Finite Group Databasebeta

← #15774082

Subgroups — #15774082

Order 3328.

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

normal subgroups only

This group has 372 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, 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#11718586—21no—
16#11718585—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—42no—
43C22⋊#1055—22no—
44C4⋊#1055—41no—
45C4⋊#1055—41no—
46C4⋊#1055—41no—
47C4×#1055—41no—
48#11907—131nomaximal, Sylow
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—44no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13SD1612yes—
55C2×Q8×C13Q1612yes—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—42no—
78#6099—42no—
79#6099—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82#2568D1311yescharacteristic
83#1801—131no—
84#1461—131no—
85#1353—134no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—42no—
88Q8×C13—42no—
89Q8×C13—82no—
90Q8×C13—82no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—44no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#10312yes—
112C2×C4×C13#10312yes—
113C2×C4×C13C2×SD1611yescharacteristic
114C2×C4×C13C2×Q1611yescharacteristic
115#1055—82no—
116#1055—82no—
117C2×C4⋊Q8Dic1311yescharacteristic
118C2×C4×Q8C2×D1311yescharacteristic
119#431—261no—
120#423—261no—
121C2×#101—261no—
122#400Dic1312yes—
123#400C2×D1312yes—
124#391—21no—
125#391—21no—
126#391—21no—
127#382—21no—
128C4×C4⋊C4Dic1311yescharacteristic
129#343—132no—
130#324—132no—
131#324—261no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13C2×#9911yescharacteristic
135C22×C13C2×#10311yescharacteristic
136C22×C13#42111yescharacteristic
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—21no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13—41no—
145C4×C13—82no—
146C4×C13—82no—
147C4×C13#35512yes—
148C22×Q8—21no—
149C22×Q8C22⋊D1311yescharacteristic
150C2×M16—262no—
151C4⋊Q8—41no—
152C4⋊Q8—41no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×Dic1312yes—
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—
166C4⋊C8—521no—
167C4⋊C8—521no—
168#101—522no—
169C22⋊C8—262no—
170C4×C8—521no—
171#95—22no—
172#95—22no—
173#95—22no—
174#95—22no—
175#95C2×Dic1312yes—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13#152011yescharacteristic
179C2×C13#212311yescharacteristic
180C2×C13C2×#35511yescharacteristic
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8#610612yes—
187C2×Q8#610712yes—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4C22⋊Dic1311yescharacteristic
191C22×C4C22⋊Dic1311yescharacteristic
192C22×C4C22⋊Dic1311yescharacteristic
193C22×C4C22⋊Dic1311yescharacteristic
194C22×C4C22×Dic1311yescharacteristic
195C22×C4C2×C22⋊D1311yescharacteristic
196C22×C4C2×C22⋊D1311yescharacteristic
197M16—522no—
198M16—522no—
199C2×C8—522no—
200C2×C8—522no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C13#1190711yescharacteristic, complemented, Sylow
215C23C2×C22⋊Dic1311yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4#8807411yescharacteristic
239C2×C4#8807411yescharacteristic
240C2×C4#8807512yes—
241C2×C4#8807512yes—
242C2×C4C2×#610611yescharacteristic
243C2×C4C2×#610711yescharacteristic
244C8—1042no—
245C8—1042no—
246C22—21no—
247C22—21no—
248C22C2×#8807411yescharacteristic
249C22C2×#8807511yescharacteristic
250C22#1171889711yescharacteristic
251C4—21no—
252C4—22no—
253C4—22no—
254C4—21no—
255C4—21no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—82no—
260C4—82no—
261C4#1171813412yes—
262C2—21no—
263C2—21no—
264C2#1311340811yescharacteristic
265C2#1311649011yescharacteristic
266C2C2×#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#11907
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
214. C13#11907semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131128632
C13×#25682
#1190713