Finite Group Databasebeta

← #16786822

Subgroups — #16786822

Order 3328.

364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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
1D13⋊#349C212yesmaximal
2#13129783C212yesmaximal, complemented
3#13129782C212yesmaximal, complemented
4#13123398C211yesmaximal, characteristic
5C2×M16×D13C411yescharacteristic
6C2×M16×D13C2211yescharacteristic
7C2×#88126C411yescharacteristic
8D13⋊M32—22no—
9C13×#423C411yescharacteristic
10#11718779C411yescharacteristic
11#11718779C2211yescharacteristic
12#11718585C2211yescharacteristic
13#11718500—22no—
14#11718500—22no—
15#11718284C2214yes—
16#11718263—22no—
17C22×C4×D13C2×C411yescharacteristic
18C2×C13×M16C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C2×C42×C13C2×C411yescharacteristic
21C2×#6103—21no—
22C2×#6101—21no—
23C2×C4×Dic13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C2×#6099C2311yescharacteristic
26M16×D13—42no—
27M16×D13—42no—
28C2×#6094—21no—
29C2×#6094D412yes—
30C2×C8×D13—21no—
31C2×C8×D13D412yes—
32#88126—21no—
33#88126—21no—
34#88126C812yes—
35#88126C812yes—
36#88106—24no—
37#88098—42no—
38D13⋊C16—42no—
39C13×C4⋊C8—22no—
40#88054—22no—
41#88054—22no—
42C4⋊#1055—22no—
43#11456—131nomaximal, Sylow
44C23×D13M1611yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C22×C411yescharacteristic
47C22×Dic13—21no—
48C22×Dic13M1611yescharacteristic
49C2×C4×D13—22no—
50C2×C4×D13—22no—
51C2×C4×D13C22⋊C411yescharacteristic
52C2×C4×D13C22⋊C411yescharacteristic
53C2×C4×D13C2×C811yescharacteristic
54C2×C4×D13C2×C811yescharacteristic
55C13×M16—41no—
56C13×M16—41no—
57C2×C8×C13—21no—
58C2×C8×C13C22⋊C412yes—
59C42×C13—21no—
60C42×C13C2×C812yes—
61#6103—22no—
62#6103—22no—
63#6101—22no—
64#6101—22no—
65C4×Dic13—21no—
66C4×Dic13C2×C812yes—
67#6099—41no—
68#6099—41no—
69C2×#1055—21no—
70C2×#1055C2×D412yes—
71#6094—42no—
72#6094—42no—
73C8×D13—22no—
74C8×D13—22no—
75C8×D13—42no—
76#6092—44no—
77#2905—131no—
78C2×#349—132no—
79#1327—132no—
80#1327—132no—
81C23×C13C2×M1611yescharacteristic
82C22×D13—22no—
83C22×D13—81no—
84C22×D13C22⋊C811yescharacteristic
85C22×D13C22⋊C811yescharacteristic
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—81no—
90C2×C4×C13C2×C22⋊C411yescharacteristic
91C2×C4×C13C22×C811yescharacteristic
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—81no—
95C2×Dic13C22⋊C811yescharacteristic
96C2×Dic13C22⋊C811yescharacteristic
97C4×D13—22no—
98C4×D13—21no—
99C4×D13—21no—
100C4×D13—22no—
101C4×D13#9912yes—
102C4×D13#10112yes—
103C8×C13—22no—
104C8×C13—41no—
105#1055—22no—
106#1055—41no—
107C22×M16—131no—
108C22×M16—131no—
109C2×#117—131no—
110C2×M32—262no—
111#424—262no—
112#424—262no—
113#423—131no—
114#423—131no—
115#423—131no—
116#423#26111yescharacteristic
117#349—134no—
118#349—262no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13C2×C22⋊C811yescharacteristic
122C2×D13—21no—
123C2×D13—41no—
124C2×D13—41no—
125C2×D13—82no—
126C2×D13#32412yes—
127C4×C13—21no—
128C4×C13—42no—
129C4×C13C2×#9911yescharacteristic
130C4×C13C2×#10111yescharacteristic
131Dic13—21no—
132Dic13—42no—
133Dic13#32412yes—
134C23×C4—131no—
135C2×M16—131no—
136C2×M16—132no—
137C2×M16—131no—
138C2×M16—261no—
139C2×M16—522no—
140C2×M16—522no—
141C2×M16C2×#26111yescharacteristic
142C2×M16C2×#26111yescharacteristic
143C22×C8—132no—
144C22×C8—261no—
145#117—132no—
146#117—132no—
147#117—261no—
148#117—261no—
149C2×C4⋊C4—261no—
150C2×C22⋊C4—261no—
151C2×C42—131no—
152C2×C42C2×#26111yescharacteristic
153M32—264no—
154M32—522no—
155C2×C16—522no—
156C4⋊C8—22no—
157C4⋊C8—262no—
158C4⋊C8—262no—
159C4⋊C8—262no—
160C2×C13—21no—
161C2×C13—41no—
162C2×C13C2×#32411yescharacteristic
163D13—22no—
164D13—41no—
165C24—131no—
166C22×C4—21no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—131no—
171C22×C4—131no—
172C22×C4—262no—
173C22×C4—262no—
174C22×C4—261no—
175C22×C4C22×#26111yescharacteristic
176M16—41no—
177M16—41no—
178M16—522no—
179M16—522no—
180M16—521no—
181M16—521no—
182C2×C8—21no—
183C2×C8—132no—
184C2×C8—262no—
185C2×C8—262no—
186C2×C8—261no—
187C2×C8—522no—
188C2×C8C22⋊#26112yes—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C22⋊C4—262no—
192C22⋊C4—262no—
193C42—21no—
194C42—132no—
195C42—261no—
196C42D13⋊C812yes—
197C16—524no—
198C13#1145611yescharacteristic, complemented, Sylow
199C23—131no—
200C23—131no—
201C23—262no—
202C23—1041no—
203C23D13⋊M1611yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—81no—
208C2×C4—131no—
209C2×C4—132no—
210C2×C4—132no—
211C2×C4—131no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—1041no—
219C2×C4C2×D13⋊C811yescharacteristic
220C2×C4C2×C22⋊#26111yescharacteristic
221C8—22no—
222C8—41no—
223C8—262no—
224C8—521no—
225C22—21no—
226C22—41no—
227C22—132no—
228C22—261no—
229C22—521no—
230C22—521no—
231C22—1042no—
232C22D13⋊(C22⋊C8)11yescharacteristic
233C4—21no—
234C4—42no—
235C4—132no—
236C4—261no—
237C4—522no—
238C4D13⋊#9911yescharacteristic
239C4D13⋊#10111yescharacteristic
240C2—21no—
241C2—41no—
242C2—262no—
243C2—521no—
244C2D13⋊#32411yescharacteristic
subgroupG/H
centerC4D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#423C4
socleC2×C13C2×#324
prime radicalC23×D13M16
cosocleC2×#6099C23
hypercenter#423#261
hypocenterC13#11456
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #13129783C2semidirect
3. #13129782C2semidirect
198. C13#11456semidirect

Maximal subgroups

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

subgroupindex
D13⋊#3492
#131297832
#131297822
#131233982
#1145613