Finite Group Databasebeta

← #13125914

Subgroups — #13125914

Order 1664.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719436C211yesmaximal, characteristic, complemented
2#11719380C211yesmaximal, characteristic
3C13×#497C211yesmaximal, characteristic, complemented
4#11718847C212yesmaximal, complemented
5#11718843C212yesmaximal, complemented
6#11718834C212yesmaximal
7#11718827C212yesmaximal, complemented
8#11718753C211yesmaximal, characteristic, complemented
9#11718717C211yesmaximal, characteristic, complemented
10#11718370C211yesmaximal, characteristic, complemented
11#11718364C211yesmaximal, characteristic, complemented
12C2×Q8×D13C2211yescharacteristic
13C2×#6129C2211yescharacteristic
14C2×C13×Q16C2212yes—
15C2×C13×SD16C2212yes—
16C13×C4⋊Q8C2211yescharacteristic
17C13×#124C2211yescharacteristic
18#88200C2212yes—
19Q8×Dic13C2212yes—
20#88198C2211yescharacteristic
21C2×#6107C2212yes—
22C2×#6107C2212yes—
23#88190C2211yescharacteristic
24#88152—22no—
25#88143—22no—
26#88137—22no—
27#88132—22no—
28#88126C2211yescharacteristic
29#88124C2211yescharacteristic
30#88123C2211yescharacteristic
31C13×#97C2211yescharacteristic
32#88075C2212yes—
33#88072C2212yes—
34#88060C2212yes—
35#88056C2212yes—
36#88056C2212yes—
37#88054C2212yes—
38C4×#1055C2211yescharacteristic
39C2×Q8×C13C2311yescharacteristic
40C2×Q8×C13C2312yes—
41C2×D4×C13C2311yescharacteristic
42C2×C22⋊D13—21no—
43C22×Dic13—21no—
44Q8×D13—42no—
45#6129—42no—
46C2×C4×D13—21no—
47C2×C4×D13C2311yescharacteristic
48C2×Dic26—21no—
49C2×Dic26C2311yescharacteristic
50C2×Dic26C2311yescharacteristic
51C13×Q16—42no—
52C13×SD16—42no—
53C2×C8×C13C2312yes—
54C13×C4⋊C4—22no—
55C13×C22⋊C4—22no—
56C42×C13C2311yescharacteristic
57C22⋊Dic13—22no—
58#6107—42no—
59#6107—42no—
60#6103—22no—
61#6103D412yes—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64C4⋊Dic13C2312yes—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68#6101D412yes—
69C4×Dic13—22no—
70C4×Dic13C2311yescharacteristic
71C2×#1055C2312yes—
72#3223—131nomaximal, Sylow
73C23×C13—21no—
74C22×D13C2×D411yescharacteristic
75Q8×C13—22no—
76Q8×C13—22no—
77Q8×C13—22no—
78D4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13C2×D412yes—
82C2×C4×C13C2411yescharacteristic
83C22⋊D13—42no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—42no—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D411yescharacteristic
90C4×D13—22no—
91C4×D13—42no—
92Dic26—22no—
93Dic26—22no—
94Dic26—42no—
95C8×C13—22no—
96#1055—22no—
97#541—131no—
98#536—131no—
99#497D1311yescharacteristic, complemented
100#494—131no—
101#491—131no—
102#488—131no—
103#464—132no—
104#462—132no—
105#452—132no—
106#451—132no—
107#433—131no—
108C22×C13—41no—
109C22×C13—42no—
110C22×C13C22×D411yescharacteristic
111C2×D13—21no—
112C2×D13—22no—
113C4×C13—22no—
114C4×C13—41no—
115C4×C13—42no—
116C4×C13H(5,𝔽2)12yes—
117Dic13—21no—
118Dic13—22no—
119Dic13—41no—
120Dic13—41no—
121Dic13—42no—
122C2×#41—131no—
123C22×Q8—131no—
124C2×Q16—132no—
125C2×Q16—132no—
126C2×Q16C2×D1312yes—
127C2×SD16C2×D1312yes—
128C4⋊Q8—131no—
129C4⋊Q8—131no—
130C4⋊Q8C2×D1311yescharacteristic
131#126—262no—
132#125—131no—
133#125—262no—
134#124—131no—
135#124C2×D1311yescharacteristic
136#123—262no—
137C22⋊Q8—132no—
138C22⋊Q8—262no—
139C4×Q8—132no—
140#117—131no—
141C4⋊C8—132no—
142#103—132no—
143#103—132no—
144#103—132no—
145#102—132no—
146C22⋊C8—132no—
147#97C2×D1311yescharacteristic
148C4×C8—131no—
149C2×C13—81no—
150C2×C13#53511yescharacteristic
151C2×C13#57812yes—
152D13—41no—
153#41—522no—
154C2×Q8—131no—
155C2×Q8—131no—
156C2×Q8—261no—
157C2×Q8—522no—
158C2×Q8C22×D1311yescharacteristic
159C2×Q8C22×D1312yes—
160C2×D4—261no—
161C2×D4C22×D1311yescharacteristic
162C22×C4—131no—
163C22×C4—261no—
164C22×C4—261no—
165Q16—42no—
166Q16—522no—
167Q16—522no—
168SD16—42no—
169C2×C8—132no—
170C2×C8C22×D1312yes—
171C4⋊C4—22no—
172C4⋊C4—132no—
173C4⋊C4—132no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C22⋊C4—22no—
180C22⋊C4—132no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C42—131no—
184C42—262no—
185C42C22×D1311yescharacteristic
186C13#322311yescharacteristic, complemented, Sylow
187C23—21no—
188C23—131no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—262no—
193Q8—262no—
194Q8—522no—
195D4—22no—
196D4—522no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—132no—
200C2×C4—131no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4D4×D1312yes—
208C2×C4C23×D1311yescharacteristic
209C8—22no—
210C8—262no—
211C22—42no—
212C22—41no—
213C22—262no—
214C22—261no—
215C22C2×D4×D1311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—262no—
220C4—261no—
221C4—522no—
222C4—521no—
223C4—521no—
224C4#8825112yes—
225C2—81no—
226C2—521no—
227C2#1171942011yescharacteristic
228C2#1171948412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
prime radicalC2×#6129C22
hypercenter#497D13
hypocenterC13#3223
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #11719436C2semidirect
3. C13×#497C2semidirect
4. #11718847C2semidirect
5. #11718843C2semidirect
7. #11718827C2semidirect
8. #11718753C2semidirect
9. #11718717C2semidirect
10. #11718370C2semidirect
11. #11718364C2semidirect
99. #497D13semidirect
186. C13#3223semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117193802
C13×#4972
#117188472
#117188432
#117188342
#117188272
#117187532
#117187172
#117183702
#117183642
#322313