Finite Group Databasebeta

← #13125002

Subgroups — #13125002

Order 1664.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic13C211yesmaximal, characteristic, complemented
2#11719305C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic
4#11718889C211yesmaximal, characteristic, complemented
5#11718827C212yesmaximal, complemented
6#11718825C212yesmaximal, complemented
7#11718695C211yesmaximal, characteristic
8#11718457C212yesmaximal, complemented
9#11718450C212yesmaximal, complemented
10#11718383C211yesmaximal, characteristic, complemented
11#11718380C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×C13×SD16C2212yes—
14C13×#121C2211yescharacteristic
15Q8×Dic13—21no—
16Q8×Dic13—21no—
17Q8×Dic13C2212yes—
18Q8×Dic13C2212yes—
19C2×#6107C2212yes—
20#88190C2211yescharacteristic
21#88189—21no—
22D4×Dic13—21no—
23D4×Dic13C2211yescharacteristic
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13C2211yescharacteristic
26#88178C2211yescharacteristic
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2211yescharacteristic
29#88144C2211yescharacteristic
30#88141C2211yescharacteristic
31#88133—21no—
32#88131—21no—
33C13×#103C2212yes—
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yes—
36#88072C2212yes—
37C22⋊#1055C2211yescharacteristic
38#88058C2212yes—
39#88056C2212yes—
40#88055C2212yes—
41#88054C2212yes—
42#88048C2212yes—
43C2×Q8×C13—24no—
44C2×Q8×C13—21no—
45C2×Q8×C13C2312yes—
46C2×D4×C13—21no—
47C2×D4×C13C2311yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13C2311yescharacteristic
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53C22×Dic13D411yescharacteristic
54C2×Dic26C2311yescharacteristic
55C13×SD16—24no—
56C2×C8×C13C2312yes—
57C13×C4⋊C4C2311yescharacteristic
58C13×C22⋊C4—21no—
59C22⋊Dic13—21no—
60C22⋊Dic13—21no—
61C22⋊Dic13—21no—
62C22⋊Dic13—21no—
63#6107—24no—
64C4⋊Dic13—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—22no—
67C4⋊Dic13—22no—
68C4⋊Dic13C2312yes—
69C4⋊Dic13C2311yescharacteristic
70#6101—21no—
71#6101—21no—
72#6101—21no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#3117—131nomaximal, Sylow
82C23×C13—21no—
83C23×C13C2×D411yescharacteristic
84Q8×C13—24no—
85Q8×C13—22no—
86Q8×C13#4114yes—
87D4×C13—22no—
88D4×C13—42no—
89C2×C4×C13—24no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—41no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106Dic26—22no—
107C8×C13—22no—
108#1055—22no—
109#529—131no—
110C2×C4×Q8—131no—
111#484—131no—
112#481—131no—
113#479—132no—
114#464—132no—
115#451—131no—
116#448D1311yescharacteristic
117#441—132no—
118#440—132no—
119#432—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13#13712yes—
126C22×C13C22×D411yescharacteristic
127C4×C13—24no—
128C4×C13—21no—
129C4×C13—41no—
130C4×C13C2×#4112yes—
131Dic13—21no—
132Dic13—21no—
133Dic13—21no—
134Dic13—21no—
135Dic13—41no—
136Dic13—42no—
137Dic13—41no—
138C22×Q8C2×D1311yescharacteristic
139C2×Q16—132no—
140C2×SD16C2×D1312yes—
141#126—261no—
142#125—131no—
143#124—131no—
144#123—261no—
145C22⋊Q8—131no—
146#121C2×D1311yescharacteristic
147C4×Q8—132no—
148C4×Q8—132no—
149C4×Q8—131no—
150C4×Q8—261no—
151C4×Q8—261no—
152C4×D4—131no—
153C4×D4—261no—
154#117—261no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—261no—
157C2×C42—131no—
158C2×C42—261no—
159#107—132no—
160#106—132no—
161C4⋊C8—132no—
162#103—132no—
163#103—132no—
164#103C2×D1312yes—
165#102—132no—
166C22⋊C8—131no—
167C22⋊C8C2×D1311yescharacteristic
168#97—132no—
169C2×C13—22no—
170C2×C13—81no—
171C2×C13#52511yescharacteristic
172C2×C13C2×#13711yescharacteristic
173C2×C13#57511yescharacteristic
174C2×Q8—24no—
175C2×Q8—21no—
176C2×Q8—131no—
177C2×Q8C22×D1312yes—
178C2×D4—21no—
179C2×D4C22×D1311yescharacteristic
180C22×C4—21no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4C22×D1311yescharacteristic
186Q16—264no—
187SD16—24no—
188C2×C8—132no—
189C2×C8C22×D1312yes—
190C4⋊C4—132no—
191C4⋊C4—131no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C4⋊C4—261no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1311yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C42—131no—
206C42—131no—
207C42—131no—
208C42—131no—
209C42—262no—
210C42—262no—
211C42—261no—
212C13#311711yescharacteristic, complemented, Sylow
213C23—21no—
214C23D4×D1311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—262no—
218Q8#612914yes—
219D4—22no—
220D4—42no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—131no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—131no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—521no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4D4×D1311yescharacteristic
237C2×C4C23×D1311yescharacteristic
238C8—22no—
239C8—262no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#8816912yes—
246C22C2×D4×D1311yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—261no—
251C4—261no—
252C4—261no—
253C4—261no—
254C4—522no—
255C4—521no—
256C4—521no—
257C4C2×#612912yes—
258C2—22no—
259C2—81no—
260C2#1171929111yescharacteristic
261C2C2×#8816911yescharacteristic
262C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#448D13
hypocenterC13#3117
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
4. #11718889C2semidirect
5. #11718827C2semidirect
6. #11718825C2semidirect
8. #11718457C2semidirect
9. #11718450C2semidirect
10. #11718383C2semidirect
11. #11718380C2semidirect
212. C13#3117semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
#117193052
C13×#4482
#117188892
#117188272
#117188252
#117186952
#117184572
#117184502
#117183832
#117183802
#311713