Finite Group Databasebeta

← #13127716

Subgroups — #13127716

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#11719435C211yesmaximal, characteristic
2#11719426C211yesmaximal, characteristic, complemented
3C13×#498C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718748C211yesmaximal, characteristic
6#11718532C212yesmaximal
7#11718519C212yesmaximal, complemented
8#11718518C212yesmaximal, complemented
9#11718513C212yesmaximal
10C4×#6095C211yesmaximal, characteristic
11C8×Dic26C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88200—22no—
15Q8×Dic13—21no—
16#88198—21no—
17C2×#6095C2211yescharacteristic
18#88151—21no—
19#88147C2212yes—
20C4⋊C4×D13—21no—
21#88144C2212yes—
22#88144C2212yes—
23#88143—22no—
24#88141C2212yes—
25C4×D52C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#106C2212yes—
29C13×#106C2212yes—
30C4×C8×C13C2211yescharacteristic
31#88061C2211yescharacteristic
32#88057C2211yescharacteristic
33#88056C2211yescharacteristic
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38#88047C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13—21no—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×C4×D13—22no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2311yescharacteristic
48C2×C8×C13C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C13×C4⋊C4—21no—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2312yes—
53C13×C4⋊C4C2312yes—
54C42×C13C2311yescharacteristic
55#6103—21no—
56#6103—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62#6101—21no—
63#6101—22no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—21no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2312yes—
71#6095Q814yescomplemented
72#3381—131nomaximal, Sylow
73C22×D13—21no—
74Q8×C13—42no—
75Q8×C13—81no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13C2×D412yes—
85C2×Dic13C2×D412yes—
86D52—21no—
87D52C2×Q812yes—
88C4×D13—42no—
89C4×D13—82no—
90Dic26—22no—
91Dic26—21no—
92Dic26C2×Q812yes—
93C8×C13—21no—
94C8×C13C2×Q812yes—
95#1055—22no—
96#557—131no—
97#554—131no—
98#499—132no—
99#498D1311yescharacteristic, complemented
100#479—132no—
101#478—132no—
102#477—131no—
103#474—131no—
104C8×Q8—131no—
105C4×SD16—132no—
106C4×SD16—131no—
107C22×C13C22×D411yescharacteristic
108C2×D13—22no—
109C2×D13—41no—
110C2×D13—41no—
111C4×C13—21no—
112C4×C13—42no—
113C4×C13—42no—
114C4×C13#13512yes—
115C4×C13C22×Q811yescharacteristic
116C4×C132−1+411yescharacteristic
117Dic13—22no—
118Dic13—22no—
119Dic13—22no—
120Dic13—41no—
121Dic13—41no—
122C2×SD16—131no—
123C4⋊Q8—261no—
124C4⋊Q8C2×D1311yescharacteristic
125C4⋊Q8C2×D1311yescharacteristic
126#125—132no—
127#125—132no—
128#125—262no—
129C22⋊Q8—261no—
130C22⋊Q8—262no—
131C4×Q8—131no—
132C4×Q8—132no—
133C4×Q8—131no—
134C4×Q8—261no—
135C4×D4—132no—
136C4×D4—131no—
137C2×C4⋊C4—261no—
138#107—132no—
139#107—132no—
140#106—131no—
141#106C2×D1312yes—
142#106C2×D1312yes—
143C4⋊C8—132no—
144C4⋊C8—131no—
145#103—131no—
146#103—132no—
147#102—131no—
148#102—132no—
149C4×C8—132no—
150C4×C8C2×D1311yescharacteristic
151C2×C13D4×Q811yescharacteristic
152C2×C13C2×#13511yescharacteristic
153C2×C13#57711yescharacteristic
154D13—42no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—131no—
158C2×Q8—131no—
159C2×D4—131no—
160C22×C4—262no—
161C22×C4—261no—
162SD16—134no—
163C2×C8—132no—
164C2×C8C22×D1311yescharacteristic
165C2×C8C22×D1311yescharacteristic
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—131no—
169C4⋊C4—132no—
170C4⋊C4—131no—
171C4⋊C4—131no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—261no—
178C4⋊C4C22×D1312yes—
179C4⋊C4C22×D1312yes—
180C22⋊C4—262no—
181C22⋊C4—261no—
182C42—132no—
183C42—262no—
184C42—261no—
185C42C22×D1311yescharacteristic
186C13#338111yescharacteristic, complemented, Sylow
187C23—261no—
188Q8—42no—
189Q8—81no—
190Q8—132no—
191Q8—262no—
192Q8—261no—
193D4—132no—
194D4—261no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—132no—
198C2×C4—132no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—522no—
203C2×C4—1042no—
204C2×C4D4×D1311yescharacteristic
205C2×C4D4×D1311yescharacteristic
206C2×C4C23×D1311yescharacteristic
207C8—21no—
208C8—262no—
209C8Q8×D1312yes—
210C22—262no—
211C22—521no—
212C22—521no—
213C22C2×D4×D1311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—262no—
218C4—262no—
219C4—262no—
220C4—521no—
221C4—521no—
222C4#8817012yes—
223C4C2×Q8×D1311yescharacteristic
224C4#8825411yescharacteristic
225C2—522no—
226C2#1171943211yescharacteristic
227C2C2×#8817011yescharacteristic
228C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#498C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#498D13
hypocenterC13#3381
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #11719426C2semidirect
3. C13×#498C2semidirect
4. #11718752C2semidirect
7. #11718519C2semidirect
8. #11718518C2semidirect
11. C8×Dic26C2semidirect
71. #6095Q8semidirect
99. #498D13semidirect
186. C13#3381semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194262
C13×#4982
#117187522
#117187482
#117185322
#117185192
#117185182
#117185132
C4×#60952
C8×Dic262
#338113