Finite Group Databasebeta

← #16786919

Subgroups — #16786919

Order 3328.

460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130072C212yesmaximal
2#13129778C212yesmaximal, complemented
3#13129766C212yesmaximal, complemented
4#13117549C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×Q8×Dic13C411yescharacteristic
7C2×D4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718891C2211yescharacteristic
10#11718882C411yescharacteristic
11#11718612—22no—
12#11718611—22no—
13#11718596C2211yescharacteristic
14#11718593C411yescharacteristic
15#11718305—22no—
16#11718285C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×Dic13D412yes—
20C22×#1057—42no—
21C13×#124—22no—
22C13×#124C814yescomplemented
23C2×C13×C22⋊C4—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13D412yes—
27Q8×Dic13—42no—
28D4×Dic13—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2311yescharacteristic
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C22⋊#1057—24no—
37C22⋊#1057—42no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41#11481—131nomaximal, Sylow
42C24×C13C22⋊C412yes—
43C2×Q8×C13—21no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13C2×C812yescomplemented
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13C2×C812yes—
50C2×D4×C13M1612yes—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13—22no—
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13—82no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D412yes—
62C2×#1057—44no—
63C2×#1057—84no—
64C13×C22⋊C4—28no—
65C42×C13—21no—
66C42×C13C2×C812yescomplemented
67C22⋊Dic13—42no—
68C22⋊Dic13—82no—
69C4⋊Dic13—41no—
70C4⋊Dic13—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13—82no—
73C4×Dic13—22no—
74C4×Dic13—42no—
75C4×Dic13—41no—
76#2326—131no—
77#1459—132no—
78#1325—132no—
79#1319—132no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13C22⋊C814yes—
85C23×C13C2×C22⋊C411yescharacteristic
86Q8×C13—42no—
87Q8×C13—42no—
88D4×C13—42no—
89D4×C13—42no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13C22×C811yescharacteristic
99C2×C4×C13C2×M1611yescharacteristic
100C2×Dic13—21no—
101C2×Dic13—22no—
102C2×Dic13—41no—
103C2×Dic13—44no—
104C2×Dic13—42no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—82no—
112C2×Dic13#9912yes—
113#1057—84no—
114C2×#124#26111yescharacteristic
115C2×C4×Q8—131no—
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×C13—24no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—82no—
133C22×C13C2×C22⋊C811yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13#41311yescharacteristic
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140Dic13—22no—
141Dic13—42no—
142Dic13—41no—
143Dic13—81no—
144Dic13—81no—
145C22×Q8C2×#26111yescharacteristic
146C22×D4C2×#26111yescharacteristic
147C23×C4—132no—
148C22×C8—522no—
149#124—22no—
150#124#105714yescomplemented
151C4×Q8—522no—
152C4×D4—522no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—131no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—262no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—262no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—261no—
163C2×C42C2×#26111yescharacteristic
164C22⋊C8—264no—
165C22⋊C8—522no—
166#95—261no—
167#95—261no—
168#95—262no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13—44no—
172C2×C13#145911yescharacteristic
173C2×C13#212711yescharacteristic
174C2×C13#213511yescharacteristic
175C24C22⋊#26112yes—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8C2×#105712yescomplemented
180C2×D4—41no—
181C2×D4—41no—
182C2×D4C2×#105712yes—
183C2×D4#612212yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—261no—
192C22×C4—261no—
193C22×C4—1042no—
194C22×C4C22×#26111yescharacteristic
195C2×C8—524no—
196C2×C8—1044no—
197C4⋊C4—521no—
198C4⋊C4—521no—
199C4⋊C4—522no—
200C4⋊C4—1042no—
201C22⋊C4—28no—
202C22⋊C4—522no—
203C22⋊C4—1042no—
204C42—21no—
205C42—262no—
206C42—521no—
207C42—522no—
208C42C2×#105712yescomplemented
209C13#1148111yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—42no—
213C23—42no—
214C23C22⋊#105714yes—
215C23C2×C22⋊#26111yescharacteristic
216Q8—42no—
217Q8—42no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—132no—
229C2×C4—261no—
230C2×C4—262no—
231C2×C4—521no—
232C2×C4—524no—
233C2×C4—522no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—522no—
237C2×C4—521no—
238C2×C4—521no—
239C2×C4—521no—
240C2×C4—1042no—
241C2×C4C22×#105711yescharacteristic
242C2×C4C2×#612211yescharacteristic
243C8—1044no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22D13⋊#9911yescharacteristic
252C22#1171914811yescharacteristic
253C22C2×C22⋊#105711yescharacteristic
254C4—21no—
255C4—21no—
256C4—42no—
257C4—42no—
258C4—262no—
259C4—522no—
260C4—521no—
261C4—1041no—
262C4—1041no—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#1313007211yescharacteristic
267C2#1313111411yescharacteristic
268C2#1313113911yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#124C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×#124#261
hypocenterC13#11481
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #13129778C2semidirect
3. #13129766C2semidirect
22. C13×#124C8semidirect
46. C2×Q8×C13C2×C8semidirect
66. C42×C13C2×C8semidirect
150. #124#1057semidirect
179. C2×Q8C2×#1057semidirect
208. C42C2×#1057semidirect
209. C13#11481semidirect

Maximal subgroups

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

subgroupindex
#131300722
#131297782
#131297662
#131175492
#1148113