Finite Group Databasebeta

← #15773571

Subgroups — #15773571

Order 3328.

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

normal subgroups only

This group has 394 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
1C4×#88076C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112866C214yesmaximal
4C13×#2567C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#395C412yes—
8C13×#395C2212yes—
9C13×#391—21no—
10C13×#389—21no—
11C13×#389—21no—
12C13×#384—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718587—21no—
16C4×#6099—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13C2×C412yes—
21C22×Q8×C13D411yescharacteristic
22C13×C4⋊Q8—41no—
23C13×C4⋊Q8—41no—
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95C2×C412yes—
42#88076—24no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45#88043—41no—
46#88043—41no—
47C4×#1055—41no—
48#11795—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C2×Q8×C13—42no—
53C2×Q8×C13—82no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C13×C4⋊C4—24no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—82no—
71C13×C4⋊C4—82no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—42no—
79#6099—24no—
80#6099—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83#2567D1311yescharacteristic
84C4×#101—131no—
85#1467—131no—
86#1354—134no—
87C23×C13C2×C22⋊C411yescharacteristic
88Q8×C13—44no—
89Q8×C13—84no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—24no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#9911yescharacteristic
112C2×C4×C13#10412yes—
113C2×C4×C13#13712yes—
114#1055—44no—
115#1055—82no—
116C2×C4⋊Q8Dic1311yescharacteristic
117C2×C4×Q8C2×D1311yescharacteristic
118#432—261no—
119C2×#101—261no—
120C4×M16—261no—
121#395Dic1312yes—
122#395C2×D1312yes—
123#391—21no—
124#389—21no—
125#389—21no—
126#384—21no—
127C4×C4⋊C4Dic1311yescharacteristic
128#343—132no—
129#324—132no—
130#324—261no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13C2×#9911yescharacteristic
134C22×C13#41911yescharacteristic
135C22×C13C2×#10411yescharacteristic
136C4×C13—21no—
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—44no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—82no—
145C4×C13#35612yes—
146C22×Q8C2×Dic1312yes—
147C22×Q8C22⋊D1311yescharacteristic
148C2×M16—262no—
149C4⋊Q8—41no—
150C4⋊Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4C2×Dic1311yescharacteristic
159C2×C4⋊C4C22⋊D1311yescharacteristic
160C2×C4⋊C4C22×D1311yescharacteristic
161C2×C42—21no—
162C2×C42C2×Dic1311yescharacteristic
163C2×C42C22⋊D1311yescharacteristic
164C2×C42C22⋊D1311yescharacteristic
165C4⋊C8—521no—
166#101—264no—
167C22⋊C8—262no—
168#97—521no—
169#97—521no—
170C4×C8—521no—
171#95—22no—
172#95—22no—
173#95C2×Dic1312yes—
174C2×C13—21no—
175C2×C13—21no—
176C2×C13#150811yescharacteristic
177C2×C13#212211yescharacteristic
178C2×C13C2×#35611yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—42no—
183C2×Q8—82no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic1311yescharacteristic
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22⋊Dic1311yescharacteristic
189C22×C4C22⋊Dic1311yescharacteristic
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1311yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193M16—264no—
194M16—522no—
195C2×C8—522no—
196C2×C8—522no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—42no—
213C13#1179511yescharacteristic, complemented, Sylow
214C23C2×C22⋊Dic1311yescharacteristic
215Q8—44no—
216Q8—84no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4#8807411yescharacteristic
238C2×C4#8807411yescharacteristic
239C2×C4#8807712yes—
240C2×C4#8819612yes—
241C8—524no—
242C8—1042no—
243C22—21no—
244C22—21no—
245C22C2×#8807411yescharacteristic
246C22#1171888611yescharacteristic
247C22C2×#8807711yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4#1171814012yes—
258C2—21no—
259C2—21no—
260C2#1311335611yescharacteristic
261C2#1311648611yescharacteristic
262C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2567C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2567D13
hypocenterC13#11795
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
213. C13#11795semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131802
#131128662
C13×#25672
#1179513