Finite Group Databasebeta

← #11792674

Subgroups — #11792674

Order 1152.

1146 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1146 conjugacy classes of subgroups — too many to draw. Only its 191 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×C32×D8C211yesmaximal, characteristic, complemented
2C2×#64141C212yesmaximal, complemented
3C2×#63660C212yesmaximal, complemented
4#10592809C211yesmaximal, characteristic, complemented
5#10589418C211yesmaximal, characteristic, complemented
6#72046—34nomaximal
7C22×C32×D4C2212yes—
8C2×#3828C2211yescharacteristic
9C2×C32×D8—24no—
10C2×C32×D8—22no—
11C22×C32×C8C2211yescharacteristic
12C2×#3754—22no—
13#64141—24no—
14#64141—24no—
15C2×#3753—22no—
16C2×#3748C2211yescharacteristic
17C2×#3748C2212yes—
18#63660—24no—
19#63647—22no—
20C22×C3×D8D314yescomplemented
21C2×#932—38no—
22C2×#833—38no—
23#5110—34no—
24#4552—34no—
25C24×C32—22no—
26C2×C32×D4—22no—
27C2×C32×D4—22no—
28C2×C32×D4—22no—
29C2×C32×D4—22no—
30C2×C32×D4—22no—
31C2×C32×D4D414yes—
32C22×C32×C4C2311yescharacteristic
33C2×#638—21no—
34#3828—22no—
35#3828—22no—
36C2×C4⋊(C3⋊D3)D411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×#634D411yescharacteristic
39C32×D8—28no—
40C2×C32×C8—22no—
41C2×C32×C8D412yes—
42#3754—28no—
43#3753—28no—
44#3748—22no—
45#3748—22no—
46#3748D414yes—
47C2×C3⋊(C3⋊C8)—22no—
48C2×C3⋊(C3⋊C8)—21no—
49#2018—91noSylow
50C22×C3×D4C2×D318yes—
51C2×#235—34no—
52C2×C3×D8—216no—
53C2×C3×D8—28no—
54C22×C3×C8C2×D314yes—
55C2×#214—68no—
56#932—616no—
57#932—616no—
58C2×#213—68no—
59C2×#208—38no—
60C2×#208—34no—
61#833—616no—
62(C2×D3)⋊C8—68no—
63C23×C32—24no—
64C23×C32—42no—
65C23×C32—42no—
66C23×C32—84no—
67C23×C32#4111yescharacteristic
68C22×C3⋊D3—21no—
69C32×D4—24no—
70C32×D4—24no—
71C32×D4—42no—
72C32×D4—42no—
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2×D412yes—
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77#638—42no—
78C2×C3⋊Dic3—21no—
79C4⋊(C3⋊D3)—22no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3—41no—
82#634—22no—
83C32×C8—22no—
84C3⋊(C3⋊C8)—24no—
85C3⋊(C3⋊C8)—41no—
86C2×AGL(1,ℤ/8)—92no—
87C22×D8C3⋊D311yescharacteristic, complemented
88C2×#100—92no—
89#408—91no—
90#341—91no—
91C24×C3—28no—
92C2×C3×D4—28no—
93C2×C3×D4—28no—
94C2×C3×D4—28no—
95C2×C3×D4—28no—
96C2×C3×D4—28no—
97C2×C3×D4#67116yes—
98C22×C3×C4C22×D314yes—
99C2×#67—64no—
100#235—68no—
101#235—68no—
102C2×D12—34no—
103C2×C4×D3—64no—
104C2×Dic6—34no—
105C3×D8—232no—
106C2×C3×C8—28no—
107C2×C3×C8#6718yes—
108#214—632no—
109#213—632no—
110#208—316no—
111#208—68no—
112#208—68no—
113C2×C3⋊C8—68no—
114C2×C3⋊C8—64no—
115C22×C32—22no—
116C22×C32—44no—
117C22×C32—84no—
118C22×C32—84no—
119C22×C32—84no—
120C22×C32#12111yescharacteristic
121C22×C32#12112yes—
122C2×C3⋊D3—41no—
123C2×C3⋊D3—42no—
124C32×C4#12012yes—
