Finite Group Databasebeta

← #13125798

Subgroups — #13125798

Order 1664.

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

normal subgroups only

This group has 410 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
1C2×#88190C211yesmaximal, characteristic, complemented
2#11719305C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic
4#11718879C211yesmaximal, characteristic, complemented
5#11718816C212yesmaximal, complemented
6#11718814C212yesmaximal, complemented
7#11718701C211yesmaximal, characteristic, complemented
8#11718429C212yesmaximal, complemented
9#11718428C212yesmaximal, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718379C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×D8C2212yes—
15C13×#121C2211yescharacteristic
16C2×C22⋊Dic13—21no—
17C2×C22⋊Dic13—21no—
18#88190—21no—
19#88190—21no—
20#88190C2212yes—
21#88190C2212yes—
22#88190C2211yescharacteristic, complemented
23#88189—21no—
24D4×Dic13—21no—
25D4×Dic13C2211yescharacteristic, complemented
26C2×#6105C2212yes—
27C2×#6105C2212yescomplemented
28#88178C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30C2×Dic52C2212yescomplemented
31#88144C2211yescharacteristic, complemented
32#88141C2211yescharacteristic, complemented
33#88133—21no—
34#88131—21no—
35C13×#102C2212yes—
36C13×C22⋊C8C2211yescharacteristic
37#88072C2212yes—
38C22⋊#1055C2211yescharacteristic
39#88056C2212yescomplemented
40#88054C2212yescomplemented
41C8×Dic13C2212yescomplemented
42#88050C2212yescomplemented
43C24×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—42no—
47C2×D4×C13C2312yes—
48C2×D4×C13C2311yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54C2×Dic26—21no—
55C2×Dic26—42no—
56C2×Dic26C2311yescharacteristic
57C2×Dic26C2312yes—
58C13×D8—42no—
59C2×C8×C13C2312yes—
60C13×C4⋊C4C2311yescharacteristic
61C13×C22⋊C4—21no—
62C22⋊Dic13—21no—
63C22⋊Dic13—21no—
64C22⋊Dic13—21no—
65C22⋊Dic13—21no—
66C22⋊Dic13—22no—
67C22⋊Dic13—22no—
68C22⋊Dic13—22no—
69C22⋊Dic13—22no—
70#6105—42no—
71#6105—42no—
72C4⋊Dic13—21no—
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77C4×Dic13—21no—
78C4×Dic13D411yescharacteristic
79C4×Dic13D411yescharacteristic
80C4×Dic13C2311yescharacteristic
81C4×Dic13C2311yescharacteristic
82C2×#1055C2312yes—
83Dic52—42no—
84#3211—131nomaximal, Sylow
85C23×C13—22no—
86C23×C13—21no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13C2×D411yescharacteristic
91D4×C13—22no—
92D4×C13—22no—
93D4×C13—22no—
94D4×C13—42no—
95D4×C13—42no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—41no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13C2×D411yescharacteristic
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110C2×Dic13C2×D411yescharacteristic
111Dic26—22no—
112Dic26—22no—
113Dic26—22no—
114Dic26—42no—
115C8×C13—22no—
116#1055—22no—
117#529—131no—
118C2×#124—131no—
119#495—132no—
120#488—132no—
121#464—132no—
122#463—132no—
123#451—131no—
124#450—131no—
125#448—131no—
126#447D1311yescharacteristic
127#431—131no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—42no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13—42no—
134C22×C13—41no—
135C22×C13—42no—
136C22×C13—84no—
137C22×C13#13512yes—
138C22×C13C22×D411yescharacteristic
139C4×C13—21no—
140C4×C13—41no—
141C4×C13H(5,𝔽2)12yes—
142Dic13—21no—
143Dic13—21no—
144Dic13—21no—
