Finite Group Databasebeta

← #15767430

Subgroups — #15767430

Order 3328.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123111C211yesmaximal, characteristic
2#13114970C212yesmaximal
3#13114969C211yesmaximal, characteristic
4#13112718C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×#97C2212yes—
7C13×#382C2211yescharacteristic
8#11718645—22no—
9#11718597C2212yes—
10#11718596C2211yescharacteristic
11C2×#88043C2211yescharacteristic
12#11718322—22no—
13#11718318—22no—
14#11718143—22no—
15#11718143—22no—
16#11718121—22no—
17C22×C8×C13—22no—
18C2×C13×C4⋊C4D412yes—
19C2×C42×C13C2311yescharacteristic
20C2×C4⋊Dic13—21no—
21C2×C4⋊Dic13—22no—
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13D412yes—
24C2×C4⋊Dic13D412yes—
25C2×#6101—22no—
26C2×#6101—22no—
27C22×#1055—21no—
28C13×#97—22no—
29C13×#97Q814yes—
30C13×#95—22no—
31#88071—22no—
32#88071—22no—
33#88071—22no—
34#88043—21no—
35#88043Q812yes—
36#10586—131nomaximal, Sylow
37C22×C4×C13—22no—
38C22×C4×C13C2×D411yescharacteristic
39C22×C4×C13C2×D412yes—
40C22×Dic13—22no—
41C22×Dic13—22no—
42C22×Dic13—41no—
43C2×C8×C13—24no—
44C2×C8×C13—42no—
45C2×C8×C13—42no—
46C13×C4⋊C4—42no—
47C42×C13C2×Q812yes—
48C42×C13C2×Q811yescharacteristic
49C42×C13#4111yescharacteristic
50C4⋊Dic13—42no—
51C4⋊Dic13—42no—
52C4⋊Dic13—42no—
53C4⋊Dic13—44no—
54C4⋊Dic13—82no—
55#6101—82no—
56#6101—82no—
57C2×#1055—22no—
58C2×#1055—41no—
59C2×#1055—41no—
60#2845—131no—
61#1836—132no—
62#1836—131no—
63#1295—132no—
64#1295D1311yescharacteristic
65C23×C13#12011yescharacteristic
66C2×C4×C13—21no—
67C2×C4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13C22⋊Q812yes—
74C2×C4×C13C22⋊Q811yescharacteristic
75C2×C4×C13C4⋊Q811yescharacteristic
76C2×C4×C13C4⋊Q812yes—
77C2×Dic13—42no—
78C2×Dic13—42no—
79C2×Dic13—42no—
80C2×Dic13—42no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—81no—
84C2×Dic13—82no—
85C8×C13—44no—
86#1055—42no—
87C2×#97—131no—
88C2×#97C2×D1312yes—
89#398—262no—
90#398—262no—
91#398—262no—
92#384—131no—
93#382—132no—
94#382C2×D1311yescharacteristic
95#340—262no—
96#340—262no—
97#340—262no—
98C22×C13#39511yescharacteristic
99C22×C13#45411yescharacteristic
100C22×C13#45412yes—
101C22×C13#45511yescharacteristic
102C22×C13#45512yes—
103C4×C13—21no—
104C4×C13—22no—
105C4×C13—22no—
106C4×C13—21no—
107C4×C13—82no—
108Dic13—82no—
109Dic13—82no—
110Dic13—161no—
111C22×C8—22no—
112C22×C8—261no—
113C2×C4⋊C4—132no—
114C2×C4⋊C4—132no—
115C2×C4⋊C4—261no—
116C2×C4⋊C4—262no—
117C2×C4⋊C4—262no—
118C2×C4⋊C4—262no—
119C2×C4⋊C4—262no—
120C2×C4⋊C4D5212yes—
121C2×C42C22×D1311yescharacteristic
122#97—22no—
123#97—132no—
124#97—261no—
125#97Dic2614yes—
126#95—22no—
127#95—262no—
128#95—262no—
129#95—262no—
130C2×C13#165811yescharacteristic
131C2×C13#166211yescharacteristic
132C2×C13#166212yes—
133C2×C13#206112yes—
134C2×C13#206111yescharacteristic
135C22×C4—22no—
136C22×C4—262no—
137C22×C4—262no—
138C22×C4—521no—
139C22×C4C2×D5211yescharacteristic
140C22×C4D4×D1312yes—
141C2×C8—24no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8—262no—
145C2×C8—521no—
146C2×C8—521no—
147C4⋊C4—42no—
148C4⋊C4—522no—
149C4⋊C4—522no—
150C4⋊C4—522no—
151C4⋊C4—524no—
152C4⋊C4—1042no—
153C4⋊C4—1042no—
154C4⋊C4—1042no—
155C42C2×Dic2612yes—
156C42#612911yescharacteristic
157C42Q8×D1311yescharacteristic
158C13#1058611yescharacteristic, complemented, Sylow
159C23#8813611yescharacteristic
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—522no—
173C2×C4—1041no—
174C2×C4—1042no—
175C2×C4#8812311yescharacteristic
176C2×C4#8813212yes—
177C2×C4#8814212yes—
178C2×C4#8815111yescharacteristic
179C8—44no—
180C8—522no—
181C22#1171831711yescharacteristic
182C22#1171840711yescharacteristic
183C22#1171841411yescharacteristic
184C22#1171848612yes—
185C22#1171848812yes—
186C4—22no—
187C4—22no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—1042no—
192C4—1042no—
193C4—2081no—
194C2#1311413911yescharacteristic
195C2#1311416011yescharacteristic
196C2#1311416112yes—
197C2#1311618512yes—
198C2#1311618711yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13#120
hypercenter#1295D13
hypocenterC13#10586
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
158. C13#10586semidirect

Maximal subgroups

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

subgroupindex
#131231112
#131149702
#131149692
#131127182
C13×#12952
#1058613