Finite Group Databasebeta

← #15756364

Subgroups — #15756364

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#117×Dic13C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112668C212yesmaximal, complemented
4#13112664C212yesmaximal, complemented
5C13×#1458C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88180C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C13×#431C2212yes—
10C4⋊C4×Dic13—21no—
11C4⋊C4×Dic13—21no—
12C22⋊C4×Dic13—21no—
13C22⋊C4×Dic13—21no—
14#11718593C411yescharacteristic
15#11718593C2211yescharacteristic
16C42×Dic13C411yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718586C2212yes—
19C13×#324—21no—
20C13×#323—21no—
21#11718120—21no—
22#11718117—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13—21no—
25C13×#117—22no—
26C13×#117—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34#88180—22no—
35#88180C814yescomplemented
36C2×C4⋊Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—22no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13C2×C411yescharacteristic
48C13×C4⋊C8—22no—
49C13×C22⋊C8—22no—
50C4×C8×C13—22no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—22no—
57C4×#1055—22no—
58#8731—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C2×C812yes—
68C22×C4×C13M1612yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—24no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C2×C8×C13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13#4112yes—
87C42×C13#4112yes—
88C22⋊Dic13—24no—
89C4⋊Dic13—24no—
90C4×Dic13—24no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—42no—
96C4×Dic13—42no—
97C4×Dic13—42no—
98C4×Dic13—42no—
99C4×Dic13C2×C812yes—
100C4×Dic13C2×C812yes—
101C4×Dic13M1612yes—
102C4×Dic13M1612yes—
103C2×#1055—42no—
104C4×#117—131no—
105#1458—131no—
106#1458D1311yescharacteristic
107#1276—132no—
108#1274—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13C22⋊C812yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13C22⋊C812yes—
128C2×C4×C13#11711yescharacteristic
129C2×C4×C13#11711yescharacteristic
130C2×C4×C13#12312yes—
131C2×C4×C13#12312yes—
132C2×C4×C13C22×C811yescharacteristic
133C2×C4×C13C2×M1611yescharacteristic
134C2×C4×C13C2×M1611yescharacteristic
135C2×C4×C13C2×M1611yescharacteristic
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—22no—
139C2×Dic13—22no—
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—48no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C8×C13—82no—
150#1055—82no—
151C2×#117—131no—
152C2×#117C2×D1311yescharacteristic
153C22×C42—131no—
154#431—132no—
155#431C2×D1312yes—
156C4×C4⋊C4—261no—
157C4×C4⋊C4—261no—
158C4×C22⋊C4—261no—
159C4×C22⋊C4—261no—
160#376—131no—
161#376—131no—
162C43—131no—
163C43—131no—
164#324—21no—
165#324—261no—
166#323—21no—
167#323—261no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13#38111yescharacteristic
176C22×C13C2×C22⋊C811yescharacteristic
177C22×C13#40711yescharacteristic
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13#43111yescharacteristic
184C4×C13#43111yescharacteristic
185C4×C13#43211yescharacteristic
186C4×C13#43211yescharacteristic
187Dic13—24no—
188Dic13—42no—
189Dic13—42no—
190Dic13—42no—
191C23×C4—261no—
192C23×C4C4×D1311yescharacteristic
193#117—22no—
194#117—22no—
195#117—134no—
196#117—262no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4D5211yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C22⋊C4—261no—
201C2×C22⋊C4D5211yescharacteristic
202C2×C22⋊C4C22⋊D1311yescharacteristic
203C2×C42—131no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—262no—
208C2×C42—262no—
209C2×C42—261no—
210C2×C42—261no—
211C2×C42—261no—
212C2×C42—261no—
213C2×C42—261no—
214C2×C42C4×D1311yescharacteristic
215C2×C42C22×D1311yescharacteristic
216C4⋊C8—22no—
217C4⋊C8—262no—
218C22⋊C8—22no—
219C22⋊C8—262no—
220C4×C8—22no—
221C4×C8—262no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13#181711yescharacteristic
230C2×C13#182711yescharacteristic
231C2×C13#182711yescharacteristic
232C24#610311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—261no—
238C22×C4—264no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—522no—
243C22×C4—522no—
244C22×C4C8×D1312yes—
245C22×C4#609412yes—
246C22×C4#610311yescharacteristic
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4C2×D5211yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252C2×C8—42no—
253C2×C8—522no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—264no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—264no—
260C42—21no—
261C42—21no—
262C42—132no—
263C42—132no—
264C42—132no—
265C42—132no—
266C42—264no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—522no—
272C42—522no—
273C42—522no—
274C42—522no—
275C42#612912yes—
276C42#612912yes—
277C13#873111yescharacteristic, complemented, Sylow
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23#8806012yes—
283C23C2×#610311yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—262no—
299C2×C4—262no—
300C2×C4—262no—
301C2×C4—262no—
302C2×C4—528no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4#8806012yes—
310C2×C4#8813111yescharacteristic
311C2×C4#8813111yescharacteristic
312C2×C4#8814012yes—
313C2×C4C2×C8×D1311yescharacteristic
314C2×C4C2×#609411yescharacteristic
315C2×C4M16×D1311yescharacteristic
316C2×C4M16×D1311yescharacteristic
317C2×C4#8818912yes—
318C8—82no—
319C8—1042no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22#1171860411yescharacteristic
328C22C2×#8806011yescharacteristic
329C22#1171878711yescharacteristic
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—264no—
336C4—522no—
337C4—522no—
338C4—522no—
339C4#1171837911yescharacteristic
340C4#1171837911yescharacteristic
341C4#1171838011yescharacteristic
342C4#1171838011yescharacteristic
343C2—21no—
344C2—21no—
345C2—42no—
346C2#1311490211yescharacteristic
347C2#1311493711yescharacteristic
348C2#1311494111yescharacteristic
subgroupG/H
centerC2×C4#88131
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1458C2
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1458D13
hypocenterC13#8731
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13112668C2semidirect
4. #13112664C2semidirect
35. #88180C8semidirect
277. C13#8731semidirect

Maximal subgroups

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

subgroupindex
#117×Dic132
#131131502
#131126682
#131126642
C13×#14582
#873113