Finite Group Databasebeta

← #15773572

Subgroups — #15773572

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#13120041C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13112867C214yesmaximal
4C13×#1467C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88123C411yescharacteristic
7C13×#432—21no—
8#11718891—21no—
9C2×#88076—21no—
10#11718640C412yes—
11#11718640C2212yes—
12#11718637—21no—
13C4×C4⋊Dic13C411yescharacteristic
14#11718589—21no—
15#11718589—21no—
16C4×#6099—21no—
17C13×#324—21no—
18C13×#324C2212yes—
19#11718122C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
22C4×Q8×C13—41no—
23C4×Q8×C13—41no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×C4×Dic13—21no—
36C2×#6099—22no—
37#88123—41no—
38#88123—41no—
39C13×C4⋊C8—41no—
40C13×C22⋊C8—22no—
41C13×#97—41no—
42#88076—24no—
43#88071—22no—
44#88071—22no—
45#88071C2×C412yes—
46#88043—41no—
47C4×#1055—41no—
48#11795—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—42no—
62C2×Dic26—82no—
63C2×C8×C13—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C42×C13—21no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—21no—
73C4⋊Dic13—24no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—82no—
78#6101—82no—
79C4×Dic13—42no—
80#6099—24no—
81#6099—42no—
82C2×#1055—42no—
83#2567—131no—
84C4×#101—131no—
85#1467D1311yescharacteristic
86#1354—134no—
87C23×C13C2×C22⋊C411yescharacteristic
88Q8×C13—44no—
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#9911yescharacteristic
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13#10412yes—
106C2×C4×C13#13712yes—
107C2×Dic13—24no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113Dic26—84no—
114C8×C13—82no—
115#1055—44no—
116C2×C4⋊Q8—131no—
117C2×C4×Q8C2×D1311yescharacteristic
118#432—21no—
119C2×#101—261no—
120C4×M16—261no—
121#395—132no—
122#395—132no—
123#391—261no—
124#389—261no—
125#389—261no—
126#384—261no—
127C4×C4⋊C4—131no—
128#343—132no—
129#324—21no—
130#324C2×D1312yes—
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—41no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13#35612yes—
144Dic13—44no—
145Dic13—82no—
146C22×Q8—132no—
147C22×Q8D5211yescharacteristic
148C2×M16—262no—
149C4⋊Q8—521no—
150C4⋊Q8—521no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4—262no—
158C2×C4⋊C4C4×D1311yescharacteristic
159C2×C4⋊C4C22⋊D1311yescharacteristic
160C2×C4⋊C4C22×D1311yescharacteristic
161C2×C42—261no—
162C2×C42C4×D1311yescharacteristic
163C2×C42D5211yescharacteristic
164C2×C42C22⋊D1311yescharacteristic
165C4⋊C8—41no—
166#101—264no—
167C22⋊C8—22no—
168#97—41no—
169#97—521no—
170C4×C8—521no—
171#95—132no—
172#95—262no—
173#95—262no—
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—522no—
183C2×Q8—1042no—
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
193M16—264no—
194M16—522no—
195C2×C8—42no—
196C2×C8—522no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—264no—
201C4⋊C4—522no—
202C4⋊C4—521no—
203C4⋊C4—521no—
204C4⋊C4—1042no—
205C4⋊C4—1042no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—522no—
213C13#1179511yescharacteristic, complemented, Sylow
214C23C2×#610311yescharacteristic
215Q8—44no—
216Q8—1044no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—264no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4#8804611yescharacteristic
238C2×C4#8804611yescharacteristic
239C2×C4#8806512yes—
240C2×C4#8816312yes—
241C8—82no—
242C8—524no—
243C22—21no—
244C22—21no—
245C22C2×#8804611yescharacteristic
246C22#1171878111yescharacteristic
247C22C2×#8806511yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—524no—
256C4—1042no—
257C4#1171807012yes—
258C2—21no—
259C2—21no—
260C2#1311335711yescharacteristic
261C2#1311648511yescharacteristic
262C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11795
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

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
#131200412
C4×#880762
#131128672
C13×#14672
#1179513