Finite Group Databasebeta

← #13126073

Subgroups — #13126073

Order 1664.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719433C211yesmaximal, characteristic, complemented
2#11719385C211yesmaximal, characteristic
3C13×#489C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718716C211yesmaximal, characteristic, complemented
6#11718475C212yesmaximal, complemented
7#11718460C212yesmaximal, complemented
8#11718440C212yesmaximal
9#11718427C212yesmaximal, complemented
10#11718366C211yesmaximal, characteristic, complemented
11#11718363C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#124C2211yescharacteristic
14#88200—21no—
15#88200C2211yescharacteristic
16Q8×Dic13—21no—
17Q8×Dic13C2211yescharacteristic
18#88192C2211yescharacteristic
19D4×Dic13C2211yescharacteristic
20#88151—21no—
21#88146C2212yes—
22#88144C2212yes—
23#88141—21no—
24#88137—21no—
25#88135—21no—
26#88133—21no—
27#88131—21no—
28C42×D13C2211yescharacteristic
29#88124C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#103C2212yes—
32C13×#102C2212yes—
33C13×#97C2211yescharacteristic
34#88075C2212yes—
35#88072C2212yes—
36#88060C2212yes—
37#88058C2212yes—
38#88057C2212yes—
39#88054C2212yes—
40#88048C2212yes—
41#88047C2212yes—
42#88043C2211yescharacteristic
43C2×Q8×C13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13C2311yescharacteristic
46C2×C22⋊D13—21no—
47C22×Dic13—21no—
48C2×C4×D13D411yescharacteristic
49C2×C4×D13D411yescharacteristic
50C2×C4×D13C2311yescharacteristic
51C2×Dic26—21no—
52C2×C8×C13C2312yes—
53C13×C4⋊C4—21no—
54C13×C4⋊C4C2312yes—
55C13×C22⋊C4—21no—
56C13×C22⋊C4—21no—
57C42×C13C2311yescharacteristic
58C22⋊Dic13—21no—
59C22⋊Dic13—21no—
60#6103—21no—
61#6103—22no—
62C4⋊Dic13—21no—
63C4⋊Dic13—21no—
64C4⋊Dic13—22no—
65C4⋊Dic13C2312yes—
66C4⋊Dic13C2311yescharacteristic
67C4⋊Dic13C2311yescharacteristic
68#6101—21no—
69#6101—21no—
70#6101—21no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—22no—
74C4×Dic13D411yescharacteristic
75C4×Dic13D411yescharacteristic
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78#3240—131nomaximal, Sylow
79C23×C13—21no—
80C22×D13C2×D411yescharacteristic
81Q8×C13—22no—
82Q8×C13—42no—
83D4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13C2×D411yescharacteristic
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—42no—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—42no—
94C2×Dic13C2×D411yescharacteristic
95C2×Dic13C2×D411yescharacteristic
96C2×Dic13C2×D411yescharacteristic
97C4×D13—22no—
98C4×D13—41no—
99C4×D13—41no—
100Dic26—42no—
101C8×C13—22no—
102#1055—22no—
103#533—131no—
104#529—131no—
105#501—131no—
106#501—131no—
107#489—131no—
108#489D1311yescharacteristic, complemented
109#485—132no—
110#482—132no—
111#479—132no—
112#478—132no—
113#432—131no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—41no—
117C22×C13C22×D411yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—21no—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—41no—
124C4×C13—42no—
125C4×C132−1+412yes—
126Dic13—21no—
127Dic13—21no—
128Dic13—21no—
129Dic13—42no—
130Dic13—41no—
131Dic13—41no—
132C4⋊Q8—131no—
133C4⋊Q8C2×D1311yescharacteristic
134#126—261no—
135#125—132no—
136#125—131no—
137#124C2×D1311yescharacteristic
138#123—261no—
139C22⋊Q8—131no—
140C22⋊Q8—261no—
141C22⋊Q8—261no—
142#121—131no—
143C4×Q8—131no—
144C4×Q8—261no—
145C4×Q8—261no—
146C4×D4—131no—
147C4×D4—261no—
148#117—132no—
149#117—261no—
150C2×C42—131no—
151#107—132no—
152#107—132no—
153#106—132no—
154#106—132no—
155C4⋊C8—132no—
156#103—132no—
157#103C2×D1312yes—
158#102—132no—
159#102C2×D1312yes—
160C22⋊C8—132no—
161#97—131no—
162#97C2×D1311yescharacteristic
163C2×C13—81no—
164C2×C13#53611yescharacteristic
165C2×C13#57511yescharacteristic
166C2×C13#57511yescharacteristic
167D13—41no—
168C2×Q8—21no—
169C2×Q8—261no—
170C2×Q8C22×D1311yescharacteristic
171C2×D4—261no—
172C2×D4C22×D1311yescharacteristic
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—131no—
176C22×C4—261no—
177C2×C8—132no—
178C2×C8C22×D1312yes—
179C4⋊C4—21no—
180C4⋊C4—132no—
181C4⋊C4—131no—
182C4⋊C4—131no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—262no—
186C4⋊C4—262no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4C22×D1312yes—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C42—131no—
198C42—131no—
199C42—131no—
200C42—262no—
201C42—261no—
202C42C22×D1311yescharacteristic
203C13#324011yescharacteristic, complemented, Sylow
204C23—21no—
205C23—131no—
206Q8—22no—
207Q8—42no—
208Q8—522no—
209D4—22no—
210D4—522no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—131no—
214C2×C4—131no—
215C2×C4—131no—
216C2×C4—262no—
217C2×C4—261no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—521no—
221C2×C4—521no—
222C2×C4—522no—
223C2×C4D4×D1311yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4C23×D1311yescharacteristic
226C8—22no—
227C8—262no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—261no—
232C22—261no—
233C22—261no—
234C22C2×D4×D1311yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—41no—
239C4—261no—
240C4—261no—
241C4—261no—
242C4—521no—
243C4—521no—
244C4—522no—
245C4#8825712yes—
246C2—81no—
247C2—521no—
248C2#1171938011yescharacteristic
249C2#1171947811yescharacteristic
250C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#489D13
hypocenterC13#3240
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#489C2semidirect
4. #11718741C2semidirect
5. #11718716C2semidirect
6. #11718475C2semidirect
7. #11718460C2semidirect
9. #11718427C2semidirect
10. #11718366C2semidirect
11. #11718363C2semidirect
108. #489D13semidirect
203. C13#3240semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117193852
C13×#4892
#117187412
#117187162
#117184752
#117184602
#117184402
#117184272
#117183662
#117183632
#324013