Finite Group Databasebeta

← #15759596

Subgroups — #15759596

Order 3328.

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

normal subgroups only

This group has 426 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#13125982C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic
3#13115656C211yesmaximal, characteristic
4#13113507C211yesmaximal, characteristic
5#13113401C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic
7C13×#1275C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C2×C13×#97C2211yescharacteristic
13C2×#88056—21no—
14C2×#88056—21no—
15#11718763—21no—
16#11718762—21no—
17#11718597C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718512—22no—
20#11718382—22no—
21#11718362—22no—
22#11718362—22no—
23#11718342C412yescomplemented
24#11718341C412yescomplemented
25#11718078—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#88057—24no—
58#88056—24no—
59#88056—42no—
60#88056—42no—
61#88055—22no—
62#88054—24no—
63C8×Dic13—22no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66#9292—131nomaximal, Sylow
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×Dic13—41no—
71C22×Dic13—41no—
72C2×Dic26—22no—
73C2×Dic26—21no—
74C2×Dic26—41no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26C22⋊C412yes—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—22no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—41no—
87C2×C8×C13SD1612yes—
88C42×C13C22×C411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92C22⋊Dic13—22no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13C22⋊C412yes—
103#6101—22no—
104#6101—22no—
105C4×Dic13—22no—
106#6099—41no—
107#6099—41no—
108C2×#1055—22no—
109#3229—131no—
110#2961—131no—
111#1960—131no—
112#1546—131no—
113#1518—131no—
114#1286—131no—
115#1275D1311yescharacteristic
116C23×C13#12111yescharacteristic
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13C2×C22⋊C411yescharacteristic
120C2×C4×C13C4×D411yescharacteristic
121C2×C4×C13C4×D411yescharacteristic
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13C2×SD1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—42no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137Dic26—42no—
138Dic26—42no—
139Dic26—42no—
140Dic26—81no—
141Dic26—81no—
142Dic26—81no—
143C8×C13—22no—
144C8×C13—42no—
145C8×C13—41no—
146C8×C13—81no—
147#1055—42no—
148#533—131no—
149C2×C4⋊Q8—131no—
150#498—132no—
151#487—132no—
152#483—262no—
153#475—262no—
154#446—262no—
155#446—262no—
156#431C2×D1311yescharacteristic
157#431C2×D1311yescharacteristic
158#424—261no—
159#423—131no—
160C2×#103—261no—
161C2×#103—261no—
162#405—261no—
163C2×#97C2×D1311yescharacteristic
164#382—131no—
165#332—262no—
166#328—262no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C22×C13#46011yescharacteristic
171C22×C13#46411yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13C4×SD1611yescharacteristic
177C4×C13#44011yescharacteristic
178C4×C13#44811yescharacteristic
179C4×C13#44911yescharacteristic
180Dic13—42no—
181Dic13—42no—
182Dic13—82no—
183Dic13—161no—
184C22×Q8—261no—
185C2×M16—261no—
186C22×C8D5211yescharacteristic
187C22×C8D5211yescharacteristic
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190C4⋊Q8—132no—
191C4⋊Q8—261no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194#125—261no—
195C22⋊Q8—132no—
196C22⋊Q8—261no—
197C4×Q8—132no—
198C4×Q8—261no—
199#117—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C42C22×D1311yescharacteristic
204#106—264no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—132no—
208C4⋊C8—264no—
209C4⋊C8—261no—
210#103—264no—
211#103—522no—
212#103—522no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215#97—21no—
216#97—21no—
217#97—262no—
218C4×C8—21no—
219C4×C8—262no—
220C4×C8C4×D1312yes—
221#95—261no—
222#95—261no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13#188011yescharacteristic
226C2×C13#190211yescharacteristic
227C2×C13#190911yescharacteristic
228C2×Q8—132no—
229C2×Q8—261no—
230C2×Q8—262no—
231C2×Q8—521no—
232C2×Q8—521no—
233C2×Q8—521no—
234C2×Q8—521no—
235C2×Q8—521no—
236C22×C4—521no—
237C22×C4—521no—
238C22×C4C2×D5211yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4#613111yescharacteristic
241M16—521no—
242M16—521no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—22no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—41no—
250C2×C8—262no—
251C2×C8#609512yes—
252C4⋊C4—132no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—262no—
256C4⋊C4—261no—
257C4⋊C4—262no—
258C4⋊C4—262no—
259C4⋊C4—262no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C22⋊C4—262no—
265C42—262no—
266C42C2×C4×D1311yescharacteristic
267C42#612711yescharacteristic
268C42D4×D1311yescharacteristic
269C42D4×D1311yescharacteristic
270C13#929211yescharacteristic, complemented, Sylow
271C23#8814911yescharacteristic
272Q8—522no—
273Q8—522no—
274Q8—522no—
275Q8—1041no—
276Q8—1041no—
277Q8—1041no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—522no—
283C2×C4—1041no—
284C2×C4—1041no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4—1041no—
288C2×C4C4×D5211yescharacteristic
289C2×C4C22⋊C4×D1311yescharacteristic
290C2×C4#8813611yescharacteristic
291C2×C4#8813811yescharacteristic
292C2×C4#8814711yescharacteristic
293C2×C4#8814811yescharacteristic
294C2×C4C2×#609511yescharacteristic
295C2×C4#8815811yescharacteristic
296C2×C4#8816211yescharacteristic
297C2×C4#8816311yescharacteristic
298C8—22no—
299C8—42no—
300C8—41no—
301C8—81no—
302C8—522no—
303C22—21no—
304C22—21no—
305C22#1171832611yescharacteristic
306C22#1171850611yescharacteristic
307C22#1171850911yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—522no—
313C4—522no—
314C4—1042no—
315C4—2081no—
316C4C4×#609511yescharacteristic
317C4#1171837111yescharacteristic
318C4#1171839511yescharacteristic
319C4#1171839911yescharacteristic
320C2—21no—
321C2—21no—
322C2#1311519011yescharacteristic
323C2#1311531011yescharacteristic
324C2#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#9292
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
23. #11718342C4semidirect
24. #11718341C4semidirect
270. C13#9292semidirect

Maximal subgroups

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

subgroupindex
#131259822
#131237762
#131156562
#131135072
#131134012
#131126952
C13×#12752
#929213