Finite Group Databasebeta

← #13127715

Subgroups — #13127715

Order 1664.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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×#474C211yesmaximal, characteristic
4#11718740C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic
6#11718539C212yesmaximal, complemented
7#11718538C212yesmaximal, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718491C211yesmaximal, characteristic, complemented
10#11718427C212yesmaximal
11#11718419C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14Q8×Dic13—21no—
15#88198—21no—
16D4×Dic13C2212yes—
17C2×#6105C2211yescharacteristic
18C2×C4⋊Dic13—21no—
19#88178—21no—
20#88144C2212yes—
21#88144C2212yes—
22#88143—22no—
23#88141C2212yes—
24#88132—22no—
25#88123C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#107C2212yes—
29C13×C4⋊C8C2211yescharacteristic
30C13×#102C2212yes—
31#88072C2211yescharacteristic
32#88058C2212yes—
33#88056C2212yes—
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2211yescharacteristic
37#88048C2212yes—
38#88048C2211yescharacteristic
39#88048C2212yes—
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C22×Dic13—22no—
45C2×Dic26—21no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2311yescharacteristic
48C2×C8×C13C2312yes—
49C13×C4⋊C4—21no—
50C13×C4⋊C4C2312yes—
51C13×C4⋊C4C2311yescharacteristic
52C13×C22⋊C4—21no—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55#6105Q814yescomplemented
56C4⋊Dic13—21no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61C4⋊Dic13C2312yes—
62#6101—21no—
63#6101—22no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72#3381—131nomaximal, Sylow
73C23×C13—21no—
74Q8×C13—42no—
75D4×C13—21no—
76D4×C13C2×Q812yes—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—42no—
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—82no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89Dic26—22no—
90Dic26—21no—
91Dic26—81no—
92Dic26C2×Q812yes—
93C8×C13—22no—
94#1055—21no—
95#1055C2×Q812yes—
96#557—131no—
97#554—131no—
98#499—132no—
99#498—131no—
100#479—132no—
101#478—132no—
102#477—131no—
103#474D1311yescharacteristic
104C8×Q8—131no—
105C4×SD16—131no—
106C4×SD16—132no—
107C22×C13—22no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13C22×D411yescharacteristic
111C4×C13—21no—
112C4×C13—41no—
113C4×C13—42no—
114C4×C13#13512yes—
115C4×C13C22×Q811yescharacteristic
116C4×C132−1+411yescharacteristic
117Dic13—22no—
118Dic13—22no—
119Dic13—22no—
120Dic13—42no—
121Dic13—41no—
122C2×SD16—131no—
123C4⋊Q8—131no—
124C4⋊Q8—261no—
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—132no—
128#125—262no—
129C22⋊Q8—262no—
130C22⋊Q8—261no—
131C4×Q8—131no—
132C4×Q8—132no—
133C4×Q8—131no—
134C4×Q8—261no—
135C4×D4—132no—
136C4×D4C2×D1311yescharacteristic
137C2×C4⋊C4—261no—
138#107—132no—
139#107C2×D1312yes—
140#106—132no—
141#106—131no—
142#106—132no—
143C4⋊C8—132no—
144C4⋊C8C2×D1311yescharacteristic
145#103—132no—
146#103—131no—
147#102—131no—
148#102C2×D1312yes—
149C4×C8—132no—
150C4×C8—131no—
151C2×C13—42no—
152C2×C13D4×Q811yescharacteristic
153C2×C13C2×#13511yescharacteristic
154C2×C13#57711yescharacteristic
155C2×Q8—21no—
156C2×Q8—131no—
157C2×Q8—131no—
158C2×Q8—261no—
159C2×D4C22×D1311yescharacteristic
160C22×C4—21no—
161C22×C4—262no—
162SD16—134no—
163C2×C8—131no—
164C2×C8—131no—
165C2×C8C22×D1312yes—
166C4⋊C4—21no—
167C4⋊C4—131no—
168C4⋊C4—132no—
169C4⋊C4—131no—
170C4⋊C4—132no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—261no—
177C4⋊C4—261no—
178C4⋊C4C22×D1312yes—
179C4⋊C4C22×D1311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—262no—
182C42—132no—
183C42—262no—
184C42—261no—
185C42C22×D1311yescharacteristic
186C13#338111yescharacteristic, complemented, Sylow
187C23—21no—
188Q8—42no—
189Q8—132no—
190Q8—262no—
191Q8—261no—
192Q8—1041no—
193D4—21no—
194D4Q8×D1312yes—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—132no—
199C2×C4—132no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—262no—
203C2×C4—1042no—
204C2×C4D4×D1311yescharacteristic
205C2×C4D4×D1311yescharacteristic
206C2×C4C23×D1311yescharacteristic
207C8—22no—
208C8—132no—
209C8—261no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22C2×D4×D1311yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—262no—
218C4—262no—
219C4—262no—
220C4—521no—
221C4—522no—
222C4#8816612yes—
223C4C2×Q8×D1311yescharacteristic
224C4#8825711yescharacteristic
225C2—42no—
226C2#1171933711yescharacteristic
227C2C2×#8816611yescharacteristic
228C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#474D13
hypocenterC13#3381
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
4. #11718740C2semidirect
6. #11718539C2semidirect
7. #11718538C2semidirect
8. #11718511C2semidirect
9. #11718491C2semidirect
55. #6105Q8semidirect
186. C13#3381semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192482
C13×#4742
#117187402
C4×#61052
#117185392
#117185382
#117185112
#117184912
#117184272
#117184192
#338113