Finite Group Databasebeta

← #15753920

Subgroups — #15753920

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#13123531C211yesmaximal, characteristic
2#13114614C211yesmaximal, characteristic, complemented
3#13114610C211yesmaximal, characteristic, complemented
4#13113327C211yesmaximal, characteristic
5#13112724C211yesmaximal, characteristic, complemented
6#13112722C211yesmaximal, characteristic, complemented
7C13×#1501C211yesmaximal, characteristic
8C13×#525C2211yescharacteristic
9C2×#88202C411yescharacteristic, complemented
10C23×#1055C2211yescharacteristic
11C2×C13×C22⋊C8C2211yescharacteristic
12C4×C13×C22⋊C4C2211yescharacteristic
13#11718895C411yescharacteristic, complemented
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17C2×C8×Dic13—21no—
18#11718672—21no—
19#11718672—21no—
20D4×#1055—21no—
21D4×#1055—21no—
22#11718660C411yescharacteristic, complemented
23#11718658C411yescharacteristic, complemented
24C2×#88043—21no—
25C13×#328C412yescomplemented
26C13×#327C412yescomplemented
27#11718142—21no—
28#11718130C412yescomplemented
29#11718129C412yescomplemented
30#11718116—21no—
31C2×C13×#41C2×C411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C22×C8×C13—21no—
34C13×#123—21no—
35C13×C22⋊Q8C2×C411yescharacteristic
36C13×C22⋊Q8C2×C411yescharacteristic
37C13×#121C2×C411yescharacteristic
38C13×#121C2×C411yescharacteristic
39C13×#120—21no—
40C4×D4×C13—21no—
41C4×D4×C13—21no—
42C13×#117C2×C411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C42×C13—21no—
45C2×C22⋊Dic13—21no—
46#88202—42no—
47C2×C4×Dic13—21no—
48C2×#6099—21no—
49C2×#6099C2×C411yescharacteristic
50C2×#6099C2×C411yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C22×#1055—42no—
54C22×#1055C2×C411yescharacteristic
55C22×#1055C2×C411yescharacteristic
56C22×#1055D411yescharacteristic
57C22×#1055D411yescharacteristic
58C22×#1055D411yescharacteristic
59C22×#1055D411yescharacteristic
60C13×C22⋊C8—21no—
61C13×C22⋊C8C2×C412yes—
62C13×#95C2×C412yes—
63#88071C2×C412yes—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055C2×C412yes—
70C8×Dic13—42no—
71C4⋊#1055—21no—
72C4⋊#1055—21no—
73#88043—21no—
74#88043—42no—
75C4×#1055—21no—
76#8240—131nomaximal, Sylow
77C24×C13#4111yescharacteristic
78C13×#41—41no—
79C13×#41—41no—
80C2×Q8×C13C4211yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13C4211yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—22no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×Dic13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4C4211yescharacteristic
102C13×C4⋊C4C4211yescharacteristic
103C13×C22⋊C4—21no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C13×C22⋊C4—42no—
109C42×C13—21no—
110C42×C13—41no—
111C42×C13—41no—
112C22⋊Dic13—24no—
113C4×Dic13—41no—
114C4×Dic13—41no—
115#6099—42no—
116#6099—41no—
117#6099—41no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055—21no—
122C2×#1055—21no—
123C2×#1055—22no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—42no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055C22⋊C411yescharacteristic
131C2×#1055C22⋊C411yescharacteristic
132C2×#1055C22⋊C411yescharacteristic
133C2×#1055C22⋊C411yescharacteristic
134#2929—131no—
135#1752—131no—
136C8×C22⋊C4—131no—
137#1501—131no—
138#1501D1311yescharacteristic
139#1298—131no—
140#1297—131no—
141C23×C13—22no—
142C23×C13—22no—
143C23×C13—21no—
144C23×C13—41no—
145C23×C13#11711yescharacteristic
146C23×C13C4×D411yescharacteristic
147C23×C13C4×D411yescharacteristic
148Q8×C13—41no—
149D4×C13—41no—
150D4×C13—42no—
151D4×C13—42no—
152D4×C13—42no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13C2×C4211yescharacteristic
171C2×C4×C13C2×C22⋊C411yescharacteristic
172C2×C4×C13C4×D411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C2×Dic13—24no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C8×C13—42no—
178#1055—21no—
179#1055—21no—
180#1055—21no—
181#1055—42no—
182#1055—41no—
183#1055—41no—
184#1055#9912yes—
185C2×#131—131no—
186C23×C8—131no—
187#525C2×D1311yescharacteristic
188#435—261no—
189#435—261no—
190C8×D4—261no—
191C8×D4—261no—
192#424—131no—
193#408—131no—
194#407—131no—
195C2×C22⋊C8—131no—
196C2×C22⋊C8C2×D1311yescharacteristic
197#405—131no—
198C2×#97—261no—
199C2×C4×C8—261no—
200C4×C22⋊C4—131no—
201C4×C22⋊C4C2×D1311yescharacteristic
202#336—261no—
203#336—261no—
204#328—132no—
205#328Dic1312yescomplemented
