Finite Group Databasebeta

← #15756521

Subgroups — #15756521

Order 3328.

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

normal subgroups only

This group has 426 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#13117809C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13112738C212yesmaximal, complemented
4#13112695C212yesmaximal, complemented
5C13×#1460C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#431C2212yes—
8#11718882—21no—
9C2×#88073—21no—
10#11718872C412yes—
11C4×C22⋊Dic13C412yes—
12C4⋊C4×Dic13—21no—
13#11718612—22no—
14#11718597C2211yescharacteristic
15C4×C4⋊Dic13C2211yescharacteristic
16#11718585C2212yes—
17C13×#323—22no—
18#11718122—21no—
19C22×D4×C13D411yescharacteristic
20C23×C4×C13C2×C412yes—
21C4×D4×C13—22no—
22C4×D4×C13—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C13×C22⋊C4D412yes—
25C2×C42×C13C2311yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—22no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—22no—
32C2×#6099—22no—
33C13×C4⋊C8—22no—
34C13×C22⋊C8—22no—
35C4×C8×C13—22no—
36#88073—42no—
37#88071—22no—
38#88071—21no—
39#88071C2×C411yescharacteristic
40#88071C2×C411yescharacteristic
41#88071C2×C412yes—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44#8771—131nomaximal, Sylow
45C24×C13C22⋊C412yes—
46C2×D4×C13—22no—
47C2×D4×C13—22no—
48C2×D4×C13—21no—
49C2×D4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—82no—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—22no—
59C22×Dic13—21no—
60C2×C8×C13—42no—
61C13×C4⋊C4—22no—
62C13×C22⋊C4—24no—
63C42×C13#4112yes—
64C42×C13#4112yes—
65C22⋊Dic13—44no—
66C22⋊Dic13—82no—
67C4⋊Dic13—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70C4×Dic13—42no—
71C4×Dic13—82no—
72#6099—42no—
73#6099—42no—
74C2×#1055—42no—
75#2357—131no—
76#1800—131no—
77#1460D1311yescharacteristic
78#1303—132no—
79#1286—132no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—42no—
85C23×C13C2×C22⋊C411yescharacteristic
86D4×C13—42no—
87D4×C13—42no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—82no—
93C2×C4×C13—82no—
94C2×C4×C13#11711yescharacteristic
95C2×C4×C13#11711yescharacteristic
96C2×C4×C13#12312yes—
97C2×C4×C13#12312yes—
98C2×C4×C13#13512yes—
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C13#13711yescharacteristic
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—41no—
104C2×Dic13—42no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C8×C13—82no—
111#1055—82no—
112C2×C4×D4C2×D1311yescharacteristic
113#431C2×D1312yes—
114#423—132no—
115C2×#100—261no—
116#390—261no—
117#388—262no—
118#382—131no—
119#381—132no—
120C4×C4⋊C4—131no—
121C4×C4⋊C4—261no—
122C4×C22⋊C4—132no—
123#343—261no—
124#323—22no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—82no—
131C22×C13—82no—
132C22×C13#38111yescharacteristic
133C22×C13#41611yescharacteristic
134C22×C13#41711yescharacteristic
135C4×C13—22no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13#48212yes—
140C4×C13#48512yes—
141Dic13—42no—
142Dic13—81no—
143Dic13—82no—
144C22×D4D5211yescharacteristic
145C23×C4C4×D1312yes—
146C2×M16—262no—
147C4×D4—22no—
148C4×D4—22no—
149C2×C4⋊C4—261no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4D5211yescharacteristic
152C2×C22⋊C4—262no—
153C2×C22⋊C4—262no—
154C2×C22⋊C4C22⋊D1312yes—
155C2×C42—261no—
156C2×C42—262no—
157C2×C42C22×D1311yescharacteristic
158C4⋊C8—22no—
159C4⋊C8—262no—
160C4⋊C8—262no—
161#100—522no—
162C22⋊C8—22no—
163C4×C8—22no—
164#95—131no—
165#95—132no—
166#95—131no—
167#95—262no—
168#95—261no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13—82no—
172C2×C13#182511yescharacteristic
173C2×C13#182711yescharacteristic
174C2×C13#182911yescharacteristic
175C24#610312yes—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—21no—
179C2×D4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—82no—
183C22×C4—261no—
184C22×C4—262no—
185C22×C4—261no—
186C22×C4#610312yes—
187C22×C4C2×C4×D1311yescharacteristic
188C22×C4C2×D5211yescharacteristic
189C22×C4C2×C22⋊D1311yescharacteristic
190M16—522no—
191M16—522no—
192C2×C8—42no—
193C2×C8—522no—
194C4⋊C4—22no—
195C4⋊C4—522no—
196C4⋊C4—521no—
197C4⋊C4—521no—
198C22⋊C4—24no—
199C22⋊C4—524no—
200C22⋊C4—1042no—
201C42—522no—
202C42—1042no—
203C42#612912yes—
204C42#612912yes—
205C13#877111yescharacteristic, complemented, Sylow
206C23—22no—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C2×#610311yescharacteristic
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4—262no—
221C2×C4—521no—
222C2×C4—521no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—521no—
228C2×C4—522no—
229C2×C4#8813111yescharacteristic
230C2×C4#8813111yescharacteristic
231C2×C4#8814012yes—
232C2×C4#8815812yes—
233C2×C4#8816211yescharacteristic
234C2×C4#8816311yescharacteristic
235C2×C4#8818912yes—
236C8—82no—
237C8—1042no—
238C22—21no—
239C22—21no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22—82no—
245C22#1171860411yescharacteristic
246C22#1171877411yescharacteristic
247C22#1171879411yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—522no—
253C4—1041no—
254C4—1042no—
255C4#1171838412yes—
256C4#1171839812yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1311493211yescharacteristic
261C2#1311493711yescharacteristic
262C2#1311494511yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1460C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#1460D13
hypocenterC13#8771
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13112738C2semidirect
4. #13112695C2semidirect
205. C13#8771semidirect

Maximal subgroups

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

subgroupindex
#131178092
#131148282
#131127382
#131126952
C13×#14602
#877113