Finite Group Databasebeta

← C89×#36608 #36414456

Subgroups — C89×#36608 #36414456

Order 22784.

1626 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#2862C213yesmaximal
2C89×#2581C216yesmaximal
3C89×#2514C2112yesmaximal
4C89×#2356C216yesmaximal
5C4×C4⋊Q8×C89C213yesmaximal
6C42×Q8×C89C211yesmaximal, characteristic
7C2×C4⋊Q8×C89C2213yes—
8C2×C4×Q8×C89C2216yes—
9C2×C4×Q8×C89C2213yes—
10#401×C89C2218yes—
11#400×C89C22112yes—
12#395×C89C2214yes—
13#391×C89C2216yes—
14#391×C89C22112yes—
15#391×C89C22112yes—
16#389×C89C22112yes—
17#387×C89C22124yes—
18#384×C89C2211yescharacteristic
19#383×C89C22112yes—
20#382×C89C2216yes—
21#382×C89C2216yes—
22C4×C4⋊C4×C89C22112yes—
23C4×C4⋊C4×C89C2213yes—
24C4×C4⋊C4×C89C2216yes—
25#376×C89C2214yes—
26C43×C89C2213yes—
27C22×Q8×C89C2316yes—
28C22×Q8×C89C2311yescharacteristic
29C4⋊Q8×C89—212no—
30C4×Q8×C89—212no—
31C4×Q8×C89—224no—
32C2×C4⋊C4×C89C2316yes—
33C2×C4⋊C4×C89C2316yes—
34C2×C4⋊C4×C89C2313yes—
35C2×C4⋊C4×C89C23112yes—
36C2×C4⋊C4×C89C23112yes—
37C2×C42×C89C2316yes—
38C2×C42×C89C2313yes—
39C2×C42×C89C2316yes—
40C2×C42×C89C23112yes—
41C2×C42×C89C2311yescharacteristic
42C2×C42×C89C2313yes—
43#95×C89C2311yescharacteristic
44#95×C89C23112yes—
45#95×C89C2313yes—
46#95×C89C2312yes—
47#95×C89C23124yes—
48#95×C89C23124yes—
49#95×C89C23112yes—
50C2×Q8×C89—26no—
51C2×Q8×C89—212no—
52C2×Q8×C89—212no—
53C2×Q8×C89—212no—
54C22×C4×C89C2416yes—
55C22×C4×C89C24112yes—
56C22×C4×C89C2414yes—
57C22×C4×C89C2413yes—
58C22×C4×C89C2413yes—
59C22×C4×C89C2413yes—
60C4⋊C4×C89—212no—
61C4⋊C4×C89—26no—
62C4⋊C4×C89—212no—
63C4⋊C4×C89—224no—
64C4⋊C4×C89—224no—
65C42×C89—212no—
66C42×C89—224no—
67C42×C89—212no—
68C42×C89—26no—
69C42×C89#41112yes—
70C42×C89#4114yes—
71C23×C89C2511yescharacteristic
72Q8×C89—28no—
73Q8×C89—424no—
74C2×C4×C89—26no—
75C2×C4×C89—26no—
76C2×C4×C89—212no—
77C2×C4×C89—26no—
78C2×C4×C89—212no—
79C2×C4×C89—212no—
80C2×C4×C89—26no—
81C2×C4×C89—26no—
82C2×C4×C89—212no—
83C2×C4×C89C2×#4116yes—
84C2×C4×C89C2×#4116yes—
85C2×C4×C89C2×#4116yes—
86C2×C4×C89C2×#4116yes—
87C2×C4×C892−1+416yes—
88C22×C89C22×#4113yes—
89C22×C89C22×#4111yescharacteristic
90C22×C89C2×2−1+413yes—
91C4×C89—26no—
92C4×C89—26no—
93C4×C89—44no—
94C4×C89—412no—
95C4×C89—46no—
96C4×C89#556112yes—
97#36608C8911yesmaximal, characteristic, direct product factor, Sylow
98C2×C89#344411yescharacteristic
99C2×C89C2×#55613yes—
100C2×C89#350913yes—
101#2862C2×C8913yes—
102#2581C2×C8916yes—
103#2514C2×C89112yes—
104#2356C2×C8916yes—
