Finite Group Databasebeta

← #15752651

Subgroups — #15752651

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123469C211yesmaximal, characteristic
2#13117234C211yesmaximal, characteristic
3#13112689C214yesmaximal
4C13×#2283C211yesmaximal, characteristic
5C22×C42×C13C2211yescharacteristic
6C13×#383—21no—
7C13×#382—21no—
8C13×#381—21no—
9C13×#380—21no—
10C4×C13×C4⋊C4C412yescomplemented
11C4×C13×C22⋊C4C2212yes—
12C13×#376C412yescomplemented
13#11718873—21no—
14#11718872C2212yes—
15C4×C22⋊Dic13—21no—
16#11718868C2212yes—
17#11718598—21no—
18#11718597C412yescomplemented
19C4×C4⋊Dic13—21no—
20#11718593C412yescomplemented
21#11718587—21no—
22#11718587C412yescomplemented
23#11718586—21no—
24#11718586C412yescomplemented
25#11718585—21no—
26C4×#6099—21no—
27C23×C4×C13D411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C2×C13×C4⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C414yes—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13Q811yescharacteristic
44C2×C42×C13Q811yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×C4×Dic13—22no—
48C2×#6099—22no—
49C13×#95—22no—
50C13×#95—22no—
51C13×#95—22no—
52C13×#95—22no—
53#88071—22no—
54#88071—22no—
55#88071—22no—
56#88071C2×C414yes—
57C22⋊#1055—22no—
58C22⋊#1055C2×C414yes—
59C4⋊#1055—22no—
60C4⋊#1055—22no—
61#88043—22no—
62C4×#1055—22no—
63#7944—131nomaximal, Sylow
64C24×C13C2×D411yescharacteristic
65C22×C4×C13—24no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C4⋊C411yescharacteristic
78C22×C4×C13C4⋊C411yescharacteristic
79C22×C4×C13C4⋊C411yescharacteristic
80C22×C4×C13C4⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×Q811yescharacteristic
87C22×Dic13—24no—
88C13×C4⋊C4—44no—
89C13×C22⋊C4—44no—
90C42×C13—44no—
91C42×C13C4211yescharacteristic
92C42×C13C4211yescharacteristic
93C42×C13C4211yescharacteristic
94C42×C13C4211yescharacteristic
95C42×C13C22⋊C411yescharacteristic
96C42×C13C22⋊C411yescharacteristic
97C42×C13C22⋊C411yescharacteristic
98C42×C13C22⋊C411yescharacteristic
99C42×C13C4⋊C411yescharacteristic
100C42×C13C4⋊C411yescharacteristic
101C42×C13C4⋊C411yescharacteristic
102C42×C13C4⋊C411yescharacteristic
103C42×C13C4⋊C411yescharacteristic
104C42×C13C4⋊C411yescharacteristic
105C42×C13C4⋊C411yescharacteristic
106C42×C13C4⋊C411yescharacteristic
107C22⋊Dic13—44no—
108C4⋊Dic13—44no—
109C4×Dic13—44no—
110#6099—44no—
111C2×#1055—24no—
112#2920—131no—
113#2283—131no—
114#2283D1311yescharacteristic
115#1284—134no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—41no—
119C23×C13C2×C22⋊C411yescharacteristic
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C2×C4⋊C411yescharacteristic
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
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—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—44no—
141C2×C4×C13—44no—
142C2×C4×C13—44no—
143C2×C4×C13#9511yescharacteristic
144C2×C4×C13#9511yescharacteristic
145C2×C4×C13#9511yescharacteristic
146C2×C4×C13#9511yescharacteristic
147C2×C4×C13#9511yescharacteristic
148C2×C4×C13#9511yescharacteristic
149C2×C4×C13#9511yescharacteristic
150C2×C4×C13#9511yescharacteristic
151C2×C4×C13C2×C4211yescharacteristic
152C2×C4×C13C2×C22⋊C411yescharacteristic
153C2×C4×C13C2×C4⋊C411yescharacteristic
154C2×C4×C13C2×C4⋊C411yescharacteristic
155C2×Dic13—44no—
156C2×Dic13—44no—
157C2×Dic13—44no—
158#1055—44no—
159C22×C42C2×D1311yescharacteristic
160#432—132no—
161#432—261no—
162#431—132no—
163#431—261no—
164#423—261no—
165#407—132no—
166C4×M16—261no—
167#383—21no—
168#383—261no—
169#382—21no—
170#382—132no—
171#381—21no—
172#381—132no—
173#380—21no—
174#380—261no—
175C4×C4⋊C4—261no—
176C4×C4⋊C4Dic1312yescomplemented
177C4×C22⋊C4—261no—
178C4×C22⋊C4C2×D1312yes—
179#376—132no—
180#376Dic1312yescomplemented
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—44no—
189C22×C13C2×#9511yescharacteristic
190C22×C13#41012yes—
191C22×C13#42112yes—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—84no—
204C4×C13H(3,ℤ/4)12yes—
205Dic13—84no—
