Finite Group Databasebeta

← #15751005

Subgroups — #15751005

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117300C211yesmaximal, characteristic
2#13114953C211yesmaximal, characteristic, complemented
3#13112660C212yesmaximal, complemented
4#13112656C212yesmaximal
5C13×#1839C211yesmaximal, characteristic, complemented
6C2×C4×D52C411yescharacteristic
7C2×#88126—21no—
8C43×C13C2211yescharacteristic
9#11718601—21no—
10#11718601—21no—
11#11718600C411yescharacteristic
12#11718600C2211yescharacteristic
13C4×#6103—21no—
14C4×C4⋊Dic13C411yescharacteristic
15#11718589C411yescharacteristic
16#11718589C2211yescharacteristic
17C2×C4⋊#1055—21no—
18C13×#336—21no—
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C4×D13—21no—
25C22×C8×C13—22no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C22×#1055—22no—
45C4×D52—22no—
46C4×D52C814yescomplemented
47#88126—44no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51C4⋊#1055—42no—
52#7594—131nomaximal, Sylow
53C23×D13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×D52—21no—
65C2×D52—41no—
66C2×D52—41no—
67C2×D52C2×C812yes—
68C2×C4×D13—24no—
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×C8×C13—42no—
72C2×C8×C13—42no—
73C2×C8×C13—42no—
74C42×C13—22no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13—41no—
79C42×C13—41no—
80C42×C13—41no—
81C42×C13C2×C812yes—
82C42×C13M1612yes—
83#6103—24no—
84#6103—42no—
85#6103—42no—
86#6103—42no—
87#6103—41no—
88#6103—41no—
89C4⋊Dic13—21no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13C2×C812yes—
93#6101—42no—
94#6101—42no—
95C4×Dic13—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99#2293—131no—
100#1839D1311yescharacteristic, complemented
101#1831—131no—
102#1271—132no—
103#1270—132no—
104C23×C13C2×C22⋊C411yescharacteristic
105C22×D13—22no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
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×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13C22⋊C812yes—
129C2×C4×C13C22⋊C812yes—
130C2×C4×C13C22×C811yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)12yes—
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—22no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144D52—42no—
145D52—42no—
146C4×D13—48no—
147C8×C13—82no—
148#1055—82no—
149C2×C4×D4—131no—
150C2×#117—261no—
151C2×C4⋊C8—261no—
152#390—131no—
153#390—131no—
154#389—131no—
155#389—131no—
156#388—261no—
157#388—261no—
158C4×C4⋊C4—131no—
159C4×C22⋊C4—261no—
160C43C2×D1311yescharacteristic
161#336—21no—
162#336—21no—
163#336—132no—
164#336—261no—
165#336C2×D1312yes—
166C22×C13C2×C22⋊C811yescharacteristic
167C22×C13#41011yescharacteristic
168C22×C13#41311yescharacteristic
169C22×C13#41711yescharacteristic
170C22×C13#41811yescharacteristic
171C22×C13#42111yescharacteristic
172C22×C13#42111yescharacteristic
173C2×D13—42no—
174C2×D13—42no—
175C2×D13—42no—
176C2×D13—81no—
177C2×D13—81no—
178C2×D13—81no—
179C2×D13—81no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—41no—
189Dic13—42no—
190Dic13—81no—
191Dic13—81no—
192C22×D4—131no—
193C23×C4—261no—
194C22×C8—22no—
195C22×C8—262no—
196C4×D4—134no—
197C4×D4—262no—
198#117—524no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C42—261no—
210C2×C42C4×D1311yescharacteristic
211C2×C42C4×D1311yescharacteristic
212C2×C42D5211yescharacteristic
213C2×C42D5211yescharacteristic
214C2×C42C22⋊D1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C2×C42C22×D1311yescharacteristic
217C4⋊C8—522no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13#145811yescharacteristic
222C2×C13#147711yescharacteristic
223C2×C13#147811yescharacteristic
224C2×C13#151211yescharacteristic
225C2×C13#151411yescharacteristic
226C2×C13#153511yescharacteristic
227C2×C13#155711yescharacteristic
228D13—82no—
229C24—261no—
230C2×D4—132no—
231C2×D4—261no—
232C2×D4—521no—
233C2×D4—521no—
234C22×C4—261no—
235C22×C4—264no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4C2×D5211yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C4⋊C4—132no—
254C4⋊C4—261no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—522no—
258C4⋊C4—522no—
259C22⋊C4—264no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C22⋊C4—521no—
263C22⋊C4—521no—
264C22⋊C4—522no—
265C42—21no—
266C42—21no—
267C42—22no—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—522no—
273C42C8×D1312yes—
274C42#609412yes—
275C13#759411yescharacteristic, complemented, Sylow
276C23—262no—
277C23—521no—
278C23—521no—
279C23—521no—
280C23—521no—
281C23—521no—
282C23—521no—
283C23C2×#610311yescharacteristic
284D4—522no—
285D4—522no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—262no—
303C2×C4—528no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4#8806012yes—
313C2×C4#8806012yes—
314C2×C4C2×C8×D1311yescharacteristic
315C2×C4C2×#609411yescharacteristic
316C2×C4#8816211yescharacteristic
317C2×C4#8816311yescharacteristic
318C2×C4#8820312yes—
319C8—82no—
320C8—1042no—
321C22—522no—
322C22—522no—
323C22—522no—
324C22—1041no—
325C22—1041no—
326C22—1041no—
327C22—1041no—
328C22#1171866211yescharacteristic
329C22#1171866611yescharacteristic
330C22#1171866711yescharacteristic
331C22C2×#8806011yescharacteristic
332C22#1171879311yescharacteristic
333C22#1171879411yescharacteristic
334C22#1171880011yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C2—1042no—
348C2#1311314811yescharacteristic
349C2#1311322411yescharacteristic
350C2#1311322611yescharacteristic
351C2#1311337511yescharacteristic
352C2#1311338211yescharacteristic
353C2#1311346811yescharacteristic
354C2#1311355911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1839C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1839D13
hypocenterC13#7594
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #13114953C2semidirect
3. #13112660C2semidirect
5. C13×#1839C2semidirect
46. C4×D52C8semidirect
100. #1839D13semidirect
275. C13#7594semidirect

Maximal subgroups

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

subgroupindex
#131173002
#131149532
#131126602
#131126562
C13×#18392
#759413