Finite Group Databasebeta

← #15759568

Subgroups — #15759568

Order 3328.

410 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125989C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic
3#13115809C211yesmaximal, characteristic
4#13113516C211yesmaximal, characteristic
5#13113401C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic
7C13×#1275C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C2×C13×#97C2211yescharacteristic
13#11718763—21no—
14#11718762—21no—
15#11718597C2211yescharacteristic
16#11718585C2211yescharacteristic
17#11718511—22no—
18#11718383—22no—
19#11718362—22no—
20#11718362—22no—
21#11718343C412yescomplemented
22#11718342C412yescomplemented
23#11718143—21no—
24#11718143—21no—
25#11718073—22no—
26#11718059—22no—
27C22×Dic26—21no—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13D411yescharacteristic
30C2×C42×C13C2311yescharacteristic
31#88180—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35#88178—21no—
36#88178D412yes—
37C2×#6099—21no—
38#88124—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123C2×C412yes—
43#88123C2×C411yescharacteristic
44#88123C2×C411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26D412yes—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C22⋊C8—21no—
50C13×C22⋊C8—21no—
51C13×#97—21no—
52C13×#97—21no—
53C4×C8×C13—21no—
54C4×C8×C13C2×C412yes—
55#88071—21no—
56#88071—21no—
57#88058—24no—
58#88056—24no—
59#88055—22no—
60#88054—24no—
61C8×Dic13—22no—
62C4⋊#1055—21no—
63C4⋊#1055D412yes—
64#9288—131nomaximal, Sylow
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—41no—
69C22×Dic13—41no—
70C2×Dic26—21no—
71C2×Dic26—22no—
72C2×Dic26—41no—
73C2×Dic26—82no—
74C2×Dic26C22⋊C412yes—
75C2×C8×C13—21no—
76C2×C8×C13—21no—
77C2×C8×C13—22no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C2×C8×C13—41no—
82C2×C8×C13Q1612yes—
83C42×C13C22×C411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13#4111yescharacteristic
87C22⋊Dic13—22no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—22no—
92C4⋊Dic13—22no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13C22⋊C412yes—
98#6101—22no—
99#6101—22no—
100C4×Dic13—22no—
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104#3230—131no—
105#2961—131no—
106#1993—131no—
107#1548—131no—
108#1518—131no—
109#1286—131no—
110#1275D1311yescharacteristic
111C23×C13#12111yescharacteristic
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13C4×D411yescharacteristic
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12311yescharacteristic
120C2×C4×C13C2×Q1611yescharacteristic
121C2×C4×C13#13511yescharacteristic
122C2×C4×C13#13711yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—42no—
127C2×Dic13—82no—
128C2×Dic13—81no—
129C2×Dic13—81no—
130C2×Dic13—81no—
131Dic26—42no—
132Dic26—81no—
133Dic26—82no—
134Dic26—82no—
135C8×C13—22no—
136C8×C13—42no—
137C8×C13—41no—
138C8×C13—81no—
139#1055—42no—
140#533—131no—
141C2×C4⋊Q8—131no—
142#500—132no—
143#487—132no—
144#484—262no—
145#477—262no—
146#446—262no—
147#446—262no—
148#431C2×D1311yescharacteristic
149#431C2×D1311yescharacteristic
150#424—261no—
151#423—131no—
152#405—261no—
153C2×#97C2×D1311yescharacteristic
154#382—131no—
155#340—261no—
156#340—261no—
157#333—262no—
158#328—262no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#38611yescharacteristic
162C22×C13#46211yescharacteristic
163C22×C13#46411yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13C4×Q1611yescharacteristic
169C4×C13#44111yescharacteristic
170C4×C13#45111yescharacteristic
171C4×C13#45211yescharacteristic
172Dic13—42no—
173Dic13—42no—
174Dic13—82no—
175Dic13—161no—
176C22×Q8—261no—
177C2×M16—261no—
178C22×C8D5211yescharacteristic
179C22×C8D5211yescharacteristic
180C4⋊Q8—131no—
181C4⋊Q8—131no—
182C4⋊Q8—132no—
183C4⋊Q8—261no—
184C4⋊Q8—261no—
185C4⋊Q8—261no—
186#125—261no—
187C22⋊Q8—132no—
188C22⋊Q8—261no—
189C4×Q8—132no—
190C4×Q8—261no—
191#117—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C42C22×D1311yescharacteristic
196#107—264no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—132no—
200C4⋊C8—264no—
201C4⋊C8—261no—
202#103—264no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#97—21no—
206#97—21no—
207#97—262no—
208C4×C8—21no—
209C4×C8—262no—
210C4×C8C4×D1312yes—
211#95—261no—
212#95—261no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13#187811yescharacteristic
216C2×C13#190311yescharacteristic
217C2×C13#190911yescharacteristic
218C2×Q8—132no—
219C2×Q8—261no—
220C2×Q8—262no—
221C2×Q8—521no—
222C2×Q8—1042no—
223C22×C4—521no—
224C22×C4—521no—
225C22×C4C2×D5211yescharacteristic
226C22×C4D4×D1311yescharacteristic
227C22×C4#613111yescharacteristic
228M16—521no—
229M16—521no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—262no—
238C2×C8Dic5212yes—
239C4⋊C4—132no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—262no—
243C4⋊C4—261no—
244C4⋊C4—262no—
245C4⋊C4—262no—
246C4⋊C4—262no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C22⋊C4—262no—
252C42—262no—
253C42C2×C4×D1311yescharacteristic
254C42#612711yescharacteristic
255C42D4×D1311yescharacteristic
256C42D4×D1311yescharacteristic
257C13#928811yescharacteristic, complemented, Sylow
258C23#8814911yescharacteristic
259Q8—522no—
260Q8—1041no—
261Q8—1042no—
262Q8—1042no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—522no—
268C2×C4—1042no—
269C2×C4—1041no—
270C2×C4—1041no—
271C2×C4—1041no—
272C2×C4C4×D5211yescharacteristic
273C2×C4C22⋊C4×D1311yescharacteristic
274C2×C4#8813611yescharacteristic
275C2×C4#8813811yescharacteristic
276C2×C4#8814711yescharacteristic
277C2×C4#8814811yescharacteristic
278C2×C4#8815811yescharacteristic
279C2×C4C2×Dic5211yescharacteristic
280C2×C4#8816311yescharacteristic
281C2×C4#8816311yescharacteristic
282C8—22no—
283C8—42no—
284C8—41no—
285C8—81no—
286C8—522no—
287C22—21no—
288C22—21no—
289C22#1171832611yescharacteristic
290C22#1171850611yescharacteristic
291C22#1171851011yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—522no—
297C4—522no—
298C4—1042no—
299C4—2081no—
300C4C4×Dic5211yescharacteristic
301C4#1171837711yescharacteristic
302C4#1171839411yescharacteristic
303C4#1171840011yescharacteristic
304C2—21no—
305C2—21no—
306C2#1311517611yescharacteristic
307C2#1311531711yescharacteristic
308C2#1311535711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1275C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1275D13
hypocenterC13#9288
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
21. #11718343C4semidirect
22. #11718342C4semidirect
257. C13#9288semidirect

Maximal subgroups

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

subgroupindex
#131259892
#131237762
#131158092
#131135162
#131134012
#131126952
C13×#12752
#928813