Finite Group Databasebeta

← #46834890

Subgroups — #46834890

Order 34688.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#31774431C211yesmaximal, characteristic
2C4×C4⋊Dic271C211yesmaximal, characteristic, complemented
3#31773635C212yesmaximal, complemented
4#31773632C212yesmaximal
5#432×C271C211yesmaximal, characteristic, complemented
6#22576154—21no—
7#22576152C411yescharacteristic, complemented
8#22576148C411yescharacteristic, complemented
9#22576143—21no—
10#22576139C2211yescharacteristic
11#22576134C2211yescharacteristic
12C4×Dic542C411yescharacteristic, complemented
13C4×D1084C411yescharacteristic, complemented
14C4×C22⋊D271—21no—
15#22576117—21no—
16C2×C4⋊Dic271—21no—
17C2×C4×Dic271—21no—
18C271⋊#95C2212yes—
19C2×C42×C271C2211yescharacteristic
20C4⋊C8×C271—21no—
21C22⋊C8×C271C2212yes—
22#97×C271—21no—
23C2×Dic542C2×C411yescharacteristic
24C2×D1084C2×C411yescharacteristic
25C2×C22⋊D271—21no—
26C22×Dic271—22no—
27C2×C4×D271—21no—
28C4⋊Dic271—24no—
29C4⋊Dic271C2×C411yescharacteristic
30C4⋊Dic271C2×C411yescharacteristic
31Dic271⋊C4—21no—
32Dic271⋊C4—21no—
33Dic271⋊C4—21no—
34Dic271⋊C4—21no—
35C22⋊Dic271—21no—
36(C2×D271)⋊C4—21no—
37(C2×D271)⋊C4—21no—
38(C2×D271)⋊C4—21no—
39(C2×D271)⋊C4—21no—
40C4×Dic271—21no—
41C4×Dic271—42no—
42C22×C4×C271D411yescharacteristic
43C22×C4×C271D411yescharacteristic
44C22×C4×C271C2311yescharacteristic
45C2×C8×C271—22no—
46C42×C271C2×C411yescharacteristic
47C42×C271C2×C411yescharacteristic
48C42×C271D411yescharacteristic
49C42×C271D411yescharacteristic
50C22×D271—21no—
51Dic542—41no—
52D1084—41no—
53C22⋊D271—41no—
54C22⋊D271—41no—
55C2×Dic271—24no—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—42no—
60C2×Dic271—42no—
61C4×D271—42no—
62C23×C271C2×D411yescharacteristic
63C2×C4×C271—21no—
64C2×C4×C271—21no—
65C2×C4×C271—22no—
66C2×C4×C271—41no—
67C2×C4×C271C22⋊C411yescharacteristic
68C2×C4×C271C22⋊C411yescharacteristic
69C2×C4×C271C22⋊C411yescharacteristic
70C2×C4×C271C22⋊C411yescharacteristic
71C2×C4×C271C22×C411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C8×C271—42no—
74C22×C271—21no—
75C22×C271—21no—
76C22×C271C2×C22⋊C411yescharacteristic
77C22×C271AGL(1,ℤ/8)11yescharacteristic
78C22×C271#13711yescharacteristic
79C2×D271—41no—
80C2×D271—41no—
81C2×D271—41no—
82C4×C271—21no—
83C4×C271—21no—
84C4×C271—21no—
85C4×C271—21no—
86C4×C271—21no—
87C4×C271#10412yes—
88Dic271—44no—
89Dic271—41no—
90Dic271—41no—
91Dic271—41no—
92C2×C271—21no—
93C2×C271—21no—
94C2×C271#41011yescharacteristic
95C2×C271#41711yescharacteristic
96C2×C271C2×#10411yescharacteristic
97D271—81no—
98C271#150911yescharacteristic, complemented, Sylow
99#1509—2711nomaximal, Sylow
100#529—2711no—
101#432D27111yescharacteristic, complemented
102C4×C4⋊C4—2711no—
103#328—2712no—
104#327—2712no—
105#126—5421no—
106#125—2711no—
107#124—2711no—
108#123—5421no—
109C22⋊Q8—2711no—
110#121—2711no—
111C4×Q8—2711no—
112C4×D4—2711no—
113C4×D4—5421no—
114#117—5421no—
115C2×C4⋊C4—5421no—
116C2×C42—5421no—
117C2×C42C2×D27111yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C2×D27112yes—
120#97—21no—
121#95—2712no—
122C2×Q8—2711no—
123C2×D4—2711no—
124C2×D4—5421no—
125C22×C4—5422no—
126C22×C4—5421no—
127C22×C4D108411yescharacteristic
128C22×C4D108411yescharacteristic
129C22×C4C22×D27111yescharacteristic
130C2×C8—22no—
131C4⋊C4—2711no—
132C4⋊C4—2711no—
133C4⋊C4—5424no—
134C4⋊C4—5421no—
135C4⋊C4—5421no—
136C4⋊C4—5421no—
137C4⋊C4—5421no—
138C22⋊C4—5421no—
139C22⋊C4—5421no—
140C22⋊C4—5421no—
141C22⋊C4—5421no—
142C22⋊C4—5421no—
143C42—5421no—
144C42—10842no—
145C42C4×D27111yescharacteristic
146C42C4×D27111yescharacteristic
147C42C22⋊D27111yescharacteristic
148C42C22⋊D27111yescharacteristic
149C23—5421no—
150C23C2×D108411yescharacteristic
151Q8—10841no—
152D4—10841no—
153D4—10841no—
154D4—10841no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—5424no—
160C2×C4—5421no—
161C2×C4—5421no—
162C2×C4—5421no—
163C2×C4—10842no—
164C2×C4—10842no—
165C2×C4—10842no—
166C2×C4(C2×D271)⋊C411yescharacteristic
167C2×C4(C2×D271)⋊C411yescharacteristic
168C2×C4(C2×D271)⋊C411yescharacteristic
169C2×C4(C2×D271)⋊C411yescharacteristic
170C2×C4C2×C4×D27111yescharacteristic
171C2×C4C2×C22⋊D27111yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—10841no—
176C22—10841no—
177C22—10841no—
178C22C2×(C2×D271)⋊C411yescharacteristic
179C22#2257618811yescharacteristic
180C22#2257619311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—10844no—
187C4—10841no—
188C4—10841no—
189C4—10841no—
190C4#2257608612yes—
191C2—21no—
192C2—21no—
193C2—21681no—
194C2#3177387011yescharacteristic
195C2#3177389911yescharacteristic
196C2C2×#2257608611yescharacteristic
subgroupG/H
centerC22C2×(C2×D271)⋊C4
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
Fitting#432×C271C2
socleC22×C271C2×C22⋊C4
prime radical#22576134C22
cosocleC22×C4×C271C23
hypercenter#432D271
hypocenterC271#1509
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic271C2semidirect
3. #31773635C2semidirect
5. #432×C271C2semidirect
7. #22576152C4semidirect
8. #22576148C4semidirect
12. C4×Dic542C4semidirect
13. C4×D1084C4semidirect
98. C271#1509semidirect
101. #432D271semidirect

Maximal subgroups

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

subgroupindex
#317744312
C4×C4⋊Dic2712
#317736352
#317736322
#432×C2712
#1509271