Finite Group Databasebeta

← #15764154

Subgroups — #15764154

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2#13120010C211yesmaximal, characteristic
3#13115760C211yesmaximal, characteristic, complemented
4C2×#11718138C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, 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
15#11718892—22no—
16C2×#88075—22no—
17#11718748—22no—
18#11718748—22no—
19#11718649—21no—
20#11718648—22no—
21#11718638—21no—
22C2×#88049—21no—
23C2×#88047—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718138—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13—21no—
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⋊Q8—21no—
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×#6103—24no—
49C2×C4⋊Dic13D411yescharacteristic
50C2×C4⋊Dic13D412yes—
51C2×C4×Dic13—21no—
52C22×#1055—21no—
53C22×#1055—21no—
54C4×D52—21no—
55C4×D52—21no—
56C4×D52—21no—
57C4×D52—21no—
58C13×#103—28no—
59C4×C8×C13—21no—
60C4×C8×C13D412yes—
61#88075—44no—
62#88071—24no—
63#88071—21no—
64#88049—24no—
65#88047—24no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70#10072—131nomaximal, Sylow
71C23×D13—21no—
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—22no—
75C2×Q8×C13—44no—
76C2×Q8×C13—41no—
77C2×Q8×C13—42no—
78C2×Q8×C13—42no—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—22no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52Q1612yes—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—42no—
95C2×C4×D13—42no—
96C2×C8×C13—22no—
97C2×C8×C13—42no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
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×C13#4111yescharacteristic
110#6103—41no—
111#6103—41no—
112#6103—84no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4×Dic13—41no—
118C4×Dic13—41no—
119C2×#1055—22no—
120C2×#1055—41no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—42no—
124C2×#487D1311yescharacteristic, complemented
125C2×#474—131no—
126#2563—131no—
127#1981—131no—
128C2×#333—131no—
129C2×D4⋊C8—131no—
130#1279—131no—
131C23×C13#12011yescharacteristic
132C22×D13—22no—
133C22×D13—41no—
134C22×D13—42no—
135C22×D13—41no—
136C22×D13—42no—
137Q8×C13—44no—
138Q8×C13—44no—
139Q8×C13—82no—
140Q8×C13—81no—
141Q8×C13—81no—
142C2×C4×C13—22no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—44no—
146C2×C4×C13—82no—
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12711yescharacteristic
153C2×C4×C13C2×Q1611yescharacteristic
154C2×C4×C13#13511yescharacteristic
155C2×C4×C13#13512yes—
156C2×C4×C13AGL(1,ℤ/8)12yes—
157C2×C4×C13#13711yescharacteristic
158C2×C4×C13#13711yescharacteristic
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164D52—22no—
165D52—22no—
166D52—41no—
167D52—41no—
168C4×D13—82no—
169C4×D13—81no—
170C4×D13—81no—
171C8×C13—42no—
172#1055—42no—
173#1055—81no—
174C2×C4⋊Q8C2×D1311yescharacteristic
175C2×C4⋊Q8C2×D1311yescharacteristic
176C2×C4×D4—131no—
177#487—22no—
178#487—22no—
179#474—262no—
180#474—262no—
181C2×#107—261no—
182C2×C4⋊C8—131no—
183C2×C4⋊C8—131no—
184C2×#103—22no—
185C2×#103—262no—
186C2×#102—261no—
187C2×C4×C8C2×D1311yescharacteristic
188#393—262no—
189#390—261no—
190#382—261no—
191#380—262no—
192C4×C4⋊C4—131no—
193#333—262no—
194D4⋊C8—262no—
195C22×C13#39211yescharacteristic
196C22×C13#44912yes—
197C22×C13#45111yescharacteristic
198C22×C13#45211yescharacteristic
199C22×C13#45512yes—
200C2×D13—44no—
201C2×D13—42no—
202C2×D13—82no—
203C2×D13—81no—
204C2×D13—81no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—82no—
208C4×C13—82no—
209C4×C13#45111yescharacteristic
210C4×C13#45211yescharacteristic
211C4×C13#46312yes—
212C4×C13#46711yescharacteristic
213C4×C13#47011yescharacteristic
