Finite Group Databasebeta

← #15779203

Subgroups — #15779203

Order 3328.

334 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 95 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#13114940C212yesmaximal
2#13112965C212yesmaximal
3#13112959C211yesmaximal, characteristic
4#13112957C211yesmaximal, characteristic
5C13×#2923C211yesmaximal, characteristic
6C4×C13×#41C2211yescharacteristic
7C13×#433—22no—
8C13×#432—22no—
9C13×#424C411yescharacteristic, complemented
10C13×#424C411yescharacteristic, complemented
11C13×#408C2211yescharacteristic
12C13×#408C2211yescharacteristic
13C4×C13×M16C411yescharacteristic, complemented
14C2×C13×#97C411yescharacteristic, complemented
15#11718901C2212yes—
16#11718898C2212yes—
17#11718123—22no—
18#11718115—22no—
19C2×C13×#41C2311yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C13×M16C2×C411yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2×C411yescharacteristic
24C4×Q8×C13—21no—
25C4×D4×C13—21no—
26C4×D4×C13—22no—
27C13×#117C2×C411yescharacteristic
28C13×#117D412yes—
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D412yes—
31#88180—22no—
32C2×#6099—22no—
33C13×C4⋊C8—22no—
34C13×C4⋊C8—22no—
35C13×C22⋊C8—22no—
36C13×C22⋊C8—22no—
37C13×#97—21no—
38C13×#97—21no—
39C13×#97—21no—
40C4×C8×C13—21no—
41#88076—22no—
42#88074—22no—
43#88074—22no—
44#88073—22no—
45#12865—131nomaximal, Sylow
46C13×#41—41no—
47C13×#41—41no—
48C2×Q8×C13#4111yescharacteristic
49C2×D4×C13#4111yescharacteristic
50C2×D4×C13#4112yes—
51C22×C4×C13—21no—
52C22×C4×C13—22no—
53C22×C4×C13C22×C411yescharacteristic
54C22×C4×C13C2×D412yes—
55C13×M16—41no—
56C13×M16—41no—
57C2×C8×C13—21no—
58C2×C8×C13—21no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13—41no—
62C2×C8×C13—41no—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—22no—
65C13×C22⋊C4—21no—
66C13×C22⋊C4—22no—
67C42×C13—21no—
68C42×C13—22no—
69C42×C13C22⋊C411yescharacteristic
70C42×C13C22⋊C412yes—
71C42×C13C22⋊C411yescharacteristic
72C22⋊Dic13—42no—
73C4⋊Dic13—42no—
74C4×Dic13—42no—
75#6099—42no—
76#6099—42no—
77C2×#1055—42no—
78#2923D1311yescharacteristic
79#1827—132no—
80#1395—132no—
81#1392—131no—
82#1391—131no—
83C23×C13#11711yescharacteristic
84C23×C13#12312yes—
85Q8×C13—41no—
86D4×C13—42no—
87D4×C13—41no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—81no—
96C2×C4×C13—82no—
97C2×C4×C13C2×C22⋊C411yescharacteristic
98C2×C4×C13#11711yescharacteristic
99C2×C4×C13#12312yes—
100C2×Dic13—82no—
101C8×C13—41no—
102C8×C13—41no—
103C8×C13—41no—
104C8×C13—41no—
105#1055—82no—
106C4×#41C2×D1311yescharacteristic
107#433—22no—
108#432—22no—
109#424Dic1311yescharacteristic, complemented
110#424Dic1311yescharacteristic, complemented
111#413—132no—
112#410—132no—
113#408C2×D1311yescharacteristic
114#408C2×D1311yescharacteristic
115C4×M16Dic1311yescharacteristic, complemented
116C2×#97Dic1311yescharacteristic, complemented
117#339—262no—
118H(3,ℤ/4)—262no—
119C22×C13—22no—
120C22×C13—21no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13#38111yescharacteristic
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13—41no—
129C4×C13#41011yescharacteristic
130C4×C13#41011yescharacteristic
131Dic13—162no—
132C2×#41C22×D1311yescharacteristic
133C2×M16—262no—
134C2×M16C2×Dic1311yescharacteristic
135C2×M16C2×Dic1311yescharacteristic
136C22×C8C2×Dic1311yescharacteristic
137C22×C8C2×Dic1311yescharacteristic
138C4×Q8—21no—
139C4×D4—21no—
140C4×D4—22no—
141#117—262no—
142#117C2×Dic1311yescharacteristic
143#117C22⋊D1312yes—
144C2×C42C2×Dic1311yescharacteristic
145C2×C42C22⋊D1312yes—
146C4⋊C8—22no—
147C4⋊C8—22no—
148#101—262no—
149#100—262no—
150#99—262no—
151#99—262no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154#97—21no—
155#97—21no—
156#97—21no—
157C4×C8—21no—
158C2×C13—21no—
159C2×C13—42no—
160C2×C13—41no—
161C2×C13#182011yescharacteristic
162#41—41no—
163#41—41no—
164C2×Q8#612711yescharacteristic
165C2×D4#612711yescharacteristic
166C2×D4#612712yes—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4C22×Dic1311yescharacteristic
170C22×C4C2×C22⋊D1312yes—
171M16—41no—
172M16—41no—
173M16—522no—
174M16—522no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—522no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—522no—
185C22⋊C4—21no—
186C22⋊C4—22no—
187C22⋊C4—522no—
188C42—21no—
189C42—22no—
190C42—522no—
191C42C22⋊Dic1311yescharacteristic
192C42C22⋊Dic1312yes—
193C42C22⋊Dic1311yescharacteristic
194C13#1286511yescharacteristic, complemented, Sylow
195C23#8818011yescharacteristic
196C23#8818312yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—81no—
208C2×C4—82no—
209C2×C4—1042no—
210C2×C4#8818011yescharacteristic
211C2×C4#8818312yes—
212C2×C4C2×C22⋊Dic1311yescharacteristic
213C8—41no—
214C8—41no—
215C8—41no—
216C8—41no—
217C8—1042no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1171887211yescharacteristic
223C4—22no—
224C4—21no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—2082no—
229C4#1171890111yescharacteristic
230C4#1171890111yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1311491311yescharacteristic
subgroupG/H
centerC4#11718901
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#2923C2
socleC2×C13#1820
prime radical, cosocleC2×C13×#41C23
hypercenter#2923D13
hypocenterC13#12865
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
9. C13×#424C4semidirect
10. C13×#424C4semidirect
13. C4×C13×M16C4semidirect
14. C2×C13×#97C4semidirect
109. #424Dic13semidirect
110. #424Dic13semidirect
115. C4×M16Dic13semidirect
116. C2×#97Dic13semidirect
194. C13#12865semidirect

Maximal subgroups

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

subgroupindex
#131149402
#131129652
#131129592
#131129572
C13×#29232
#1286513