Finite Group Databasebeta

← #15774008

Subgroups — #15774008

Order 3328.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13116447C211yesmaximal, characteristic, complemented
2#13114865C211yesmaximal, characteristic, complemented
3#13112848C212yesmaximal, complemented
4#13112845C212yesmaximal, complemented
5C13×#3050C211yesmaximal, characteristic
6C2×C13×#135C411yescharacteristic, complemented
7C23×C8×C13C2211yescharacteristic
8C13×#525—21no—
9C13×#467C411yescharacteristic, complemented
10C13×#467C2211yescharacteristic
11C13×#466C411yescharacteristic, complemented
12C13×#466C2211yescharacteristic
13C13×#465—21no—
14C13×#465—21no—
15C13×#427C411yescharacteristic, complemented
16C13×#416—21no—
17#11718873—21no—
18C2×#88058—21no—
19C2×#88052—21no—
20#11718143C2212yes—
21C22⋊#6090—21no—
22C22⋊#6090C2212yes—
23C2×C13×#41—21no—
24C23×C4×C13D411yescharacteristic
25C13×#135—42no—
26C2×C13×Q16C2×C411yescharacteristic
27C2×C13×SD16—21no—
28C2×C13×D8C2×C411yescharacteristic
29C22×C8×C13—42no—
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13C2×C411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35C22×C8×C13C2311yescharacteristic
36C13×#123—41no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×#121—21no—
40C13×#121—21no—
41C13×#120—41no—
42C4×D4×C13—41no—
43C4×D4×C13—41no—
44C13×#117—21no—
45C2×C22⋊Dic13—41no—
46C2×C4⋊Dic13—22no—
47C13×#107C2×C411yescharacteristic
48C13×#107C2×C411yescharacteristic
49C13×#106—21no—
50C13×#103—21no—
51C13×#103—21no—
52C13×#102—21no—
53C13×#102—21no—
54#88071—41no—
55#88058—42no—
56#88052—42no—
57C2×#6090—22no—
58#11890—131nomaximal, Sylow
59C24×C13D811yescharacteristic
60C13×#41—42no—
61C13×#41—42no—
62C2×Q8×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13D811yescharacteristic
73C22×C4×C13SD1611yescharacteristic
74C22×C4×C13SD1611yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—42no—
77C13×Q16—41no—
78C13×SD16—42no—
79C13×D8—41no—
80C2×C8×C13—22no—
81C2×C8×C13—22no—
82C2×C8×C13—22no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13C22⋊C411yescharacteristic
87C2×C8×C13C22⋊C411yescharacteristic
88C2×C8×C13C22×C411yescharacteristic
89C2×C8×C13C2×D411yescharacteristic
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C42×C13—41no—
100C22⋊Dic13—82no—
101C4⋊Dic13—42no—
102C4⋊Dic13—42no—
103#6090—42no—
104#3050D1311yescharacteristic
105#2112—131no—
106#1808—131no—
107#1348—132no—
108#1347—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#10211yescharacteristic
115C23×C13#10211yescharacteristic
116C23×C13C2×D811yescharacteristic
117Q8×C13—41no—
118Q8×C13—41no—
119D4×C13—41no—
120D4×C13—41no—
121D4×C13—82no—
122D4×C13—82no—
123D4×C13—81no—
124D4×C13—81no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—82no—
138C2×C4×C13#10211yescharacteristic
139C2×C4×C13#10211yescharacteristic
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13C2×SD1611yescharacteristic
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13#9912yes—
149C2×#135Dic1311yescharacteristic, complemented
150C23×C8C2×D1311yescharacteristic
151#525—21no—
152C2×M32—261no—
153#467Dic1311yescharacteristic, complemented
154#467C2×D1311yescharacteristic
155#466Dic1311yescharacteristic, complemented
156#466C2×D1311yescharacteristic
157#465—21no—
158#465—21no—
159#427Dic1311yescharacteristic, complemented
160C2×#107—261no—
161#416—21no—
162#380—261no—
163C22⋊C16—132no—
164C22⋊C16—261no—
165#340—132no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13C2×#10211yescharacteristic