145Dic13—21no—
146Dic13—42no—
147Dic13—41no—
148Dic13—41no—
149C22×Q8—131no—
150C22×D4C2×D1311yescharacteristic
151C2×Q16—132no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×D8C2×D1312yes—
155#126—261no—
156#125—131no—
157#124—132no—
158#124—132no—
159#124—131no—
160#124—261no—
161#124—261no—
162#123—261no—
163C22⋊Q8—131no—
164#121C2×D1311yescharacteristic
165C4×Q8—131no—
166C4×D4—131no—
167C4×D4—261no—
168#117—261no—
169C2×C22⋊C4—261no—
170C2×C22⋊C4—261no—
171C2×C42—131no—
172C4⋊C8—132no—
173#103—132no—
174#103—132no—
175#102—132no—
176#102C2×D1312yes—
177C22⋊C8—131no—
178C22⋊C8C2×D1311yescharacteristic
179C4×C8—132no—
180C2×C13—22no—
181C2×C13—81no—
182C2×C13—82no—
183C2×C13#53511yescharacteristic
184C2×C13C2×#13511yescharacteristic
185C2×C13#57511yescharacteristic
186C24—21no—
187C2×Q8—132no—
188C2×Q8—131no—
189C2×Q8—261no—
190C2×Q8—522no—
191C2×D4—21no—
192C2×D4—21no—
193C2×D4—42no—
194C2×D4C22×D1312yes—
195C2×D4C22×D1311yescharacteristic
196C22×C4—131no—
197C22×C4—131no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4C22×D1311yescharacteristic
201Q16—522no—
202SD16—522no—
203SD16—522no—
204D8—42no—
205C2×C8—132no—
206C2×C8C22×D1312yes—
207C4⋊C4—131no—
208C4⋊C4—261no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4C22×D1311yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—262no—
215C22⋊C4—262no—
216C22⋊C4—262no—
217C22⋊C4—262no—
218C22⋊C4—261no—
219C22⋊C4—261no—
220C22⋊C4—261no—
221C22⋊C4—261no—
222C42—131no—
223C42—131no—
224C42—131no—
225C42—131no—
226C42—261no—
227C13#321111yescharacteristic, complemented, Sylow
228C23—21no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23D4×D1311yescharacteristic
234Q8—262no—
235Q8—262no—
236Q8—262no—
237Q8—522no—
238D4—22no—
239D4—22no—
240D4—22no—
241D4—42no—
242D4—42no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—131no—
248C2×C4—131no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—262no—
252C2×C4—261no—
253C2×C4—521no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4D4×D1311yescharacteristic
257C2×C4C23×D1311yescharacteristic
258C8—22no—
259C8—262no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—42no—
264C22—41no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—84no—
269C22#8816612yes—
270C22C2×D4×D1311yescharacteristic
271C4—21no—
272C4—41no—
273C4—261no—
274C4—261no—
275C4—261no—
276C4—261no—
277C4—521no—
278C4—522no—
279C4—521no—
280C4#8825112yes—
281C2—22no—
282C2—82no—
283C2—81no—
284C2#1171929711yescharacteristic
285C2C2×#8816611yescharacteristic
286C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3211
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#88190C2semidirect
2. #11719305C2semidirect
4. #11718879C2semidirect
5. #11718816C2semidirect
6. #11718814C2semidirect
7. #11718701C2semidirect
8. #11718429C2semidirect
9. #11718428C2semidirect
10. #11718400C2semidirect
11. #11718379C2semidirect
22. #88190C22semidirect
25. D4×Dic13C22semidirect
27. C2×#6105C22semidirect
30. C2×Dic52C22semidirect
31. #88144C22semidirect
32. #88141C22semidirect
39. #88056C22semidirect
40. #88054C22semidirect
41. C8×Dic13C22semidirect
42. #88050C22semidirect
227. C13#3211semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
#117193052
C13×#4472
#117188792
#117188162
#117188142
#117187012
#117184292
#117184282
#117184002
#117183792
#321113