Finite Group Databasebeta

← #15785582

Subgroups — #15785582

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 388 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#13113101C212yesmaximal
4#13113093C212yesmaximal
5#13113070C214yesmaximal
6#13113066C212yesmaximal
7#13113063C212yesmaximal
8C2×C13×#376C211yesmaximal, characteristic
9C22×C42×C13C2212yes—
10C22×C42×C13C2211yescharacteristic
11C22×C4⋊Dic13C2212yes—
12C22×C4⋊Dic13C2214yes—
13C22×C4×Dic13C2212yes—
14C13×#376C418yescomplemented
15C2×C13×#95C2211yescharacteristic
16C2×C13×#95C2211yescharacteristic
17C2×C13×#95C2212yes—
18C2×#88071C2212yes—
19C2×#88071C2214yes—
20C2×#88071C2214yes—
21C2×#88071C2211yescharacteristic
22C2×#88071C2211yescharacteristic
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2214yes—
26#11718598—24no—
27C4×C4⋊Dic13—24no—
28C23×C4×C13C2312yes—
29C23×C4×C13C2311yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C23×C4×C13C2312yes—
33C23×Dic13C2312yes—
34C23×Dic13C2312yes—
35C23×Dic13C2314yes—
36C2×C42×C13—28no—
37C2×C42×C13C2×C418yes—
38C2×C42×C13C2×C414yes—
39C2×C42×C13D414yes—
40C2×C42×C13Q814yes—
41C2×C4⋊Dic13—24no—
42C2×C4⋊Dic13—28no—
43C2×C4⋊Dic13—28no—
44C2×C4⋊Dic13—28no—
45C2×C4⋊Dic13—44no—
46C2×C4×Dic13—24no—
47C2×C4×Dic13—42no—
48C2×C4×Dic13—42no—
49C13×#95C2×C414yes—
50C13×#95C2×C418yes—
51C13×#95C2×C414yes—
52#88071—24no—
53#88071—22no—
54#88071—22no—
55#88071—24no—
56#88071—24no—
57#88071—28no—
58#88071—28no—
59#88071—44no—
60#13952—131nomaximal, Sylow
61C24×C13C2411yescharacteristic
62C22×C4×C13—24no—
63C22×C4×C13—24no—
64C22×C4×C13—24no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—24no—
72C22×C4×C13—24no—
73C22×C4×C13—22no—
74C22×C4×C13—22no—
75C22×C4×C13C22×C414yes—
76C22×C4×C13C22×C412yes—
77C22×C4×C13C22×C412yes—
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C414yes—
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×Q812yes—
84C22×C4×C13C2×Q812yes—
85C22×C4×C13C2×Q812yes—
86C22×C4×C13#4118yes—
87C22×Dic13—24no—
88C22×Dic13—24no—
89C22×Dic13—24no—
90C22×Dic13—24no—
91C22×Dic13—24no—
92C22×Dic13—24no—
93C22×Dic13—22no—
94C22×Dic13—22no—
95C22×Dic13—24no—
96C22×Dic13—24no—
97C22×Dic13—24no—
98C22×Dic13—24no—
99C22×Dic13—22no—
100C22×Dic13—22no—
101C22×Dic13—22no—
102C22×Dic13—22no—
103C22×Dic13#4118yes—
104C42×C13—216no—
105C42×C13C4⋊C4116yescomplemented
106C4⋊Dic13—216no—
107C4⋊Dic13—416no—
108C4×Dic13—48no—
109C2×#383—131no—
110C2×C4×C4⋊C4—131no—
111C2×#376D1311yescharacteristic
112#1444—132no—
113#1442—132no—
114#1436—134no—
115C4⋊#95—132no—
116#1434—132no—
117C23×C13C23×C411yescharacteristic
118C23×C13C22×D411yescharacteristic
119C23×C13C22×Q811yescharacteristic
120C23×C13C2×#4114yes—
121C23×C13C2×#4114yes—
122C23×C13H(5,𝔽2)11yescharacteristic
123C23×C13H(5,𝔽2)11yescharacteristic
124C23×C132−1+411yescharacteristic
125C23×C132−1+411yescharacteristic
126C2×C4×C13—24no—
127C2×C4×C13—24no—
128C2×C4×C13—24no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—24no—
132C2×C4×C13—24no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13—28no—
141C2×C4×C13—28no—
142C2×C4×C13—24no—
143C2×C4×C13—24no—
144C2×C4×C13—24no—
145C2×C4×C13—44no—
146C2×C4×C13—44no—
147C2×C4×C13C2×C4⋊C414yes—
148C2×C4×C13C2×C4⋊C414yes—
149C2×C4×C13C2×C4⋊C414yes—
150C2×C4×C13#11718yes—
151C2×Dic13—28no—
152C2×Dic13—28no—
153C2×Dic13—28no—
154C2×Dic13—44no—
155C2×Dic13—44no—
156C2×Dic13—44no—
157C2×Dic13—44no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—44no—
165C2×Dic13—44no—
166C2×Dic13—44no—
167C2×Dic13—44no—
168C22×C4⋊C4—132no—
169C22×C4⋊C4—134no—
170C22×C42—132no—
171C22×C42C2×D1312yes—
172C22×C42C2×D1311yescharacteristic
173#383—264no—
174C4×C4⋊C4—264no—
175#376Dic1318yescomplemented
176C2×#95—131no—
177C2×#95—132no—
178C2×#95—134no—
179C2×#95—134no—
180C2×#95—131no—
181C2×#95—132no—
182C2×#95—132no—
183C2×#95—134no—
184C2×#95C2×D1312yes—
185C2×#95C2×D1311yescharacteristic
186C2×#95C2×D1311yescharacteristic
187C22×C13C22×C4⋊C411yescharacteristic
188C22×C13C2×#11712yes—
189C22×C13C4×#4112yes—
190C22×C13#52011yescharacteristic
