Finite Group Databasebeta

← #97×C9⋊D9 #72244013

Subgroups — #97×C9⋊D9 #72244013

Order 5184.

1679 conjugacy classes of subgroups; only the 461 normal subgroups are shown.

normal subgroups only

This group has 1679 conjugacy classes of subgroups — too many to draw. Only its 461 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72244001C211yesmaximal, characteristic, complemented
2#72243951C212yesmaximal, complemented
3C92×#97C211yesmaximal, characteristic, complemented
4C2×C8×C9⋊D9C212yesmaximal
5C42×C9⋊D9C211yesmaximal, characteristic
6#97×C3⋊D9—34nomaximal
7C2×C4×C9⋊D9C412yes—
8C2×C4×C9⋊D9C2211yescharacteristic
9C2×C8×C92C2212yes—
10C42×C92C2211yescharacteristic
11C4×C9⋊Dic9C412yes—
12C4×C9⋊Dic9C2211yescharacteristic
13C2×C9⋊(C9⋊C8)C2212yes—
14C8×C9⋊D9C418yescomplemented
15C2×C8×C3⋊D9—38no—
16C42×C3⋊D9—34no—
17C3×C9×#97D314yes—
18#11720538—38no—
19#11720516—34no—
20C22×C9⋊D9C2×C411yescharacteristic
21C2×C4×C92C2×C412yes—
22C2×C4×C92C2311yescharacteristic
23C2×C9⋊Dic9C2×C412yes—
24C2×C9⋊Dic9C2×C411yescharacteristic
25C4×C9⋊D9—24no—
26C4×C9⋊D9C2×C414yes—
27C8×C92C2×C414yescomplemented
28C9⋊(C9⋊C8)C2×C414yescomplemented
29C3⋊D3×#97—91no—
30D9×#97—912no—
31C2×C4×C3⋊D9—34no—
32C2×C4×C3⋊D9—38no—
33C2×C3×C8×C9C2×D318yes—
34C3×C42×C9C2×D314yes—
35C4×C3⋊Dic9—38no—
36C4×C3⋊Dic9—34no—
37C2×C3⋊(C9⋊C8)—38no—
38C8×C3⋊D9—332no—
39C22×C92C22×C411yescharacteristic
40C2×C9⋊D9C4212yes—
41C2×C9⋊D9M1614yes—
42C4×C92—22no—
43C4×C92C22×C412yes—
44C9⋊Dic9—22no—
45C9⋊Dic9C4212yes—
46C2×C8×C3⋊D3—92no—
47C42×C3⋊D3—91no—
48C32×#97C3⋊D311yescharacteristic
49#63642—92no—
50#63630—91no—
51C2×C8×D9—924no—
52C42×D9—912no—
53C9×#97D9112yescomplemented
54#63375—924no—
55#63362—912no—
56C22×C3⋊D9—34no—
57C2×C3×C4×C9C4×D318yes—
58C2×C3×C4×C9C22×D314yes—
59C2×C3⋊Dic9—34no—
60C2×C3⋊Dic9—38no—
61C4×C3⋊D9—316no—
62C4×C3⋊D9—616no—
63C3×C8×C9C4×D3116yes—
64C3⋊(C9⋊C8)—316no—
65D3×#97—274no—
66C2×C92C2×C4211yescharacteristic
67C2×C92C2×M1612yes—
68C9⋊D9#9714yesdirect product factor
69C2×C4×C3⋊D3—91no—
70C2×C4×C3⋊D3—92no—
71C2×C32×C8C2×C3⋊D312yes—
72C32×C42C2×C3⋊D311yescharacteristic
73C4×C3⋊Dic3—92no—
74C4×C3⋊Dic3—91no—
75C2×C3⋊(C3⋊C8)—92no—
76C8×C3⋊D3—98no—
77C2×C4×D9—912no—
78C2×C4×D9—924no—
79C2×C8×C9C2×D9124yes—
80C42×C9C2×D9112yes—
81C4×Dic9—924no—
82C4×Dic9—912no—
83C2×C9⋊C8—924no—
84C8×D9—996no—
85C22×C3×C9C2×C4×D314yes—
86C2×C3⋊D9—38no—
87C2×C3⋊D9—316no—
88C3×C4×C9—28no—
89C3×C4×C9C2×C4×D318yes—
90C3⋊Dic9—38no—
91C3⋊Dic9—68no—
92C2×D3×C8—278no—
93C42×D3—274no—
94C3×#97C3⋊D914yes—
95#815—278no—
96#803—274no—
97C92C2×#9711yescharacteristic, complemented, Sylow
98C22×C3⋊D3—91no—
99C2×C32×C4C4×C3⋊D312yes—
100C2×C32×C4C22×C3⋊D311yescharacteristic
101C2×C3⋊Dic3—91no—
102C2×C3⋊Dic3—92no—
103C4×C3⋊D3—94no—
104C4×C3⋊D3—184no—
105C22×D9—912no—
