Finite Group Databasebeta

← #15774073

Subgroups — #15774073

Order 3328.

372 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 103 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112866C212yesmaximal
4#13112863C212yesmaximal
5C13×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400C411yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#395C411yescharacteristic
11C13×#395C2211yescharacteristic
12C13×#391—21no—
13C13×#389—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#382C411yescharacteristic
17C2×#88076—21no—
18#11718586—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×#6099—22no—
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88076—42no—
52C22⋊#1055—22no—
53C4⋊#1055—41no—
54C4⋊#1055—41no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11905—131nomaximal, Sylow
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C2×Q8×C13SD1612yes—
63C2×Q8×C13Q1612yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—42no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94C2×#1055—42no—
95#2581D1311yescharacteristic
96#1801—131no—
97#1461—131no—
98#1354—132no—
99#1353—132no—
100C23×C13C2×C22⋊C411yescharacteristic
101Q8×C13—42no—
102Q8×C13—42no—
103Q8×C13—42no—
104Q8×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#10312yes—
132C2×C4×C13#10312yes—
133C2×C4×C13C2×SD1611yescharacteristic
134C2×C4×C13C2×Q1611yescharacteristic
135#1055—82no—
136#1055—82no—
137C2×C4×Q8Dic1311yescharacteristic
138C2×C4×Q8C2×D1311yescharacteristic
139#431—261no—
140#423—261no—
141C2×#101—261no—
142#400Dic1311yescharacteristic
143#400C2×D1311yescharacteristic
144#395Dic1311yescharacteristic
145#395C2×D1311yescharacteristic
146#391—21no—
147#389—21no—
148#387—21no—
149#387—21no—
150#382Dic1311yescharacteristic
151#343—132no—
152#324—132no—
153#324—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13C2×#9911yescharacteristic
157C22×C13C2×#10311yescharacteristic
158C22×C13#42111yescharacteristic
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—42no—
168C4×C13—41no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C22×Q8C2×Dic1311yescharacteristic
173C22×Q8C22⋊D1311yescharacteristic
174C2×M16—262no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—41no—
178C4×Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C42—21no—
188C2×C42C2×Dic1311yescharacteristic
189C2×C42C22⋊D1311yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C4⋊C8—521no—
192C4⋊C8—521no—
193C4⋊C8—521no—
194#101—522no—
195C22⋊C8—262no—
196C4×C8—521no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95C2×Dic1311yescharacteristic
205#95C2×Dic1311yescharacteristic
206C2×C13—21no—
207C2×C13—21no—
208C2×C13#152011yescharacteristic
209C2×C13#212011yescharacteristic
210C2×C13#213311yescharacteristic
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—42no—
214C2×Q8—41no—
215C2×Q8#610612yes—
216C2×Q8#610712yes—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22⋊Dic1311yescharacteristic
225C22×C4C22×Dic1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—522no—
229M16—522no—
230C2×C8—522no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—42no—
248C13#1190511yescharacteristic, complemented, Sylow
249C23C2×C22⋊Dic1311yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#8807411yescharacteristic
279C2×C4#8807411yescharacteristic
280C2×C4#8807512yes—
281C2×C4#8807512yes—
282C2×C4C2×#610611yescharacteristic
283C2×C4C2×#610711yescharacteristic
284C8—1042no—
285C8—1042no—
286C22—21no—
287C22—21no—
288C22C2×#8807411yescharacteristic
289C22C2×#8807511yescharacteristic
290C22#1171889711yescharacteristic
291C4—21no—
292C4—22no—
293C4—22no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—42no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2#1311340811yescharacteristic
307C2#1311647711yescharacteristic
308C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2581C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2581D13
hypocenterC13#11905
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
248. C13#11905semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131128662
#131128632
C13×#25812
#1190513