Finite Group Databasebeta

← #13130261

Subgroups — #13130261

Order 1664.

284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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#11719311C211yesmaximal, characteristic
2#11719135C211yesmaximal, characteristic, complemented
3D13⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#11718292C212yesmaximal, complemented
5#11718241C212yesmaximal, complemented
6C2×#6129C411yescharacteristic, complemented
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×D13⋊C8—21no—
10C13×#121C411yescharacteristic, complemented
11#88192C2211yescharacteristic
12#88191—21no—
13D4×Dic13—21no—
14#88178C411yescharacteristic, complemented
15#88151C2211yescharacteristic
16#88146C411yescharacteristic, complemented
17#88137—21no—
18#88135—21no—
19C22⋊#1057—21no—
20(C2×#261)⋊C4—21no—
21(C2×#261)⋊C4C2212yes—
22#88111C2212yes—
23C23×D13D411yescharacteristic
24C22×#261—22no—
25C2×D4×C13—21no—
26C2×D4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C2×C22⋊D13—21no—
29C2×C22⋊D13—21no—
30C22×Dic13—21no—
31C22×Dic13D411yescharacteristic
32#6129—42no—
33C2×C4×D13—42no—
34C2×C4×D13C2×C411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×C4×D13C2311yescharacteristic
38C2×Dic26C2×C411yescharacteristic
39C22⋊#261—42no—
40C2×#1057—22no—
41D13⋊C8—42no—
42C13×C4⋊C4C2×C411yescharacteristic
43C13×C22⋊C4—21no—
44C22⋊Dic13—21no—
45C22⋊Dic13—21no—
46#6103—21no—
47#6103—21no—
48C4⋊Dic13—21no—
49C4⋊Dic13C2×C411yescharacteristic
50#6101—21no—
51C4×Dic13—21no—
52#1516—131nomaximal, Sylow
53C23×C13—21no—
54C23×C13C22⋊C411yescharacteristic
55C22×D13—22no—
56C22×D13—22no—
57C22×D13—41no—
58C22×D13C22⋊C411yescharacteristic
59C22×D13C2×D411yescharacteristic
60C2×#261—42no—
61C2×#261—42no—
62C2×#261—42no—
63D4×C13—41no—
64D4×C13—42no—
65C2×C4×C13—21no—
66C2×C4×C13—41no—
67C2×C4×C13C22⋊C411yescharacteristic
68C2×C4×C13C22×C411yescharacteristic
69C22⋊D13—42no—
70C22⋊D13—42no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—41no—
74C2×Dic13—42no—
75C2×Dic13C22⋊C411yescharacteristic
76C2×Dic13C2×D411yescharacteristic
77C4×D13—22no—
78C4×D13—22no—
79C4×D13—41no—
80C4×D13—41no—
81Dic26—41no—
82#1057—42no—
83#525—131no—
84C2×C22⋊C8—131no—
85#381—131no—
86#328—132no—
87#327—132no—
88C22×C13—21no—
89C22×C13—21no—
90C22×C13—21no—
91C22×C13—41no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13C2×C22⋊C411yescharacteristic
95C2×D13—21no—
96C2×D13—21no—
97C2×D13—21no—
98C2×D13—21no—
99C2×D13—44no—
100C2×D13#9912yes—
101C2×D13#13512yes—
102#261—82no—
103C4×C13—21no—
104C4×C13—21no—
105C4×C13—41no—
106Dic13—21no—
107Dic13—21no—
108Dic13—41no—
109Dic13—41no—
110C2×#41—131no—
111C23×C4—131no—
112C22×C8—261no—
113#123—261no—
114C22⋊Q8—131no—
115C22⋊Q8—131no—
116#121—131no—
117#121#26111yescharacteristic, complemented
118#120—261no—
119C4×D4—261no—
120C4×D4—261no—
121#117—131no—
122C2×C22⋊C4—261no—
123C22⋊C8—132no—
124C22⋊C8—261no—
125#95—132no—
126#95—261no—
127C2×C13—41no—
128C2×C13—81no—
129C2×C13C2×#9911yescharacteristic
130C2×C13#41611yescharacteristic
131C2×C13#42111yescharacteristic
132D13—22no—
133D13—22no—
134C24—131no—
135#41—522no—
136C2×Q8—131no—
137C2×D4—21no—
138C2×D4—261no—
139C2×D4—261no—
140C2×D4C2×#26111yescharacteristic
141C22×C4—131no—
142C22×C4—131no—
143C22×C4—131no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—261no—
147C22×C4—262no—
148C22×C4—522no—
149C22×C4C2×#26111yescharacteristic
150C2×C8—262no—
151C2×C8—522no—
152C4⋊C4—131no—
153C4⋊C4—261no—
154C4⋊C4—261no—
155C4⋊C4C2×#26111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—261no—
158C22⋊C4—261no—
159C22⋊C4—261no—
160C22⋊C4—261no—
161C22⋊C4—522no—
162C42—261no—
163C13#151611yescharacteristic, complemented, Sylow
164C23—21no—
165C23—131no—
166C23—131no—
167C23—262no—
168C23—262no—
169C23—521no—
170C23C22⋊#26111yescharacteristic
171Q8—521no—
172D4—41no—
173D4—42no—
174D4—522no—
175D4—522no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—131no—
179C2×C4—131no—
180C2×C4—262no—
181C2×C4—262no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—521no—
185C2×C4—521no—
186C2×C4—521no—
187C2×C4—522no—
188C2×C4—522no—
189C2×C4—522no—
190C2×C4—522no—
191C2×C4C22⋊#26111yescharacteristic
192C2×C4C22×#26111yescharacteristic
193C8—522no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—132no—
201C22—132no—
202C22—261no—
203C22—261no—
204C22—261no—
205C22—261no—
206C22—524no—
207C22C2×C22⋊#26111yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—261no—
212C4—261no—
213C4—521no—
214C4—521no—
215C4—1042no—
216C2—41no—
217C2—81no—
218C2—262no—
219C2—262no—
220C2#1171914011yescharacteristic
221C2D13⋊#9911yescharacteristic
222C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radical#11719311C2
cosocleC2×C4×D13C23
hypercenter#121#261
hypocenterC13#1516
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11719135C2semidirect
3. D13⋊(C22⋊C8)C2semidirect
4. #11718292C2semidirect
5. #11718241C2semidirect
6. C2×#6129C4semidirect
10. C13×#121C4semidirect
14. #88178C4semidirect
16. #88146C4semidirect
117. #121#261semidirect
163. C13#1516semidirect

Maximal subgroups

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

subgroupindex
#117193112
#117191352
D13⋊(C22⋊C8)2
#117182922
#117182412
#151613