Finite Group Databasebeta

← #16778795

Subgroups — #16778795

Order 3328.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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#13130763C211yesmaximal, characteristic
2#13130752C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5#13123222C211yesmaximal, characteristic
6C2×#88112—21no—
7C13×#389C411yescharacteristic
8#11718646C2211yescharacteristic
9#11718642—21no—
10#11718639—21no—
11#11718638C411yescharacteristic
12#11718638C411yescharacteristic
13#11718634C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718589C411yescharacteristic
16#11718314—21no—
17#11718313—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
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—42no—
41C13×#95—21no—
42#88071—21no—
43#88071—21no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#7717—131nomaximal, Sylow
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—21no—
56C22×Dic13—21no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×#1057—42no—
62C2×#1057—42no—
63C2×#1057—42no—
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—42no—
70C42×C13—22no—
71C4⋊Dic13—22no—
72C4⋊Dic13—41no—
73C4⋊Dic13—41no—
74C4⋊Dic13—41no—
75#6101—42no—
76#6101—42no—
77C4×Dic13—22no—
78C4×Dic13—22no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—41no—
82C4×Dic13—41no—
83C4×Dic13—41no—
84#2864—131no—
85#1839—131no—
86#1831—131no—
87#1271—132no—
88#1271—132no—
89C23×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13—21no—
91C2×C4×C13—21no—
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—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13#13112yes—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13#10112yes—
121C2×Dic13#13512yes—
122C2×Dic13AGL(1,ℤ/8)11yescharacteristic
123C2×Dic13#13711yescharacteristic
124#1057—82no—
125#1057—82no—
126C2×C4⋊C8—261no—
127#389—131no—
128#389—131no—
129#389—131no—
130#389#26111yescharacteristic
131#387—261no—
132#387—261no—
133#387—261no—
134#387—261no—
135#382—131no—
136#382—131no—
137C43—131no—
138#336—132no—
139#336—132no—
140#336—261no—
141#336—261no—
142#336—261no—
143C22×C13#40811yescharacteristic
144C22×C13#41011yescharacteristic
145C22×C13C2×#10111yescharacteristic
146C22×C13#41611yescharacteristic
147C22×C13#41711yescharacteristic
148C22×C13#42111yescharacteristic
149C22×C13#42111yescharacteristic
150C4×C13—22no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—81no—
154C4×C13—81no—
155Dic13—22no—
156Dic13—21no—
157Dic13—21no—
158Dic13—22no—
159Dic13—41no—
160Dic13—81no—
161Dic13—81no—
162C22×C8—262no—
163C22×C8—262no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4C2×#26111yescharacteristic
171C2×C4⋊C4C2×#26111yescharacteristic
172C2×C42—131no—
173C2×C42—131no—
174C2×C42—131no—
175C2×C42—131no—
176C2×C42—131no—
177C2×C42—131no—
178C2×C42C2×#26111yescharacteristic
179C4⋊C8—522no—
180#95—21no—
181#95—261no—
182#95—261no—
183#95—261no—
184#95—261no—
185#95—261no—
186#95—261no—
187#95—261no—
188C2×C13#147011yescharacteristic
189C2×C13#148211yescharacteristic
190C2×C13#149511yescharacteristic
191C2×C13#151211yescharacteristic
192C2×C13#152111yescharacteristic
193C2×C13#153711yescharacteristic
194C2×C13#155211yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4C22⋊#26111yescharacteristic
204C22×C4C22⋊#26111yescharacteristic
205C22×C4C22×#26111yescharacteristic
206C2×C8—522no—
207C2×C8—522no—
208C2×C8—522no—
209C2×C8—522no—
210C2×C8—522no—
211C2×C8—522no—
212C4⋊C4—22no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—262no—
216C4⋊C4—521no—
217C4⋊C4—522no—
218C4⋊C4—522no—
219C4⋊C4—521no—
220C4⋊C4—521no—
221C42—22no—
222C42—261no—
223C42—262no—
224C42—261no—
225C42—262no—
226C42—521no—
227C42—521no—
228C42—521no—
229C13#771711yescharacteristic, complemented, Sylow
230C23C2×C22⋊#26111yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—132no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—132no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4#8823812yes—
265C8—1042no—
266C8—1042no—
267C22#1171911611yescharacteristic
268C22#1171914011yescharacteristic
269C22#1171914611yescharacteristic
270C22#1171915511yescharacteristic
271C22D13⋊#10111yescharacteristic
272C22#1171916411yescharacteristic
273C22#1171916511yescharacteristic
274C4—22no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C4—261no—
280C4—261no—
281C4—262no—
282C4—262no—
283C4—521no—
284C4—1041no—
285C4—1041no—
286C2#1313010811yescharacteristic
287C2#1313014911yescharacteristic
288C2#1313019111yescharacteristic
289C2#1313024911yescharacteristic
290C2#1313027811yescharacteristic
291C2#1313032811yescharacteristic
292C2#1313035811yescharacteristic
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#7717
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
229. C13#7717semidirect

Maximal subgroups

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

subgroupindex
#131307632
#131307522
#131296552
#131296542
#131232222
#771713