Finite Group Databasebeta

← #15765470

Subgroups — #15765470

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718746C211yesmaximal, characteristic
2C2×#11718688C211yesmaximal, characteristic
3#13115773C211yesmaximal, characteristic, complemented
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic, complemented
7C2×C13×#475C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C22×#6106—21no—
11C22×#6106—22no—
12C2×#88128C2211yescharacteristic
13C13×#475—22no—
14C13×#475—22no—
15C2×C13×#106—21no—
16C2×C13×C4⋊C8C2211yescharacteristic
17C2×C13×#103—21no—
18#11718746—22no—
19#11718746—22no—
20#11718688—22no—
21#11718688—22no—
22C2×#88049—21no—
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4×#1055C2211yescharacteristic
26#11718139—22no—
27#11718116—22no—
28#11718077—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D411yescharacteristic
31C22×D52—21no—
32C22×D52—21no—
33C22×D52—21no—
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
49C2×#6106—24no—
50C2×#6106—28no—
51C2×#6106—44no—
52C2×#6106—42no—
53C2×#6106—42no—
54C2×#6106—44no—
55C22×#1055—21no—
56C22×#1055—21no—
57C22×#1055D412yes—
58#88128—21no—
59#88128—21no—
60#88128—21no—
61#88128D412yes—
62C13×#106—24no—
63C13×C4⋊C8—21no—
64C13×C4⋊C8D412yes—
65C13×#103—24no—
66#88049—24no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71C4×#1055—21no—
72C4×#1055—21no—
73#10268—131nomaximal, Sylow
74C23×D13—41no—
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—22no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—41no—
82C2×Q8×C13—42no—
83C2×Q8×C13—42no—
84C2×Q8×C13SD1612yescomplemented
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—41no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13#4111yescharacteristic
91C2×D52—22no—
92C2×D52—22no—
93C2×D52—22no—
94C2×D52—41no—
95C2×D52—42no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—42no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—41no—
103C2×D52—82no—
104C2×C8×C13—22no—
105C2×C8×C13—41no—
106C2×C8×C13—41no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
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×C13C2×D411yescharacteristic
121#6106—416no—
122#6106—48no—
123C2×#1055—22no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055—42no—
130C2×#1055SD1614yescomplemented
131C2×#492—131no—
132C2×#475D1311yescharacteristic, complemented
133C2×#460—131no—
134#1984—131no—
135C2×#332—131no—
136C2×#331—131no—
137#1277—131no—
138C23×C13#12111yescharacteristic
139C22×D13—42no—
140C22×D13—82no—
141C22×D13—81no—
142C22×D13—81no—
143C22×D13—82no—
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#12011yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12711yescharacteristic
165C2×C4×C13C2×SD1611yescharacteristic
166C2×C4×C13C2×SD1612yes—
167C2×C4×C13#13511yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C13AGL(1,ℤ/8)12yes—
170C2×C4×C13#13711yescharacteristic
171D52—42no—
172D52—44no—
173D52—42no—
174D52—82no—
175D52—82no—
176D52—81no—
177D52—81no—
178D52—81no—
179D52—81no—
180C8×C13—42no—
181#1055—24no—
182#1055—42no—
183#1055—81no—
184C22×SD16—262no—
185C22×SD16—261no—
186C2×C4⋊Q8C2×D1311yescharacteristic
187C2×#127—131no—
188C2×C4×Q8C2×D1311yescharacteristic
189#492—262no—
190#492—262no—
191#475—22no—
192#475—22no—
193#460—262no—
194#460—262no—
195C2×#106—21no—
196C2×C4⋊C8—131no—
197C2×C4⋊C8—131no—
198C2×C4⋊C8C2×D1311yescharacteristic
199C2×#103—21no—
200C2×#102—261no—
201C2×C4×C8—131no—
202#336—262no—
203#332—262no—
204#331—262no—
205C22×C13#39211yescharacteristic
206C22×C13#46012yes—
207C22×C13#46511yescharacteristic
208C22×C13#46811yescharacteristic
209C22×C13#47112yes—
210C2×D13—82no—
211C2×D13—82no—
212C2×D13—82no—
213C2×D13—162no—
214C2×D13—162no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—42no—
218C4×C13—82no—
219C4×C13—81no—
220C4×C13#44811yescharacteristic
221C4×C13#44911yescharacteristic
222C4×C13#45011yescharacteristic
223C4×C13#45012yes—
224C4×C13#45211yescharacteristic
225C4×C13#49211yescharacteristic
