Finite Group Databasebeta

← #15765950

Subgroups — #15765950

Order 3328.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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#13120078C211yesmaximal, characteristic
2#13115783C212yesmaximal
3#13115637C211yesmaximal, characteristic
4#13112675C212yesmaximal
5C13×#1296C211yesmaximal, characteristic
6C2×#88123C2211yescharacteristic
7C2×C13×C4⋊C8C2212yes—
8C13×#384C2211yescharacteristic
9#11718647—22no—
10#11718646—22no—
11#11718638—22no—
12C2×#88050—22no—
13C4×C4⋊Dic13C2212yes—
14C2×C4×#1055C2211yescharacteristic
15#11718143—22no—
16#11718143—22no—
17C22×Dic26—21no—
18C22×C8×C13—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4D412yes—
21C2×C42×C13C2311yescharacteristic
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13—22no—
24C2×C4⋊Dic13D412yes—
25C2×C4⋊Dic13D412yes—
26C2×C4×Dic13—22no—
27C22×#1055—21no—
28#88123—22no—
29#88123—21no—
30#88123Q812yes—
31C13×C4⋊C8—22no—
32C13×C4⋊C8—22no—
33#88071—22no—
34#88071—24no—
35#88071—22no—
36#88050—44no—
37C4×#1055—22no—
38#10352—131nomaximal, Sylow
39C22×C4×C13—22no—
40C22×C4×C13C2×D411yescharacteristic
41C22×C4×C13C2×D412yes—
42C22×Dic13—22no—
43C22×Dic13—22no—
44C22×Dic13—41no—
45C2×Dic26—22no—
46C2×Dic26—42no—
47C2×Dic26—42no—
48C2×Dic26—41no—
49C2×C8×C13—42no—
50C2×C8×C13—42no—
51C2×C8×C13—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C42×C13C2×Q811yescharacteristic
56C42×C13#4112yes—
57C42×C13#4111yescharacteristic
58C4⋊Dic13—24no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13—42no—
64C4⋊Dic13—82no—
65C4×Dic13—42no—
66C4×Dic13—42no—
67C2×#1055—22no—
68C2×#1055—41no—
69C2×#1055—41no—
70#2571—131no—
71#1987—132no—
72#1956—131no—
73#1296D1311yescharacteristic
74#1279—132no—
75C23×C13#12011yescharacteristic
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—44no—
79C2×C4×C13—42no—
80C2×C4×C13C22⋊Q811yescharacteristic
81C2×C4×C13C22⋊Q812yes—
82C2×C4×C13#12411yescharacteristic
83C2×C4×C13#12412yes—
84C2×C4×C13#13512yes—
85C2×C4×C13#13512yes—
86C2×C4×C13#13712yes—
87C2×C4×C13#13712yes—
88C2×Dic13—42no—
89C2×Dic13—42no—
90C2×Dic13—42no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—81no—
96C2×Dic13—81no—
97Dic26—44no—
98Dic26—82no—
99C8×C13—82no—
100#1055—42no—
101C2×C4⋊Q8—131no—
102C2×C4⋊C8C2×D1312yes—
103C2×#103—262no—
104C2×C4×C8—131no—
105#400—262no—
106#389—262no—
107#384C2×D1311yescharacteristic
108#382—262no—
109C4×C4⋊C4—132no—
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#47912yes—
121C4×C13#47912yes—
122C4×C13#48812yes—
123C4×C13#49112yes—
124Dic13—82no—
125Dic13—82no—
126Dic13—82no—
127C22×Q8—261no—
128C22×C8—22no—
129C22×C8—261no—
130C4⋊Q8—132no—
131C4⋊Q8—262no—
132C4⋊Q8—261no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—262no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4D5212yes—
139C2×C42—262no—
140C2×C42C22×D1311yescharacteristic
141C4⋊C8—22no—
142C4⋊C8—22no—
143#103—524no—
144C4×C8—262no—
145#95—262no—
146#95—264no—
147#95—262no—
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—262no—
159C22×C4—262no—
160C22×C4—521no—
161C22×C4C2×D5211yescharacteristic
162C22×C4D4×D1312yes—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—262no—
167C2×C8—521no—
168C2×C8—521no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—264no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—522no—
178C4⋊C4—1042no—
179C42—522no—
180C42—522no—
181C42#612712yes—
182C42#612911yescharacteristic
183C42Q8×D1311yescharacteristic
184C13#1035211yescharacteristic, complemented, Sylow
185C23#8813611yescharacteristic
186Q8—524no—
187Q8—1042no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—44no—
192C2×C4—522no—
193C2×C4—522no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—1041no—
200C2×C4—1041no—
201C2×C4#8812911yescharacteristic
202C2×C4#8813912yes—
203C2×C4#8815012yes—
204C2×C4#8815111yescharacteristic
205C2×C4#8816612yes—
206C2×C4#8816912yes—
207C2×C4#8817012yes—
208C2×C4#8817212yes—
209C8—82no—
210C8—522no—
211C22#1171833411yescharacteristic
212C22#1171840811yescharacteristic
213C22#1171841411yescharacteristic
214C22#1171844412yes—
215C22#1171847112yes—
216C4—21no—
217C4—21no—
218C4—82no—
219C4—1042no—
220C4—1042no—
221C4—1042no—
222C4#1171842912yes—
223C4#1171845812yes—
224C4#1171851812yes—
225C4#1171853812yes—
226C2#1311395811yescharacteristic
227C2#1311398211yescharacteristic
228C2#1311400912yes—
229C2#1311598612yes—
230C2#1311599311yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13#120
hypercenter#1296D13
hypocenterC13#10352
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

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
#131200782
#131157832
#131156372
#131126752
C13×#12962
#1035213