Finite Group Databasebeta

← #15785631

Subgroups — #15785631

Order 3328.

2230 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718598C211yesmaximal, characteristic, complemented
2C2×#11718593C211yesmaximal, characteristic, complemented
3#13113104C212yesmaximal, complemented
4#13113077C212yesmaximal
5#13113073C214yesmaximal, complemented
6#13113059C214yesmaximal, complemented
7C22×C4×D4×C13C211yesmaximal, characteristic
8C23×D4×C13C2211yescharacteristic
9C24×C4×C13C2212yes—
10C2×C4×D4×C13—24no—
11C2×C4×D4×C13—24no—
12C2×C4×D4×C13C418yescomplemented
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C42×C13C2211yescharacteristic
16C22×C22⋊Dic13C2218yes—
17C22×C4×Dic13C2212yes—
18C2×#88071C2212yes—
19C2×#88071C2212yes—
20C2×#88071C2212yes—
21C2×#88071C2212yes—
22C2×#88071C2212yes—
23C2×#88071C2218yes—
24#11718598—24no—
25#11718593—24no—
26C25×C13C2312yes—
27C22×D4×C13—28no—
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13C2×C414yes—
31C23×C4×C13—24no—
32C23×C4×C13—24no—
33C23×C4×C13—48no—
34C23×C4×C13C2×C418yes—
35C23×C4×C13C2312yes—
36C23×C4×C13C2311yescharacteristic
37C23×C4×C13C2311yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C23×Dic13C2314yes—
40C23×Dic13C2314yes—
41C4×D4×C13—232no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4—22no—
44C2×C13×C4⋊C4C2×C414yes—
45C2×C13×C22⋊C4—24no—
46C2×C13×C22⋊C4—24no—
47C2×C13×C22⋊C4C2×C418yes—
48C2×C42×C13C2×C414yes—
49C2×C42×C13D414yes—
50C2×C42×C13D414yes—
51C2×C22⋊Dic13—216no—
52C2×C22⋊Dic13—216no—
53C2×C22⋊Dic13—48no—
54C2×C4×Dic13—24no—
55C2×C4×Dic13—28no—
56#88071—24no—
57#88071—24no—
58#88071—24no—
59#88071—24no—
60#88071—24no—
61#88071—48no—
62#13959—131nomaximal, Sylow
63C24×C13—22no—
64C24×C13—22no—
65C24×C13—28no—
66C24×C13—24no—
67C24×C13—28no—
68C24×C13C22×C414yes—
69C24×C13#4118yes—
70C24×C13C2411yescharacteristic
71C2×D4×C13—216no—
72C2×D4×C13—216no—
73C2×D4×C13—216no—
74C2×D4×C13—28no—
75C22×C4×C13—24no—
76C22×C4×C13—24no—
77C22×C4×C13—24no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—28no—
81C22×C4×C13—216no—
82C22×C4×C13—416no—
83C22×C4×C13—416no—
84C22×C4×C13—416no—
85C22×C4×C13C22×C414yes—
86C22×C4×C13C22×C412yes—
87C22×C4×C13C22×C412yes—
88C22×C4×C13C22×C412yes—
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2×D412yes—
93C22×C4×C13C2×D412yes—
94C22×C4×C13C2×D412yes—
95C22×Dic13—24no—
96C22×Dic13—24no—
97C22×Dic13—28no—
98C22×Dic13—28no—
99C22×Dic13—24no—
100C22×Dic13—28no—
101C22×Dic13—28no—
102C22×Dic13—24no—
103C22×Dic13—24no—
104C22×Dic13#4118yes—
105C13×C4⋊C4—28no—
106C13×C22⋊C4—216no—
107C42×C13C22⋊C4116yescomplemented
108C22⋊Dic13—432no—
109C4×Dic13—216no—
110C22×C4×D4D1311yescharacteristic
111C2×#383—131no—
112C2×#376—131no—
113#1445—132no—
114#1438—132no—
115#1437—134no—
116C22⋊#95—134no—
117C23×C13—24no—
118C23×C13—24no—
119C23×C13—28no—
120C23×C13—28no—
