Finite Group Databasebeta

← #15783330

Subgroups — #15783330

Order 3328.

336 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 75 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#13116508C211yesmaximal, characteristic
2#13116505C211yesmaximal, characteristic
3#13113007C212yesmaximal, complemented
4#13113001C212yesmaximal, complemented
5C13×#3222C211yesmaximal, characteristic
6C13×#541C411yescharacteristic, complemented
7C13×#535C2211yescharacteristic
8C13×#497C411yescharacteristic, complemented
9C13×#492C2211yescharacteristic
10C13×#490C2211yescharacteristic
11C13×#488C411yescharacteristic, complemented
12C13×#464—21no—
13C13×#460—21no—
14C13×#452—21no—
15C13×#450—21no—
16C13×#433C411yescharacteristic, complemented
17#11718901—21no—
18C2×#88074—21no—
19#11718137—21no—
20#11718137C2212yes—
21#11718137C2212yes—
22#11718133—21no—
23C2×C13×#41D411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C2×C13×Q16—21no—
26C2×C13×SD16—21no—
27C2×C13×SD16—21no—
28C2×C13×SD16—21no—
29C13×C4⋊Q8C2×C411yescharacteristic, complemented
30C13×#127D411yescharacteristic
31C13×#127C2311yescharacteristic
32C13×#126—41no—
33C13×#125—41no—
34C13×#125C2×C411yescharacteristic, complemented
35C13×#124C2×C411yescharacteristic
36C13×#124D411yescharacteristic
37C13×C22⋊Q8—21no—
38C13×#121—41no—
39C13×#120—41no—
40C4×Q8×C13—21no—
41C13×#117C2×C411yescharacteristic
42C2×C22⋊Dic13—41no—
43#88180—41no—
44C13×C4⋊C8—21no—
45C13×#103—21no—
46C13×#102—21no—
47C13×#102—21no—
48C13×#102—21no—
49C13×C22⋊C8—21no—
50C13×#97C2×C411yescharacteristic, complemented
51C4×C8×C13C2×C411yescharacteristic, complemented
52#88074—22no—
53#88074—22no—
54#88074—41no—
55#88074—41no—
56#13610—131nomaximal, Sylow
57C24×C13—21no—
58C13×#41—81no—
59C2×Q8×C13—21no—
60C2×Q8×C13C22⋊C411yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—81no—
66C2×D4×C13C22⋊C411yescharacteristic
67C2×D4×C13C2×D411yescharacteristic
68C2×D4×C13C2×D411yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×Dic13—81no—
72C13×Q16—81no—
73C13×SD16—81no—
74C13×SD16—81no—
75C13×SD16—81no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—41no—
89C42×C13C22⋊C411yescharacteristic
90C42×C13C22×C411yescharacteristic
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C22⋊Dic13—81no—
94C4⋊Dic13—81no—
95C4×Dic13—81no—
96#3222D1311yescharacteristic
97#2128—131no—
98#2127—131no—
99#1412—132no—
100#1409—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—161no—
107C23×C13#9911yescharacteristic
108Q8×C13—41no—
109Q8×C13—41no—
110Q8×C13—41no—
111D4×C13—41no—
112D4×C13—41no—
113D4×C13—41no—
114D4×C13—81no—
115D4×C13—81no—
116D4×C13—161no—
117D4×C13—161no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13C2×C22⋊C411yescharacteristic
128C2×Dic13—82no—
129C2×Dic13—82no—
130C2×Dic13—162no—
131C8×C13—41no—
132C8×C13—41no—
133#541Dic1311yescharacteristic, complemented
134#535C2×D1311yescharacteristic
135#497Dic1311yescharacteristic, complemented
136#492C2×D1311yescharacteristic
137#490C2×D1311yescharacteristic
138#488Dic1311yescharacteristic, complemented
139#464—21no—
140#460—21no—
141#452—21no—
142#450—21no—
143#433Dic1311yescharacteristic, complemented
144#410—261no—
145C2×#99—261no—
146#354—261no—
147#353—132no—
148#353—132no—
149#353—261no—
150C22×C13—21no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—81no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13—82no—
159C22×C13—161no—
