteristic
74C23×C89C4⋊Q813yes—
75C2×C4×C89—224no—
76C2×C4×C89—212no—
77C2×C4×C89—224no—
78C2×C4×C89—212no—
79C2×C4×C89—248no—
80C2×C4×C89—248no—
81C2×C4×C89—248no—
82C2×C4×C89—424no—
83C2×C4×C89—448no—
84C2×C4×C89—424no—
85C2×C4×C89#95124yescomplemented
86C22×C89C4311yescharacteristic
87C22×C89C2×#9513yes—
88C22×C89#37613yes—
89C22×C89C4×C22⋊C416yes—
90C22×C89C4×C22⋊C4112yes—
91C22×C89C4×C4⋊C416yes—
92C22×C89C4×C4⋊C4112yes—
93C22×C89#37911yescharacteristic
94C22×C89#38016yes—
95C22×C89#38113yes—
96C22×C89#38213yes—
97C22×C89#38312yes—
98C22×C89#38411yescharacteristic
99C22×C89#385112yes—
100C22×C89#386112yes—
101C22×C89#387124yes—
102C22×C89#388124yes—
103C22×C89#389112yes—
104C22×C89#39016yes—
105C22×C89#39116yes—
106C4×C89—224no—
107C4×C89—416no—
108#7554C8911yesmaximal, characteristic, direct product factor, Sylow
109C2×C89C4×#9513yes—
110C2×C89C22⋊#9513yes—
111C2×C89#143416yes—
112C2×C89C4⋊#9513yes—
113C2×C89#1436112yes—
114C2×C89#143714yes—
115C23×C42C2×C8911yescharacteristic
116C22×#95C2×C8916yes—
117C89#755411yescharacteristic, direct product factor, Sylow
118C24×C4C22×C8914yes—
119C24×C4C22×C8913yes—
120C22×C42—212no—
121C22×C42C4×C8914yescomplemented
122C2×#95—212no—
123C2×#95—212no—
124C2×#95C4×C89124yescomplemented
125C25C23×C8911yescharacteristic
126C23×C4—212no—
127C23×C4—212no—
128C23×C4—212no—
129C23×C4—212no—
130C23×C4—224no—
131C23×C4C2×C4×C89124yes—
132C23×C4C2×C4×C89112yes—
133C23×C4C2×C4×C8916yes—
134C23×C4D4×C8916yes—
135C23×C4D4×C89112yes—
136C23×C4Q8×C8916yes—
137C2×C42—232no—
138C2×C42—224no—
139#95—248no—
140C24C22×C4×C8911yescharacteristic
141C24C22×C4×C8916yes—
142C24C2×D4×C8916yes—
143C24C2×D4×C8913yes—
144C24C2×Q8×C8913yes—
145C24#41×C89112yes—
146C22×C4—212no—
147C22×C4—212no—
148C22×C4—248no—
149C22×C4—224no—
150C22×C4—224no—
151C22×C4—224no—
152C22×C4—224no—
153C22×C4—224no—
154C22×C4—224no—
155C22×C4—248no—
156C22×C4—248no—
157C22×C4—44no—
158C22×C4—424no—
159C22×C4—412no—
160C22×C4—412no—
161C22×C4—48no—
162C22×C4—44no—
163C22×C4C42×C89112yes—
164C22×C4C42×C89116yescomplemented
165C22×C4C22⋊C4×C89124yes—
166C22×C4C22⋊C4×C89112yes—
167C22×C4C4⋊C4×C89112yes—
168C22×C4C4⋊C4×C89124yes—
169C42—232no—
170C23C2×C42×C8913yes—
171C23C2×C42×C8914yes—
172C23C2×C22⋊C4×C8913yes—
173C23C2×C22⋊C4×C8916yes—
174C23C2×C4⋊C4×C8913yes—
175C23C2×C4⋊C4×C8916yes—
176C23#117×C8916yes—
177C23#117×C89112yes—
178C23C4×D4×C89124yes—
179C23C4×D4×C89112yes—
180C23C4×Q8×C89112yes—
181C23#120×C8914yes—
182C23#121×C89112yes—
183C23C22⋊Q8×C89112yes—
184C23#123×C89112yes—
185C23#124×C8916yes—
186C23#125×C8916yes—
187C23#126×C8918yes—
188C23#127×C8911yescharacteristic
189C23C4⋊Q8×C8913yes—
190C2×C4—224no—
191C2×C4—212no—
192C2×C4—224no—
193C2×C4—212no—
194C2×C4—248no—
195C2×C4—248no—
196C2×C4—248no—
197C2×C4—424no—
198C2×C4—448no—
199C2×C4—424no—
200C2×C4#95×C89124yescomplemented
201C22C43×C8911yescharacteristic
202C22C2×#95×C8913yes—
203C22#376×C8913yes—
204C22C4×C22⋊C4×C8916yes—
205C22C4×C22⋊C4×C89112yes—
206C22C4×C4⋊C4×C8916yes—
207C22C4×C4⋊C4×C89112yes—
208C22#379×C8911yescharacteristic
209C22#380×C8916yes—
210C22#381×C8913yes—
211C22#382×C8913yes—
212C22#383×C8912yes—
213C22#384×C8911yescharacteristic
214C22#385×C89112yes—
215C22#386×C89112yes—
216C22#387×C89124yes—
217C22#388×C89124yes—
218C22#389×C89112yes—
219C22#390×C8916yes—
220C22#391×C8916yes—
221C4—224no—
222C4—416no—
223C2C4×#95×C8913yes—
224C2C89×C22⋊#9513yes—
225C2C89×#143416yes—
226C2C89×C4⋊#9513yes—
227C2C89×#1436112yes—
228C2C89×#143714yes—
subgroupG/H
center, socle, prime radicalC25×C89C23
commutatorC22C43×C89
Frattini, cosocleC25C23×C89
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C89 ◁ G

Complements

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

NH ≅ G/Ntype
6. C22×C42×C89C4semidirect
9. C2×#95×C89C4semidirect
49. C22×C4×C89C42semidirect
85. C2×C4×C89#95semidirect
108. #7554C89direct (N × H)
117. C89#7554direct (N × H)
121. C22×C42C4×C89semidirect
124. C2×#95C4×C89semidirect
164. C22×C4C42×C89semidirect
200. C2×C4#95×C89semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C892
C22×#95×C892
#755489