Finite Group Databasebeta

← #15830657

Subgroups — #15830657

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128688C211yesmaximal, characteristic
2#13123860C211yesmaximal, characteristic, complemented
3#13113399C211yesmaximal, characteristic, complemented
4#13113395C211yesmaximal, characteristic, complemented
5#13113390C214yesmaximal, complemented
6#13113334C211yesmaximal, characteristic, complemented
7#13113330C211yesmaximal, characteristic, complemented
8#13113325C214yesmaximal, complemented
9C13×#2357C211yesmaximal, characteristic, complemented
10C2×C4×D4×C13C2211yescharacteristic
11#11719510—21no—
12#11719496C2214yes—
13#11719268C412yescomplemented
14#11719264—22no—
15#11719263—22no—
16#11719258C412yescomplemented
17#11719256C412yescomplemented
18#11719247C412yescomplemented
19#11719209—21no—
20#11719199—22no—
21#11719182C2211yescharacteristic
22#11719175C2211yescharacteristic
23C13×#390—21no—
24C13×#388—22no—
25C13×#382C2211yescharacteristic
26C13×#381C2212yes—
27C4×C13×C4⋊C4—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2212yes—
30C2×C22⋊#1055C2214yes—
31D4×#1055—22no—
32D4×#1055—22no—
33#11718586C2211yescharacteristic
34#11718586C2211yescharacteristic
35#11718044C2212yes—
36#11718044C2214yes—
37#11718044C2212yes—
38#11718043C2212yes—
39#11718043C2214yes—
40#11718043C2212yes—
41C22×D4×C13D411yescharacteristic
42C23×C4×C13C2312yes—
43C2×#6127—21no—
44C2×#6127C2×C414yes—
45C4×D4×C13C2×C412yes—
46C4×D4×C13C2×C412yes—
47C4×D4×C13D412yes—
48C4×D4×C13D412yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C22⋊C4—22no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4D412yes—
55C2×C42×C13—21no—
56C2×C42×C13—22no—
57C2×C42×C13C2311yescharacteristic
58#88207—24no—
59#88194—22no—
60#88192—22no—
61#88192—22no—
62#88190—22no—
63#88184—21no—
64#88184C2×C414yes—
65#88184C2312yes—
66#88183—24no—
67C4×C22⋊D13—24no—
68C4×C22⋊D13—24no—
69#88180—21no—
70#88180C2×C414yes—
71#88178—21no—
72#88178C2×C414yes—
73#88178C2312yes—
74C22×#1055—24no—
75#88147—22no—
76#88146—22no—
77C4⋊C4×D13—22no—
78#88141—22no—
79#88139—24no—
80#88138—24no—
81#88137—24no—
82#88133—24no—
83#88129—21no—
84#88128C2×C411yescharacteristic
85C4×D52—21no—
86C4×D52C2×C412yes—
87#88124—21no—
88#88123C2×C411yescharacteristic
89#88123C2×C411yescharacteristic
90#88123C2×C411yescharacteristic
91C4×Dic26—21no—
92C4×Dic26C2×C412yes—
93C13×#95—22no—
94C13×#95—21no—
95C13×#95C2311yescharacteristic
96C13×#95C2312yes—
97C13×#95C2311yescharacteristic
98C22⋊#1055—24no—
99C22⋊#1055C2312yes—
100C22⋊#1055C2312yes—
101C4⋊#1055—21no—
102C4⋊#1055—21no—
103C4×#1055—21no—
104C4×#1055—21no—
105#17617—131nomaximal, Sylow
106C24×C13C2×D412yes—
107C2×D4×C13—22no—
108C2×D4×C13—22no—
109C2×D4×C13C22⋊C412yes—
110C2×D4×C13C22⋊C412yes—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—82no—
115C22×C4×C13C22×C414yes—
116C22×C4×C13C2×D414yes—
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2411yescharacteristic
121C2×C22⋊D13—22no—
122C2×C22⋊D13—24no—
123C2×C22⋊D13—24no—
124#6127—42no—
125#6127—42no—
126#6127—84no—
127C2×D52—21no—
128C2×D52—21no—
129C2×D52C22×C412yes—
130C2×C4×D13—22no—
131C2×C4×D13—24no—
132C2×Dic26—21no—
133C2×Dic26—21no—
134C2×Dic26C22×C412yes—
135C13×C4⋊C4—42no—
136C13×C4⋊C4—42no—
137C13×C4⋊C4C22⋊C412yes—
138C13×C4⋊C4C22⋊C412yes—
139C13×C22⋊C4—44no—
140C13×C22⋊C4—82no—
141C13×C22⋊C4C22⋊C414yes—
142C13×C22⋊C4C22⋊C414yes—
143C42×C13—42no—
144C42×C13—82no—
145C42×C13C22×C411yescharacteristic