125C32×C4#12011yescharacteristic
126C32×C4#12711yescharacteristic
127C3⋊Dic3—41no—
128C2×#41—91no—
129C22×D4C2×C3⋊D312yes—
130AGL(1,ℤ/8)—184no—
131AGL(1,ℤ/8)—184no—
132C2×SD16—182no—
133C2×D8—24no—
134C2×D8—22no—
135C2×D8—182no—
136C2×M16—92no—
137C2×M16—91no—
138C22×C8C2×C3⋊D311yescharacteristic
139#100—184no—
140C22⋊C8—182no—
141C23×C3—216no—
142C23×C3—48no—
143C23×C3—48no—
144C23×C3—816no—
145C23×C3#23714yes—
146C22×D3—64no—
147C3×D4—216no—
148C3×D4—216no—
149C3×D4—48no—
150C3×D4—48no—
151C2×C3×C4D3×D414yes—
152C2×C3×C4D3×D418yes—
153C2×C3×C4C2×#6718yes—
154C2×C3×C4C2×#6714yes—
155#67—128no—
156C2×Dic3—64no—
157D12—68no—
158C4×D3—124no—
159C4×D3—124no—
160Dic6—68no—
161C3×C8—28no—
162C3⋊C8—616no—
163C3⋊C8—124no—
164C2×C32—22no—
165C2×C32—84no—
166C2×C32#39211yescharacteristic
167C2×C32#47212yes—
168C3⋊D3—81no—
169C24—22no—
170#41—182no—
171#41—182no—
172C2×Q8—91no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—91no—
179C2×D4—181no—
180C2×D4#63814yes—
181C22×C4—181no—
182C22×C4C22×C3⋊D311yescharacteristic
183SD16—188no—
184D8—28no—
185D8—188no—
186M16—94no—
187M16—182no—
188M16—182no—
189C2×C8—22no—
190C2×C8—182no—
191C2×C8—181no—
192C2×C8#63812yes—
193C22×C3—28no—
194C22×C3—416no—
195C22×C3—816no—
196C22×C3—816no—
197C22×C3—816no—
198C22×C3#93814yes—
199C22×C3#93918yes—
200C2×D3—128no—
201C2×D3—124no—
202C3×C4#93718yes—
203C3×C4#94014yes—
204C3×C4#95314yes—
205Dic3—124no—
206C32#201811yescharacteristic, complemented, Sylow
207C23—24no—
208C23—42no—
209C23—42no—
210C23—84no—
211C23—181no—
212C23#383011yescharacteristic
213Q8—182no—
214D4—24no—
215D4—24no—
216D4—42no—
217D4—42no—
218D4—182no—
219D4—362no—
220C2×C4—181no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4D4×C3⋊D311yescharacteristic
224C2×C4D4×C3⋊D312yes—
225C2×C4C2×#63812yes—
226C2×C4C2×#63811yescharacteristic
227C8—22no—
228C8—184no—
229C8—361no—
230C2×C3—28no—
231C2×C3—816no—
232C2×C3#516018yes—
233C2×C3#522314yes—
234D3—244no—
235C22—22no—
236C22—44no—
237C22—84no—
238C22—84no—
239C22—84no—
240C22—362no—
241C22—361no—
242C22#6414711yescharacteristic
243C22#6414812yes—
244C4—361no—
245C4#6414612yes—
246C4#6414911yescharacteristic
247C4#6416211yescharacteristic
248C3#7204614yescomplemented
249C2—22no—
250C2—84no—
251C2—721no—
252C2#1059285912yes—
253C2#1059292211yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×D8C2
socleC22×C32#121
hypercenterC22×D8C3⋊D3
hypocenterC32#2018
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. C2×#64141C2semidirect
3. C2×#63660C2semidirect
4. #10592809C2semidirect
5. #10589418C2semidirect
20. C22×C3×D8D3semidirect
87. C22×D8C3⋊D3semidirect
206. C32#2018semidirect
248. C3#72046semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D82
C2×#641412
C2×#636602
#105928092
#105894182
#720463