Finite Group Databasebeta

← #13127751

Subgroups — #13127751

Order 1664.

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

normal subgroups only

This group has 340 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#11719427C211yesmaximal, characteristic, complemented
3C13×#500C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718745C211yesmaximal, characteristic
6#11718551C212yesmaximal
7#11718550C212yesmaximal
8#11718538C212yesmaximal, complemented
9#11718537C212yesmaximal, complemented
10C4×#6095C211yesmaximal, characteristic
11#11718340C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×C4⋊Q8C2211yescharacteristic
14#88200—22no—
15#88198—22no—
16C2×#6095C2211yescharacteristic
17#88151—21no—
18#88147C2212yes—
19C4⋊C4×D13—21no—
20#88144C2212yes—
21#88142—21no—
22#88142C2212yes—
23#88141—21no—
24#88141C2212yes—
25C4×D52C2211yescharacteristic
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C13×#107C2212yes—
29C13×#107C2212yes—
30C4×C8×C13C2211yescharacteristic
31#88061C2211yescharacteristic
32#88057C2211yescharacteristic
33#88056C2211yescharacteristic
34#88055C2212yes—
35#88054C2212yes—
36#88050C2212yes—
37#88049C2212yes—
38#88048C2212yes—
39#88047C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×Q8×C13—21no—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×C4×D13—22no—
46C2×Dic26—22no—
47C2×Dic26D411yescharacteristic
48C2×Dic26C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2311yescharacteristic
51C13×C4⋊C4—21no—
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C13×C4⋊C4C2312yes—
55C42×C13C2311yescharacteristic
56#6103—21no—
57#6103—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#3385—131nomaximal, Sylow
73C22×D13—21no—
74Q8×C13—81no—
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—
92Dic26—82no—
93Dic26C2×Q812yes—
94C8×C13—21no—
95C8×C13C2×Q812yes—
96#1055—22no—
97Q82—131no—
98#554—131no—
99#501—132no—
100#500D1311yescharacteristic, complemented
101#479—132no—
102#477—131no—
103#476—131no—
104#474—132no—
105#446—131no—
106#440—132no—
107C4×SD16—131no—
108C22×C13C22×D411yescharacteristic
109C2×D13—22no—
110C2×D13—41no—
111C2×D13—41no—
112C4×C13—21no—
113C4×C13—42no—
114C4×C13—42no—
115C4×C13#13712yes—
116C4×C13C22×Q811yescharacteristic
117C4×C132−1+411yescharacteristic
118Dic13—22no—
119Dic13—22no—
120Dic13—22no—
121Dic13—41no—
122Dic13—41no—
123C2×SD16—131no—
124C4⋊Q8—132no—
125C4⋊Q8—261no—
126C4⋊Q8—262no—
127C4⋊Q8C2×D1311yescharacteristic
128C4⋊Q8C2×D1311yescharacteristic
129#125—132no—
130C22⋊Q8—261no—
131C22⋊Q8—262no—
132C4×Q8—131no—
133C4×Q8—132no—
134C4×Q8—131no—
135C4×Q8—261no—
136C4×D4—132no—
137C4×D4—131no—
138C2×C4⋊C4—261no—
139#107—132no—
140#107C2×D1312yes—
141#107C2×D1312yes—
142#106—131no—
143#106—132no—
144C4⋊C8—132no—
145C4⋊C8—131no—
146#103—131no—
147#103—132no—
148#102—131no—
149#102—132no—
150#97—132no—
151C4×C8C2×D1311yescharacteristic
152C2×C13D4×Q811yescharacteristic
153C2×C13C2×#13711yescharacteristic
154C2×C13#57611yescharacteristic
155D13—42no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—131no—
159C2×Q8—131no—
160C2×Q8—262no—
161C2×D4—131no—
162C22×C4—262no—
163C22×C4—261no—
164SD16—134no—
165C2×C8—132no—
166C2×C8C22×D1311yescharacteristic
167C2×C8C22×D1311yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—131no—
171C4⋊C4—132no—
172C4⋊C4—131no—
173C4⋊C4—131no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—261no—
179C4⋊C4C22×D1312yes—
180C4⋊C4C22×D1312yes—
181C22⋊C4—262no—
182C22⋊C4—261no—
183C42—132no—
184C42—262no—
185C42—261no—
186C42C22×D1311yescharacteristic
187C13#338511yescharacteristic, complemented, Sylow
188C23—261no—
189Q8—81no—
190Q8—81no—
191Q8—132no—
192Q8—262no—
193Q8—261no—
194Q8—1042no—
195D4—132no—
196D4—261no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—261no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—522no—
205C2×C4—1042no—
206C2×C4D4×D1311yescharacteristic
207C2×C4D4×D1311yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—21no—
210C8—262no—
211C8Q8×D1312yes—
212C22—262no—
213C22—521no—
214C22—521no—
215C22C2×D4×D1311yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—262no—
220C4—262no—
221C4—262no—
222C4—521no—
223C4—521no—
224C4#8817212yes—
225C4C2×Q8×D1311yescharacteristic
226C4#8825411yescharacteristic
227C2—522no—
228C2#1171943211yescharacteristic
229C2#1171946211yescharacteristic
230C2C2×#8817211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#500C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#500D13
hypocenterC13#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #11719427C2semidirect
3. C13×#500C2semidirect
4. #11718752C2semidirect
8. #11718538C2semidirect
9. #11718537C2semidirect
11. #11718340C2semidirect
71. #6095Q8semidirect
100. #500D13semidirect
187. C13#3385semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117194272
C13×#5002
#117187522
#117187452
#117185512
#117185502
#117185382
#117185372
C4×#60952
#117183402
#338513