Finite Group Databasebeta

← #13130822

Subgroups — #13130822

Order 1664.

360 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 78 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×#88237C211yesmaximal, characteristic
2D13×C22⋊Q8C211yesmaximal, characteristic
3C2×#88117C212yesmaximal, complemented
4D13⋊(C22⋊C8)C211yesmaximal, characteristic
5#11718246C212yesmaximal, complemented
6C2×Q8×D13C2211yescharacteristic
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9#88237—24no—
10C2×C4⋊#261C2212yes—
11C2×C4×#261—21no—
12C2×D13⋊C8C2212yes—
13C13×C22⋊Q8C411yescharacteristic, complemented
14#88200C411yescharacteristic, complemented
15#88178C411yescharacteristic, complemented
16#88151C411yescharacteristic, complemented
17#88150—21no—
18C4⋊C4×D13—21no—
19C4⋊C4×D13C2211yescharacteristic
20C22⋊C4×D13—21no—
21#88132—21no—
22C22⋊#1057—21no—
23#88117—24no—
24#88111—21no—
25C23×D13D411yescharacteristic
26C22×#261—22no—
27C2×Q8×C13C2×C411yescharacteristic
28C22×C4×C13C2×C411yescharacteristic
29C22×Dic13D411yescharacteristic
30Q8×D13—22no—
31Q8×D13—22no—
32C2×C4×D13—22no—
33C2×C4×D13—22no—
34C2×C4×D13—21no—
35C2×C4×D13—21no—
36C2×C4×D13C2×C411yescharacteristic
37C2×C4×D13D411yescharacteristic
38C2×C4×D13D411yescharacteristic
39C2×C4×D13C2311yescharacteristic
40C2×Dic26—21no—
41C2×Dic26C2×C411yescharacteristic
42C22⋊#261—24no—
43C2×#1057—22no—
44C4⋊#261—22no—
45C4⋊#261D414yes—
46C4×#261—24no—
47D13⋊C8—22no—
48D13⋊C8—22no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4C2×C411yescharacteristic
51C13×C22⋊C4—21no—
52C22⋊Dic13—21no—
53#6103—21no—
54#6103—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13C2×C411yescharacteristic
57#6101—21no—
58#6101—21no—
59#6101—21no—
60#1873—131nomaximal, Sylow
61C23×C13C22⋊C411yescharacteristic
62C22×D13—21no—
63C22×D13—21no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13C22⋊C411yescharacteristic
67C22×D13C2×D411yescharacteristic
68C2×#261—24no—
69C2×#261—42no—
70C2×#261—42no—
71Q8×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13C22⋊C411yescharacteristic
76C2×C4×C13C22×C411yescharacteristic
77C2×Dic13—22no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13C22⋊C411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82C4×D13—21no—
83C4×D13—21no—
84C4×D13—22no—
85C4×D13—22no—
86C4×D13—41no—
87C4×D13—41no—
88C4×D13—42no—
89C4×D13C2×D412yes—
90C4×D13#4112yes—
91Dic26—22no—
92Dic26—42no—
93#1057—42no—
94C2×C22⋊Q8—131no—
95C2×#117—131no—
96C2×#103—132no—
97C2×C22⋊C8—131no—
98#340—132no—
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13C2×C22⋊C411yescharacteristic
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C2×D13—42no—
107C2×D13—42no—
108C2×D13#12011yescharacteristic
109C2×D13#12311yescharacteristic
110C2×D13#13512yes—
111C2×D13#13712yes—
112#261—44no—
113C4×C13—21no—
114C4×C13—41no—
115C4×C13—41no—
116C4×C13C4×D412yes—
117Dic13—21no—
118Dic13—41no—
119Dic13—41no—
120Dic13#12112yes—
121C22×Q8—131no—
122C23×C4—131no—
123C22×C8—132no—
124C22⋊Q8—131no—
125C22⋊Q8—131no—
126C22⋊Q8—131no—
127C22⋊Q8—261no—
128C22⋊Q8—261no—
129C22⋊Q8#26111yescharacteristic, complemented
130#117—264no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—261no—
134C2×C22⋊C4—261no—
135C2×C22⋊C4—261no—
136C2×C42—261no—
137#103—264no—
138C22⋊C8—261no—
139C22⋊C8—261no—
140C2×C13—41no—
141C2×C13#38611yescharacteristic
142C2×C13#41611yescharacteristic
143C2×C13#41911yescharacteristic
144D13—41no—
145D13#45212yes—
146D13#48512yes—
147C24—131no—
148C2×Q8—131no—
149C2×Q8—261no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8C2×#26111yescharacteristic
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—262no—
159C22×C4—262no—
160C22×C4—261no—
161C22×C4—261no—
162C22×C4—262no—
163C22×C4C2×#26111yescharacteristic
164C2×C8—262no—
165C2×C8—262no—
166C2×C8—262no—
167C4⋊C4—21no—
168C4⋊C4—134no—
169C4⋊C4—131no—
170C4⋊C4—261no—
171C4⋊C4—261no—
172C4⋊C4—261no—
173C4⋊C4—262no—
174C4⋊C4—261no—
175C4⋊C4C2×#26111yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—261no—
178C22⋊C4—261no—
179C22⋊C4—264no—
180C22⋊C4—261no—
181C42—264no—
182C13#187311yescharacteristic, complemented, Sylow
183C23—131no—
184C23—131no—
185C23—261no—
186C23—261no—
187C23—262no—
188C23—262no—
189C23C22⋊#26111yescharacteristic
190Q8—22no—
191Q8—262no—
192Q8—522no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—131no—
197C2×C4—132no—
198C2×C4—132no—
199C2×C4—131no—
200C2×C4—262no—
201C2×C4—261no—
202C2×C4—261no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—264no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—522no—
209C2×C4—521no—
210C2×C4—521no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4C22⋊#26111yescharacteristic
214C2×C4C22×#26111yescharacteristic
215C8—522no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22—131no—
220C22—131no—
221C22—132no—
222C22—132no—
223C22—261no—
224C22—261no—
225C22—261no—
226C22—522no—
227C22—522no—
228C22C2×C22⋊#26111yescharacteristic
229C4—21no—
230C4—41no—
231C4—41no—
232C4—132no—
233C4—261no—
234C4—524no—
235C4—521no—
236C4—521no—
237C4D4×#26112yes—
238C2—41no—
239C2—132no—
240C2—132no—
241C2—521no—
242C2#1171915011yescharacteristic
243C2#1171915311yescharacteristic
244C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC23×D13D4
cosocleC2×C4×D13C23
hypercenterC22⋊Q8#261
hypocenterC13#1873
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#88117C2semidirect
5. #11718246C2semidirect
13. C13×C22⋊Q8C4semidirect
14. #88200C4semidirect
15. #88178C4semidirect
16. #88151C4semidirect
129. C22⋊Q8#261semidirect
182. C13#1873semidirect

Maximal subgroups

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

subgroupindex
C2×#882372
D13×C22⋊Q82
C2×#881172
D13⋊(C22⋊C8)2
#117182462
#187313