Finite Group Databasebeta

← #46837593

Subgroups — #46837593

Order 34688.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#31774478C211yesmaximal, characteristic
2C2×#22576088C212yesmaximal, complemented
3#31773896C212yesmaximal, complemented
4#31773666C211yesmaximal, characteristic, complemented
5#382×C271C211yesmaximal, characteristic, complemented
6C2×#16864654C2212yes—
7C2×#16864638C2212yes—
8#22576140—22no—
9#22576135—22no—
10#22576134—22no—
11#22576088—24no—
12#22576083—22no—
13#22576080—22no—
14C2×C4⋊C4×C271C2211yescharacteristic
15C2×C4⋊C4×C271C2211yescharacteristic
16C2×C42×C271C2211yescharacteristic
17#95×C271—22no—
18#16864654—22no—
19#16864654—22no—
20#16864654—22no—
21#16864654—22no—
22C2×Dic542D412yes—
23C2×D1084—22no—
24C2×D1084D412yes—
25C2×C22⋊D271—22no—
26C2×C4×D271—22no—
27#16864638—22no—
28#16864638—22no—
29C2×C271⋊C8—22no—
30C4⋊Dic271—22no—
31(C2×D271)⋊C4—24no—
32C22×C4×C271—21no—
33C22×C4×C271—21no—
34C22×C4×C271D412yes—
35C22×C4×C271C2311yescharacteristic
36C4⋊C4×C271—22no—
37C4⋊C4×C271—22no—
38C42×C271—21no—
39C42×C271D412yescomplemented
40C22×D271—22no—
41Dic542—22no—
42Dic542—22no—
43D1084—22no—
44D1084—22no—
45D1084—82no—
46C22⋊D271—42no—
47C22⋊D271—42no—
48C2×Dic271—22no—
49C4×D271—42no—
50C4×D271—42no—
51C271⋊C8—42no—
52C23×C271C2×D411yescharacteristic
53C2×C4×C271—22no—
54C2×C4×C271—22no—
55C2×C4×C271—41no—
56C2×C4×C271—41no—
57C2×C4×C271—42no—
58C2×C4×C271—42no—
59C2×C4×C271—41no—
60C2×C4×C271C2×D412yes—
61C2×C4×C271C2×D411yescharacteristic
62C2×C4×C271#4111yescharacteristic
63C2×C4×C271#4112yes—
64C22×C271—21no—
65C22×C271—21no—
66C22×C271#12011yescharacteristic
67C22×C271#12111yescharacteristic
68C22×C271#12411yescharacteristic
69C2×D271—42no—
70C2×D271—42no—
71C2×D271—42no—
72C4×C271—42no—
73C4×C271—42no—
74C4×C271—81no—
75C4×C271#12112yes—
76C4×C271#12312yes—
77Dic271—42no—
78C2×C271—21no—
79C2×C271—21no—
80C2×C271#39411yescharacteristic
81C2×C271#45411yescharacteristic
82C2×C271#45511yescharacteristic
83D271—82no—
84C271#204011yescharacteristic, complemented, Sylow
85#2040—2711nomaximal, Sylow
86#537—2711no—
87C2×#104—2712no—
88#417—2712no—
89#382D27111yescharacteristic, complemented
90#343—2711no—
91C2×#41—2712no—
92C2×M16—2712no—
93C22⋊Q8—5422no—
94#121—5422no—
95#121—5422no—
96C2×C4⋊C4C2×D27111yescharacteristic
97C2×C4⋊C4C2×D27111yescharacteristic
98C2×C42C2×D27111yescharacteristic
99#104—5424no—
100#103—5422no—
101#102—5422no—
102#95—22no—
103#41—5422no—
104#41—5422no—
105#41—5422no—
106#41—5422no—
107C2×Q8—2712no—
108C2×D4—2712no—
109C2×D4—5422no—
110C2×D4—5422no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—5422no—
114C22×C4C22⋊D27112yes—
115C22×C4C22×D27111yescharacteristic
116M16—5422no—
117M16—5422no—
118C2×C8—5422no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—5422no—
122C22⋊C4—5424no—
123C42—21no—
124C42D108412yescomplemented
125C23—5422no—
126C23C2×C22⋊D27111yescharacteristic
127Q8—5422no—
128Q8—5422no—
129D4—5422no—
130D4—5422no—
131D4—10842no—
132D4—10842no—
133D4—21682no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—5422no—
142C2×C4—10842no—
143C2×C4—10842no—
144C2×C4D4×D27112yes—
145C2×C4C2×D108411yescharacteristic
146C2×C4#1686465411yescharacteristic
147C2×C4#1686465512yes—
148C8—10842no—
149C22—21no—
150C22—21no—
151C22—10842no—
152C22—10842no—
153C22—10842no—
154C22#2257612811yescharacteristic
155C22#2257613411yescharacteristic
156C22#2257614911yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—10842no—
161C4#2257613512yes—
162C4#2257614512yes—
163C2—21no—
164C2—21no—
165C2—21682no—
166C2#3177381411yescharacteristic
167C2#3177406911yescharacteristic
168C2#3177407411yescharacteristic
subgroupG/H
centerC22#22576128
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#382×C271C2
socleC22×C271#120
prime radical#31774478C2
hypercenter#382D271
hypocenterC271#2040
LCSG ▷ C22×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#22576088C2semidirect
3. #31773896C2semidirect
4. #31773666C2semidirect
5. #382×C271C2semidirect
39. C42×C271D4semidirect
84. C271#2040semidirect
89. #382D271semidirect
124. C42D1084semidirect

Maximal subgroups

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

subgroupindex
#317744782
C2×#225760882
#317738962
#317736662
#382×C2712
#2040271