Finite Group Databasebeta

← #15794127

Subgroups — #15794127

Order 3328.

6494 conjugacy classes of subgroups; only the 675 normal subgroups are shown.

normal subgroups only

This group has 6494 conjugacy classes of subgroups — too many to draw. Only its 675 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
1C25×Dic13C211yesmaximal, characteristic
2C2×#11718607C216yesmaximal, complemented
3C2×#11718908C211yesmaximal, characteristic
4#13113058C216yesmaximal, complemented
5C2×C13×#379C211yesmaximal, characteristic
6C26×C13C2211yescharacteristic
7C24×Dic13—24no—
8C24×Dic13—224no—
9C24×Dic13C2216yes—
10C22×C13×C22⋊C4C2213yes—
11C22×C13×C22⋊C4C2213yes—
12C22×C22⋊Dic13C2216yes—
13C22×#6101C2214yescomplemented
14C13×#379—24no—
15#11718908C418yescomplemented
16C2×#88071C22112yescomplemented
17#11718607—224no—
18C25×C13—212no—
19C25×C13—212no—
20C25×C13C2×C414yes—
21C25×C13D414yes—
22C25×C13Q814yes—
23C25×C13C2313yes—
24C23×C4×C13C2311yescharacteristic
25C23×C4×C13C2313yes—
26C23×Dic13—296no—
27C23×Dic13—2128no—
28C23×Dic13—212no—
29C23×Dic13—212no—
30C23×Dic13—248no—
31C23×Dic13D4124yes—
32C23×Dic13C2314yes—
33C23×Dic13C2314yes—
34C2×C13×C22⋊C4—26no—
35C2×C13×C22⋊C4—26no—
36C2×C13×C22⋊C4—212no—
37C2×C13×C22⋊C4—212no—
38C2×C22⋊Dic13—212no—
39C2×C22⋊Dic13—212no—
40C2×C22⋊Dic13C2×C4124yescomplemented
41C2×#6101—224no—
42#88071—224no—
43#14693—131nomaximal, Sylow
44C24×C13—232no—
45C24×C13—296no—
46C24×C13—248no—
47C24×C13—224no—
48C24×C13—248no—
49C24×C13—224no—
50C24×C13—212no—
51C24×C13—212no—
52C24×C13C4⋊C4116yescomplemented
53C24×C13C22×C416yes—
54C24×C13C2×D4112yes—
55C24×C13C2×D416yes—
56C24×C13C2×Q816yes—
57C24×C13#41112yes—
58C24×C13C2411yescharacteristic
59C22×C4×C13—26no—
60C22×C4×C13—26no—
61C22×C4×C13—21no—
62C22×C4×C13—23no—
63C22×C4×C13—212no—
64C22×Dic13—2256no—
65C22×Dic13—296no—
66C22×Dic13—296no—
67C22×Dic13—248no—
68C22×Dic13—212no—
69C22×Dic13—24no—
70C22×Dic13—296no—
71C22×Dic13—212no—
72C22×Dic13—212no—
73C22×Dic13C22×C418yescomplemented
74C22×Dic13C2×D4124yes—
75C13×C22⋊C4—412no—
76C13×C22⋊C4—412no—
77C22⋊Dic13—248no—
78#6101—416no—
79C25×C4—131no—
80C2×#385—136no—
81C2×#379—131no—
82C2×#379D1311yescharacteristic
83C22⋊#95—136no—
84C23×C13—232no—
85C23×C13—2128no—
86C23×C13—296no—
87C23×C13—2128no—
88C23×C13—224no—
89C23×C13—224no—
90C23×C13—212no—
91C23×C13—224no—
92C23×C13—212no—
93C23×C13—224no—
94C23×C13—248no—
95C23×C13—296no—
96C23×C13C2×C4⋊C4112yes—
97C23×C13C4×D4124yes—
98C23×C13#120112yes—
99C23×C13C22⋊Q8124yes—
100C23×C13#123112yes—
101C23×C13C23×C411yescharacteristic
102C23×C13C22×D411yescharacteristic
103C23×C13C22×D416yes—
104C23×C13C22×Q811yescharacteristic
105C23×C13C2×#4116yes—
106C2×C4×C13—44no—
107C2×C4×C13—43no—
108C2×C4×C13—43no—
109C2×C4×C13—46no—
110C2×C4×C13—412no—
111C2×Dic13—2192no—
112C2×Dic13—224no—
113C2×Dic13—224no—
114C2×Dic13—224no—
115C2×Dic13—44no—
116C2×Dic13—412no—
117C2×Dic13#120116yes—
118C26C2×D1311yescharacteristic
119C24×C4—136no—
120C24×C4—2624no—
121C24×C4—264no—
122C22×C4⋊C4—134no—
123C22×C22⋊C4—136no—
124C22×C22⋊C4C2×D1313yes—
125C22×C22⋊C4C2×D1313yes—
126#385—2624no—
127#379—24no—
128#379—138no—
129C2×#95—1312no—
130C22×C13—2128no—
131C22×C13—212no—
132C22×C13—248no—
133C22×C13—212no—
134C22×C13—224no—
135C22×C13—224no—
136C22×C13—248no—
137C22×C13#385124yescomplemented
