Finite Group Databasebeta

← #13131708

Subgroups — #13131708

Order 1664.

422 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 152 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#11719291C211yesmaximal, characteristic
2C2×C22⋊#1057C212yesmaximal, complemented
3#11719147C211yesmaximal, characteristic, complemented
4#11719146C211yesmaximal, characteristic, complemented
5#11719144C212yesmaximal, complemented
6D4×#1057C212yesmaximal, complemented
7#11719068C212yesmaximal, complemented
8#11719064C212yesmaximal, complemented
9#11719063C212yesmaximal, complemented
10C23×Dic13C2211yescharacteristic
11C2×#6129C2211yescharacteristic
12C2×#6122C2211yescharacteristic, complemented
13C22×#1057C2212yes—
14C22×#1057C2212yes—
15C22×#1057C2211yescharacteristic, complemented
16C2×#6118C2211yescharacteristic, complemented
17C2×D13⋊C8C2211yescharacteristic, complemented
18C13×#120C411yescharacteristic
19#88207C411yescharacteristic
20#88193C412yes—
21#88189C411yescharacteristic
22D4×Dic13C2212yes—
23#88140C411yescharacteristic
24#88135C2212yes—
25#88132C412yes—
26#88131C2211yescharacteristic
27C22⋊#1057C2212yes—
28C22⋊#1057C2212yes—
29C22⋊#1057C2212yes—
30C22⋊#1057C2212yes—
31C22⋊#1057C2212yescomplemented
32#88112C2212yescomplemented
33#88111C2212yescomplemented
34#88110C2212yescomplemented
35C4⋊#1057C2212yescomplemented
36C4×#1057C2212yescomplemented
37C24×C13C2×C411yescharacteristic
38C2×D4×C13C2×C412yes—
39C2×D4×C13C2×C411yescharacteristic
40C2×C22⋊D13C2×C412yes—
41C2×C22⋊D13C2×C411yescharacteristic
42C2×C22⋊D13C2×C411yescharacteristic
43C22×Dic13—41no—
44C22×Dic13—41no—
45C22×Dic13C2×C412yes—
46C22×Dic13C2×C411yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50#6129—41no—
51#6129—41no—
52C2×C4×D13C2311yescharacteristic
53C2×Dic26C2×C411yescharacteristic
54#6122—41no—
55C2×#1057—42no—
56C2×#1057—42no—
57C2×#1057—41no—
58C2×#1057C2312yes—
59C2×#1057C2312yes—
60C2×#1057C2312yes—
61C2×#1057C2312yes—
62#6118—41no—
63D13⋊C8—41no—
64C13×C22⋊C4C2×C411yescharacteristic
65C13×C22⋊C4C2×C412yes—
66C22⋊Dic13C2×C411yescharacteristic
67C22⋊Dic13C2×C412yes—
68C22⋊Dic13C2×C412yes—
69#6103C2×C412yes—
70C4⋊Dic13C2×C412yes—
71#6101C2×C412yes—
72#6101C2×C412yes—
73C4×Dic13C2312yes—
74#2977—131nomaximal, Sylow
75C23×C13—24no—
76C23×C13—41no—
77C23×C13C22×C411yescharacteristic
78C23×C13C22×C411yescharacteristic
79C23×C13C22×C412yes—
80C22×D13C22×C411yescharacteristic
81D4×C13—24no—
82D4×C13—41no—
83C2×C4×C13C22×C412yes—
84C2×C4×C13C22×C411yescharacteristic
85C22⋊D13—24no—
86C22⋊D13—41no—
87C22⋊D13—41no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—42no—
95C2×Dic13—41no—
96C2×Dic13C22×C412yes—
97C2×Dic13C22×C411yescharacteristic
98C2×Dic13C22×C412yes—
99C2×Dic13C22×C411yescharacteristic
100C2×Dic13C2411yescharacteristic
101C4×D13—21no—
102C4×D13—21no—
103Dic26—41no—
104#1057—22no—
105#1057—22no—
106#1057—22no—
107#1057—22no—
108#525—131no—
109#435—132no—
110#435—132no—
111C8×D4—132no—
112C8×D4—132no—
113#433—132no—
114#408—131no—
115#408—131no—
116C2×C22⋊C8—132no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—44no—
124C22×C13#13114yes—
125C22×C13C23×C411yescharacteristic
