Finite Group Databasebeta

← #16784597

Subgroups — #16784597

Order 3328.

482 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 124 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#13131006C212yesmaximal
2C2×#11718256C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal
4C2×#1057⋊C8C211yesmaximal, characteristic
5C2×#11718534C211yesmaximal, characteristic
6C22×Dic52C411yescharacteristic
7C2×#88141C2212yes—
8C2×C4⋊#1057C2212yes—
9C2×C4×#1057C2211yescharacteristic
10C2×C4×#1057C2211yescharacteristic
11C2×C13×#107C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13C2×#88050C412yes—
14#11718534—22no—
15#11718534—22no—
16#11718290—24no—
17#11718256—22no—
18#1057⋊C8—22no—
19#11718244—24no—
20C22×Dic26C2×C412yes—
21C22×#1057—21no—
22C22×#1057—22no—
23C22×#1057D412yes—
24C22×C8×C13C2×C411yescharacteristic
25C2×C13×C4⋊C4C2×C412yes—
26C2×#6101—22no—
27C2×C4×Dic13—22no—
28C2×C4×Dic13C2311yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C2×Dic52—24no—
31C2×Dic52—22no—
32#88141—22no—
33#88141—22no—
34#88141—22no—
35#88141—22no—
36C4⋊#1057—22no—
37C4⋊#1057—22no—
38C4×#1057—21no—
39C4×#1057—21no—
40C4×#1057—21no—
41C4×#1057D412yes—
42C13×#107—22no—
43C8×Dic13D412yes—
44C8×Dic13D412yes—
45#88050—24no—
46#9662—131nomaximal, Sylow
47C22×C4×C13—22no—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13C2×D411yescharacteristic
51C22×Dic13#4111yescharacteristic
52C2×Dic26—22no—
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×Dic26—22no—
56C2×Dic26—22no—
57C2×Dic26M1614yes—
58C2×#1057—22no—
59C2×#1057—22no—
60C2×#1057—22no—
61C2×#1057—42no—
62C2×#1057—42no—
63C2×#1057—44no—
64C2×#1057Q1614yescomplemented
65C2×C8×C13—22no—
66C2×C8×C13C22⋊C412yes—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69#6101—42no—
70#6101—42no—
71C4×Dic13—42no—
72C4×Dic13—42no—
73C4×Dic13C2×D411yescharacteristic
74C4×Dic13C2×D411yescharacteristic
75C4×Dic13C2×D411yescharacteristic
76C4×Dic13#4111yescharacteristic
77C2×#1055—22no—
78C2×#1055C22⋊C412yes—
79Dic52—28no—
80C2×C4×Q16—131no—
81#1984—132no—
82C2×#335—131no—
83C2×Q8⋊C8—132no—
84C2×#322—131no—
85C23×C13C4×D411yescharacteristic
86C2×C4×C13—42no—
87C2×C4×C13—44no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13C4×D411yescharacteristic
90C2×C4×C13C2×M1612yes—
91C2×C4×C13#13112yes—
92C2×Dic13—22no—
93C2×Dic13—24no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13#12111yescharacteristic
97C2×Dic13#12111yescharacteristic
98C2×Dic13#12411yescharacteristic
99C2×Dic13#12711yescharacteristic
100C2×Dic13C2×Q1612yes—
101C2×Dic13#13512yes—
102Dic26—24no—
103Dic26—24no—
104Dic26—42no—
105Dic26—42no—
106#1057—24no—
107#1057—42no—
108#1057—82no—
109C8×C13—22no—
110#1055—22no—
111C22×Q16—131no—
112C2×C4×Q8—132no—
113C4×Q16—262no—
114C4×Q16—262no—
115C2×#107#26111yescharacteristic
116C2×C4⋊C8—132no—
117C2×#103—132no—
118C2×C4×C8—131no—
119C2×C4×C8—131no—
120C2×C4×C8—131no—
121#336—264no—
122#335—262no—
123Q8⋊C8—264no—
124#322—262no—
125C22×C13#39011yescharacteristic
126C22×C13#43512yes—
127C22×C13C4×Q1612yes—
128C22×C13#44412yes—
129C4×C13—82no—
130C4×C13#40711yescharacteristic
131C4×C13#40811yescharacteristic
132C4×C13#43512yes—
133Dic13—21no—
134Dic13—21no—
135Dic13—44no—
136Dic13#46712yes—
137Dic13#49411yescharacteristic
138Dic13#49511yescharacteristic
139C22×Q8—132no—
140C2×Q16—264no—
141C2×Q16—262no—
142C22×C8—132no—
143C22×C8—131no—
144C22×C8—261no—
145C22×C8—262no—
146C22×C8C2×#26111yescharacteristic
147C4×Q8—262no—
148C4×Q8—262no—
149C4×Q8—262no—
150C4×Q8—262no—
151C2×C4⋊C4—262no—
152C2×C4⋊C4C2×#26112yes—
153C2×C42—131no—
154C2×C42—262no—
155#107—22no—
156C4⋊C8—262no—
157C4⋊C8—262no—
158#103—264no—
159C4×C8—132no—
160C4×C8—132no—
161C4×C8—132no—
162C4×C8—261no—
163C4×C8—261no—
164C4×C8—261no—
165C2×C13#158414yes—
166C2×C13#195511yescharacteristic
167C2×C13#196911yescharacteristic
168C2×C13#197511yescharacteristic
169C2×Q8—134no—
170C2×Q8—262no—
171C2×Q8—262no—
172C2×Q8—262no—
173C2×Q8—262no—
174C2×Q8—262no—
175C22×C4—22no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—262no—
179C22×C4C22×#26111yescharacteristic
180Q16—268no—
181C2×C8—22no—
182C2×C8—134no—
183C2×C8—132no—
184C2×C8—262no—
185C2×C8—262no—
186C2×C8—262no—
187C2×C8—262no—
188C2×C8—522no—
189C2×C8—522no—
190C2×C8—524no—
191C2×C8C22⋊#26112yes—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C42—131no—
197C42—131no—
198C42—131no—
199C42—131no—
200C42—522no—
201C42—522no—
202C13#966211yescharacteristic, complemented, Sylow
203C23D4×#26111yescharacteristic
204Q8—264no—
205Q8—264no—
206Q8—522no—
207Q8—522no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—131no—
213C2×C4—131no—
214C2×C4—131no—
215C2×C4—131no—
216C2×C4—262no—
217C2×C4—264no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4D13⋊M1612yes—
221C2×C4D4×#26111yescharacteristic
222C2×C4#8824012yes—
223C2×C4C2×C22⋊#26111yescharacteristic
224C8—22no—
225C8—264no—
226C8—262no—
227C8—522no—
228C8—1042no—
229C22#1171907512yes—
230C22#1171910412yes—
231C22Q16×#26112yes—
232C22#1171915111yescharacteristic
233C4—82no—
234C4—132no—
235C4—131no—
236C4—131no—
237C4—261no—
238C4—261no—
239C4—524no—
240C4#1171907512yes—
241C4#1171912611yescharacteristic
242C4#1171915911yescharacteristic
243C2#1313044814yes—
244C2#1313096211yescharacteristic
245C2#1313098211yescharacteristic
246C2#1313099111yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#107C4
socle, prime radicalC23×C13C4×D4
cosocleC2×C4×Dic13C23
hypercenterC2×#107#261
hypocenterC13#9662
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
64. C2×#1057Q16semidirect
202. C13#9662semidirect

Maximal subgroups

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

subgroupindex
#131310062
C2×#117182562
C2×#117182442
C2×#1057⋊C82
C2×#117185342
#966213