121C23×C13—28no—
122C23×C13—28no—
123C23×C13—216no—
124C23×C13—216no—
125C23×C13—44no—
126C23×C13—44no—
127C23×C13—44no—
128C23×C13—44no—
129C23×C13—48no—
130C23×C13—48no—
131C23×C13#11718yes—
132C23×C13C23×C411yescharacteristic
133C23×C13C22×D411yescharacteristic
134C23×C13C22×D411yescharacteristic
135C23×C13C2×#4114yes—
136C23×C13C2×#4114yes—
137C23×C13H(5,𝔽2)14yes—
138D4×C13—232no—
139C2×C4×C13—24no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—24no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—24no—
148C2×C4×C13—24no—
149C2×C4×C13—28no—
150C2×C4×C13—432no—
151C2×C4×C13—44no—
152C2×C4×C13—44no—
153C2×C4×C13C2×C22⋊C414yes—
154C2×C4×C13C2×C22⋊C414yes—
155C2×C4×C13C2×C22⋊C414yes—
156C2×Dic13—28no—
157C2×Dic13—216no—
158C2×Dic13—44no—
159C2×Dic13—44no—
160C2×Dic13—48no—
161C2×Dic13—44no—
162C2×Dic13—44no—
163C2×Dic13—44no—
164C2×Dic13—48no—
165C2×Dic13—48no—
166C23×D4C2×D1311yescharacteristic
167C24×C4C2×D1312yes—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4Dic1318yescomplemented
171C22×C4⋊C4C2×D1311yescharacteristic
172C22×C22⋊C4—138no—
173C22×C22⋊C4C2×D1312yes—
174C22×C42—132no—
175C22×C42C2×D1311yescharacteristic
176#383—264no—
177#376—264no—
178C2×#95—132no—
179C2×#95—132no—
180C2×#95—132no—
181C2×#95—132no—
182C2×#95—132no—
183C2×#95—138no—
184C22×C13—216no—
185C22×C13—28no—
186C22×C13—44no—
187C22×C13—416no—
188C22×C13—416no—
189C22×C13—48no—
190C22×C13—44no—
191C22×C13C22×C22⋊C411yescharacteristic
192C22×C13C2×#11712yes—
193C22×C13C4×#4112yes—
194C22×C13#51812yes—
195C22×C13#52512yes—
196C22×C13#52512yes—
197C22×C13#52512yes—
198C22×C13#53212yes—
199C22×C13#53512yes—
200C22×C13#53512yes—
201C22×C13#55118yes—
202C22×C13#55318yes—
203C4×C13—24no—
204C4×C13—24no—
205C4×C13—24no—
206C4×C13—44no—
207Dic13—48no—
208Dic13—84no—
209C25C22×D1312yes—
210C22×D4—28no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4C2×Dic1314yes—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—48no—
217C23×C4—134no—
218C23×C4—134no—
219C23×C4C2×Dic1318yes—
220C23×C4C22×D1312yes—
221C23×C4C22×D1311yescharacteristic
222C23×C4C22×D1311yescharacteristic
223C23×C4C22×D1311yescharacteristic
224C4×D4—232no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C2×Dic1314yes—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—2616no—
231C2×C22⋊C4—2616no—
232C2×C22⋊C4—528no—
233C2×C22⋊C4C2×Dic1318yes—
234C2×C42—268no—
235C2×C42—264no—
236C2×C42C2×Dic1314yes—
237C2×C42C22⋊D1314yes—
238C2×C42C22⋊D1314yes—
239#95—264no—
240#95—264no—
241#95—264no—
242#95—264no—
243#95—264no—
244#95—528no—
245C2×C13—48no—
246C2×C13#228011yescharacteristic
247C2×C13#229711yescharacteristic
248C2×C13#230911yescharacteristic
249C2×C13#235314yes—
250C2×C13#259814yes—
251C2×C13#260314yes—
252C24—24no—
253C24—28no—
254C24—28no—
255C24—22no—
256C24—22no—
257C24#612718yes—
258C24C22×Dic1314yes—