160C22×C13C2×#9911yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—81no—
167C4×C13—81no—
168Dic13—162no—
169Dic13—162no—
170C2×#41C22⋊D1311yescharacteristic
171C22×D4C22⋊D1311yescharacteristic
172C2×Q16—21no—
173C2×SD16—21no—
174C2×SD16—21no—
175C2×SD16—21no—
176C4⋊Q8C2×Dic1311yescharacteristic, complemented
177#127C22⋊D1311yescharacteristic
178#127C22×D1311yescharacteristic
179#126—41no—
180#125—41no—
181#125C2×Dic1311yescharacteristic, complemented
182#124C2×Dic1311yescharacteristic
183#124C22⋊D1311yescharacteristic
184C22⋊Q8—21no—
185#121—41no—
186#120—41no—
187C4×Q8—21no—
188#117—521no—
189#117C2×Dic1311yescharacteristic
190C2×C22⋊C4—521no—
191C4⋊C8—21no—
192#103—21no—
193#102—21no—
194#102—21no—
195#102—21no—
196#99—262no—
197#99—262no—
198#99—521no—
199#99—521no—
200C22⋊C8—21no—
201#97C2×Dic1311yescharacteristic, complemented
202C4×C8C2×Dic1311yescharacteristic, complemented
203C2×C13—21no—
204C2×C13—41no—
205C2×C13—81no—
206C2×C13—81no—
207C2×C13—81no—
208C2×C13#212711yescharacteristic
209C24—21no—
210#41—81no—
211C2×Q8—21no—
212C2×Q8C22⋊Dic1311yescharacteristic
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—81no—
218C2×D4C22⋊Dic1311yescharacteristic
219C2×D4C2×C22⋊D1311yescharacteristic
220C2×D4C2×C22⋊D1311yescharacteristic
221C22×C4—21no—
222C22×C4—1041no—
223C22×C4C22⋊Dic1311yescharacteristic
224Q16—81no—
225SD16—81no—
226SD16—81no—
227SD16—81no—
228C2×C8—21no—
229C2×C8—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—1041no—
237C22⋊C4—21no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C22⋊C4—1041no—
244C42—41no—
245C42—1041no—
246C42C22⋊Dic1311yescharacteristic
247C42C22×Dic1311yescharacteristic
248C13#1361011yescharacteristic, complemented, Sylow
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—161no—
255C23#8807411yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262D4—81no—
263D4—81no—
264D4—161no—
265D4—161no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—1042no—
275C2×C4—1042no—
276C2×C4—2082no—
277C2×C4#8807411yescharacteristic
278C2×C4C2×C22⋊Dic1311yescharacteristic
279C8—41no—
280C8—41no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—81no—
287C22—81no—
288C22—81no—
289C22—82no—
290C22—161no—
291C22C2×#8807411yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—2082no—
300C4—2082no—
301C2—21no—
302C2—41no—
303C2—81no—
304C2—81no—
305C2—81no—
306C2#1311650511yescharacteristic
subgroupG/H
centerC2#13116505
commutatorC42×C13C22×C4
Frattini#127C22×D13
FittingC13×#3222C2
socleC2×C13#2127
prime radicalC13×#535C22
cosocleC13×#127C23
hypercenter#3222D13
hypocenterC13#13610
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #535 ◁ #3222

Complements

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

NH ≅ G/Ntype
3. #13113007C2semidirect
4. #13113001C2semidirect
6. C13×#541C4semidirect
8. C13×#497C4semidirect
11. C13×#488C4semidirect
16. C13×#433C4semidirect
29. C13×C4⋊Q8C2×C4semidirect
34. C13×#125C2×C4semidirect
50. C13×#97C2×C4semidirect
51. C4×C8×C13C2×C4semidirect
133. #541Dic13semidirect
135. #497Dic13semidirect
138. #488Dic13semidirect
143. #433Dic13semidirect
176. C4⋊Q8C2×Dic13semidirect
181. #125C2×Dic13semidirect
201. #97C2×Dic13semidirect
202. C4×C8C2×Dic13semidirect
248. C13#13610semidirect

Maximal subgroups

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

subgroupindex
#131165082
#131165052
#131130072
#131130012
C13×#32222
#1361013