Finite Group Databasebeta

← #15759513

Subgroups — #15759513

Order 3328.

382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125991C211yesmaximal, characteristic
2#13113349C211yesmaximal, characteristic
3#13113348C211yesmaximal, characteristic
4#13113310C211yesmaximal, characteristic
5#13112699C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#2985C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#446—22no—
11C13×#446—21no—
12C8×Q8×C13—21no—
13C13×#433—22no—
14C13×#432C2211yescharacteristic
15C13×#431C2211yescharacteristic
16#11718742C411yescharacteristic, complemented
17#11718742C411yescharacteristic, complemented
18#11718740C411yescharacteristic, complemented
19#11718739C411yescharacteristic, complemented
20#11718706—22no—
21#11718683—22no—
22#11718593C2211yescharacteristic
23#11718587C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718130—22no—
26#11718059—22no—
27#11718048—21no—
28#11718048—21no—
29C13×C4⋊Q8C2×C411yescharacteristic
30C13×C4⋊Q8C2×C411yescharacteristic
31C13×#125—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8D412yes—
34C4×Q8×C13—21no—
35C4×Q8×C13D412yes—
36C13×#117—21no—
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178—21no—
41C2×C4×Dic13—21no—
42#88124—21no—
43#88123C2×C411yescharacteristic
44#88123C2×C411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—22no—
48C13×C4⋊C8—22no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C13×C22⋊C8D412yes—
53C13×#97—22no—
54C13×#97—21no—
55C4×C8×C13—22no—
56C4×C8×C13D411yescharacteristic
57C4×C8×C13D411yescharacteristic
58#88075—22no—
59#88075—22no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64#88048—22no—
65#88047—22no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#88043—21no—
69C4×#1055C2×C411yescharacteristic
70C4×#1055C2×C411yescharacteristic
71#9280—131nomaximal, Sylow
72C2×Q8×C13—21no—
73C2×Q8×C13C22⋊C412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—41no—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×C8×C13—21no—
81C2×C8×C13—22no—
82C2×C8×C13—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4C22⋊C412yes—
89C13×C22⋊C4—22no—
90C42×C13—22no—
91C42×C13C22×C411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13#4111yescharacteristic
95C22⋊Dic13—41no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100#6101—41no—
101#6101—41no—
102C4×Dic13—22no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—41no—
108#3231—131no—
109#2985D1311yescharacteristic
110#1506—131no—
111#1506—131no—
112#1497—131no—
113#1287—131no—
114#1274—131no—
115C23×C13#12111yescharacteristic
116Q8×C13—42no—
117Q8×C13—41no—
118Q8×C13—41no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13C2×C22⋊C411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×Dic13—42no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136Dic26—41no—
137Dic26—41no—
138Dic26—81no—
139C8×C13—41no—
140C8×C13—42no—
141C8×C13—41no—
142#1055—41no—
143#1055—41no—
144#1055—81no—
145#533—131no—
146#533C2×D1311yescharacteristic
147#500—131no—
148#498—131no—
149#487—131no—
150#487—131no—
151#485—262no—
152#479—262no—
153#446—22no—
154#446—21no—
155C8×Q8—21no—
156#433—22no—
157#432—131no—
158#432C2×D1311yescharacteristic
159#431—131no—
160#431C2×D1311yescharacteristic
161#376—131no—
162#328—262no—
163#328—262no—
164Q8⋊C8—261no—
165Q8⋊C8—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—42no—
176C4×C13—42no—
177C4×C13#44311yescharacteristic
178C4×C13#44411yescharacteristic
179Dic13—82no—
180Dic13—81no—
181Dic13—81no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8C4×D1311yescharacteristic
185C4⋊Q8C4×D1311yescharacteristic
186#125—21no—
187#125—261no—
188C22⋊Q8—21no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191C22⋊Q8D5212yes—
192C4×Q8—21no—
193C4×Q8—261no—
194C4×Q8—261no—
195C4×Q8C22⋊D1312yes—
196#117—21no—
197#117—261no—
198C2×C42—261no—
199C2×C42C22×D1311yescharacteristic
200#107—262no—
201#106—262no—
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208#103—262no—
209#103—262no—
210C22⋊C8—21no—
211C22⋊C8—261no—
212C22⋊C8—261no—
213C22⋊C8C22⋊D1312yes—
214#97—22no—
215#97—21no—
216#97—261no—
217C4×C8—22no—
218C4×C8—131no—
219C4×C8—131no—
220C4×C8C22⋊D1311yescharacteristic
221C4×C8C22⋊D1311yescharacteristic
222#95—261no—
223#95—261no—
224C2×C13—41no—
225C2×C13#187611yescharacteristic
226C2×C13#190511yescharacteristic
227C2×C13#190911yescharacteristic
228C2×Q8—21no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8#610312yes—
232C22×C4—521no—
233C22×C4C2×D5211yescharacteristic
234C22×C4#612711yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236C2×C8—21no—
237C2×C8—22no—
238C2×C8—21no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—521no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4#610312yes—
254C22⋊C4—22no—
255C22⋊C4—521no—
256C42—22no—
257C42—262no—
258C42—521no—
259C42—521no—
260C42C2×C4×D1311yescharacteristic
261C42#612711yescharacteristic
262C42C2×C22⋊D1311yescharacteristic
263C42C2×C22⋊D1311yescharacteristic
264C13#928011yescharacteristic, complemented, Sylow
265C23#8818411yescharacteristic
266Q8—42no—
267Q8—41no—
268Q8—41no—
269Q8—521no—
270Q8—521no—
271Q8—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—522no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—1041no—
282C2×C4—1041no—
283C2×C4C2×#610311yescharacteristic
284C2×C4C4×C22⋊D1311yescharacteristic
285C2×C4C4×C22⋊D1311yescharacteristic
286C2×C4#8818311yescharacteristic
287C2×C4#8818411yescharacteristic
288C2×C4#8820711yescharacteristic
289C8—41no—
290C8—42no—
291C8—41no—
292C8—521no—
293C8—521no—
294C8—1041no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22#1171887411yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—42no—
306C4—1042no—
307C4—1041no—
308C4—1041no—
309C4#1171880511yescharacteristic
310C4#1171880611yescharacteristic
311C2—41no—
312C2#1311516311yescharacteristic
313C2#1311533011yescharacteristic
314C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2985C2
socleC22×C13#386
prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#2985D13
hypocenterC13#9280
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2985

Complements

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

NH ≅ G/Ntype
16. #11718742C4semidirect
17. #11718742C4semidirect
18. #11718740C4semidirect
19. #11718739C4semidirect
264. C13#9280semidirect

Maximal subgroups

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

subgroupindex
#131259912
#131133492
#131133482
#131133102
#131126992
#131126642
C13×#29852
#928013