Finite Group Databasebeta

← #13127621

Subgroups — #13127621

Order 1664.

340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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#11719426C211yesmaximal, characteristic, complemented
2#11719248C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic
4#11718825C212yesmaximal
5#11718823C212yesmaximal
6#11718742C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic
8#11718511C211yesmaximal, characteristic, complemented
9#11718492C211yesmaximal, characteristic, complemented
10#11718458C212yesmaximal, complemented
11#11718457C212yesmaximal, complemented
12C2×C13×SD16C2212yes—
13C13×C4⋊Q8C2211yescharacteristic
14C4×D4×C13C2211yescharacteristic
15Q8×Dic13C2212yes—
16#88198C2212yes—
17D4×Dic13C2212yes—
18C2×#6105C2211yescharacteristic
19C2×C4⋊Dic13—21no—
20#88178—21no—
21#88144—21no—
22#88144C2212yes—
23#88143—22no—
24#88141—21no—
25#88132—22no—
26#88123C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×C4⋊C8C2211yescharacteristic
30C13×#103C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88072C2211yescharacteristic
34#88058C2212yes—
35#88056C2212yes—
36#88055C2212yes—
37#88054C2212yes—
38#88050C2211yescharacteristic
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13C2312yes—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×Dic26—21no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2311yescharacteristic
48C13×SD16—24no—
49C2×C8×C13C2312yes—
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2311yescharacteristic
53C13×C22⋊C4—21no—
54C42×C13C2311yescharacteristic
55C22⋊Dic13—22no—
56#6105—22no—
57C4⋊Dic13—21no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62C4⋊Dic13C2312yes—
63#6101—21no—
64#6101—22no—
65#6101—22no—
66#6101—22no—
67#6101D412yes—
68C4×Dic13—21no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2311yescharacteristic
72C2×#1055C2311yescharacteristic
73#3372—131nomaximal, Sylow
74C23×C13—21no—
75Q8×C13—22no—
76Q8×C13—22no—
77D4×C13—21no—
78D4×C13#4112yes—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—42no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2411yescharacteristic
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—22no—
88C2×Dic13—82no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91Dic26—22no—
92Dic26—21no—
93Dic26—21no—
94Dic26—81no—
95C8×C13—22no—
96#1055—21no—
97#1055—21no—
98#557—131no—
99#554—131no—
100#491—132no—
101#487—131no—
102#479—132no—
103#477—131no—
104#461—132no—
105#461D1311yescharacteristic
106#446—131no—
107#440—132no—
108C4×SD16—131no—
109C22×C13—22no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13C22×D411yescharacteristic
113C4×C13—21no—
114C4×C13—42no—
115C4×C13—41no—
116C4×C13#13712yes—
117C4×C13C2×#4111yescharacteristic
118C4×C132−1+411yescharacteristic
119Dic13—22no—
120Dic13—22no—
121Dic13—41no—
122Dic13—42no—
123Dic13—41no—
124C2×SD16—131no—
125C2×SD16C2×D1312yes—
126C4⋊Q8—132no—
127C4⋊Q8—131no—
128C4⋊Q8C2×D1311yescharacteristic
129#125—132no—
130#125—262no—
131#125—261no—
132C22⋊Q8—262no—
133C22⋊Q8—261no—
134C4×Q8—131no—
135C4×Q8—132no—
136C4×Q8—131no—
137C4×Q8—261no—
138C4×D4—132no—
139C4×D4C2×D1311yescharacteristic
140C2×C4⋊C4—261no—
141#107—132no—
142#106—131no—
143C4⋊C8—132no—
144C4⋊C8C2×D1311yescharacteristic
145#103—132no—
146#103—132no—
147#103—132no—
148#103—131no—
149#103C2×D1312yes—
150#102—131no—
151#97—132no—
152C4×C8—131no—
153C2×C13—42no—
154C2×C13#54811yescharacteristic
155C2×C13C2×#13711yescharacteristic
156C2×C13#57711yescharacteristic
157C2×Q8—131no—
158C2×Q8—131no—
159C2×Q8—261no—
160C2×Q8C22×D1312yes—
161C2×D4C22×D1311yescharacteristic
162C22×C4—21no—
163C22×C4—262no—
164SD16—24no—
165SD16—262no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8C22×D1312yes—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—131no—
172C4⋊C4—132no—
173C4⋊C4—131no—
174C4⋊C4—132no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—261no—
181C4⋊C4—261no—
182C4⋊C4C22×D1311yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—262no—
185C42—132no—
186C42—262no—
187C42—261no—
188C42C22×D1311yescharacteristic
189C13#337211yescharacteristic, complemented, Sylow
190C23—21no—
191Q8—22no—
192Q8—22no—
193Q8—262no—
194Q8—261no—
195Q8—261no—
196Q8—1041no—
197D4—21no—
198D4#612912yes—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—262no—
207C2×C4—1042no—
208C2×C4D4×D1311yescharacteristic
209C2×C4D4×D1311yescharacteristic
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—261no—
213C8—261no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C2×D4×D1311yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—262no—
222C4—262no—
223C4—521no—
224C4—522no—
225C4—521no—
226C4#8816912yes—
227C4C2×#612911yescharacteristic
228C4#8825711yescharacteristic
229C2—42no—
230C2#1171930311yescharacteristic
231C2C2×#8816911yescharacteristic
232C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#461D13
hypocenterC13#3372
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
6. #11718742C2semidirect
8. #11718511C2semidirect
9. #11718492C2semidirect
10. #11718458C2semidirect
11. #11718457C2semidirect
189. C13#3372semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192482
C13×#4612
#117188252
#117188232
#117187422
C4×#61052
#117185112
#117184922
#117184582
#117184572
#337213