Finite Group Databasebeta

← #46846295

Subgroups — #46846295

Order 34688.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#31774408C211yesmaximal, characteristic
2#31774238C214yesmaximal, complemented
3#31774221C214yesmaximal, complemented
4#31773937C212yesmaximal, complemented
5#31773896C212yesmaximal, complemented
6#31773861C211yesmaximal, characteristic, complemented
7C2×#117×C271C211yesmaximal, characteristic, complemented
8C2×#16864654C2211yescharacteristic
9C2×#16864638C2212yes—
10#22576143—21no—
11#22576139C2212yes—
12#22576134C2212yes—
13#22576129—21no—
14C4×C22⋊D271—22no—
15#22576119C2211yescharacteristic
16#22576093C2214yescomplemented
17#22576091C2214yescomplemented
18#22576083C2214yescomplemented
19#22576080C2214yescomplemented
20C22⋊(C271⋊C8)C2214yes—
21C23×C4×C271C2211yescharacteristic
22#117×C271—22no—
23#117×C271C2214yes—
24C2×C4⋊C4×C271C2212yes—
25C2×C22⋊C4×C271—21no—
26C2×C42×C271—21no—
27#16864654—24no—
28C2×Dic542C2311yescharacteristic
29C2×D1084C2311yescharacteristic
30C2×C22⋊D271—22no—
31C2×C22⋊D271—21no—
32C2×C4×D271—21no—
33#16864638—24no—
34C2×C271⋊C8C2314yes—
35C4⋊Dic271C2312yes—
36Dic271⋊C4—22no—
37C22⋊Dic271—22no—
38C22⋊Dic271—21no—
39(C2×D271)⋊C4—22no—
40C4×Dic271—21no—
41C24×C271D411yescharacteristic
42C22×C4×C271—24no—
43C22×C4×C271—22no—
44C22×C4×C271D411yescharacteristic
45C22×C4×C271D412yes—
46C22×C4×C271C2312yes—
47C22×C4×C271C2311yescharacteristic
48C4⋊C4×C271—22no—
49C4⋊C4×C271C2314yes—
50C22⋊C4×C271—24no—
51C42×C271—24no—
52C22×D271—21no—
53Dic542—22no—
54D1084—22no—
55C22⋊D271—44no—
56C22⋊D271—42no—
57C2×Dic271—22no—
58C2×Dic271—21no—
59C4×D271—42no—
60C271⋊C8—24no—
61C23×C271—22no—
62C23×C271—42no—
63C23×C271C2×D412yes—
64C23×C271C2×D411yescharacteristic
65C2×C4×C271—22no—
66C2×C4×C271—24no—
67C2×C4×C271—24no—
68C2×C4×C271—24no—
69C2×C4×C271—44no—
70C2×C4×C271C2×D412yes—
71C2×C4×C271C2×D411yescharacteristic
72C2×C4×C271#4114yes—
73C2×C4×C271C2411yescharacteristic
74C22×C271—22no—
75C22×C271—22no—
76C22×C271—22no—
77C22×C271—22no—
78C22×C271—44no—
79C22×C271#12312yes—
80C22×C271C22×D411yescharacteristic
81C2×D271—41no—
82C2×D271—42no—
83C4×C271—22no—
84C4×C271—44no—
85C4×C271#12312yes—
86C4×C271C2×#4112yes—
87Dic271—41no—
88Dic271—42no—
89C2×C271—22no—
90C2×C271—42no—
91C2×C271C2×#12311yescharacteristic
92C2×C271#57512yes—
93D271—81no—
94C271#309311yescharacteristic, complemented, Sylow
95#3093—2711nomaximal, Sylow
96#525—2711no—
97C2×#117D27111yescharacteristic, complemented
98#485—2714no—
99#482—2714no—
100#428—2712no—
101#417—2712no—
102#407—2711no—
103C2×#41—2711no—
104C23×C4C2×D27111yescharacteristic
105C2×M16—2712no—
106#123—5421no—
107C22⋊Q8—2712no—
108#121—2712no—
109#120—5421no—
110C4×D4—5422no—
111#117—22no—
112#117—2711no—
113#117C2×D27114yes—
114C2×C4⋊C4C2×D27112yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—2714no—
118#106—2714no—
119#103—2714no—
120#102—2714no—
121C22⋊C8—2714no—
122C24C22⋊D27111yescharacteristic
123#41—5424no—
124C2×Q8—2711no—
125C2×D4—2711no—
126C2×D4—5422no—
127C2×D4—5421no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—5421no—
131C22×C4C22⋊D27111yescharacteristic
132C22×C4C22⋊D27112yes—
133C22×C4C22×D27112yes—
134C22×C4C22×D27111yescharacteristic
135M16—5424no—
136C2×C8—2714no—
137C4⋊C4—22no—
138C4⋊C4—2712no—
139C4⋊C4—5422no—
140C4⋊C4C22×D27114yes—
141C22⋊C4—24no—
142C22⋊C4—5421no—
143C22⋊C4—5422no—
144C22⋊C4—5422no—
145C42—24no—
146C42—5421no—
147C23—22no—
148C23—42no—
149C23—5421no—
150C23C2×C22⋊D27112yes—
151C23C2×C22⋊D27111yescharacteristic
152Q8—5422no—
153D4—5422no—
154D4—10844no—
155D4—10842no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—5422no—
162C2×C4—5421no—
163C2×C4—10842no—
164C2×C4C2×C22⋊D27112yes—
165C2×C4C2×C22⋊D27111yescharacteristic
166C2×C4#1686465414yes—
167C2×C4C23×D27111yescharacteristic
168C8—5424no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—10841no—
175C22—10842no—
176C22#2257614312yes—
177C22C22×C22⋊D27111yescharacteristic
178C4—22no—
179C4—44no—
180C4—10841no—
181C4—10842no—
182C4#2257614312yes—
183C4C2×#1686465412yes—
184C2—22no—
185C2—42no—
186C2—21681no—
187C2C2×#2257614311yescharacteristic
188C2#3177469512yes—
subgroupG/H
centerC22C22×C22⋊D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC2×#117×C271C2
socleC22×C271C22×D4
prime radical#31774408C2
hypercenterC2×#117D271
hypocenterC271#3093
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #31774238C2semidirect
3. #31774221C2semidirect
4. #31773937C2semidirect
5. #31773896C2semidirect
6. #31773861C2semidirect
7. C2×#117×C271C2semidirect
16. #22576093C22semidirect
17. #22576091C22semidirect
18. #22576083C22semidirect
19. #22576080C22semidirect
94. C271#3093semidirect
97. C2×#117D271semidirect

Maximal subgroups

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

subgroupindex
#317744082
#317742382
#317742212
#317739372
#317738962
#317738612
C2×#117×C2712
#3093271