Finite Group Databasebeta

← #16778555

Subgroups — #16778555

Order 3328.

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

normal subgroups only

This group has 384 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#13130764C211yesmaximal, characteristic
2#13130764C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5C4×#88144C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic
7C4×C13×C4⋊C4C411yescharacteristic
8#11718646C2211yescharacteristic
9#11718638C411yescharacteristic
10#11718634C2211yescharacteristic
11C4×C4⋊Dic13—21no—
12C4×C4⋊Dic13C411yescharacteristic
13C4×#6101—21no—
14C42×Dic13C2211yescharacteristic
15#11718316—21no—
16#11718315—21no—
17#11718290—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13—21no—
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88144—22no—
43#88144—22no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#7650—131nomaximal, Sylow
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C2×#1057—42no—
63C2×#1057—42no—
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4M1612yes—
71C42×C13—22no—
72C42×C13—42no—
73C4⋊Dic13—24no—
74C4⋊Dic13—21no—
75C4⋊Dic13—42no—
76C4⋊Dic13—41no—
77C4⋊Dic13M1612yes—
78#6101—24no—
79#6101—42no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—41no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13—42no—
88C4×#125—131no—
89#1839—131no—
90#1839—131no—
91#1271—132no—
92#1271—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13#10112yes—
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—22no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13#13512yes—
127C2×Dic13#13512yes—
128#1057—82no—
129#1057—82no—
130C2×#125—131no—
131#389—131no—
132#389—131no—
133#387—261no—
134#387—261no—
135#382—131no—
136C4×C4⋊C4—131no—
137C4×C4⋊C4—261no—
138C4×C4⋊C4—261no—
139C4×C4⋊C4#26111yescharacteristic
140C43—131no—
141#336—132no—
142#336—132no—
143#336—261no—
144#336—261no—
145#336—261no—
146#336—261no—
147C22×C13#40711yescharacteristic
148C22×C13#41011yescharacteristic
149C22×C13C2×#10111yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13#41611yescharacteristic
152C22×C13#42111yescharacteristic
153C22×C13#42111yescharacteristic
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—22no—
157C4×C13—41no—
158C4×C13—42no—
159C4×C13—81no—
160Dic13—22no—
161Dic13—22no—
162Dic13—41no—
163Dic13—41no—
164Dic13—42no—
165Dic13—81no—
166C22×C8—262no—
167C22×C8—262no—
168#125—262no—
169#125—262no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C2×#26111yescharacteristic
177C2×C4⋊C4C2×#26111yescharacteristic
178C2×C42—21no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—261no—
186C2×C42C2×#26111yescharacteristic
187#95—21no—
188#95—261no—
189#95—261no—
190#95—261no—
191#95—261no—
192#95—261no—
193C2×C13#146711yescharacteristic
194C2×C13#148811yescharacteristic
195C2×C13#148811yescharacteristic
196C2×C13#152111yescharacteristic
197C2×C13#152111yescharacteristic
198C2×C13#153411yescharacteristic
199C2×C13#154411yescharacteristic
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—522no—
212C2×C8—522no—
213C2×C8—522no—
214C2×C8—522no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—132no—
220C4⋊C4—264no—
221C4⋊C4—264no—
222C4⋊C4—261no—
223C4⋊C4—521no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4#611812yes—
227C42—22no—
228C42—42no—
229C42—262no—
230C42—262no—
231C42—261no—
232C42—261no—
233C42—521no—
234C42—521no—
235C42—521no—
236C42—522no—
237C13#765011yescharacteristic, complemented, Sylow
238C23C2×C22⋊#26111yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—132no—
253C2×C4—132no—
254C2×C4—261no—
255C2×C4—261no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4#8811312yes—
271C2×C4C2×#611811yescharacteristic
272C2×C4D13⋊M1611yescharacteristic
273C8—1042no—
274C8—1042no—
275C22#1171911611yescharacteristic
276C22#1171912711yescharacteristic
277C22C2×#8811311yescharacteristic
278C22#1171914011yescharacteristic
279C22#1171915511yescharacteristic
280C22#1171916511yescharacteristic
281C22#1171916511yescharacteristic
282C4—22no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—42no—
287C4—81no—
288C4—262no—
289C4—262no—
290C4—521no—
291C4—521no—
292C4—522no—
293C4—1041no—
294C2#1313009811yescharacteristic
295C2#1313016811yescharacteristic
296C2#1313017011yescharacteristic
297C2#1313027811yescharacteristic
298C2#1313028011yescharacteristic
299C2#1313031811yescharacteristic
300C2#1313034111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7650
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
237. C13#7650semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131296552
#131296542
C4×#881442
#765013