Finite Group Databasebeta

← #16792650

Subgroups — #16792650

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131515C211yesmaximal, characteristic
2D13⋊#431C211yesmaximal, characteristic
3#13130058C214yesmaximal, complemented
4#13130055C214yesmaximal, complemented
5#13130048C212yesmaximal, complemented
6#13130038C212yesmaximal, complemented
7#13123468C211yesmaximal, characteristic
8C2×C42×D13C2211yescharacteristic
9#11719128C412yes—
10#11719127C412yes—
11#11719125C2212yes—
12#11719125C2212yes—
13D13⋊(C22⋊C8)C412yes—
14#11719119C412yes—
15#11719055C412yes—
16#11719053C412yes—
17#11719051C2212yes—
18D13⋊(C4⋊C8)C412yes—
19#11719049C412yes—
20#11719049C2212yes—
21C4×#6118C2212yes—
22C4×D13⋊C8C2211yescharacteristic
23C4×D13⋊C8C2211yescharacteristic
24C13×#423C411yescharacteristic
25#11718787C412yes—
26M16×Dic13C2212yes—
27#11718585C411yescharacteristic
28#11718496C412yes—
29#11718496C412yes—
30#11718494C2212yes—
31#11718494C2212yes—
32#1057⋊C8C2214yescomplemented
33#1057⋊C8C2214yescomplemented
34#11718251C2214yescomplemented
35C8×#1057C2214yescomplemented
36C22×C4×D13C2×C411yescharacteristic
37C22×C4×D13C2×C411yescharacteristic
38C22×C4×D13C2×C411yescharacteristic
39C2×#6118C2×C414yes—
40C2×D13⋊C8C2×C412yes—
41C2×D13⋊C8C2×C412yes—
42C2×C13×M16C2×C412yes—
43C2×C42×C13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2311yescharacteristic
47C2×#6099C2×C412yes—
48C42×D13C2×C411yescharacteristic
49C42×D13C2×C411yescharacteristic
50C42×D13C2×C411yescharacteristic
51C42×D13C2×C411yescharacteristic
52C42×D13C2×C411yescharacteristic
53C42×D13C2×C411yescharacteristic
54C42×D13C2311yescharacteristic
55C42×D13C2311yescharacteristic
56C22⋊#1057C2×C414yes—
57C22⋊#1057C2×C414yes—
58#88112C2×C414yes—
59#88112C2×C414yes—
60#88112C2×C414yes—
61#88111C2×C414yes—
62#88111C2×C414yes—
63#88110C2×C414yes—
64C4⋊#1057C2×C414yes—
65C4×#1057C2×C412yes—
66C4×#1057C2×C412yes—
67C4×#1057C2312yes—
68C4×#1057C2314yes—
69C4×#1057C2312yes—
70C13×C4⋊C8C2×C412yes—
71C13×C4⋊C8C2×C412yes—
72#88060C2×C414yes—
73#88060C2×C414yes—
74#88055C2×C414yes—
75C8×Dic13C2314yes—
76C4⋊#1055C2×C412yes—
77C4⋊#1055C2×C412yes—
78#17324—131nomaximal, Sylow
79C23×D13C4211yescharacteristic
80C22×C4×C13C4211yescharacteristic
81C22×C4×C13C4211yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×Dic13C4211yescharacteristic
84C22×Dic13C22×C411yescharacteristic
85C22×Dic13C22×C411yescharacteristic
86C2×C4×D13—24no—
87C2×C4×D13—42no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C2×C4×D13C4211yescharacteristic
91C2×C4×D13C4211yescharacteristic
92C2×C4×D13C4211yescharacteristic
93C2×C4×D13C4211yescharacteristic
94C2×C4×D13C4211yescharacteristic
95C2×C4×D13C4211yescharacteristic
96C2×C4×D13C22×C411yescharacteristic
97C2×C4×D13C22×C411yescharacteristic
98C2×C4×D13C22×C411yescharacteristic
99C2×C4×D13C22×C411yescharacteristic
100C2×C4×D13C22×C411yescharacteristic
101C2×C4×D13C22×C411yescharacteristic
102C2×#1057C22×C414yes—
