Finite Group Databasebeta

← #11792755

Subgroups — #11792755

Order 1152.

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

normal subgroups only

This group has 513 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
1C22×C9×Q16C211yesmaximal, characteristic, complemented
2C2×#63505C212yesmaximal
3C2×#63394C212yesmaximal, complemented
4#10588791C211yesmaximal, characteristic
5#10588227C211yesmaximal, characteristic, complemented
6#72074—31nomaximal
7C22×Q8×C9C2212yes—
8C2×#3697C2211yescharacteristic
9C2×C9×Q16—24no—
10C2×C9×Q16—22no—
11C22×C8×C9C2211yescharacteristic
12#63505—24no—
13#63505—24no—
14C2×#3675—22no—
15C2×#3674—22no—
16C2×#3667C2211yescharacteristic
17C2×#3667C2212yes—
18#63394—24no—
19(C2×D9)⋊C8—22no—
20C22×C3×Q16D311yescharacteristic
21C2×#942—32no—
22C2×#836—32no—
23#5110—31no—
24#4552—31no—
25C2×Q8×C9—22no—
26C2×Q8×C9—22no—
27C2×Q8×C9—22no—
28C2×Q8×C9—22no—
29C2×Q8×C9—22no—
30C2×Q8×C9D414yes—
31C22×C4×C9—22no—
32C22×C4×C9C2311yescharacteristic
33C2×#611—21no—
34#3697—22no—
35#3697—22no—
36C2×D36D411yescharacteristic
37C2×C4×D9—21no—
38C2×Dic18D411yescharacteristic
39C9×Q16—28no—
40C2×C8×C9—22no—
41C2×C8×C9D412yes—
42#3675—28no—
43#3674—28no—
44#3667—22no—
45#3667—22no—
46#3667D414yes—
47C2×C9⋊C8—22no—
48C2×C9⋊C8—21no—
49#2020—91noSylow
50C22×C3×Q8C2×D312yes—
51C2×#235—31no—
52C2×C3×Q16—24no—
53C2×C3×Q16—22no—
54C22×C3×C8C2×D311yescharacteristic
55C2×#216—62no—
56#942—64no—
57#942—64no—
58C2×#215—62no—
59C2×#208—32no—
60C2×#208—31no—
61#836—64no—
62(C2×D3)⋊C8—62no—
63C23×C9#4111yescharacteristic
64C22×D9—21no—
65Q8×C9—24no—
66Q8×C9—24no—
67Q8×C9—42no—
68Q8×C9—42no—
69C2×C4×C9—24no—
70C2×C4×C9—42no—
71C2×C4×C9—42no—
72C2×C4×C9C2×D411yescharacteristic
73C2×C4×C9C2×D412yes—
74C2×C4×C9C2×D412yes—
75C2×C4×C9C2×D411yescharacteristic
76#611—42no—
77C2×Dic9—21no—
78D36—22no—
79C4×D9—41no—
80C4×D9—41no—
81Dic18—22no—
82C8×C9—22no—
83C9⋊C8—24no—
84C9⋊C8—41no—
85C2×#137—92no—
86C22×Q16D911yescharacteristic, complemented
87C2×#101—92no—
88#408—91no—
89#341—91no—
90C2×C3×Q8—22no—
91C2×C3×Q8—22no—
92C2×C3×Q8—22no—
93C2×C3×Q8—22no—
94C2×C3×Q8—22no—
95C2×C3×Q8#6714yes—
96C22×C3×C4—22no—
97C22×C3×C4C22×D311yescharacteristic
98C2×#67—61no—
99#235—62no—
100#235—62no—
101C2×D12—31no—
102C2×C4×D3—61no—
103C2×Dic6—31no—
104C3×Q16—28no—
105C2×C3×C8—22no—
106C2×C3×C8#6712yes—
107#216—68no—
108#215—68no—
109#208—34no—
110#208—62no—
111#208—62no—
112C2×C3⋊C8—62no—
113C2×C3⋊C8—61no—
114C22×C9—22no—
115C22×C9#12111yescharacteristic
116C22×C9#12112yes—
117C2×D9—41no—
118C2×D9—42no—
119C4×C9—44no—
120C4×C9#12012yes—
121C4×C9#12011yescharacteristic
122C4×C9#12711yescharacteristic
