Finite Group Databasebeta

← #13131027

Subgroups — #13131027

Order 1664.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#88150C211yesmaximal, characteristic
2#11719136C211yesmaximal, characteristic
3C4×C22⋊#261C211yesmaximal, characteristic
4#11718289C212yesmaximal
5#11718289C212yesmaximal
6C22×C4×D13C2211yescharacteristic
7C22×Dic26C411yescharacteristic, complemented
8C2×C22⋊#261C2212yes—
9C2×C22⋊#261C2212yes—
10C2×C4⋊#261—21no—
11C2×C4×#261—21no—
12C2×C13×C4⋊C4C411yescharacteristic, complemented
13C2×#6103C2211yescharacteristic
14C2×#6103C2211yescharacteristic
15C2×#6101C411yescharacteristic, complemented
16C2×#6101C411yescharacteristic, complemented
17#88150—21no—
18#88150—21no—
19#88150—21no—
20#88150—21no—
21(C2×#261)⋊C4—21no—
22(C2×#261)⋊C4—21no—
23C23×D13C2311yescharacteristic
24C22×#261—22no—
25C22×#261—22no—
26C22×C4×C13C2×C411yescharacteristic
27C22×C4×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C22×Dic13C2×C411yescharacteristic
30C22×Dic13C2×C411yescharacteristic
31C22×Dic13C2×C411yescharacteristic
32C2×C4×D13—42no—
33C2×C4×D13D411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13D411yescharacteristic
37C2×Dic26—21no—
38C2×Dic26—21no—
39C2×Dic26—42no—
40C22⋊#261—22no—
41C22⋊#261—24no—
42C22⋊#261Q814yescomplemented
43C4⋊#261—42no—
44C4×#261—42no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4—21no—
47#6103—21no—
48#6103—21no—
49#6103—21no—
50#6103—21no—
51#6101—21no—
52#6101—21no—
53#6101—21no—
54#6101—21no—
55#1996—131nomaximal, Sylow
56C23×C13C22×C411yescharacteristic
57C22×D13—41no—
58C22×D13—41no—
59C22×D13C2×D411yescharacteristic
60C22×D13C2×D411yescharacteristic
61C22×D13C2×Q812yes—
62C22×D13#4112yes—
63C2×#261—24no—
64C2×#261—42no—
65C2×#261—42no—
66C2×#261—42no—
67C2×#261—42no—
68C2×#261—42no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—41no—
72C2×C4×C13—41no—
73C2×C4×C13—41no—
74C2×C4×C13C22⋊C411yescharacteristic
75C2×C4×C13C22⋊C411yescharacteristic
76C2×Dic13—22no—
77C2×Dic13—21no—
78C2×Dic13—21no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13C22⋊C411yescharacteristic
82C2×Dic13C22⋊C411yescharacteristic
83C4×D13—22no—
84C4×D13—22no—
85C4×D13—41no—
86C4×D13—41no—
87Dic26—42no—
88Dic26—42no—
89C2×C22⋊Q8—131no—
90#380—131no—
91C4×C22⋊C4—131no—
92#342—132no—
93#342—132no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13C2×C22⋊C411yescharacteristic
97C22×C13C4×Q812yes—
98C2×D13—21no—
99C2×D13—21no—
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—42no—
103C2×D13—42no—
104C2×D13C22⋊Q812yes—
105C2×D13#12411yescharacteristic
106C2×D13C4⋊Q811yescharacteristic
107#261—44no—
108#261—82no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—41no—
112C4×C13—41no—
113Dic13—21no—
114Dic13—41no—
115Dic13—41no—
116Dic13#9912yes—
117C22×Q8—131no—
118C23×C4—131no—
119C22⋊Q8—261no—
120C22⋊Q8—261no—
121C22⋊Q8—261no—
122C22⋊Q8—261no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4—261no—
126C2×C4⋊C4#26111yescharacteristic, complemented
127C2×C22⋊C4—132no—
128C2×C22⋊C4—131no—
129C2×C22⋊C4—131no—
130C2×C22⋊C4—132no—
131C2×C42—261no—
132#95—261no—
133#95—261no—
134C2×C13—22no—
135C2×C13#39111yescharacteristic
136C2×C13C2×#9911yescharacteristic
137C2×C13#41011yescharacteristic
138D13—22no—
139D13—21no—
140D13—21no—
141C24—131no—
142C2×Q8—261no—
143C2×Q8—261no—
144C2×Q8—522no—
145C22×C4—131no—
146C22×C4—131no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150C22×C4—131no—
151C22×C4—131no—
152C22×C4—262no—
153C22×C4—262no—
154C22×C4—522no—
155C22×C4C2×#26111yescharacteristic
156C22×C4C2×#26111yescharacteristic
157C22×C4C2×#26111yescharacteristic
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—261no—
161C4⋊C4—261no—
162C4⋊C4—261no—
163C4⋊C4—261no—
164C4⋊C4—522no—
165C22⋊C4—134no—
166C22⋊C4—261no—
167C22⋊C4—261no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C22⋊C4—262no—
171C22⋊C4—264no—
172C42—522no—
173C13#199611yescharacteristic, complemented, Sylow
174C23—131no—
175C23—131no—
176C23—132no—
177C23—132no—
178C23—521no—
179C23—521no—
180C23C22×#26111yescharacteristic
181Q8—522no—
182Q8—522no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—131no—
189C2×C4—131no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—264no—
194C2×C4—261no—
195C2×C4—261no—
196C2×C4—521no—
197C2×C4—521no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—521no—
201C2×C4—521no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4C22⋊#26111yescharacteristic
206C2×C4C22⋊#26111yescharacteristic
207C22—21no—
208C22—21no—
209C22—132no—
210C22—131no—
211C22—131no—
212C22—261no—
213C22—261no—
214C22—261no—
215C22—261no—
216C22—522no—
217C22—522no—
218C22Q8×#26112yes—
219C22C2×C22⋊#26111yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—132no—
225C4—261no—
226C4—524no—
227C4—521no—
228C4—521no—
229C4—1042no—
230C2—22no—
231C2—262no—
232C2—261no—
233C2—261no—
234C2#1171911611yescharacteristic
235C2D13⋊#9911yescharacteristic
236C2(C2×#261)⋊Q811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radical, cosocleC23×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1996
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C22×Dic26C4semidirect
12. C2×C13×C4⋊C4C4semidirect
15. C2×#6101C4semidirect
16. C2×#6101C4semidirect
42. C22⋊#261Q8semidirect
126. C2×C4⋊C4#261semidirect
173. C13#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
#117191362
C4×C22⋊#2612
#117182892
#199613