Finite Group Databasebeta

← #11787901

Subgroups — #11787901

Order 1152.

1032 conjugacy classes of subgroups; only the 261 normal subgroups are shown.

normal subgroups only

This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 261 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
1C2×C32×#124C211yesmaximal, characteristic
2#10596283C211yesmaximal, characteristic, complemented
3C2×#63663C211yesmaximal, characteristic, complemented
4#10592914C212yesmaximal
5#10589389C212yesmaximal, complemented
6#71724—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×C32×D4C2211yescharacteristic
9C32×#124—22no—
10C32×#124C414yescomplemented
11C2×C32×C22⋊C4—22no—
12C2×C32×C42C2211yescharacteristic
13Q8×C3⋊Dic3—24no—
14#64135—22no—
15#64135C2212yes—
16C2×#3748C2212yes—
17#63663—22no—
18#63659—24no—
19C2×C3×#124D314yes—
20#5812—34no—
21C2×#836—34no—
22#5215—38no—
23#4523—38no—
24C24×C32—21no—
25C2×C32×Q8—22no—
26C2×C32×Q8—22no—
27C2×C32×Q8C2×C412yes—
28C2×C32×Q8D412yes—
29C2×C32×D4—22no—
30C2×C32×D4—21no—
31C2×C32×D4—22no—
32C2×C32×D4C2×C412yes—
33C22×C32×C4—21no—
34C22×C32×C4D412yes—
35C22×C32×C4C2311yescharacteristic
36C32×C22⋊C4—28no—
37C32×C42—21no—
38C32×C42C2×C412yes—
39#3757—22no—
40C4⋊(C3⋊Dic3)—24no—
41C4⋊(C3⋊Dic3)D414yes—
42C4×C3⋊Dic3—24no—
43C4×C3⋊Dic3—22no—
44#3748—22no—
45#3748—22no—
46C2×C3⋊(C3⋊C8)—22no—
47#1888—91noSylow
48C22×C3×Q8C2×D314yes—
49C22×C3×D4C2×D314yes—
50C3×#124—28no—
51C3×#124Dic3116yescomplemented
52C2×C3×C22⋊C4—28no—
53C2×C3×C42C2×D314yes—
54Q8×Dic3—616no—
55#926—38no—
56#926—68no—
57C2×#208—38no—
58#836—68no—
59#832—616no—
60C23×C32—22no—
61C23×C32—44no—
62C23×C32—41no—
63C23×C32—41no—
64C23×C32C2×D411yescharacteristic
65C32×Q8—24no—
66C32×Q8—24no—
67C32×D4—24no—
68C32×D4—42no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—42no—
73C2×C32×C4C22⋊C414yes—
74C2×C32×C4C22×C411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C32×C4C2×D411yescharacteristic
77C2×C32×C4#4112yes—
78C2×C3⋊Dic3—24no—
79C3⋊(C3⋊C8)—42no—
80C2×#124C3⋊D311yescharacteristic
81#519—91no—
82#418—92no—
83C2×#101—91no—
84#339—92no—
85C24×C3—24no—
86C2×C3×Q8—28no—
87C2×C3×Q8—28no—
88C2×C3×Q8C2×Dic318yes—
89C2×C3×Q8#6718yes—
90C2×C3×D4—28no—
91C2×C3×D4—28no—
92C2×C3×D4—24no—
93C2×C3×D4C2×Dic318yes—
94C22×C3×C4—24no—
95C22×C3×C4#6718yes—
96C22×C3×C4C22×D314yes—
97C3×C22⋊C4—232no—
98C3×C42—24no—
99C3×C42C2×Dic318yes—
100#217—68no—
101C4⋊Dic3—316no—
102C4⋊Dic3—616no—
103C4×Dic3—616no—
104C4×Dic3—68no—
105#208—68no—
106#208—68no—
107C2×C3⋊C8—68no—
108C22×C32—22no—
109C22×C32—44no—
110C22×C32—42no—
111C22×C32—82no—
112C22×C32—82no—
113C22×C32C2×C22⋊C411yescharacteristic
114C22×C32#12011yescharacteristic
115C22×C32#12311yescharacteristic
116C32×C4—24no—
117C32×C4—42no—
118C32×C4C4×D412yes—
119C32×C4#12112yes—
120C3⋊Dic3—44no—
