Finite Group Databasebeta

← #16802187

Subgroups — #16802187

Order 3328.

578 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 176 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#13131629C212yesmaximal
2#13131024C212yesmaximal
3#13130903C214yesmaximal
4#13130902C214yesmaximal
5#13130761C211yesmaximal, characteristic
6#13130554C211yesmaximal, characteristic
7#13125345C211yesmaximal, characteristic
8#11719433C2212yes—
9#11719158—24no—
10#11719079C2214yes—
11#11719078—24no—
12#11719072C2214yes—
13#11719057C2211yescharacteristic
14#11719053C2212yes—
15#11719047C2211yescharacteristic
16C13×#498C411yescharacteristic, complemented
17#11718739C412yescomplemented
18#11718521C2214yes—
19#11718519C414yescomplemented
20C4×C8×D13C2211yescharacteristic
21#11718341C411yescharacteristic, complemented
22#11718268C2214yes—
23(C2×#261)⋊C8C2212yes—
24(C2×#261)⋊C8C2212yes—
25#11718247C2214yes—
26#11718247C2214yes—
27C2×C4×#261C2311yescharacteristic
28C2×C4×#261C2311yescharacteristic
29C2×#6118C2314yes—
30C2×D13⋊C8C2312yes—
31C13×C4⋊Q8C2×C412yes—
32#88200—22no—
33Q8×Dic13—22no—
34C2×C8×D13C2312yes—
35#88151—22no—
36#88146C2314yes—
37#88144C2×C414yes—
38#88141—22no—
39C42×D13C2311yescharacteristic
40#88123C2×C412yes—
41(C2×#261)⋊C4—22no—
42#88112—24no—
43#88112—22no—
44#88112—22no—
45#88110—24no—
46#88110D414yes—
47C4⋊#1057—24no—
48C4×#1057—24no—
49C13×#106C2×C414yes—
50C4×C8×C13C2×C411yescharacteristic
51#88057C2×C414yes—
52C8×Dic13C2×C412yes—
53#88047C2×C418yes—
54C4×#1055C2×C411yescharacteristic
55#22258—131nomaximal, Sylow
56C22×#261—21no—
57C22×#261—21no—
58C2×Q8×C13—22no—
59C2×C4×D13#4112yes—
60C2×C4×D13C2411yescharacteristic
61C2×Dic26—22no—
62C2×#1057—24no—
63C2×#1057C2×D414yes—
64C4×#261—22no—
65C4×#261—22no—
66#6118—24no—
67#6118—24no—
68D13⋊C8—22no—
69D13⋊C8—22no—
70C2×C8×C13C22×C412yes—
71C13×C4⋊C4—22no—
72C13×C4⋊C4C22×C414yes—
73C42×C13C22×C411yescharacteristic
74#6103—24no—
75C4⋊Dic13—22no—
76C4⋊Dic13—24no—
77C4⋊Dic13C22×C414yes—
78#6101—24no—
79C4×Dic13—24no—
80C4×Dic13C22×C411yescharacteristic
81C4×Dic13C2×D412yes—
82C2×#1055C22×C412yes—
83C8×D13—22no—
84C8×D13—22no—
85#3160—131no—
86#2961—132no—
87#1995—132no—
88#1922—134no—
89#1922—134no—
90#1837—131no—
91#1746—131no—
92C22×D13C2×#4111yescharacteristic
93C2×#261—42no—
94C2×#261—42no—
95C2×#261—41no—
96C2×#261—41no—
97Q8×C13—82no—
98C2×C4×C13—24no—
99C2×C4×C13C4×D412yes—
100C2×C4×C13C23×C411yescharacteristic
101C2×Dic13—24no—
102C2×Dic13C4×D412yes—
103C2×Dic13C22×D411yescharacteristic
104C4×D13—42no—
105C4×D132−1+412yes—
106C4×D132−1+412yes—
107Dic26—82no—
108#1057—24no—
109#1057—44no—
110C8×C13—22no—
111#1055—22no—
112#533—132no—
113#500—132no—
114#499—134no—
115#498—131no—
116#498#26111yescharacteristic, complemented
