Finite Group Databasebeta

← #15751471

Subgroups — #15751471

Order 3328.

410 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123214C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic
3#13112661C214yesmaximal
4C13×#1839C211yesmaximal, characteristic
5C2×#88123C411yescharacteristic
6C2×#88123C411yescharacteristic
7C43×C13C2211yescharacteristic
8#11718597—21no—
9#11718597—21no—
10#11718590—21no—
11#11718590—21no—
12#11718590C412yes—
13#11718590C2212yes—
14C2×#88043—21no—
15C13×#336—21no—
16C13×#336—21no—
17C13×#336C2212yes—
18#11718116—21no—
19#11718116C2212yes—
20C22×Dic26—21no—
21C22×Dic26C2×C412yes—
22C22×C8×C13—22no—
23C2×C42×C13C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C42×C13D411yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C412yes—
34C22×#1055—22no—
35#88123—42no—
36#88123—42no—
37#88071—22no—
38#88071—22no—
39#88071—22no—
40#88071—22no—
41#88043—24no—
42#7702—131nomaximal, Sylow
43C22×C4×C13C22⋊C411yescharacteristic
44C22×C4×C13C22⋊C411yescharacteristic
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13C2×D411yescharacteristic
50C22×Dic13—22no—
51C22×Dic13—22no—
52C2×Dic26—24no—
53C2×Dic26—42no—
54C2×Dic26—42no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C2×Dic26—42no—
58C2×C8×C13—42no—
59C2×C8×C13—42no—
60C2×C8×C13—42no—
61C42×C13—22no—
62C42×C13—22no—
63C42×C13—22no—
64C42×C13—22no—
65C42×C13—22no—
66C42×C13—41no—
67C42×C13—41no—
68C4⋊Dic13—42no—
69C4⋊Dic13—42no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72C2×#1055—24no—
73C2×#1055—42no—
74C2×#1055—42no—
75#2862—131no—
76#1839D1311yescharacteristic
77#1745—131no—
78#1272—134no—
79C23×C13C2×C22⋊C411yescharacteristic
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13#10012yes—
97C2×C4×C13#10412yes—
98C2×C4×C13#13112yes—
99C2×C4×C13#13712yes—
100C2×C4×C13#13712yes—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107Dic26—84no—
108Dic26—84no—
109C8×C13—82no—
110#1055—44no—
111C2×C4⋊Q8—131no—
112C2×C4⋊Q8—131no—
113C2×#97—261no—
114#391—132no—
115#391—132no—
116#391—261no—
117#391—261no—
118#382—261no—
119#382—261no—
120C43C2×D1311yescharacteristic
121#336—21no—
122#336—21no—
123#336—132no—
124#336—261no—
125#336C2×D1312yes—
126C22×C13#40811yescharacteristic
127C22×C13#41011yescharacteristic
128C22×C13C2×#10011yescharacteristic
129C22×C13#41911yescharacteristic
130C22×C13#41911yescharacteristic
131C22×C13C2×#10411yescharacteristic
132C22×C13#42111yescharacteristic
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—41no—
139C4×C13—41no—
140Dic13—82no—
141Dic13—82no—
142C22×Q8—132no—
143C22×Q8—261no—
144C22×C8—22no—
145C22×C8—262no—
146C4⋊Q8—522no—
147C4⋊Q8—522no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—261no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—261no—
152C2×C42C4×D1311yescharacteristic
153C2×C42C4×D1311yescharacteristic
154C2×C42D5211yescharacteristic
155C2×C42D5211yescharacteristic
156C2×C42C22⋊D1311yescharacteristic
157C2×C42C22⋊D1311yescharacteristic
158C2×C42C22×D1311yescharacteristic
159#97—264no—
160#95—262no—
161#95—262no—
162#95—262no—
163#95—262no—
164C2×C13#146911yescharacteristic
165C2×C13#148511yescharacteristic
166C2×C13#149711yescharacteristic
167C2×C13#150611yescharacteristic
168C2×C13#151511yescharacteristic
169C2×C13#152711yescharacteristic
170C2×C13#155811yescharacteristic
171C2×Q8—264no—
172C2×Q8—522no—
173C2×Q8—522no—
174C2×Q8—522no—
175C2×Q8—522no—
176C2×Q8—522no—
177C22×C4—262no—
178C22×C4—262no—
179C22×C4#610311yescharacteristic
180C22×C4#610311yescharacteristic
181C22×C4#610311yescharacteristic
182C22×C4#610311yescharacteristic
183C22×C4C2×C4×D1311yescharacteristic
184C22×C4C2×D5211yescharacteristic
185C22×C4C2×C22⋊D1311yescharacteristic
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—264no—
190C2×C8—522no—
191C2×C8—522no—
192C4⋊C4—522no—
193C4⋊C4—522no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42—41no—
203C13#770211yescharacteristic, complemented, Sylow
204C23C2×#610311yescharacteristic
205Q8—1044no—
206Q8—1044no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4#8806312yes—
230C2×C4#8806512yes—
231C2×C4#8815512yes—
232C2×C4#8816312yes—
233C2×C4#8820512yes—
234C8—82no—
235C8—524no—
236C22#1171866511yescharacteristic
237C22#1171866611yescharacteristic
238C22#1171866711yescharacteristic
239C22#1171877111yescharacteristic
240C22#1171878111yescharacteristic
241C22C2×#8806311yescharacteristic
242C22C2×#8806511yescharacteristic
243C4—22no—
244C4—22no—
245C4—22no—
246C4—22no—
247C4—22no—
248C4—41no—
249C4—41no—
250C4—1042no—
251C4—1042no—
252C2#1311318711yescharacteristic
253C2#1311325611yescharacteristic
254C2#1311331011yescharacteristic
255C2#1311334911yescharacteristic
256C2#1311338611yescharacteristic
257C2#1311343511yescharacteristic
258C2#1311356111yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1839C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1839D13
hypocenterC13#7702
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
203. C13#7702semidirect

Maximal subgroups

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

subgroupindex
#131232142
#131145852
#131126612
C13×#18392
#770213