106C32×C8C4×C3⋊D314yes—
107C3⋊(C3⋊C8)—94no—
108C2×C4×C9C4×D9124yes—
109C2×C4×C9C22×D9112yes—
110C2×Dic9—912no—
111C2×Dic9—924no—
112C4×D9—948no—
113C4×D9—1848no—
114C8×C9C4×D9148yescomplemented
115C9⋊C8—948no—
116C2×#97—811noSylow
117C2×C3×C9C42×D314yes—
118C2×C3×C9D3×M1618yes—
119C3⋊D9—316no—
120C2×C4×D3—274no—
121C2×C4×D3—278no—
122C2×C3×C8C2×C3⋊D918yes—
123C3×C42C2×C3⋊D914yes—
124C4×Dic3—278no—
125C4×Dic3—274no—
126C2×C3⋊C8—278no—
127D3×C8—2732no—
128C22×C32C2×C4×C3⋊D311yescharacteristic
129C2×C3⋊D3—92no—
130C2×C3⋊D3—94no—
131C32×C4—22no—
132C32×C4C2×C4×C3⋊D312yes—
133C3⋊Dic3—92no—
134C3⋊Dic3—182no—
135C22×C9C2×C4×D9112yes—
136C2×D9—924no—
137C2×D9—948no—
138C4×C9—224no—
139C4×C9C2×C4×D9124yes—
140Dic9—924no—
141Dic9—1824no—
142C22×C8—812no—
143C2×C42—811no—
144#97—812no—
145#97—811no—
146#97C9⋊D911yescharacteristic, direct product factor
147C3×C9D3×#9714yes—
148C22×D3—274no—
149C2×C3×C4C4×C3⋊D918yes—
150C2×C3×C4C22×C3⋊D914yes—
151C2×Dic3—274no—
152C2×Dic3—278no—
153C4×D3—2716no—
154C4×D3—5416no—
155C3×C8C4×C3⋊D9116yes—
156C3⋊C8—2716no—
157C2×C32C42×C3⋊D311yescharacteristic
158C2×C32M16×C3⋊D312yes—
159C3⋊D3—94no—
160C2×C9C42×D9112yes—
161C2×C9M16×D9124yes—
162D9—948no—
163C22×C4—811no—
164C22×C4—812no—
165C2×C8—812no—
166C2×C8—818no—
167C2×C8C2×C9⋊D912yes—
168C42—812no—
169C42—811no—
170C42C2×C9⋊D911yescharacteristic
171C22×C3C2×C4×C3⋊D914yes—
172C2×D3—2716no—
173C2×D3—278no—
174C3×C4—28no—
175C3×C4C2×C4×C3⋊D918yes—
176Dic3—278no—
177Dic3—548no—
178C32C3⋊D3×#9711yescharacteristic
179C9D9×#97112yescomplemented
180C23—811no—
181C2×C4—811no—
182C2×C4—814no—
183C2×C4—812no—
184C2×C4—1624no—
185C2×C4C4×C9⋊D912yes—
186C2×C4C22×C9⋊D911yescharacteristic
187C8—814no—
188C8C4×C9⋊D914yescomplemented
189C2×C3C42×C3⋊D914yes—
190C2×C3M16×C3⋊D918yes—
191D3—2716no—
192C22—814no—
193C22—812no—
194C22C2×C4×C9⋊D911yescharacteristic
195C4—22no—
196C4—812no—
197C4—1622no—
198C4C2×C4×C9⋊D912yes—
199C3#97×C3⋊D914yes—
200C2—814no—
201C2C42×C9⋊D911yescharacteristic
202C2M16×C9⋊D912yes—
subgroupG/H
centerC2×C4C22×C9⋊D9
commutatorC2×C92C2×C42
FrattiniC2×C32×C4C22×C3⋊D3
FittingC92×#97C2
socleC22×C32C2×C4×C3⋊D3
prime radicalC22×C9⋊D9C2×C4
cosocleC2×C4×C92C23
hypercenter#97C9⋊D9
hypocenterC92C2×#97
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #72244001C2semidirect
2. #72243951C2semidirect
3. C92×#97C2semidirect
14. C8×C9⋊D9C4semidirect
27. C8×C92C2×C4semidirect
28. C9⋊(C9⋊C8)C2×C4semidirect
53. C9×#97D9semidirect
68. C9⋊D9#97direct (N × H)
97. C92C2×#97semidirect
114. C8×C9C4×D9semidirect
146. #97C9⋊D9direct (N × H)
179. C9D9×#97semidirect
188. C8C4×C9⋊D9semidirect

Maximal subgroups

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

subgroupindex
#722440012
#722439512
C92×#972
C2×C8×C9⋊D92
C42×C9⋊D92
#97×C3⋊D93