Finite Group Databasebeta

← #15764148

Subgroups — #15764148

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718749C211yesmaximal, characteristic
2#13119835C211yesmaximal, characteristic
3#13115760C211yesmaximal, characteristic, complemented
4C2×#11718077C211yesmaximal, characteristic
5C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
6#13112675C211yesmaximal, characteristic, complemented
7C2×C13×#475C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×#88201—21no—
11C2×#88128C2211yescharacteristic
12C13×#475—22no—
13C13×#475—22no—
14C2×C13×#106—21no—
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17C2×#88075—22no—
18#11718749—22no—
19#11718749—22no—
20#11718652—22no—
21#11718649—21no—
22C2×#88049—22no—
23#11718600—22no—
24C4×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4×#1055C2211yescharacteristic
27Q8⋊#1055—22no—
28#11718077—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D411yescharacteristic
31C22×D52—21no—
32C22×D52—21no—
33C22×D52D412yes—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D412yes—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13C2311yescharacteristic
49#88201—42no—
50#88201—42no—
51C2×#6103—24no—
52C2×#6103—24no—
53C2×C4⋊Dic13D412yes—
54C2×C4×Dic13—21no—
55C22×#1055—21no—
56C22×#1055—21no—
57#88128—21no—
58#88128—21no—
59#88128—21no—
60#88128—21no—
61C13×#106—24no—
62C13×C4⋊C8—21no—
63C13×C4⋊C8D412yes—
64C13×#103—24no—
65#88075—44no—
66#88071—21no—
67#88049—28no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4×#1055—21no—
71C4×#1055D412yes—
72#10071—131nomaximal, Sylow
73C23×D13—22no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C2×Q8×C13—22no—
78C2×Q8×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—41no—
81C2×Q8×C13—42no—
82C2×Q8×C13—42no—
83C2×Q8×C13SD1612yes—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×Dic13—22no—
91C2×D52—22no—
92C2×D52—22no—
93C2×D52—44no—
94C2×D52—41no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—41no—
99C2×D52—41no—
100C2×D52—42no—
101C2×D52—41no—
102C2×D52—42no—
103C2×D52—41no—
104C2×C8×C13—22no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C42×C13—41no—
116C42×C13—41no—
117C42×C13C2×D411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13#4111yescharacteristic
121#6103—48no—
122#6103—84no—
123C4⋊Dic13—22no—
124C4⋊Dic13—22no—
125C4×Dic13—41no—
126C4×Dic13—41no—
127C2×#1055—22no—
128C2×#1055—42no—
129C2×#1055—41no—
130C2×#1055—42no—
131C2×#486—131no—
132C2×#475D1311yescharacteristic, complemented
133#2548—131no—
134#1981—131no—
135C2×#331—131no—
136C2×Q8⋊C8—131no—
137#1279—131no—
138C23×C13#12011yescharacteristic
139C22×D13—42no—
140C22×D13—44no—
141C22×D13—42no—
142C22×D13—42no—
143C22×D13—44no—
144Q8×C13—22no—
145Q8×C13—22no—
146Q8×C13—41no—
147Q8×C13—41no—
148Q8×C13—44no—
149Q8×C13—81no—
150Q8×C13—81no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—42no—
158C2×C4×C13—82no—
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12711yescharacteristic
165C2×C4×C13C2×SD1611yescharacteristic
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13#13512yes—
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)12yes—
170C2×C4×C13#13711yescharacteristic
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—42no—
174D52—44no—
175D52—82no—
176D52—81no—
177D52—81no—
178D52—82no—
179D52—81no—
180D52—81no—
181D52—81no—
182D52—81no—
183C8×C13—42no—
184#1055—42no—
185#1055—81no—
186C2×C4⋊Q8C2×D1311yescharacteristic
187C2×#127—131no—
188C2×#124—261no—
189C2×C4×Q8C2×D1311yescharacteristic
190#486—262no—
191#486—262no—
192#475—22no—
193#475—22no—
194C2×#106—21no—
195C2×C4⋊C8—131no—
196C2×C4⋊C8C2×D1311yescharacteristic
197C2×#103—21no—
198C2×#103—262no—
199C2×#102—262no—
200C2×C4×C8—131no—
201#394—262no—
202#390—262no—
203#390—261no—
204C4×C4⋊C4—131no—
205#331—262no—
206Q8⋊C8—262no—
207C22×C13#39211yescharacteristic
208C22×C13#44912yes—
209C22×C13#45011yescharacteristic
210C22×C13#45211yescharacteristic
211C22×C13#45512yes—
212C2×D13—84no—
213C2×D13—84no—
214C2×D13—82no—
215C2×D13—82no—
216C2×D13—82no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—81no—
221C4×C13—82no—
