Finite Group Databasebeta

← #15754507

Subgroups — #15754507

Order 3328.

846 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114935C212yesmaximal, complemented
2C4×#88074C211yesmaximal, characteristic, complemented
3#13113352C212yesmaximal, complemented
4#13113174C211yesmaximal, characteristic, complemented
5C2×C13×#555C211yesmaximal, characteristic
6C13×#555—24no—
7C13×#555—24no—
8C2×C13×C4⋊Q8C411yescharacteristic, complemented
9C2×C13×#124—21no—
10C2×C13×#124—21no—
11C2×C13×#121—21no—
12C2×C13×#121C411yescharacteristic, complemented
13C2×C13×#121C2211yescharacteristic
14C2×C4×D4×C13C411yescharacteristic, complemented
15C2×C4×D4×C13C2211yescharacteristic
16C2×C13×#117—21no—
17C2×C13×#117C411yescharacteristic, complemented
18C2×C13×#117C2211yescharacteristic
19C2×#88074—21no—
20C4×C22⋊Dic13C2212yes—
21#11718868C2212yes—
22#11718129—24no—
23#11718124—24no—
24#11718120—21no—
25#11718118—21no—
26#11718117—21no—
27C22×Q8×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D4×C13C2×C411yescharacteristic
31C22×D4×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C13×C4⋊Q8—22no—
36C13×C4⋊Q8—22no—
37C13×#124—28no—
38C13×#124—28no—
39C13×#121—28no—
40C13×#121—22no—
41C13×#121—22no—
42C13×#121—22no—
43C13×#121D414yes—
44C4×D4×C13—22no—
45C4×D4×C13—22no—
46C4×D4×C13—22no—
47C4×D4×C13—22no—
48C13×#117—28no—
49C13×#117—22no—
50C13×#117—22no—
51C13×#117—22no—
52C13×#117D414yes—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4D411yescharacteristic
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×C4×Dic13—22no—
70C2×#6099—22no—
71#88074—24no—
72#88071—22no—
73C22⋊#1055—22no—
74C22⋊#1055—22no—
75#8360—131nomaximal, Sylow
76C24×C13—21no—
77C24×C13C22⋊C411yescharacteristic
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—24no—
80C2×Q8×C13—82no—
81C2×D4×C13—22no—
82C2×D4×C13—24no—
83C2×D4×C13—24no—
84C2×D4×C13—22no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C2×D4×C13—42no—
88C2×D4×C13—82no—
89C2×D4×C13—82no—
90C2×D4×C13C22⋊C412yes—
91C22×C4×C13—24no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13C22⋊C411yescharacteristic
102C22×C4×C13C22⋊C411yescharacteristic
103C22×C4×C13C22⋊C411yescharacteristic
104C22×C4×C13C22×C411yescharacteristic
105C22×C4×C13C2×D412yes—
106C22×C4×C13C2×D412yes—
107C22×C4×C13C2×D411yescharacteristic
108C22×Dic13—42no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4C22⋊C412yes—
115C13×C4⋊C4C22⋊C412yes—
116C13×C4⋊C4C22⋊C412yes—
117C13×C22⋊C4—24no—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—24no—
120C13×C22⋊C4—24no—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—24no—
123C13×C22⋊C4—22no—
124C42×C13—24no—
125C42×C13—21no—
126C42×C13—21no—
127C42×C13—24no—
128C22⋊Dic13—24no—
129C22⋊Dic13—42no—
130C4×Dic13—44no—
131#6099—44no—
132C2×#1055—42no—
133C2×#555D1311yescharacteristic
134#1826—132no—
135C4×#99—131no—
136#1507—132no—
137#1465—131no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—22no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13C2×C22⋊C411yescharacteristic
153C23×C13#12012yes—
154Q8×C13—84no—
155D4×C13—44no—
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—84no—
159D4×C13—84no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—24no—
163C2×C4×C13—22no—
164C2×C4×C13—21no—
165C2×C4×C13—22no—
166C2×C4×C13—21no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—41no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—48no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13#10412yes—
181C2×C4×C13C2×C22⋊C411yescharacteristic
182C2×C4×C13C2×C22⋊C411yescharacteristic
183C2×C4×C13#12012yes—
184C2×Dic13—44no—
185C2×Dic13—82no—
186C2×Dic13—82no—
187#1055—82no—
188#555—24no—
189#555—24no—
190C2×C4⋊Q8Dic1311yescharacteristic, complemented
191C2×#124—21no—
192C2×#124—21no—
193C2×#121—21no—
194C2×#121Dic1311yescharacteristic, complemented
195C2×#121C2×D1311yescharacteristic
196C2×C4×D4Dic1311yescharacteristic, complemented
197C2×C4×D4C2×D1311yescharacteristic
198C2×#117—21no—
199C2×#117Dic1311yescharacteristic, complemented
200C2×#117C2×D1311yescharacteristic
201C2×#99—261no—
202#407—132no—
203C4×C22⋊C4—132no—
204#342—261no—
205#339—264no—
206#327—264no—
207#324—261no—
208#323—261no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—41no—
215C22×C13—42no—
