Finite Group Databasebeta

← #13115901

Subgroups — #13115901

Order 1664.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C13×#525C211yesmaximal, characteristic, complemented
2#11719527C211yesmaximal, characteristic, complemented
3#11719496C211yesmaximal, characteristic, complemented
4#11718897C211yesmaximal, characteristic, complemented
5#11718868C211yesmaximal, characteristic, complemented
6#11718666C211yesmaximal, characteristic, complemented
7#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#41C2211yescharacteristic
9C23×C4×C13C2211yescharacteristic
10C2×#6127C2211yescharacteristic
11C13×#123—21no—
12C13×C22⋊Q8—21no—
13C13×#121—21no—
14C13×#120—21no—
15C4×D4×C13—22no—
16C13×#117C2211yescharacteristic
17#88207—21no—
18#88205—21no—
19#88204—22no—
20#88203—21no—
21#88196—21no—
22#88186—21no—
23#88184—21no—
24#88183—21no—
25C4×C22⋊D13—22no—
26#88180C2211yescharacteristic
27#88178—21no—
28C2×#6099C2211yescharacteristic
29C2×#6099C2211yescharacteristic
30#88077—22no—
31C22⋊#1055—22no—
32#88045—22no—
33C24×C13D411yescharacteristic
34C13×#41—21no—
35C13×#41—21no—
36C13×#41—21no—
37C13×#41—21no—
38C2×Q8×C13D411yescharacteristic, complemented
39C2×D4×C13—22no—
40C2×D4×C13—21no—
41C2×D4×C13D411yescharacteristic, complemented
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13D411yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—22no—
52C2×C22⋊D13—21no—
53#6127—21no—
54#6127—21no—
55#6127—21no—
56#6127—21no—
57C2×D52D411yescharacteristic, complemented
58C2×C4×D13—21no—
59C2×Dic26D411yescharacteristic, complemented
60C13×C4⋊C4—22no—
61C13×C4⋊C4—21no—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—21no—
65C42×C13D412yescomplemented
66C22⋊Dic13—22no—
67C22⋊Dic13—21no—
68#6107—22no—
69#6106—22no—
70#6105—22no—
71#6104—22no—
72#6103—22no—
73C4⋊Dic13—21no—
74#6101—22no—
75C4×Dic13D412yescomplemented
76#6099—21no—
77#6099—21no—
78#6099—21no—
79#6099—21no—
80C2×#1055—21no—
81C2×#1055D412yescomplemented
82#2010—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13—21no—
87C23×C13—42no—
88C23×C13C2×D411yescharacteristic
89C22×D13—21no—
90Q8×C13—21no—
91Q8×C13—21no—
92D4×C13—21no—
93D4×C13—21no—
94D4×C13—44no—
95D4×C13—41no—
96D4×C13—41no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13C2×D411yescharacteristic
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13#4111yescharacteristic
114C22⋊D13—44no—
115C22⋊D13—41no—
116C22⋊D13—41no—
117C2×Dic13—22no—
118C2×Dic13—21no—
119D52—21no—
120D52—21no—
121C4×D13—41no—
122C4×D13—41no—
123Dic26—21no—
124Dic26—21no—
125#1055—22no—
126#1055—41no—
127#575—131no—
128#525—131no—
129#525D1311yescharacteristic, complemented
130#421—131no—
131#421—131no—
132#407—131no—
133H(3,ℤ/4)—131no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—42no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13#12011yescharacteristic
145C22×C13#12011yescharacteristic
146C22×C13#12111yescharacteristic
147C2×D13—42no—
148C2×D13—41no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13—41no—
152C4×C13#12011yescharacteristic
153C4×C13#12111yescharacteristic
154C4×C13#12111yescharacteristic
155C4×C13#12711yescharacteristic
156Dic13—42no—
157Dic13—41no—
158C2×#41—131no—
159C2×#41C2×D1311yescharacteristic
160C23×C4C2×D1311yescharacteristic
