Finite Group Databasebeta

← #15765518

Subgroups — #15765518

Order 3328.

562 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×#11718745C211yesmaximal, characteristic
2C2×#11718748C211yesmaximal, characteristic
3#13115630C211yesmaximal, characteristic
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718139C211yesmaximal, characteristic, complemented
6#13112671C211yesmaximal, characteristic, complemented
7C2×C13×#487C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C13×#487—22no—
12C13×#487—22no—
13C2×C13×#103—22no—
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88060—22no—
16#11718748—22no—
17#11718748—22no—
18#11718745—22no—
19#11718745—22no—
20C2×#88049—21no—
21C2×#88049—21no—
22C2×#88048—21no—
23C2×#88047—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—22no—
28#11718138—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13D412yes—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8D412yes—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6103—21no—
48C2×C4⋊Dic13D411yescharacteristic
49C22×#1055—21no—
50C22×#1055—21no—
51C22×#1055—21no—
52C4×D52—21no—
53C4×D52—21no—
54C4×D52—21no—
55C4×D52—21no—
56C13×#103—28no—
57C4×C8×C13—21no—
58C4×C8×C13—21no—
59#88060—44no—
60#88049—24no—
61#88049—24no—
62#88048—24no—
63#88047—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055D412yes—
69C4⋊#1055D412yes—
70#10275—131nomaximal, Sylow
71C23×D13—21no—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—42no—
77C2×Q8×C13—42no—
78C2×Q8×C13—82no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52Q1612yes—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—42no—
94C2×C4×D13—42no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110#6103—41no—
111#6103—41no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C2×#1055—22no—
115C2×#1055—22no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#1055—42no—
122C2×#487D1311yescharacteristic, complemented
123C2×#476—131no—
124C2×#474—131no—
125#1954—131no—
126C2×#333—131no—
127C2×#332—131no—
128#1277—131no—
129C23×C13#12111yescharacteristic
130C22×D13—22no—
131C22×D13—41no—
132C22×D13—42no—
133C22×D13—41no—
134C22×D13—42no—
135Q8×C13—44no—
136Q8×C13—82no—
137Q8×C13—82no—
138Q8×C13—81no—
139Q8×C13—81no—
140C2×C4×C13—22no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—82no—
144C2×C4×C13—82no—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12711yescharacteristic
151C2×C4×C13C2×Q1611yescharacteristic
152C2×C4×C13#13512yes—
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)12yes—
155C2×C4×C13#13711yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—41no—
158C2×Dic13—42no—
159D52—22no—
160D52—22no—
161D52—41no—
162D52—41no—
163C4×D13—82no—
164C4×D13—81no—
165C4×D13—81no—
166C8×C13—42no—
167#1055—42no—
168#1055—42no—
169#1055—81no—
170C2×C4⋊Q8C2×D1311yescharacteristic
171C2×C4⋊Q8C2×D1311yescharacteristic
172C2×C4×D4—131no—
173#487—22no—
174#487—22no—
175#476—262no—
176#476—262no—
177#474—262no—
178#474—262no—
179C2×#107—261no—
180C2×#106—261no—
181C2×C4⋊C8—131no—
182C2×C4⋊C8—131no—
183C2×C4⋊C8—131no—
184C2×#103—22no—
185C2×#102—261no—
186C2×#102—261no—
187C2×C22⋊C8—262no—
188C2×C4×C8C2×D1311yescharacteristic
189#333—262no—
190#332—262no—
191C22×C13#39211yescharacteristic
192C22×C13#46312yes—
193C22×C13#46711yescharacteristic
194C22×C13#47011yescharacteristic
195C22×C13#47112yes—
196C2×D13—44no—
197C2×D13—42no—
198C2×D13—82no—
199C2×D13—81no—
200C2×D13—81no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—82no—
204C4×C13—82no—
205C4×C13#44912yes—
206C4×C13#45111yescharacteristic
207C4×C13#45111yescharacteristic
208C4×C13#45211yescharacteristic