206#327—132no—
207#327Dic1312yescomplemented
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×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13C4×C22⋊C411yescharacteristic
220C22×C13#44312yes—
221C22×C13#44412yes—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—41no—
226C4×C13—41no—
227C4×C13—41no—
228C4×C13—82no—
229C4×C13C2×#9911yescharacteristic
230C4×C13#41011yescharacteristic
231Dic13—44no—
232C2×#41C4×D1311yescharacteristic
233C23×C4C22×D1311yescharacteristic
234#131—522no—
235C2×M16—131no—
236C2×M16—131no—
237C2×M16—261no—
238C22×C8—21no—
239C22×C8—131no—
240C22×C8—131no—
241C22×C8—131no—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8—261no—
246C22×C8—261no—
247C22×C8—522no—
248#123—21no—
249C22⋊Q8C4×D1311yescharacteristic
250C22⋊Q8C2×Dic1311yescharacteristic
251#121C4×D1311yescharacteristic
252#121C2×Dic1311yescharacteristic
253#120—21no—
254C4×D4—21no—
255C4×D4—21no—
256#117C4×D1311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—261no—
259C2×C42—21no—
260C2×C42—261no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C22⋊C8—21no—
264C22⋊C8—132no—
265C22⋊C8—261no—
266C22⋊C8—261no—
267C22⋊C8—261no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C22⋊C8C2×Dic1312yes—
271#97—261no—
272#97—522no—
273C4×C8—261no—
274C4×C8—522no—
275#95—132no—
276#95C2×Dic1312yes—
277C2×C13—22no—
278C2×C13—22no—
279C2×C13—41no—
280C2×C13—81no—
281C2×C13C4×#9911yescharacteristic
282C2×C13#176411yescharacteristic
283C2×C13#176511yescharacteristic
284C24#612911yescharacteristic
285#41—41no—
286#41—41no—
287C2×Q8C4×Dic1311yescharacteristic
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4C4×Dic1311yescharacteristic
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—262no—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4C2×C4×D1311yescharacteristic
299C22×C4D4×D1311yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C22×C4#612911yescharacteristic
302C22×C4C22×Dic1311yescharacteristic
303M16—522no—
304M16—521no—
305M16—521no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—131no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—131no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—261no—
317C2×C8—261no—
318C2×C8—262no—
319C2×C8—521no—
320C2×C8—521no—
321C2×C8—521no—
322C2×C8—522no—
323C2×C8—521no—
324C2×C8—521no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4C4×Dic1311yescharacteristic
328C4⋊C4C4×Dic1311yescharacteristic
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—42no—
335C22⋊C4—264no—
336C42—21no—
337C42—41no—
338C42—41no—
339C42—521no—
340C42—521no—
341C13#824011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23—21no—
345C23—41no—
346C23#8813111yescharacteristic
347C23#8813511yescharacteristic
348C23D4×Dic1311yescharacteristic
349Q8—41no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—42no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—264no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4C22⋊C4×D1311yescharacteristic
375C2×C4#8813511yescharacteristic
376C2×C4C2×C4×Dic1311yescharacteristic
377C2×C4D4×Dic1311yescharacteristic
378C8—42no—
379C8—132no—
380C8—261no—
381C8—261no—
382C8—261no—
383C8—522no—
384C8—521no—
385C8—521no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22#1171848412yes—
398C22C22⋊C4×Dic1311yescharacteristic
399C22#1171885712yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—82no—
407C4—524no—
408C4#1171840111yescharacteristic
409C4D13×#9911yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—81no—
414C2#99×Dic1311yescharacteristic
415C2#1311467611yescharacteristic
416C2#1311468111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#1501C2
socleC22×C13C4×C22⋊C4
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#1501D13
hypocenterC13#8240
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #13114614C2semidirect
3. #13114610C2semidirect
5. #13112724C2semidirect
6. #13112722C2semidirect
9. C2×#88202C4semidirect
13. #11718895C4semidirect
22. #11718660C4semidirect
23. #11718658C4semidirect
25. C13×#328C4semidirect
26. C13×#327C4semidirect
28. #11718130C4semidirect
29. #11718129C4semidirect
205. #328Dic13semidirect
207. #327Dic13semidirect
341. C13#8240semidirect

Maximal subgroups

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

subgroupindex
#131235312
#131146142
#131146102
#131133272
#131127242
#131127222
C13×#15012
#824013