Finite Group Databasebeta

← #15772358

Subgroups — #15772358

Order 3328.

280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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#13123486C211yesmaximal, characteristic
2#13116645C212yesmaximal, complemented
3#13112789C211yesmaximal, characteristic, complemented
4#13112773C212yesmaximal
5C13×#1328C211yesmaximal, characteristic, complemented
6#11719227C411yescharacteristic
7C13×#424C2211yescharacteristic
8#11718790C2211yescharacteristic
9M16×Dic13C2211yescharacteristic
10#11718771C411yescharacteristic
11C2×#88055C411yescharacteristic
12#11718660C411yescharacteristic
13#11718501—22no—
14#11718496—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C2×#6127C2×C411yescharacteristic
20C2×C13×M16C2311yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C13×#117C2×C411yescharacteristic
23C2×C4×Dic13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88147—21no—
27#88141—21no—
28#88135—22no—
29#88126—21no—
30C42×D13—21no—
31C13×M32—22no—
32C13×C4⋊C8—22no—
33#88060—22no—
34#88060—22no—
35#88055—21no—
36#88055—21no—
37#88055D412yes—
38C8×Dic13D412yes—
39#88052—22no—
40C4⋊#1055—22no—
41#11523—131nomaximal, Sylow
42C22×C4×C13C22×C411yescharacteristic
43C2×C22⋊D13—21no—
44C22×Dic13—21no—
45#6127—41no—
46#6127—41no—
47C2×D52M1611yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×Dic26M1611yescharacteristic
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D412yes—
55C13×C4⋊C4—21no—
56C13×C22⋊C4M1612yes—
57C42×C13—21no—
58#6103—22no—
59#6101—22no—
60C4×Dic13—22no—
61C4×Dic13—21no—
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13C22⋊C411yescharacteristic
64#6099—41no—
65C2×#1055—21no—
66C2×#1055—41no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2923—131no—
71#2165—132no—
72#1328—131no—
73#1328D1311yescharacteristic, complemented
74#1321—132no—
75C23×C13C2×M1611yescharacteristic
76C22×D13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13C2×M1611yescharacteristic
82C22⋊D13—42no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—81no—
87D52—41no—
88C4×D13—41no—
89C4×D13—41no—
90C4×D13—82no—
91Dic26—41no—
92C8×C13—22no—
93C8×C13—41no—
94#1055—22no—
95#1055—41no—
96C4×#41—131no—
97#433—262no—
98#432—262no—
99#424—131no—
100#424C2×D1311yescharacteristic
101#408—131no—
102#408—131no—
103C4×M16—131no—
104C2×#97—131no—
105#364—262no—
106#349—132no—
107#349C2×D1312yes—
108#347—262no—
109C22×C13—21no—
110C22×C13—41no—
111C22×C13#40711yescharacteristic
112C2×D13—42no—
113C2×D13—41no—
114C4×C13—21no—
115C4×C13—42no—
116C4×C13#41011yescharacteristic
117C4×C13#41311yescharacteristic
118Dic13—41no—
119Dic13—41no—
120Dic13—41no—
121C2×#41—131no—
122C2×M16—131no—
123C2×M16C22×D1311yescharacteristic
124C22×C8—131no—
125C22×C8C4×D1311yescharacteristic
126C4×Q8—261no—
127C4×D4—261no—
128C4×D4—262no—
129#117—261no—
130#117C4×D1311yescharacteristic
131C2×C42—131no—
132C2×C42—261no—
133M32—22no—
134M32—262no—
135C4⋊C8—22no—
136C4⋊C8—262no—
137C22⋊C8—262no—
138C22⋊C8—262no—
139#97—132no—
140#97—261no—
141#97—261no—
142C4×C8—132no—
143C2×C13—21no—
144C2×C13—41no—
145C2×C13#146411yescharacteristic
146D13—81no—
147#41—521no—
148#41—521no—
149C2×Q8—131no—
150C2×D4—131no—
151C2×D4—261no—
152C22×C4—262no—
153C22×C4—261no—
154C22×C4—261no—
155C22×C4C2×C4×D1311yescharacteristic
156M16—41no—
157M16—521no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—132no—
161C2×C8—261no—
162C2×C8—521no—
163C2×C8D4×D1312yes—
164C4⋊C4—21no—
165C4⋊C4—262no—
166C22⋊C4—262no—
167C22⋊C4#609412yes—
168C42—21no—
169C42—131no—
170C42—131no—
171C42—262no—
172C42—261no—
173C16—42no—
174C16—522no—
175C13#1152311yescharacteristic, complemented, Sylow
176C23—261no—
177C23C2×#609411yescharacteristic
178Q8—521no—
179D4—521no—
180D4—522no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—261no—
185C2×C4—261no—
186C2×C4—261no—
187C2×C4—521no—
188C2×C4—521no—
189C2×C4—1042no—
190C2×C4—1041no—
191C2×C4C22⋊C4×D1311yescharacteristic
192C2×C4M16×D1311yescharacteristic
193C8—22no—
194C8—41no—
195C8—262no—
196C8—521no—
197C22—21no—
198C22—41no—
199C22—522no—
200C22—521no—
201C22#1171838711yescharacteristic
202C4—21no—
203C4—42no—
204C4—521no—
205C4—521no—
206C4—521no—
207C4#1171840111yescharacteristic
208C4#1171841211yescharacteristic
209C2—21no—
210C2—41no—
211C2—1041no—
212C2#1311316911yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1328C2
socleC2×C13#1464
prime radicalC2×#6127C2×C4
cosocleC2×C13×M16C23
hypercenter#1328D13
hypocenterC13#11523
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #13116645C2semidirect
3. #13112789C2semidirect
5. C13×#1328C2semidirect
73. #1328D13semidirect
175. C13#11523semidirect

Maximal subgroups

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

subgroupindex
#131234862
#131166452
#131127892
#131127732
C13×#13282
#1152313