Finite Group Databasebeta

← #16786911

Subgroups — #16786911

Order 3328.

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

normal subgroups only

This group has 524 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, complemented
2#13129776C212yesmaximal, complemented
3#13129764C212yesmaximal, complemented
4#13117562C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×D4×Dic13C411yescharacteristic
7C2×D4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—22no—
9#11718882C411yescharacteristic
10#11718882C2211yescharacteristic
11#11718881—22no—
12#11718881—22no—
13#11718597C2211yescharacteristic
14#11718593C411yescharacteristic
15#11718305—22no—
16#11718285C2214yes—
17C22×D4×C13—22no—
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×Dic13—21no—
21C23×Dic13D412yes—
22C22×#1057—42no—
23C13×#127—22no—
24C13×#127C814yescomplemented
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—21no—
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13D412yes—
30D4×Dic13—42no—
31D4×Dic13—42no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2311yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C22⋊#1057—24no—
37C22⋊#1057—42no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41#11479—131nomaximal, Sylow
42C24×C13—21no—
43C24×C13C22⋊C412yes—
44C2×D4×C13—28no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13—82no—
51C2×D4×C13—82no—
52C2×D4×C13C2×C812yes—
53C2×D4×C13C2×C812yescomplemented
54C2×D4×C13M1612yes—
55C22×C4×C13—21no—
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13—22no—
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13—42no—
62C22×Dic13—82no—
63C22×Dic13—82no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C2×D412yes—
67C2×#1057—44no—
68C2×#1057—84no—
69C42×C13—21no—
70C42×C13C2×C812yescomplemented
71C22⋊Dic13—42no—
72C22⋊Dic13—42no—
73C22⋊Dic13—82no—
74C22⋊Dic13—82no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77C4×Dic13—22no—
78C4×Dic13—41no—
79#2328—131no—
80#1459—132no—
81#1324—132no—
82#1318—132no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13C22⋊C814yes—
93C23×C13C2×C22⋊C411yescharacteristic
94D4×C13—42no—
95D4×C13—42no—
96D4×C13—42no—
97D4×C13—42no—
98D4×C13—88no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13C22×C811yescharacteristic
105C2×C4×C13C2×M1611yescharacteristic
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—41no—
109C2×Dic13—44no—
110C2×Dic13—42no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—82no—
118C2×Dic13—84no—
119C2×Dic13#9912yes—
120#1057—84no—
121C2×#127#26111yescharacteristic
122C2×C4×D4—131no—
123C2×C4×D4—131no—
124C2×C22⋊C8—262no—
125#390—131no—
126#390—131no—
127#386—262no—
128#386—262no—
129#382—131no—
130#376—131no—
131#324—134no—
132#323—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—24no—
136C22×C13—44no—
137C22×C13—44no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—82no—
142C22×C13—82no—
143C22×C13—81no—
144C22×C13—81no—
145C22×C13C2×C22⋊C811yescharacteristic
146C22×C13C2×#9911yescharacteristic
147C22×C13#41311yescharacteristic
148C4×C13—21no—
149C4×C13—21no—
150C4×C13—42no—
151Dic13—22no—
152Dic13—42no—
153Dic13—41no—
154Dic13—81no—
155Dic13—81no—
156C22×D4—22no—
157C22×D4C2×#26111yescharacteristic
158C22×D4C2×#26111yescharacteristic
159C23×C4—132no—
160C23×C4—261no—
161C22×C8—522no—
162#127—22no—
163#127#105714yescomplemented
164C4×D4—522no—
165C4×D4—522no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—131no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—261no—
170C2×C22⋊C4—262no—
171C2×C22⋊C4—262no—
172C2×C42—131no—
173C2×C42—131no—
174C2×C42C2×#26111yescharacteristic
175C22⋊C8—264no—
176C22⋊C8—522no—
177#95—261no—
178#95—261no—
179#95—262no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13—44no—
183C2×C13—82no—
184C2×C13#145911yescharacteristic
185C2×C13#212711yescharacteristic
186C2×C13#213411yescharacteristic
187C24—21no—
188C24C22⋊#26112yes—
189C2×D4—28no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—82no—
196C2×D4—82no—
197C2×D4C2×#105712yes—
198C2×D4C2×#105712yescomplemented
199C2×D4#612212yes—
200C22×C4—21no—
201C22×C4—131no—
202C22×C4—132no—
203C22×C4—131no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—522no—
209C22×C4—1042no—
210C22×C4—1042no—
211C22×C4C22×#26111yescharacteristic
212C2×C8—524no—
213C2×C8—1044no—
214C4⋊C4—521no—
215C4⋊C4—521no—
216C22⋊C4—522no—
217C22⋊C4—522no—
218C22⋊C4—1042no—
219C22⋊C4—1042no—
220C42—21no—
221C42—262no—
222C42—521no—
223C42C2×#105712yescomplemented
224C13#1147911yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—22no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C22⋊#105714yes—
235C23C2×C22⋊#26111yescharacteristic
236D4—42no—
237D4—42no—
238D4—42no—
239D4—42no—
240D4—88no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—132no—
247C2×C4—261no—
248C2×C4—262no—
249C2×C4—521no—
250C2×C4—524no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—522no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—1042no—
259C2×C4—1044no—
260C2×C4C22×#105711yescharacteristic
261C2×C4C2×#612211yescharacteristic
262C8—1044no—
263C22—21no—
264C22—21no—
265C22—24no—
266C22—44no—
267C22—44no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—82no—
272C22—82no—
273C22—81no—
274C22—81no—
275C22D13⋊#9911yescharacteristic
276C22#1171914811yescharacteristic
277C22C2×C22⋊#105711yescharacteristic
278C4—21no—
279C4—21no—
280C4—42no—
281C4—262no—
282C4—522no—
283C4—521no—
284C4—1041no—
285C4—1041no—
286C2—21no—
287C2—21no—
288C2—44no—
289C2—82no—
290C2#1313007211yescharacteristic
291C2#1313111211yescharacteristic
292C2#1313113611yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC22×C13C2×#99
cosocleC2×C4⋊Dic13C23
hypercenterC2×#127#261
hypocenterC13#11479
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #13130072C2semidirect
2. #13129776C2semidirect
3. #13129764C2semidirect
24. C13×#127C8semidirect
53. C2×D4×C13C2×C8semidirect
70. C42×C13C2×C8semidirect
163. #127#1057semidirect
198. C2×D4C2×#1057semidirect
223. C42C2×#1057semidirect
224. C13#11479semidirect

Maximal subgroups

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

subgroupindex
#131300722
#131297762
#131297642
#131175622
#1147913