Finite Group Databasebeta

← #46834900

Subgroups — #46834900

Order 34688.

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

normal subgroups only

This group has 222 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#31774431C211yesmaximal, characteristic
2#31773954C211yesmaximal, characteristic, complemented
3#31773633C212yesmaximal, complemented
4#31773630C212yesmaximal
5#382×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—
16C4⋊(C271⋊C8)—21no—
17C22⋊(C271⋊C8)C2212yes—
18#22576071—21no—
19C2×C4⋊C4×C271—21no—
20C2×C42×C271C2211yescharacteristic
21#95×C271—21no—
22#95×C271C2212yes—
23C2×Dic542C2×C411yescharacteristic
24C2×D1084C2×C411yescharacteristic
25C2×C22⋊D271—21no—
26C2×C4×D271—21no—
27C2×C271⋊C8—22no—
28C4⋊Dic271C2×C411yescharacteristic
29C4⋊Dic271C2×C411yescharacteristic
30Dic271⋊C4—21no—
31Dic271⋊C4—21no—
32Dic271⋊C4—21no—
33Dic271⋊C4—21no—
34C22⋊Dic271—21no—
35(C2×D271)⋊C4—21no—
36(C2×D271)⋊C4—21no—
37(C2×D271)⋊C4—21no—
38(C2×D271)⋊C4—21no—
39C4×Dic271—21no—
40C22×C4×C271—22no—
41C22×C4×C271D411yescharacteristic
42C22×C4×C271D411yescharacteristic
43C22×C4×C271C2311yescharacteristic
44C4⋊C4×C271—42no—
45C42×C271C2×C411yescharacteristic
46C42×C271C2×C411yescharacteristic
47C42×C271D411yescharacteristic
48C42×C271D411yescharacteristic
49C22×D271—21no—
50Dic542—41no—
51D1084—41no—
52C22⋊D271—41no—
53C22⋊D271—41no—
54C2×Dic271—21no—
55C2×Dic271—21no—
56C2×Dic271—21no—
57C4×D271—42no—
58C271⋊C8—42no—
59C23×C271C2×D411yescharacteristic
60C2×C4×C271—21no—
61C2×C4×C271—21no—
62C2×C4×C271—41no—
63C2×C4×C271—41no—
64C2×C4×C271—42no—
65C2×C4×C271—42no—
66C2×C4×C271—42no—
67C2×C4×C271C22⋊C411yescharacteristic
68C2×C4×C271C22⋊C411yescharacteristic
69C2×C4×C271C22⋊C411yescharacteristic
70C2×C4×C271C22⋊C411yescharacteristic
71C2×C4×C271C22×C411yescharacteristic
72C2×C4×C271C2×D411yescharacteristic
73C22×C271—21no—
74C22×C271—21no—
75C22×C271C2×C22⋊C411yescharacteristic
76C22×C271AGL(1,ℤ/8)11yescharacteristic
77C22×C271#13711yescharacteristic
78C2×D271—41no—
79C2×D271—41no—
80C2×D271—41no—
81C4×C271—21no—
82C4×C271—21no—
83C4×C271—21no—
84C4×C271—21no—
85C4×C271—21no—
86C4×C271—21no—
87C4×C271—82no—
88Dic271—41no—
89Dic271—41no—
90Dic271—41no—
91C2×C271—21no—
92C2×C271—21no—
93C2×C271#41011yescharacteristic
94C2×C271#41711yescharacteristic
95C2×C271#42111yescharacteristic
96D271—81no—
97C271#151211yescharacteristic, complemented, Sylow
98#1512—2711nomaximal, Sylow
99#529—2711no—
100#432—2711no—
101#382D27111yescharacteristic, complemented
102#328—2712no—
103#327—2712no—
104#126—5421no—
105#125—2711no—
106#124—2711no—
107#123—5421no—
108C22⋊Q8—2711no—
109#121—2711no—
110C4×Q8—2711no—
111C4×D4—2711no—
112C4×D4—5421no—
113#117—5421no—
114C2×C4⋊C4—21no—
115C2×C42C2×D27111yescharacteristic
116C4⋊C8—5421no—
117C22⋊C8—2712no—
118#97—5421no—
119#95—21no—
120#95C2×D27112yes—
121C2×Q8—2711no—
122C2×D4—2711no—
123C2×D4—5421no—
124C22×C4—22no—
125C22×C4—5421no—
126C22×C4C22⋊D27111yescharacteristic
127C22×C4C22⋊D27111yescharacteristic
128C22×C4C22×D27111yescharacteristic
129C2×C8—5422no—
130C4⋊C4—42no—
131C4⋊C4—2711no—
132C4⋊C4—2711no—
133C4⋊C4—5421no—
134C4⋊C4—5421no—
135C4⋊C4—5421no—
136C4⋊C4—5421no—
137C22⋊C4—5421no—
138C22⋊C4—5421no—
139C22⋊C4—5421no—
140C22⋊C4—5421no—
141C22⋊C4—5421no—
142C42—5421no—
143C42C4×D27111yescharacteristic
144C42C4×D27111yescharacteristic
145C42D108411yescharacteristic
146C42D108411yescharacteristic
147C23—5421no—
148C23C2×C22⋊D27111yescharacteristic
149Q8—10841no—
150D4—10841no—
151D4—10841no—
152D4—10841no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—5421no—
161C2×C4—5421no—
162C2×C4—5421no—
163C2×C4—10842no—
164C2×C4(C2×D271)⋊C411yescharacteristic
165C2×C4(C2×D271)⋊C411yescharacteristic
166C2×C4(C2×D271)⋊C411yescharacteristic
167C2×C4(C2×D271)⋊C411yescharacteristic
168C2×C4C2×C4×D27111yescharacteristic
169C2×C4C2×D108411yescharacteristic
170C8—10842no—
171C22—21no—
172C22—21no—
173C22—10841no—
174C22—10841no—
175C22—10841no—
176C22C2×(C2×D271)⋊C411yescharacteristic
177C22#2257618611yescharacteristic
178C22#2257619111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—10841no—
187C4—10841no—
188C4—10841no—
189C2—21no—
190C2—21no—
191C2—21681no—
192C2#3177387011yescharacteristic
193C2#3177389611yescharacteristic
194C2#3177391511yescharacteristic
subgroupG/H
centerC22C2×(C2×D271)⋊C4
commutatorC2×C4×C271C22×C4
FrattiniC22×C4C22×D271
Fitting#382×C271C2
socleC22×C271C2×C22⋊C4
prime radical#22576134C22
cosocleC22×C4×C271C23
hypercenter#382D271
hypocenterC271#1512
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #31773954C2semidirect
3. #31773633C2semidirect
5. #382×C271C2semidirect
7. #22576152C4semidirect
8. #22576148C4semidirect
12. C4×Dic542C4semidirect
13. C4×D1084C4semidirect
97. C271#1512semidirect
101. #382D271semidirect

Maximal subgroups

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

subgroupindex
#317744312
#317739542
#317736332
#317736302
#382×C2712
#1512271