Finite Group Databasebeta

← #15757911

Subgroups — #15757911

Order 3328.

756 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#11718640C211yesmaximal, characteristic
2#13117439C211yesmaximal, characteristic
3#13114772C212yesmaximal
4#13112716C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×#6101—21no—
9C2×C13×C22⋊C8C2212yes—
10#11718873C2212yes—
11#11718872—21no—
12C4×C22⋊Dic13—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×#88056—24no—
16#11718642—24no—
17#11718640—22no—
18#11718640C414yescomplemented
19C13×#324—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×Dic26—22no—
26C22×Dic26—22no—
27C22×Dic26—21no—
28C22×Dic26—44no—
29C22×Dic26C2×C412yes—
30C22×C8×C13—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D412yes—
35C2×C22⋊Dic13—22no—
36C2×C4⋊Dic13D414yes—
37C2×#6101—24no—
38C2×#6101—44no—
39C2×C4×Dic13—22no—
40C13×C22⋊C8—22no—
41C13×C22⋊C8—22no—
42#88071—22no—
43#88071—24no—
44#88071—24no—
45#88071—21no—
46#88071—22no—
47#88071C2×C412yes—
48#88056—48no—
49#9014—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4112yes—
65C22×Dic13—24no—
66C22×Dic13—24no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—24no—
70C22×Dic13—42no—
71C22×Dic13—42no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13—42no—
75C2×Dic26—28no—
76C2×Dic26—24no—
77C2×Dic26—44no—
78C2×Dic26—48no—
79C2×Dic26—44no—
80C2×Dic26—44no—
81C2×Dic26—42no—
82C2×C8×C13—44no—
83C2×C8×C13—42no—
84C13×C4⋊C4—24no—
85C13×C4⋊C4—24no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—44no—
89#6101—48no—
90C4×Dic13—82no—
91C2×#395—131no—
92#2313—131no—
93#1787—132no—
94C2×#324D1311yescharacteristic
95#1294—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#12011yescharacteristic
100C23×C13#12311yescharacteristic
101C23×C13#13512yes—
102C23×C13#13712yes—
103C2×C4×C13—24no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—81no—
116C2×C4×C13C4×D412yes—
117C2×C4×C13#12112yes—
118C2×Dic13—24no—
119C2×Dic13—24no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—44no—
123C2×Dic13—48no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—44no—
127C2×Dic13—44no—
128C2×Dic13—44no—
129C2×Dic13—44no—
130Dic26—28no—
131Dic26—48no—
132Dic26—44no—
133C8×C13—82no—
134C23×Q8—131no—
135C22×C4⋊C4—261no—
136C22×C4⋊C4C2×D1311yescharacteristic
137C2×#103—264no—
138C2×C22⋊C8C2×D1312yes—
139#395—134no—
140#395—262no—
141#387—264no—
142#381—261no—
143#380—132no—
144C4×C22⋊C4—261no—
145C2×#95—131no—
146C2×#95—261no—
147#324—22no—
148C22×C13—24no—
149C22×C13—24no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13#38611yescharacteristic
155C22×C13#41611yescharacteristic
156C22×C13#41911yescharacteristic
157C22×C13#45212yes—
158C22×C13#45612yes—
159C22×C13B(4,𝔽2)12yes—
160C22×C13#48512yes—
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—42no—
164C4×C13—42no—
165Dic13—44no—
166Dic13—44no—
167Dic13—84no—
168C22×Q8—132no—
169C22×Q8—261no—
170C22×Q8—262no—
171C22×Q8—262no—
172C22×Q8—524no—
173C23×C4—261no—
174C23×C4—261no—
175C23×C4D5211yescharacteristic
176C23×C4D5211yescharacteristic
177C23×C4C22×D1311yescharacteristic
178C22×C8—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—134no—
182C2×C4⋊C4—264no—
183C2×C4⋊C4—524no—
184C2×C4⋊C4C4×D1312yes—
185C2×C4⋊C4C22⋊D1312yes—
186C2×C22⋊C4—262no—
187C2×C42—262no—
188#103—528no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#95—132no—
192#95—262no—
193#95—264no—
194#95—264no—
195#95—262no—
196#95—261no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—22no—
200C2×C13#160314yes—
201C2×C13#187311yescharacteristic
202C2×C13#188611yescharacteristic
203C2×C13#188911yescharacteristic
204C24C2×D5211yescharacteristic
205C2×Q8—268no—
206C2×Q8—264no—
207C2×Q8—524no—
208C2×Q8—524no—
209C2×Q8—524no—
210C2×Q8—528no—
211C2×Q8—522no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—264no—
221C22×C4—264no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—264no—
225C22×C4—522no—
226C22×C4—522no—
227C22×C4—521no—
228C22×C4—521no—
229C22×C4—522no—
230C22×C4#610312yes—
231C22×C4#610312yes—
232C22×C4C2×C4×D1311yescharacteristic
233C22×C4D4×D1312yes—
234C22×C4#612912yes—
235C22×C4C2×C22⋊D1311yescharacteristic
236C2×C8—44no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—524no—
241C4⋊C4—528no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C42—1042no—
245C13#901411yescharacteristic, complemented, Sylow
246C23—22no—
247C23—22no—
248C23#8813611yescharacteristic
249C23#8814011yescharacteristic
250C23#8815812yes—
251C23#8816312yes—
252C23C2×#610311yescharacteristic
253Q8—268no—
254Q8—528no—
255Q8—524no—
256C2×C4—24no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—81no—
269C2×C4—264no—
270C2×C4—264no—
271C2×C4—522no—
272C2×C4—528no—
273C2×C4—522no—
274C2×C4—524no—
275C2×C4—524no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—524no—
279C2×C4—524no—
280C2×C4—524no—
281C2×C4#8813512yes—
282C2×C4#8819312yes—
283C8—82no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—24no—
289C22—24no—
290C22#1171838412yes—
291C22#1171839412yes—
292C22#1171840212yes—
293C22#1171841312yes—
294C22#1171861911yescharacteristic
295C22#1171877411yescharacteristic
296C22#1171878111yescharacteristic
297C4—22no—
298C4—22no—
299C4—42no—
300C4—42no—
301C4—524no—
302C4—524no—
303C4—1044no—
304C2—21no—
305C2—21no—
306C2—22no—
307C2#1311380114yes—
308C2#1311514611yescharacteristic
309C2#1311522711yescharacteristic
310C2#1311524211yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9014
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
18. #11718640C4semidirect
245. C13#9014semidirect

Maximal subgroups

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

subgroupindex
C2×#117186402
#131174392
#131147722
#131127162
C2×C13×#3242
#901413