Finite Group Databasebeta

← #16786872

Subgroups — #16786872

Order 3328.

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

normal subgroups only

This group has 386 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
1#13131064C212yesmaximal, complemented
2#13129774C212yesmaximal, complemented
3#13129759C212yesmaximal, complemented
4#13123532C211yesmaximal, characteristic
5C2×#88155C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7#11719229C411yescharacteristic
8C2×#88098—22no—
9C13×#405C411yescharacteristic
10#11718790C2211yescharacteristic
11#11718787C411yescharacteristic
12#11718660C2211yescharacteristic
13#11718367—22no—
14C8×D52—22no—
15C22⋊#6092C2214yes—
16#11718259—22no—
17C2×#6127C2×C411yescharacteristic
18C22×C4×D13C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C13×#117C2×C411yescharacteristic
22C2×#6099C2×C411yescharacteristic
23C22×#1055C2311yescharacteristic
24#88155—42no—
25C2×#6094—21no—
26C2×C8×D13—21no—
27C2×C8×D13—42no—
28C2×C8×D13D412yes—
29C2×C8×D13D412yes—
30#88151C812yes—
31#88149C812yes—
32#88140—21no—
33#88136—21no—
34C4×D52—22no—
35C2×#6092—24no—
36#88098—44no—
37C13×#97—21no—
38C4×C8×C13—21no—
39#88060—22no—
40#88060—22no—
41C4⋊#1055—22no—
42#11469—131nomaximal, Sylow
43C23×D13M1611yescharacteristic
44C22×C4×C13C22×C411yescharacteristic
45C2×C22⋊D13—21no—
46C22×Dic13M1611yescharacteristic
47#6127—41no—
48#6127—41no—
49C2×D52—22no—
50C2×D52C2×C811yescharacteristic
51C2×C4×D13—21no—
52C2×C4×D13—41no—
53C2×C4×D13—41no—
54C2×C4×D13C22⋊C412yes—
55C2×C4×D13C2×C812yes—
56C2×Dic26C2×C811yescharacteristic
57C13×M16—41no—
58C2×C8×C13—22no—
59C2×C8×C13—21no—
60C2×C8×C13C22⋊C411yescharacteristic
61C2×C8×C13C22⋊C411yescharacteristic
62C13×C4⋊C4C2×C812yes—
63C13×C22⋊C4—21no—
64C42×C13—21no—
65#6103—22no—
66#6103—22no—
67C4⋊Dic13—22no—
68#6099—41no—
69C2×#1055—21no—
70C2×#1055—41no—
71C2×#1055C2×D412yes—
72#6094—42no—
73C8×D13—24no—
74C8×D13—42no—
75C8×D13—42no—
76#6092—44no—
77#2929—131no—
78#2112—132no—
79#1323—132no—
80#1315—132no—
81C23×C13C2×M1611yescharacteristic
82C22×D13—21no—
83C22×D13—41no—
84C22×D13—42no—
85C22×D13C22⋊C812yes—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13C22×C811yescharacteristic
91C22⋊D13—42no—
92C2×Dic13—21no—
93C2×Dic13—41no—
94C2×Dic13C22⋊C812yes—
95D52—41no—
96D52—44no—
97C4×D13—22no—
98C4×D13—22no—
99C4×D13—42no—
100C4×D13—41no—
101C4×D13—41no—
102Dic26—41no—
103C8×C13—21no—
104C8×C13—41no—
105C8×C13#9912yes—
106#1055—22no—
107#1055—41no—
108C2×#131—131no—
109C23×C8—131no—
110#525—131no—
111C2×M32—262no—
112#435—262no—
113C8×D4—262no—
114#424—131no—
115#408—131no—
116#407—131no—
117#405#26111yescharacteristic
118C22⋊C16—134no—
119C22⋊C16—262no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13C2×C22⋊C811yescharacteristic
123C2×D13—22no—
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—44no—
127C2×D13—42no—
128C2×D13—41no—
129C4×C13—21no—
130C4×C13—42no—
131C4×C13C2×#9911yescharacteristic
132C4×C13#41311yescharacteristic
133Dic13—22no—
134Dic13—41no—
135C2×#41—131no—
136C23×C4—131no—
137#131—522no—
138C2×M16—131no—
139C2×M16—261no—
140C2×M16C2×#26111yescharacteristic
141C22×C8—131no—
142C22×C8—132no—
143C22×C8—132no—
144C22×C8—261no—
145C22×C8—522no—
146C22×C8C2×#26111yescharacteristic
147#123—261no—
148C22⋊Q8—132no—
149#121—132no—
150#120—261no—
151C4×D4—262no—
152#117C2×#26111yescharacteristic
153M32—524no—
154C2×C16—264no—
155C4⋊C8—262no—
156C22⋊C8—262no—
157C22⋊C8—262no—
158#97—21no—
159C4×C8—21no—
160C2×C13—41no—
161C2×C13#145911yescharacteristic
162C2×C13#211712yes—
163D13—42no—
164D13—81no—
165C24—131no—
166#41—521no—
167#41—521no—
168C2×Q8—131no—
169C2×D4—131no—
170C2×D4—262no—
171C2×D4—261no—
172C22×C4—131no—
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—261no—
176C22×C4—521no—
177C22×C4—521no—
178C22×C4C22×#26111yescharacteristic
179M16—41no—
180M16—522no—
181M16—521no—
182C2×C8—22no—
183C2×C8—21no—
184C2×C8—132no—
185C2×C8—264no—
186C2×C8—261no—
187C2×C8—522no—
188C2×C8—521no—
189C2×C8—522no—
190C2×C8C22⋊#26111yescharacteristic
191C2×C8C22⋊#26111yescharacteristic
192C4⋊C4—262no—
193C4⋊C4D13⋊C812yes—
194C22⋊C4—21no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C42—21no—
198C16—524no—
199C13#1146911yescharacteristic, complemented, Sylow
200C23—132no—
201C23—261no—
202C23—521no—
203C23—522no—
204C23D13⋊M1611yescharacteristic
205Q8—521no—
206D4—521no—
207D4—524no—
208D4—522no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—132no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—522no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—521no—
220C2×C4C2×D13⋊C811yescharacteristic
221C2×C4C2×C22⋊#26111yescharacteristic
222C8—21no—
223C8—41no—
224C8—262no—
225C8—521no—
226C8#8810712yes—
227C22—22no—
228C22—21no—
229C22—262no—
230C22—262no—
231C22—262no—
232C22—524no—
233C22—522no—
234C22—521no—
235C22D13⋊(C22⋊C8)11yescharacteristic
236C4—21no—
237C4—42no—
238C4—262no—
239C4—521no—
240C4C2×#8810711yescharacteristic
241C4#1171913211yescharacteristic
242C2—41no—
243C2—522no—
244C2—1041no—
245C2#1313007311yescharacteristic
246C2#1313107912yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#405C4
socleC22×C13C2×C22⋊C8
prime radical#11719229C4
cosocleC22×#1055C23
hypercenter#405#261
hypocenterC13#11469
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #13131064C2semidirect
2. #13129774C2semidirect
3. #13129759C2semidirect
199. C13#11469semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131297742
#131297592
#131235322
#1146913