Finite Group Databasebeta

← #16782444

Subgroups — #16782444

Order 3328.

306 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 108 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#13130760C211yesmaximal, characteristic
2#13130760C211yesmaximal, characteristic
3#13130395C211yesmaximal, characteristic
4#13130394C211yesmaximal, characteristic
5#13130392C211yesmaximal, characteristic
6#13130391C211yesmaximal, characteristic
7D13×#322C211yesmaximal, characteristic
8#11719052C2211yescharacteristic
9#11719052C2211yescharacteristic
10#11719052C2211yescharacteristic
11#11719052C2211yescharacteristic
12C4×C8×D13C2211yescharacteristic
13C4×C8×D13C2211yescharacteristic
14C4×C8×D13C2211yescharacteristic
15#11718268—22no—
16#11718268—22no—
17#11718256—22no—
18#11718255—22no—
19#11718254—22no—
20#11718253—22no—
21C13×#322C411yescharacteristic
22#11718047C411yescharacteristic
23#11718046C411yescharacteristic
24#11718046C411yescharacteristic
25C2×#6118—21no—
26C2×#6118—21no—
27C2×#6118—21no—
28C2×#6118—21no—
29C2×C8×D13D412yes—
30C2×C8×D13Q812yes—
31C2×C8×D13Q812yes—
32C42×D13C2311yescharacteristic
33C4⋊#1057—21no—
34C4⋊#1057—21no—
35C4⋊#1057—21no—
36C4⋊#1057—21no—
37C4⋊#1057—21no—
38C4⋊#1057—21no—
39C4⋊#1057—21no—
40C4⋊#1057—21no—
41C4×C8×C13C2×C411yescharacteristic
42C4×C8×C13C2×C411yescharacteristic
43C4×C8×C13C2×C411yescharacteristic
44C8×Dic13D412yes—
45C8×Dic13D412yes—
46C8×Dic13Q812yes—
47C4×#1055C2×C411yescharacteristic
48C4×#1055C2×C411yescharacteristic
49C4×#1055C2×C411yescharacteristic
50#8827—131nomaximal, Sylow
51C2×C4×D13C2×D411yescharacteristic
52C2×C4×D13C2×Q811yescharacteristic
53C2×C4×D13C2×Q811yescharacteristic
54C2×#1057—41no—
55C2×#1057—41no—
56C2×#1057—41no—
57C2×#1057—41no—
58#6118—42no—
59#6118—42no—
60#6118—42no—
61#6118—42no—
62C2×C8×C13C4⋊C412yes—
63C2×C8×C13C4⋊C412yes—
64C2×C8×C13C4⋊C412yes—
65C42×C13C22×C411yescharacteristic
66C4×Dic13C2×D411yescharacteristic
67C4×Dic13C2×D411yescharacteristic
68C4×Dic13C2×Q811yescharacteristic
69C2×#1055C4⋊C412yes—
70C2×#1055C4⋊C412yes—
71C2×#1055C4⋊C412yes—
72C8×D13—22no—
73C8×D13—22no—
74C8×D13—42no—
75C8×D13—42no—
76#1837—131no—
77#1837—131no—
78#1567—131no—
79#1567—131no—
80#1566—131no—
81#1566—131no—
82C2×#322—131no—
83C22×D13C4⋊Q811yescharacteristic
84C2×C4×C13C2×C4⋊C411yescharacteristic
85C2×C4×C13C2×C4⋊C411yescharacteristic
86C2×C4×C13C2×C4⋊C411yescharacteristic
87C2×Dic13#12711yescharacteristic
88C2×Dic13C4⋊Q811yescharacteristic
89C2×Dic13C4⋊Q811yescharacteristic
90C4×D13—22no—
91C4×D13—22no—
92C4×D13#13512yes—
93C4×D13#13512yes—
94#1057—81no—
95#1057—81no—
96#1057—81no—
97#1057—81no—
98C8×C13—22no—
99C8×C13—22no—
100C8×C13—22no—
101#1055—22no—
102#1055—22no—
103#1055—22no—
104#423—131no—
105#423—131no—
106#423—131no—
107#423—131no—
108C2×C4×C8—131no—
109C2×C4×C8—131no—
110C2×C4×C8—131no—
111#341—262no—
112#341—262no—
113#335—262no—
114#335—262no—
115#334—262no—
116#334—262no—
117#322—131no—
118#322—131no—
119#322—131no—
120#322#26111yescharacteristic
121C22×C13#38411yescharacteristic
122C2×D13—21no—
123C2×D13—21no—
124C2×D13#49912yes—
125C4×C13#42712yes—
126C4×C13#43012yes—
127C4×C13#43012yes—
128Dic13—21no—
129Dic13—21no—
130Dic13#49511yescharacteristic
131Dic13#49511yescharacteristic
132C2×M16—261no—
133C2×M16—261no—
134C2×M16—261no—
135C2×M16—261no—
136C22×C8—132no—
137C22×C8—132no—
138C22×C8—132no—
139C2×C42—131no—
140C4⋊C8—261no—
141C4⋊C8—261no—
142C4⋊C8—261no—
143C4⋊C8—261no—
144C4⋊C8—261no—
145C4⋊C8—261no—
146C4⋊C8—261no—
147C4⋊C8—261no—
148C4×C8—132no—
149C4×C8—132no—
150C4×C8—132no—
151C4×C8—131no—
152C4×C8—131no—
153C4×C8—131no—
154C4×C8C2×#26111yescharacteristic
155C4×C8C2×#26111yescharacteristic
156C4×C8C2×#26111yescharacteristic
157C2×C13#184611yescharacteristic
158C2×C13#184911yescharacteristic
159C2×C13#184911yescharacteristic
160D13—22no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—131no—
164M16—522no—
165M16—522no—
166M16—522no—
167M16—522no—
168C2×C8—132no—
169C2×C8—132no—
170C2×C8—132no—
171C2×C8—262no—
172C2×C8—262no—
173C2×C8—522no—
174C2×C8—522no—
175C2×C8—521no—
176C2×C8—521no—
177C2×C8—521no—
178C2×C8—521no—
179C2×C8C4⋊#26112yes—
180C2×C8C4⋊#26112yes—
181C2×C8C4⋊#26112yes—
182C42—131no—
183C42—131no—
184C42—131no—
185C42C22×#26111yescharacteristic
186C13#882711yescharacteristic, complemented, Sylow
187C23—131no—
188C2×C4—131no—
189C2×C4—132no—
190C2×C4—132no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4C2×C4⋊#26111yescharacteristic
196C2×C4C2×C4⋊#26111yescharacteristic
197C2×C4C2×C4⋊#26111yescharacteristic
198C8—22no—
199C8—22no—
200C8—22no—
201C8—262no—
202C8—262no—
203C8—262no—
204C8—1041no—
205C8—1041no—
206C8—1041no—
207C8—1041no—
208C22—132no—
209C22—261no—
210C22—261no—
211C22#1171905911yescharacteristic
212C4—131no—
213C4—131no—
214C4—261no—
215C4—261no—
216C4#1171909212yes—
217C4#1171910012yes—
218C4#1171910012yes—
219C2—262no—
220C2#1313077311yescharacteristic
221C2#1313077811yescharacteristic
222C2#1313077811yescharacteristic
subgroupG/H
centerC22#11719059
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#322C4
socleC22×C13#384
prime radicalC22×D13C4⋊Q8
cosocleC42×D13C23
hypercenter#322#261
hypocenterC13#8827
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
186. C13#8827semidirect

Maximal subgroups

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

subgroupindex
#131307602
#131303952
#131303942
#131303922
#131303912
D13×#3222
#882713