Finite Group Databasebeta

← #15794132

Subgroups — #15794132

Order 3328.

7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.

normal subgroups only

This group has 7034 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, complemented
2C22×#88207C211yesmaximal, characteristic
3C2×#11718619C216yesmaximal, complemented
4#13113058C216yesmaximal, complemented
5C2×C13×#379C211yesmaximal, characteristic, complemented
6C26×C13C2211yescharacteristic
7C23×C22⋊D13C2213yes—
8C24×Dic13—24no—
9C24×Dic13—224no—
10C24×Dic13C2216yes—
11C22×C13×C22⋊C4C2216yes—
12C2×#88207—24no—
13C2×#88207—24no—
14C2×#88207C418yescomplemented
15C22×C22⋊Dic13C2213yes—
16C22×#6103C2214yescomplemented
17C13×#379—24no—
18C2×#88071C22112yescomplemented
19#11718619—224no—
20C25×C13—212no—
21C25×C13—212no—
22C25×C13C2×C414yes—
23C25×C13D414yes—
24C25×C13D414yes—
25C25×C13C2313yes—
26C24×D13C2311yescharacteristic
27C23×C4×C13C2314yes—
28C22×C22⋊D13—26no—
29C22×C22⋊D13—26no—
30C22×C22⋊D13—212no—
31C22×C22⋊D13—212no—
32C22×C22⋊D13C2×C4112yescomplemented
33C23×Dic13—296no—
34C23×Dic13—2128no—
35C23×Dic13—212no—
36C23×Dic13—212no—
37C23×Dic13—248no—
38C23×Dic13D4124yescomplemented
39C23×Dic13C2313yes—
40C23×Dic13C2314yes—
41C2×C13×C22⋊C4—212no—
42C2×C13×C22⋊C4—212no—
43C2×C13×C22⋊C4—212no—
44#88207—232no—
45C2×C22⋊Dic13—26no—
46C2×C22⋊Dic13—26no—
47C2×C22⋊Dic13C2×C4112yescomplemented
48C2×#6103—224no—
49#88071—224no—
50#14694—131nomaximal, Sylow
51C24×C13—232no—
52C24×C13—296no—
53C24×C13—248no—
54C24×C13—224no—
55C24×C13—248no—
56C24×C13—224no—
57C24×C13—212no—
58C24×C13—212no—
59C24×C13C22⋊C4116yescomplemented
60C24×C13C22×C416yes—
61C24×C13C2×D416yes—
62C24×C13C2×D4112yes—
63C24×C13C2×D416yes—
64C24×C13#41112yes—
65C24×C13C2411yescharacteristic
66C23×D13—26no—
67C23×D13—21no—
68C23×D13—21no—
69C23×D13—26no—
70C23×D13C22×C412yescomplemented
71C22×C4×C13—212no—
72C22×C4×C13—24no—
73C22×C4×C13—212no—
74C2×C22⋊D13—224no—
75C2×C22⋊D13—248no—
76C2×C22⋊D13—412no—
77C2×C22⋊D13—424no—
78C2×C22⋊D13—412no—
79C22×Dic13—2256no—
80C22×Dic13—296no—
81C22×Dic13—296no—
82C22×Dic13—248no—
83C22×Dic13—24no—
84C22×Dic13—212no—
85C22×Dic13—296no—
86C22×Dic13—26no—
87C22×Dic13—23no—
88C22×Dic13—23no—
89C22×Dic13—26no—
90C22×Dic13C22×C416yescomplemented
91C22×Dic13C2×D4124yes—
92C13×C22⋊C4—424no—
93C22⋊Dic13—224no—
94#6103—416no—
95C25×C4—131no—
96C22×#120—131no—
97C2×#386—136no—
98C2×#379D1311yescharacteristic, complemented
99C22⋊#95—136no—
100C23×C13—232no—
101C23×C13—2128no—
102C23×C13—296no—
103C23×C13—2128no—
104C23×C13—224no—
105C23×C13—224no—
106C23×C13—212no—
107C23×C13—224no—