138C22×C13C22×C4⋊C411yescharacteristic
139C22×C13C2×C4×D416yes—
140C22×C13C2×#12013yes—
141C22×C13C2×#12014yes—
142C22×C13C2×C22⋊Q816yes—
143C22×C13C2×#12313yes—
144C22×C13#525112yes—
145C4×C13—81no—
146C4×C13—83no—
147Dic13—216no—
148Dic13—48no—
149C25—212no—
150C25—212no—
151C25Dic2614yes—
152C25C4×D1314yes—
153C25C22⋊D1314yes—
154C25C22×D1313yes—
155C23×C4—134no—
156C23×C4—1324no—
157C23×C4—134no—
158C23×C4—2648no—
159C23×C4—26128no—
160C23×C4—2696no—
161C23×C4—2612no—
162C23×C4—2612no—
163C23×C4C22×D1311yescharacteristic
164C23×C4C22×D1313yes—
165C2×C4⋊C4—2624no—
166C2×C22⋊C4—212no—
167C2×C22⋊C4—212no—
168C2×C22⋊C4—26no—
169C2×C22⋊C4—26no—
170C2×C22⋊C4—1324no—
171C2×C22⋊C4—2612no—
172C2×C22⋊C4—2612no—
173#95—2624no—
174C2×C13—224no—
175C2×C13C2×#38513yes—
176C2×C13C4×#12014yes—
177C2×C13#284611yescharacteristic
178C2×C13#284814yes—
179C2×C13#284913yes—
180C24—232no—
181C24—296no—
182C24—248no—
183C24—248no—
184C24—224no—
185C24—224no—
186C24—212no—
187C24—212no—
188C24#6101116yescomplemented
189C24C2×Dic2616yes—
190C24C2×C4×D1316yes—
191C24D4×D13112yes—
192C24#6129112yes—
193C24C2×C22⋊D1316yes—
194C24C23×D1311yescharacteristic
195C22×C4—26no—
196C22×C4—26no—
197C22×C4—212no—
198C22×C4—23no—
199C22×C4—21no—
200C22×C4—1324no—
201C22×C4—138no—
202C22×C4—2696no—
203C22×C4—26256no—
204C22×C4—2696no—
205C22×C4—2696no—
206C22×C4—2648no—
207C22×C4—2612no—
208C22×C4—264no—
209C22×C4—2612no—
210C22×C4—2612no—
211C4⋊C4—5216no—
212C22⋊C4—412no—
213C22⋊C4—412no—
214C22⋊C4—2648no—
215C13#1469311yescharacteristic, complemented, Sylow
216C23—232no—
217C23—2128no—
218C23—296no—
219C23—2128no—
220C23—224no—
221C23—224no—
222C23—212no—
223C23—212no—
224C23—224no—
225C23—248no—
226C23—224no—
227C23—296no—
228C23#88132124yes—
229C23#88135124yes—
230C23C2×#6101112yes—
231C23#88189112yes—
232C23#88191112yes—
233C23C22×Dic2611yescharacteristic
234C23C22×C4×D1311yescharacteristic
235C23C2×D4×D1316yes—
236C23C2×#612916yes—
237C23C22×C22⋊D1311yescharacteristic
238C2×C4—46no—
239C2×C4—43no—
240C2×C4—43no—
241C2×C4—412no—
242C2×C4—44no—
243C2×C4—1316no—
244C2×C4—26192no—
245C2×C4—2624no—
246C2×C4—2624no—
247C2×C4—2624no—
248C2×C4—5212no—
249C2×C4—524no—
250C22—2128no—
251C22—212no—
252C22—248no—
253C22—224no—
254C22—212no—
255C22—224no—
256C22—248no—
257C22#11718607124yescomplemented
258C22C2×#8813216yes—
259C22C2×#8813516yes—
260C22#11719291112yes—
261C22D13×#12014yes—
262C22C22×#610111yescharacteristic
263C22C2×#8818913yes—
264C22C2×#8819113yes—
265C4—81no—
266C4—83no—
267C4—2616no—
268C4—528no—
269C2—224no—
270C2C2×#1171860713yes—
271C2#1311733514yes—
272C2#1312311211yescharacteristic
273C2#1312312114yes—
274C2#1312312613yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#379C2
socle, cosocleC24×C13C24
prime radicalC26×C13C22
hypercenterC2×#379D13
hypocenterC13#14693
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#11718607C2semidirect
4. #13113058C2semidirect
13. C22×#6101C22semidirect
15. #11718908C4semidirect
16. C2×#88071C22semidirect
40. C2×C22⋊Dic13C2×C4semidirect
52. C24×C13C4⋊C4semidirect
73. C22×Dic13C22×C4semidirect
137. C22×C13#385semidirect
188. C24#6101semidirect
215. C13#14693semidirect
257. C22#11718607semidirect

Maximal subgroups

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

subgroupindex
C25×Dic132
C2×#117186072
C2×#117189082
#131130582
C2×C13×#3792
#1469313