Finite Group Databasebeta

← #15759582

Subgroups — #15759582

Order 3328.

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

normal subgroups only

This group has 422 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#13125786C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic
3#13115809C211yesmaximal, characteristic
4#13113520C211yesmaximal, 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#11718510—22no—
18#11718400—22no—
19#11718362—22no—
20#11718362—22no—
21#11718360C412yescomplemented
22#11718342C412yescomplemented
23#11718143—21no—
24#11718143—21no—
25#11718074—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—
38C2×Dic52—24no—
39#88124—21no—
40#88123—21no—
41#88123—21no—
42#88123—21no—
43#88123C2×C412yes—
44#88123C2×C411yescharacteristic
45#88123C2×C411yescharacteristic
46C4×Dic26—21no—
47C4×Dic26D412yes—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C22⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×#97—21no—
53C13×#97—21no—
54C4×C8×C13—21no—
55C4×C8×C13C2×C412yes—
56#88071—21no—
57#88071—21no—
58#88056—24no—
59#88055—22no—
60#88054—24no—
61C8×Dic13—22no—
62C4⋊#1055—21no—
63C4⋊#1055D412yes—
64#9290—131nomaximal, Sylow
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—41no—
69C22×Dic13—41no—
70C2×Dic26—22no—
71C2×Dic26—21no—
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×C13Q1612yescomplemented
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—
104Dic52—84no—
105#3209—131no—
106#2961—131no—
107#1993—131no—
108#1549—131no—
109#1518—131no—
110#1286—131no—
111#1275D1311yescharacteristic
112C23×C13#12111yescharacteristic
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13C4×D411yescharacteristic
117C2×C4×C13C4×D411yescharacteristic
118C2×C4×C13#12011yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13C2×Q1611yescharacteristic
122C2×C4×C13#13511yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—42no—
128C2×Dic13—82no—
129C2×Dic13—81no—
130C2×Dic13—81no—
131C2×Dic13—81no—
132Dic26—42no—
133Dic26—44no—
134Dic26—81no—
135Dic26—82no—
136C8×C13—22no—
137C8×C13—42no—
138C8×C13—41no—
139C8×C13—81no—
140#1055—42no—
141#533—131no—
142C2×C4⋊Q8—131no—
143#494—132no—
144#487—132no—
145#462—262no—
146#451—262no—
147#446—262no—
148#446—262no—
149#431C2×D1311yescharacteristic
150#431C2×D1311yescharacteristic
151#424—261no—
152#423—131no—
153#405—261no—
154C2×#97C2×D1311yescharacteristic
155#382—131no—
156#340—261no—
157#340—261no—
158#332—262no—
159#328—262no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13#38611yescharacteristic
163C22×C13#46211yescharacteristic
164C22×C13#46411yescharacteristic
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13C4×Q1611yescharacteristic
170C4×C13#44111yescharacteristic
171C4×C13#45111yescharacteristic
172C4×C13#45211yescharacteristic
173Dic13—42no—
174Dic13—42no—
175Dic13—82no—
176Dic13—161no—
177C22×Q8—261no—
178C2×Q16—264no—
179C2×M16—261no—
180C22×C8D5211yescharacteristic
181C22×C8D5211yescharacteristic
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8—132no—
185C4⋊Q8—261no—
186C4⋊Q8—261no—
187C4⋊Q8—261no—
188#125—261no—
189C22⋊Q8—132no—
190C22⋊Q8—261no—
191C4×Q8—132no—
192C4×Q8—261no—
193#117—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C42C22×D1311yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—132no—
201C4⋊C8—264no—
202C4⋊C8—261no—
203#103—264no—
204C22⋊C8—21no—
205C22⋊C8—21no—
206#97—21no—
207#97—21no—
208#97—262no—
209C4×C8—21no—
210C4×C8—262no—
211C4×C8C4×D1312yes—
212#95—261no—
213#95—261no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#187811yescharacteristic
217C2×C13#190211yescharacteristic
218C2×C13#191011yescharacteristic
219C2×Q8—132no—
220C2×Q8—261no—
221C2×Q8—262no—
222C2×Q8—521no—
223C2×Q8—1042no—
224C22×C4—521no—
225C22×C4—521no—
226C22×C4C2×D5211yescharacteristic
227C22×C4D4×D1311yescharacteristic
228C22×C4#613111yescharacteristic
229Q16—1044no—
230M16—521no—
231M16—521no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—41no—
239C2×C8—262no—
240C2×C8Dic5212yescomplemented
241C4⋊C4—132no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—262no—
245C4⋊C4—261no—
246C4⋊C4—262no—
247C4⋊C4—262no—
248C4⋊C4—262no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C22⋊C4—262no—
254C42—262no—
255C42C2×C4×D1311yescharacteristic
256C42#612711yescharacteristic
257C42D4×D1311yescharacteristic
258C42D4×D1311yescharacteristic
259C13#929011yescharacteristic, complemented, Sylow
260C23#8814911yescharacteristic
261Q8—522no—
262Q8—524no—
263Q8—1041no—
264Q8—1042no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—522no—
270C2×C4—1042no—
271C2×C4—1041no—
272C2×C4—1041no—
273C2×C4—1041no—
274C2×C4C4×D5211yescharacteristic
275C2×C4C22⋊C4×D1311yescharacteristic
276C2×C4#8813611yescharacteristic
277C2×C4#8813811yescharacteristic
278C2×C4#8814711yescharacteristic
279C2×C4#8814811yescharacteristic
280C2×C4#8815811yescharacteristic
281C2×C4C2×Dic5211yescharacteristic
282C2×C4#8816311yescharacteristic
283C2×C4#8816311yescharacteristic
284C8—22no—
285C8—42no—
286C8—41no—
287C8—81no—
288C8—522no—
289C22—21no—
290C22—21no—
291C22#1171832611yescharacteristic
292C22#1171850611yescharacteristic
293C22#1171851011yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—522no—
299C4—522no—
300C4—1042no—
301C4—2081no—
302C4C4×Dic5211yescharacteristic
303C4#1171837711yescharacteristic
304C4#1171839411yescharacteristic
305C4#1171840011yescharacteristic
306C2—21no—
307C2—21no—
308C2#1311517611yescharacteristic
309C2#1311531011yescharacteristic
310C2#1311536211yescharacteristic
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#9290
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. #11718360C4semidirect
22. #11718342C4semidirect
82. C2×C8×C13Q16semidirect
240. C2×C8Dic52semidirect
259. C13#9290semidirect

Maximal subgroups

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

subgroupindex
#131257862
#131237762
#131158092
#131135202
#131134012
#131126952
C13×#12752
#929013