Finite Group Databasebeta

← #16784619

Subgroups — #16784619

Order 3328.

446 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 118 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#13130383C211yesmaximal, characteristic
2#13130140C212yesmaximal
3#13130080C212yesmaximal
4#13130039C211yesmaximal, characteristic
5C2×#11718534C211yesmaximal, characteristic
6C22×Dic52C411yescharacteristic
7C2×#88141C2212yes—
8#11719119C2212yes—
9#11719119C2211yescharacteristic
10#11719119C2211yescharacteristic
11C2×C13×#107C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13C2×#88050C412yes—
14#11718534—21no—
15#11718534—21no—
16#11718534—21no—
17#11718534—21no—
18#11718286—24no—
19#11718254—21no—
20#11718253—21no—
21#11718251—21no—
22C8×#1057—21no—
23#11718244—24no—
24C22×Dic26C2×C412yes—
25C22×C8×C13C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C412yes—
27C2×#6101—22no—
28C2×C4×Dic13—22no—
29C2×C4×Dic13C2311yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C2×Dic52—21no—
32C2×Dic52—21no—
33C2×Dic52—22no—
34C2×Dic52C814yescomplemented
35#88141—22no—
36#88141—22no—
37#88141—22no—
38#88141—22no—
39C22⋊#1057—21no—
40C22⋊#1057—22no—
41C22⋊#1057D412yes—
42C4⋊#1057—22no—
43C4⋊#1057—21no—
44C4⋊#1057D412yes—
45C4×#1057—21no—
46C4×#1057—21no—
47C4×#1057—22no—
48C13×#107—21no—
49C13×#107—21no—
50C8×Dic13D411yescharacteristic
51C8×Dic13D411yescharacteristic
52C8×Dic13D411yescharacteristic
53C8×Dic13D411yescharacteristic
54#88050—22no—
55#88050—22no—
56#9669—131nomaximal, Sylow
57C22×C4×C13—22no—
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13C2×D411yescharacteristic
61C22×Dic13#4111yescharacteristic
62C2×Dic26—22no—
63C2×Dic26—22no—
64C2×Dic26—22no—
65C2×Dic26—22no—
66C2×Dic26—22no—
67C2×Dic26C2×C814yes—
68C2×#1057—22no—
69C2×#1057—22no—
70C2×#1057—42no—
71C2×C8×C13C22⋊C411yescharacteristic
72C2×C8×C13C22⋊C411yescharacteristic
73C2×C8×C13C2×C812yes—
74C2×C8×C13M1612yes—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77#6101—42no—
78#6101—42no—
79C4×Dic13—42no—
80C4×Dic13—42no—
81C4×Dic13C2×D411yescharacteristic
82C4×Dic13C2×D411yescharacteristic
83C4×Dic13C2×D411yescharacteristic
84C4×Dic13#4111yescharacteristic
85C2×#1055—21no—
86C2×#1055—21no—
87C2×#1055C22⋊C411yescharacteristic
88C2×#1055C22⋊C411yescharacteristic
89Dic52—24no—
90Dic52—24no—
91C2×C4×Q16—131no—
92#1564—131no—
93#1479—132no—
94#1461—132no—
95#1450—131no—
96C23×C13C4×D411yescharacteristic
97C2×C4×C13—42no—
98C2×C4×C13—82no—
99C2×C4×C13C2×C22⋊C411yescharacteristic
100C2×C4×C13C4×D411yescharacteristic
101C2×C4×C13C22×C811yescharacteristic
102C2×C4×C13C2×M1611yescharacteristic
103C2×C4×C13#13111yescharacteristic
104C2×C4×C13#13111yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—24no—
107C2×Dic13—41no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13#12111yescharacteristic
111C2×Dic13#12111yescharacteristic
112C2×Dic13#12411yescharacteristic
113C2×Dic13#12711yescharacteristic
114Dic26—24no—
115Dic26—24no—
116Dic26—42no—
117Dic26—42no—
118#1057—42no—
119#1057—42no—
120#1057—82no—
121C8×C13C22⋊C812yes—
122C8×C13C22⋊C812yes—
123#1055—21no—
124#1055—21no—
125C22×Q16—131no—
126C2×C4×Q8—132no—
127C4×Q16—261no—
128C4×Q16—261no—
129C4×Q16—261no—
130C4×Q16—261no—
131#431—131no—
132#431—131no—
133#431—132no—
134C2×#107#26111yescharacteristic
135C2×#103—132no—
136C2×C4×C8—131no—
137#335—261no—
