Finite Group Databasebeta

← #15789663

Subgroups — #15789663

Order 3328.

1262 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718598C211yesmaximal, characteristic
2C2×C4×C4⋊Dic13C211yesmaximal, characteristic
3#13113100C212yesmaximal
4#13113099C212yesmaximal
5#13113095C212yesmaximal
6#13113092C212yesmaximal
7#13113067C214yesmaximal
8C2×C13×#382C211yesmaximal, characteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6101C2214yes—
15C22×C4×Dic13C2212yes—
16C13×#382—24no—
17C2×C13×#95C2212yes—
18C2×C13×#95C2212yes—
19C2×#88071C2214yes—
20C2×#88071C2212yes—
21C2×#88071C2214yes—
22C2×#88071C2214yes—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26#11718598C418yescomplemented
27C4×C4⋊Dic13—24no—
28C23×C4×C13C2312yes—
29C23×C4×C13C2312yes—
30C23×C4×C13C2311yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C23×Dic13C2314yes—
34C23×Dic13C2312yes—
35C23×Dic13C2312yes—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—22no—
38C2×C13×C4⋊C4—42no—
39C2×C13×C4⋊C4—42no—
40C2×C42×C13C2×C414yes—
41C2×C42×C13D414yes—
42C2×C42×C13Q814yes—
43C2×C4⋊Dic13—22no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—24no—
46C2×C4⋊Dic13—24no—
47C2×#6101—28no—
48C2×#6101—44no—
49C2×#6101—44no—
50C2×C4×Dic13—24no—
51C2×C4×Dic13—44no—
52C13×#95—24no—
53C13×#95—24no—
54#88071—24no—
55#88071—28no—
56#88071—44no—
57#88071—44no—
58#88071C2×C418yes—
59#88071C2×C418yes—
60#88071C2×C418yes—
61#14298—131nomaximal, Sylow
62C24×C13C2411yescharacteristic
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—24no—
72C22×C4×C13—24no—
73C22×C4×C13—22no—
74C22×C4×C13—24no—
75C22×C4×C13—22no—
76C22×C4×C13—24no—
77C22×C4×C13—24no—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C412yes—
80C22×C4×C13C22×C412yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×Q812yes—
85C22×C4×C13C2×Q812yes—
86C22×C4×C13C2×Q812yes—
87C22×Dic13—22no—
88C22×Dic13—22no—
89C22×Dic13—24no—
90C22×Dic13—24no—
91C22×Dic13—22no—
92C22×Dic13—22no—
93C22×Dic13—24no—
94C22×Dic13—24no—
95C22×Dic13—24no—
96C22×Dic13—24no—
97C22×Dic13—24no—
98C22×Dic13—24no—
99C22×Dic13—24no—
100C22×Dic13—24no—
101C22×Dic13C22×C418yes—
102C22×Dic13#4114yes—
103C22×Dic13#4114yes—
104C13×C4⋊C4—44no—
105C13×C4⋊C4—44no—
106C42×C13C4⋊C4116yescomplemented
107C4⋊Dic13—28no—
108C4⋊Dic13—28no—
109#6101—416no—
110C4×Dic13—48no—
111C2×#383—131no—
112C2×#382D1311yescharacteristic
113C2×C4×C4⋊C4—131no—
114#1444—132no—
115#1444—132no—
116#1442—132no—
117#1442—132no—
118#1436—134no—
119C23×C13C23×C411yescharacteristic
120C23×C13C22×D411yescharacteristic
121C23×C13C22×Q811yescharacteristic
122C23×C13C2×#4112yes—
123C23×C13C2×#4112yes—
124C23×C13H(5,𝔽2)12yes—
125C23×C13H(5,𝔽2)12yes—
126C23×C132−1+412yes—
127C23×C132−1+412yes—
128C2×C4×C13—24no—
129C2×C4×C13—24no—
130C2×C4×C13—24no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—24no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—44no—
147C2×C4×C13—44no—
148C2×C4×C13—48no—
149C2×C4×C13C2×C4⋊C414yes—
150C2×C4×C13C2×C4⋊C414yes—
151C2×C4×C13C2×C4⋊C414yes—
152C2×Dic13—28no—
153C2×Dic13—28no—
154C2×Dic13—28no—
155C2×Dic13—24no—
156C2×Dic13—24no—
157C2×Dic13—28no—
158C2×Dic13—28no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—44no—
164C2×Dic13—44no—
165C2×Dic13—44no—
166C2×Dic13—44no—
167C2×Dic13—44no—
168C2×Dic13—44no—
169C22×C4⋊C4—131no—
170C22×C4⋊C4—131no—
171C22×C4⋊C4—134no—
172C22×C4⋊C4C2×D1311yescharacteristic
173C22×C4⋊C4C2×D1311yescharacteristic
174C22×C42—132no—
175C22×C42C2×D1311yescharacteristic
176#383—138no—
177#382—24no—
178C4×C4⋊C4—264no—
179C2×#95—132no—
180C2×#95—132no—
181C2×#95—132no—
182C2×#95—134no—
183C2×#95—132no—
184C2×#95—134no—
185C2×#95—134no—
186C2×#95C2×D1312yes—
187C2×#95C2×D1312yes—
188C22×C13C22×C4⋊C411yescharacteristic
189C22×C13C4×#4112yes—
190C22×C13#52012yes—
191C22×C13#52012yes—
192C22×C13#52511yescharacteristic
193C22×C13#52511yescharacteristic
194C22×C13#53312yes—
195C22×C13#53511yescharacteristic
196C22×C13#53511yescharacteristic
197C22×C13#53611yescharacteristic
