Finite Group Databasebeta

← #15773877

Subgroups — #15773877

Order 3328.

336 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 81 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#13125407C211yesmaximal, characteristic
2#13116636C211yesmaximal, characteristic, complemented
3#13114962C211yesmaximal, characteristic, complemented
4#13112848C211yesmaximal, characteristic, complemented
5#13112846C211yesmaximal, characteristic
6#13112844C211yesmaximal, characteristic
7C13×#1348C211yesmaximal, characteristic, complemented
8#11719329—21no—
9C13×#467C2211yescharacteristic
10#11718852C411yescharacteristic, complemented
11Q16×Dic13C411yescharacteristic, complemented
12#11718776C2211yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718709—21no—
15#11718637—21no—
16#11718539C411yescharacteristic, complemented
17#11718533C411yescharacteristic, complemented
18#11718461—21no—
19#11718449—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—
31#88201—21no—
32Q8×Dic13—21no—
33C2×#6106—21no—
34#88184—21no—
35C2×C4⋊Dic13—21no—
36C2×#6101—41no—
37C2×#6101—41no—
38C2×C4×Dic13D411yescharacteristic
39C22×#1055D411yescharacteristic
40C2×D104C2×C411yescharacteristic
41#88152—41no—
42#88147—21no—
43#88146—41no—
44#88144—21no—
45#88140—41no—
46#88135—41no—
47C2×C13×C16—21no—
48C13×#107C2×C411yescharacteristic
49C13×#103—21no—
50#88075—21no—
51#88061—21no—
52#88058C2×C411yescharacteristic
53C8×Dic13C2×C411yescharacteristic
54C8×Dic13C2×C411yescharacteristic
55C8×Dic13D411yescharacteristic
56C8×Dic13D411yescharacteristic
57C2×#6090—21no—
58#88049—21no—
59#88048—21no—
60#11860—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C2×D411yescharacteristic
64C2×C22⋊D13—41no—
65C22×Dic13—41no—
66C22×Dic13D811yescharacteristic
67C22×Dic13D811yescharacteristic
68C2×D52—21no—
69C2×C4×D13—41no—
70C13×Q16—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×C4⋊C4—41no—
78C13×C22⋊C4—41no—
79#6106—42no—
80#6103—41no—
81#6103—41no—
82#6103—41no—
83#6103—41no—
84C4⋊Dic13—21no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89#6101—41no—
90#6101—82no—
91#6101—82no—
92C4×Dic13—41no—
93C4×Dic13C22⋊C411yescharacteristic
94C4×Dic13C22⋊C411yescharacteristic
95C4×Dic13SD1611yescharacteristic
96C4×Dic13SD1611yescharacteristic
97C2×#1055—41no—
98C2×#1055C22⋊C411yescharacteristic
99C2×#1055C22⋊C411yescharacteristic
100D104—41no—
101C13×C16—41no—
102#6090—41no—
103#3168—131no—
104#2163—131no—
105#1834—131no—
106#1348—131no—
107#1348D1311yescharacteristic, complemented
108#1347—131no—
109#1347—131no—
110C23×C13C2×D811yescharacteristic
111C22×D13—41no—
112Q8×C13—41no—
113Q8×C13—41no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13C2×SD1611yescharacteristic
123C22⋊D13—81no—
124C22⋊D13—81no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—81no—
130C2×Dic13—81no—
131C2×Dic13—81no—
132C2×Dic13#10211yescharacteristic
133C2×Dic13#10211yescharacteristic
134C2×Dic13#10211yescharacteristic
135C2×Dic13#10211yescharacteristic
136D52—41no—
137D52—41no—
138C4×D13—82no—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#529—261no—
144#499—131no—
145#495—131no—
146#488—261no—
147#467C2×D1311yescharacteristic
148#466—131no—
149#465—261no—
150C4×Q16—131no—
151C4×SD16—261no—
152C4×D8—131no—
153C2×C4×C8—131no—
154#384—261no—
155C4⋊C16—261no—
156C22⋊C16—131no—
157C22⋊C16C2×D1311yescharacteristic
158#346—261no—
159#340—131no—
160#340—261no—
161#340C2×D1311yescharacteristic
162C22×C13—21no—
163C22×C13—21no—
