Finite Group Databasebeta

← #46837432

Subgroups — #46837432

Order 34688.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#31774697C211yesmaximal, characteristic, complemented
2#31774409C212yesmaximal, complemented
3#31773915C212yesmaximal, complemented
4#31773860C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C271C211yesmaximal, characteristic, complemented
6C2×#16864654C2212yes—
7C22×C4×D271C2211yescharacteristic
8#22576193—22no—
9#22576188—22no—
10#22576182—22no—
11C2×#16864638C2211yescharacteristic
12#22576144—22no—
13#22576140—22no—
14#22576135—22no—
15#22576130—22no—
16C4×D1084—24no—
17#22576088—24no—
18(C2×D271)⋊C8—22no—
19C2×M16×C271C2211yescharacteristic
20#117×C271C2212yes—
21C23×D271D411yescharacteristic
22#16864654—22no—
23#16864654—22no—
24#16864654—22no—
25#16864654—22no—
26C2×Dic542D412yescomplemented
27C2×D1084—24no—
28C2×D1084D412yescomplemented
29C2×C22⋊D271—22no—
30C22×Dic271D411yescharacteristic
31C2×C4×D271—22no—
32C2×C4×D271—21no—
33C2×C4×D271—22no—
34C2×C4×D271—22no—
35C2×C4×D271—21no—
36Dic1084—22no—
37#16864643—24no—
38D2168—22no—
39#16864638—22no—
40C2×C271⋊C8—21no—
41C4⋊Dic271—24no—
42(C2×D271)⋊C4—24no—
43(C2×D271)⋊C4—24no—
44C22×C4×C271C2311yescharacteristic
45M16×C271—22no—
46C2×C8×C271D412yescomplemented
47C4⋊C4×C271—22no—
48C22⋊C4×C271—22no—
49C42×C271D414yescomplemented
50C22×D271—22no—
51C22×D271—21no—
52C22×D271—22no—
53C22×D271—42no—
54Dic542—22no—
55Dic542—22no—
56D1084—22no—
57D1084—22no—
58D1084—48no—
59C22⋊D271—42no—
60C22⋊D271—42no—
61C2×Dic271—22no—
62C2×Dic271—22no—
63C2×Dic271—21no—
64C4×D271—41no—
65C4×D271—42no—
66C4×D271—42no—
67C4×D271—41no—
68C4×D271—42no—
69C271⋊C8—41no—
70C23×C271C2×D411yescharacteristic
71C2×C4×C271—24no—
72C2×C4×C271C2×D412yes—
73C2×C4×C271C2×D411yescharacteristic
74C2×C4×C271C2×D412yes—
75C2×C4×C271#4111yescharacteristic
76C8×C271—22no—
77C22×C271—41no—
78C22×C271#12012yes—
79C22×C271#12111yescharacteristic
80C2×D271—24no—
81C2×D271—22no—
82C2×D271—42no—
83C2×D271—41no—
84C2×D271—41no—
85C2×D271—44no—
86C2×D271—42no—
87C4×C271—44no—
88C4×C271#12011yescharacteristic
89C4×C271#12112yes—
90C4×C271#12711yescharacteristic
91Dic271—41no—
92Dic271—42no—
93C2×C271—22no—
94C2×C271—21no—
95C2×C271#39211yescharacteristic
96D271—42no—
97D271—82no—
98C271#201011yescharacteristic, complemented, Sylow
99#2010—2711nomaximal, Sylow
100#575—2711no—
101#525—2712no—
102#421—2712no—
103#407—2711no—
104H(3,ℤ/4)D27111yescharacteristic, complemented
105C2×#41—2712no—
106C23×C4—2711no—
107#137—5422no—
108AGL(1,ℤ/8)—5422no—
109#135—5422no—
110C2×M16—2711no—
111C2×M16C2×D27111yescharacteristic
112#123—5422no—
113C22⋊Q8—5422no—
114#121—5422no—
115#120—5422no—
116C4×D4—5424no—
117#117C2×D27112yes—
118#104—5424no—
119C22⋊C8—5422no—
120C24—2711no—
121#41—5422no—
122#41—5422no—
123#41—5422no—
124#41—5422no—
125C2×Q8—2712no—
126C2×D4—2712no—
127C2×D4—5424no—
128C2×D4—5422no—
129C22×C4—2711no—
130C22×C4—5422no—
131C22×C4—5421no—
132C22×C4—5422no—
133C22×C4—5422no—
134C22×C4—5421no—
135C22×C4C22×D27111yescharacteristic
136Q16—5422no—
137SD16—5424no—
138D8—5422no—
139M16—22no—
140M16—5422no—
141C2×C8—5421no—
142C2×C8D108412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—5424no—
145C22⋊C4—22no—
146C22⋊C4—5424no—
147C22⋊C4—5424no—
148C42D108414yescomplemented
149C23—5422no—
150C23—5421no—
151C23—5422no—
152C23—10842no—
153C23D4×D27111yescharacteristic
154Q8—5422no—
155Q8—5422no—
156D4—5422no—
157D4—5422no—
158D4—10848no—
159D4—10842no—
160D4—10842no—
161C2×C4—24no—
162C2×C4—5422no—
163C2×C4—5422no—
164C2×C4—5421no—
165C2×C4—10841no—
166C2×C4—10842no—
167C2×C4—10842no—
168C2×C4—10841no—
169C2×C4—10842no—
170C2×C4D4×D27112yes—
171C2×C4C2×D108411yescharacteristic
172C2×C4C2×D108412yes—
173C2×C4#1686465511yescharacteristic
174C8—22no—
175C8—10841no—
176C22—41no—
177C22—5424no—
178C22—5422no—
179C22—10842no—
180C22—10841no—
181C22—10844no—
182C22—10841no—
183C22—10842no—
184C22#2257613012yes—
185C22#2257613511yescharacteristic
186C4—44no—
187C4—10841no—
188C4—10842no—
189C4#2257613011yescharacteristic
190C4#2257613512yes—
191C4#2257615711yescharacteristic
192C2—22no—
193C2—21no—
194C2—10842no—
195C2—21682no—
196C2#3177380711yescharacteristic
subgroupG/H
centerC4#22576157
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
FittingH(3,ℤ/4)×C271C2
socleC2×C271#392
hypercenterH(3,ℤ/4)D271
hypocenterC271#2010
LCSG ▷ C22×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #31774697C2semidirect
2. #31774409C2semidirect
3. #31773915C2semidirect
4. #31773860C2semidirect
5. H(3,ℤ/4)×C271C2semidirect
26. C2×Dic542D4semidirect
28. C2×D1084D4semidirect
46. C2×C8×C271D4semidirect
49. C42×C271D4semidirect
98. C271#2010semidirect
104. H(3,ℤ/4)D271semidirect
142. C2×C8D1084semidirect
148. C42D1084semidirect

Maximal subgroups

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

subgroupindex
#317746972
#317744092
#317739152
#317738602
H(3,ℤ/4)×C2712
#2010271