Finite Group Databasebeta

← #11802673

Subgroups — #11802673

Order 1152.

2352 conjugacy classes of subgroups; only the 425 normal subgroups are shown.

normal subgroups only

This group has 2352 conjugacy classes of subgroups — too many to draw. Only its 425 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
1C23×#634C211yesmaximal, characteristic
2C2×#64086C212yesmaximal
3C32×#381C211yesmaximal, characteristic
4#10592910C211yesmaximal, characteristic
5#10592642C212yesmaximal
6#10592345C218yesmaximal, complemented
7#74053—34nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3⋊Dic3C2211yescharacteristic
11C22×#634—28no—
12C22×#634C418yescomplemented
13C22×#634C2214yes—
14C2×C32×C22⋊C4C2212yes—
15C2×#3757C2212yes—
16C2×#3750C2214yes—
17C2×C4×C3⋊Dic3C2214yes—
18#64086—28no—
19C32×#95C2214yes—
20#63658C2218yes—
21#63658C2214yes—
22C23×Dic6—34no—
23C2×#877—38no—
24C3×#381D314yes—
25#5211—34no—
26#4943—38no—
27#4646—332no—
28C24×C32C2311yescharacteristic
29C22×C32×C4—24no—
30C22×C32×C4C2×C414yes—
31C22×C32×C4C2314yes—
32C22×C32×C4C2312yes—
33C22×C3⋊Dic3—24no—
34C22×C3⋊Dic3C2×C414yes—
35C22×C3⋊Dic3C2×C414yes—
36C22×C3⋊Dic3D418yes—
37C22×C3⋊Dic3C2314yes—
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C2×#634—232no—
41C2×#634—28no—
42C2×#634—28no—
43C2×#634C2×C4116yes—
44C32×C22⋊C4—24no—
45#3757—24no—
46#3750—28no—
47C4×C3⋊Dic3—28no—
48#2310—91noSylow
49C23×C3×C4C2×D314yes—
50C23×Dic3—34no—
51C23×Dic3—34no—
52C22×Dic6—332no—
53C22×Dic6—316no—
54C22×Dic6—632no—
55C2×C3×C22⋊C4C2×D318yes—
56C2×#217—38no—
57C2×Dic3⋊C4—316no—
58C2×C4×Dic3—316no—
59#877—632no—
60C3×#95C2×D3116yes—
61C3⋊#95—332no—
62C3⋊#95—316no—
63C23×C32—24no—
64C23×C32C22×C412yes—
65C23×C32C2×D414yes—
66C23×C32C2411yescharacteristic
67C2×C32×C4—28no—
68C2×C32×C4—24no—
69C2×C32×C4—24no—
70C2×C32×C4—28no—
71C2×C32×C4C22×C414yes—
72C2×C3⋊Dic3—28no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3—24no—
75C2×C3⋊Dic3—28no—
76C2×C3⋊Dic3C22⋊C4116yes—
77C2×C3⋊Dic3C22×C414yes—
78C2×C3⋊Dic3C22×C414yes—
79C2×C3⋊Dic3C2×D414yes—
80C2×C3⋊Dic3C2×D414yes—
81#634—232no—
82C23×Q8—91no—
83C2×#117—92no—
84#391—98no—
85#381—91no—
86#381—92no—
87#381C3⋊D311yescharacteristic
88C24×C3C22×D314yes—
89C22×C3×C4—216no—
90C22×C3×C4C4×D3116yes—
91C22×C3×C4C22×D3116yes—
92C22×C3×C4C22×D318yes—
93C22×Dic3—316no—
94C22×Dic3—332no—
95C22×Dic3—38no—
96C22×Dic3—316no—
97C22×Dic3—38no—
98C22×Dic3—316no—
99C22×Dic3—616no—
100C2×Dic6—364no—
101C2×Dic6—6128no—
102C2×Dic6—632no—
103C2×Dic6—632no—
104C3×C22⋊C4—216no—
105#217—616no—
106Dic3⋊C4—632no—
107C4×Dic3—632no—
108C22×C32—24no—
109C22×C32—28no—
110C22×C32C2×C22⋊C414yes—
111C22×C32C23×C411yescharacteristic