191C22×C13#52011yescharacteristic
192C22×C13#52512yes—
193C22×C13#53212yes—
194C22×C13#53312yes—
195C22×C13#53312yes—
196C22×C13#53511yescharacteristic
197C22×C13#53611yescharacteristic
198C22×C13#54411yescharacteristic
199C22×C13#54411yescharacteristic
200C22×C13#55114yes—
201C22×C13#55214yes—
202C22×C13#55314yes—
203C22×C13#55614yes—
204C4×C13—24no—
205C4×C13—28no—
206C4×C13—24no—
207C4×C13—24no—
208C4×C13—44no—
209Dic13—48no—
210Dic13—82no—
211Dic13—82no—
212C23×C4—134no—
213C23×C4—132no—
214C23×C4—132no—
215C23×C4C22×D1312yes—
216C23×C4C22×D1311yescharacteristic
217C23×C4C22×D1311yescharacteristic
218C23×C4C22×D1311yescharacteristic
219C23×C4C22×D1312yes—
220C2×C4⋊C4—268no—
221C2×C4⋊C4—264no—
222C2×C4⋊C4—268no—
223C2×C4⋊C4—268no—
224C2×C4⋊C4—524no—
225C2×C42—28no—
226C2×C42—264no—
227C2×C42—522no—
228C2×C42—522no—
229C2×C42Dic2614yes—
230C2×C42D5214yes—
231C2×C42C2×Dic1318yes—
232C2×C42C2×Dic1314yes—
233#95—268no—
234#95—264no—
235#95—262no—
236#95—262no—
237#95—264no—
238#95—264no—
239#95—268no—
240#95—524no—
241#95C2×Dic1314yes—
242#95C2×Dic1318yes—
243#95C2×Dic1314yes—
244C2×C13#228511yescharacteristic
245C2×C13#229611yescharacteristic
246C2×C13#231711yescharacteristic
247C2×C13#234312yes—
248C2×C13#234712yes—
249C2×C13#260312yes—
250C2×C13#260412yes—
251C2×C13#260512yes—
252C2×C13#260612yes—
253C24C23×D1311yescharacteristic
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—138no—
268C22×C4—264no—
269C22×C4—264no—
270C22×C4—264no—
271C22×C4—264no—
272C22×C4—264no—
273C22×C4—264no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—264no—
277C22×C4—264no—
278C22×C4—264no—
279C22×C4—264no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—262no—
284C22×C4C2×Dic2612yes—
285C22×C4C2×Dic2612yes—
286C22×C4C2×Dic2612yes—
287C22×C4C2×D5212yes—
288C22×C4C2×D5212yes—
289C22×C4C2×D5212yes—
290C22×C4#612718yes—
291C22×C4C22×Dic1314yes—
292C22×C4C22×Dic1312yes—
293C22×C4C22×Dic1312yes—
294C22×C4C22×Dic1312yes—
295C22×C4C22×Dic1314yes—
296C4⋊C4—2616no—
297C4⋊C4—5216no—
298C42—216no—
299C42—528no—
300C42C4⋊Dic13116yescomplemented
301C13#1395211yescharacteristic, complemented, Sylow
302C23C22×Dic2611yescharacteristic
303C23C22×D5211yescharacteristic
304C23C2×#612714yes—
305C23#41×D1314yes—
306C23#8825611yescharacteristic
307C23#8825611yescharacteristic
308C23#8825711yescharacteristic
309C23#8825711yescharacteristic
310C23C23×Dic1311yescharacteristic
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—268no—
333C2×C4—268no—
334C2×C4—268no—
335C2×C4—524no—
336C2×C4—524no—
337C2×C4—524no—
338C2×C4—524no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—524no—
346C2×C4—524no—
347C2×C4—524no—
348C2×C4—524no—
349C2×C4C2×C4⋊Dic1314yes—
350C2×C4C2×C4⋊Dic1314yes—
351C2×C4C2×C4⋊Dic1314yes—
352C2×C4#8818018yes—
353C22#1171917512yes—
354C22#1171918212yes—
355C22#1171922212yes—
356C22#1171922411yescharacteristic
357C22#1171922411yescharacteristic
358C22#1171922912yes—
359C22#1171923011yescharacteristic
360C22#1171923111yescharacteristic
361C22#1171923214yes—
362C22#1171923514yes—
363C22#1171923614yes—
364C22#1171923814yes—
365C22C22×C4⋊Dic1311yescharacteristic
366C22C2×#8818012yes—
367C22#41×Dic1312yes—
368C22#1171953211yescharacteristic
369C22#1171953211yescharacteristic
370C4—28no—
371C4—24no—
372C4—24no—
373C4—24no—
374C4—44no—
375C4—528no—
376C4—1042no—
377C4—1042no—
378C2#1311724311yescharacteristic
379C2#1311732011yescharacteristic
380C2#1311745911yescharacteristic
381C2#1311769612yes—
382C2#1311772912yes—
383C2#1312046312yes—
384C2#1312047412yes—
385C2#1312048412yes—
386C2#1312049312yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#376C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#376D13
hypocenterC13#13952
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
14. C13×#376C4semidirect
105. C42×C13C4⋊C4semidirect
175. #376Dic13semidirect
300. C42C4⋊Dic13semidirect
301. C13#13952semidirect

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
#131131012
#131130932
#131130702
#131130662
#131130632
C2×C13×#3762
#1395213