222C4×C13#44811yescharacteristic
223C4×C13#44911yescharacteristic
224C4×C13#46312yes—
225C4×C13#46511yescharacteristic
226C4×C13#46811yescharacteristic
227C4×C13#49511yescharacteristic
228C4×C13#49611yescharacteristic
229Dic13—82no—
230C22×Q8—21no—
231C22×Q8C22⋊D1311yescharacteristic
232C22×D4—132no—
233C22×D4—261no—
234C22×D4—261no—
235C22×C8—21no—
236C22×C8—261no—
237C22×C8—261no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8C22⋊D1312yes—
242#127—261no—
243#127—261no—
244#127—261no—
245#127—261no—
246#124—522no—
247#124—522no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—132no—
256C2×C4⋊C4C22⋊D1311yescharacteristic
257C2×C22⋊C4—264no—
258C2×C22⋊C4—264no—
259C2×C42—21no—
260C2×C42—261no—
261C2×C42C22×D1311yescharacteristic
262#106—24no—
263C4⋊C8—21no—
264C4⋊C8—261no—
265C4⋊C8—261no—
266C4⋊C8C22⋊D1312yes—
267#103—24no—
268#103—524no—
269#102—268no—
270C4×C8—132no—
271C4×C8—261no—
272#95—261no—
273C2×C13#164012yes—
274C2×C13#164212yes—
275C2×C13#200011yescharacteristic
276C2×C13#200411yescharacteristic
277C2×C13#201211yescharacteristic
278D13—162no—
279C24—262no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—41no—
287C2×Q8—42no—
288C2×Q8—42no—
289C2×Q8#610612yes—
290C2×D4—262no—
291C2×D4—262no—
292C2×D4—524no—
293C2×D4—522no—
294C2×D4—522no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C2×D4—521no—
299C2×D4—521no—
300C2×D4—521no—
301C2×D4—521no—
302C2×D4—521no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—262no—
307C22×C4D4×D1311yescharacteristic
308C22×C4D4×D1311yescharacteristic
309C22×C4C2×C22⋊D1311yescharacteristic
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—262no—
314C2×C8—522no—
315C2×C8—522no—
316C2×C8—521no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—262no—
326C4⋊C4—262no—
327C22⋊C4—528no—
328C22⋊C4—1044no—
329C42—41no—
330C42—41no—
331C42—521no—
332C42—521no—
333C42D4×D1311yescharacteristic
334C42#612911yescharacteristic
335C42C2×C22⋊D1311yescharacteristic
336C42C2×C22⋊D1311yescharacteristic
337C13#1007111yescharacteristic, complemented, Sylow
338C23—522no—
339C23—522no—
340C23—524no—
341C23—524no—
342C23—522no—
343C23#8819111yescharacteristic
344Q8—22no—
345Q8—22no—
346Q8—41no—
347Q8—41no—
348Q8—44no—
349Q8—81no—
350Q8—81no—
351D4—524no—
352D4—1042no—
353D4—1041no—
354D4—1041no—
355D4—1042no—
356D4—1041no—
357D4—1041no—
358D4—1041no—
359D4—1041no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—82no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4—522no—
371C2×C4#8816812yes—
372C2×C4#8817012yes—
373C2×C4#8819111yescharacteristic
374C2×C4#8819211yescharacteristic
375C2×C4#8819311yescharacteristic
376C2×C4#8819311yescharacteristic
377C2×C4#8819411yescharacteristic
378C2×C4C2×#610611yescharacteristic
379C2×C4#8819611yescharacteristic
380C2×C4#8820311yescharacteristic
381C2×C4#8820411yescharacteristic
382C2×C4#8820711yescharacteristic
383C8—42no—
384C8—522no—
385C8—1041no—
386C22—1042no—
387C22—1044no—
388C22—1044no—
389C22—1042no—
390C22—1042no—
391C22#1171870711yescharacteristic
392C22#1171870811yescharacteristic
393C22#1171883312yes—
394C22#1171886312yes—
395C22#1171888411yescharacteristic
396C4—21no—
397C4—21no—
398C4—42no—
399C4—82no—
400C4—81no—
401C4—1042no—
402C4#1171870911yescharacteristic
403C4#1171871011yescharacteristic
404C4#1171882612yes—
405C4#1171882911yescharacteristic
406C4#1171883711yescharacteristic
407C4#1171888811yescharacteristic
408C4#1171889911yescharacteristic
409C2—2082no—
410C2#1311402112yes—
411C2#1311403512yes—
412C2#1311583711yescharacteristic
413C2#1311586211yescharacteristic
414C2#1311591011yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#475C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenterC2×#475D13
hypocenterC13#10071
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13115760C2semidirect
5. C2×Q8⋊#1055C2semidirect
6. #13112675C2semidirect
7. C2×C13×#475C2semidirect
132. C2×#475D13semidirect
337. C13#10071semidirect

Maximal subgroups

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

subgroupindex
C2×#117187492
#131198352
#131157602
C2×#117180772
C2×Q8⋊#10552
#131126752
C2×C13×#4752
#1007113