Finite Group Databasebeta

← #15757305

Subgroups — #15757305

Order 3328.

396 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 119 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#13118022C211yesmaximal, characteristic
2#13115806C211yesmaximal, characteristic
3#13114970C212yesmaximal
4#13112718C212yesmaximal
5C2×C13×#330C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C13×#97C2212yes—
8#11718646—22no—
9#11718642—22no—
10#11718642—22no—
11#11718597C2212yes—
12#11718596C2211yescharacteristic
13C2×#88043C2211yescharacteristic
14C13×#330C414yescomplemented
15#11718143—22no—
16#11718143—22no—
17#11718121—22no—
18C22×C8×C13—22no—
19C13×#125—22no—
20C13×#125C2×C412yes—
21C13×#125Q812yes—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13—22no—
28C2×C4⋊Dic13D412yes—
29C2×C4⋊Dic13D412yes—
30C2×C4×Dic13—22no—
31C22×#1055—21no—
32C13×#97—22no—
33C13×#97C2×C414yes—
34#88071—22no—
35#88071—22no—
36#88071—22no—
37#88071—22no—
38#88043—22no—
39#8915—131nomaximal, Sylow
40C22×C4×C13—22no—
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13C2×D412yes—
43C22×Dic13—22no—
44C22×Dic13—22no—
45C22×Dic13—41no—
46C2×C8×C13—24no—
47C2×C8×C13—42no—
48C2×C8×C13—42no—
49C13×C4⋊C4—24no—
50C13×C4⋊C4—24no—
51C13×C4⋊C4—22no—
52C13×C4⋊C4C4⋊C414yes—
53C42×C13C22×C411yescharacteristic
54C42×C13C2×Q811yescharacteristic
55C42×C13#4112yes—
56C4⋊Dic13—42no—
57C4⋊Dic13—42no—
58C4⋊Dic13—42no—
59C4⋊Dic13—44no—
60C4⋊Dic13—82no—
61C4×Dic13—82no—
62C2×#1055—22no—
63C2×#1055—41no—
64C2×#1055—41no—
65#2382—131no—
66#1992—131no—
67#1836—132no—
68C2×#330D1311yescharacteristic
69#1295—132no—
70C23×C13#12011yescharacteristic
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—24no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13C2×C4⋊C411yescharacteristic
79C2×C4×C13C4×D412yes—
80C2×C4×C13C22⋊Q812yes—
81C2×C4×C13#12311yescharacteristic
82C2×Dic13—42no—
83C2×Dic13—42no—
84C2×Dic13—42no—
85C2×Dic13—42no—
86C2×Dic13—42no—
87C2×Dic13—42no—
88C2×Dic13—81no—
89C2×Dic13—82no—
90C8×C13—44no—
91#1055—42no—
92C2×#125C2×D1311yescharacteristic
93C2×#97—131no—
94C2×#97C2×D1312yes—
95#389—262no—
96#387—262no—
97#387—262no—
98#384—131no—
99#382—132no—
100#340—262no—
101#340—262no—
102#340—262no—
103#330Dic1314yescomplemented
104C22×C13#38511yescharacteristic
105C22×C13#45411yescharacteristic
106C22×C13#45412yes—
107C22×C13#45512yes—
108C22×C13#45611yescharacteristic
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—44no—
114Dic13—82no—
115Dic13—82no—
116Dic13—161no—
117C22×C8—22no—
118C22×C8—261no—
119#125—22no—
120#125Dic2612yes—
121#125C2×Dic1312yes—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—132no—
125C2×C4⋊C4—261no—
126C2×C4⋊C4—262no—
127C2×C4⋊C4—262no—
128C2×C4⋊C4D5212yes—
129C2×C42—262no—
130C2×C42C22×D1311yescharacteristic
131#97—22no—
132#97—262no—
133#97C2×Dic1314yes—
134#95—262no—
135#95—262no—
136#95—262no—
137#95—262no—
138C2×C13#165811yescharacteristic
139C2×C13#166211yescharacteristic
140C2×C13#166412yes—
141C2×C13#185711yescharacteristic
142C2×C13#186012yes—
143C22×C4—22no—
144C22×C4—262no—
145C22×C4—262no—
146C22×C4—521no—
147C22×C4C2×D5211yescharacteristic
148C22×C4D4×D1312yes—
149C2×C8—24no—
150C2×C8—42no—
151C2×C8—42no—
152C2×C8—262no—
153C2×C8—521no—
154C2×C8—521no—
155C4⋊C4—24no—
156C4⋊C4—22no—
157C4⋊C4—24no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C4⋊C4—522no—
161C4⋊C4—524no—
162C4⋊C4—1042no—
163C4⋊C4C4⋊Dic1314yes—
164C42—1042no—
165C42C2×Dic2611yescharacteristic
166C42#612912yes—
167C42C22×Dic1311yescharacteristic
168C13#891511yescharacteristic, complemented, Sylow
169C23#8813611yescharacteristic
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—522no—
178C2×C4—522no—
179C2×C4—522no—
180C2×C4—522no—
181C2×C4—522no—
182C2×C4—522no—
183C2×C4—1041no—
184C2×C4—1042no—
185C2×C4#8813212yes—
186C2×C4#8814011yescharacteristic
187C2×C4C2×C4⋊Dic1311yescharacteristic
188C2×C4D4×Dic1312yes—
189C8—44no—
190C8—522no—
191C22#1171841311yescharacteristic
192C22#1171841411yescharacteristic
193C22#1171848612yes—
194C22#1171848812yes—
195C22#1171861111yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—1042no—
202C4—1042no—
203C4—2081no—
204C2#1311413911yescharacteristic
205C2#1311416011yescharacteristic
206C2#1311417212yes—
207C2#1311505311yescharacteristic
208C2#1311507112yes—
subgroupG/H
centerC23#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#330C2
socle, prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenterC2×#330D13
hypocenterC13#8915
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
14. C13×#330C4semidirect
103. #330Dic13semidirect
168. C13#8915semidirect

Maximal subgroups

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

subgroupindex
#131180222
#131158062
#131149702
#131127182
C2×C13×#3302
#891513