259C24C23×D1311yescharacteristic
260C2×D4—216no—
261C2×D4—216no—
262C2×D4—216no—
263C2×D4—28no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—28no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—216no—
271C22×C4—416no—
272C22×C4—416no—
273C22×C4—416no—
274C22×C4—138no—
275C22×C4—268no—
276C22×C4—268no—
277C22×C4—264no—
278C22×C4—264no—
279C22×C4—268no—
280C22×C4—264no—
281C22×C4—264no—
282C22×C4—268no—
283C22×C4—264no—
284C22×C4C22×Dic1314yes—
285C22×C4C22×Dic1312yes—
286C22×C4C22×Dic1312yes—
287C22×C4C22×Dic1312yes—
288C22×C4C2×C22⋊D1312yes—
289C22×C4C2×C22⋊D1312yes—
290C22×C4C2×C22⋊D1312yes—
291C22×C4C2×C22⋊D1312yes—
292C22×C4C2×C22⋊D1312yes—
293C22×C4C2×C22⋊D1312yes—
294C4⋊C4—28no—
295C22⋊C4—216no—
296C22⋊C4—5232no—
297C42—2616no—
298C42C22⋊Dic13116yescomplemented
299C13#1395911yescharacteristic, complemented, Sylow
300C23—24no—
301C23—28no—
302C23—28no—
303C23—216no—
304C23—28no—
305C23—216no—
306C23—28no—
307C23—24no—
308C23—48no—
309C23—44no—
310C23—44no—
311C23—48no—
312C23—44no—
313C23—44no—
314C23#8818018yes—
315C23C2×#612714yes—
316C23#8825114yes—
317C23#41×D1314yes—
318C23C23×Dic1311yescharacteristic
319C23C22×C22⋊D1311yescharacteristic
320C23C22×C22⋊D1311yescharacteristic
321D4—232no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—432no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—2616no—
337C2×C4—268no—
338C2×C4—524no—
339C2×C4—528no—
340C2×C4—524no—
341C2×C4—524no—
342C2×C4—528no—
343C2×C4—524no—
344C2×C4—528no—
345C2×C4—524no—
346C2×C4C2×C22⋊Dic1314yes—
347C2×C4C2×C22⋊Dic1314yes—
348C2×C4C2×C22⋊Dic1314yes—
349C22—28no—
350C22—216no—
351C22—48no—
352C22—416no—
353C22—44no—
354C22—416no—
355C22—44no—
356C22#1171924518yes—
357C22#1171926118yes—
358C22C2×#8818012yes—
359C22#1171949612yes—
360C22#1171949612yes—
361C22#1171950312yes—
362C22#1171951012yes—
363C22#1171951012yes—
364C22#41×Dic1312yes—
365C22#1171953312yes—
366C22#1171953712yes—
367C22C22×C22⋊Dic1311yescharacteristic
368C4—24no—
369C4—24no—
370C4—24no—
371C4—44no—
372C4—528no—
373C4—1044no—
374C2—48no—
375C2#1311721911yescharacteristic
376C2#1311732711yescharacteristic
377C2#1311741811yescharacteristic
378C2#1311777614yes—
379C2#1312039614yes—
380C2#1312045714yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×D4×C13C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13#13959
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11718598C2semidirect
2. C2×#11718593C2semidirect
3. #13113104C2semidirect
5. #13113073C2semidirect
6. #13113059C2semidirect
12. C2×C4×D4×C13C4semidirect
107. C42×C13C22⋊C4semidirect
170. C2×C4×D4Dic13semidirect
298. C42C22⋊Dic13semidirect
299. C13#13959semidirect

Maximal subgroups

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

subgroupindex
C2×#117185982
C2×#117185932
#131131042
#131130772
#131130732
#131130592
C22×C4×D4×C132
#1395913