Finite Group Databasebeta

← #16786918

Subgroups — #16786918

Order 3328.

460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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#13129779C212yesmaximal, complemented
3#13129766C212yesmaximal, complemented
4#13117543C211yesmaximal, characteristic
5C2×C4×Q8×C13C411yescharacteristic
6C2×#88201C411yescharacteristic
7C2×C4×D52C2211yescharacteristic
8D13⋊(C22⋊C8)—22no—
9#11718891C2211yescharacteristic
10#11718650—22no—
11#11718649C411yescharacteristic
12#11718637C2211yescharacteristic
13#11718601—22no—
14#11718593C411yescharacteristic
15#11718287—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D52C2×C411yescharacteristic
19C22×C4×D13D412yes—
20C2×D13⋊C8—42no—
21C4×Q8×C13—42no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C42×C13—21no—
25C2×C42×C13C2×C411yescharacteristic
26#88201—22no—
27#88201C814yescomplemented
28C2×#6103—22no—
29C2×#6103—22no—
30C2×#6103D412yes—
31C2×C4⋊Dic13C2311yescharacteristic
32C2×#6101—22no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C4×D52—42no—
36C22⋊#1057—24no—
37#88111—42no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41#11481—131nomaximal, Sylow
42C23×D13C22⋊C412yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13C2×C812yescomplemented
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—21no—
53C22×Dic13—21no—
54C22×Dic13C2×D412yes—
55C2×D52—41no—
56C2×D52—41no—
57C2×D52C2×C812yes—
58C2×D52M1612yes—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—82no—
62C2×#1057—44no—
63D13⋊C8—84no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C42×C13—22no—
67C42×C13—42no—
68#6103—28no—
69#6103—42no—
70#6103—82no—
71C4⋊Dic13—41no—
72#6101—82no—
73C4×Dic13—21no—
74C4×Dic13—41no—
75C4×Dic13C2×C812yescomplemented
76#2326—131no—
77#1459—132no—
78#1325—132no—
79#1319—132no—
80C23×C13C2×C22⋊C411yescharacteristic
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—42no—
84C22×D13—42no—
85C22×D13C22⋊C814yes—
86Q8×C13—42no—
87Q8×C13—42no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13#9912yes—
99C2×C4×C13C22×C811yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—41no—
104C2×Dic13—41no—
105C2×Dic13—42no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109D52—42no—
110D52—42no—
111C4×D13—44no—
112C4×D13—82no—
113#1057—84no—
114C2×#124—131no—
115C2×C4×Q8#26111yescharacteristic
116C2×C4×D4—131no—
117C2×C22⋊C8—262no—
118#391—131no—
119#390—131no—
120#388—262no—
121#385—262no—
122#384—131no—
123#376—131no—
124#324—134no—
125#323—262no—
126C22×C13—21no—
127C22×C13—21no—
128C22×C13C2×C22⋊C811yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13#41311yescharacteristic
131C2×D13—24no—
132C2×D13—42no—
133C2×D13—42no—
134C2×D13—44no—
135C2×D13—82no—
136C4×C13—22no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—41no—
140C4×C13—42no—
141C4×C13—81no—
142Dic13—42no—
143Dic13—42no—
144Dic13—81no—
145C22×Q8C2×#26111yescharacteristic
146C22×D4—131no—
147C23×C4—132no—
148C22×C8—522no—
149#124—134no—
150#124—262no—
151C4×Q8—42no—
152C4×D4—522no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4C2×#26111yescharacteristic
157C2×C22⋊C4—132no—
158C2×C22⋊C4—262no—
159C2×C22⋊C4—262no—
160C2×C42—21no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42C2×#26111yescharacteristic
164C22⋊C8—264no—
165C22⋊C8—522no—
166#95—262no—
167#95—261no—
168#95—261no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13#145911yescharacteristic
172C2×C13#212711yescharacteristic
173C2×C13#213511yescharacteristic
174D13—44no—
175C24—132no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8D13⋊C812yescomplemented
180C2×D4—132no—
181C2×D4—132no—
182C2×D4—521no—
183C2×D4—521no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—132no—
187C22×C4—261no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4—261no—
191C22×C4—1042no—
192C22×C4C22⋊#26111yescharacteristic
193C22×C4C22⋊#26111yescharacteristic
194C22×C4C22×#26111yescharacteristic
195C2×C8—524no—
196C2×C8—1044no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—521no—
200C4⋊C4—1042no—
201C22⋊C4—268no—
202C22⋊C4—522no—
203C22⋊C4—1042no—
204C42—22no—
205C42—42no—
206C42—132no—
207C42—261no—
208C42—521no—
209C13#1148111yescharacteristic, complemented, Sylow
210C23—134no—
211C23—262no—
212C23—262no—
213C23—522no—
214C23—522no—
215C23C2×C22⋊#26111yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—522no—
219D4—522no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—524no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4—522no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4—1042no—
240C2×C4#8811912yes—
241C2×C4C2×D13⋊C811yescharacteristic
242C2×C4D13⋊M1611yescharacteristic
243C8—1044no—
244C22—21no—
245C22—21no—
246C22—264no—
247C22—524no—
248C22—522no—
249C22—522no—
250C22—1042no—
251C22D13⋊(C22⋊C8)11yescharacteristic
252C22#1171913211yescharacteristic
253C22C2×#8811911yescharacteristic
254C4—21no—
255C4—21no—
256C4—22no—
257C4—42no—
258C4—41no—
259C4—81no—
260C4—522no—
261C4—522no—
262C4—1041no—
263C2—21no—
264C2—21no—
265C2—524no—
266C2#1313007111yescharacteristic
267C2#1313111111yescharacteristic
268C2#1313113811yescharacteristic
subgroupG/H
centerC22C2×#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#11481
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13129779C2semidirect
3. #13129766C2semidirect
27. #88201C8semidirect
46. C2×Q8×C13C2×C8semidirect
75. C4×Dic13C2×C8semidirect
179. C2×Q8D13⋊C8semidirect
209. C13#11481semidirect

Maximal subgroups

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

subgroupindex
#131300732
#131297792
#131297662
#131175432
#1148113