Finite Group Databasebeta

← #13127520

Subgroups — #13127520

Order 1664.

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

normal subgroups only

This group has 336 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#11719247C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic
4#11718754C211yesmaximal, characteristic, complemented
5C4×#6105C211yesmaximal, characteristic
6#11718538C212yesmaximal, complemented
7#11718534C212yesmaximal, complemented
8#11718510C211yesmaximal, characteristic, complemented
9#11718491C211yesmaximal, characteristic, complemented
10#11718429C212yesmaximal
11#11718428C212yesmaximal
12C13×C4⋊Q8C2211yescharacteristic
13C4×D4×C13C2211yescharacteristic
14Q8×Dic13—21no—
15#88198—21no—
16#88190C2212yes—
17C2×#6105C2211yescharacteristic
18#88180—21no—
19#88178—21no—
20C2×Dic52C2212yes—
21#88144C2212yes—
22#88143—22no—
23#88141C2212yes—
24#88141C2212yes—
25#88133—22no—
26#88123C2211yescharacteristic
27C4×Dic26C2211yescharacteristic
28C4×Dic26C2211yescharacteristic
29C13×#107C2212yes—
30C13×C4⋊C8C2211yescharacteristic
31C13×#102C2212yes—
32#88072C2211yescharacteristic
33#88056C2212yes—
34#88054C2212yes—
35C8×Dic13C2212yes—
36#88050C2211yescharacteristic
37#88050C2212yes—
38#88050C2212yes—
39#88048C2211yescharacteristic
40C4×#1055C2211yescharacteristic
41C2×Q8×C13—21no—
42C2×D4×C13C2311yescharacteristic
43C22×C4×C13—21no—
44C2×Dic26D411yescharacteristic
45C2×Dic26C2312yes—
46C2×Dic26C2311yescharacteristic
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C13×C4⋊C4C2311yescharacteristic
51C13×C22⋊C4—21no—
52C42×C13C2311yescharacteristic
53C22⋊Dic13—22no—
54C22⋊Dic13—22no—
55#6105—22no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13—22no—
59C4⋊Dic13D411yescharacteristic
60C4⋊Dic13C2311yescharacteristic
61#6101—21no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101D412yes—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13—22no—
69C4×Dic13C2312yes—
70C2×#1055C2311yescharacteristic
71C2×#1055C2311yescharacteristic
72Dic52—24no—
73#3364—131nomaximal, Sylow
74C23×C13—21no—
75Q8×C13—42no—
76D4×C13—21no—
77D4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—42no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89Dic26—22no—
90Dic26—21no—
91Dic26—22no—
92Dic26—22no—
93Dic26#4112yes—
94C8×C13—22no—
95#1055—21no—
96#1055—21no—
97#557—131no—
98#556—131no—
99#488—132no—
100#487—131no—
101#479—132no—
102#474D1311yescharacteristic
103#464—132no—
104#462—131no—
105C8×Q8—131no—
106C4×Q16—132no—
107C4×SD16—131no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13—41no—
111C22×C13C22×D411yescharacteristic
112C4×C13—21no—
113C4×C13—41no—
114C4×C13—42no—
115C4×C13#13512yes—
116C4×C13C2×#4111yescharacteristic
117C4×C132−1+411yescharacteristic
118Dic13—22no—
119Dic13—22no—
120Dic13—22no—
121Dic13—42no—
122Dic13—41no—
123C2×Q16—132no—
124C2×SD16—131no—
125C4⋊Q8—131no—
126C4⋊Q8—261no—
127C4⋊Q8C2×D1311yescharacteristic
128#126—262no—
129#125—132no—
130#125—262no—
131#124—132no—
132C22⋊Q8—261no—
133C4×Q8—131no—
134C4×Q8—132no—
135C4×Q8—132no—
136C4×Q8—131no—
137C4×Q8—261no—
138C4×D4C2×D1311yescharacteristic
139#117—261no—
140#107C2×D1312yes—
141#106—131no—
142C4⋊C8—132no—
143C4⋊C8C2×D1311yescharacteristic
144#103—132no—
145#103—131no—
146#103—132no—
147#103—132no—
148#102—131no—
149#102C2×D1312yes—
150C4×C8—132no—
151C4×C8—131no—
152C2×C13—81no—
153C2×C13#54811yescharacteristic
154C2×C13C2×#13511yescharacteristic
155C2×C13#57811yescharacteristic
156C2×Q8—21no—
157C2×Q8—131no—
158C2×Q8—131no—
159C2×Q8—132no—
160C2×D4C22×D1311yescharacteristic
161C22×C4—21no—
162Q16—264no—
163SD16—262no—
164C2×C8—131no—
165C2×C8—131no—
166C2×C8C22×D1312yes—
167C4⋊C4—21no—
168C4⋊C4—131no—
169C4⋊C4—132no—
170C4⋊C4—131no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—261no—
178C4⋊C4C22×D1312yes—
179C4⋊C4C22×D1311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—262no—
182C22⋊C4—262no—
183C42—132no—
184C42—262no—
185C42—262no—
186C42—261no—
187C42C22×D1311yescharacteristic
188C13#336411yescharacteristic, complemented, Sylow
189C23—21no—
190Q8—42no—
191Q8—132no—
192Q8—262no—
193Q8—261no—
194Q8—262no—
195Q8—262no—
196D4—21no—
197D4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—261no—
206C2×C4D4×D1311yescharacteristic
207C2×C4D4×D1311yescharacteristic
208C2×C4C23×D1311yescharacteristic
209C8—22no—
210C8—261no—
211C8—261no—
212C22—41no—
213C22—41no—
214C22—41no—
215C22C2×D4×D1311yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—262no—
220C4—262no—
221C4—262no—
222C4—521no—
223C4—522no—
224C4#8816612yes—
225C4#8825411yescharacteristic
226C4#41×D1311yescharacteristic
227C2—81no—
228C2#1171933811yescharacteristic
229C2C2×#8816611yescharacteristic
230C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#474D13
hypocenterC13#3364
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. #11718754C2semidirect
6. #11718538C2semidirect
7. #11718534C2semidirect
8. #11718510C2semidirect
9. #11718491C2semidirect
188. C13#3364semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117192472
C13×#4742
#117187542
C4×#61052
#117185382
#117185342
#117185102
#117184912
#117184292
#117184282
#336413