Finite Group Databasebeta

← #16786902

Subgroups — #16786902

Order 3328.

480 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130073C212yesmaximal
2#13129777C212yesmaximal, complemented
3#13129766C212yesmaximal, complemented
4C4×#88201C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88201C411yescharacteristic
7C2×C4×D52C2211yescharacteristic
8D13⋊(C22⋊C8)—22no—
9#11718891C2211yescharacteristic
10#11718651—22no—
11#11718649C411yescharacteristic
12#11718638C2211yescharacteristic
13C4×#6103—22no—
14C42×Dic13C411yescharacteristic
15#11718287—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D52C2×C411yescharacteristic
19C22×C4×D13D412yes—
20C2×D13⋊C8—42no—
21C4×Q8×C13—41no—
22C4×Q8×C13—41no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C42×C13—21no—
26C2×C42×C13C2×C411yescharacteristic
27#88201—22no—
28#88201C814yescomplemented
29C2×#6103—22no—
30C2×#6103—22no—
31C2×#6103D412yes—
32C2×C4⋊Dic13C2311yescharacteristic
33C2×C4×Dic13—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C4×D52—41no—
38C4×D52—41no—
39C22⋊#1057—24no—
40#88111—42no—
41#88071—22no—
42#88071—22no—
43#11477—131nomaximal, Sylow
44C23×D13C22⋊C412yes—
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13C2×C812yescomplemented
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—21no—
55C22×Dic13—21no—
56C22×Dic13C2×D412yes—
57C2×D52—41no—
58C2×D52—41no—
59C2×D52C2×C812yes—
60C2×D52M1612yes—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—44no—
64C2×#1057—44no—
65D13⋊C8—84no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—41no—
71C42×C13—41no—
72#6103—28no—
73#6103—42no—
74#6103—44no—
75C4⋊Dic13—41no—
76C4×Dic13—21no—
77C4×Dic13—42no—
78C4×Dic13—42no—
79C4×Dic13—41no—
80C4×Dic13C2×C812yescomplemented
81C4×#124—131no—
82#1459—132no—
83#1324—132no—
84#1319—132no—
85C23×C13C2×C22⋊C411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—42no—
89C22×D13—42no—
90C22×D13C22⋊C814yes—
91Q8×C13—42no—
92Q8×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13#9911yescharacteristic
104C2×C4×C13#9911yescharacteristic
105C2×C4×C13C22×C811yescharacteristic
106C2×C4×C13C2×M1611yescharacteristic
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115D52—42no—
116D52—42no—
117C4×D13—44no—
118C4×D13—82no—
119#1057—84no—
120C2×#124—131no—
121C2×C4×Q8#26111yescharacteristic
122C2×C4×D4—131no—
123C2×C22⋊C8—262no—
124#391—131no—
125#390—131no—
126#388—262no—
127#382—131no—
128C4×C22⋊C4—262no—
129C43—131no—
130#324—134no—
131#323—262no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13C2×C22⋊C811yescharacteristic
135C22×C13C2×#9911yescharacteristic
136C22×C13#41311yescharacteristic
137C2×D13—24no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—44no—
141C2×D13—82no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—41no—
146C4×C13—42no—
147C4×C13—81no—
148C4×C13#35412yes—
149Dic13—42no—
150Dic13—42no—
151Dic13—42no—
152C22×Q8C2×#26111yescharacteristic
153C22×D4—131no—
154C23×C4—132no—
155C22×C8—522no—
156#124—134no—
157#124—262no—
158C4×Q8—41no—
159C4×Q8—41no—
160C4×D4—521no—
161C4×D4—521no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4C2×#26111yescharacteristic
165C2×C22⋊C4—132no—
166C2×C22⋊C4—262no—
167C2×C22⋊C4—262no—
168C2×C42—21no—
169C2×C42—131no—
170C2×C42—131no—
171C2×C42—261no—
172C2×C42—261no—
173C2×C42C2×#26111yescharacteristic
174C22⋊C8—264no—
175C22⋊C8—522no—
176#95—262no—
177#95—262no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#145911yescharacteristic
181C2×C13C2×#35411yescharacteristic
182C2×C13#213211yescharacteristic
183D13—44no—
184C24—132no—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8D13⋊C812yescomplemented
189C2×D4—132no—
190C2×D4—132no—
191C2×D4—521no—
192C2×D4—521no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—132no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—524no—
201C22×C4C22⋊#26111yescharacteristic
202C22×C4C22⋊#26111yescharacteristic
203C22×C4C22×#26111yescharacteristic
204C2×C8—524no—
205C2×C8—1044no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—521no—
209C22⋊C4—268no—
210C22⋊C4—522no—
211C22⋊C4—524no—
212C42—21no—
213C42—21no—
214C42—41no—
215C42—41no—
216C42—132no—
217C42—261no—
218C42—521no—
219C42—522no—
220C42—522no—
221C13#1147711yescharacteristic, complemented, Sylow
222C23—134no—
223C23—262no—
224C23—262no—
225C23—522no—
226C23—522no—
227C23C2×C22⋊#26111yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—522no—
231D4—522no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—524no—
250C2×C4—522no—
251C2×C4—1042no—
252C2×C4#8811911yescharacteristic
253C2×C4#8811911yescharacteristic
254C2×C4C2×D13⋊C811yescharacteristic
255C2×C4D13⋊M1611yescharacteristic
256C8—1044no—
257C22—21no—
258C22—21no—
259C22—264no—
260C22—524no—
261C22—522no—
262C22—522no—
263C22—1042no—
264C22D13⋊(C22⋊C8)11yescharacteristic
265C22#1171913211yescharacteristic
266C22C2×#8811911yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—41no—
272C4—81no—
273C4—522no—
274C4—522no—
275C4—522no—
276C4#1171830012yes—
277C2—21no—
278C2—21no—
279C2—524no—
280C2#1313007111yescharacteristic
281C2C2×#1171830011yescharacteristic
282C2#1313112711yescharacteristic
subgroupG/H
centerC2×C4#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4×Q8#261
hypocenterC13#11477
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13129777C2semidirect
3. #13129766C2semidirect
28. #88201C8semidirect
48. C2×Q8×C13C2×C8semidirect
80. C4×Dic13C2×C8semidirect
188. C2×Q8D13⋊C8semidirect
221. C13#11477semidirect

Maximal subgroups

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

subgroupindex
#131300732
#131297772
#131297662
C4×#882012
#1147713