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22⋊D1311yescharacteristic
208C23×C4C22×D1311yescharacteristic
209C2×M16—262no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—262no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—262no—
214C2×C42—262no—
215C2×C42Dic2611yescharacteristic
216C2×C42Dic2611yescharacteristic
217C2×C42C4×D1311yescharacteristic
218C2×C42C4×D1311yescharacteristic
219C2×C42C4×D1311yescharacteristic
220C2×C42C4×D1311yescharacteristic
221C2×C42D5211yescharacteristic
222C2×C42D5211yescharacteristic
223C2×C42C2×Dic1314yes—
224C2×C42C2×Dic1311yescharacteristic
225C2×C42C2×Dic1311yescharacteristic
226C2×C42C22⋊D1311yescharacteristic
227C2×C42C22⋊D1311yescharacteristic
228C4⋊C8—262no—
229C4⋊C8—262no—
230C22⋊C8—134no—
231C22⋊C8—262no—
232#97—262no—
233C4×C8—262no—
234#95—22no—
235#95—22no—
236#95—22no—
237#95—22no—
238#95—134no—
239#95—262no—
240#95—262no—
241#95—262no—
242C2×C13—22no—
243C2×C13—22no—
244C2×C13—41no—
245C2×C13C2×H(3,ℤ/4)11yescharacteristic
246C2×C13#173311yescharacteristic
247C2×C13#174011yescharacteristic
248C24C2×C22⋊D1311yescharacteristic
249C22×C4—24no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—264no—
254C22×C4#610111yescharacteristic
255C22×C4#610111yescharacteristic
256C22×C4#610111yescharacteristic
257C22×C4#610111yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4#610311yescharacteristic
261C22×C4#610311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4C2×Dic2611yescharacteristic
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4C2×C4×D1311yescharacteristic
269C22×C4C2×D5211yescharacteristic
270C22×C4C22×Dic1311yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272M16—524no—
273C2×C8—264no—
274C4⋊C4—44no—
275C4⋊C4—524no—
276C22⋊C4—44no—
277C22⋊C4—524no—
278C42—44no—
279C42—524no—
280C42C4×Dic1311yescharacteristic
281C42C4×Dic1311yescharacteristic
282C42C4×Dic1311yescharacteristic
283C42C4×Dic1311yescharacteristic
284C42#610111yescharacteristic
285C42#610111yescharacteristic
286C42#610111yescharacteristic
287C42#610111yescharacteristic
288C42C4⋊Dic1311yescharacteristic
289C42C4⋊Dic1311yescharacteristic
290C42C4⋊Dic1311yescharacteristic
291C42C4⋊Dic1311yescharacteristic
292C42#610311yescharacteristic
293C42#610311yescharacteristic
294C42#610311yescharacteristic
295C42#610311yescharacteristic
296C13#794411yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—41no—
300C23C2×#610111yescharacteristic
301C23C2×#610311yescharacteristic
302C23C2×C22⋊Dic1311yescharacteristic
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—524no—
325C2×C4—524no—
326C2×C4—524no—
327C2×C4#8807111yescharacteristic
328C2×C4#8807111yescharacteristic
329C2×C4#8807111yescharacteristic
330C2×C4#8807111yescharacteristic
331C2×C4#8807111yescharacteristic
332C2×C4#8807111yescharacteristic
333C2×C4#8807111yescharacteristic
334C2×C4#8807111yescharacteristic
335C2×C4C2×C4×Dic1311yescharacteristic
336C2×C4C2×#610111yescharacteristic
337C2×C4C2×C4⋊Dic1311yescharacteristic
338C2×C4C2×#610311yescharacteristic
339C8—524no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22#1171866612yes—
349C22C2×#8807111yescharacteristic
350C22#1171890112yes—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—84no—
363C4—1044no—
364C4#1171812312yes—
365C2—22no—
366C2—22no—
367C2—41no—
368C2C2×#1171812311yescharacteristic
369C2#1311454611yescharacteristic
370C2#1311456911yescharacteristic
subgroupG/H
centerC22C2×#88071
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#2283C2
socleC22×C13C2×#95
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2283D13
hypocenterC13#7944
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
10. C4×C13×C4⋊C4C4semidirect
12. C13×#376C4semidirect
18. #11718597C4semidirect
20. #11718593C4semidirect
22. #11718587C4semidirect
24. #11718586C4semidirect
176. C4×C4⋊C4Dic13semidirect
180. #376Dic13semidirect
296. C13#7944semidirect

Maximal subgroups

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

subgroupindex
#131234692
#131172342
#131126892
C13×#22832
#794413