105C4×C4⋊Q8C2×C8913yes—
106C42×Q8C2×C8911yescharacteristic
107C89#3660811yescharacteristic, direct product factor, Sylow
108C2×C4⋊Q8C22×C8913yes—
109C2×C4×Q8C22×C8916yes—
110C2×C4×Q8C22×C8913yes—
111#401C22×C8918yes—
112#400C22×C89112yes—
113#395C22×C8914yes—
114#391C22×C8916yes—
115#391C22×C89112yes—
116#391C22×C89112yes—
117#389C22×C89112yes—
118#387C22×C89124yes—
119#384C22×C8911yescharacteristic
120#383C22×C89112yes—
121#382C22×C8916yes—
122#382C22×C8916yes—
123C4×C4⋊C4C22×C89112yes—
124C4×C4⋊C4C22×C8913yes—
125C4×C4⋊C4C22×C8916yes—
126#376C22×C8914yes—
127C43C22×C8913yes—
128C22×Q8C23×C8911yescharacteristic
129C22×Q8C23×C8916yes—
130C4⋊Q8—212no—
131C4×Q8—212no—
132C4×Q8—224no—
133C2×C4⋊C4C23×C8916yes—
134C2×C4⋊C4C23×C8916yes—
135C2×C4⋊C4C23×C8913yes—
136C2×C4⋊C4C23×C89112yes—
137C2×C4⋊C4C23×C89112yes—
138C2×C42C23×C8916yes—
139C2×C42C23×C89112yes—
140C2×C42C23×C8916yes—
141C2×C42C23×C8913yes—
142C2×C42C23×C8913yes—
143C2×C42C23×C8911yescharacteristic
144#95C23×C8911yescharacteristic
145#95C23×C89112yes—
146#95C23×C8913yes—
147#95C23×C8912yes—
148#95C23×C89124yes—
149#95C23×C89124yes—
150#95C23×C89112yes—
151C2×Q8—26no—
152C2×Q8—212no—
153C2×Q8—212no—
154C2×Q8—212no—
155C22×C4C24×C8916yes—
156C22×C4C24×C89112yes—
157C22×C4C24×C8914yes—
158C22×C4C24×C8913yes—
159C22×C4C24×C8913yes—
160C22×C4C24×C8913yes—
161C4⋊C4—212no—
162C4⋊C4—26no—
163C4⋊C4—212no—
164C4⋊C4—224no—
165C4⋊C4—224no—
166C42—212no—
167C42—224no—
168C42—212no—
169C42—26no—
170C42#41×C89112yes—
171C42#41×C8914yes—
172C23C25×C8911yescharacteristic
173Q8—28no—
174Q8—424no—
175C2×C4—26no—
176C2×C4—26no—
177C2×C4—212no—
178C2×C4—26no—
179C2×C4—212no—
180C2×C4—212no—
181C2×C4—26no—
182C2×C4—26no—
183C2×C4—212no—
184C2×C4C2×#41×C8916yes—
185C2×C4C2×#41×C8916yes—
186C2×C4C2×#41×C8916yes—
187C2×C4C2×#41×C8916yes—
188C2×C42−1+4×C8916yes—
189C22C22×#41×C8913yes—
190C22C22×#41×C8911yescharacteristic
191C22C2×2−1+4×C8913yes—
192C4—26no—
193C4—26no—
194C4—44no—
195C4—412no—
196C4—46no—
197C4#556×C89112yes—
198C2C89×#344411yescharacteristic
199C2C2×#556×C8913yes—
200C2C89×#350913yes—
subgroupG/H
center, socle, prime radicalC23×C89C25
commutator, Frattini, cosocleC23C25×C89
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C89 ◁ G

Complements

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

NH ≅ G/Ntype
97. #36608C89direct (N × H)
107. C89#36608direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#28622
C89×#25812
C89×#25142
C89×#23562
C4×C4⋊Q8×C892
C42×Q8×C892
#3660889