Finite Group Databasebeta

← #11772567

Subgroups — #11772567

Order 1152.

249 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 249 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C9×#410C211yesmaximal, characteristic
2#10588920C211yesmaximal, characteristic
3#10588912C211yesmaximal, characteristic
4#67696—31nomaximal
5C2×C9×#41C2211yescharacteristic
6C9×#117—21no—
7#63488—21no—
8C2×#3667C411yescharacteristic, complemented
9C22×C9⋊C8C411yescharacteristic, complemented
10C9×#99—21no—
11C9×#99C412yescomplemented
12#63393—21no—
13#63393C412yescomplemented
14#63389—21no—
15#63389—21no—
16C3×#410D311yescharacteristic
17#5240—31no—
18#5234—31no—
19C9×#41—41no—
20C9×#41—41no—
21C2×Q8×C9Q811yescharacteristic
22C2×D4×C9C2×C411yescharacteristic
23C2×D4×C9C2×C411yescharacteristic
24C2×D4×C9D411yescharacteristic
25C22×C4×C9C2×C411yescharacteristic
26C22×C4×C9D411yescharacteristic
27C22×C4×C9D411yescharacteristic
28C9×C4⋊C4—41no—
29C9×C22⋊C4—22no—
30C42×C9—41no—
31#3676—22no—
32C4⋊Dic9—41no—
33C4×Dic9—41no—
34#3667—41no—
35C2×C9⋊C8—21no—
36C2×C9⋊C8—21no—
37C2×C9⋊C8—41no—
38#1391—91noSylow
39C2×C3×#41C2×D311yescharacteristic
40C3×#117—21no—
41#926—61no—
42C2×#208—31no—
43C22×C3⋊C8—31no—
44C3×#99—21no—
45C3×#99Dic312yes—
46#834—32no—
47#834—61no—
48#830—61no—
49#830—61no—
50C23×C9C4211yescharacteristic
51C23×C9C22⋊C411yescharacteristic
52C23×C9C22⋊C411yescharacteristic
53Q8×C9—41no—
54D4×C9—41no—
55D4×C9—41no—
56D4×C9—41no—
57C2×C4×C9—21no—
58C2×C4×C9—21no—
59C2×C4×C9—21no—
60C2×C4×C9—21no—
61C2×C4×C9—21no—
62C2×C4×C9—21no—
63C2×C4×C9—42no—
64C2×C4×C9C22⋊C411yescharacteristic
65C2×C4×C9C4⋊C411yescharacteristic
66C2×C4×C9C4⋊C411yescharacteristic
67C2×C4×C9C4⋊C411yescharacteristic
68C2×Dic9—42no—
69C9⋊C8—41no—
70C9⋊C8—41no—
71#410—91no—
72#410D911yescharacteristic
73#408—91no—
74C3×#41—41no—
75C3×#41—41no—
76C2×C3×Q8Dic611yescharacteristic
77C2×C3×D4C4×D311yescharacteristic
78C2×C3×D4C2×Dic311yescharacteristic
79C2×C3×D4#6711yescharacteristic
80C22×C3×C4C4×D311yescharacteristic
81C22×C3×C4D1211yescharacteristic
82C22×C3×C4#6711yescharacteristic
83C3×C4⋊C4—41no—
84C3×C22⋊C4—22no—
85C3×C42—41no—
86#217—62no—
87C4⋊Dic3—121no—
88C4×Dic3—121no—
89#208—121no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—121no—
93C22×C9—21no—
94C22×C9—21no—
95C22×C9—21no—
96C22×C9—41no—
97C22×C9—41no—
98C22×C9—41no—
99C22×C9#9511yescharacteristic
100C4×C9—21no—
101C4×C9—21no—
102C4×C9—21no—
103C4×C9—82no—
104C4×C9#9911yescharacteristic
105C4×C9#9911yescharacteristic
106Dic9—82no—
107C2×#41C2×D911yescharacteristic
108C2×M16—91no—
109C22×C8—91no—
110#117—21no—
111#117—181no—
112#99—21no—
113#99—92no—
114#99—181no—
115#99Dic912yescomplemented
116C22⋊C8—181no—
117C22⋊C8—181no—
118C23×C3C4×Dic311yescharacteristic
119C23×C3(C2×D3)⋊C411yescharacteristic
120C23×C3#21711yescharacteristic
121C3×Q8—41no—
122C3×D4—41no—
123C3×D4—41no—
124C3×D4—41no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—42no—
132C2×C3×C4Dic3⋊C411yescharacteristic
133C2×C3×C4Dic3⋊C411yescharacteristic
134C2×C3×C4C4⋊Dic311yescharacteristic
135C2×C3×C4(C2×D3)⋊C411yescharacteristic
136C2×Dic3—122no—
137C3⋊C8—121no—
138C3⋊C8—121no—
139C2×C9—21no—
140C2×C9—41no—
141C2×C9—41no—
142C2×C9—41no—
143C2×C9#34211yescharacteristic
144#41—41no—
145#41—41no—
146C2×Q8Dic1811yescharacteristic
147C2×D4C4×D911yescharacteristic
148C2×D4C2×Dic911yescharacteristic
149C2×D4#61111yescharacteristic
150C22×C4C4×D911yescharacteristic
151C22×C4D3611yescharacteristic
152C22×C4#61111yescharacteristic
153M16—361no—
154C2×C8—181no—
155C2×C8—181no—
156C2×C8—361no—
157C4⋊C4—41no—
158C4⋊C4—361no—
159C22⋊C4—22no—
160C22⋊C4—182no—
161C42—41no—
162C42—361no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—41no—
167C22×C3—41no—
168C22×C3—41no—
169C22×C3C3⋊#9511yescharacteristic
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—82no—
174C3×C4#80611yescharacteristic
175C3×C4#80611yescharacteristic
176Dic3—242no—
177C9#139111yescharacteristic, complemented, Sylow
178C23C4×Dic911yescharacteristic
179C23(C2×D9)⋊C411yescharacteristic
180C23#367611yescharacteristic
181Q8—41no—
182D4—41no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—42no—
192C2×C4—362no—
193C2×C4Dic9⋊C411yescharacteristic
194C2×C4Dic9⋊C411yescharacteristic
195C2×C4C4⋊Dic911yescharacteristic
196C2×C4(C2×D9)⋊C411yescharacteristic
197C8—361no—
198C8—361no—
199C2×C3—21no—
200C2×C3—41no—
201C2×C3—41no—
202C2×C3—41no—
203C2×C3#452711yescharacteristic
204C22—21no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22C9⋊#9511yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—722no—
216C4#6336511yescharacteristic
217C4#6336511yescharacteristic
218C3#6769611yescharacteristic
219C2—21no—
220C2—41no—
221C2—41no—
222C2—41no—
223C2#1058820411yescharacteristic
subgroupG/H
centerC4#63365
commutatorC23×C9C42
Frattini, prime radicalC2×C3×#41C2×D3
FittingC9×#410C2
socleC2×C3#4527
cosocleC2×C9×#41C22
hypercenter#410D9
hypocenterC9#1391
LCSG ▷ C23×C9 ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
8. C2×#3667C4semidirect
9. C22×C9⋊C8C4semidirect
11. C9×#99C4semidirect
13. #63393C4semidirect
115. #99Dic9semidirect
177. C9#1391semidirect

Maximal subgroups

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

subgroupindex
C9×#4102
#105889202
#105889122
#676963