Finite Group Databasebeta

← #15753914

Subgroups — #15753914

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123526C211yesmaximal, characteristic
2#13114614C211yesmaximal, characteristic, complemented
3C22⋊C4×#1055C211yesmaximal, characteristic, complemented
4#13113325C211yesmaximal, characteristic
5#13113325C211yesmaximal, characteristic
6#13112723C211yesmaximal, characteristic, complemented
7C13×#1297C211yesmaximal, characteristic, complemented
8#11719496C2211yescharacteristic
9C23×#1055C2211yescharacteristic
10C2×#88161C411yescharacteristic, complemented
11C13×#407C2211yescharacteristic
12C4×C13×C22⋊C4C2211yescharacteristic
13C4×C13×C22⋊C4C2211yescharacteristic
14C2×C22⋊#1055C2211yescharacteristic
15C2×C22⋊#1055C2211yescharacteristic
16#11718790C411yescharacteristic, complemented
17#11718783C411yescharacteristic, complemented
18#11718780C411yescharacteristic, complemented
19C2×#88043—21no—
20C2×C4×#1055—21no—
21#11718391—21no—
22#11718391—21no—
23#11718386—21no—
24#11718386—21no—
25#11718116—21no—
26#11718116—21no—
27#11718044C412yescomplemented
28#11718044C412yescomplemented
29#11718043C412yescomplemented
30#11718043C412yescomplemented
31C23×C4×C13C2311yescharacteristic
32C2×#6127C2×C411yescharacteristic
33C2×C13×M16C2×C411yescharacteristic
34C2×C13×M16C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39#88207—21no—
40#88184C2×C411yescharacteristic
41#88184C2×C411yescharacteristic
42#88183—21no—
43C4×C22⋊D13—21no—
44C4×C22⋊D13—21no—
45#88180C2×C411yescharacteristic
46#88178C2×C411yescharacteristic
47#88178C2×C411yescharacteristic
48C22×#1055—21no—
49C22×#1055—21no—
50C22×#1055—42no—
51C22×#1055C2×C411yescharacteristic
52C22×#1055C2×C411yescharacteristic
53C22×#1055D411yescharacteristic
54C22×#1055D411yescharacteristic
55C22×#1055D411yescharacteristic
56C22×#1055D411yescharacteristic
57#88161—42no—
58C2×#6094—21no—
59C2×C8×D13—21no—
60C13×C22⋊C8—21no—
61C13×C22⋊C8—21no—
62C13×#95C2×C412yes—
63C13×#95C2×C412yes—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66C22⋊#1055C2×C412yes—
67C22⋊#1055C2×C412yes—
68#88060—21no—
69#88060—21no—
70#88055—21no—
71#88054—21no—
72#88054—21no—
73C8×Dic13—21no—
74#88043—42no—
75C4×#1055—42no—
76#8240—131nomaximal, Sylow
77C24×C13#4111yescharacteristic
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4111yescharacteristic
88C2×C22⋊D13—21no—
89C2×C22⋊D13—21no—
90C2×C22⋊D13—21no—
91#6127—41no—
92#6127—41no—
93C2×D52C4211yescharacteristic
94C2×C4×D13—21no—
95C2×Dic26C4211yescharacteristic
96C13×M16—41no—
97C13×M16—41no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C13×C22⋊C4—24no—
101C13×C22⋊C4—42no—
102C42×C13—41no—
103C42×C13—41no—
104C42×C13—41no—
105C42×C13—41no—
106C22⋊Dic13—21no—
107C22⋊Dic13—21no—
108C22⋊Dic13—21no—
109#6103—21no—
110#6103—21no—
111C4⋊Dic13C4211yescharacteristic
112C4⋊Dic13C4211yescharacteristic
113#6101—21no—
114#6101—21no—
115C4×Dic13—21no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—41no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055C22⋊C411yescharacteristic
129C2×#1055C22⋊C411yescharacteristic
130C2×#1055C22⋊C411yescharacteristic
131C2×#1055C22⋊C411yescharacteristic
132#6094—42no—
133C8×D13—42no—
134#2929—131no—
135#1752—131no—
136C8×C22⋊C4—131no—
137#1501—131no—
138#1501—131no—
139#1298—131no—
140#1297D1311yescharacteristic, complemented
141C23×C13—22no—
142C23×C13—22no—
143C23×C13—41no—
144C23×C13#11711yescharacteristic
145C23×C13C4×D411yescharacteristic
146C23×C13C4×D411yescharacteristic
147C22×D13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—24no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13C2×C4211yescharacteristic
164C2×C4×C13C2×C22⋊C411yescharacteristic
165C2×C4×C13C4×D411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C22⋊D13—42no—
168C22⋊D13—42no—
169C22⋊D13—42no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173D52—41no—
174C4×D13—41no—
175C4×D13—41no—
176Dic26—41no—
177C8×C13—41no—
178C8×C13—41no—
179#1055—21no—
180#1055—21no—
181#1055—21no—
182#1055—42no—
183#1055—42no—
184#1055#9912yes—
185C2×#131—131no—
186C23×C8—131no—
187#525—131no—
188#435—261no—
189#435—261no—
190C8×D4—261no—
191C8×D4—261no—
192#424—131no—
193#408—131no—
194#407C2×D1311yescharacteristic
195C2×C22⋊C8—131no—
196C2×C22⋊C8—131no—
197#405—131no—
198C2×#97—261no—
199C2×C4×C8—261no—
200C4×C22⋊C4C2×D1311yescharacteristic
