Finite Group Databasebeta

← #15773854

Subgroups — #15773854

Order 3328.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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#13125401C211yesmaximal, characteristic
2#13116632C211yesmaximal, characteristic, complemented
3#13114965C211yesmaximal, characteristic, complemented
4#13112849C211yesmaximal, characteristic, complemented
5#13112847C211yesmaximal, characteristic, complemented
6#13112845C211yesmaximal, characteristic
7C13×#1347C211yesmaximal, characteristic
8#11719305—21no—
9C13×#466C2211yescharacteristic
10#11718816C411yescharacteristic, complemented
11D8×Dic13C411yescharacteristic, complemented
12#11718777C2211yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718702—21no—
15#11718638—21no—
16#11718539C411yescharacteristic, complemented
17#11718534C411yescharacteristic, complemented
18#11718429—21no—
19#11718419—21no—
20C13×C22⋊C16C2211yescharacteristic
21C13×#340C2211yescharacteristic
22#11718143C2211yescharacteristic
23C22⋊#6090C2211yescharacteristic
24#11718121—21no—
25#11718093—21no—
26C16×Dic13—21no—
27C2×C13×D8C2×C411yescharacteristic
28C22×C8×C13C2311yescharacteristic
29C13×#121—21no—
30C2×C13×C4⋊C4—21no—
31#88190—21no—
32#88189—41no—
33D4×Dic13—21no—
34D4×Dic13—41no—
35C2×#6105—21no—
36C2×C4⋊Dic13—21no—
37#88178—21no—
38C2×C4×Dic13D411yescharacteristic
39C22×#1055D411yescharacteristic
40C2×Dic52C2×C411yescharacteristic
41#88144—21no—
42#88141—21no—
43#88133—41no—
44#88131—41no—
45C2×C13×C16—21no—
46C13×#107C2×C411yescharacteristic
47C13×#102—21no—
48#88072—21no—
49#88071—41no—
50#88071—41no—
51#88058C2×C411yescharacteristic
52#88056—21no—
53C8×Dic13C2×C411yescharacteristic
54C8×Dic13C2×C411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C2×#6090—21no—
58#88050—21no—
59#88048—21no—
60#11855—131nomaximal, Sylow
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—41no—
66C22×Dic13—41no—
67C22×Dic13D811yescharacteristic
68C22×Dic13D811yescharacteristic
69C2×Dic26—21no—
70C13×D8—41no—
71C2×C8×C13—41no—
72C2×C8×C13C22×C411yescharacteristic
73C2×C8×C13C2×D411yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C22⋊Dic13—41no—
82#6105—42no—
83C4⋊Dic13—21no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90C4×Dic13—41no—
91C4×Dic13C22⋊C411yescharacteristic
92C4×Dic13C22⋊C411yescharacteristic
93C4×Dic13SD1611yescharacteristic
94C4×Dic13SD1611yescharacteristic
95C2×#1055—41no—
96C2×#1055C22⋊C411yescharacteristic
97C2×#1055C22⋊C411yescharacteristic
98Dic52—41no—
99C13×C16—41no—
100#6090—41no—
101#3168—131no—
102#2162—131no—
103#1835—131no—
104#1348—131no—
105#1348—131no—
106#1347—131no—
107#1347D1311yescharacteristic
108C23×C13—41no—
109C23×C13C2×D811yescharacteristic
110D4×C13—41no—
111D4×C13—41no—
112D4×C13—81no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13C2×C22⋊C411yescharacteristic
121C2×C4×C13C2×SD1611yescharacteristic
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—82no—
128C2×Dic13—81no—
129C2×Dic13—81no—
130C2×Dic13—81no—
131C2×Dic13#10211yescharacteristic
132C2×Dic13#10211yescharacteristic
133C2×Dic13#10211yescharacteristic
134C2×Dic13#10211yescharacteristic
135Dic26—41no—
136Dic26—41no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055—21no—
141#529—261no—
142#499—131no—
143#495—131no—
144#488—261no—
145#467—131no—
146#466C2×D1311yescharacteristic
147#465—261no—
148C4×Q16—131no—
149C4×SD16—261no—