138#334—261no—
139Q8⋊C8—264no—
140#324—264no—
141#322—261no—
142C82—261no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13#39011yescharacteristic
146C22×C13C8×D411yescharacteristic
147C22×C13#43611yescharacteristic
148C4×C13—82no—
149C4×C13C2×C22⋊C811yescharacteristic
150C4×C13#40811yescharacteristic
151C4×C13C8×D411yescharacteristic
152C4×C13#43611yescharacteristic
153Dic13—21no—
154Dic13—21no—
155Dic13—21no—
156Dic13—44no—
157Dic13#47312yes—
158C22×Q8—132no—
159C2×Q16—134no—
160C2×Q16—262no—
161C2×Q16—261no—
162C2×Q16—261no—
163C22×C8—131no—
164C22×C8C2×#26111yescharacteristic
165C4×Q8—262no—
166C4×Q8—262no—
167C4×Q8—262no—
168C4×Q8—262no—
169C2×C4⋊C4—262no—
170C2×C4⋊C4C2×#26112yes—
171C2×C42—131no—
172C2×C42—262no—
173#107—21no—
174#107—21no—
175C4⋊C8—132no—
176C4⋊C8—261no—
177C4⋊C8—262no—
178#103—262no—
179#103—262no—
180C22⋊C8—132no—
181C22⋊C8—261no—
182C22⋊C8—262no—
183C4×C8—131no—
184C4×C8—131no—
185C4×C8—131no—
186C4×C8—131no—
187C4×C8—261no—
188C4×C8—261no—
189C4×C8—262no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13#195411yescharacteristic
193C2×C13#197611yescharacteristic
194C2×C13#197911yescharacteristic
195C2×Q8—134no—
196C2×Q8—262no—
197C2×Q8—262no—
198C2×Q8—262no—
199C2×Q8—262no—
200C2×Q8—262no—
201C22×C4—22no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—262no—
205C22×C4C22×#26111yescharacteristic
206Q16—264no—
207Q16—264no—
208C2×C8—131no—
209C2×C8—131no—
210C2×C8—261no—
211C2×C8—261no—
212C2×C8—262no—
213C2×C8—262no—
214C2×C8—522no—
215C2×C8D13⋊C812yes—
216C2×C8#611812yes—
217C2×C8C22⋊#26111yescharacteristic
218C2×C8C22⋊#26111yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—522no—
222C4⋊C4—522no—
223C42—131no—
224C42—131no—
225C42—131no—
226C42—131no—
227C42—522no—
228C42—522no—
229C13#966911yescharacteristic, complemented, Sylow
230C23D4×#26111yescharacteristic
231Q8—264no—
232Q8—264no—
233Q8—522no—
234Q8—522no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—131no—
238C2×C4—131no—
239C2×C4—131no—
240C2×C4—131no—
241C2×C4—262no—
242C2×C4—264no—
243C2×C4—521no—
244C2×C4—522no—
245C2×C4—522no—
246C2×C4C2×D13⋊C811yescharacteristic
247C2×C4C2×#611811yescharacteristic
248C2×C4D4×#26111yescharacteristic
249C2×C4#8824011yescharacteristic
250C2×C4#8824011yescharacteristic
251C2×C4C2×C22⋊#26111yescharacteristic
252C8—261no—
253C8—261no—
254C8—522no—
255C8—522no—
256C8—1042no—
257C8#8811112yes—
258C8#8811112yes—
259C22—21no—
260C22—21no—
261C22#1171907311yescharacteristic
262C22#1171907611yescharacteristic
263C22#1171915111yescharacteristic
264C4—82no—
265C4—132no—
266C4—261no—
267C4—261no—
268C4—261no—
269C4—524no—
270C4#1171907311yescharacteristic
271C4#1171907611yescharacteristic
272C4C2×#8811111yescharacteristic
273C4#1171915911yescharacteristic
274C2—21no—
275C2—21no—
276C2#1313095811yescharacteristic
277C2#1313099311yescharacteristic
278C2#1313099811yescharacteristic
subgroupG/H
centerC22#11719151
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#107C4
socleC22×C13#390
prime radicalC23×C13C4×D4
cosocleC2×C4×Dic13C23
hypercenterC2×#107#261
hypocenterC13#9669
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
34. C2×Dic52C8semidirect
229. C13#9669semidirect

Maximal subgroups

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

subgroupindex
#131303832
#131301402
#131300802
#131300392
C2×#117185342
#966913