164C22×C13C2×#10211yescharacteristic
165C22×C13#50911yescharacteristic
166C22×C13#51011yescharacteristic
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—81no—
170C4×C13—21no—
171C4×C13—81no—
172C4×C13—81no—
173C4×C13—161no—
174C4×C13#41011yescharacteristic
175C4×C13#42111yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—81no—
180Dic13—161no—
181Dic13#36012yes—
182C2×Q16C4×D1311yescharacteristic
183C2×SD16—261no—
184C2×D8—131no—
185C22×C8—131no—
186C22×C8C22×D1311yescharacteristic
187#126—521no—
188#125—261no—
189#124—261no—
190#123—521no—
191C22⋊Q8—21no—
192#121—261no—
193C4×Q8—261no—
194C4×D4—261no—
195C4×D4—521no—
196#117—521no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—521no—
200C2×C4⋊C4—521no—
201C2×C42—131no—
202C2×C16—21no—
203C2×C16—261no—
204#107—131no—
205#107C4×D1311yescharacteristic
206#106—261no—
207#103—21no—
208#103—261no—
209#102—261no—
210#102—261no—
211C4×C8—131no—
212C4×C8—131no—
213C4×C8—131no—
214C4×C8—131no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#151711yescharacteristic
218C2×C13#213911yescharacteristic
219C2×C13C2×#36011yescharacteristic
220D13—161no—
221C2×Q8—21no—
222C2×D4—261no—
223C2×D4—521no—
224C22×C4—41no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—521no—
228C22×C4—521no—
229C22×C4D4×D1311yescharacteristic
230Q16—41no—
231SD16—522no—
232D8—521no—
233C2×C8—41no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8—521no—
237C2×C8C2×C4×D1311yescharacteristic
238C2×C8D4×D1311yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—261no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—1042no—
250C4⋊C4—1042no—
251C22⋊C4—41no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—521no—
255C22⋊C4—521no—
256C42—131no—
257C42—131no—
258C42—131no—
259C42—131no—
260C42—521no—
261C16—41no—
262C16—521no—
263C13#1186011yescharacteristic, complemented, Sylow
264C23—521no—
265C23D8×D1311yescharacteristic
266Q8—41no—
267Q8—41no—
268D4—521no—
269D4—521no—
270D4—1041no—
271D4—1041no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—262no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—521no—
287C2×C4—1042no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4C22⋊C4×D1311yescharacteristic
292C2×C4SD16×D1311yescharacteristic
293C8—21no—
294C8—21no—
295C8—261no—
296C8—261no—
297C22—21no—
298C22—21no—
299C22—1041no—
300C22—1041no—
301C22—1041no—
302C22D13×#10211yescharacteristic
303C22#1171857511yescharacteristic
304C22#1171857911yescharacteristic
305C4—21no—
306C4—81no—
307C4—81no—
308C4—132no—
309C4—161no—
310C4—261no—
311C4—261no—
312C4—261no—
313C4—1041no—
314C4—2081no—
315C4#1171840111yescharacteristic
316C4#1171848211yescharacteristic
317C2—21no—
318C2—21no—
319C2—2081no—
320C2#1311339411yescharacteristic
321C2#1311654711yescharacteristic
322C2D13×#36011yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1348C2
socleC22×C13C2×#102
prime radical#11718776C22
cosocleC22×C8×C13C23
hypercenter#1348D13
hypocenterC13#11860
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
2. #13116636C2semidirect
3. #13114962C2semidirect
4. #13112848C2semidirect
7. C13×#1348C2semidirect
10. #11718852C4semidirect
11. Q16×Dic13C4semidirect
16. #11718539C4semidirect
17. #11718533C4semidirect
107. #1348D13semidirect
263. C13#11860semidirect

Maximal subgroups

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

subgroupindex
#131254072
#131166362
#131149622
#131128482
#131128462
#131128442
C13×#13482
#1186013