121C22×Q8C2×C3⋊D311yescharacteristic
122C22×D4C2×C3⋊D311yescharacteristic
123C2×M16—92no—
124#124—22no—
125#124C3⋊Dic314yescomplemented
126C4×Q8—184no—
127#117—92no—
128#117—182no—
129C2×C22⋊C4—22no—
130C2×C42C2×C3⋊D311yescharacteristic
131#102—184no—
132#101—182no—
133C23×C3—28no—
134C23×C3—416no—
135C23×C3—44no—
136C23×C3—44no—
137C23×C3C2×#6714yes—
138C3×Q8—216no—
139C3×Q8—216no—
140C3×D4—216no—
141C3×D4—48no—
142C2×C3×C4—28no—
143C2×C3×C4—28no—
144C2×C3×C4—28no—
145C2×C3×C4—48no—
146C2×C3×C4#217116yes—
147C2×C3×C4D3×D418yes—
148C2×C3×C4#23718yes—
149C2×C3×C4C22×Dic314yes—
150C2×C3×C4C2×#6714yes—
151C2×Dic3—616no—
152C3⋊C8—128no—
153C2×C32—21no—
154C2×C32—21no—
155C2×C32—82no—
156C2×C32#38611yescharacteristic
157C2×C32#45412yes—
158C24—21no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8C2×C3⋊Dic312yes—
162C2×Q8#63812yes—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—21no—
166C2×D4C2×C3⋊Dic312yes—
167C22×C4—21no—
168C22×C4#63812yes—
169C22×C4C22×C3⋊D311yescharacteristic
170M16—182no—
171M16—182no—
172C2×C8—182no—
173C4⋊C4—94no—
174C4⋊C4—184no—
175C22⋊C4—28no—
176C22⋊C4—182no—
177C42—21no—
178C42—184no—
179C42—182no—
180C42C2×C3⋊Dic312yes—
181C22×C3—28no—
182C22×C3—416no—
183C22×C3—48no—
184C22×C3—88no—
185C22×C3—88no—
186C22×C3#93514yes—
187C22×C3#93714yes—
188C22×C3C2×#21714yes—
189C3×C4—216no—
190C3×C4—48no—
191C3×C4D4×Dic318yes—
192C3×C4#93918yes—
193Dic3—1216no—
194C32#188811yescharacteristic, complemented, Sylow
195C23—22no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23C2×#63811yescharacteristic
200Q8—24no—
201Q8—24no—
202D4—24no—
203D4—42no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—184no—
209C2×C4#375714yes—
210C2×C4D4×C3⋊D312yes—
211C2×C4#383012yes—
212C2×C4C22×C3⋊Dic311yescharacteristic
213C2×C4C2×#63811yescharacteristic
214C8—362no—
215C2×C3—24no—
216C2×C3—24no—
217C2×C3—88no—
218C2×C3#506218yes—
219C2×C3#522014yes—
220C22—22no—
221C22—44no—
222C22—42no—
223C22—82no—
224C22—82no—
225C22#6414411yescharacteristic
226C22#6414611yescharacteristic
227C22C2×#375711yescharacteristic
228C4—24no—
229C4—42no—
230C4—364no—
231C4D4×C3⋊Dic312yes—
232C4#6414812yes—
233C3#7172414yescomplemented
234C2—21no—
235C2—21no—
236C2—82no—
237C2#1059276112yes—
238C2#1059291911yescharacteristic
subgroupG/H
centerC22#64146
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#124C2
socleC22×C32#120
prime radicalC22×C32×D4C22
cosocleC22×C32×C4C23
hypercenterC2×#124C3⋊D3
hypocenterC32#1888
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #10596283C2semidirect
3. C2×#63663C2semidirect
5. #10589389C2semidirect
10. C32×#124C4semidirect
51. C3×#124Dic3semidirect
125. #124C3⋊Dic3semidirect
194. C32#1888semidirect
233. C3#71724semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1242
#105962832
C2×#636632
#105929142
#105893892
#717243