Finite Group Databasebeta

← #15761508

Subgroups — #15761508

Order 3328.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114953C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic
3C2×#11718050C211yesmaximal, characteristic
4C2×#11718049C211yesmaximal, characteristic
5#13112671C211yesmaximal, characteristic
6#13112671C211yesmaximal, characteristic
7C4×C13×C4⋊C8C211yesmaximal, characteristic
8C2×C13×C4⋊C8C411yescharacteristic
9C2×C13×C4⋊C8C411yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C43×C13C2211yescharacteristic
13C2×C4⋊#1055C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C2×C4×#1055—21no—
18C13×#336C411yescharacteristic
19C13×#336C411yescharacteristic
20#11718116—21no—
21#11718116—21no—
22#11718116—21no—
23#11718050—22no—
24#11718049—22no—
25C22×C8×C13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13Q811yescharacteristic
34C2×C42×C13Q811yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C22×#1055—21no—
37C22×#1055—21no—
38C22×#1055—21no—
39C22×#1055—21no—
40C13×C4⋊C8—22no—
41C13×C4⋊C8C814yescomplemented
42C4×C8×C13—21no—
43C4×C8×C13—21no—
44C4×C8×C13—21no—
45C4×C8×C13—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055D412yes—
53C4⋊#1055Q812yes—
54C4×#1055—42no—
55#9603—131nomaximal, Sylow
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C4⋊C411yescharacteristic
58C22×C4×C13C4⋊C411yescharacteristic
59C22×C4×C13C4⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×Q811yescharacteristic
63C2×C8×C13—21no—
64C2×C8×C13—21no—
65C2×C8×C13—21no—
66C2×C8×C13—21no—
67C2×C8×C13—21no—
68C2×C8×C13—21no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—21no—
73C2×C8×C13C2×C812yes—
74C2×C8×C13C2×C812yes—
75C42×C13—22no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—41no—
83C42×C13C2×C812yes—
84C42×C13M1612yes—
85C42×C13C2×D411yescharacteristic
86C42×C13C2×Q811yescharacteristic
87C42×C13#4111yescharacteristic
88C42×C13#4111yescharacteristic
89C2×#1055—22no—
90C2×#1055—22no—
91C2×#1055—41no—
92C2×#1055—41no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101#1831—131no—
102C4×C4⋊C8—131no—
103C4×C4⋊C8D1311yescharacteristic
104C2×#335—131no—
105C2×#334—131no—
106#1277—131no—
107#1277—131no—
108C23×C13C2×C4⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C4⋊C812yes—
121C2×C4×C13C4⋊C812yes—
122C2×C4×C13#10812yes—
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13C4×Q811yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13#12511yescharacteristic
128C2×C4×C13C4⋊Q811yescharacteristic
129C2×C4×C13C22×C811yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13#13111yescharacteristic
132C2×C4×C13#13111yescharacteristic
133C2×C4×C13#13511yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C8×C13—22no—
138C8×C13—22no—
139C8×C13—41no—
140C8×C13—41no—
141#1055—42no—
142#1055—42no—
143#1055—81no—
144#1055—81no—
145C2×C4⋊C8—131no—
146C2×C4⋊C8—131no—
147C2×C4⋊C8—131no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8Dic1311yescharacteristic
150C2×C4⋊C8Dic1311yescharacteristic
151C2×C4×C8—261no—
152C2×C4×C8C2×D1311yescharacteristic
153C2×C4×C8C2×D1311yescharacteristic
154C43C2×D1311yescharacteristic
155#336—261no—
156#336—261no—
157#336—261no—
158#336Dic1311yescharacteristic
159#336Dic1311yescharacteristic
160#335—262no—
161#334—262no—
162C22×C13#38911yescharacteristic
163C22×C13C2×C4⋊C811yescharacteristic
164C22×C13#42411yescharacteristic
165C22×C13#42711yescharacteristic
166C22×C13#42811yescharacteristic
167C22×C13C2×#10811yescharacteristic
168C22×C13#43011yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13C8×D411yescharacteristic
176C4×C13#43611yescharacteristic
177C4×C13C8×Q811yescharacteristic
178C4×C13#44611yescharacteristic
179C4×C13#46311yescharacteristic
180C4×C13#46411yescharacteristic