103C2×#1057C22×C414yes—
104C2×#1057C22×C418yes—
105#6118—28no—
106D13⋊C8—42no—
107D13⋊C8—42no—
108C13×M16—42no—
109C2×C8×C13C22×C414yes—
110C42×C13C4211yescharacteristic
111C42×C13C4211yescharacteristic
112C42×C13C22×C411yescharacteristic
113C42×C13C22×C411yescharacteristic
114C4×Dic13C4211yescharacteristic
115C4×Dic13C4211yescharacteristic
116C4×Dic13C4211yescharacteristic
117C4×Dic13C4211yescharacteristic
118C4×Dic13C22×C411yescharacteristic
119C4×Dic13C22×C411yescharacteristic
120C4×Dic13C22×C411yescharacteristic
121C4×Dic13C22×C411yescharacteristic
122C4×Dic13C22×C411yescharacteristic
123C4×Dic13C22×C411yescharacteristic
124C4×Dic13C22×C411yescharacteristic
125C4×Dic13C2411yescharacteristic
126#6099—42no—
127C2×#1055C22×C414yes—
128#2920—131no—
129#2920—131no—
130C2×#431—131no—
131#1454—134no—
132#1453—134no—
133#1451—132no—
134C8×M16—132no—
135C23×C13C2×C4211yescharacteristic
136C22×D13—22no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13C2×C4211yescharacteristic
140C22×D13C2×C4211yescharacteristic
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13C2×C4211yescharacteristic
146C2×C4×C13C2×C4211yescharacteristic
147C2×C4×C13C2×C4211yescharacteristic
148C2×C4×C13C2×C4211yescharacteristic
149C2×C4×C13C2×C4211yescharacteristic
150C2×C4×C13C23×C411yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—41no—
154C2×Dic13C2×C4211yescharacteristic
155C2×Dic13C2×C4211yescharacteristic
156C2×Dic13C2×C4211yescharacteristic
157C2×Dic13C2×C4211yescharacteristic
158C2×Dic13C23×C411yescharacteristic
159C2×Dic13C23×C411yescharacteristic
160C4×D13—22no—
161C4×D13—21no—
162C4×D13—21no—
163C4×D13—21no—
164C4×D13—21no—
165C4×D13—22no—
166C4×D13—22no—
167C4×D13—22no—
168C4×D13—22no—
169C4×D13—41no—
170C4×D13—41no—
171C4×D13—41no—
172C4×D13—41no—
173C4×D13#13114yes—
174#1057—28no—
175#1057—24no—
176#1057—24no—
177C8×C13—24no—
178#1055—24no—
179C22×C42—131no—
180#432—132no—
181#432—132no—
182#432—132no—
183#432—132no—
184#431—132no—
185#431—132no—
186#431—132no—
187#431—132no—
188#431—132no—
189#431—132no—
190#431—132no—
191#431—132no—
192#423—132no—
193#423—131no—
194#423#26111yescharacteristic
195C2×C4⋊C8—132no—
196#407—132no—
197#407—132no—
198C2×C22⋊C8—132no—
199C4×M16—132no—
200C4×M16—132no—
201C2×C4×C8—131no—
202C2×C4×C8—131no—
203#322—134no—
204#322—134no—
205#322—134no—
206C82—134no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13C22×C4211yescharacteristic
211C2×D13—21no—
212C2×D13—21no—
213C2×D13—21no—
214C2×D13—21no—
215C2×D13—21no—
216C2×D13—44no—
217C2×D13#40512yes—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13#40512yes—
223C4×C13#56811yescharacteristic
224C4×C13#56811yescharacteristic
225Dic13—21no—
226Dic13—21no—
227Dic13—21no—
228Dic13—21no—
229Dic13C2×#13112yes—
230Dic13#56812yes—
231C23×C4—131no—
232C23×C4—131no—
233C23×C4—131no—
234C2×M16—134no—
235C2×M16—132no—
236C2×M16C2×#26112yes—
237C22×C8—132no—
238C22×C8—132no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42C2×#26111yescharacteristic
