Finite Group Databasebeta

← #11800924

Subgroups — #11800924

Order 1152.

1649 conjugacy classes of subgroups; only the 416 normal subgroups are shown.

normal subgroups only

This group has 1649 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×#625C213yesmaximal
2#10592347C211yesmaximal, characteristic, complemented
3C3×D3×#95C212yesmaximal, complemented
4#10591257C213yesmaximal, complemented
5#10591237C216yesmaximal, complemented
6#73322—32nomaximal
7C22×C3×C4×D3C2216yes—
8C22×#625C2211yescharacteristic
9C2×C4×C3⋊Dic3C2213yes—
10C2×#3724C2213yes—
11C2×(C2×D3)⋊Dic3C2216yes—
12C2×Dic32C2216yes—
13C4×#625C4124yescomplemented
14C32×#95C2211yescharacteristic
15#63658C2213yes—
16C3×C3⋊#95C2216yes—
17C2×C4×#67—36no—
18C2×C3×#95—32no—
19C4×#217—36no—
20#4666—36no—
21D3×#95D312yescomplemented
22#4649—36no—
23#4648—32no—
24#4648—61no—
25C23×C3×D3C2312yes—
26C22×C32×C4C2313yes—
27C22×C3⋊Dic3C2313yes—
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3C2316yes—
30C2×C3×C4×D3—412no—
31C2×C3×C4×D3C2×C4124yescomplemented
32C2×#625C2×C4112yes—
33C4×C3⋊Dic3C2×C4112yescomplemented
34#3724C2×C4112yescomplemented
35(C2×D3)⋊Dic3C2×C4124yescomplemented
36Dic32—46no—
37#2275—91noSylow
38C23×C3×C4—36no—
39C22×#67—32no—
40C22×C4×D3C2×D316yes—
41C2×#217—36no—
42C4×#67—348no—
43C2×(C2×D3)⋊C4—36no—
44C2×Dic3⋊C4—36no—
45C2×C4×Dic3—36no—
46C2×C4×Dic3—312no—
47C2×C4×Dic3—63no—
48C3×#95—21no—
49C3×#95—36no—
50C3×#95C2×D312yes—
51C3⋊#95—36no—
52C3⋊#95—63no—
53C3⋊#95C2×D316yes—
54C23×C32C2411yescharacteristic
55C22×C3×D3—26no—
56C22×C3×D3—22no—
57C22×C3×D3C22×C4112yes—
58C2×C32×C4—26no—
59C2×C32×C4C22×C416yes—
60C2×C3⋊Dic3—23no—
61C2×C3⋊Dic3—23no—
62C2×C3⋊Dic3C22×C416yes—
63C2×C3⋊Dic3C22×C416yes—
64C2×C3×Dic3—212no—
65C2×C3×Dic3C22×C4112yes—
66C3×C4×D3—424no—
67#625C42116yescomplemented
68C2×C4×D4—93no—
69C4×C4⋊C4—93no—
70C4×C22⋊C4—96no—
71#376—91no—
72C2×#95—32no—
73C24×C3—32no—
74C23×D3C22×D312yes—
75C22×C3×C4—23no—
76C22×C3×C4—36no—
77C22×C3×C4—324no—
78C22×C3×C4—1212no—
79C22×C3×C4C22×D316yes—
80C2×#67—324no—
81C22×Dic3—32no—
82C22×Dic3—36no—
83C22×Dic3—61no—
84C22×Dic3—63no—
85C22×Dic3C22×D316yes—
86C2×C4×D3—412no—
87C2×C4×D3C4×D3124yescomplemented
88#217—324no—
89(C2×D3)⋊C4—324no—
90Dic3⋊C4—324no—
91C4×Dic3—324no—
92C4×Dic3—612no—
93C4×Dic3—1212no—
94C22×C32C23×C413yes—
95C22×C32H(5,𝔽2)13yes—
96C22×C322−1+411yescharacteristic
97C2×C3×D3—212no—
98C2×C3×D3—212no—
99C2×C3×D3C2×C4218yes—
100C32×C4—26no—
101C3⋊Dic3—26no—
102C3⋊Dic3C2×C4214yes—
103C3×Dic3—212no—
104C22×D4—91no—
105C23×C4—36no—
106C4×D4—924no—
