Finite Group Databasebeta

← #15765948

Subgroups — #15765948

Order 3328.

416 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 125 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#13115784C212yesmaximal
2#13115637C211yesmaximal, characteristic
3#13112719C211yesmaximal, characteristic
4#13112677C212yesmaximal
5C13×#2571C211yesmaximal, characteristic
6C2×#88123C2211yescharacteristic
7C13×#400—22no—
8C13×#389—22no—
9C13×#384C2211yescharacteristic
10C13×#382—22no—
11C4×C13×C4⋊C4C2212yes—
12C2×#88050—22no—
13C2×C4⋊#1055C2212yes—
14C2×C4×#1055C2211yescharacteristic
15#11718121—22no—
16#11718121—22no—
17C22×Dic26—21no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4D412yes—
21C2×C13×C4⋊C4D412yes—
22C2×C13×C4⋊C4D412yes—
23C2×C42×C13—22no—
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—24no—
33C13×#95—22no—
34#88050—44no—
35C4⋊#1055—22no—
36C4⋊#1055—22no—
37C4×#1055—22no—
38#10352—131nomaximal, Sylow
39C22×C4×C13—22no—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13C2×D412yes—
44C22×Dic13—41no—
45C2×Dic26—22no—
46C2×Dic26—42no—
47C2×Dic26—42no—
48C2×Dic26—41no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—22no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—82no—
57C42×C13—42no—
58C42×C13—42no—
59C42×C13C2×Q811yescharacteristic
60C42×C13#4112yes—
61C42×C13#4111yescharacteristic
62C4⋊Dic13—24no—
63C4⋊Dic13—42no—
64C2×#1055—22no—
65C2×#1055—41no—
66C2×#1055—41no—
67C2×#1055—42no—
68C2×#1055—42no—
69C2×#1055—42no—
70#2571D1311yescharacteristic
71#1987—132no—
72#1956—131no—
73#1296—131no—
74#1279—132no—
75C23×C13#12011yescharacteristic
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13C22⋊Q811yescharacteristic
87C2×C4×C13C22⋊Q812yes—
88C2×C4×C13#12411yescharacteristic
89C2×C4×C13#12412yes—
90C2×C4×C13#13512yes—
91C2×C4×C13#13512yes—
92C2×C4×C13#13712yes—
93C2×C4×C13#13712yes—
94C2×Dic13—42no—
95C2×Dic13—81no—
96C2×Dic13—81no—
97Dic26—44no—
98Dic26—82no—
99#1055—42no—
100#1055—82no—
101C2×C4⋊Q8—131no—
102C2×C4⋊C8—132no—
103C2×#103—262no—
104C2×C4×C8—131no—
105#400—22no—
106#389—22no—
107#384C2×D1311yescharacteristic
108#382—22no—
109C4×C4⋊C4C2×D1312yes—
110#340—262no—
111#340—262no—
112C22×C13#39311yescharacteristic
113C22×C13#45212yes—
114C22×C13#45212yes—
115C22×C13#45311yescharacteristic
116C22×C13#45411yescharacteristic
117C4×C13—21no—
118C4×C13—21no—
119C4×C13—82no—
120C4×C13—82no—
121C4×C13—82no—
122C4×C13#47912yes—
123C4×C13#47912yes—
124C4×C13#48812yes—
125C4×C13#49112yes—
126Dic13—82no—
127C22×Q8—261no—
128C22×C8—261no—
129C22×C8—262no—
130C4⋊Q8—132no—
131C4⋊Q8—262no—
132C4⋊Q8—261no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—262no—
136C2×C4⋊C4C22⋊D1312yes—
137C2×C4⋊C4C22⋊D1312yes—
138C2×C4⋊C4C22⋊D1312yes—
139C2×C42—22no—
140C2×C42C22×D1311yescharacteristic
141C4⋊C8—262no—
142C4⋊C8—262no—
143#103—524no—
144C4×C8—262no—
145#95—22no—
146#95—24no—
147#95—22no—
148C2×C13#163011yescharacteristic
149C2×C13#163411yescharacteristic
150C2×C13#163812yes—
151C2×C13#202612yes—
152C2×C13#202711yescharacteristic
153C2×Q8—262no—
154C2×Q8—522no—
155C2×Q8—522no—
156C2×Q8—521no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—521no—
161C22×C4C2×C22⋊D1311yescharacteristic
162C22×C4C2×C22⋊D1312yes—
163C2×C8—262no—
164C2×C8—521no—
165C2×C8—521no—
166C2×C8—522no—
167C2×C8—522no—
168C2×C8—522no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—82no—
177C4⋊C4—264no—
178C4⋊C4—522no—
179C42—42no—
180C42—42no—
181C42Q8×D1311yescharacteristic
182C42#613112yes—
183C42#613111yescharacteristic
184C13#1035211yescharacteristic, complemented, Sylow
185C23#8820711yescharacteristic
186Q8—524no—
187Q8—1042no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—522no—
199C2×C4—1041no—
200C2×C4—1041no—
201C2×C4#8820011yescharacteristic
202C2×C4#8820012yes—
203C2×C4#8820111yescharacteristic
204C2×C4#8820112yes—
205C2×C4#8820412yes—
206C2×C4#8820412yes—
207C2×C4#8820512yes—
208C2×C4#8820512yes—
209C8—522no—
210C8—1042no—
211C22#1171889211yescharacteristic
212C22#1171890012yes—
213C22#1171890012yes—
214C22#1171890211yescharacteristic
215C22#1171890611yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—1042no—
222C4#1171872412yes—
223C4#1171872412yes—
224C4#1171872912yes—
225C4#1171873012yes—
226C2#1311395711yescharacteristic
227C2#1311398111yescharacteristic
228C2#1311400812yes—
229C2#1311598412yes—
230C2#1311598911yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2571C2
socle, prime radicalC23×C13#120
hypercenter#2571D13
hypocenterC13#10352
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
184. C13#10352semidirect

Maximal subgroups

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

subgroupindex
#131157842
#131156372
#131127192
#131126772
C13×#25712
#1035213