123Dic9—41no—
124C2×#41—91no—
125C22×Q8C2×D912yes—
126#137—184no—
127#137—184no—
128C2×Q16—24no—
129C2×Q16—22no—
130C2×Q16—182no—
131C2×SD16—182no—
132C2×M16—92no—
133C2×M16—91no—
134C22×C8C2×D911yescharacteristic
135#101—184no—
136C22⋊C8—182no—
137C23×C3#23711yescharacteristic
138C22×D3—61no—
139C3×Q8—24no—
140C3×Q8—24no—
141C3×Q8—42no—
142C3×Q8—42no—
143C2×C3×C4—24no—
144C2×C3×C4—42no—
145C2×C3×C4—42no—
146C2×C3×C4D3×D411yescharacteristic
147C2×C3×C4D3×D412yes—
148C2×C3×C4C2×#6712yes—
149C2×C3×C4C2×#6711yescharacteristic
150#67—122no—
151C2×Dic3—61no—
152D12—62no—
153C4×D3—121no—
154C4×D3—121no—
155Dic6—62no—
156C3×C8—22no—
157C3⋊C8—64no—
158C3⋊C8—121no—
159C2×C9—22no—
160C2×C9#39211yescharacteristic
161C2×C9#47312yes—
162D9—81no—
163#41—182no—
164#41—182no—
165C2×Q8—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—91no—
171C2×Q8#61114yes—
172C2×D4—91no—
173C2×D4—181no—
174C22×C4—22no—
175C22×C4—181no—
176C22×C4C22×D911yescharacteristic
177Q16—28no—
178Q16—188no—
179SD16—188no—
180M16—94no—
181M16—182no—
182M16—182no—
183C2×C8—22no—
184C2×C8—182no—
185C2×C8—181no—
186C2×C8#61112yes—
187C22×C3—22no—
188C22×C3#93811yescharacteristic
189C22×C3#93912yes—
190C2×D3—122no—
191C2×D3—121no—
192C3×C4—44no—
193C3×C4#93712yes—
194C3×C4#94011yescharacteristic
195C3×C4#95311yescharacteristic
196Dic3—121no—
197C9#202011yescharacteristic, complemented, Sylow
198C23—181no—
199C23#369911yescharacteristic
200Q8—24no—
201Q8—24no—
202Q8—42no—
203Q8—42no—
204Q8—182no—
205D4—182no—
206D4—362no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—181no—
211C2×C4—361no—
212C2×C4—361no—
213C2×C4D4×D911yescharacteristic
214C2×C4D4×D912yes—
215C2×C4C2×#61112yes—
216C2×C4C2×#61111yescharacteristic
217C8—22no—
218C8—184no—
219C8—361no—
220C2×C3—22no—
221C2×C3#519212yes—
222C2×C3#522311yescharacteristic
223D3—241no—
224C22—22no—
225C22—362no—
226C22—361no—
227C22#6350011yescharacteristic
228C22#6350112yes—
229C4—44no—
230C4—361no—
231C4#6349912yes—
232C4#6350211yescharacteristic
233C4#6351511yescharacteristic
234C3#7207411yescharacteristic
235C2—22no—
236C2—721no—
237C2#1058887212yes—
238C2#1058890311yescharacteristic
subgroupG/H
centerC22#63500
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC22×C9×Q16C2
socleC22×C3#938
prime radicalC2×#3697C22
hypercenterC22×Q16D9
hypocenterC9#2020
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C22×C9×Q16C2semidirect
3. C2×#63394C2semidirect
5. #10588227C2semidirect
86. C22×Q16D9semidirect
197. C9#2020semidirect

Maximal subgroups

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

subgroupindex
C22×C9×Q162
C2×#635052
C2×#633942
#105887912
#105882272
#720743