Finite Group Databasebeta

← #15773567

Subgroups — #15773567

Order 3328.

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

normal subgroups only

This group has 378 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#13112863C214yesmaximal
4C13×#2568C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#400C412yes—
8C13×#400C2212yes—
9C13×#391—21no—
10C13×#391—21no—
11C13×#391—21no—
12C13×#382—21no—
13C4×C13×C4⋊C4C411yescharacteristic
14C2×#88076—21no—
15#11718587—21no—
16C4×#6099—21no—
17#11718122C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13—21no—
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⋊C4C2×C412yes—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C42×C13—21no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×#6099—22no—
37C13×#95—22no—
38C13×#95—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#11794—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C2×Q8×C13—44no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—42no—
77#6099—24no—
78#6099—42no—
79C2×#1055—42no—
80C2×#1055—42no—
81#2568D1311yescharacteristic
82C4×#101—131no—
83#1467—131no—
84#1353—134no—
85C23×C13C2×C22⋊C411yescharacteristic
86Q8×C13—44no—
87Q8×C13—82no—
88Q8×C13—82no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—44no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#10412yes—
111C2×C4×C13#13712yes—
112#1055—44no—
113#1055—82no—
114C2×C4⋊Q8Dic1311yescharacteristic
115C2×C4×Q8C2×D1311yescharacteristic
116#432—261no—
117C2×#101—261no—
118C4×M16—261no—
119#400Dic1312yes—
120#400C2×D1312yes—
121#391—21no—
122#391—21no—
123#391—21no—
124#382—21no—
125C4×C4⋊C4Dic1311yescharacteristic
126#343—132no—
127#324—132no—
128#324—261no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13C2×#9911yescharacteristic
132C22×C13#41911yescharacteristic
133C22×C13C2×#10411yescharacteristic
134C4×C13—21no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—41no—
138C4×C13—41no—
139C4×C13—41no—
140C4×C13—41no—
141C4×C13—82no—
142C4×C13—82no—
143C4×C13#35512yes—
144C22×Q8—21no—
145C22×Q8C22⋊D1311yescharacteristic
146C2×M16—262no—
147C4⋊Q8—41no—
148C4⋊Q8—41no—
149C4×Q8—41no—
150C4×Q8—41no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic1312yes—
154C2×C4⋊C4C2×Dic1311yescharacteristic
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C4⋊C4C22×D1311yescharacteristic
157C2×C42—21no—
158C2×C42C2×Dic1311yescharacteristic
159C2×C42C22⋊D1311yescharacteristic
160C2×C42C22⋊D1311yescharacteristic
161C4⋊C8—521no—
162#101—264no—
163C22⋊C8—262no—
164#97—521no—
165#97—521no—
166C4×C8—521no—
167#95—22no—
168#95—22no—
169#95—22no—
170#95—22no—
171#95C2×Dic1312yes—
172C2×C13—21no—
173C2×C13—21no—
174C2×C13#150811yescharacteristic
175C2×C13#212311yescharacteristic
176C2×C13C2×#35511yescharacteristic
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—44no—
181C2×Q8—41no—
182C2×Q8—41no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C22⋊Dic1311yescharacteristic
186C22×C4C22⋊Dic1311yescharacteristic
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22⋊Dic1311yescharacteristic
189C22×C4C22×Dic1311yescharacteristic
190C22×C4C2×C22⋊D1311yescharacteristic
191C22×C4C2×C22⋊D1311yescharacteristic
192M16—264no—
193M16—522no—
194C2×C8—522no—
195C2×C8—522no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—42no—
209C13#1179411yescharacteristic, complemented, Sylow
210C23C2×C22⋊Dic1311yescharacteristic
211Q8—44no—
212Q8—82no—
213Q8—82no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4#8807411yescharacteristic
234C2×C4#8807411yescharacteristic
235C2×C4#8807712yes—
236C2×C4#8819612yes—
237C8—524no—
238C8—1042no—
239C22—21no—
240C22—21no—
241C22C2×#8807411yescharacteristic
242C22#1171888611yescharacteristic
243C22C2×#8807711yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—82no—
252C4—82no—
253C4#1171813412yes—
254C2—21no—
255C2—21no—
256C2#1311335611yescharacteristic
257C2#1311649011yescharacteristic
258C2C2×#1171813411yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2568C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2568D13
hypocenterC13#11794
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
209. C13#11794semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131802
#131128632
C13×#25682
#1179413