161#137—261no—
162#137—261no—
163AGL(1,ℤ/8)—261no—
164AGL(1,ℤ/8)—261no—
165#135—262no—
166C2×M16—131no—
167C2×M16—131no—
168#123—21no—
169#123—261no—
170C22⋊Q8—21no—
171C22⋊Q8—261no—
172#121—21no—
173#121—261no—
174#120—21no—
175#120—261no—
176C4×D4—22no—
177C4×D4—262no—
178#117—131no—
179#117C2×D1311yescharacteristic
180#104—262no—
181#104—262no—
182C22⋊C8—262no—
183C2×C13—21no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13—42no—
187C2×C13—81no—
188C2×C13#39211yescharacteristic
189D13—81no—
190C24C22⋊D1311yescharacteristic
191#41—21no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—261no—
196#41—261no—
197#41—261no—
198#41—261no—
199C2×Q8—131no—
200C2×Q8C22⋊D1311yescharacteristic, complemented
201C2×D4—22no—
202C2×D4—21no—
203C2×D4—131no—
204C2×D4—262no—
205C2×D4—261no—
206C2×D4C22⋊D1311yescharacteristic, complemented
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—261no—
215C22×C4C22⋊D1311yescharacteristic
216C22×C4C22×D1311yescharacteristic
217Q16—262no—
218SD16—262no—
219SD16—262no—
220D8—262no—
221M16—261no—
222M16—261no—
223M16—261no—
224M16—261no—
225C2×C8—132no—
226C2×C8—261no—
227C4⋊C4—22no—
228C4⋊C4—21no—
229C4⋊C4—262no—
230C4⋊C4—261no—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—21no—
234C22⋊C4—262no—
235C22⋊C4—262no—
236C22⋊C4—261no—
237C42—132no—
238C42C22⋊D1312yescomplemented
239C13#201011yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—42no—
245C23—261no—
246C23C2×C22⋊D1311yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—261no—
250Q8—261no—
251D4—21no—
252D4—21no—
253D4—44no—
254D4—41no—
255D4—41no—
256D4—261no—
257D4—261no—
258D4—524no—
259D4—521no—
260D4—521no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4D4×D1311yescharacteristic
277C2×C4D4×D1311yescharacteristic
278C2×C4D4×D1311yescharacteristic
279C2×C4#612911yescharacteristic
280C2×C4C2×C22⋊D1311yescharacteristic
281C2×C4C2×C22⋊D1311yescharacteristic
282C8—262no—
283C8—521no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—522no—
295C22—521no—
296C22#8819111yescharacteristic
297C22#8819311yescharacteristic
298C22#8820711yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—522no—
303C4—521no—
304C4#8819111yescharacteristic
305C4#8819211yescharacteristic
306C4#8819311yescharacteristic
307C4#8819411yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—42no—
312C2—81no—
313C2—1041no—
314C2#1171888411yescharacteristic
subgroupG/H
centerC4#88194
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#525C2
socleC2×C13#392
hypercenter#525D13
hypocenterC13#2010
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C13×#525C2semidirect
2. #11719527C2semidirect
3. #11719496C2semidirect
4. #11718897C2semidirect
5. #11718868C2semidirect
6. #11718666C2semidirect
7. #11718123C2semidirect
38. C2×Q8×C13D4semidirect
41. C2×D4×C13D4semidirect
57. C2×D52D4semidirect
59. C2×Dic26D4semidirect
65. C42×C13D4semidirect
75. C4×Dic13D4semidirect
81. C2×#1055D4semidirect
129. #525D13semidirect
200. C2×Q8C22⋊D13semidirect
206. C2×D4C22⋊D13semidirect
238. C42C22⋊D13semidirect
239. C13#2010semidirect

Maximal subgroups

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

subgroupindex
C13×#5252
#117195272
#117194962
#117188972
#117188682
#117186662
#117181232
#201013