251C4⋊C8—134no—
252C4⋊C8—134no—
253C4⋊C8—134no—
254C4⋊C8—134no—
255C4⋊C8—132no—
256C4⋊C8—132no—
257C4⋊C8C2×#26112yes—
258C4⋊C8C2×#26112yes—
259C22⋊C8—134no—
260C22⋊C8—134no—
261C22⋊C8—134no—
262C22⋊C8—134no—
263C22⋊C8—134no—
264C22⋊C8—134no—
265#97—134no—
266#97—134no—
267C4×C8—132no—
268C4×C8—132no—
269C4×C8—132no—
270C4×C8—134no—
271C4×C8—132no—
272C4×C8—134no—
273C2×C13—41no—
274C2×C13C2×#40511yescharacteristic
275C2×C13#287311yescharacteristic
276C2×C13#287311yescharacteristic
277D13—22no—
278D13—41no—
279C24—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—131no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—264no—
296C22×C4—521no—
297C22×C4—521no—
298C22×C4—522no—
299C22×C4C4×#26111yescharacteristic
300C22×C4C4×#26111yescharacteristic
301C22×C4C22×#26111yescharacteristic
302M16—42no—
303M16—268no—
304M16—522no—
305C2×C8—134no—
306C2×C8—134no—
307C2×C8—138no—
308C2×C8—134no—
309C2×C8—522no—
310C2×C8—522no—
311C2×C8C22×#26114yes—
312C42—131no—
313C42—131no—
314C42—131no—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42C4×#26111yescharacteristic
325C42C4×#26111yescharacteristic
326C42C22×#26111yescharacteristic
327C42C22×#26111yescharacteristic
328C13#1732411yescharacteristic, complemented, Sylow
329C23—131no—
330C23—131no—
331C23—262no—
332C23—521no—
333C23—521no—
334C23C2×C4×#26111yescharacteristic
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—134no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—262no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4C2×C4×#26111yescharacteristic
363C2×C4C2×C4×#26111yescharacteristic
364C2×C4C2×C4×#26111yescharacteristic
365C2×C4C2×C4×#26111yescharacteristic
366C2×C4C2×C4×#26111yescharacteristic
367C2×C4C23×#26111yescharacteristic
368C8—24no—
369C8—264no—
370C8—264no—
371C8—268no—
372C8—264no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—132no—
377C22—261no—
378C22—261no—
379C22—261no—
380C22—261no—
381C22—261no—
382C22—524no—
383C22C22×C4×#26111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—132no—
389C4—132no—
390C4—261no—
391C4—261no—
392C4—261no—
393C4—261no—
394C4#1171909912yes—
395C4#1171962111yescharacteristic
396C4#1171962511yescharacteristic
397C2—41no—
398C2—262no—
399C2—521no—
400C2C2×#1171909911yescharacteristic
401C2#1313139911yescharacteristic
402C2#1313140211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#423C4
prime radicalC23×D13C42
cosocleC4×Dic13C24
hypercenter#423#261
hypocenterC13#17324
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
3. #13130058C2semidirect
4. #13130055C2semidirect
5. #13130048C2semidirect
6. #13130038C2semidirect
32. #1057⋊C8C22semidirect
33. #1057⋊C8C22semidirect
34. #11718251C22semidirect
35. C8×#1057C22semidirect
328. C13#17324semidirect

Maximal subgroups

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

subgroupindex
#131315152
D13⋊#4312
#131300582
#131300552
#131300482
#131300382
#131234682
#1732413