226C4×C13#49611yescharacteristic
227C22×Q8—21no—
228C22×Q8C22⋊D1311yescharacteristic
229C22×D4—261no—
230C22×D4—261no—
231C22×D4—261no—
232C2×SD16—264no—
233C2×SD16—268no—
234C2×SD16—524no—
235C2×SD16—524no—
236C2×SD16—522no—
237C2×SD16—522no—
238C22×C8—21no—
239C22×C8—132no—
240C22×C8—261no—
241C22×C8—261no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8C22⋊D1312yes—
246#127—132no—
247#127—261no—
248#127—261no—
249#127—261no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C22⋊D1311yescharacteristic
258C2×C42—21no—
259C2×C42C22×D1311yescharacteristic
260#106—24no—
261C4⋊C8—21no—
262C4⋊C8—132no—
263C4⋊C8—261no—
264C4⋊C8—261no—
265C4⋊C8—261no—
266C4⋊C8C22⋊D1312yes—
267#103—24no—
268#102—264no—
269C4×C8—261no—
270C4×C8—261no—
271C2×C13#166612yes—
272C2×C13#168612yes—
273C2×C13#200011yescharacteristic
274C2×C13#201411yescharacteristic
275C2×C13#201911yescharacteristic
276D13—162no—
277C24—521no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—41no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8#610612yescomplemented
288C2×D4—262no—
289C2×D4—262no—
290C2×D4—262no—
291C2×D4—522no—
292C2×D4—522no—
293C2×D4—521no—
294C2×D4—521no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C2×D4—521no—
299C2×D4—521no—
300C2×D4—1042no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4D4×D1311yescharacteristic
305C22×C4#612911yescharacteristic
306C22×C4C2×C22⋊D1311yescharacteristic
307SD16—5216no—
308SD16—528no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—134no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—521no—
317C2×C8—521no—
318C2×C8—522no—
319C2×C8—521no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C42—41no—
329C42—41no—
330C42D4×D1311yescharacteristic
331C42D4×D1311yescharacteristic
332C42C2×C22⋊D1311yescharacteristic
333C42C2×C22⋊D1311yescharacteristic
334C13#1026811yescharacteristic, complemented, Sylow
335C23—522no—
336C23—1041no—
337C23—1041no—
338C23—1042no—
339C23—1042no—
340C23#8819311yescharacteristic
341Q8—22no—
342Q8—22no—
343Q8—41no—
344Q8—41no—
345Q8—44no—
346Q8—81no—
347Q8—81no—
348D4—522no—
349D4—522no—
350D4—524no—
351D4—1042no—
352D4—1042no—
353D4—1041no—
354D4—1041no—
355D4—1041no—
356D4—1041no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4SD16×D1312yes—
366C2×C4#8816812yes—
367C2×C4#8819111yescharacteristic
368C2×C4#8819111yescharacteristic
369C2×C4#8819211yescharacteristic
370C2×C4#8819311yescharacteristic
371C2×C4#8819411yescharacteristic
372C2×C4C2×#610611yescharacteristic
373C2×C4#8819611yescharacteristic
374C2×C4#8820311yescharacteristic
375C2×C4#8820411yescharacteristic
376C2×C4#8820711yescharacteristic
377C8—42no—
378C8—264no—
379C8—522no—
380C8—1041no—
381C22—1042no—
382C22—1042no—
383C22—1042no—
384C22—2082no—
385C22—2082no—
386C22#1171870911yescharacteristic
387C22#1171871011yescharacteristic
388C22#1171882412yes—
389C22#1171886412yes—
390C22#1171888411yescharacteristic
391C4—21no—
392C4—21no—
393C4—42no—
394C4—82no—
395C4—81no—
396C4#1171870711yescharacteristic
397C4#1171870811yescharacteristic
398C4#1171883012yes—
399C4#1171883611yescharacteristic
400C4#1171883711yescharacteristic
401C4#1171888811yescharacteristic
402C4#1171889911yescharacteristic
403C2—2082no—
404C2#1311418612yes—
405C2#1311431012yes—
406C2#1311583711yescharacteristic
407C2#1311592211yescharacteristic
408C2#1311594711yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#475C2
socleC23×C13#121
prime radicalC2×#88128C22
hypercenterC2×#475D13
hypocenterC13#10268
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. #13115773C2semidirect
4. C2×#11718139C2semidirect
6. #13112670C2semidirect
7. C2×C13×#475C2semidirect
84. C2×Q8×C13SD16semidirect
130. C2×#1055SD16semidirect
132. C2×#475D13semidirect
287. C2×Q8#6106semidirect
334. C13#10268semidirect

Maximal subgroups

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

subgroupindex
C2×#117187462
C2×#117186882
#131157732
C2×#117181392
C2×#117180772
#131126702
C2×C13×#4752
#1026813