Finite Group Databasebeta

← #16786781

Subgroups — #16786781

Order 3328.

382 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 90 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#13131064C212yesmaximal
2#13129775C212yesmaximal, complemented
3#13129774C212yesmaximal, complemented
4D13×#424C211yesmaximal, characteristic
5C2×M16×D13C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7D13×#117C411yescharacteristic
8C2×#88098—22no—
9C13×#424C411yescharacteristic
10#11718780C2211yescharacteristic
11#11718763C411yescharacteristic
12#11718660C2211yescharacteristic
13#11718500—22no—
14D13×C4⋊C8—22no—
15C22⋊#6092C2214yes—
16#11718259—22no—
17C22×C4×D13C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C22×C8×C13C2×C411yescharacteristic
20C13×#117C2×C411yescharacteristic
21#88180C2×C411yescharacteristic
22C2×#6099C2×C411yescharacteristic
23C22×#1055C2311yescharacteristic
24M16×D13—42no—
25C2×#6094—21no—
26C2×C8×D13—21no—
27C2×C8×D13—42no—
28C2×C8×D13D412yes—
29C2×C8×D13D412yes—
30#88146C812yes—
31C4⋊C4×D13C812yes—
32C22⋊C4×D13—21no—
33#88131—21no—
34#88126—21no—
35C42×D13—21no—
36C2×#6092—24no—
37#88098—44no—
38C13×C4⋊C8—22no—
39#88054—22no—
40#88054—22no—
41C4⋊#1055—22no—
42#11443—131nomaximal, Sylow
43C23×D13M1611yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C22×Dic13M1611yescharacteristic
46C2×C4×D13—22no—
47C2×C4×D13—22no—
48C2×C4×D13—22no—
49C2×C4×D13C22⋊C411yescharacteristic
50C2×C4×D13C22⋊C411yescharacteristic
51C2×C4×D13C2×C811yescharacteristic
52C2×C4×D13C2×C811yescharacteristic
53C13×M16—41no—
54C2×C8×C13—21no—
55C2×C8×C13—41no—
56C2×C8×C13C22⋊C412yes—
57C13×C4⋊C4C2×C812yes—
58C13×C22⋊C4—21no—
59C42×C13—21no—
60C22⋊Dic13—21no—
61#6103—22no—
62C4⋊Dic13C2×C812yes—
63#6101—22no—
64C4×Dic13—21no—
65C4×Dic13—22no—
66#6099—41no—
67C2×#1055—21no—
68C2×#1055—41no—
69C2×#1055C2×D412yes—
70#6094—42no—
71C8×D13—24no—
72C8×D13—42no—
73C8×D13—42no—
74#6092—44no—
75C2×#424—131no—
76#2112—132no—
77#1323—132no—
78#1323—132no—
79C23×C13C2×M1611yescharacteristic
80C22×D13—22no—
81C22×D13—42no—
82C22×D13C22⋊C811yescharacteristic
83C22×D13C22⋊C811yescharacteristic
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C2×C4×C13C22×C811yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13C22⋊C811yescharacteristic
92C2×Dic13C22⋊C811yescharacteristic
93C4×D13—22no—
94C4×D13—21no—
95C4×D13—21no—
96C4×D13—22no—
97C4×D13—44no—
98C4×D13#9912yes—
99C4×D13#10112yes—
100C8×C13—22no—
101C8×C13—41no—
102#1055—22no—
103#1055—41no—
104C22×M16—131no—
105C23×C8—131no—
106C2×#117—131no—
107C2×M32—262no—
108#424—131no—
109#424—131no—
110#424—131no—
111#424—262no—
112#424#26111yescharacteristic
113C2×C4⋊C8—262no—
114C22⋊C16—134no—
115C22⋊C16—262no—
116C22×C13—22no—
117C22×C13—21no—
118C22×C13C2×C22⋊C811yescharacteristic
119C2×D13—22no—
120C2×D13—22no—
121C2×D13—21no—
122C2×D13—44no—
123C2×D13#32412yes—
124C4×C13—21no—
125C4×C13—42no—
126C4×C13C2×#9911yescharacteristic
127C4×C13C2×#10111yescharacteristic
128Dic13—21no—
129Dic13—42no—
130Dic13#32412yes—
131C23×C4—131no—
132C2×M16—131no—
133C2×M16—261no—
134C2×M16—522no—
135C2×M16C2×#26111yescharacteristic
136C22×C8—131no—
137C22×C8—132no—
138C22×C8—132no—
139C22×C8—261no—
140C22×C8—522no—
141C22×C8C2×#26111yescharacteristic
142#117—131no—
143#117—132no—
144#117—261no—
145#117—261no—
146#117C2×#26111yescharacteristic
147C2×C4⋊C4—132no—
148C2×C22⋊C4—261no—
149C2×C42—261no—
150M32—524no—
151C2×C16—264no—
152C4⋊C8—22no—
153C4⋊C8—262no—
154C4⋊C8—262no—
155C4⋊C8—262no—
156C2×C13—41no—
157C2×C13C2×#32411yescharacteristic
158C2×C13#211712yes—
159D13—22no—
160D13—41no—
161C24—131no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4—262no—
170C22×C4C22×#26111yescharacteristic
171M16—41no—
172M16—522no—
173M16—521no—
174C2×C8—21no—
175C2×C8—41no—
176C2×C8—132no—
177C2×C8—264no—
178C2×C8—261no—
179C2×C8—522no—
180C2×C8—522no—
181C2×C8—521no—
182C2×C8C22⋊#26112yes—
183C4⋊C4—132no—
184C4⋊C4—262no—
185C4⋊C4D13⋊C812yes—
186C22⋊C4—21no—
187C22⋊C4—262no—
188C22⋊C4—261no—
189C42—21no—
190C42—262no—
191C42—261no—
192C16—524no—
193C13#1144311yescharacteristic, complemented, Sylow
194C23—131no—
195C23—131no—
196C23—262no—
197C23—522no—
198C23D13⋊M1611yescharacteristic
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—131no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—131no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—261no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—524no—
213C2×C4C2×D13⋊C811yescharacteristic
214C2×C4C2×C22⋊#26111yescharacteristic
215C8—22no—
216C8—41no—
217C8—262no—
218C8—521no—
219C22—22no—
220C22—21no—
221C22—132no—
222C22—262no—
223C22—262no—
224C22—261no—
225C22—524no—
226C22D13⋊(C22⋊C8)11yescharacteristic
227C4—21no—
228C4—42no—
229C4—132no—
230C4—261no—
231C4—522no—
232C4D13⋊#9911yescharacteristic
233C4D13⋊#10111yescharacteristic
234C2—41no—
235C2—262no—
236C2—521no—
237C2D13⋊#32411yescharacteristic
238C2#1313107912yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#424C4
socleC22×C13C2×C22⋊C8
prime radicalC23×D13M16
cosocleC22×#1055C23
hypercenter#424#261
hypocenterC13#11443
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #13129775C2semidirect
3. #13129774C2semidirect
193. C13#11443semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131297752
#131297742
D13×#4242
#1144313