181C4×C13#47811yescharacteristic
182C4×C13#47911yescharacteristic
183C22×C8—261no—
184C22×C8—261no—
185C22×C8—261no—
186C22×C8—261no—
187C22×C8C2×Dic1311yescharacteristic
188C22×C8C2×Dic1311yescharacteristic
189C22×C8C2×Dic1311yescharacteristic
190C22×C8C2×Dic1311yescharacteristic
191C2×C42Dic2611yescharacteristic
192C2×C42Dic2611yescharacteristic
193C2×C42D5211yescharacteristic
194C2×C42D5211yescharacteristic
195C2×C42C2×Dic1311yescharacteristic
196C2×C42C2×Dic1311yescharacteristic
197C2×C42C22×D1311yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—132no—
200C4⋊C8—132no—
201C4⋊C8—261no—
202C4⋊C8—261no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8#105514yescomplemented
208C4×C8—21no—
209C4×C8—21no—
210C4×C8—21no—
211C4×C8—21no—
212C4×C8—522no—
213C2×C13#156411yescharacteristic
214C2×C13#156511yescharacteristic
215C2×C13#157211yescharacteristic
216C2×C13#157311yescharacteristic
217C2×C13#193911yescharacteristic
218C2×C13#194911yescharacteristic
219C2×C13#195011yescharacteristic
220C22×C4C4⋊Dic1311yescharacteristic
221C22×C4C4⋊Dic1311yescharacteristic
222C22×C4C4⋊Dic1311yescharacteristic
223C22×C4C4⋊Dic1311yescharacteristic
224C22×C4C2×Dic2611yescharacteristic
225C22×C4C2×D5211yescharacteristic
226C22×C4C22×Dic1311yescharacteristic
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—262no—
238C2×C8—262no—
239C2×C8—521no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8C2×#105512yes—
250C2×C8C2×#105512yes—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—22no—
258C42—41no—
259C42C2×#105512yes—
260C42#609912yes—
261C42D4×D1311yescharacteristic
262C42#612911yescharacteristic
263C42Q8×D1311yescharacteristic
264C42#613111yescharacteristic
265C13#960311yescharacteristic, complemented, Sylow
266C23C2×C4⋊Dic1311yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4C4⋊#105512yes—
279C2×C4C4⋊#105512yes—
280C2×C4#8805912yes—
281C2×C4#8814211yescharacteristic
282C2×C4#8814411yescharacteristic
283C2×C4#8814911yescharacteristic
284C2×C4#8815111yescharacteristic
285C2×C4#8815811yescharacteristic
286C2×C4#8815811yescharacteristic
287C2×C4#8816211yescharacteristic
288C2×C4#8816311yescharacteristic
289C2×C4C22×#105511yescharacteristic
290C2×C4C2×#609911yescharacteristic
291C2×C4D4×Dic1311yescharacteristic
292C2×C4Q8×Dic1311yescharacteristic
293C2×C4#8820211yescharacteristic
294C2×C4#8820211yescharacteristic
295C8—22no—
296C8—22no—
297C8—41no—
298C8—41no—
299C8—522no—
300C8—522no—
301C8—1041no—
302C8—1041no—
303C22C2×C4⋊#105511yescharacteristic
304C22#1171864611yescharacteristic
305C22#1171866011yescharacteristic
306C22#1171876711yescharacteristic
307C22C2×#8805911yescharacteristic
308C22#1171878211yescharacteristic
309C22#1171878611yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4#1171849011yescharacteristic
317C4#1171850511yescharacteristic
318C4#1171850611yescharacteristic
319C4#1171850811yescharacteristic
320C4D4×#105511yescharacteristic
321C4#1171867311yescharacteristic
322C4Q8×#105511yescharacteristic
323C4#1171868511yescharacteristic
324C2#1311358411yescharacteristic
325C2#1311358811yescharacteristic
326C2#1311361611yescharacteristic
327C2#1311362111yescharacteristic
328C2#1311555511yescharacteristic
329C2#1311560611yescharacteristic
330C2#1311561211yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC4×C13×C4⋊C8C2
socle, prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C4⋊C8D13
hypocenterC13#9603
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
41. C13×C4⋊C8C8semidirect
207. C4⋊C8#1055semidirect
265. C13#9603semidirect

Maximal subgroups

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

subgroupindex
#131149532
C4×C4⋊#10552
C2×#117180502
C2×#117180492
#131126712
C4×C13×C4⋊C82
#960313