Finite Group Databasebeta

← #15759636

Subgroups — #15759636

Order 3328.

442 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 107 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#13125984C211yesmaximal, characteristic
2#13117582C211yesmaximal, characteristic
3#13115818C211yesmaximal, characteristic
4#13113520C211yesmaximal, characteristic
5#13112694C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1518C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#382C2211yescharacteristic
12#11718742C412yescomplemented
13#11718739C412yescomplemented
14#11718705—22no—
15#11718682—22no—
16C4⋊C4×Dic13—21no—
17#11718634—21no—
18#11718593C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21#11718314—22no—
22#11718307—22no—
23C13×#328—22no—
24#11718124—21no—
25#11718124—21no—
26#11718074—22no—
27C22×Dic26—21no—
28C13×C4⋊Q8C2×C411yescharacteristic
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×#125—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C13×#117—21no—
36C2×C13×C4⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13D412yes—
40C2×#6101—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×#6099—21no—
45#88123—21no—
46#88123—21no—
47#88123C2×C412yes—
48#88123D412yes—
49C13×C4⋊C8—21no—
50C13×C22⋊C8—21no—
51C4×C8×C13—21no—
52C13×#95—21no—
53C13×#95D412yes—
54#88075—24no—
55#88071—22no—
56#88071—22no—
57#88071—21no—
58#88071—21no—
59C22⋊#1055—21no—
60#88047—24no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055C2×C412yes—
65#9298—131nomaximal, Sylow
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—22no—
74C22×Dic13—21no—
75C2×Dic26—22no—
76C2×Dic26—22no—
77C2×Dic26—82no—
78C2×C8×C13—41no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—41no—
89C42×C13C22×C411yescharacteristic
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—22no—
96C4⋊Dic13C22⋊C414yes—
97#6101—82no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—82no—
102C4×Dic13Q1612yes—
103#6099—41no—
104#6099—41no—
105C2×#1055—22no—
106C2×#1055—41no—
107#3230—131no—
108#2331—131no—
109#1995—131no—
110#1549—131no—
111#1518D1311yescharacteristic
112#1286—131no—
113#1274—131no—
114C23×C13#12011yescharacteristic
115Q8×C13—42no—
116Q8×C13—81no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13C2×C22⋊C411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×C4×C13C2×Q1611yescharacteristic
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×Dic13—24no—
135C2×Dic13—22no—
136C2×Dic13—41no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143Dic26—82no—
144Dic26—82no—
145C8×C13—81no—
146#1055—42no—
147#1055—81no—
148#533C2×D1311yescharacteristic
149C2×C4⋊Q8—131no—
150#500—132no—
151#487—132no—
152#484—262no—
153#477—262no—
154#431—131no—
155#431C2×D1311yescharacteristic
156#423—131no—
157#391—262no—
158#389—261no—
159#387—262no—
160#382C2×D1311yescharacteristic
161C4×C4⋊C4—261no—
162#376—131no—
163#339—261no—
164#339—261no—
165#332—262no—
166#328—22no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C22×C13#45111yescharacteristic
171C22×C13#45211yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—82no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13C4×Q1611yescharacteristic
180C4×C13#44111yescharacteristic
181C4×C13#46211yescharacteristic
182C4×C13#46411yescharacteristic
183Dic13—42no—
184Dic13—44no—
185Dic13—81no—
186C22×Q8—261no—
187C2×M16—261no—
188C4⋊Q8—132no—
189C4⋊Q8—132no—
190C4⋊Q8—261no—
191C4⋊Q8—261no—
192C4⋊Q8C4×D1311yescharacteristic
193C4⋊Q8C4×D1311yescharacteristic
194#125—21no—
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199#117—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—132no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—262no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—262no—
207C2×C42C22×D1311yescharacteristic
208#107—264no—
209C4⋊C8—21no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C4⋊C8—261no—
213#103—264no—
214C22⋊C8—21no—
215C22⋊C8—261no—
216C4×C8—21no—
217C4×C8—132no—
218#95—21no—
219#95—262no—
220#95—262no—
221#95—261no—
222#95—261no—
223#95C22⋊D1312yes—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#187811yescharacteristic
227C2×C13#190411yescharacteristic
228C2×C13#191211yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—262no—
232C2×Q8—262no—
233C2×Q8—1042no—
234C22×C4—22no—
235C22×C4—261no—
236C22×C4—262no—
237C22×C4—261no—
238C22×C4D4×D1311yescharacteristic
239C22×C4D4×D1311yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—521no—
242M16—521no—
243C2×C8—41no—
244C2×C8—262no—
245C2×C8—521no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—134no—
255C4⋊C4—262no—
256C4⋊C4—262no—
257C4⋊C4—262no—
258C4⋊C4—1042no—
259C22⋊C4—41no—
260C42—41no—
261C42—132no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42—1042no—
266C42C2×C4×D1311yescharacteristic
267C42#612711yescharacteristic
268C42D4×D1311yescharacteristic
269C42#612911yescharacteristic
270C13#929811yescharacteristic, complemented, Sylow
271C23#8819111yescharacteristic
272Q8—42no—
273Q8—81no—
274Q8—1042no—
275Q8—1042no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—262no—
284C2×C4—264no—
285C2×C4—521no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4C22⋊C4×D1311yescharacteristic
293C2×C4#8813511yescharacteristic
294C2×C4#8813711yescharacteristic
295C2×C4#8813811yescharacteristic
296C2×C4#8816911yescharacteristic
297C2×C4#8817011yescharacteristic
298C2×C4Q16×D1311yescharacteristic
299C2×C4#8817211yescharacteristic
300C2×C4C4×C22⋊D1311yescharacteristic
301C2×C4#8819211yescharacteristic
302C8—81no—
303C8—522no—
304C8—1041no—
305C22—21no—
306C22—21no—
307C22#1171861711yescharacteristic
308C22#1171883411yescharacteristic
309C22#1171884711yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—82no—
315C4—81no—
316C4—81no—
317C4—522no—
318C4—524no—
319C4—1041no—
320C4#1171845011yescharacteristic
321C4#1171845111yescharacteristic
322C4#1171845411yescharacteristic
323C4#1171845911yescharacteristic
324C2—21no—
325C2—21no—
326C2#1311517411yescharacteristic
327C2#1311532611yescharacteristic
328C2#1311537011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1518C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#1518D13
hypocenterC13#9298
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #11718742C4semidirect
13. #11718739C4semidirect
270. C13#9298semidirect

Maximal subgroups

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

subgroupindex
#131259842
#131175822
#131158182
#131135202
#131126942
#131126642
C13×#15182
#929813