Finite Group Databasebeta

← #16792648

Subgroups — #16792648

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
2#13131513C211yesmaximal, characteristic
3#13130057C214yesmaximal, complemented
4#13130054C214yesmaximal, complemented
5#13130046C212yesmaximal, complemented
6C8×#6118C212yesmaximal, complemented
7D13×#431C211yesmaximal, characteristic
8C2×C42×D13C2211yescharacteristic
9#11719130C412yes—
10#11719128C412yes—
11#11719127C412yes—
12#11719127C412yes—
13#11719125C2212yes—
14#11719119C2212yes—
15#11719055C412yes—
16#11719054C412yes—
17#11719053C412yes—
18#11719052C412yes—
19#11719051C2212yes—
20#11719049C2212yes—
21C4×#6118C2212yes—
22C4×#6118C2212yes—
23C13×#431C411yescharacteristic
24#11718586C411yescharacteristic
25#11718494C2212yes—
26D13×C4⋊C8C412yes—
27D13×C22⋊C8C412yes—
28#11718379C2212yes—
29#11718346C411yescharacteristic
30#11718346C411yescharacteristic
31C4×C8×D13C2211yescharacteristic
32C4×C8×D13C2211yescharacteristic
33#1057⋊C8C2214yescomplemented
34#1057⋊C8C2214yescomplemented
35#11718251C2214yescomplemented
36C8×#1057C2214yescomplemented
37C22×C4×D13C2×C411yescharacteristic
38C22×C4×D13C2×C411yescharacteristic
39C22×C4×D13C2×C411yescharacteristic
40C2×#6118C2×C414yes—
41C2×#6118C2×C414yes—
42C2×C42×C13C2×C411yescharacteristic
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2311yescharacteristic
46C2×C8×D13C2×C412yes—
47C2×C8×D13C2×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#88111C2×C414yes—
61#88111C2×C414yes—
62#88110C2×C414yes—
63#88110C2×C414yes—
64C4⋊#1057C2×C414yes—
65C4⋊#1057C2×C414yes—
66C4×#1057C2314yes—
67C4×#1057C2314yes—
68C13×C4⋊C8C2×C412yes—
69C13×C22⋊C8C2×C412yes—
70C4×C8×C13C2×C411yescharacteristic
71C4×C8×C13C2×C411yescharacteristic
72C22⋊#1055C2×C412yes—
73#88060C2×C412yes—
74#88060C2×C412yes—
75#88054C2×C412yes—
76#88054C2×C412yes—
77C8×Dic13C2312yes—
78C8×Dic13C2312yes—
79C4⋊#1055C2×C412yes—
80C4×#1055C2×C411yescharacteristic
81C4×#1055C2×C411yescharacteristic
82#17324—131nomaximal, Sylow
83C23×D13C4211yescharacteristic
84C22×C4×C13C4211yescharacteristic
85C22×C4×C13C4211yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×Dic13C4211yescharacteristic
88C22×Dic13C22×C411yescharacteristic
89C22×Dic13C22×C411yescharacteristic
90C2×C4×D13—24no—
91C2×C4×D13—42no—
92C2×C4×D13—42no—
93C2×C4×D13C4211yescharacteristic
94C2×C4×D13C4211yescharacteristic
95C2×C4×D13C4211yescharacteristic
96C2×C4×D13C4211yescharacteristic
97C2×C4×D13C4211yescharacteristic
98C2×C4×D13C4211yescharacteristic
99C2×C4×D13C22×C411yescharacteristic
100C2×C4×D13C22×C411yescharacteristic
101C2×C4×D13C22×C411yescharacteristic
102C2×C4×D13C22×C411yescharacteristic
103C2×C4×D13C22×C411yescharacteristic
104C2×C4×D13C22×C411yescharacteristic
105C2×#1057C22×C418yes—
106C2×#1057C22×C418yes—
107#6118—28no—
108#6118—44no—
109C2×C8×C13C22×C412yes—
110C2×C8×C13C22×C412yes—
111C42×C13C4211yescharacteristic
112C42×C13C4211yescharacteristic
113C42×C13C22×C411yescharacteristic
114C42×C13C22×C411yescharacteristic
115C4×Dic13C4211yescharacteristic
116C4×Dic13C4211yescharacteristic
117C4×Dic13C4211yescharacteristic
118C4×Dic13C4211yescharacteristic
119C4×Dic13C22×C411yescharacteristic
120C4×Dic13C22×C411yescharacteristic
121C4×Dic13C22×C411yescharacteristic
122C4×Dic13C22×C411yescharacteristic
123C4×Dic13C22×C411yescharacteristic
124C4×Dic13C22×C411yescharacteristic
125C4×Dic13C22×C411yescharacteristic
126C4×Dic13C2411yescharacteristic
127C2×#1055C22×C412yes—
128C2×#1055C22×C412yes—
129C8×D13—42no—
130C8×D13—42no—
131#2920—131no—
132#2920—131no—
133C2×#431—131no—
134#1454—134no—
135#1453—134no—
136#1451—132no—
137C8×M16—132no—
138C23×C13C2×C4211yescharacteristic
139C22×D13—22no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13C2×C4211yescharacteristic
143C22×D13C2×C4211yescharacteristic
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13C2×C4211yescharacteristic
148C2×C4×C13C2×C4211yescharacteristic
149C2×C4×C13C2×C4211yescharacteristic
150C2×C4×C13C2×C4211yescharacteristic
151C2×C4×C13C2×C4211yescharacteristic
152C2×C4×C13C23×C411yescharacteristic