108C23×C13—212no—
109C23×C13—224no—
110C23×C13—248no—
111C23×C13—296no—
112C23×C13C2×C22⋊C4112yes—
113C23×C13C4×D4124yes—
114C23×C13#120112yes—
115C23×C13#121124yes—
116C23×C13#123112yes—
117C23×C13C23×C411yescharacteristic
118C23×C13C22×D411yescharacteristic
119C23×C13C22×D411yescharacteristic
120C23×C13C22×D416yes—
121C23×C13C2×#4116yes—
122C22×D13—22no—
123C22×D13—212no—
124C22×D13—44no—
125C22×D13—43no—
126C22×D13—46no—
127C22×D13—43no—
128C22×D13—412no—
129C2×C4×C13—44no—
130C2×C4×C13—412no—
131C2×C4×C13—412no—
132C22⋊D13—448no—
133C2×Dic13—2192no—
134C2×Dic13—224no—
135C2×Dic13—224no—
136C2×Dic13—26no—
137C2×Dic13—212no—
138C2×Dic13—43no—
139C2×Dic13—46no—
140C2×Dic13—43no—
141C2×Dic13#120116yescomplemented
142C26C2×D1311yescharacteristic
143C23×D4—133no—
144C24×C4—136no—
145C24×C4—2624no—
146C24×C4—264no—
147C2×#120—138no—
148C2×#120—264no—
149C2×#120—264no—
150C22×C22⋊C4—133no—
151C22×C22⋊C4—134no—
152C22×C22⋊C4C2×D1316yes—
153#386—2624no—
154#379—24no—
155C2×#95—1312no—
156C22×C13—2128no—
157C22×C13—212no—
158C22×C13—248no—
159C22×C13—212no—
160C22×C13—224no—
161C22×C13—224no—
162C22×C13—248no—
163C22×C13#386124yescomplemented
164C22×C13C22×C22⋊C411yescharacteristic
165C22×C13C2×C4×D416yes—
166C22×C13C2×#12013yes—
167C22×C13C2×#12014yes—
168C22×C13C2×#12116yes—
169C22×C13C2×#12313yes—
170C22×C13#525112yes—
171C2×D13—46no—
172C2×D13—48no—
173C2×D13—81no—
174C2×D13—84no—
175C2×D13—83no—
176C4×C13—84no—
177Dic13—216no—
178Dic13—46no—
179C25—212no—
180C25—212no—
181C25—131no—
182C25C4×D1314yes—
183C25D5214yes—
184C25C22⋊D1314yes—
185C25C22×D1313yes—
186C22×D4—1312no—
187C22×D4—266no—
188C22×D4—2612no—
189C22×D4—2612no—
190C22×D4—266no—
191C23×C4—134no—
192C23×C4—1324no—
193C23×C4—133no—
194C23×C4—2648no—
195C23×C4—26128no—
196C23×C4—2696no—
197C23×C4—2612no—
198C23×C4—2612no—
199C23×C4C22×D1314yes—
200#120—2632no—
201C2×C22⋊C4—212no—
202C2×C22⋊C4—212no—
203C2×C22⋊C4—212no—
204C2×C22⋊C4—1312no—
205C2×C22⋊C4—266no—
206C2×C22⋊C4—266no—
207C2×C22⋊C4—2624no—
208#95—2624no—
209C2×C13—224no—
210C2×C13C2×#38613yes—
211C2×C13C4×#12014yes—
212C2×C13#284611yescharacteristic
213C2×C13#284714yes—
214C2×C13#284913yes—
215D13—82no—
216C24—232no—
217C24—296no—
218C24—248no—
219C24—224no—
220C24—224no—
221C24—248no—
222C24—212no—
223C24—212no—
224C24—132no—
225C24—261no—
226C24—266no—
227C24—266no—
228C24—261no—
229C24#6103116yescomplemented
230C24C2×C4×D1316yes—
231C24C2×D5216yes—
232C24D4×D13112yes—
233C24#6129112yes—
234C24C2×C22⋊D1316yes—
235C24C23×D1311yescharacteristic
236C2×D4—2648no—
237C2×D4—2624no—
238C2×D4—5212no—
239C2×D4—5212no—