112C22×C32C22×D412yes—
113C22×C322−1+414yes—
114C32×C4—24no—
115C32×C4—44no—
116C3⋊Dic3—24no—
117C3⋊Dic3—44no—
118C3⋊Dic3C2×C22⋊C418yes—
119C22×Q8—98no—
120C22×Q8—94no—
121C22×Q8—188no—
122C23×C4—91no—
123C23×C4—91no—
124C23×C4C2×C3⋊D311yescharacteristic
125#117—188no—
126C2×C4⋊C4—94no—
127C2×C22⋊C4—92no—
128C2×C22⋊C4C2×C3⋊D312yes—
129C2×C42—94no—
130#95—98no—
131#95—94no—
132#95C2×C3⋊D314yes—
133C23×C3—216no—
134C23×C3C2×C4×D318yes—
135C23×C3D3×D4116yes—
136C23×C3C23×D314yes—
137C2×C3×C4—232no—
138C2×C3×C4—216no—
139C2×C3×C4—216no—
140C2×C3×C4—232no—
141C2×C3×C4C2×C4×D3116yes—
142C2×Dic3—364no—
143C2×Dic3—316no—
144C2×Dic3—316no—
145C2×Dic3—316no—
146C2×Dic3—316no—
147C2×Dic3—632no—
148C2×Dic3—616no—
149C2×Dic3—616no—
150C2×Dic3—632no—
151Dic6—6128no—
152C2×C32—24no—
153C2×C32C22×C22⋊C411yescharacteristic
154C2×C32#51912yes—
155C2×C32#53614yes—
156C24C22×C3⋊D311yescharacteristic
157C2×Q8—916no—
158C2×Q8—1832no—
159C2×Q8—188no—
160C2×Q8—188no—
161C22×C4—24no—
162C22×C4—92no—
163C22×C4—94no—
164C22×C4—98no—
165C22×C4—92no—
166C22×C4—94no—
167C22×C4—94no—
168C22×C4—184no—
169C22×C4C4×C3⋊D314yes—
170C22×C4C22×C3⋊D314yes—
171C22×C4C22×C3⋊D312yes—
172C4⋊C4—188no—
173C22⋊C4—24no—
174C22⋊C4—184no—
175C42—188no—
176C22×C3—232no—
177C22×C3—216no—
178C22×C3D3×C22⋊C4116yes—
179C22×C3C22×C4×D314yes—
180C22×C3C2×D3×D418yes—
181C22×C3#1010116yes—
182C3×C4—216no—
183C3×C4—416no—
184Dic3—332no—
185Dic3—616no—
186Dic3—1216no—
187C32#231011yescharacteristic, complemented, Sylow
188C23—24no—
189C23C2×C4×C3⋊D312yes—
190C23D4×C3⋊D314yes—
191C23C23×C3⋊D311yescharacteristic
192Q8—1832no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—28no—
197C2×C4—916no—
198C2×C4—94no—
199C2×C4—94no—
200C2×C4—94no—
201C2×C4—94no—
202C2×C4—188no—
203C2×C4—184no—
204C2×C4—184no—
205C2×C4—188no—
206C2×C4C2×C4×C3⋊D314yes—
207C2×C3—216no—
208C2×C3C2×D3×C22⋊C414yes—
209C2×C3#551618yes—
210C2×C3#5648116yes—
211C22—28no—
212C22—24no—
213C22C22⋊C4×C3⋊D314yes—
214C22C22×C4×C3⋊D311yescharacteristic
215C22C2×D4×C3⋊D312yes—
216C22#6436714yes—
217C4—24no—
218C4—44no—
219C4—98no—
220C4—184no—
221C4—364no—
222C3#7405314yescomplemented
223C2—24no—
224C2C2×C22⋊C4×C3⋊D311yescharacteristic
225C2#1059598712yes—
226C2#1059611914yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#381C2
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenter#381C3⋊D3
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #10592345C2semidirect
12. C22×#634C4semidirect
187. C32#2310semidirect
222. C3#74053semidirect

Maximal subgroups

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

subgroupindex
C23×#6342
C2×#640862
C32×#3812
#105929102
#105926422
#105923452
#740533