Finite Group Databasebeta

← #11795026

Subgroups — #11795026

Order 1152.

552 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C32×#430C211yesmaximal, characteristic
2C2×#63651C211yesmaximal, characteristic
3#10592819C211yesmaximal, characteristic
4#10592819C211yesmaximal, characteristic
5#10589425C211yesmaximal, characteristic
6#10589423C211yesmaximal, characteristic
7#10589422C211yesmaximal, characteristic
8#70733—34nomaximal
9C22×#634C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14#64135C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C32×#108—22no—
17#63651—22no—
18#63643—22no—
19#63643—22no—
20C3×#430D314yes—
21C2×#824—34no—
22#5120—34no—
23#5120—34no—
24#4559—34no—
25#4557—34no—
26#4556—34no—
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3—21no—
29C2×#634—21no—
30C2×#634—21no—
31C2×#634—21no—
32C2×#634—21no—
33C2×#634—21no—
34C2×#634D412yes—
35C32×M16—21no—
36C32×M16—21no—
37C32×M16—21no—
38C32×M16—21no—
39C32×M16—21no—
40C32×M16—21no—
41C2×C32×C8—21no—
42C2×C32×C8—21no—
43C2×C32×C8D412yes—
44#3757—21no—
45#3757—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3—21no—
50#3748—21no—
51#3748—21no—
52C2×C3⋊(C3⋊C8)—21no—
53#2082—91noSylow
54C22×Dic6—34no—
55C2×C3×M16C2×D314yes—
56C2×C3×M16C2×D314yes—
57C2×C3×M16C2×D314yes—
58#926—34no—
59#926—34no—
60C2×#208—34no—
61C3×#108—28no—
62#824—68no—
63#816—68no—
64#816—68no—
65C23×C32#4111yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77#634—22no—
78#634—22no—
79#634—41no—
80#634—41no—
81C32×C8—22no—
82C32×C8—41no—
83C32×C8—41no—
84C3⋊(C3⋊C8)—41no—
85#430C3⋊D311yescharacteristic
86#419—91no—
87#419—91no—
88C2×#101—91no—
89#344—91no—
90#344—91no—
91H(3,ℤ/4)—91no—
92C22×C3×C4C22×D314yes—
93C22×Dic3—64no—
94C2×Dic6—38no—
95C2×Dic6—64no—
96C2×Dic6—64no—
97C2×Dic6—64no—
98C2×Dic6—64no—
99C2×Dic6—64no—
100C3×M16—24no—
101C3×M16—24no—
102C3×M16—24no—
103C3×M16—24no—
104C3×M16—24no—
105C3×M16—24no—
106C2×C3×C8—24no—
107C2×C3×C8—24no—
108C2×C3×C8#6718yes—
109#217—64no—
110#217—64no—
111C4⋊Dic3—64no—
112C4⋊Dic3—64no—
113C4×Dic3—64no—
114C4×Dic3—64no—
115#208—64no—
116#208—64no—
117C2×C3⋊C8—64no—
118C22×C32—41no—
119C22×C32#12311yescharacteristic
120C22×C32#12411yescharacteristic
121C22×C32#12611yescharacteristic
122C32×C4#12111yescharacteristic
123C32×C4#12311yescharacteristic
124C32×C4#12311yescharacteristic
125C32×C4#12611yescharacteristic
126C3⋊Dic3—42no—
127C3⋊Dic3—81no—
128C3⋊Dic3—81no—
129C22×Q8—91no—
130C2×M16—91no—
131C2×M16C2×C3⋊D311yescharacteristic
132C2×M16C2×C3⋊D311yescharacteristic
133C2×M16C2×C3⋊D311yescharacteristic
134#117—91no—
135#117—91no—
136#108—22no—
137#103—182no—
138#103—182no—
139#101—182no—
140C23×C3#23914yes—
141C2×C3×C4#23514yes—
142C2×C3×C4#23514yes—
143C2×C3×C4D3×D414yes—
144C2×C3×C4#23714yes—
145C2×C3×C4#23914yes—
146C2×C3×C4C2×#6714yes—
147C2×Dic3—68no—
148C2×Dic3—124no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151C2×Dic3—124no—
152Dic6—68no—
153Dic6—68no—
154Dic6—124no—
155Dic6—124no—
156C3×C8—28no—
157C3×C8—44no—
158C3×C8—44no—
159C3⋊C8—124no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32#39711yescharacteristic
164C2×Q8—92no—
165C2×Q8—181no—
166C2×Q8—181no—
167C2×Q8—181no—
168C2×Q8—181no—
169C2×Q8—181no—
170C22×C4—181no—
171C22×C4C22×C3⋊D311yescharacteristic
172M16—21no—
173M16—21no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—21no—
178M16—181no—
179M16—181no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—181no—
183C2×C8#63812yes—
184C4⋊C4—181no—
185C4⋊C4—181no—
186C22⋊C4—181no—
187C22⋊C4—181no—
188C42—181no—
189C42—181no—
190C22×C3—44no—
191C22×C3#89414yes—
192C22×C3#89814yes—
193C22×C3#94714yes—
194C3×C4#89414yes—
195C3×C4#89814yes—
196C3×C4#92914yes—
197C3×C4#93814yes—
198Dic3—128no—
199Dic3—244no—
200Dic3—244no—
201C32#208211yescharacteristic, complemented, Sylow
202C23#383211yescharacteristic
203Q8—182no—
204Q8—182no—
205Q8—361no—
206Q8—361no—
207C2×C4—182no—
208C2×C4—361no—
209C2×C4—361no—
210C2×C4—361no—
211C2×C4—361no—
212C2×C4#382811yescharacteristic
213C2×C4#382811yescharacteristic
214C2×C4D4×C3⋊D311yescharacteristic
215C2×C4#383011yescharacteristic
216C2×C4#383211yescharacteristic
217C2×C4C2×#63811yescharacteristic
218C8—22no—
219C8—41no—
220C8—41no—
221C8—361no—
222C2×C3—24no—
223C2×C3—24no—
224C2×C3—24no—
225C2×C3#499214yes—
226C22—41no—
227C22#6410311yescharacteristic
228C22#6410711yescharacteristic
229C22#6415611yescharacteristic
230C4—362no—
231C4—721no—
232C4—721no—
233C4#6410311yescharacteristic
234C4#6410711yescharacteristic
235C4#6413811yescharacteristic
236C4#6414711yescharacteristic
237C3#7073314yescomplemented
238C2—21no—
239C2—21no—
240C2—21no—
241C2#1059269111yescharacteristic
subgroupG/H
centerC2#10592691
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#430C2
socleC2×C32#397
prime radicalC23×C32#41
hypercenter#430C3⋊D3
hypocenterC32#2082
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
201. C32#2082semidirect
237. C3#70733semidirect

Maximal subgroups

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

subgroupindex
C32×#4302
C2×#636512
#105928192
#105894252
#105894232
#105894222
#707333