Finite Group Databasebeta

← #13125007

Subgroups — #13125007

Order 1664.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Q8×C13C211yesmaximal, characteristic, complemented
2#11719184C211yesmaximal, characteristic
3#11718889C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic
5#11718691C212yesmaximal, complemented
6#11718689C212yesmaximal, complemented
7#11718687C212yesmaximal, complemented
8#11718683C212yesmaximal, complemented
9#11718631C211yesmaximal, characteristic, complemented
10#11718629C211yesmaximal, characteristic
11#11718587C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C4×Q8×C13—21no—
14C4×Q8×C13—21no—
15C4×Q8×C13C2212yes—
16C4×Q8×C13C2212yes—
17C2×C13×C4⋊C4—21no—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C42×C13—21no—
20C2×C42×C13C2211yescharacteristic
21C2×#6107C2212yes—
22C2×#6106C2212yes—
23#88184C2211yescharacteristic
24#88183—21no—
25C4×C22⋊D13—21no—
26#88178C2211yescharacteristic
27#88130—21no—
28#88129C2211yescharacteristic
29C4×D52C2211yescharacteristic
30#88126—21no—
31#88124C2211yescharacteristic
32C4×Dic26C2211yescharacteristic
33#88075C2212yes—
34#88075C2212yes—
35C22⋊#1055C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88050C2212yes—
38#88049C2212yes—
39#88048C2212yes—
40#88047C2212yes—
41C4⋊#1055C2212yes—
42#88043C2212yes—
43C2×Q8×C13—24no—
44C2×Q8×C13—21no—
45C2×Q8×C13C2312yes—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13D411yescharacteristic
49C22×C4×C13D411yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C2×C22⋊D13—21no—
52C2×D52C2311yescharacteristic
53C2×C4×D13—21no—
54C2×Dic26C2311yescharacteristic
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2312yes—
59C42×C13—22no—
60C42×C13—22no—
61C42×C13D411yescharacteristic
62C42×C13D411yescharacteristic
63C42×C13C2311yescharacteristic
64C42×C13C2311yescharacteristic
65C22⋊Dic13—21no—
66#6107—24no—
67#6106—24no—
68#6103—21no—
69#6103—21no—
70#6103—21no—
71#6103—21no—
72C4⋊Dic13C2311yescharacteristic
73C4⋊Dic13C2311yescharacteristic
74#6101—21no—
75#6101—21no—
76#6101—21no—
77#6101—21no—
78C4×Dic13—21no—
79C2×#1055C2312yes—
80C2×#1055C2312yes—
81#3117—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84Q8×C13—24no—
85Q8×C13—22no—
86Q8×C13#4114yes—
87C2×C4×C13—24no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D411yescharacteristic
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—42no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104D52—22no—
105C4×D13—42no—
106Dic26—22no—
107#1055—22no—
108#1055—22no—
109#529—131no—
110C2×C4×Q8D1311yescharacteristic, complemented
111#484—131no—
112#481—131no—
113#479—132no—
114#464—132no—
115#451—131no—
116#448—131no—
117#441—132no—
118#440—132no—
119#432—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#13712yes—
123C22×C13C22×D411yescharacteristic
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C4×C13—24no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—21no—
133C4×C13—42no—
134C4×C13C2×#4112yes—
135Dic13—41no—
136Dic13—41no—
137Dic13—41no—
138C22×Q8C2×D1311yescharacteristic
139C2×Q16—132no—
140C2×SD16—132no—
141#126—261no—
142#125—131no—
143#124—131no—
144#123—261no—
145C22⋊Q8—131no—
146#121—131no—
147C4×Q8—21no—
148C4×Q8—21no—
149C4×Q8—131no—
150C4×Q8C2×D1312yes—
151C4×Q8C2×D1312yes—
152C4×D4—131no—
153C4×D4—261no—
154#117—261no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×D1311yescharacteristic
157C2×C42—21no—
158C2×C42C2×D1311yescharacteristic
159#107—132no—
160#106—132no—
161C4⋊C8—132no—
162#103—132no—
163#103—132no—
164#103—132no—
165#102—132no—
166C22⋊C8—131no—
167C22⋊C8—131no—
168#97—132no—
169C2×C13—22no—
170C2×C13#52511yescharacteristic
171C2×C13C2×#13711yescharacteristic
172C2×C13#57511yescharacteristic
173D13—81no—
174C2×Q8—24no—
175C2×Q8—21no—
176C2×Q8—131no—
177C2×Q8C22×D1312yes—
178C2×D4—131no—
179C2×D4—261no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—261no—
183C22×C4C22⋊D1311yescharacteristic
184C22×C4C22⋊D1311yescharacteristic
185C22×C4C22×D1311yescharacteristic
186Q16—264no—
187SD16—264no—
188C2×C8—132no—
189C2×C8—132no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C4⋊C4—131no—
194C4⋊C4—131no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1312yes—
200C22⋊C4—261no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C42—22no—
206C42—22no—
207C42—261no—
208C42C22⋊D1311yescharacteristic
209C42C22⋊D1311yescharacteristic
210C42C22×D1311yescharacteristic
211C42C22×D1311yescharacteristic
212C13#311711yescharacteristic, complemented, Sylow
213C23—261no—
214C23C2×C22⋊D1311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—262no—
218Q8#612714yes—
219D4—262no—
220D4—522no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—522no—
232C2×C4C2×C22⋊D1311yescharacteristic
233C2×C4C2×C22⋊D1311yescharacteristic
234C2×C4C2×C22⋊D1311yescharacteristic
235C2×C4C2×C22⋊D1311yescharacteristic
236C2×C4C2×C22⋊D1311yescharacteristic
237C2×C4C23×D1311yescharacteristic
238C8—262no—
239C8—262no—
240C22—21no—
241C22—21no—
242C22—521no—
243C22—521no—
244C22—521no—
245C22#8819612yes—
246C22C22×C22⋊D1311yescharacteristic
247C4—24no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—42no—
254C4—521no—
255C4—521no—
256C4—521no—
257C4C2×#612712yes—
258C2—22no—
259C2—1041no—
260C2#1171949611yescharacteristic
261C2C2×#8819611yescharacteristic
262C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C4×Q8×C13C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenterC2×C4×Q8D13
hypocenterC13#3117
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C13C2semidirect
3. #11718889C2semidirect
5. #11718691C2semidirect
6. #11718689C2semidirect
7. #11718687C2semidirect
8. #11718683C2semidirect
9. #11718631C2semidirect
11. #11718587C2semidirect
110. C2×C4×Q8D13semidirect
212. C13#3117semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C132
#117191842
#117188892
#117188882
#117186912
#117186892
#117186872
#117186832
#117186312
#117186292
#117185872
#311713