Finite Group Databasebeta

← #15758823

Subgroups — #15758823

Order 3328.

566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124629C211yesmaximal, characteristic
2#13117744C211yesmaximal, characteristic
3#13113335C211yesmaximal, characteristic, complemented
4#13113228C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic, complemented
6#13112694C211yesmaximal, characteristic, complemented
7C13×#1518C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×#88147—21no—
10C2×C4×D52C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#382C2211yescharacteristic
13#11718748C412yescomplemented
14#11718745C412yescomplemented
15#11718727—22no—
16#11718662—21no—
17#11718656—21no—
18#11718634—21no—
19C4×C4⋊Dic13C2211yescharacteristic
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22#11718329—22no—
23#11718328—21no—
24D13×#95—21no—
25C13×#328—22no—
26#11718130—21no—
27#11718130—21no—
28#11718051—22no—
29C22×D52D411yescharacteristic
30C22×C4×D13—21no—
31C22×C4×D13—22no—
32C13×C4⋊Q8C2×C411yescharacteristic, complemented
33C13×C4⋊Q8C2×C411yescharacteristic, complemented
34C13×#125—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C13×#117—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6103—21no—
43C2×#6103—22no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13D411yescharacteristic
46C2×#6101—22no—
47C2×C4×Dic13—21no—
48C2×#6099—21no—
49#88147—42no—
50#88147—42no—
51C4×D52—21no—
52C4×D52—21no—
53C4×D52C2×C412yes—
54C4×D52D412yes—
55C13×C4⋊C8—21no—
56C13×C22⋊C8—21no—
57C4×C8×C13—21no—
58C13×#95—21no—
59C13×#95D412yes—
60#88071—22no—
61#88071D411yescharacteristic
62#88071D411yescharacteristic
63C22⋊#1055—21no—
64#88049—22no—
65#88049—22no—
66#88048—22no—
67#88047—22no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055C2×C412yescomplemented
71C4×#1055—21no—
72#9175—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C2×D52—21no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52C22⋊C412yes—
87C2×D52SD1612yes—
88C2×D52Q1612yes—
89C2×C4×D13—22no—
90C2×C4×D13—22no—
91C2×C4×D13—44no—
92C2×C4×D13—44no—
93C2×C4×D13—82no—
94C2×C4×D13—82no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C22⋊C4—41no—
105C42×C13—41no—
106C42×C13C22×C411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109C42×C13#4111yescharacteristic
110#6103—22no—
111#6103—22no—
112#6103—44no—
113C4⋊Dic13—21no—
114C4⋊Dic13—42no—
115C4⋊Dic13C22⋊C412yes—
116#6101—82no—
117C4×Dic13—41no—
118C4×Dic13—41no—
119#6099—41no—
120#6099—41no—
121C2×#1055—22no—
122C2×#1055—41no—
123#3077—131no—
124#2349—131no—
125#1518D1311yescharacteristic, complemented
126#1503—131no—
127#1478—131no—
128#1303—131no—
129#1286—131no—
130C23×C13#12011yescharacteristic
131C22×D13—22no—
132C22×D13—22no—
133C22×D13—22no—
134C22×D13—42no—
135C22×D13—42no—
136Q8×C13—81no—
137Q8×C13—81no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13C2×C22⋊C411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12311yescharacteristic
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13C2×Q1611yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—42no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163D52—22no—
164D52—22no—
165D52—22no—
166D52#10314yes—
167C4×D13—82no—
168C4×D13—82no—
169C4×D13—88no—
170C8×C13—81no—
171#1055—42no—
172#1055—81no—
173#533C2×D1311yescharacteristic
174C2×C4×D4—131no—
175C2×C4×D4—261no—
176#478—262no—
177#476—132no—
178#474—132no—
179#431—131no—
180#431C2×D1311yescharacteristic
181#428—261no—
182#423—131no—
183#418—261no—
184#389—261no—
185#385—262no—
186#382C2×D1311yescharacteristic
187#380—261no—
188C4×C4⋊C4—131no—
189C2×#95—261no—
190#328—22no—
191#328—261no—
192#328—261no—
193D4⋊C8—262no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13#38611yescharacteristic
197C22×C13#45011yescharacteristic
198C22×C13#45111yescharacteristic
199C2×D13—24no—
200C2×D13—44no—
201C2×D13—44no—
202C2×D13—42no—
203C2×D13—42no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—82no—
209C4×C13—81no—
210C4×C13—81no—
