Finite Group Databasebeta

← #16785122

Subgroups — #16785122

Order 3328.

388 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130621C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3#13129712C212yesmaximal
4#13129712C212yesmaximal
5#13123222C211yesmaximal, characteristic
6C2×#88112—21no—
7C2×#88110C2212yes—
8C2×#88110C2212yes—
9C13×#389C411yescharacteristic
10#11718646C411yescharacteristic
11#11718642—21no—
12#11718639—21no—
13#11718638C2211yescharacteristic
14#11718638C2211yescharacteristic
15#11718634C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718589C411yescharacteristic
18#11718314—21no—
19#11718313—21no—
20#11718290—21no—
21#11718290—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13C2311yescharacteristic
40#88112—24no—
41#88110—22no—
42#88110—24no—
43#88110Q814yes—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#9893—131nomaximal, Sylow
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×#1057—24no—
65C2×#1057—24no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C42×C13—41no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—42no—
78#6101—42no—
79C4×Dic13—22no—
80C4×Dic13—41no—
81C4×Dic13—41no—
82C4×Dic13—41no—
83C4×Dic13—41no—
84C4×Dic13C2×Q812yes—
85C4×Dic13#4112yes—
86#2864—131no—
87#1767—131no—
88#1745—131no—
89#1295—132no—
90#1295—132no—
91C23×C13C2×C22⋊C411yescharacteristic
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13C4×Q812yes—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13#10412yes—
123C2×Dic13C22⋊Q812yes—
124C2×Dic13#12411yescharacteristic
125C2×Dic13C4⋊Q811yescharacteristic
126#1057—44no—
127#1057—44no—
128C2×C4⋊C8—261no—
129C2×#97—132no—
130C2×#97—132no—
131#389—131no—
132#389—131no—
133#389—131no—
134#389#26111yescharacteristic
135#387—261no—
136#387—261no—
137#387—261no—
138#387—261no—
139#382—131no—
140#382—131no—
141C43—131no—
142#336—261no—
143#336—261no—
144#336—261no—
145C22×C13#39111yescharacteristic
146C22×C13#41311yescharacteristic
147C22×C13#41311yescharacteristic
148C22×C13C2×#10411yescharacteristic
149C22×C13#42111yescharacteristic
150C22×C13#42111yescharacteristic
151C22×C13#42111yescharacteristic
152C4×C13—22no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—81no—
156C4×C13—81no—
157Dic13—21no—
158Dic13—21no—
159Dic13—22no—
160Dic13—22no—
161Dic13—41no—
162Dic13—81no—
163Dic13—81no—
164C22×C8—262no—
165C22×C8—262no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4C2×#26111yescharacteristic
173C2×C4⋊C4C2×#26111yescharacteristic
174C2×C42—131no—
175C2×C42—131no—
176C2×C42—131no—
177C2×C42—131no—
178C2×C42—131no—
179C2×C42—131no—
180C2×C42C2×#26111yescharacteristic
181C4⋊C8—264no—
182#97—134no—
183#97—262no—
184#97—264no—
185#95—21no—
186#95—261no—
187#95—261no—
188#95—261no—
189#95—261no—
190#95—261no—
191#95—261no—
192#95—261no—
193C2×C13#152911yescharacteristic
194C2×C13#153211yescharacteristic
195C2×C13#153511yescharacteristic
196C2×C13#153511yescharacteristic
197C2×C13#198611yescharacteristic
198C2×C13#199511yescharacteristic
199C2×C13#199811yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22×#26111yescharacteristic
211C2×C8—264no—
212C2×C8—264no—
213C2×C8—522no—
214C2×C8—522no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—521no—
221C4⋊C4—521no—
222C4⋊C4—522no—
223C4⋊C4—522no—
224C4⋊C4—522no—
225C42—41no—
226C42—132no—
227C42—132no—
228C42—262no—
229C42—521no—
230C42—521no—
231C42—521no—
232C42—521no—
233C13#989311yescharacteristic, complemented, Sylow
234C23C2×C22⋊#26111yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—132no—
250C2×C4—131no—
251C2×C4—131no—
252C2×C4—132no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4Q8×#26112yes—
269C8—524no—
270C8—524no—
271C22#1171913211yescharacteristic
272C22#1171914011yescharacteristic
273C22#1171914811yescharacteristic
274C22#1171915511yescharacteristic
275C22(C2×#261)⋊Q811yescharacteristic
276C22D13⋊#10411yescharacteristic
277C22#1171916611yescharacteristic
278C4—22no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—81no—
283C4—261no—
284C4—261no—
285C4—262no—
286C4—262no—
287C4—521no—
288C4—1041no—
289C4—1041no—
290C2#1313030211yescharacteristic
291C2#1313031311yescharacteristic
292C2#1313032011yescharacteristic
293C2#1313032311yescharacteristic
294C2#1313101311yescharacteristic
295C2#1313102411yescharacteristic
296C2#1313103011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9893
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
233. C13#9893semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131305532
#131297122
#131232222
#989313