Finite Group Databasebeta

← #16786903

Subgroups — #16786903

Order 3328.

480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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#13129776C212yesmaximal, complemented
3#13129766C212yesmaximal, complemented
4#124×Dic13C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×Q8×Dic13C411yescharacteristic
7C2×D4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718891C2211yescharacteristic
10#11718882C411yescharacteristic
11#11718612—22no—
12C22⋊C4×Dic13—22no—
13#11718597C2211yescharacteristic
14C42×Dic13C411yescharacteristic
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—41no—
28Q8×Dic13—41no—
29D4×Dic13—41no—
30D4×Dic13—41no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2311yescharacteristic
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13C2×C411yescharacteristic
39C22⋊#1057—24no—
40C22⋊#1057—42no—
41#88071—22no—
42#88071—22no—
43#11477—131nomaximal, Sylow
44C24×C13C22⋊C412yes—
45C2×Q8×C13—21no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13C2×C812yescomplemented
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13C2×C812yes—
52C2×D4×C13M1612yes—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13—22no—
58C22×Dic13—22no—
59C22×Dic13—21no—
60C22×Dic13—44no—
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C2×D412yes—
64C2×#1057—44no—
65C2×#1057—84no—
66C13×C22⋊C4—28no—
67C42×C13—21no—
68C42×C13C2×C812yescomplemented
69C22⋊Dic13—42no—
70C22⋊Dic13—44no—
71C4⋊Dic13—41no—
72C4⋊Dic13—42no—
73C4⋊Dic13—41no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—42no—
77C4×Dic13—42no—
78C4×Dic13—41no—
79C4×Dic13—41no—
80C4×Dic13—41no—
81C4×#124—131no—
82#1459—132no—
83#1324—132no—
84#1319—132no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13C22⋊C814yes—
90C23×C13C2×C22⋊C411yescharacteristic
91Q8×C13—42no—
92Q8×C13—42no—
93D4×C13—42no—
94D4×C13—42no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—21no—
108C2×Dic13—22no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13—44no—
112C2×Dic13—41no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—41no—
116C2×Dic13—82no—
117C2×Dic13#9911yescharacteristic
118C2×Dic13#9911yescharacteristic
119#1057—84no—
120C2×#124#26111yescharacteristic
121C2×C4×Q8—131no—
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×C13—24no—
135C22×C13—44no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—82no—
139C22×C13C2×C22⋊C811yescharacteristic
140C22×C13C2×#9911yescharacteristic
141C22×C13#41311yescharacteristic
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—42no—
145C4×C13—42no—
146Dic13—21no—
147Dic13—42no—
148Dic13—42no—
149Dic13—41no—
150Dic13—81no—
151Dic13#35412yes—
152C22×Q8C2×#26111yescharacteristic
153C22×D4C2×#26111yescharacteristic
154C23×C4—132no—
155C22×C8—522no—
156#124—22no—
157#124#105714yescomplemented
158C4×Q8—521no—
159C4×Q8—521no—
160C4×D4—521no—
161C4×D4—521no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—261no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—262no—
168C2×C42—131no—
169C2×C42—131no—
170C2×C42—261no—
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—44no—
181C2×C13#145911yescharacteristic
182C2×C13C2×#35411yescharacteristic
183C2×C13#213211yescharacteristic
184C24C22⋊#26112yes—
185C2×Q8—21no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8C2×#105712yescomplemented
189C2×D4—41no—
190C2×D4—41no—
191C2×D4C2×#105712yes—
192C2×D4#612212yes—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—131no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—262no—
199C22×C4—262no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—524no—
203C22×C4C22×#26111yescharacteristic
204C2×C8—524no—
205C2×C8—1044no—
206C4⋊C4—521no—
207C4⋊C4—521no—
208C4⋊C4—522no—
209C22⋊C4—28no—
210C22⋊C4—522no—
211C22⋊C4—524no—
212C42—21no—
213C42—261no—
214C42—261no—
215C42—521no—
216C42—521no—
217C42—521no—
218C42—522no—
219C42—522no—
220C42C2×#105712yescomplemented
221C13#1147711yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23—42no—
225C23—42no—
226C23C22⋊#105714yes—
227C23C2×C22⋊#26111yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—261no—
245C2×C4—262no—
246C2×C4—524no—
247C2×C4—521no—
248C2×C4—521no—
249C2×C4—521no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—1042no—
254C2×C4C22×#105711yescharacteristic
255C2×C4C2×#612211yescharacteristic
256C8—1044no—
257C22—21no—
258C22—21no—
259C22—24no—
260C22—44no—
261C22—42no—
262C22—42no—
263C22—82no—
264C22D13⋊#9911yescharacteristic
265C22#1171914811yescharacteristic
266C22C2×C22⋊#105711yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—132no—
272C4—261no—
273C4—522no—
274C4—522no—
275C4—521no—
276C4—1041no—
277C2—21no—
278C2—21no—
279C2—44no—
280C2#1313007211yescharacteristic
281C2D13⋊#35411yescharacteristic
282C2#1313113011yescharacteristic
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#11477
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. #13129776C2semidirect
3. #13129766C2semidirect
22. C13×#124C8semidirect
48. C2×Q8×C13C2×C8semidirect
68. C42×C13C2×C8semidirect
157. #124#1057semidirect
188. C2×Q8C2×#1057semidirect
220. C42C2×#1057semidirect
221. C13#11477semidirect

Maximal subgroups

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

subgroupindex
#131300722
#131297762
#131297662
#124×Dic132
#1147713