Finite Group Databasebeta

← #15765999

Subgroups — #15765999

Order 3328.

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

normal subgroups only

This group has 392 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#13115808C212yesmaximal
2#13115655C211yesmaximal, characteristic
3#13112717C211yesmaximal, characteristic
4#13112717C212yesmaximal
5C13×#2845C211yesmaximal, characteristic
6C2×#88123C2211yescharacteristic
7C13×#398—22no—
8C13×#398—22no—
9C13×#398—22no—
10C13×#382C2211yescharacteristic
11C13×#382C2212yes—
12C2×#88050—22no—
13C2×#88043C2211yescharacteristic
14C2×#88043C2212yes—
15#11718121—22no—
16#11718121—22no—
17C22×Dic26—21no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4D412yes—
22C2×C13×C4⋊C4D412yes—
23C2×C13×C4⋊C4D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—22no—
26C22×#1055—21no—
27C22×#1055—22no—
28#88123—22no—
29#88123—21no—
30#88123Q812yes—
31C13×#95—22no—
32C13×#95—22no—
33C13×#95—22no—
34C13×#95—22no—
35#88050—44no—
36#88043—22no—
37#88043—22no—
38#88043—22no—
39#10361—131nomaximal, Sylow
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13C2×D412yes—
44C22×C4×C13C2×D411yescharacteristic
45C22×Dic13—41no—
46C2×Dic26—22no—
47C2×Dic26—42no—
48C2×Dic26—42no—
49C2×Dic26—41no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—82no—
54C13×C4⋊C4—82no—
55C13×C4⋊C4—82no—
56C42×C13C2×Q811yescharacteristic
57C42×C13#4112yes—
58C42×C13#4111yescharacteristic
59C4⋊Dic13—24no—
60C4⋊Dic13—42no—
61C2×#1055—24no—
62C2×#1055—22no—
63C2×#1055—41no—
64C2×#1055—42no—
65C2×#1055—42no—
66C2×#1055—41no—
67#2845D1311yescharacteristic
68#1993—132no—
69#1960—131no—
70#1295—131no—
71#1295—132no—
72C23×C13#12011yescharacteristic
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—42no—
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×C13C22⋊Q812yes—
87C2×C4×C13C22⋊Q811yescharacteristic
88C2×C4×C13#12412yes—
89C2×C4×C13#12411yescharacteristic
90C2×Dic13—42no—
91C2×Dic13—81no—
92C2×Dic13—81no—
93Dic26—44no—
94Dic26—82no—
95#1055—42no—
96#1055—44no—
97C2×C4⋊Q8—131no—
98C2×#103—262no—
99C2×#97—131no—
100C2×#97—132no—
101#398—22no—
102#398—22no—
103#398—22no—
104#382C2×D1311yescharacteristic
105#382C2×D1312yes—
106#340—262no—
107#340—262no—
108C22×C13#39311yescharacteristic
109C22×C13#45311yescharacteristic
110C22×C13#45411yescharacteristic
111C22×C13#45512yes—
112C22×C13#45612yes—
113C4×C13—21no—
114C4×C13—21no—
115C4×C13—22no—
116C4×C13—22no—
117C4×C13—82no—
118C4×C13—82no—
119C4×C13—82no—
120Dic13—82no—
121C22×Q8—261no—
122C22×C8—262no—
123C22×C8—261no—
124C4⋊Q8—132no—
125C4⋊Q8—262no—
126C4⋊Q8—261no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—262no—
131C2×C4⋊C4C22⋊D1312yes—
132C2×C4⋊C4C22⋊D1312yes—
133C2×C4⋊C4C22⋊D1312yes—
134C2×C42C22×D1311yescharacteristic
135#103—524no—
136#97—262no—
137#97—262no—
138#97—262no—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—22no—
143C2×C13#166112yes—
144C2×C13#166211yescharacteristic
145C2×C13#166311yescharacteristic
146C2×C13#202711yescharacteristic
147C2×C13#202812yes—
148C2×Q8—262no—
149C2×Q8—522no—
150C2×Q8—522no—
151C2×Q8—521no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—521no—
156C22×C4C2×C22⋊D1312yes—
157C22×C4C2×C22⋊D1311yescharacteristic
158C2×C8—262no—
159C2×C8—264no—
160C2×C8—522no—
161C2×C8—521no—
162C2×C8—522no—
163C2×C8—521no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—82no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—264no—
171C4⋊C4—522no—
172C42Q8×D1311yescharacteristic
173C42#613112yes—
174C42#613111yescharacteristic
175C13#1036111yescharacteristic, complemented, Sylow
176C23#8820711yescharacteristic
177Q8—524no—
178Q8—1042no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—522no—
193C2×C4—1041no—
194C2×C4—1041no—
195C2×C4#8820012yes—
196C2×C4#8820011yescharacteristic
197C2×C4#8820112yes—
198C2×C4#8820111yescharacteristic
199C8—522no—
200C8—524no—
201C22#1171889211yescharacteristic
202C22#1171890211yescharacteristic
203C22#1171890312yes—
204C22#1171890611yescharacteristic
205C22#1171890712yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—1042no—
214C2#1311415312yes—
215C2#1311415911yescharacteristic
216C2#1311416411yescharacteristic
217C2#1311598911yescharacteristic
218C2#1311599412yes—
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2845C2
socle, prime radicalC23×C13#120
hypercenter#2845D13
hypocenterC13#10361
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
175. C13#10361semidirect

Maximal subgroups

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

subgroupindex
#131158082
#131156552
#131127172
C13×#28452
#1036113