Finite Group Databasebeta

← #15778107

Subgroups — #15778107

Order 3328.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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#13117556C211yesmaximal, characteristic
2C2×#11718140C211yesmaximal, characteristic
3#101×Dic13C212yesmaximal
4#13112962C212yesmaximal
5C2×C13×#356C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×Q8×Dic13C411yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9C2×C13×#101C2212yes—
10#11718891C411yescharacteristic
11#11718891C2211yescharacteristic
12C2×#88076C2212yes—
13M16×Dic13—22no—
14#11718642—22no—
15#11718642—22no—
16#11718597C411yescharacteristic
17#11718593C411yescharacteristic
18C13×#356C414yescomplemented
19#11718146—22no—
20#11718140C414yescomplemented
21C22×Q8×C13C2×C411yescharacteristic
22C22×Q8×C13C2311yescharacteristic
23C2×C13×M16—22no—
24C13×C4⋊Q8—22no—
25C13×C4⋊Q8C2×C412yes—
26C13×C4⋊Q8C2×C412yes—
27C2×C13×C4⋊C4—22no—
28C2×C42×C13C2×C411yescharacteristic
29Q8×Dic13—42no—
30Q8×Dic13—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13D412yes—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D412yes—
39C2×#6099—22no—
40C13×#101—22no—
41C13×#101C2×C414yes—
42#88076—22no—
43#88076C2×C414yes—
44#88071—22no—
45#88071—21no—
46#88071—21no—
47#88071—22no—
48#88071—22no—
49#88055—42no—
50C8×Dic13—42no—
51#12631—131nomaximal, Sylow
52C2×Q8×C13—21no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13C4212yes—
58C2×Q8×C13C22×C411yescharacteristic
59C2×Q8×C13C22×C411yescharacteristic
60C2×Q8×C13#4112yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D412yes—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C412yes—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C13×M16—24no—
71C13×M16—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C42×C13—21no—
76C42×C13C4212yes—
77C4⋊Dic13—41no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80C4⋊Dic13—41no—
81C4×Dic13—22no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—42no—
85C4×Dic13—41no—
86#6099—24no—
87#6099—42no—
88C2×#1055—42no—
89#2327—131no—
90C2×#356—131no—
91C2×#356D1311yescharacteristic
92C4×#101—132no—
93#1394—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95Q8×C13—41no—
96Q8×C13—41no—
97Q8×C13—42no—
98Q8×C13—42no—
99Q8×C13—42no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13C2×C4211yescharacteristic
111C2×C4×C13#11711yescharacteristic
112C2×C4×C13C4×D412yes—
113C2×C4×C13C4×D412yes—
114C2×Dic13—21no—
115C2×Dic13—22no—
116C2×Dic13—41no—
117C2×Dic13—42no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13#9912yes—
125C8×C13—44no—
126#1055—44no—
127C2×C4⋊Q8C2×D1311yescharacteristic
128C2×C4×Q8—131no—
129C2×C4×Q8—131no—
130C2×#101—132no—
131C2×#101C2×D1312yes—
132C4×M16—262no—
133#391—131no—
134#391—131no—
135#387—262no—
136#387—262no—
137#382—131no—
138#376—131no—
139#356—134no—
140#356Dic1314yescomplemented
141#343—262no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13C4×C22⋊C411yescharacteristic
145C22×C13C2×#9911yescharacteristic
146C22×C13#41011yescharacteristic
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—42no—
152C4×C13—42no—
153Dic13—22no—
154Dic13—41no—
155Dic13—42no—
156Dic13—81no—
157Dic13—81no—
158C22×Q8C4×D1311yescharacteristic
159C22×Q8C22×D1311yescharacteristic
160C2×M16—22no—
161C2×M16—262no—
162C4⋊Q8—22no—
163C4⋊Q8C4×D1312yes—
164C4⋊Q8C2×Dic1312yes—
165C4×Q8—522no—
166C4×Q8—522no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—132no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—261no—
172C2×C42—131no—
173C2×C42—132no—
174C2×C42—131no—
175C2×C42—261no—
176C2×C42C4×D1311yescharacteristic
177#101—22no—
178#101—134no—
179#101—262no—
180#101C2×Dic1314yes—
181#97—522no—
182C4×C8—522no—
183#95—261no—
184#95—261no—
185#95—262no—
186#95—262no—
187#95—262no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13C4×#9911yescharacteristic
191C2×C13#213311yescharacteristic
192C2×C13#213511yescharacteristic
193C2×Q8—21no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8C4×Dic1312yes—
199C2×Q8C2×C4×D1311yescharacteristic
200C2×Q8#612912yes—
201C2×Q8C22×Dic1311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—131no—
205C22×C4—132no—
206C22×C4—131no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4C2×C4×D1311yescharacteristic
210C22×C4D4×D1312yes—
211M16—24no—
212M16—42no—
213M16—264no—
214M16—522no—
215C2×C8—42no—
216C2×C8—522no—
217C4⋊C4—24no—
218C4⋊C4—24no—
219C4⋊C4—521no—
220C4⋊C4—522no—
221C4⋊C4—521no—
222C4⋊C4—522no—
223C42—21no—
224C42—262no—
225C42—262no—
226C42—262no—
227C42—521no—
228C42—522no—
229C42C4×Dic1312yes—
230C13#1263111yescharacteristic, complemented, Sylow
231C23C22⋊C4×D1311yescharacteristic
232Q8—41no—
233Q8—42no—
234Q8—41no—
235Q8—42no—
236Q8—42no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—132no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—521no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—522no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4#8813111yescharacteristic
259C2×C4#8813512yes—
260C2×C4C2×C4×Dic1311yescharacteristic
261C2×C4D4×Dic1312yes—
262C8—44no—
263C8—524no—
264C22—21no—
265C22—21no—
266C22#1171840111yescharacteristic
267C22D13×#9911yescharacteristic
268C22C22⋊C4×Dic1311yescharacteristic
269C4—22no—
270C4—22no—
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—262no—
276C4—521no—
277C4—522no—
278C4—1041no—
279C4—1041no—
280C2—21no—
281C2—21no—
282C2#99×Dic1311yescharacteristic
283C2#1311652411yescharacteristic
284C2#1311652911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C2×C42
FrattiniC22×Q8C22×D13
FittingC2×C13×#356C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC2×#356D13
hypocenterC13#12631
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
18. C13×#356C4semidirect
20. #11718140C4semidirect
140. #356Dic13semidirect
230. C13#12631semidirect

Maximal subgroups

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

subgroupindex
#131175562
C2×#117181402
#101×Dic132
#131129622
C2×C13×#3562
#1263113