Finite Group Databasebeta

← #11800947

Subgroups — #11800947

Order 1152.

1345 conjugacy classes of subgroups; only the 416 normal subgroups are shown.

normal subgroups only

This group has 1345 conjugacy classes of subgroups — too many to draw. Only its 416 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×C4×#627C213yesmaximal
2#10592347C211yesmaximal, characteristic
3C3×#4648C212yesmaximal
4#10591257C213yesmaximal
5#10591242C216yesmaximal
6#73383—32nomaximal
7C22×#627C2211yescharacteristic
8C2×C4×C3⋊Dic3C2213yes—
9C2×C3×C4×Dic3C2216yes—
10C2×#3724C2213yes—
11C2×Dic3⋊Dic3C2216yes—
12C2×Dic32C2216yes—
13C4×#627C4124yescomplemented
14C32×#95C2211yescharacteristic
15#63658C2213yes—
16C3×C3⋊#95C2216yes—
17C2×C4×Dic6—36no—
18C3×#376—32no—
19C4×C4⋊Dic3—36no—
20#4649—36no—
21#4649—36no—
22#4648—32no—
23#4648—61no—
24#4648D312yes—
25C22×C32×C4C2313yes—
26C22×C3⋊Dic3C2313yes—
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3C2316yes—
29C22×C3×Dic3C2312yes—
30C2×#627C2×C4112yes—
31C4×C3⋊Dic3C2×C4112yes—
32C3×C4×Dic3C2×C4124yes—
33#3724C2×C4112yes—
34Dic3⋊Dic3C2×C4124yes—
35Dic32—46no—
36#2276—91noSylow
37C22×Dic6—32no—
38C2×C3×C42—36no—
39C2×C4⋊Dic3—36no—
40C2×Dic3⋊C4—36no—
41C2×Dic3⋊C4—36no—
42C2×C4×Dic3—36no—
43C2×C4×Dic3—312no—
44C2×C4×Dic3—63no—
45C2×C4×Dic3C2×D316yes—
46C4×Dic6—348no—
47C3×#95—21no—
48C3×#95—36no—
49C3×#95C2×D312yes—
50C3⋊#95—36no—
51C3⋊#95—63no—
52C3⋊#95C2×D316yes—
53C23×C32C2411yescharacteristic
54C2×C32×C4—26no—
55C2×C32×C4C22×C416yes—
56C2×C3⋊Dic3—23no—
57C2×C3⋊Dic3—23no—
58C2×C3⋊Dic3C22×C416yes—
59C2×C3⋊Dic3C22×C416yes—
60C2×C3×Dic3—26no—
61C2×C3×Dic3—26no—
62C2×C3×Dic3C22×C4112yes—
63C2×C3×Dic3C22×C4112yes—
64#627C42116yescomplemented
65C2×C4×Q8—93no—
66C4×C4⋊C4—93no—
67C4×C4⋊C4—96no—
68#376—32no—
69#376—91no—
70C22×C3×C4—23no—
71C22×C3×C4—32no—
72C22×C3×C4—36no—
73C22×C3×C4C22×D316yes—
74C22×Dic3—32no—
75C22×Dic3—36no—
76C22×Dic3—61no—
77C22×Dic3—63no—
78C22×Dic3C22×D316yes—
79C22×Dic3C22×D312yes—
80C2×Dic6—324no—
81C3×C42—324no—
82C4⋊Dic3—324no—
83Dic3⋊C4—324no—
84Dic3⋊C4—324no—
85C4×Dic3—324no—
86C4×Dic3—612no—
87C4×Dic3—1212no—
88C4×Dic3C4×D3124yes—
89C22×C32C23×C413yes—
90C22×C32H(5,𝔽2)11yescharacteristic
91C22×C322−1+413yes—
92C32×C4—26no—
93C3⋊Dic3—26no—
94C3⋊Dic3C2×C4214yes—
95C3×Dic3—212no—
96C3×Dic3C2×C4218yes—
97C22×Q8—91no—
98C4×Q8—924no—
99C2×C4⋊C4—93no—
100C2×C4⋊C4—96no—
101C2×C42—36no—
102C2×C42—93no—
103C2×C42—96no—
104#95—36no—
105#95—93no—
106#95D3211yescharacteristic
107C23×C3—21no—
108C23×C3C23×D312yes—
109C2×C3×C4—212no—
110C2×C3×C4—26no—
111C2×C3×C4—312no—
112C2×C3×C4—312no—
113C2×C3×C4—46no—
114C2×C3×C4—66no—
115C2×C3×C4—66no—
116C2×C3×C4C2×C4×D3112yes—
117C2×Dic3—26no—
118C2×Dic3—26no—
119C2×Dic3—312no—
120C2×Dic3—312no—
121C2×Dic3—66no—
122C2×Dic3—66no—
123C2×Dic3—66no—
124C2×Dic3—66no—
125C2×Dic3—123no—
126C2×Dic3—123no—
127C2×Dic3C2×C4×D3112yes—
128C2×Dic3C2×C4×D3112yes—
129Dic6—332no—
130C2×C32C22×C4211yescharacteristic
131C2×C32#51913yes—
132C2×C32#52013yes—
133C2×Q8—912no—
134C22×C4—32no—
135C22×C4—36no—
136C22×C4—91no—
137C22×C4—93no—
138C22×C4C2×D3213yes—
139C4⋊C4—912no—
140C4⋊C4—924no—
141C42—324no—
142C42—912no—
143C42—366no—
144C22×C3—23no—
145C22×C3—23no—
146C22×C3—21no—
147C22×C3C22×C4×D316yes—
148C22×C3#100912yes—
149C22×C3#101016yes—
150C3×C4—212no—
151C3×C4—38no—
152C3×C4—46no—
153C3×C4—612no—
154Dic3—212no—
155Dic3—38no—
156Dic3—64no—
157Dic3—612no—
158Dic3—126no—
159Dic3C42×D318yes—
160C32#227611yescharacteristic, complemented, Sylow
161C23C22×D3211yescharacteristic
162Q8—916no—
163C2×C4—26no—
164C2×C4—312no—
165C2×C4—312no—
166C2×C4—66no—
167C2×C4—66no—
168C2×C4—96no—
169C2×C4—96no—
170C2×C4—183no—
171C2×C4—183no—
172C2×C4C4×D3216yes—
173C2×C3—23no—
174C2×C3—21no—
175C2×C3—23no—
176C2×C3C2×C42×D312yes—
177C2×C3#551616yes—
178C2×C3#552316yes—
179C22C2×C4×D3213yes—
180C22#6430913yes—
181C22#6432011yescharacteristic
182C4—26no—
183C4—38no—
184C4—612no—
185C4—94no—
186C4—186no—
187C3—21no—
188C3#7338312yescomplemented
189C2C42×D3211yescharacteristic
190C2#1059424513yes—
191C2#1059451113yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2276
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
13. C4×#627C4semidirect
64. #627C42semidirect
160. C32#2276semidirect
188. C3#73383semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
#105923472
C3×#46482
#105912572
#105912422
#733833