Finite Group Databasebeta

← #15772561

Subgroups — #15772561

Order 3328.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#13119821C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112769C214yesmaximal
4C13×#1461C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88198C412yes—
7C2×#88123C411yescharacteristic
8C13×#431—21no—
9#11718644—21no—
10#11718644—21no—
11#11718635C2212yes—
12C4×C4⋊Dic13C411yescharacteristic
13#11718589—21no—
14#11718589—21no—
15#11718587—21no—
16C13×#324—21no—
17C13×#324C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13C2×C411yescharacteristic
21C22×Dic26C2×C412yes—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30#88198—44no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×#6101—22no—
35C2×#6101—22no—
36C2×C4×Dic13C2×C412yes—
37#88123—41no—
38#88123—41no—
39C13×C4⋊C8—41no—
40C13×C22⋊C8—22no—
41C4×C8×C13—41no—
42#88071—21no—
43#88071—22no—
44#88071—22no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47#88043—41no—
48#11568—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C2×Dic26—24no—
62C2×Dic26—42no—
63C2×Dic26—42no—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C4⋊Dic13—24no—
75C4⋊Dic13—42no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78#6101—44no—
79#6101—44no—
80C4×Dic13—42no—
81C2×#1055—42no—
82#2546—131no—
83#1467—131no—
84#1461D1311yescharacteristic
85#1319—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—44no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13#9911yescharacteristic
104C2×C4×C13#10012yes—
105C2×C4×C13#13112yes—
106C2×Dic13—24no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112Dic26—84no—
113C8×C13—82no—
114#1055—82no—
115C2×C4⋊Q8—132no—
116C2×C4⋊Q8—131no—
117C2×C4×Q8C2×D1311yescharacteristic
118#432—261no—
119#431—21no—
120#398—261no—
121#398—261no—
122#391—132no—
123#389—261no—
124#389—261no—
125C4×C4⋊C4—131no—
126#324—21no—
127#324—132no—
128#324—261no—
129#324C2×D1312yes—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13#40811yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13C2×#10011yescharacteristic
135C4×C13—21no—
136C4×C13—22no—
137C4×C13—22no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13#35612yes—
143Dic13—44no—
144Dic13—82no—
145C22×Q8—132no—
146C22×Q8C4×D1311yescharacteristic
147C4⋊Q8—521no—
148C4⋊Q8—521no—
149C4⋊Q8—524no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—261no—
153C2×C4⋊C4—262no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4D5211yescharacteristic
158C2×C4⋊C4C22⋊D1311yescharacteristic
159C2×C4⋊C4C22×D1311yescharacteristic
160C2×C42—132no—
161C2×C42C4×D1311yescharacteristic
162C2×C42D5211yescharacteristic
163C2×C42C22⋊D1311yescharacteristic
164C4⋊C8—41no—
165C4⋊C8—521no—
166C22⋊C8—22no—
167C22⋊C8—262no—
168#97—521no—
169C4×C8—41no—
170#95—261no—
171#95—262no—
172#95—262no—
173C2×C13—21no—
174C2×C13—21no—
175C2×C13#147111yescharacteristic
176C2×C13#212911yescharacteristic
177C2×C13C2×#35611yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—264no—
182C2×Q8—522no—
183C2×Q8—522no—
184C22×C4—262no—
185C22×C4—262no—
186C22×C4#610311yescharacteristic
187C22×C4#610311yescharacteristic
188C22×C4#610311yescharacteristic
189C22×C4#610311yescharacteristic
190C22×C4C2×C4×D1311yescharacteristic
191C22×C4C2×D5211yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193C2×C8—42no—
194C2×C8—522no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—264no—
199C4⋊C4—524no—
200C4⋊C4—522no—
201C4⋊C4—521no—
202C4⋊C4—521no—
203C4⋊C4—524no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—522no—
211C13#1156811yescharacteristic, complemented, Sylow
212C23C2×#610311yescharacteristic
213Q8—44no—
214Q8—1044no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—264no—
230C2×C4—522no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4#8804611yescharacteristic
236C2×C4#8804611yescharacteristic
237C2×C4#8806312yes—
238C2×C4#8815512yes—
239C8—82no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22C2×#8804611yescharacteristic
244C22#1171877111yescharacteristic
245C22C2×#8806311yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—524no—
254C4—1042no—
255C4#1171807012yes—
256C2—21no—
257C2—21no—
258C2#1311319511yescharacteristic
259C2#1311651011yescharacteristic
260C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11568
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
211. C13#11568semidirect

Maximal subgroups

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

subgroupindex
#131198212
#131131802
#131127692
C13×#14612
#1156813