180C22×C13#50911yescharacteristic
181C22×C13#51011yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13C2×#9911yescharacteristic
189C4×C13#42111yescharacteristic
190Dic13—162no—
191C2×#41—21no—
192C23×C4C22⋊D1311yescharacteristic
193#135—42no—
194C2×Q16C2×Dic1311yescharacteristic
195C2×SD16—21no—
196C2×D8C2×Dic1311yescharacteristic
197C22×C8—42no—
198C22×C8C2×Dic1311yescharacteristic
199C22×C8C2×Dic1311yescharacteristic
200C22×C8C22⋊D1311yescharacteristic
201C22×C8C22⋊D1311yescharacteristic
202C22×C8C22⋊D1311yescharacteristic
203C22×C8C22×D1311yescharacteristic
204#123—41no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207#121—21no—
208#121—21no—
209#120—41no—
210C4×D4—41no—
211C4×D4—41no—
212#117—21no—
213C2×C4⋊C4—262no—
214C2×C22⋊C4—521no—
215M32—522no—
216C2×C16—262no—
217#107—522no—
218#107C2×Dic1311yescharacteristic
219#107C2×Dic1311yescharacteristic
220#106—21no—
221#103—21no—
222#103—21no—
223#102—21no—
224#102—21no—
225#95—521no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—41no—
229C2×C13—41no—
230C2×C13—161no—
231C2×C13#151911yescharacteristic
232C2×C13#213911yescharacteristic
233C2×C13#214511yescharacteristic
234C24#610411yescharacteristic
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—522no—
246C22×C4#610411yescharacteristic
247C22×C4#610511yescharacteristic
248C22×C4#610511yescharacteristic
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252Q16—41no—
253SD16—42no—
254D8—41no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8C22⋊Dic1311yescharacteristic
262C2×C8C22⋊Dic1311yescharacteristic
263C2×C8C22×Dic1311yescharacteristic
264C2×C8C2×C22⋊D1311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—522no—
270C4⋊C4—522no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—1042no—
277C42—41no—
278C16—522no—
279C13#1189011yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#8807211yescharacteristic
286C23#8807211yescharacteristic
287C23C2×#610411yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—41no—
291D4—41no—
292D4—82no—
293D4—82no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—82no—
309C2×C4—1042no—
310C2×C4—1042no—
311C2×C4—1042no—
312C2×C4#8807211yescharacteristic
313C2×C4#8807211yescharacteristic
314C2×C4C2×#610511yescharacteristic
315C2×C4C2×C22⋊Dic1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8#8807412yes—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22#1171885411yescharacteristic
334C22#1171885611yescharacteristic
335C22C2×#8807211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—2082no—
343C4C2×#8807411yescharacteristic
344C4#1171889711yescharacteristic
345C2—21no—
346C2—21no—
347C2—41no—
348C2—41no—
349C2—161no—
350C2#1311340411yescharacteristic
351C2#1311654811yescharacteristic
352C2#1311657211yescharacteristic
subgroupG/H
centerC22C2×#88072
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C2×#102
cosocleC22×C8×C13C23
hypercenter#3050D13
hypocenterC13#11890
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #13116447C2semidirect
2. #13114865C2semidirect
3. #13112848C2semidirect
4. #13112845C2semidirect
6. C2×C13×#135C4semidirect
9. C13×#467C4semidirect
11. C13×#466C4semidirect
15. C13×#427C4semidirect
149. C2×#135Dic13semidirect
153. #467Dic13semidirect
155. #466Dic13semidirect
159. #427Dic13semidirect
279. C13#11890semidirect

Maximal subgroups

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

subgroupindex
#131164472
#131148652
#131128482
#131128452
C13×#30502
#1189013