216C22×C13—41no—
217C22×C13—42no—
218C22×C13—42no—
219C22×C13—41no—
220C22×C13—81no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—82no—
225C22×C13—82no—
226C22×C13#37911yescharacteristic
227C22×C13C2×#10411yescharacteristic
228C22×C13#42111yescharacteristic
229C4×C13—22no—
230C4×C13—21no—
231C4×C13—22no—
232C4×C13—42no—
233C4×C13—42no—
234C4×C13—41no—
235C4×C13—41no—
236C4×C13—42no—
237C4×C13#41012yes—
238Dic13—84no—
239C22×Q8—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4C2×Dic1311yescharacteristic
243C22×D4C22⋊D1311yescharacteristic
244C23×C4—21no—
245C23×C4C2×Dic1311yescharacteristic
246C23×C4C22×D1311yescharacteristic
247C2×M16—262no—
248C4⋊Q8—22no—
249C4⋊Q8—22no—
250#124—28no—
251#124—28no—
252#121—28no—
253#121—22no—
254#121—22no—
255#121—22no—
256#121C22⋊D1314yes—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261#117—28no—
262#117—22no—
263#117—22no—
264#117—22no—
265#117C22⋊D1314yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C2×Dic1311yescharacteristic
268C2×C4⋊C4C2×Dic1311yescharacteristic
269C2×C4⋊C4C2×Dic1311yescharacteristic
270C2×C4⋊C4C22⋊D1311yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—262no—
277C2×C22⋊C4C22⋊D1311yescharacteristic
278C2×C22⋊C4C22⋊D1311yescharacteristic
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—262no—
282C2×C42C2×Dic1311yescharacteristic
283#99—264no—
284C22⋊C8—262no—
285C22⋊C8—262no—
286#95—262no—
287C2×C13—21no—
288C2×C13—21no—
289C2×C13—42no—
290C2×C13—81no—
291C2×C13—82no—
292C2×C13#178211yescharacteristic
293C2×C13#178911yescharacteristic
294C2×C13#179511yescharacteristic
295C24—21no—
296C24C22⋊Dic1311yescharacteristic
297C24C2×C22⋊D1311yescharacteristic
298C2×Q8—24no—
299C2×Q8—82no—
300C2×D4—22no—
301C2×D4—24no—
302C2×D4—24no—
303C2×D4—22no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—82no—
308C2×D4—82no—
309C2×D4C22⋊Dic1312yes—
310C22×C4—24no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—522no—
321C22×C4C22⋊Dic1311yescharacteristic
322C22×C4C22⋊Dic1311yescharacteristic
323C22×C4C22⋊Dic1311yescharacteristic
324C22×C4C22×Dic1311yescharacteristic
325C22×C4C2×C22⋊D1312yes—
326C22×C4C2×C22⋊D1312yes—
327C22×C4C2×C22⋊D1311yescharacteristic
328M16—524no—
329C2×C8—522no—
330C4⋊C4—24no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—22no—
335C4⋊C4C22⋊Dic1312yes—
336C4⋊C4C22⋊Dic1312yes—
337C4⋊C4C22⋊Dic1312yes—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—22no—
343C22⋊C4—24no—
344C22⋊C4—22no—
345C22⋊C4—264no—
346C22⋊C4—522no—
347C42—24no—
348C42—21no—
349C42—21no—
350C42—24no—
351C42—524no—
352C13#836011yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C2×C22⋊Dic1311yescharacteristic
368C23#8820712yes—
369Q8—84no—
370D4—44no—
371D4—42no—
372D4—42no—
373D4—84no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—48no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—524no—
396C2×C4—1042no—
397C2×C4—1042no—
398C2×C4#8807712yes—
399C2×C4C2×C22⋊Dic1311yescharacteristic
400C2×C4C2×C22⋊Dic1311yescharacteristic
401C2×C4#8820712yes—
402C8—1042no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—41no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22C2×#8807711yescharacteristic
421C22#1171889711yescharacteristic
422C22#1171890811yescharacteristic
423C4—22no—
424C4—21no—
425C4—22no—
426C4—41no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—41no—
431C4—1044no—
432C4#1171890112yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—82no—
437C2—81no—
438C2#1311475411yescharacteristic
439C2#1311478011yescharacteristic
440C2#1311480611yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#555C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenterC2×#555D13
hypocenterC13#8360
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #13114935C2semidirect
2. C4×#88074C2semidirect
3. #13113352C2semidirect
4. #13113174C2semidirect
8. C2×C13×C4⋊Q8C4semidirect
12. C2×C13×#121C4semidirect
14. C2×C4×D4×C13C4semidirect
17. C2×C13×#117C4semidirect
190. C2×C4⋊Q8Dic13semidirect
194. C2×#121Dic13semidirect
196. C2×C4×D4Dic13semidirect
199. C2×#117Dic13semidirect
352. C13#8360semidirect

Maximal subgroups

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

subgroupindex
#131149352
C4×#880742
#131133522
#131131742
C2×C13×#5552
#836013