Finite Group Databasebeta

← #11794277

Subgroups — #11794277

Order 1152.

345 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 104 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#10589602C211yesmaximal, characteristic
2#10588805C212yesmaximal
3#10588657C211yesmaximal, characteristic
4C9×#343C211yesmaximal, characteristic
5#10588235C212yesmaximal
6#68979—31nomaximal
7C2×C9×M16C2212yes—
8C2×C9×C4⋊C4C2211yescharacteristic
9#63488C2212yes—
10C2×C4⋊Dic9C2211yescharacteristic
11#63486—22no—
12C2×C4×Dic9C2211yescharacteristic
13#63452—22no—
14#63450—22no—
15C9⋊#95—22no—
16#63378—22no—
17#63377—22no—
18#5500—31no—
19#5121—32no—
20#4977—31no—
21C3×#343D311yescharacteristic
22#4555—32no—
23C22×C4×C9D412yes—
24C22×C4×C9C2311yescharacteristic
25C22×Dic9—21no—
26C22×Dic9—21no—
27C2×Dic18—22no—
28C9×M16—22no—
29C9×M16Q814yescomplemented
30C2×C8×C9—22no—
31C9×C4⋊C4—22no—
32#3676—22no—
33C4⋊Dic9—22no—
34C4⋊Dic9—22no—
35C4⋊Dic9D412yes—
36C4⋊Dic9D412yes—
37Dic9⋊C4—24no—
38C4×Dic9—22no—
39C4×Dic9—21no—
40C4×Dic9Q812yescomplemented
41#2061—91noSylow
42C2×C3×M16C2×D312yes—
43C2×C3×C4⋊C4C2×D311yescharacteristic
44#926—32no—
45C2×C4⋊Dic3—31no—
46#924—62no—
47C2×C4×Dic3—31no—
48#890—62no—
49#888—62no—
50C3⋊#95—62no—
51#818—62no—
52#817—62no—
53C23×C9C2×D411yescharacteristic
54C2×C4×C9—22no—
55C2×C4×C9—42no—
56C2×C4×C9C2×D412yes—
57C2×C4×C9C2×Q812yes—
58C2×C4×C9C2×Q811yescharacteristic
59C2×C4×C9#4111yescharacteristic
60C2×Dic9—22no—
61C2×Dic9—22no—
62C2×Dic9—22no—
63C2×Dic9—41no—
64C2×Dic9—41no—
65C2×Dic9—42no—
66C2×Dic9—41no—
67Dic18—82no—
68C8×C9—24no—
69#544—91no—
70#428—92no—
71#382—91no—
72#343D911yescharacteristic
73#339—92no—
74C22×C3×C4D1212yes—
75C22×C3×C4C22×D311yescharacteristic
76C22×Dic3—61no—
77C22×Dic3—61no—
78C2×Dic6—62no—
79C3×M16—22no—
80C3×M16Dic614yes—
81C2×C3×C8—22no—
82C3×C4⋊C4—22no—
83#217—62no—
84C4⋊Dic3—32no—
85C4⋊Dic3—32no—
86C4⋊Dic3—62no—
87C4⋊Dic3—62no—
88Dic3⋊C4—64no—
89C4×Dic3—32no—
90C4×Dic3—62no—
91C4×Dic3—61no—
92C22×C9—21no—
93C22×C9—21no—
94C22×C9#12011yescharacteristic
95C22×C9C22⋊Q811yescharacteristic
96C22×C9C4⋊Q811yescharacteristic
97C4×C9—42no—
98C4×C9C22⋊Q812yes—
99C4×C9C4⋊Q812yes—
100Dic9—42no—
101Dic9—42no—
102Dic9—42no—
103Dic9—81no—
104C2×M16C2×D912yes—
105C4⋊Q8—182no—
106#125—182no—
107C22⋊Q8—182no—
108#117—92no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4C2×D911yescharacteristic
111C2×C42—91no—
112#107—182no—
113#106—182no—
114#95—182no—
115C23×C3C2×D1211yescharacteristic
116C2×C3×C4—22no—
117C2×C3×C4—42no—
118C2×C3×C4C2×Dic612yes—
119C2×C3×C4D3×D412yes—
120C2×C3×C4#23711yescharacteristic
121C2×C3×C4D3×Q811yescharacteristic
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127C2×Dic3—122no—
128C2×Dic3—121no—
129Dic6—242no—
130C3×C8—24no—
131C2×C9—21no—
132C2×C9—21no—
133C2×C9#39511yescharacteristic
134C2×C9#45411yescharacteristic
135C2×C9#45511yescharacteristic
136C2×Q8—182no—
137C22×C4—181no—
138C22×C4—181no—
139C22×C4D3612yes—
140C22×C4C22×D911yescharacteristic
141M16—22no—
142M16Dic1814yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—92no—
146C4⋊C4—92no—
147C4⋊C4—182no—
148C4⋊C4—184no—
149C4⋊C4—182no—
150C22⋊C4—182no—
151C42—92no—
152C42—182no—
153C42—181no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3#86911yescharacteristic
157C22×C3#88211yescharacteristic
158C22×C3#89711yescharacteristic
159C3×C4—42no—
160C3×C4#87812yes—
161C3×C4#88812yes—
162Dic3—122no—
163Dic3—122no—
164Dic3—122no—
165Dic3—241no—
166C9#206111yescharacteristic, complemented, Sylow
167C23C2×D3611yescharacteristic
168Q8—722no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—182no—
172C2×C4—182no—
173C2×C4—182no—
174C2×C4—361no—
175C2×C4—361no—
176C2×C4—362no—
177C2×C4—361no—
178C2×C4C2×Dic1812yes—
179C2×C4D4×D912yes—
180C2×C4#369911yescharacteristic
181C2×C4Q8×D911yescharacteristic
182C8—24no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3#465611yescharacteristic
186C2×C3#474611yescharacteristic
187C2×C3#475311yescharacteristic
188C22—21no—
189C22—21no—
190C22#6343111yescharacteristic
191C22#6344411yescharacteristic
192C22#6345911yescharacteristic
193C4—42no—
194C4—362no—
195C4—362no—
196C4—362no—
197C4—721no—
198C4#6344012yes—
199C4#6345012yes—
200C3#6897911yescharacteristic
201C2—21no—
202C2—21no—
203C2#1058833611yescharacteristic
204C2#1058842611yescharacteristic
205C2#1058843311yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#343C2
socleC22×C3#882
prime radicalC23×C3C2×D12
hypercenter#343D9
hypocenterC9#2061
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
29. C9×M16Q8semidirect
40. C4×Dic9Q8semidirect
142. M16Dic18semidirect
166. C9#2061semidirect

Maximal subgroups

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

subgroupindex
#105896022
#105888052
#105886572
C9×#3432
#105882352
#689793