Finite Group Databasebeta

← #13124670

Subgroups — #13124670

Order 1664.

398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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#11719226C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3C13×#427C211yesmaximal, characteristic, complemented
4C2×#88061C211yesmaximal, characteristic
5#11718763C211yesmaximal, characteristic, complemented
6#11718662C211yesmaximal, characteristic
7#11718656C211yesmaximal, characteristic, complemented
8#11718552C212yesmaximal, complemented
9#11718551C212yesmaximal, complemented
10#11718532C212yesmaximal, complemented
11#11718531C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C8×C13C2211yescharacteristic
14C13×#117C2211yescharacteristic
15C13×#117C2211yescharacteristic
16#88180C2211yescharacteristic
17C2×C4⋊Dic13C2211yescharacteristic
18C2×#6099C2211yescharacteristic
19#88147C2212yes—
20#88147C2212yes—
21#88144C2212yescomplemented
22#88142C2212yescomplemented
23C22⋊C4×D13—22no—
24#88132—22no—
25C4×D52—21no—
26C4×D52—21no—
27#88124—21no—
28#88123—21no—
29C13×#107C2211yescharacteristic, complemented
30C13×#107C2211yescharacteristic, complemented
31C13×#106C2211yescharacteristic, complemented
32C13×#106C2211yescharacteristic, complemented
33#88061C2212yes—
34#88061C2212yes—
35#88054C2212yescomplemented
36#88054C2212yescomplemented
37#88049C2212yes—
38#88049C2212yes—
39#88048C2212yescomplemented
40#88047C2212yescomplemented
41C23×D13—21no—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13—21no—
44C2×D52—21no—
45C2×D52—22no—
46C2×D52Q814yescomplemented
47C2×D52C2312yes—
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×Dic26—22no—
51C2×C8×C13—22no—
52C2×C8×C13C2311yescharacteristic
53C2×C8×C13C2311yescharacteristic
54C13×C4⋊C4C2311yescharacteristic
55C13×C4⋊C4C2311yescharacteristic
56C13×C4⋊C4C2311yescharacteristic
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C13×C22⋊C4—21no—
60C42×C13—21no—
61C42×C13—21no—
62C22⋊Dic13D412yes—
63#6103—22no—
64#6103—22no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13D411yescharacteristic
68C4⋊Dic13D411yescharacteristic
69C4⋊Dic13C2312yes—
70#6101—22no—
71#6101—22no—
72C4×Dic13C2312yes—
73#6099—22no—
74C2×#1055C2312yes—
75#3081—131nomaximal, Sylow
76C23×C13C2×D411yescharacteristic
77C22×D13—22no—
78C22×D13—24no—
79C22×D13—81no—
80C22×D13—81no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2×Q812yes—
87C2×C4×C13#4112yes—
88C2×C4×C13C2411yescharacteristic
89C2×Dic13—22no—
90C2×Dic13—81no—
91C2×Dic13C2×D412yes—
92C2×Dic13C2×D412yes—
93D52—24no—
94D52—22no—
95D52C2×Q814yes—
96C4×D13—82no—
97C4×D13—82no—
98Dic26—82no—
99C8×C13—21no—
100C8×C13—21no—
101#1055—22no—
102#544—131no—
103#518—131no—
104#478—132no—
105#478—132no—
106#476—132no—
107#474—132no—
108#428—131no—
109#427D1311yescharacteristic, complemented
110#424—131no—
111#418—131no—
112C2×#102—131no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13C22⋊Q812yes—
116C22×C13C22×D411yescharacteristic
117C2×D13—24no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—84no—
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—41no—
124C4×C13—41no—
125C4×C13C22⋊Q812yes—
126C4×C13C22×Q811yescharacteristic
127C4×C13C2×#4111yescharacteristic
128Dic13—22no—
129Dic13—22no—
130Dic13—42no—
131C22×D4—131no—
132C2×M16—131no—
133C22×C8C2×D1311yescharacteristic