209C4×C13#45211yescharacteristic
210C4×C13#49511yescharacteristic
211C4×C13#49611yescharacteristic
212Dic13—81no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×D4—131no—
216C23×C4—261no—
217C22×C8—261no—
218C22×C8—261no—
219C22×C8—261no—
220C22×C8C22⋊D1312yes—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22⋊D1312yes—
228C4⋊Q8C22⋊D1312yes—
229C4×D4—261no—
230C4×D4—261no—
231C4×D4—261no—
232C4×D4—261no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—131no—
238C2×C22⋊C4—261no—
239C2×C42C22×D1311yescharacteristic
240#107—264no—
241#106—264no—
242C4⋊C8—132no—
243C4⋊C8—132no—
244C4⋊C8—261no—
245C4⋊C8—261no—
246C4⋊C8—261no—
247C4⋊C8—261no—
248#103—28no—
249#102—264no—
250#102—264no—
251C22⋊C8—524no—
252C4×C8—21no—
253C4×C8—21no—
254C2×C13#168312yes—
255C2×C13#170312yes—
256C2×C13#200111yescharacteristic
257C2×C13#201211yescharacteristic
258C2×C13#201911yescharacteristic
259D13—82no—
260C24—261no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—82no—
268C2×D4—132no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C2×D4—261no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—261no—
277C22×C4—521no—
278C22×C4—522no—
279C22×C4—522no—
280C22×C4—521no—
281C22×C4D4×D1311yescharacteristic
282C22×C4#612911yescharacteristic
283C22×C4C2×C22⋊D1311yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—521no—
290C2×C8—521no—
291C2×C8—521no—
292C2×C8—521no—
293C2×C8—521no—
294C2×C8—522no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—261no—
304C4⋊C4—261no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C42D4×D1311yescharacteristic
308C42D4×D1311yescharacteristic
309C42C2×C22⋊D1311yescharacteristic
310C42C2×C22⋊D1311yescharacteristic
311C13#1027511yescharacteristic, complemented, Sylow
312C23—262no—
313C23—522no—
314C23—522no—
315C23—521no—
316C23—521no—
317C23#8819211yescharacteristic
318Q8—44no—
319Q8—82no—
320Q8—82no—
321Q8—81no—
322Q8—81no—
323D4—262no—
324D4—262no—
325D4—521no—
326D4—521no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—522no—
333C2×C4—521no—
334C2×C4—1041no—
335C2×C4—1041no—
336C2×C4—1042no—
337C2×C4Q16×D1311yescharacteristic
338C2×C4#8817211yescharacteristic
339C2×C4#8817211yescharacteristic
340C2×C4#8817311yescharacteristic
341C2×C4#8819111yescharacteristic
342C2×C4#8819111yescharacteristic
343C2×C4#8819311yescharacteristic
344C2×C4#8819311yescharacteristic
345C2×C4#8819411yescharacteristic
346C2×C4#8820312yes—
347C2×C4#8820412yes—
348C2×C4#8820711yescharacteristic
349C8—42no—
350C8—522no—
351C8—522no—
352C8—1041no—
353C22—524no—
354C22—522no—
355C22—1041no—
356C22—1042no—
357C22—1041no—
358C22#1171871812yes—
359C22#1171883812yes—
360C22#1171884911yescharacteristic
361C22#1171885011yescharacteristic
362C22#1171888411yescharacteristic
363C4—21no—
364C4—21no—
365C4—82no—
366C4—82no—
367C4—1041no—
368C4#1171871911yescharacteristic
369C4#1171872011yescharacteristic
370C4#1171884711yescharacteristic
371C4#1171884711yescharacteristic
372C4#1171884811yescharacteristic
373C4#1171884811yescharacteristic
374C4#1171889912yes—
375C2—1042no—
376C2#1311428412yes—
377C2#1311440812yes—
378C2#1311584311yescharacteristic
379C2#1311591311yescharacteristic
380C2#1311594811yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#487D13
hypocenterC13#10275
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. C2×#11718138C2semidirect
5. C2×#11718139C2semidirect
6. #13112671C2semidirect
7. C2×C13×#487C2semidirect
122. C2×#487D13semidirect
311. C13#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×#117187482
#131156302
C2×#117181382
C2×#117181392
#131126712
C2×C13×#4872
#1027513