201C4×C22⋊C4C2×D1311yescharacteristic
202#336—261no—
203#336—261no—
204#328—132no—
205#328—132no—
206#327—132no—
207#327—132no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—44no—
216C22×C13C4×C22⋊C411yescharacteristic
217C22×C13#44312yes—
218C22×C13#44412yes—
219C2×D13—41no—
220C2×D13—41no—
221C2×D13—41no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—44no—
226C4×C13—82no—
227C4×C13C2×#9911yescharacteristic
228C4×C13#41011yescharacteristic
229Dic13—41no—
230Dic13—41no—
231Dic13—41no—
232C2×#41—131no—
233C23×C4C22×D1311yescharacteristic
234#131—522no—
235C2×M16—261no—
236C2×M16C4×D1311yescharacteristic
237C2×M16C4×D1311yescharacteristic
238C22×C8—131no—
239C22×C8—131no—
240C22×C8—131no—
241C22×C8—131no—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8—261no—
245C22×C8—261no—
246C22×C8—261no—
247C22×C8—522no—
248#123—261no—
249C22⋊Q8—131no—
250C22⋊Q8—131no—
251#121—131no—
252#121—131no—
253#120—261no—
254C4×D4—261no—
255C4×D4—261no—
256#117—131no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C42—21no—
260C2×C42—21no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—132no—
266C22⋊C8—132no—
267C22⋊C8—261no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C22⋊C8—261no—
271#97—261no—
272#97—522no—
273C4×C8—261no—
274C4×C8—522no—
275#95C4×D1312yes—
276#95C4×D1312yes—
277C2×C13—22no—
278C2×C13—22no—
279C2×C13—41no—
280C2×C13C4×#9911yescharacteristic
281C2×C13#176411yescharacteristic
282C2×C13#176511yescharacteristic
283D13—81no—
284C24#612911yescharacteristic
285#41—521no—
286#41—521no—
287C2×Q8—131no—
288C2×D4—131no—
289C2×D4—261no—
290C2×D4—261no—
291C2×D4—261no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—261no—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4C2×C4×D1311yescharacteristic
299C22×C4C2×C4×D1311yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C22×C4D4×D1311yescharacteristic
302C22×C4#613111yescharacteristic
303M16—41no—
304M16—41no—
305M16—522no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—131no—
309C2×C8—131no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—262no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—262no—
317C2×C8—522no—
318C2×C8—521no—
319C2×C8—521no—
320C2×C8—521no—
321C2×C8—521no—
322C2×C8—521no—
323C2×C8—521no—
324C2×C8—521no—
325C4⋊C4—131no—
326C4⋊C4—131no—
327C4⋊C4—261no—
328C4⋊C4—261no—
329C22⋊C4—24no—
330C22⋊C4—42no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—261no—
335C22⋊C4—261no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—261no—
341C13#824011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23—41no—
345C23—261no—
346C23#8813511yescharacteristic
347C23#8813511yescharacteristic
348C23#8814611yescharacteristic
349Q8—521no—
350D4—521no—
351D4—522no—
352D4—522no—
353D4—522no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—261no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4C42×D1311yescharacteristic
375C2×C4C22⋊C4×D1311yescharacteristic
376C2×C4#8814711yescharacteristic
377C2×C4#8814711yescharacteristic
378C8—41no—
379C8—41no—
380C8—132no—
381C8—261no—
382C8—261no—
383C8—261no—
384C8—522no—
385C8—522no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—521no—
395C22—521no—
396C22—521no—
397C22#1171832711yescharacteristic
398C22#1171848412yes—
399C22#1171848512yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—82no—
405C4—521no—
406C4—521no—
407C4—521no—
408C4#1171840111yescharacteristic
409C4D13×#9911yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—1041no—
414C2#1311462311yescharacteristic
415C2#1311467011yescharacteristic
416C2#1311467711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1297C2
socleC22×C13C4×C22⋊C4
prime radical#11719496C22
cosocleC23×C4×C13C23
hypercenter#1297D13
hypocenterC13#8240
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #13114614C2semidirect
3. C22⋊C4×#1055C2semidirect
6. #13112723C2semidirect
7. C13×#1297C2semidirect
10. C2×#88161C4semidirect
16. #11718790C4semidirect
17. #11718783C4semidirect
18. #11718780C4semidirect
27. #11718044C4semidirect
28. #11718044C4semidirect
29. #11718043C4semidirect
30. #11718043C4semidirect
140. #1297D13semidirect
341. C13#8240semidirect

Maximal subgroups

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

subgroupindex
#131235262
#131146142
C22⋊C4×#10552
#131133252
#131127232
C13×#12972
#824013