Finite Group Databasebeta

← #15773977

Subgroups — #15773977

Order 3328.

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

normal subgroups only

This group has 408 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#13112842C214yesmaximal
4C13×#2546C211yesmaximal, characteristic
5C2×C13×C4⋊Q8—21no—
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#398C412yes—
9C13×#398C2212yes—
10C13×#391—21no—
11C13×#389—21no—
12C13×#389—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—
24C13×C4⋊Q8—42no—
25C13×C4⋊Q8—42no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4C2311yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×#6099—22no—
41C13×#95—22no—
42C13×#95—22no—
43C13×#95C2×C412yes—
44#88076—42no—
45C22⋊#1055—22no—
46C4⋊#1055—41no—
47C4⋊#1055—41no—
48C4⋊#1055—41no—
49C4×#1055—41no—
50#11883—131nomaximal, Sylow
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C2×Q8×C13—42no—
56C2×Q8×C13D812yes—
57C2×Q8×C13SD1612yes—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C13×C4⋊C4—24no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—44no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—42no—
84#6099—42no—
85#6099—42no—
86C2×#1055—42no—
87C2×#1055—42no—
88#2546D1311yescharacteristic
89#1801—131no—
90#1461—131no—
91#1346—134no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—42no—
94Q8×C13—42no—
95Q8×C13—84no—
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—22no—
103C2×C4×C13—24no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C2×C4×C13#10212yes—
118C2×C4×C13#10212yes—
119C2×C4×C13C2×D811yescharacteristic
120C2×C4×C13C2×SD1611yescharacteristic
121#1055—82no—
122#1055—82no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8Dic1311yescharacteristic
125C2×C4×Q8C2×D1311yescharacteristic
126#431—261no—
127#423—261no—
128C2×#101—261no—
129#398Dic1312yes—
130#398C2×D1312yes—
131#391—21no—
132#389—21no—
133#389—21no—
134C4×C4⋊C4Dic1311yescharacteristic
135#343—132no—
136#324—132no—
137#324—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13C2×#9911yescharacteristic
141C22×C13C2×#10211yescharacteristic
142C22×C13#42111yescharacteristic
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—22no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—44no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13—82no—
153C4×C13#35612yes—
154C22×Q8—21no—
155C22×Q8C22⋊D1311yescharacteristic
156C2×M16—262no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—42no—
160C4⋊Q8—42no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×Dic1312yes—
168C2×C4⋊C4C2×Dic1311yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C4⋊C4C22×D1311yescharacteristic
171C2×C42—21no—
172C2×C42C2×Dic1311yescharacteristic
173C2×C42C22⋊D1311yescharacteristic
174C2×C42C22⋊D1311yescharacteristic
175C4⋊C8—521no—
176C4⋊C8—521no—
177C4⋊C8—521no—
178#101—522no—
179C22⋊C8—262no—
180C4×C8—521no—
181#95—22no—
182#95—22no—
183#95C2×Dic1312yes—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#151911yescharacteristic
187C2×C13#212311yescharacteristic
188C2×C13C2×#35611yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8#610412yes—
195C2×Q8#610512yes—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4C22⋊Dic1311yescharacteristic
199C22×C4C22⋊Dic1311yescharacteristic
200C22×C4C22⋊Dic1311yescharacteristic
201C22×C4C22⋊Dic1311yescharacteristic
202C22×C4C22×Dic1311yescharacteristic
203C22×C4C2×C22⋊D1311yescharacteristic
204C22×C4C2×C22⋊D1311yescharacteristic
205M16—522no—
206M16—522no—
207C2×C8—522no—
208C2×C8—522no—
209C4⋊C4—24no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—42no—
226C13#1188311yescharacteristic, complemented, Sylow
227C23C2×C22⋊Dic1311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#8807212yes—
251C2×C4#8807212yes—
252C2×C4#8807411yescharacteristic
253C2×C4#8807411yescharacteristic
254C2×C4C2×#610411yescharacteristic
255C2×C4C2×#610511yescharacteristic
256C8—1042no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22C2×#8807211yescharacteristic
261C22C2×#8807411yescharacteristic
262C22#1171889711yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1171814012yes—
274C2—21no—
275C2—21no—
276C2#1311340411yescharacteristic
277C2#1311649011yescharacteristic
278C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2546C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2546D13
hypocenterC13#11883
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
226. C13#11883semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131128422
C13×#25462
#1188313