Finite Group Databasebeta

← #15756515

Subgroups — #15756515

Order 3328.

426 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114828C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112739C212yesmaximal, complemented
4#13112694C212yesmaximal, complemented
5C13×#2357C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#390—21no—
8C13×#388—22no—
9C13×#382C2211yescharacteristic
10C13×#381C412yes—
11C4×C13×C4⋊C4—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C4×C13×C22⋊C4C412yes—
14C2×#88073—21no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718122—21no—
18#11718117—22no—
19C22×D4×C13D411yescharacteristic
20C23×C4×C13C2×C412yes—
21C4×D4×C13—22no—
22C4×D4×C13—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4D412yes—
29C2×C42×C13—21no—
30C2×C42×C13—22no—
31C2×C42×C13C2311yescharacteristic
32C2×#6099—22no—
33C13×#95—22no—
34C13×#95—21no—
35C13×#95C2×C411yescharacteristic
36C13×#95C2×C412yes—
37C13×#95C2×C411yescharacteristic
38#88073—42no—
39C22⋊#1055—22no—
40C4⋊#1055—22no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43C4×#1055—22no—
44#8770—131nomaximal, Sylow
45C24×C13C22⋊C412yes—
46C2×D4×C13—22no—
47C2×D4×C13—22no—
48C2×D4×C13—21no—
49C2×D4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—21no—
55C22×C4×C13—82no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C13×C4⋊C4—22no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—24no—
64C13×C22⋊C4—44no—
65C13×C22⋊C4—82no—
66C42×C13—41no—
67C42×C13—41no—
68C42×C13—82no—
69C42×C13#4112yes—
70C42×C13#4112yes—
71#6099—42no—
72#6099—42no—
73C2×#1055—42no—
74C2×#1055—42no—
75#2357D1311yescharacteristic
76#1800—131no—
77#1460—131no—
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—22no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—82no—
102C2×C4×C13—82no—
103C2×C4×C13#11711yescharacteristic
104C2×C4×C13#11711yescharacteristic
105C2×C4×C13#12312yes—
106C2×C4×C13#12312yes—
107C2×C4×C13#13512yes—
108C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C13#13711yescharacteristic
110#1055—82no—
111#1055—82no—
112C2×C4×D4C2×D1311yescharacteristic
113#431—132no—
114#423—132no—
115C2×#100—261no—
116#390—21no—
117#388—22no—
118#382C2×D1311yescharacteristic
119#381Dic1312yes—
120C4×C4⋊C4—21no—
121C4×C4⋊C4C2×D1311yescharacteristic
122C4×C22⋊C4Dic1312yes—
123#343—261no—
124#323—262no—
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—42no—
140C4×C13—81no—
141C4×C13—82no—
142C4×C13#48212yes—
143C4×C13#48512yes—
144C22×D4C22⋊D1311yescharacteristic
145C23×C4C2×Dic1312yes—
146C2×M16—262no—
147C4×D4—22no—
148C4×D4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D1311yescharacteristic
152C2×C22⋊C4—22no—
153C2×C22⋊C4—22no—
154C2×C22⋊C4C22⋊D1312yes—
155C2×C42—21no—
156C2×C42—22no—
157C2×C42C22×D1311yescharacteristic
158C4⋊C8—262no—
159C4⋊C8—262no—
160C4⋊C8—262no—
161#100—522no—
162C22⋊C8—262no—
163C4×C8—262no—
164#95—22no—
165#95—21no—
166#95C2×Dic1311yescharacteristic
167#95C2×Dic1312yes—
168#95C2×Dic1311yescharacteristic
169C2×C13—21no—
170C2×C13—21no—
171C2×C13—82no—
172C2×C13#182511yescharacteristic
173C2×C13#182711yescharacteristic
174C2×C13#182911yescharacteristic
175C24C22⋊Dic1312yes—
176C2×D4—22no—
177C2×D4—21no—
178C2×D4—22no—
179C2×D4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—21no—
185C22×C4—82no—
186C22×C4C22⋊Dic1312yes—
187C22×C4C22×Dic1311yescharacteristic
188C22×C4C2×C22⋊D1311yescharacteristic
189C22×C4C2×C22⋊D1311yescharacteristic
190M16—522no—
191M16—522no—
192C2×C8—522no—
193C2×C8—522no—
194C4⋊C4—22no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C22⋊C4—24no—
198C22⋊C4—44no—
199C22⋊C4—82no—
200C42—41no—
201C42—41no—
202C42—82no—
203C42#612712yes—
204C42#612712yes—
205C13#877011yescharacteristic, complemented, Sylow
206C23—22no—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C2×C22⋊Dic1311yescharacteristic
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4—82no—
229C2×C4#8818011yescharacteristic
230C2×C4#8818011yescharacteristic
231C2×C4#8818312yes—
232C2×C4#8818312yes—
233C2×C4#8820311yescharacteristic
234C2×C4#8820412yes—
235C2×C4#8820511yescharacteristic
236C8—1042no—
237C8—1042no—
238C22—21no—
239C22—21no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22—82no—
245C22#1171887211yescharacteristic
246C22#1171889311yescharacteristic
247C22#1171889411yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—82no—
255C4#1171865712yes—
256C4#1171866412yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1311493111yescharacteristic
261C2#1311494011yescharacteristic
262C2#1311494711yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2357C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2357D13
hypocenterC13#8770
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #13112739C2semidirect
4. #13112694C2semidirect
205. C13#8770semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131572
#131127392
#131126942
C13×#23572
#877013