Finite Group Databasebeta

← #11778812

Subgroups — #11778812

Order 1152.

303 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 72 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#10588666C211yesmaximal, characteristic
3#10588402C212yesmaximal
4C9×#324C211yesmaximal, characteristic
5#10588144C212yesmaximal
6#68141—31nomaximal
7C2×C9×C4⋊C4C2211yescharacteristic
8#63488—21no—
9C2×C4⋊Dic9C2211yescharacteristic
10#63486—21no—
11#63486C2212yes—
12#63452—22no—
13#63450—22no—
14C9×C22⋊C8C2212yes—
15C9⋊#95—21no—
16C9⋊#95—21no—
17C9⋊#95C2211yescharacteristic
18#63378—22no—
19#63376—22no—
20#5500—31no—
21#4986—31no—
22#4722—32no—
23C3×#324D311yescharacteristic
24#4467—32no—
25C22×C4×C9D411yescharacteristic
26C22×C4×C9D411yescharacteristic
27C22×C4×C9C2311yescharacteristic
28C22×Dic9—21no—
29C22×Dic9—21no—
30C2×Dic18—21no—
31C2×Dic18D412yes—
32C2×C8×C9—22no—
33C9×C4⋊C4—22no—
34#3676—22no—
35C4⋊Dic9—21no—
36C4⋊Dic9—21no—
37C4⋊Dic9—21no—
38C4⋊Dic9—22no—
39C4⋊Dic9D412yes—
40Dic9⋊C4—22no—
41Dic9⋊C4—22no—
42C4×Dic9—22no—
43#1617—91noSylow
44C2×C3×C4⋊C4C2×D311yescharacteristic
45#926—61no—
46C2×C4⋊Dic3—31no—
47#924—32no—
48#924—61no—
49#890—62no—
50#888—62no—
51C3×C22⋊C8C2×D312yes—
52C3⋊#95—31no—
53C3⋊#95—61no—
54C3⋊#95—61no—
55#818—62no—
56#816—62no—
57C23×C9C2×D411yescharacteristic
58C2×C4×C9—21no—
59C2×C4×C9—21no—
60C2×C4×C9—21no—
61C2×C4×C9—41no—
62C2×C4×C9—41no—
63C2×C4×C9Q1612yes—
64C2×C4×C9C2×D412yes—
65C2×Dic9—22no—
66C2×Dic9—22no—
67C2×Dic9—41no—
68C2×Dic9—41no—
69C2×Dic9—42no—
70C2×Dic9—41no—
71C2×Dic9—41no—
72Dic18—42no—
73Dic18—81no—
74C8×C9—42no—
75#544—91no—
76#484—92no—
77#400—91no—
78#328—92no—
79#324D911yescharacteristic
80C22×C3×C4D1211yescharacteristic
81C22×C3×C4D1211yescharacteristic
82C22×C3×C4C22×D311yescharacteristic
83C22×Dic3—61no—
84C22×Dic3—61no—
85C2×Dic6—32no—
86C2×Dic6—61no—
87C2×C3×C8—22no—
88C3×C4⋊C4—22no—
89#217—62no—
90C4⋊Dic3—32no—
91C4⋊Dic3—61no—
92C4⋊Dic3—61no—
93C4⋊Dic3—61no—
94C4⋊Dic3—62no—
95Dic3⋊C4—62no—
96Dic3⋊C4—62no—
97C4×Dic3—62no—
98C22×C9—21no—
99C22×C9—21no—
100C22×C9#12011yescharacteristic
101C22×C9C2×Q1611yescharacteristic
102C22×C9#13711yescharacteristic
103C4×C9—22no—
104C4×C9—22no—
105C4×C9—41no—
106Dic9—42no—
107Dic9—42no—
108Dic9—81no—
109Dic9—81no—
110C4⋊Q8—182no—
111#125—182no—
112C22⋊Q8—92no—
113C22⋊Q8—181no—
114#117—181no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4C2×D911yescharacteristic
117#107—182no—
118#103—182no—
119C22⋊C8C2×D912yes—
120#95—91no—
121#95—181no—
122#95—181no—
123C23×C3C2×D1211yescharacteristic
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—41no—
128C2×C3×C4—41no—
129C2×C3×C4Dic1212yes—
130C2×C3×C4D3×D412yes—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—121no—
134C2×Dic3—121no—
135C2×Dic3—122no—
136C2×Dic3—121no—
137C2×Dic3—121no—
138Dic6—122no—
139Dic6—241no—
140C3×C8—42no—
141C2×C9—21no—
142C2×C9—21no—
143C2×C9#45111yescharacteristic
144C2×C9#45411yescharacteristic
145C2×C9#45811yescharacteristic
146C2×Q8—92no—
147C2×Q8—181no—
148C22×C4—181no—
149C22×C4—181no—
150C22×C4D3611yescharacteristic
151C22×C4D3611yescharacteristic
152C22×C4C22×D911yescharacteristic
153C2×C8—22no—
154C4⋊C4—22no—
155C4⋊C4—92no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C4⋊C4—182no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C22⋊C4—182no—
163C42—182no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3#88211yescharacteristic
167C22×C3C2×Dic1211yescharacteristic
168C22×C3#90911yescharacteristic
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—41no—
172Dic3—122no—
173Dic3—122no—
174Dic3—241no—
175Dic3—241no—
176C9#161711yescharacteristic, complemented, Sylow
177C23C2×D3611yescharacteristic
178Q8—362no—
179Q8—721no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—182no—
186C2×C4—182no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—362no—
190C2×C4—361no—
191C2×C4—361no—
192C2×C4Dic3612yes—
193C2×C4D4×D912yes—
194C8—42no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3#473911yescharacteristic
198C2×C3#474211yescharacteristic
199C2×C3#475311yescharacteristic
200C22—21no—
201C22—21no—
202C22#6344411yescharacteristic
203C22C2×Dic3611yescharacteristic
204C22#6347111yescharacteristic
205C4—22no—
206C4—22no—
207C4—41no—
208C4—362no—
209C4—362no—
210C4—721no—
211C4—721no—
212C3#6814111yescharacteristic
213C2—21no—
214C2—21no—
215C2#1058840511yescharacteristic
216C2#1058842211yescharacteristic
217C2#1058843311yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3#882
prime radicalC23×C3C2×D12
hypercenter#324D9
hypocenterC9#1617
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
176. C9#1617semidirect

Maximal subgroups

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

subgroupindex
#105896022
#105886662
#105884022
C9×#3242
#105881442
#681413