Finite Group Databasebeta

← #46835364

Subgroups — #46835364

Order 34688.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#31774496C211yesmaximal, characteristic
2#31774225C211yesmaximal, characteristic, complemented
3#31774211C211yesmaximal, characteristic
4#31773829C211yesmaximal, characteristic, complemented
5#31773630C211yesmaximal, characteristic
6#31773622C211yesmaximal, characteristic, complemented
7#328×C271C211yesmaximal, characteristic, complemented
8#22576155—21no—
9#22576151—21no—
10#22576145—21no—
11#22576144—21no—
12#22576136—21no—
13#22576134C2211yescharacteristic
14(C22⋊D271)⋊C4—21no—
15C2×C4⋊Dic271—21no—
16C2×C4⋊Dic271C2211yescharacteristic
17C2×Dic271⋊C4C2211yescharacteristic
18#22576094—21no—
19#22576091—21no—
20#22576084—21no—
21#22576082—21no—
22C22⋊(C271⋊C8)C2211yescharacteristic
23C271⋊#95—21no—
24C22⋊Q8×C271C2211yescharacteristic
25C22⋊C8×C271C2211yescharacteristic
26#95×C271C2211yescharacteristic
27C2×D1084D411yescharacteristic
28C2×C22⋊D271—21no—
29C22×Dic271—21no—
30C22×Dic271D411yescharacteristic
31C22×Dic271D411yescharacteristic
32C2×C4×D271—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271—21no—
37C4⋊Dic271—21no—
38C4⋊Dic271—42no—
39C4⋊Dic271D411yescharacteristic
40Dic271⋊C4—21no—
41Dic271⋊C4—21no—
42Dic271⋊C4—21no—
43(C2×D271)⋊C4—21no—
44(C2×D271)⋊C4—21no—
45(C2×D271)⋊C4—21no—
46(C2×D271)⋊C4—21no—
47C4×Dic271—21no—
48C2×Q8×C271D411yescharacteristic
49C22×C4×C271—21no—
50C22×C4×C271C2311yescharacteristic
51C2×C8×C271—21no—
52C4⋊C4×C271—21no—
53C4⋊C4×C271D411yescharacteristic
54C22⋊C4×C271—21no—
55C22×D271—21no—
56D1084—41no—
57C22⋊D271—41no—
58C22⋊D271—41no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—21no—
62C2×Dic271—21no—
63C2×Dic271—21no—
64C2×Dic271—41no—
65C2×Dic271—41no—
66C2×Dic271—41no—
67C2×Dic271—41no—
68C4×D271—81no—
69C271⋊C8—41no—
70C23×C271C2×D411yescharacteristic
71Q8×C271—41no—
72C2×C4×C271—22no—
73C2×C4×C271—21no—
74C2×C4×C271—21no—
75C2×C4×C271—41no—
76C2×C4×C271—41no—
77C2×C4×C271—41no—
78C2×C4×C271C2×D411yescharacteristic
79C2×C4×C271C2×D411yescharacteristic
80C8×C271—41no—
81C22×C271—21no—
82C22×C271—21no—
83C22×C271#12011yescharacteristic
84C22×C271#13511yescharacteristic
85C22×C271AGL(1,ℤ/8)11yescharacteristic
86C2×D271—41no—
87C2×D271—41no—
88C2×D271—41no—
89C4×C271—21no—
90C4×C271—21no—
91C4×C271—42no—
92C4×C271—41no—
93C4×C271—41no—
94Dic271—41no—
95Dic271—41no—
96Dic271—41no—
97Dic271—81no—
98C2×C271—21no—
99C2×C271—21no—
100C2×C271#44911yescharacteristic
101C2×C271#45611yescharacteristic
102C2×C271#45811yescharacteristic
103D271—81no—
104C271#160911yescharacteristic, complemented, Sylow
105#1609—2711nomaximal, Sylow
106#539—2711no—
107#483—2711no—
108#480—2711no—
109#398—2711no—
110#328D27111yescharacteristic, complemented
111#327—2711no—
112#324—2711no—
113#126—5421no—
114#125—5421no—
115#123—5421no—
116#123—5421no—
117C22⋊Q8—5421no—
118C22⋊Q8C2×D27111yescharacteristic
119#121—2711no—
120C4×D4—5421no—
121C2×C4⋊C4—2711no—
122C2×C4⋊C4—2711no—
123C2×C4⋊C4—5421no—
124#107—5421no—
125#106—5421no—
126#103—5421no—
127#102—5421no—
128C22⋊C8—2711no—
129C22⋊C8C2×D27111yescharacteristic
130#95—5421no—
131#95C2×D27111yescharacteristic
132C2×Q8D108411yescharacteristic
133C2×D4—2711no—
134C2×D4—5421no—
135C22×C4—21no—
136C22×C4—2711no—
137C22×C4—2711no—
138C22×C4—5421no—
139C22×C4—5421no—
140C22×C4C22×D27111yescharacteristic
141C2×C8—21no—
142C2×C8—5421no—
143C4⋊C4—21no—
144C4⋊C4—2711no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4—5421no—
148C4⋊C4—5421no—
149C4⋊C4—5421no—
150C4⋊C4—5421no—
151C4⋊C4—5421no—
152C4⋊C4—10842no—
153C4⋊C4D108411yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5421no—
156C22⋊C4—5421no—
157C22⋊C4—5421no—
158C22⋊C4—5421no—
159C42—5421no—
160C23—5421no—
161C23D4×D27111yescharacteristic
162Q8—41no—
163D4—10841no—
164D4—10841no—
165D4—10841no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—5421no—
173C2×C4—5421no—
174C2×C4—5421no—
175C2×C4—5421no—
176C2×C4—5421no—
177C2×C4—10841no—
178C2×C4—10841no—
179C2×C4—10841no—
180C2×C4—10841no—
181C2×C4—21681no—
182C2×C4D4×D27111yescharacteristic
183C2×C4C2×D108411yescharacteristic
184C8—41no—
185C8—10841no—
186C22—21no—
187C22—21no—
188C22—10841no—
189C22—10841no—
190C22—10841no—
191C22#2257613011yescharacteristic
192C22#2257618311yescharacteristic
193C22#2257618711yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—10841no—
200C4—10841no—
201C4—10841no—
202C4—21681no—
203C2—21no—
204C2—21no—
205C2—21681no—
206C2#3177404511yescharacteristic
207C2#3177408111yescharacteristic
208C2#3177408811yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#328×C271C2
socleC22×C271#120
prime radical#22576134C22
hypercenter#328D271
hypocenterC271#1609
LCSG ▷ C22×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31774225C2semidirect
4. #31773829C2semidirect
6. #31773622C2semidirect
7. #328×C271C2semidirect
104. C271#1609semidirect
110. #328D271semidirect

Maximal subgroups

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

subgroupindex
#317744962
#317742252
#317742112
#317738292
#317736302
#317736222
#328×C2712
#1609271