126C2×D13—21no—
127C2×D13—22no—
128C4×C13—21no—
129C4×C13—22no—
130Dic13—21no—
131Dic13—21no—
132Dic13—22no—
133Dic13—22no—
134Dic13H(5,𝔽2)11yescharacteristic
135Dic13H(5,𝔽2)11yescharacteristic
136C2×#41—131no—
137C23×C4—131no—
138C2×M16—131no—
139C2×M16—131no—
140C22×C8—132no—
141C22×C8—132no—
142C22×C8—131no—
143C22×C8—131no—
144#123—131no—
145#123—131no—
146C22⋊Q8—132no—
147#121—132no—
148#120—131no—
149#120#26111yescharacteristic
150C4×D4—132no—
151C4×D4—132no—
152#117—131no—
153C4⋊C8—132no—
154C4⋊C8—132no—
155C22⋊C8—132no—
156C22⋊C8—132no—
157C22⋊C8—132no—
158C22⋊C8—132no—
159C22⋊C8—132no—
160C22⋊C8—132no—
161#97—132no—
162C4×C8—132no—
163C2×C13—24no—
164C2×C13—41no—
165C2×C13—41no—
166C2×C13#51811yescharacteristic
167C2×C13C2×#13112yes—
168D13—41no—
169C24C2×#26111yescharacteristic
170#41—521no—
171#41—521no—
172C2×Q8—131no—
173C2×D4—132no—
174C2×D4—131no—
175C2×D4—131no—
176C2×D4C2×#26112yes—
177C2×D4C2×#26111yescharacteristic
178C22×C4—131no—
179C22×C4—132no—
180C22×C4—131no—
181C22×C4—132no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—521no—
185C22×C4—521no—
186M16—521no—
187M16—521no—
188C2×C8—132no—
189C2×C8—132no—
190C2×C8—132no—
191C2×C8—132no—
192C2×C8—521no—
193C2×C8—521no—
194C2×C8—522no—
195C2×C8—522no—
196C4⋊C4—132no—
197C4⋊C4—132no—
198C4⋊C4—132no—
199C22⋊C4—131no—
200C22⋊C4—132no—
201C22⋊C4—132no—
202C22⋊C4—132no—
203C22⋊C4C2×#26111yescharacteristic
204C22⋊C4C2×#26112yes—
205C42—132no—
206C13#297711yescharacteristic, complemented, Sylow
207C23—24no—
208C23—41no—
209C23—131no—
210C23C22×#26111yescharacteristic
211C23C22×#26111yescharacteristic
212C23C22×#26112yes—
213Q8—521no—
214D4—24no—
215D4—41no—
216D4—264no—
217D4—521no—
218D4—521no—
219C2×C4—131no—
220C2×C4—132no—
221C2×C4—132no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—521no—
233C2×C4—522no—
234C2×C4C22×#26112yes—
235C2×C4C22×#26111yescharacteristic
236C8—262no—
237C8—262no—
238C8—262no—
239C8—262no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—21no—
246C22—44no—
247C22—262no—
248C22—261no—
249C22#8823814yes—
250C22C23×#26111yescharacteristic
251C4—22no—
252C4—21no—
253C4—131no—
254C4—131no—
255C4—262no—
256C4—262no—
257C4—261no—
258C4—261no—
259C2—24no—
260C2—41no—
261C2—41no—
262C2—521no—
263C2C2×#8823812yes—
264C2#1171962311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#120C4
prime radical#11719291C2
cosocleC2×Dic13C24
hypercenter#120#261
hypocenterC13#2977
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#1057C2semidirect
3. #11719147C2semidirect
4. #11719146C2semidirect
5. #11719144C2semidirect
6. D4×#1057C2semidirect
7. #11719068C2semidirect
8. #11719064C2semidirect
9. #11719063C2semidirect
12. C2×#6122C22semidirect
15. C22×#1057C22semidirect
16. C2×#6118C22semidirect
17. C2×D13⋊C8C22semidirect
31. C22⋊#1057C22semidirect
32. #88112C22semidirect
33. #88111C22semidirect
34. #88110C22semidirect
35. C4⋊#1057C22semidirect
36. C4×#1057C22semidirect
206. C13#2977semidirect

Maximal subgroups

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

subgroupindex
#117192912
C2×C22⋊#10572
#117191472
#117191462
#117191442
D4×#10572
#117190682
#117190642
#117190632
#297713