Finite Group Databasebeta

← #13127537

Subgroups — #13127537

Order 1664.

348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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#11719418C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic
4#11718755C211yesmaximal, characteristic, complemented
5#11718736C211yesmaximal, characteristic
6#11718429C212yesmaximal, complemented
7#11718428C212yesmaximal, complemented
8#11718427C212yesmaximal, complemented
9#11718419C212yesmaximal, complemented
10C4×Dic52C211yesmaximal, characteristic, complemented
11C8×Dic26C211yesmaximal, characteristic, complemented
12C13×C4⋊Q8C2211yescharacteristic
13C13×#127C2211yescharacteristic
14Q8×Dic13—21no—
15#88198—21no—
16#88190—21no—
17#88190C2212yes—
18#88189—22no—
19D4×Dic13—21no—
20D4×Dic13C2212yes—
21C2×#6105C2212yes—
22C2×Dic52C2211yescharacteristic
23#88144C2212yes—
24#88143—22no—
25#88141C2212yes—
26C4×Dic26C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#102C2212yes—
30C13×#102C2212yes—
31C4×C8×C13C2211yescharacteristic
32#88072C2212yes—
33#88058C2211yescharacteristic
34#88056C2211yescharacteristic
35#88056C2211yescharacteristic
36#88054C2212yes—
37C8×Dic13C2212yes—
38#88050C2212yes—
39#88048C2212yes—
40C4⋊#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13—21no—
43C2×D4×C13—21no—
44C2×D4×C13C2312yes—
45C22×Dic13—22no—
46C2×Dic26D411yescharacteristic
47C2×Dic26C2311yescharacteristic
48C2×Dic26C2311yescharacteristic
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2311yescharacteristic
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2312yes—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55C22⋊Dic13—22no—
56C22⋊Dic13—22no—
57#6105—24no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61C4⋊Dic13C2311yescharacteristic
62#6101—21no—
63#6101—21no—
64#6101—22no—
65#6101—22no—
66#6101D412yes—
67C4×Dic13—21no—
68C4×Dic13—21no—
69C4×Dic13—22no—
70C4×Dic13C2312yes—
71C2×#1055C2312yes—
72Dic52—22no—
73#3365—131nomaximal, Sylow
74C23×C13—22no—
75Q8×C13—42no—
76D4×C13—22no—
77D4×C13—22no—
78D4×C13—42no—
79D4×C13—81no—
80C2×C4×C13—22no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—82no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91Dic26—22no—
92Dic26—21no—
93Dic26—21no—
94Dic26—21no—
95Dic26#4112yes—
96C8×C13—21no—
97C8×C13—21no—
98#1055—22no—
99#559—131no—
100#557—131no—
101#488—132no—
102#486D1311yescharacteristic
103#478—132no—
104#475—131no—
105#464—132no—
106#460—131no—
107C8×Q8—131no—
108C4×Q16—131no—
109C4×SD16—132no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—42no—
113C22×C13C22×D411yescharacteristic
114C4×C13—21no—
115C4×C13—42no—
116C4×C13#13512yes—
117C4×C13C2×#4111yescharacteristic
118C4×C132−1+411yescharacteristic
119Dic13—22no—
120Dic13—22no—
121Dic13—22no—
122Dic13—41no—
123Dic13—41no—
124Dic13—41no—
125C2×Q16—131no—
126C2×SD16—132no—
127C4⋊Q8—261no—
128C4⋊Q8C2×D1311yescharacteristic
129#127C2×D1311yescharacteristic
130#125—132no—
131#125—262no—
132#124—132no—
133#124—261no—
134#123—262no—
135C4×Q8—131no—
136C4×Q8—132no—
137C4×Q8—131no—
138C4×Q8—131no—
139C4×Q8—261no—
140C4×D4—132no—
141C4×D4—261no—
142#107—131no—
143#106—132no—
144C4⋊C8—132no—
145C4⋊C8—131no—
146#103—131no—
147#103—131no—
148#103—132no—
149#102—132no—
150#102C2×D1312yes—
151#102C2×D1312yes—
152C4×C8—132no—
153C4×C8C2×D1311yescharacteristic
154C2×C13—82no—
155C2×C13#54811yescharacteristic
156C2×C13C2×#13511yescharacteristic
157C2×C13#57711yescharacteristic
158C2×Q8—21no—
159C2×Q8—131no—
160C2×Q8—131no—
161C2×Q8—131no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4C22×D1312yes—
165C22×C4—262no—
166Q16—262no—
167SD16—264no—
168C2×C8—132no—
169C2×C8C22×D1311yescharacteristic
170C2×C8C22×D1311yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—131no—
173C4⋊C4—132no—
174C4⋊C4—131no—
175C4⋊C4—131no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4C22×D1312yes—
182C22⋊C4—262no—
183C22⋊C4—262no—
184C22⋊C4—262no—
185C42—132no—
186C42—262no—
187C42—261no—
188C42—261no—
189C42C22×D1311yescharacteristic
190C13#336511yescharacteristic, complemented, Sylow
191C23—22no—
192Q8—42no—
193Q8—132no—
194Q8—262no—
195Q8—261no—
196Q8—261no—
197Q8—261no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—81no—
202C2×C4—22no—
203C2×C4—132no—
204C2×C4—132no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—1042no—
210C2×C4D4×D1311yescharacteristic
211C2×C4D4×D1311yescharacteristic
212C2×C4C23×D1311yescharacteristic
213C8—21no—
214C8—21no—
215C8—262no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22C2×D4×D1311yescharacteristic
220C4—21no—
221C4—42no—
222C4—262no—
223C4—262no—
224C4—262no—
225C4—521no—
226C4—521no—
227C4—521no—
228C4#8816612yes—
229C4#41×D1311yescharacteristic
230C4#8825711yescharacteristic
231C2—82no—
232C2#1171938211yescharacteristic
233C2C2×#8816611yescharacteristic
234C2#1171946711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radicalC13×#127C22
hypercenter#486D13
hypocenterC13#3365
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
4. #11718755C2semidirect
6. #11718429C2semidirect
7. #11718428C2semidirect
8. #11718427C2semidirect
9. #11718419C2semidirect
10. C4×Dic52C2semidirect
11. C8×Dic26C2semidirect
190. C13#3365semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117194182
C13×#4862
#117187552
#117187362
#117184292
#117184282
#117184272
#117184192
C4×Dic522
C8×Dic262
#336513