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—41no—
156C2×Dic13C2×C4211yescharacteristic
157C2×Dic13C2×C4211yescharacteristic
158C2×Dic13C2×C4211yescharacteristic
159C2×Dic13C2×C4211yescharacteristic
160C2×Dic13C23×C411yescharacteristic
161C2×Dic13C23×C411yescharacteristic
162C4×D13—22no—
163C4×D13—22no—
164C4×D13—22no—
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—28no—
176C8×C13—22no—
177C8×C13—22no—
178#1055—22no—
179#1055—22no—
180C22×C42—131no—
181#432—132no—
182#432—132no—
183#432—132no—
184#432—132no—
185#431—132no—
186#431—132no—
187#431—132no—
188#431—132no—
189#431—131no—
190#431—132no—
191#431—132no—
192#431—131no—
193#431—131no—
194#431#26111yescharacteristic
195#423—132no—
196#423—132no—
197C2×C4⋊C8—132no—
198#407—132no—
199#407—132no—
200C2×C22⋊C8—132no—
201C4×M16—132no—
202C4×M16—132no—
203C2×C4×C8—131no—
204C2×C4×C8—131no—
205#322—134no—
206#322—134no—
207#322—134no—
208C82—134no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13C22×C4211yescharacteristic
213C2×D13—21no—
214C2×D13—21no—
215C2×D13—21no—
216C2×D13—21no—
217C2×D13—21no—
218C2×D13—44no—
219C2×D13#40512yes—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13#40512yes—
225C4×C13#56812yes—
226Dic13—21no—
227Dic13—21no—
228Dic13—21no—
229Dic13—21no—
230Dic13C2×#13112yes—
231Dic13#56812yes—
232C23×C4—131no—
233C23×C4—131no—
234C23×C4—131no—
235C2×M16—134no—
236C2×M16—134no—
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⋊C8—132no—
258C4⋊C8C2×#26112yes—
259C22⋊C8—134no—
260C22⋊C8—134no—
261C22⋊C8—134no—
262C22⋊C8—134no—
263C22⋊C8—132no—
264C22⋊C8—132no—
265C22⋊C8—132no—
266C22⋊C8C2×#26112yes—
267#97—134no—
268#97—134no—
269C4×C8—134no—
270C4×C8—134no—
271C4×C8—132no—
272C4×C8—132no—
273C4×C8—131no—
274C4×C8—131no—
275C4×C8C2×#26111yescharacteristic
276C4×C8C2×#26111yescharacteristic
277C2×C13—41no—
278C2×C13C2×#40511yescharacteristic
279C2×C13#287311yescharacteristic
280C2×C13#287311yescharacteristic
281D13—22no—
282D13—41no—
283C24—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—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—264no—
300C22×C4—522no—
301C22×C4—522no—
302C22×C4C4×#26111yescharacteristic
303C22×C4C4×#26111yescharacteristic
304C22×C4C22×#26111yescharacteristic
305M16—268no—
306M16—524no—
307C2×C8—138no—
308C2×C8—138no—
309C2×C8—132no—
310C2×C8—132no—
311C2×C8—522no—
312C2×C8—522no—
313C2×C8C22×#26112yes—
314C2×C8C22×#26112yes—
315C42—131no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42—131no—
325C42—131no—
326C42—131no—
327C42C4×#26111yescharacteristic
328C42C4×#26111yescharacteristic
329C42C22×#26111yescharacteristic
330C42C22×#26111yescharacteristic
331C13#1732411yescharacteristic, complemented, Sylow
332C23—131no—
333C23—131no—
334C23—262no—
335C23—521no—
336C23—521no—
337C23C2×C4×#26111yescharacteristic
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—134no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
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—22no—
369C8—22no—
370C8—268no—
371C8—268no—
372C8—262no—
373C8—262no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—132no—
378C22—261no—
379C22—261no—
380C22—261no—
381C22—261no—
382C22—261no—
383C22—524no—
384C22C22×C4×#26111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—132no—
390C4—132no—
391C4—261no—
392C4—261no—
393C4—261no—
394C4—261no—
395C4#1171908912yes—
396C4#1171962912yes—
397C2—41no—
398C2—262no—
399C2—521no—
400C2C2×#1171908911yescharacteristic
401C2#1313139911yescharacteristic
402C2#1313140111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#431C4
prime radicalC23×D13C42
cosocleC4×Dic13C24
hypercenter#431#261
hypocenterC13#17324
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #13130057C2semidirect
4. #13130054C2semidirect
5. #13130046C2semidirect
6. C8×#6118C2semidirect
33. #1057⋊C8C22semidirect
34. #1057⋊C8C22semidirect
35. #11718251C22semidirect
36. C8×#1057C22semidirect
331. C13#17324semidirect

Maximal subgroups

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

subgroupindex
#131315152
#131315132
#131300572
#131300542
#131300462
C8×#61182
D13×#4312
#1732413