Finite Group Databasebeta

← #13131099

Subgroups — #13131099

Order 1664.

234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719353C211yesmaximal, characteristic
2#11719148C211yesmaximal, characteristic
3#11719142C211yesmaximal, characteristic
4#11718288C212yesmaximal, complemented
5#11718237C212yesmaximal, complemented
6C2×#6129C2211yescharacteristic
7C22×Dic26C411yescharacteristic, complemented
8C2×#6122—21no—
9#88237—21no—
10C13×#123C411yescharacteristic, complemented
11#88189C411yescharacteristic, complemented
12#88183C2211yescharacteristic
13#88150—21no—
14#88142—21no—
15#88140C2211yescharacteristic
16#88139—21no—
17#88132—21no—
18#88131C411yescharacteristic, complemented
19#88121C2212yes—
20#88119—21no—
21#88119C2212yes—
22#88113—21no—
23C2×D4×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13D411yescharacteristic
26C2×C22⋊D13C2311yescharacteristic
27C22×Dic13C2×C411yescharacteristic
28C22×Dic13C2×C411yescharacteristic
29C22×Dic13D411yescharacteristic
30#6129—41no—
31#6129—41no—
32C2×C4×D13D411yescharacteristic
33C2×Dic26—21no—
34C2×Dic26—21no—
35C2×Dic26—41no—
36C2×Dic26—41no—
37C2×Dic26D411yescharacteristic
38C22⋊#261—22no—
39#6122—22no—
40#6122—41no—
41C2×#1057—41no—
42C4⋊#261—41no—
43C4×#261—41no—
44C13×C4⋊C4—21no—
45C13×C22⋊C4—21no—
46C13×C22⋊C4C2×C411yescharacteristic
47C22⋊Dic13—21no—
48C22⋊Dic13C2×C411yescharacteristic
49#6103—21no—
50#6103—21no—
51C4⋊Dic13—21no—
52#6101—21no—
53#6101—21no—
54#6101—21no—
55C4×Dic13—21no—
56#2123—131nomaximal, Sylow
57C23×C13C22⋊C411yescharacteristic
58C23×C13C22×C411yescharacteristic
59C22×D13C2×D411yescharacteristic
60C2×#261—42no—
61D4×C13—41no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13C22⋊C411yescharacteristic
66C22⋊D13—41no—
67C22⋊D13—41no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—41no—
75C2×Dic13C22⋊C411yescharacteristic
76C2×Dic13C22⋊C411yescharacteristic
77C2×Dic13C2×D411yescharacteristic
78C4×D13—21no—
79C4×D13—21no—
80Dic26—41no—
81Dic26—42no—
82Dic26—41no—
83Dic26—41no—
84#1057—42no—
85#536—131no—
86#413—131no—
87#410—131no—
88#352—132no—
89#352—132no—
90C22×C13—21no—
91C22×C13—21no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13C2×C22⋊C411yescharacteristic
95C2×D13—21no—
96C2×D13—41no—
97#261—82no—
98C4×C13—21no—
99C4×C13—41no—
100C4×C13—41no—
101Dic13—21no—
102Dic13—21no—
103Dic13—41no—
104Dic13—41no—
105Dic13#9911yescharacteristic
106Dic13#9911yescharacteristic
107C2×#41—131no—
108C22×Q8—131no—
109C2×M16—261no—
110C4⋊Q8—261no—
111#124—261no—
112#123—131no—
113#123—131no—
114#123—131no—
115#123#26111yescharacteristic, complemented
116C22⋊Q8—261no—
117C22⋊Q8—261no—
118#117—131no—
119#117—261no—
120#101—261no—
121#100—132no—
122#99—132no—
123#99—261no—
124C2×C13—21no—
125C2×C13—41no—
126C2×C13—41no—
127C2×C13C2×#9911yescharacteristic
128D13—41no—
129#41—521no—
130#41—521no—
131C2×Q8—131no—
132C2×Q8—261no—
133C2×Q8—261no—
134C2×Q8—521no—
135C2×Q8—521no—
136C2×D4—131no—
137C2×D4—131no—
138C2×D4C2×#26111yescharacteristic
139C22×C4—131no—
140C22×C4—131no—
141C22×C4—131no—
142C22×C4—131no—
143C22×C4C2×#26111yescharacteristic
144M16—262no—
145M16—521no—
146C2×C8—521no—
147C4⋊C4—21no—
148C4⋊C4—261no—
149C4⋊C4—261no—
150C4⋊C4—261no—
151C4⋊C4—261no—
152C4⋊C4—521no—
153C22⋊C4—21no—
154C22⋊C4—131no—
155C22⋊C4—261no—
156C22⋊C4—261no—
157C22⋊C4—261no—
158C22⋊C4—262no—
159C22⋊C4C2×#26111yescharacteristic
160C42—261no—
161C42—521no—
162C13#212311yescharacteristic, complemented, Sylow
163C23—131no—
164C23C22⋊#26111yescharacteristic
165C23C22×#26111yescharacteristic
166Q8—521no—
167Q8—521no—
168Q8—521no—
169Q8—522no—
170D4—41no—
171D4—521no—
172D4—521no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—131no—
177C2×C4—131no—
178C2×C4—131no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—261no—
183C2×C4—261no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4—261no—
187C2×C4—521no—
188C2×C4—522no—
189C2×C4C22⋊#26111yescharacteristic
190C8—522no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—261no—
196C22—521no—
197C22C2×C22⋊#26111yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—131no—
202C4—131no—
203C4—261no—
204C4—261no—
205C4—521no—
206C4—521no—
207C4—1042no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—521no—
212C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC23×C13C22×C4
FrattiniC23C22×#261
FittingC13×#123C4
socleC2×C13C2×#99
prime radicalC2×#6129C22
cosocleC2×C22⋊D13C23
hypercenter#123#261
hypocenterC13#2123
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11718288C2semidirect
5. #11718237C2semidirect
7. C22×Dic26C4semidirect
10. C13×#123C4semidirect
11. #88189C4semidirect
18. #88131C4semidirect
115. #123#261semidirect
162. C13#2123semidirect

Maximal subgroups

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

subgroupindex
#117193532
#117191482
#117191422
#117182882
#117182372
#212313