198C22×C13#53611yescharacteristic
199C22×C13#53814yes—
200C22×C13#53914yes—
201C22×C13#54114yes—
202C22×C13#54214yes—
203C22×C13#54412yes—
204C22×C13#54412yes—
205C4×C13—24no—
206C4×C13—24no—
207C4×C13—24no—
208C4×C13—82no—
209C4×C13—82no—
210Dic13—48no—
211Dic13—44no—
212Dic13—44no—
213C23×C4—132no—
214C23×C4—134no—
215C23×C4—132no—
216C23×C4C22×D1312yes—
217C23×C4C22×D1312yes—
218C23×C4C22×D1311yescharacteristic
219C23×C4C22×D1311yescharacteristic
220C23×C4C22×D1311yescharacteristic
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—264no—
226C2×C4⋊C4—264no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4—262no—
229C2×C4⋊C4—268no—
230C2×C4⋊C4—524no—
231C2×C4⋊C4—524no—
232C2×C42—264no—
233C2×C42—524no—
234C2×C42Dic2614yes—
235C2×C42C4×D1314yes—
236C2×C42C22⋊D1314yes—
237#95—24no—
238#95—24no—
239#95—138no—
240#95—138no—
241#95—138no—
242#95—268no—
243#95—264no—
244#95—524no—
245#95—524no—
246C2×C13#229611yescharacteristic
247C2×C13#231711yescharacteristic
248C2×C13#231711yescharacteristic
249C2×C13#233414yes—
250C2×C13#263111yescharacteristic
251C2×C13#263211yescharacteristic
252C2×C13#263311yescharacteristic
253C2×C13#263411yescharacteristic
254C2×C13#266614yes—
255C24C23×D1311yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—138no—
272C22×C4—134no—
273C22×C4—134no—
274C22×C4—264no—
275C22×C4—264no—
276C22×C4—264no—
277C22×C4—264no—
278C22×C4—264no—
279C22×C4—264no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—264no—
283C22×C4—264no—
284C22×C4—264no—
285C22×C4—264no—
286C22×C4—262no—
287C22×C4—262no—
288C22×C4C2×Dic2612yes—
289C22×C4C2×Dic2612yes—
290C22×C4C2×Dic2612yes—
291C22×C4C2×C4×D1312yes—
292C22×C4C2×C4×D1312yes—
293C22×C4C2×C4×D1312yes—
294C22×C4C2×C22⋊D1312yes—
295C22×C4C2×C22⋊D1312yes—
296C22×C4C2×C22⋊D1312yes—
297C4⋊C4—44no—
298C4⋊C4—44no—
299C4⋊C4—268no—
300C4⋊C4—268no—
301C4⋊C4—5216no—
302C42—528no—
303C42#6101116yescomplemented
304C13#1429811yescharacteristic, complemented, Sylow
305C23C22×Dic2611yescharacteristic
306C23C22×C4×D1311yescharacteristic
307C23#8825112yes—
308C23#8825412yes—
309C23#41×D1312yes—
310C23#41×D1312yes—
311C23#8825612yes—
312C23#8825712yes—
313C23C22×C22⋊D1311yescharacteristic
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—48no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—268no—
336C2×C4—268no—
337C2×C4—268no—
338C2×C4—264no—
339C2×C4—264no—
340C2×C4—268no—
341C2×C4—268no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—524no—
347C2×C4—524no—
348C2×C4—524no—
349C2×C4—524no—
350C2×C4—524no—
351C2×C4—524no—
352C2×C4C2×#610114yes—
353C2×C4C2×#610114yes—
354C2×C4C2×#610114yes—
355C22#1171920512yes—
356C22#1171920912yes—
357C22#1171922212yes—
358C22#1171922412yes—
359C22#1171922712yes—
360C22#1171922812yes—
361C22#1171937414yes—
362C22#1171938314yes—
363C22#1171939714yes—
364C22#1171940114yes—
365C22C22×#610111yescharacteristic
366C22#1171951011yescharacteristic
367C22#1171952111yescharacteristic
368C22#1171953011yescharacteristic
369C22#1171953311yescharacteristic
370C22#1171953311yescharacteristic
371C22#1171953511yescharacteristic
372C4—24no—
373C4—24no—
374C4—24no—
375C4—82no—
376C4—82no—
377C4—528no—
378C4—524no—
379C4—524no—
380C2#1311731811yescharacteristic
381C2#1311745611yescharacteristic
382C2#1311746011yescharacteristic
383C2#1311760714yes—
384C2#1312068911yescharacteristic
385C2#1312069711yescharacteristic
386C2#1312070511yescharacteristic
387C2#1312071311yescharacteristic
388C2#1312101714yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#382C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#382D13
hypocenterC13#14298
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
26. #11718598C4semidirect
106. C42×C13C4⋊C4semidirect
303. C42#6101semidirect
304. C13#14298semidirect

Maximal subgroups

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

subgroupindex
C2×#117185982
C2×C4×C4⋊Dic132
#131131002
#131130992
#131130952
#131130922
#131130672
C2×C13×#3822
#1429813