Finite Group Databasebeta

← #15773871

Subgroups — #15773871

Order 3328.

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

normal subgroups only

This group has 314 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#13125417C211yesmaximal, characteristic
2#13116636C211yesmaximal, characteristic
3#13114965C211yesmaximal, characteristic
4#13112849C211yesmaximal, characteristic
5#13112848C211yesmaximal, characteristic
6#13112847C211yesmaximal, characteristic
7C13×#1348C211yesmaximal, characteristic
8#11719327—21no—
9C13×#467C2211yescharacteristic
10Q16×Dic13C411yescharacteristic, complemented
11#11718842C411yescharacteristic, complemented
12#11718777C2211yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718712—21no—
15#11718638—21no—
16#11718535C411yescharacteristic, complemented
17#11718534C411yescharacteristic, complemented
18#11718453—21no—
19#11718451—21no—
20C13×C22⋊C16C2211yescharacteristic
21C13×#340C2211yescharacteristic
22#11718143C2211yescharacteristic
23C22⋊#6090C2211yescharacteristic
24#11718121—21no—
25#11718094—21no—
26#11718093—21no—
27C2×C13×Q16C2×C411yescharacteristic
28C22×C8×C13C2311yescharacteristic
29C13×C22⋊Q8—21no—
30C2×C13×C4⋊C4—21no—
31Q8×Dic13—21no—
32#88198—21no—
33C2×#6107—21no—
34C2×C4⋊Dic13—21no—
35#88178—21no—
36C2×C4×Dic13D411yescharacteristic
37C22×#1055D411yescharacteristic
38C2×Dic52C2×C411yescharacteristic
39#88143—41no—
40#88142—21no—
41#88141—21no—
42#88141—41no—
43#88132—41no—
44#88131—41no—
45C2×C13×C16—21no—
46C13×#107C2×C411yescharacteristic
47C13×#103—21no—
48#88075—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#88047—21no—
60#11859—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—41no—
65C22×Dic13D811yescharacteristic
66C22×Dic13D811yescharacteristic
67C2×Dic26—21no—
68C2×Dic26—41no—
69C13×Q16—41no—
70C2×C8×C13—41no—
71C2×C8×C13C22×C411yescharacteristic
72C2×C8×C13C2×D411yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C22⋊Dic13—41no—
79#6107—42no—
80C4⋊Dic13—21no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—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#3170—131no—
102#2163—131no—
103#1835—131no—
104#1348—131no—
105#1348—131no—
106#1348—131no—
107#1348D1311yescharacteristic
108C23×C13C2×D811yescharacteristic
109Q8×C13—41no—
110Q8×C13—41no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13C2×SD1611yescharacteristic
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—81no—
126C2×Dic13—81no—
127C2×Dic13—81no—
128C2×Dic13#10211yescharacteristic
129C2×Dic13#10211yescharacteristic
130C2×Dic13#10211yescharacteristic
131C2×Dic13#10211yescharacteristic
132Dic26—41no—
133Dic26—41no—
134Dic26—82no—
135C8×C13—21no—
136C8×C13—21no—
137#1055—21no—
138#1055—21no—
139#533—261no—
140#500—131no—
141#494—131no—
142#487—261no—
143#467—131no—
144#467—261no—
145#467C2×D1311yescharacteristic
146C4×Q16—131no—
147C4×Q16—131no—
148C4×Q16—261no—
149C2×C4×C8—131no—
150#382—261no—
151C4⋊C16—261no—
152C22⋊C16—131no—
153C22⋊C16C2×D1311yescharacteristic
154#346—261no—
155#340—131no—
156#340—261no—
157#340C2×D1311yescharacteristic
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C2×#10211yescharacteristic
161C22×C13#51011yescharacteristic
162C22×C13#51011yescharacteristic
163C4×C13—21no—
164C4×C13—81no—
165C4×C13—81no—
166C4×C13—161no—
167C4×C13#41011yescharacteristic
168C4×C13#42111yescharacteristic
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—81no—
174Dic13—81no—
175Dic13—161no—
176C2×Q16—131no—
177C2×Q16—261no—
178C2×Q16C4×D1311yescharacteristic
179C22×C8—131no—
180C22×C8C22×D1311yescharacteristic
181C4⋊Q8—261no—
182C4⋊Q8—261no—
183#125—521no—
184C22⋊Q8—21no—
185C22⋊Q8—261no—
186C22⋊Q8—521no—
187C4×Q8—261no—
188C4×Q8—261no—
189C4×Q8—521no—
190#117—521no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—261no—
193C2×C42—131no—
194C2×C16—21no—
195C2×C16—261no—
196#107—131no—
197#107—261no—
198#107C4×D1311yescharacteristic
199#103—21no—
200#103—261no—
201#103—261no—
202#103—261no—
203C4×C8—131no—
204C4×C8—131no—
205C4×C8—131no—
206C4×C8—131no—
207#95—521no—
208#95—521no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13#151711yescharacteristic
212C2×C13#214111yescharacteristic
213C2×C13#214511yescharacteristic
214C2×Q8—21no—
215C2×Q8—261no—
216C2×Q8—521no—
217C22×C4—41no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—521no—
221C22×C4D4×D1311yescharacteristic
222Q16—41no—
223Q16—521no—
224Q16—522no—
225C2×C8—41no—
226C2×C8—131no—
227C2×C8—131no—
228C2×C8—521no—
229C2×C8C2×C4×D1311yescharacteristic
230C2×C8D4×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—261no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C22⋊C4—41no—
245C22⋊C4—521no—
246C42—131no—
247C42—131no—
248C42—131no—
249C42—131no—
250C42—521no—
251C42—521no—
252C16—41no—
253C16—521no—
254C13#1185911yescharacteristic, complemented, Sylow
255C23D8×D1311yescharacteristic
256Q8—41no—
257Q8—41no—
258Q8—521no—
259Q8—521no—
260Q8—1042no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—1041no—
278C2×C4—1041no—
279C2×C4—1041no—
280C2×C4C22⋊C4×D1311yescharacteristic
281C2×C4SD16×D1311yescharacteristic
282C8—21no—
283C8—21no—
284C8—261no—
285C8—261no—
286C22—21no—
287C22—21no—
288C22D13×#10211yescharacteristic
289C22#1171857611yescharacteristic
290C22#1171857911yescharacteristic
291C4—21no—
292C4—81no—
293C4—81no—
294C4—161no—
295C4—261no—
296C4—261no—
297C4—261no—
298C4—261no—
299C4—1041no—
300C4—1041no—
301C4—2081no—
302C4#1171840111yescharacteristic
303C4#1171848211yescharacteristic
304C2—21no—
305C2—21no—
306C2#1311339411yescharacteristic
307C2#1311655411yescharacteristic
308C2#1311657011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1348C2
socleC22×C13C2×#102
prime radicalC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenter#1348D13
hypocenterC13#11859
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
10. Q16×Dic13C4semidirect
11. #11718842C4semidirect
16. #11718535C4semidirect
17. #11718534C4semidirect
254. C13#11859semidirect

Maximal subgroups

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

subgroupindex
#131254172
#131166362
#131149652
#131128492
#131128482
#131128472
C13×#13482
#1185913