134C4⋊Q8—132no—
135C4⋊Q8—261no—
136#125—132no—
137#125—261no—
138C22⋊Q8—262no—
139C4×D4—132no—
140C4×D4—132no—
141C4×D4—261no—
142C4×D4—261no—
143#117—131no—
144#117C2×D1311yescharacteristic
145#117C2×D1311yescharacteristic
146C2×C4⋊C4—131no—
147C2×C22⋊C4—262no—
148#107—132no—
149#107C2×D1311yescharacteristic, complemented
150#107C2×D1311yescharacteristic, complemented
151#106—132no—
152#106C2×D1311yescharacteristic, complemented
153#106C2×D1311yescharacteristic, complemented
154C4⋊C8—132no—
155C4⋊C8—132no—
156#102—132no—
157#102—132no—
158#102—132no—
159#102—132no—
160C2×C13—22no—
161C2×C13C2×C22⋊Q811yescharacteristic
162C2×C13#57611yescharacteristic
163C2×C13#57711yescharacteristic
164D13—44no—
165C24—261no—
166C2×Q8—262no—
167C2×D4—134no—
168C2×D4—132no—
169C2×D4—262no—
170C2×D4—261no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4—261no—
174C22×C4C22×D1311yescharacteristic
175M16—262no—
176C2×C8—22no—
177C2×C8—132no—
178C2×C8C22×D1311yescharacteristic
179C2×C8C22×D1311yescharacteristic
180C4⋊C4—131no—
181C4⋊C4—131no—
182C4⋊C4—132no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—261no—
187C4⋊C4C22×D1311yescharacteristic
188C4⋊C4C22×D1311yescharacteristic
189C4⋊C4C22×D1311yescharacteristic
190C4⋊C4C22×D1311yescharacteristic
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—132no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C42—21no—
197C42—21no—
198C42—132no—
199C13#308111yescharacteristic, complemented, Sylow
200C23—262no—
201C23—264no—
202C23—1041no—
203C23—1041no—
204C23D4×D1311yescharacteristic
205Q8—1042no—
206D4—134no—
207D4—264no—
208D4—262no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—132no—
214C2×C4—132no—
215C2×C4—262no—
216C2×C4—1042no—
217C2×C4—1042no—
218C2×C4—1041no—
219C2×C4#612712yes—
220C2×C4D4×D1311yescharacteristic
221C2×C4Q8×D1312yes—
222C2×C4C23×D1311yescharacteristic
223C8—21no—
224C8—21no—
225C8—262no—
226C22—21no—
227C22—21no—
228C22—264no—
229C22—522no—
230C22—522no—
231C22—1044no—
232C22#8815012yes—
233C22C2×D4×D1311yescharacteristic
234C4—41no—
235C4—41no—
236C4—41no—
237C4—41no—
238C4—262no—
239C4—262no—
240C4—522no—
241C4#8815012yes—
242C4C2×#612711yescharacteristic
243C4C2×Q8×D1311yescharacteristic
244C2—22no—
245C2—524no—
246C2C2×#8815011yescharacteristic
247C2#1171947411yescharacteristic
248C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#427C2
socleC22×C13C22×D4
prime radicalC22×D52C22
hypercenter#427D13
hypocenterC13#3081
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
3. C13×#427C2semidirect
5. #11718763C2semidirect
7. #11718656C2semidirect
8. #11718552C2semidirect
9. #11718551C2semidirect
10. #11718532C2semidirect
11. #11718531C2semidirect
21. #88144C22semidirect
22. #88142C22semidirect
29. C13×#107C22semidirect
30. C13×#107C22semidirect
31. C13×#106C22semidirect
32. C13×#106C22semidirect
35. #88054C22semidirect
36. #88054C22semidirect
39. #88048C22semidirect
40. #88047C22semidirect
46. C2×D52Q8semidirect
109. #427D13semidirect
149. #107C2×D13semidirect
150. #107C2×D13semidirect
152. #106C2×D13semidirect
153. #106C2×D13semidirect
199. C13#3081semidirect

Maximal subgroups

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

subgroupindex
#117192262
#117192242
C13×#4272
C2×#880612
#117187632
#117186622
#117186562
#117185522
#117185512
#117185322
#117185312
#308113