Finite Group Databasebeta

← #15756495

Subgroups — #15756495

Order 3328.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112739C212yesmaximal
4#13112694C212yesmaximal
5C13×#2351C211yesmaximal, characteristic
6C2×C4×Q8×C13—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#389—21no—
9C13×#389—22no—
10C13×#382C412yes—
11C13×#382C2211yescharacteristic
12C4×C13×C4⋊C4C412yes—
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88076—21no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718122—21no—
18#11718120—22no—
19C22×Q8×C13D411yescharacteristic
20C4×Q8×C13—22no—
21C4×Q8×C13—22no—
22C4×Q8×C13—42no—
23C4×Q8×C13—42no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13—22no—
31C2×C42×C13—21no—
32C2×C42×C13C2×C412yes—
33C2×C42×C13C2311yescharacteristic
34C2×#6099—22no—
35C13×#95—22no—
36C13×#95—21no—
37C13×#95C2×C411yescharacteristic
38C13×#95C2×C412yes—
39C13×#95C2×C411yescharacteristic
40#88076—42no—
41C22⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4⋊#1055—22no—
45C4×#1055—22no—
46#8766—131nomaximal, Sylow
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13D812yes—
50C2×Q8×C13SD1612yes—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C13×C4⋊C4—24no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—44no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C42×C13—22no—
67C42×C13—22no—
68C42×C13—44no—
69C42×C13—41no—
70C42×C13—41no—
71C42×C13#4112yes—
72C42×C13#4112yes—
73#6099—42no—
74#6099—42no—
75C2×#1055—42no—
76C2×#1055—42no—
77#2351D1311yescharacteristic
78#1801—131no—
79#1461—131no—
80#1303—132no—
81#1286—132no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—24no—
84Q8×C13—24no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13#10214yes—
101C2×C4×C13#11711yescharacteristic
102C2×C4×C13#11711yescharacteristic
103C2×C4×C13#12312yes—
104C2×C4×C13#12312yes—
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13C2×SD1611yescharacteristic
107C2×C4×C13#13712yes—
108#1055—82no—
109#1055—82no—
110C2×C4×Q8—21no—
111C2×C4×Q8C2×D1311yescharacteristic
112#431—132no—
113#423—132no—
114C2×#101—261no—
115#389—21no—
116#389—22no—
117#382Dic1312yes—
118#382C2×D1311yescharacteristic
119C4×C4⋊C4Dic1312yes—
120C4×C4⋊C4C2×D1311yescharacteristic
121#343—261no—
122#324—262no—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13#38111yescharacteristic
126C22×C13C2×#10211yescharacteristic
127C22×C13#41911yescharacteristic
128C4×C13—24no—
129C4×C13—22no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—42no—
133C4×C13—42no—
134C4×C13—82no—
135C4×C13—81no—
136C4×C13#48012yes—
137C4×C13#48312yes—
138C22×Q8C22⋊D1311yescharacteristic
139C2×M16—262no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—42no—
143C4×Q8—42no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C22⋊D1312yes—
149C2×C4⋊C4C22⋊D1311yescharacteristic
150C2×C42—22no—
151C2×C42—21no—
152C2×C42C2×Dic1312yes—
153C2×C42C22×D1311yescharacteristic
154C4⋊C8—262no—
155C4⋊C8—262no—
156C4⋊C8—262no—
157#101—522no—
158C22⋊C8—262no—
159C4×C8—262no—
160#95—22no—
161#95—21no—
162#95C2×Dic1311yescharacteristic
163#95C2×Dic1312yes—
164#95C2×Dic1311yescharacteristic
165C2×C13—21no—
166C2×C13—21no—
167C2×C13#182311yescharacteristic
168C2×C13#182711yescharacteristic
169C2×C13#183011yescharacteristic
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8#610412yes—
173C2×Q8#610512yes—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4C22⋊Dic1312yes—
178C22×C4C22⋊Dic1312yes—
179C22×C4C22×Dic1311yescharacteristic
180C22×C4C2×C22⋊D1311yescharacteristic
181C22×C4C2×C22⋊D1311yescharacteristic
182M16—522no—
183M16—522no—
184C2×C8—522no—
185C2×C8—522no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—44no—
190C4⋊C4—44no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C42—22no—
194C42—22no—
195C42—44no—
196C42—41no—
197C42—41no—
198C42#612712yes—
199C42#612712yes—
200C13#876611yescharacteristic, complemented, Sylow
201C23C2×C22⋊Dic1311yescharacteristic
202Q8—24no—
203Q8—24no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4#8807214yes—
220C2×C4#8818011yescharacteristic
221C2×C4#8818011yescharacteristic
222C2×C4#8818312yes—
223C2×C4#8818312yes—
224C2×C4C2×#610411yescharacteristic
225C2×C4C2×#610511yescharacteristic
226C2×C4#8819612yes—
227C8—1042no—
228C8—1042no—
229C22—21no—
230C22—21no—
231C22#1171887211yescharacteristic
232C22C2×#8807211yescharacteristic
233C22#1171888611yescharacteristic
234C4—24no—
235C4—22no—
236C4—21no—
237C4—21no—
238C4—42no—
239C4—42no—
240C4—82no—
241C4—81no—
242C4#1171862812yes—
243C4#1171863212yes—
244C2—21no—
245C2—21no—
246C2#1311492211yescharacteristic
247C2#1311494011yescharacteristic
248C2#1311495011yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2351C2
socleC22×C13#381
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2351D13
hypocenterC13#8766
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2351

Complements

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

NH ≅ G/Ntype
200. C13#8766semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131127392
#131126942
C13×#23512
#876613