Finite Group Databasebeta

← #15772074

Subgroups — #15772074

Order 3328.

462 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 93 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#13117242C211yesmaximal, characteristic
2#13113149C212yesmaximal
3#13112781C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#1324C211yesmaximal, characteristic, complemented
6C2×#88146C411yescharacteristic
7C2×#88146C2211yescharacteristic
8C2×C42×D13C411yescharacteristic
9C13×#382C2211yescharacteristic
10#11718637C411yescharacteristic
11#11718637C2211yescharacteristic
12#11718597C411yescharacteristic
13#11718379—22no—
14#11718328—22no—
15#11718310—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718060—22no—
19C22×C4×D13—21no—
20C22×C4×D13C2×C411yescharacteristic
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C4⋊C4C2311yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×#6103—21no—
25C2×#6103D412yes—
26C2×C4⋊Dic13C2×C411yescharacteristic
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×#6101—22no—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C2×C4×Dic13—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D412yes—
34#88146—41no—
35#88146—41no—
36#88146—41no—
37#88146—41no—
38C42×D13—22no—
39C42×D13C814yescomplemented
40C13×C22⋊C8—22no—
41C13×#95—22no—
42#88071—22no—
43C22⋊#1055—22no—
44#88054—42no—
45C8×Dic13—42no—
46#11447—131nomaximal, Sylow
47C23×D13C22⋊C411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13C22×C411yescharacteristic
51C22×C4×C13C2×D412yes—
52C22×Dic13—21no—
53C22×Dic13—21no—
54C22×Dic13C22⋊C412yes—
55C22×Dic13C22⋊C411yescharacteristic
56C2×C4×D13—21no—
57C2×C4×D13—21no—
58C2×C4×D13—22no—
59C2×C4×D13—24no—
60C2×C4×D13—42no—
61C2×C4×D13—42no—
62C2×C4×D13C2×C812yes—
63C2×C4×D13M1612yes—
64C2×C8×C13—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C42×C13—21no—
68C42×C13C2×C812yes—
69#6103—42no—
70#6103—42no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73#6101—44no—
74#6101—44no—
75C4×Dic13—21no—
76C4×Dic13—24no—
77C4×Dic13—22no—
78C4×Dic13—22no—
79C4×Dic13—41no—
80C4×Dic13—41no—
81C4×Dic13C2×C812yes—
82C2×#1055—42no—
83#2285—131no—
84#1458—132no—
85#1325—132no—
86#1324—131no—
87#1324D1311yescharacteristic, complemented
88C23×C13C2×C22⋊C411yescharacteristic
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—41no—
92C22×D13—41no—
93C22×D13C22⋊C812yes—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—41no—
112C2×Dic13C22⋊C812yes—
113C2×Dic13#9911yescharacteristic
114C2×Dic13#9911yescharacteristic
115C2×Dic13#10112yes—
116C4×D13—22no—
117C4×D13—22no—
118C4×D13—22no—
119C4×D13—22no—
120C4×D13—48no—
121C8×C13—82no—
122#1055—82no—
123C2×#117—131no—
124C2×#117—131no—
125C22×C42—131no—
126#431—262no—
127#384—131no—
128#384—131no—
129#382—131no—
130#382C2×D1311yescharacteristic
131#380—262no—
132C4×C4⋊C4—262no—
133#324—132no—
134#324C2×D1312yes—
135#323—262no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13C2×C22⋊C811yescharacteristic
139C22×C13C2×#9911yescharacteristic
140C22×C13C2×#10111yescharacteristic
141C2×D13—22no—
142C2×D13—42no—
143C2×D13—41no—
144C2×D13—41no—
145C2×D13—42no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—42no—
149C4×C13—42no—
150C4×C13—81no—
151Dic13—24no—
152Dic13—42no—
153Dic13—81no—
154Dic13#32412yes—
155Dic13#32412yes—
156C23×C4—131no—
157C23×C4—261no—
158#117—521no—
159#117—521no—
160#117—521no—
161#117—521no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4C4×D1311yescharacteristic
167C2×C4⋊C4C22×D1311yescharacteristic
168C2×C22⋊C4—132no—
169C2×C22⋊C4—261no—
170C2×C42—131no—
171C2×C42—134no—
172C2×C42—132no—
173C2×C42—262no—
174C2×C42—261no—
175C2×C42—261no—
176C2×C42C4×D1311yescharacteristic
177C4⋊C8—522no—
178C22⋊C8—22no—
179C22⋊C8—262no—
180C4×C8—522no—
181#95—22no—
182#95—262no—
183C2×C13—21no—
184C2×C13—21no—
185C2×C13C2×#32411yescharacteristic
186C2×C13#212611yescharacteristic
187C2×C13#213211yescharacteristic
188D13—42no—
189C24—131no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—131no—
193C22×C4—132no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—262no—
199C22×C4—264no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—522no—
203C22×C4—522no—
204C22×C4C2×C4×D1311yescharacteristic
205C22×C4D4×D1312yes—
206C2×C8—42no—
207C2×C8—522no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—521no—
211C4⋊C4—521no—
212C4⋊C4—524no—
213C4⋊C4—524no—
214C22⋊C4—522no—
215C22⋊C4—522no—
216C42—21no—
217C42—132no—
218C42—262no—
219C42—262no—
220C42—264no—
221C42—261no—
222C42—521no—
223C42—521no—
224C42C8×D1312yes—
225C13#1144711yescharacteristic, complemented, Sylow
226C23—132no—
227C23—261no—
228C23—261no—
229C23—521no—
230C23—521no—
231C23C22⋊C4×D1311yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—132no—
244C2×C4—132no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—528no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—521no—
257C2×C4C2×C8×D1311yescharacteristic
258C2×C4M16×D1311yescharacteristic
259C8—82no—
260C8—1042no—
261C22—21no—
262C22—21no—
263C22—262no—
264C22—522no—
265C22—522no—
266C22—521no—
267C22—521no—
268C22D13×C22⋊C811yescharacteristic
269C22D13×#9911yescharacteristic
270C22D13×#10111yescharacteristic
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—81no—
276C4—132no—
277C4—132no—
278C4—264no—
279C4—522no—
280C4—1041no—
281C2—21no—
282C2—21no—
283C2—522no—
284C2D13×#32411yescharacteristic
285C2#1311650011yescharacteristic
286C2#1311651811yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1324C2
socleC22×C13C2×#99
prime radicalC23×D13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1324D13
hypocenterC13#11447
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
4. #13112780C2semidirect
5. C13×#1324C2semidirect
39. C42×D13C8semidirect
87. #1324D13semidirect
225. C13#11447semidirect

Maximal subgroups

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

subgroupindex
#131172422
#131131492
#131127812
#131127802
C13×#13242
#1144713