Finite Group Databasebeta

← #46835373

Subgroups — #46835373

Order 34688.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#31774526C211yesmaximal, characteristic
2#31774228C211yesmaximal, characteristic
3#31774225C211yesmaximal, characteristic
4#31773829C211yesmaximal, characteristic
5#31773633C211yesmaximal, characteristic
6#31773622C211yesmaximal, characteristic
7#328×C271C211yesmaximal, characteristic
8#22576159—21no—
9#22576158—21no—
10#22576150—21no—
11#22576150—21no—
12#22576139C2211yescharacteristic
13#22576137—21no—
14#22576116—21no—
15C2×C4⋊Dic271—21no—
16C2×C4⋊Dic271C2211yescharacteristic
17C2×Dic271⋊C4C2211yescharacteristic
18#22576092—21no—
19#22576091—21no—
20#22576085—21no—
21#22576084—21no—
22C22⋊(C271⋊C8)C2211yescharacteristic
23C271⋊#95—21no—
24C22⋊Q8×C271C2211yescharacteristic
25C22⋊C8×C271C2211yescharacteristic
26#95×C271C2211yescharacteristic
27C2×Dic542—21no—
28C2×Dic542D411yescharacteristic
29C22×Dic271—21no—
30C22×Dic271D411yescharacteristic
31C22×Dic271D411yescharacteristic
32C2×C271⋊C8—21no—
33C4⋊Dic271—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271—42no—
37C4⋊Dic271D411yescharacteristic
38Dic271⋊C4—21no—
39Dic271⋊C4—21no—
40Dic271⋊C4—21no—
41Dic271⋊C4—21no—
42Dic271⋊C4—21no—
43Dic271⋊C4—21no—
44Dic271⋊C4—21no—
45C22⋊Dic271—21no—
46C4×Dic271—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—
55Dic542—41no—
56Dic542—81no—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—21no—
60C2×Dic271—21no—
61C2×Dic271—21no—
62C2×Dic271—41no—
63C2×Dic271—41no—
64C2×Dic271—41no—
65C2×Dic271—41no—
66C2×Dic271SD1612yes—
67C271⋊C8—41no—
68C23×C271C2×D411yescharacteristic
69Q8×C271—41no—
70C2×C4×C271—22no—
71C2×C4×C271—21no—
72C2×C4×C271—21no—
73C2×C4×C271—41no—
74C2×C4×C271—41no—
75C2×C4×C271—41no—
76C2×C4×C271C2×D411yescharacteristic
77C2×C4×C271C2×D411yescharacteristic
78C8×C271—41no—
79C22×C271—21no—
80C22×C271—21no—
81C22×C271#12011yescharacteristic
82C22×C271C2×SD1611yescharacteristic
83C22×C271#13711yescharacteristic
84C4×C271—21no—
85C4×C271—21no—
86C4×C271—42no—
87C4×C271—41no—
88C4×C271—41no—
89Dic271—22no—
90Dic271—41no—
91Dic271—41no—
92Dic271—41no—
93Dic271—81no—
94C2×C271—21no—
95C2×C271—21no—
96C2×C271#44811yescharacteristic
97C2×C271#45611yescharacteristic
98C2×C271#45811yescharacteristic
99C271#161111yescharacteristic, complemented, Sylow
100#1611—2711nomaximal, Sylow
101#544—2711no—
102#483—2711no—
103#483—2711no—
104#398—2711no—
105#328—2711no—
106#328D27111yescharacteristic
107#324—2711no—
108C4⋊Q8—5421no—
109C4⋊Q8—5421no—
110#125—5421no—
111#125—5421no—
112C22⋊Q8—2711no—
113C22⋊Q8—5421no—
114C22⋊Q8C2×D27111yescharacteristic
115#117—5421no—
116C2×C4⋊C4—2711no—
117C2×C4⋊C4—2711no—
118C2×C4⋊C4—5421no—
119#106—5421no—
120#106—5421no—
121#103—5421no—
122#103—5421no—
123C22⋊C8—2711no—
124C22⋊C8C2×D27111yescharacteristic
125#95—5421no—
126#95C2×D27111yescharacteristic
127C2×Q8—2711no—
128C2×Q8—5421no—
129C2×Q8D108411yescharacteristic
130C22×C4—21no—
131C22×C4—2711no—
132C22×C4—2711no—
133C22×C4—5421no—
134C22×C4C22×D27111yescharacteristic
135C2×C8—21no—
136C2×C8—5421no—
137C4⋊C4—21no—
138C4⋊C4—2711no—
139C4⋊C4—5421no—
140C4⋊C4—5421no—
141C4⋊C4—5421no—
142C4⋊C4—5421no—
143C4⋊C4—5421no—
144C4⋊C4—5421no—
145C4⋊C4—5421no—
146C4⋊C4—5421no—
147C4⋊C4—5421no—
148C4⋊C4—5421no—
149C4⋊C4—10842no—
150C4⋊C4D108411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5421no—
153C42—5421no—
154C42—5421no—
155C23D4×D27111yescharacteristic
156Q8—41no—
157Q8—10841no—
158Q8—21681no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2712no—
166C2×C4—5421no—
167C2×C4—5421no—
168C2×C4—5421no—
169C2×C4—5421no—
170C2×C4—5421no—
171C2×C4—10841no—
172C2×C4—10841no—
173C2×C4—10841no—
174C2×C4—10841no—
175C2×C4D4×D27111yescharacteristic
176C2×C4C2×D108411yescharacteristic
177C8—41no—
178C8—10841no—
179C22—21no—
180C22—21no—
181C22#2257613011yescharacteristic
182C22SD16×D27111yescharacteristic
183C22#2257619211yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—5422no—
190C4—10841no—
191C4—10841no—
192C4—10841no—
193C4—21681no—
194C2—21no—
195C2—21no—
196C2#3177403711yescharacteristic
197C2#3177408111yescharacteristic
198C2#3177408811yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC22×C4×C271C23
FrattiniC22×C4C22×D271
Fitting#328×C271C2
socleC22×C271#120
prime radicalC23×C271C2×D4
hypercenter#328D271
hypocenterC271#1611
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
99. C271#1611semidirect

Maximal subgroups

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

subgroupindex
#317745262
#317742282
#317742252
#317738292
#317736332
#317736222
#328×C2712
#1611271