Finite Group Databasebeta

← #16787250

Subgroups — #16787250

Order 3328.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#13130098C211yesmaximal, characteristic
2#13130078C211yesmaximal, characteristic
3#13129777C214yesmaximal
4#13120052C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Dic26C2211yescharacteristic
7#11719130—21no—
8#11719125—21no—
9#11718891—21no—
10#11718891—21no—
11#11718643—21no—
12#11718643—21no—
13#11718638C2212yes—
14#11718635C412yes—
15C4×C4⋊Dic13C411yescharacteristic
16#11718286—21no—
17#11718286—21no—
18#11718285C2212yes—
19#11718285C2212yes—
20C22×Q8×C13—21no—
21C22×Dic26C2×C411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13C2311yescharacteristic
29C2×#6101D411yescharacteristic
30C2×#6101D411yescharacteristic
31C2×C4×Dic13C2×C412yes—
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C4×Dic26—41no—
35C4×Dic26—41no—
36C22⋊#1057—22no—
37C22⋊#1057—22no—
38#88112—41no—
39#88110—41no—
40C4⋊#1057—41no—
41C4×#1057—41no—
42#88071—21no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#11573—131nomaximal, Sylow
48C2×Q8×C13—44no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C22×C4×C13—22no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—22no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C2×D411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C2×Dic26—22no—
61C2×Dic26—22no—
62C2×Dic26—41no—
63C2×#1057—42no—
64C2×#1057—42no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C42×C13—21no—
68C42×C13—21no—
69C4⋊Dic13—41no—
70C4⋊Dic13—42no—
71#6101—41no—
72#6101—41no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C4×Dic13—24no—
78#2568—131no—
79#1467—131no—
80#1461—131no—
81#1324—134no—
82C23×C13C2×C22⋊C411yescharacteristic
83Q8×C13—82no—
84Q8×C13—82no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—41no—
90C2×C4×C13—44no—
91C2×C4×C13—42no—
92C2×C4×C13#9911yescharacteristic
93C2×C4×C13#9911yescharacteristic
94C2×C4×C13#13112yes—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13#10112yes—
108Dic26—44no—
109#1057—82no—
110#1057—82no—
111C2×C4⋊Q8#26111yescharacteristic
112C2×C4×Q8—131no—
113#432—261no—
114#431—261no—
115#400—261no—
116#400—261no—
117#391—132no—
118#391—261no—
119#391—261no—
120#382—132no—
121C4×C4⋊C4—131no—
122#324—132no—
123#324—132no—
124#324—261no—
125#324—261no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13#40811yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13C2×#10111yescharacteristic
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—41no—
134C4×C13—82no—
135C4×C13#35512yes—
136Dic13—22no—
137Dic13—41no—
138Dic13—41no—
139Dic13—41no—
140Dic13—82no—
141C22×Q8—21no—
142C22×Q8—131no—
143C4⋊Q8—41no—
144C4⋊Q8—41no—
145C4×Q8—521no—
146C4×Q8—521no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—131no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C2×#26112yes—
153C2×C42—131no—
154C2×C42—131no—
155C2×C42—132no—
156C2×C42C2×#26111yescharacteristic
157C4⋊C8—521no—
158C4⋊C8—521no—
159C22⋊C8—262no—
160C22⋊C8—262no—
161#97—521no—
162C4×C8—521no—
163#95—262no—
164#95—262no—
165#95—262no—
166#95—262no—
167#95—261no—
168C2×C13—21no—
169C2×C13—21no—
170C2×C13#147211yescharacteristic
171C2×C13#212911yescharacteristic
172C2×C13C2×#35511yescharacteristic
173C2×Q8—44no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—262no—
177C2×Q8—262no—
178C2×Q8—521no—
179C22×C4—22no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—262no—
185C22×C4C22⋊#26111yescharacteristic
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—522no—
189C2×C8—522no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—521no—
193C4⋊C4—521no—
194C4⋊C4—521no—
195C4⋊C4—522no—
196C42—21no—
197C42—21no—
198C42—261no—
199C42—261no—
200C42—261no—
201C42—261no—
202C42—264no—
203C13#1157311yescharacteristic, complemented, Sylow
204C23C2×C22⋊#26111yescharacteristic
205Q8—82no—
206Q8—82no—
207Q8—524no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4—132no—
216C2×C4—261no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—261no—
222C2×C4—261no—
223C2×C4—521no—
224C2×C4—521no—
225C2×C4—522no—
226C2×C4—522no—
227C2×C4—522no—
228C2×C4#8811911yescharacteristic
229C2×C4#8811911yescharacteristic
230C2×C4#8824012yes—
231C8—1042no—
232C8—1042no—
233C22—21no—
234C22—21no—
235C22#1171915911yescharacteristic
236C22D13⋊#10111yescharacteristic
237C22C2×#8811911yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—82no—
242C4—262no—
243C4—521no—
244C4—521no—
245C4—521no—
246C4—1042no—
247C4#1171829512yes—
248C2—21no—
249C2—21no—
250C2#1313011611yescharacteristic
251C2#1313111811yescharacteristic
252C2C2×#1171829511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊Q8C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4⋊Q8#261
hypocenterC13#11573
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
203. C13#11573semidirect

Maximal subgroups

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

subgroupindex
#131300982
#131300782
#131297772
#131200522
#1157313