240C2×D4—5224no—
241C22×C4—212no—
242C22×C4—212no—
243C22×C4—24no—
244C22×C4—1324no—
245C22×C4—136no—
246C22×C4—2696no—
247C22×C4—26256no—
248C22×C4—2696no—
249C22×C4—2696no—
250C22×C4—2648no—
251C22×C4—264no—
252C22×C4—2612no—
253C22×C4—263no—
254C22×C4—266no—
255C22×C4—266no—
256C22×C4—263no—
257C22⋊C4—424no—
258C22⋊C4—2624no—
259C22⋊C4—5216no—
260C13#1469411yescharacteristic, complemented, Sylow
261C23—232no—
262C23—2128no—
263C23—296no—
264C23—2128no—
265C23—224no—
266C23—212no—
267C23—212no—
268C23—224no—
269C23—224no—
270C23—248no—
271C23—224no—
272C23—296no—
273C23—2612no—
274C23—262no—
275C23—523no—
276C23—523no—
277C23—526no—
278C23—5212no—
279C23—524no—
280C23#88135124yes—
281C23#88136112yes—
282C23#88140112yes—
283C23C2×#6103112yes—
284C23#88193124yes—
285C23C22×C4×D1311yescharacteristic
286C23C22×D5211yescharacteristic
287C23C2×D4×D1316yes—
288C23C2×#612916yes—
289C23C22×C22⋊D1311yescharacteristic
290D4—5248no—
291C2×C4—412no—
292C2×C4—412no—
293C2×C4—44no—
294C2×C4—1316no—
295C2×C4—26192no—
296C2×C4—2624no—
297C2×C4—2624no—
298C2×C4—2612no—
299C2×C4—266no—
300C2×C4—523no—
301C2×C4—523no—
302C2×C4—526no—
303C22—2128no—
304C22—212no—
305C22—248no—
306C22—212no—
307C22—224no—
308C22—224no—
309C22—248no—
310C22—526no—
311C22—528no—
312C22—1041no—
313C22—1044no—
314C22—1043no—
315C22#11718619124yescomplemented
316C22C2×#8813516yes—
317C22C2×#8813613yes—
318C22C2×#8814013yes—
319C22#11719291112yes—
320C22D13×#12014yes—
321C22C22×#610311yescharacteristic
322C22C2×#8819316yes—
323C4—84no—
324C4—2616no—
325C4—526no—
326C2—224no—
327C2—1042no—
328C2C2×#1171861913yes—
329C2#1311733514yes—
330C2#1312311411yescharacteristic
331C2#1312311614yes—
332C2#1312313013yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#379C2
socle, cosocleC24×C13C24
prime radicalC22×#88207C2
hypercenterC2×#379D13
hypocenterC13#14694
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C25×Dic13C2semidirect
3. C2×#11718619C2semidirect
4. #13113058C2semidirect
5. C2×C13×#379C2semidirect
14. C2×#88207C4semidirect
16. C22×#6103C22semidirect
18. C2×#88071C22semidirect
32. C22×C22⋊D13C2×C4semidirect
38. C23×Dic13D4semidirect
47. C2×C22⋊Dic13C2×C4semidirect
59. C24×C13C22⋊C4semidirect
70. C23×D13C22×C4semidirect
90. C22×Dic13C22×C4semidirect
98. C2×#379D13semidirect
141. C2×Dic13#120semidirect
163. C22×C13#386semidirect
229. C24#6103semidirect
260. C13#14694semidirect
315. C22#11718619semidirect

Maximal subgroups

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

subgroupindex
C25×Dic132
C22×#882072
C2×#117186192
#131130582
C2×C13×#3792
#1469413