107C2×C4⋊C4—93no—
108C2×C22⋊C4—96no—
109C2×C42—93no—
110C2×C42—96no—
111#95—36no—
112#95—93no—
113#95D3211yescharacteristic
114C23×C3—21no—
115C23×C3—312no—
116C23×C3—66no—
117C23×C3—62no—
118C23×C3C23×D312yes—
119C22×D3—26no—
120C22×D3—22no—
121C22×D3C2×C4×D3112yes—
122C2×C3×C4—212no—
123C2×C3×C4—26no—
124C2×C3×C4—312no—
125C2×C3×C4—46no—
126C2×C3×C4—612no—
127C2×C3×C4—1224no—
128C2×C3×C4C2×C4×D3112yes—
129#67—332no—
130C2×Dic3—212no—
131C2×Dic3—312no—
132C2×Dic3—312no—
133C2×Dic3—66no—
134C2×Dic3—66no—
135C2×Dic3—66no—
136C2×Dic3—66no—
137C2×Dic3—123no—
138C2×Dic3—123no—
139C2×Dic3C2×C4×D3112yes—
140C4×D3—424no—
141C2×C32C22×C4211yescharacteristic
142C2×C32#51813yes—
143C2×C32#52013yes—
144C3×D3—28no—
145C24—32no—
146C2×D4—912no—
147C22×C4—36no—
148C22×C4—324no—
149C22×C4—91no—
150C22×C4—93no—
151C22×C4—1212no—
152C22×C4C2×D3213yes—
153C4⋊C4—912no—
154C22⋊C4—924no—
155C42—912no—
156C42—366no—
157C22×C3—23no—
158C22×C3—23no—
159C22×C3—21no—
160C22×C3—38no—
161C22×C3—612no—
162C22×C3—612no—
163C22×C3C22×C4×D316yes—
164C22×C3#100416yes—
165C22×C3#100712yes—
166C2×D3—212no—
167C2×D3—212no—
168C2×D3C42×D318yes—
169C3×C4—212no—
170C3×C4—46no—
171C3×C4—612no—
172Dic3—212no—
173Dic3—38no—
174Dic3—64no—
175Dic3—612no—
176Dic3—126no—
177C32#227511yescharacteristic, complemented, Sylow
178C23—312no—
179C23—66no—
180C23—62no—
181C23C22×D3211yescharacteristic
182D4—916no—
183C2×C4—26no—
184C2×C4—312no—
185C2×C4—612no—
186C2×C4—96no—
187C2×C4—96no—
188C2×C4—1224no—
189C2×C4—183no—
190C2×C4—183no—
191C2×C4C4×D3216yes—
192C2×C3—23no—
193C2×C3—21no—
194C2×C3—23no—
195C2×C3—68no—
196C2×C3C2×C42×D312yes—
197C2×C3#548616yes—
198C2×C3#550416yes—
199D3—28no—
200C22—38no—
201C22—612no—
202C22—612no—
203C22C2×C4×D3213yes—
204C22#6431313yes—
205C22#6431611yescharacteristic
206C4—26no—
207C4—612no—
208C4—94no—
209C4—186no—
210C3—21no—
211C3#7332212yescomplemented
212C2—68no—
213C2C42×D3211yescharacteristic
214C2#1059418113yes—
215C2#1059450913yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenter#95D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592347C2semidirect
3. C3×D3×#95C2semidirect
4. #10591257C2semidirect
5. #10591237C2semidirect
13. C4×#625C4semidirect
21. D3×#95D3semidirect
31. C2×C3×C4×D3C2×C4semidirect
33. C4×C3⋊Dic3C2×C4semidirect
34. #3724C2×C4semidirect
35. (C2×D3)⋊Dic3C2×C4semidirect
67. #625C42semidirect
87. C2×C4×D3C4×D3semidirect
177. C32#2275semidirect
211. C3#73322semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
#105923472
C3×D3×#952
#105912572
#105912372
#733223