214C4×C13#49511yescharacteristic
215C4×C13#49611yescharacteristic
216Dic13—82no—
217Dic13—81no—
218C22×Q8—21no—
219C22×Q8C22⋊D1312yes—
220C22×D4—131no—
221C23×C4—261no—
222C22×C8—21no—
223C22×C8—261no—
224C22×C8—261no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C22⋊D1312yes—
233C4×D4—261no—
234C4×D4—261no—
235C4×D4—261no—
236C4×D4—261no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—132no—
243C2×C22⋊C4—261no—
244C2×C22⋊C4—264no—
245C2×C42—261no—
246C2×C42C22×D1311yescharacteristic
247#107—264no—
248C4⋊C8—132no—
249C4⋊C8—261no—
250C4⋊C8—261no—
251C4⋊C8—261no—
252#103—28no—
253#103—524no—
254#102—264no—
255C4×C8—21no—
256C4×C8C22⋊D1312yes—
257#95—264no—
258#95—261no—
259C2×C13#164412yes—
260C2×C13#164612yes—
261C2×C13#200111yescharacteristic
262C2×C13#200411yescharacteristic
263C2×C13#201211yescharacteristic
264D13—82no—
265C24—261no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—44no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×D4—132no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—261no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—261no—
282C22×C4—262no—
283C22×C4—522no—
284C22×C4—522no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4D4×D1311yescharacteristic
288C22×C4D4×D1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290C2×C8—22no—
291C2×C8—42no—
292C2×C8—262no—
293C2×C8—521no—
294C2×C8—521no—
295C2×C8—522no—
296C2×C8—521no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—262no—
306C4⋊C4—262no—
307C4⋊C4—261no—
308C4⋊C4—261no—
309C22⋊C4—521no—
310C22⋊C4—521no—
311C22⋊C4—1044no—
312C42—521no—
313C42—521no—
314C42D4×D1311yescharacteristic
315C42#612911yescharacteristic
316C42C2×C22⋊D1311yescharacteristic
317C42C2×C22⋊D1311yescharacteristic
318C13#1007211yescharacteristic, complemented, Sylow
319C23—262no—
320C23—522no—
321C23—522no—
322C23—521no—
323C23—521no—
324C23#8819111yescharacteristic
325Q8—44no—
326Q8—44no—
327Q8—82no—
328Q8—81no—
329Q8—81no—
330D4—262no—
331D4—262no—
332D4—521no—
333D4—521no—
334C2×C4—22no—
335C2×C4—44no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—521no—
344C2×C4—1042no—
345C2×C4—1041no—
346C2×C4—1041no—
347C2×C4#8816812yes—
348C2×C4#8817012yes—
349C2×C4Q16×D1311yescharacteristic
350C2×C4#8817211yescharacteristic
351C2×C4#8817211yescharacteristic
352C2×C4#8817311yescharacteristic
353C2×C4#8819111yescharacteristic
354C2×C4#8819211yescharacteristic
355C2×C4#8819311yescharacteristic
356C2×C4#8819311yescharacteristic
357C2×C4#8819411yescharacteristic
358C2×C4#8820711yescharacteristic
359C8—42no—
360C8—522no—
361C8—1041no—
362C22—524no—
363C22—522no—
364C22—1041no—
365C22—1042no—
366C22—1041no—
367C22#1171872212yes—
368C22#1171883312yes—
369C22#1171884711yescharacteristic
370C22#1171884811yescharacteristic
371C22#1171888411yescharacteristic
372C4—21no—
373C4—21no—
374C4—82no—
375C4—82no—
376C4—1041no—
377C4—1042no—
378C4#1171882612yes—
379C4#1171882911yescharacteristic
380C4#1171883711yescharacteristic
381C4#1171884711yescharacteristic
382C4#1171884811yescharacteristic
383C4#1171884911yescharacteristic
384C4#1171885011yescharacteristic
385C2—1042no—
386C2#1311404712yes—
387C2#1311406112yes—
388C2#1311584311yescharacteristic
389C2#1311586511yescharacteristic
390C2#1311591011yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#487D13
hypocenterC13#10072
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
3. #13115760C2semidirect
4. C2×#11718138C2semidirect
6. #13112676C2semidirect
7. C2×C13×#487C2semidirect
124. C2×#487D13semidirect
318. C13#10072semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131200102
#131157602
C2×#117181382
C2×#117180512
#131126762
C2×C13×#4872
#1007213