117#446—264no—
118#446—264no—
119#427—134no—
120#424—134no—
121#423—132no—
122#405—134no—
123C2×#97—131no—
124C2×C4×C8—131no—
125#376—131no—
126#341—134no—
127#339—134no—
128#339—134no—
129#336—132no—
130#336—132no—
131C22×C13C2×C4×D411yescharacteristic
132C2×D13—22no—
133C2×D13#54111yescharacteristic
134C2×D13#54111yescharacteristic
135#261—81no—
136#261—81no—
137C4×C13—22no—
138C4×C13—44no—
139C4×C13#51912yes—
140Dic13—22no—
141Dic13—44no—
142Dic13#53612yes—
143C2×M16—134no—
144C22×C8—132no—
145C22×C8—132no—
146C4⋊Q8—132no—
147C4⋊Q8C2×#26112yes—
148#125—134no—
149C22⋊Q8—262no—
150C22⋊Q8—262no—
151C4×Q8—262no—
152C4×Q8—262no—
153#117—134no—
154C2×C42—131no—
155C2×C42—131no—
156C2×C42—131no—
157#107—138no—
158#106—134no—
159#106C2×#26114yes—
160C4⋊C8—262no—
161C4⋊C8—262no—
162C4⋊C8—264no—
163C4⋊C8—264no—
164#97—134no—
165#97—264no—
166C4×C8—132no—
167C4×C8—131no—
168C4×C8—264no—
169C4×C8C2×#26111yescharacteristic
170#95—262no—
171C2×C13#232711yescharacteristic
172C2×C13#295712yes—
173D13—21no—
174D13—21no—
175C2×Q8—22no—
176C2×Q8—262no—
177C22×C4—131no—
178C22×C4—132no—
179C22×C4—261no—
180C22×C4—261no—
181M16—264no—
182M16—264no—
183C2×C8—134no—
184C2×C8—132no—
185C2×C8—262no—
186C2×C8—262no—
187C2×C8—262no—
188C2×C8—262no—
189C2×C8—264no—
190C2×C8C22×#26112yes—
191C4⋊C4—22no—
192C4⋊C4—134no—
193C4⋊C4—264no—
194C4⋊C4—264no—
195C4⋊C4—262no—
196C4⋊C4C22×#26114yes—
197C22⋊C4—264no—
198C42—132no—
199C42—131no—
200C42—264no—
201C42—262no—
202C42—262no—
203C42C22×#26111yescharacteristic
204C13#2225811yescharacteristic, complemented, Sylow
205C23—131no—
206Q8—82no—
207Q8—1042no—
208C2×C4—24no—
209C2×C4—131no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—132no—
213C2×C4—264no—
214C2×C4—522no—
215C2×C4—521no—
216C2×C4—521no—
217C2×C4—522no—
218C2×C4—522no—
219C2×C4D4×#26112yes—
220C2×C4C23×#26111yescharacteristic
221C8—22no—
222C8—264no—
223C8—262no—
224C8—524no—
225C22—131no—
226C22—131no—
227C22—262no—
228C22C2×D4×#26111yescharacteristic
229C4—22no—
230C4—44no—
231C4—132no—
232C4—262no—
233C4—524no—
234C4—1041no—
235C4—1041no—
236C4#1171962712yes—
237C2—261no—
238C2—261no—
239C2#1313132711yescharacteristic
240C2#1313161412yes—
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#498C4
socleC22×C13C2×C4×D4
prime radicalC22×D13C2×#41
cosocleC2×C4×D13C24
hypercenter#498#261
hypocenterC13#22258
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
16. C13×#498C4semidirect
17. #11718739C4semidirect
19. #11718519C4semidirect
21. #11718341C4semidirect
116. #498#261semidirect
204. C13#22258semidirect

Maximal subgroups

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

subgroupindex
#131316292
#131310242
#131309032
#131309022
#131307612
#131305542
#131253452
#2225813