150C4×D8—131no—
151C2×C4×C8—131no—
152#382—261no—
153C4⋊C16—261no—
154C22⋊C16—131no—
155C22⋊C16C2×D1311yescharacteristic
156C4×C16—261no—
157#340—131no—
158#340—261no—
159#340C2×D1311yescharacteristic
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13C2×#10211yescharacteristic
166C22×C13#50811yescharacteristic
167C22×C13#50811yescharacteristic
168C4×C13—21no—
169C4×C13—81no—
170C4×C13—161no—
171C4×C13#41011yescharacteristic
172C4×C13#42111yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—81no—
178Dic13—81no—
179Dic13—161no—
180C2×Q16—131no—
181C2×SD16—261no—
182C2×D8C4×D1311yescharacteristic
183C22×C8—131no—
184C22×C8C22×D1311yescharacteristic
185#126—521no—
186#125—261no—
187#124—261no—
188#123—521no—
189C22⋊Q8—261no—
190#121—21no—
191C4×Q8—261no—
192C4×D4—261no—
193C4×D4—521no—
194#117—521no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—261no—
197C2×C42—131no—
198C2×C16—21no—
199C2×C16—261no—
200#107—131no—
201#107C4×D1311yescharacteristic
202#106—261no—
203#103—261no—
204#103—261no—
205#102—21no—
206#102—261no—
207C4×C8—131no—
208C4×C8—131no—
209C4×C8—131no—
210C4×C8—131no—
211#95—521no—
212#95—521no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—161no—
216C2×C13#151711yescharacteristic
217C2×C13#213811yescharacteristic
218C2×C13#214511yescharacteristic
219C2×Q8—261no—
220C2×D4—21no—
221C2×D4—41no—
222C22×C4—41no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4D4×D1311yescharacteristic
228Q16—521no—
229SD16—522no—
230D8—41no—
231C2×C8—41no—
232C2×C8—131no—
233C2×C8—131no—
234C2×C8—521no—
235C2×C8C2×C4×D1311yescharacteristic
236C2×C8D4×D1311yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—261no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C22⋊C4—41no—
248C22⋊C4—521no—
249C22⋊C4—521no—
250C22⋊C4—521no—
251C22⋊C4—521no—
252C42—131no—
253C42—131no—
254C42—131no—
255C42—131no—
256C42—521no—
257C16—41no—
258C16—521no—
259C13#1185511yescharacteristic, complemented, Sylow
260C23—41no—
261C23D8×D1311yescharacteristic
262Q8—521no—
263Q8—521no—
264D4—41no—
265D4—41no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—1042no—
284C2×C4—1041no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4C22⋊C4×D1311yescharacteristic
288C2×C4SD16×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—261no—
292C8—261no—
293C22—21no—
294C22—21no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22D13×#10211yescharacteristic
299C22#1171857311yescharacteristic
300C22#1171857711yescharacteristic
301C4—21no—
302C4—81no—
303C4—161no—
304C4—261no—
305C4—261no—
306C4—261no—
307C4—261no—
308C4—1041no—
309C4—1041no—
310C4—2081no—
311C4#1171840111yescharacteristic
312C4#1171848211yescharacteristic
313C2—21no—
314C2—21no—
315C2—161no—
316C2#1311339411yescharacteristic
317C2#1311654011yescharacteristic
318C2#1311657011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1347C2
socleC22×C13C2×#102
prime radicalC13×#466C22
cosocleC22×C8×C13C23
hypercenter#1347D13
hypocenterC13#11855
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13114965C2semidirect
4. #13112849C2semidirect
5. #13112847C2semidirect
10. #11718816C4semidirect
11. D8×Dic13C4semidirect
16. #11718539C4semidirect
17. #11718534C4semidirect
259. C13#11855semidirect

Maximal subgroups

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

subgroupindex
#131254012
#131166322
#131149652
#131128492
#131128472
#131128452
C13×#13472
#1185513