211C4×C13C2×#10311yescharacteristic
212C4×C13#41711yescharacteristic
213C4×C13#48311yescharacteristic
214C4×C13#48411yescharacteristic
215Dic13—42no—
216Dic13—42no—
217Dic13—81no—
218C22×D4—131no—
219C23×C4—262no—
220C23×C4—261no—
221C2×M16—261no—
222C4⋊Q8C4×D1311yescharacteristic, complemented
223C4⋊Q8C4×D1311yescharacteristic, complemented
224#125—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×D4—132no—
230C4×D4—132no—
231C4×D4—261no—
232C4×D4—261no—
233C4×D4—522no—
234C4×D4—522no—
235#117—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—262no—
240C2×C22⋊C4—261no—
241C2×C22⋊C4—262no—
242C2×C42—261no—
243C2×C42C22×D1311yescharacteristic
244#107—262no—
245#106—262no—
246C4⋊C8—21no—
247C4⋊C8—132no—
248C4⋊C8—261no—
249C4⋊C8—261no—
250#102—262no—
251#102—262no—
252C22⋊C8—21no—
253C22⋊C8—261no—
254C4×C8—21no—
255C4×C8—261no—
256#95—21no—
257#95—131no—
258#95—131no—
259#95—262no—
260#95C22⋊D1312yes—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13#187211yescharacteristic
264C2×C13#190411yescharacteristic
265C2×C13#190611yescharacteristic
266D13—44no—
267C24—261no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×D4—132no—
271C2×D4—132no—
272C2×D4—132no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C22×C4—22no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—262no—
280C22×C4—262no—
281C22×C4—261no—
282C22×C4—524no—
283C22×C4—524no—
284C22×C4—1042no—
285C22×C4—1042no—
286C22×C4D4×D1311yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C22×C4C2×C22⋊D1311yescharacteristic
289M16—521no—
290M16—521no—
291C2×C8—41no—
292C2×C8—262no—
293C2×C8—521no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—132no—
303C4⋊C4—261no—
304C4⋊C4—522no—
305C4⋊C4—1042no—
306C22⋊C4—41no—
307C22⋊C4—262no—
308C22⋊C4—262no—
309C22⋊C4—524no—
310C42—41no—
311C42—521no—
312C42—521no—
313C42C2×C4×D1311yescharacteristic
314C42#612711yescharacteristic
315C42D4×D1311yescharacteristic
316C42#612911yescharacteristic
317C13#917511yescharacteristic, complemented, Sylow
318C23—262no—
319C23—262no—
320C23—262no—
321C23—522no—
322C23—522no—
323C23#8819111yescharacteristic
324Q8—81no—
325Q8—81no—
326D4—134no—
327D4—262no—
328D4—262no—
329D4—262no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—262no—
338C2×C4—262no—
339C2×C4—522no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—1042no—
346C2×C4—1042no—
347C2×C4—1048no—
348C2×C4C22⋊C4×D1311yescharacteristic
349C2×C4#8813511yescharacteristic
350C2×C4#8813711yescharacteristic
351C2×C4#8813811yescharacteristic
352C2×C4SD16×D1311yescharacteristic
353C2×C4#8816811yescharacteristic
354C2×C4Q16×D1311yescharacteristic
355C2×C4#8817211yescharacteristic
356C2×C4C4×C22⋊D1311yescharacteristic
357C2×C4#8819211yescharacteristic
358C8—81no—
359C8—522no—
360C8—1041no—
361C22—21no—
362C22—21no—
363C22—264no—
364C22—524no—
365C22—524no—
366C22—522no—
367C22—522no—
368C22#1171861711yescharacteristic
369C22#1171883011yescharacteristic
370C22#1171884711yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—522no—
379C4—522no—
380C4—1041no—
381C4D13×#10311yescharacteristic
382C4#1171846411yescharacteristic
383C4#1171846611yescharacteristic
384C4#1171847011yescharacteristic
385C2—21no—
386C2—21no—
387C2—524no—
388C2#1311514011yescharacteristic
389C2#1311532011yescharacteristic
390C2#1311533411yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1518C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1518D13
hypocenterC13#9175
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
3. #13113335C2semidirect
5. #13112738C2semidirect
6. #13112694C2semidirect
7. C13×#1518C2semidirect
13. #11718748C4semidirect
14. #11718745C4semidirect
32. C13×C4⋊Q8C2×C4semidirect
33. C13×C4⋊Q8C2×C4semidirect
70. C4⋊#1055C2×C4semidirect
125. #1518D13semidirect
222. C4⋊Q8C4×D13semidirect
223. C4⋊Q8C4×D13semidirect
317. C13#9175semidirect

Maximal subgroups

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

subgroupindex
#131246292
#131177442
#131133352
#131132282
#131127382
#131126942
C13×#15182
#917513