Finite Group Databasebeta

← #15766410

Subgroups — #15766410

Order 3328.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115806C212yesmaximal
2#13114969C211yesmaximal, characteristic
3C2×#11718135C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#2822C211yesmaximal, characteristic
6C2×C13×#125C2212yes—
7C13×#400—22no—
8C13×#398—22no—
9C13×#398—22no—
10C13×#382C2211yescharacteristic
11#11718596C2211yescharacteristic
12C2×#88043C2212yes—
13C2×#88043C2211yescharacteristic
14#11718135—24no—
15#11718121—22no—
16#11718121—22no—
17#11718121—22no—
18C13×#125—22no—
19C13×#125—22no—
20C13×#125—22no—
21C13×#125—22no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4D412yes—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C4⋊C4D412yes—
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—22no—
30C2×C4⋊Dic13—21no—
31C22×#1055—22no—
32C22×#1055—21no—
33C13×#95—24no—
34C13×#95—22no—
35C13×#95—22no—
36#88043—21no—
37#88043—22no—
38#88043—22no—
39#88043D412yes—
40#10428—131nomaximal, Sylow
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13C2×D412yes—
45C22×C4×C13C2×D411yescharacteristic
46C22×Dic13—41no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—82no—
57C42×C13C2×D411yescharacteristic
58C42×C13#4111yescharacteristic
59C42×C13#4112yes—
60C4⋊Dic13—42no—
61C4⋊Dic13—44no—
62C2×#1055—24no—
63C2×#1055—22no—
64C2×#1055—42no—
65C2×#1055—41no—
66C2×#1055—41no—
67C2×#1055—42no—
68#2822D1311yescharacteristic
69#1992—132no—
70#1836—131no—
71C2×#330—132no—
72#1295—131no—
73C23×C13#12011yescharacteristic
74C2×C4×C13—22no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13#12111yescharacteristic
88C2×C4×C13#12112yes—
89C2×C4×C13#12312yes—
90C2×C4×C13#12411yescharacteristic
91C2×Dic13—81no—
92C2×Dic13—82no—
93#1055—44no—
94#1055—42no—
95C2×#125C2×D1312yes—
96C2×#97—131no—
97C2×#97—132no—
98#400—22no—
99#398—22no—
100#398—22no—
101#384—131no—
102#382C2×D1311yescharacteristic
103#340—262no—
104#340—262no—
105#340—262no—
106#330—264no—
107C22×C13#39411yescharacteristic
108C22×C13#45411yescharacteristic
109C22×C13#45412yes—
110C22×C13#45511yescharacteristic
111C22×C13#45612yes—
112C4×C13—22no—
113C4×C13—22no—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—82no—
117C4×C13—82no—
118C4×C13—82no—
119Dic13—161no—
120C22×C8—262no—
121C22×C8—261no—
122#125—22no—
123#125—22no—
124#125—22no—
125#125—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—261no—
131C2×C4⋊C4C22⋊D1312yes—
132C2×C4⋊C4C22⋊D1312yes—
133C2×C4⋊C4C22⋊D1312yes—
134C2×C42C22×D1311yescharacteristic
135#97—132no—
136#97—262no—
137#97—261no—
138#97—262no—
139#95—24no—
140#95—22no—
141#95—22no—
142C2×C13#165811yescharacteristic
143C2×C13#166311yescharacteristic
144C2×C13#166412yes—
145C2×C13#203812yes—
146C2×C13#204011yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—521no—
151C22×C4C2×C22⋊D1312yes—
152C22×C4C2×C22⋊D1311yescharacteristic
153C2×C8—264no—
154C2×C8—262no—
155C2×C8—521no—
156C2×C8—522no—
157C2×C8—521no—
158C2×C8—522no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—524no—
170C4⋊C4—522no—
171C42D4×D1311yescharacteristic
172C42#612911yescharacteristic
173C42#612912yes—
174C13#1042811yescharacteristic, complemented, Sylow
175C23#8820711yescharacteristic
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—1041no—
190C2×C4—1042no—
191C2×C4#8818912yes—
192C2×C4#8819011yescharacteristic
193C2×C4#8819211yescharacteristic
194C2×C4#8819312yes—
195C8—524no—
196C8—522no—
197C22#1171888311yescharacteristic
198C22#1171890311yescharacteristic
199C22#1171890611yescharacteristic
200C22#1171890612yes—
201C22#1171890712yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—2081no—
210C2#1311413811yescharacteristic
211C2#1311416411yescharacteristic
212C2#1311417012yes—
213C2#1311605012yes—
214C2#1311606211yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2822C2
socle, prime radicalC23×C13#120
hypercenter#2822D13
hypocenterC13#10428
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
174. C13#10428semidirect

Maximal subgroups

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

subgroupindex
#131158062
#131149692
C2×#117181352
#131127172
C13×#28222
#1042813