146C42×C13C22×C411yescharacteristic
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C22⋊Dic13—24no—
150C22⋊Dic13—24no—
151C22⋊Dic13—22no—
152#6103—22no—
153#6103—24no—
154#6103—22no—
155C4⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13—21no—
158C4⋊Dic13—21no—
159C4⋊Dic13C22×C412yes—
160C4⋊Dic13C22×C412yes—
161#6101—22no—
162#6101—24no—
163#6101—22no—
164C4×Dic13—22no—
165C4×Dic13—24no—
166C2×#1055—22no—
167C2×#1055—22no—
168C2×#1055—84no—
169#3506—131no—
170#2972—131no—
171#2357D1311yescharacteristic, complemented
172#1518—131no—
173#1517—131no—
174#1516—134no—
175#1503—131no—
176#1502—131no—
177#1501—134no—
178C23×C13—22no—
179C23×C13—22no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13C2×C22⋊C414yes—
183C23×C13C22×D411yescharacteristic
184C22×D13—22no—
185D4×C13—24no—
186D4×C13—24no—
187C2×C4×C13—22no—
188C2×C4×C13—44no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—44no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—41no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13C2×C22⋊C414yes—
202C2×C4×C13C2×C22⋊C411yescharacteristic
203C2×C4×C13C2×C22⋊C411yescharacteristic
204C2×C4×C13C2×C22⋊C411yescharacteristic
205C2×C4×C13C2×C22⋊C411yescharacteristic
206C2×C4×C13#13512yes—
207C2×C4×C13#13512yes—
208C2×C4×C13C23×C411yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C22⋊D13—42no—
211C22⋊D13—42no—
212C22⋊D13—84no—
213C22⋊D13—84no—
214C2×Dic13—22no—
215C2×Dic13—22no—
216C2×Dic13—22no—
217D52—42no—
218D52—42no—
219D52—81no—
220C4×D13—44no—
221C4×D13—84no—
222Dic26—42no—
223Dic26—42no—
224Dic26—81no—
225#1055—42no—
226#1055—42no—
227#559—262no—
228#556—132no—
229#555—132no—
230#553—262no—
231#550—132no—
232#547—132no—
233#538—262no—
234#535—261no—
235#533—131no—
236#532—131no—
237#525—134no—
238#520—261no—
239C2×C4×D4C2×D1311yescharacteristic
240C8×D4—262no—
241C8×D4—262no—
242#431—131no—
243#431—131no—
244C2×C22⋊C8—134no—
245#390—21no—
246#388—22no—
247#382C2×D1311yescharacteristic
248#381C2×D1312yes—
249C4×C4⋊C4—21no—
250C4×C4⋊C4C2×D1311yescharacteristic
251C4×C22⋊C4C2×D1312yes—
252#328—132no—
253#328—134no—
254#328—132no—
255#327—132no—
256#327—134no—
257#327—132no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—24no—
261C22×C13—24no—
262C22×C13—24no—
263C22×C13—82no—
264C22×C13—82no—
265C22×C13C22×C22⋊C411yescharacteristic
266C22×C13C2×#13511yescharacteristic
267C22×C13C2×#13511yescharacteristic
268C2×D13—42no—
269C2×D13—42no—
270C2×D13—42no—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—24no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—42no—
277C4×C13—81no—
278C4×C13—82no—
279C4×C13#41612yes—
280C4×C13#41612yes—
281Dic13—42no—
282Dic13—42no—
283Dic13—42no—
284C2×#41—134no—
285C2×#41—261no—
286C22×D4C22⋊D1311yescharacteristic
287C23×C4C22×D1312yes—
288C22×C8—264no—
289C4⋊Q8—131no—
290C4⋊Q8—131no—
291C4⋊Q8—131no—
292#127—131no—
293#127—262no—
294#126—264no—
295#125—261no—
296#124—262no—
297#124—264no—
298#124—261no—
299#123—264no—
300#123—264no—
301C22⋊Q8—134no—
302C22⋊Q8—132no—
303C22⋊Q8—261no—
304#121—134no—
305#121—132no—
306#121—262no—
307#121—262no—
308#121—261no—
309#121—264no—
310#120—264no—
311C4×Q8—132no—
312C4×Q8—262no—
313C4×Q8—261no—
314C4×D4—132no—
315C4×D4—264no—
316C4×D4—264no—
317C4×D4—262no—
318C4×D4—261no—
319C4×D4C4×D1312yes—
320C4×D4C4×D1312yes—
321C4×D4D5212yes—
322C4×D4D5212yes—
323#117—134no—
324#117—261no—
325#117—262no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—262no—
329C2×C4⋊C4C22⋊D1311yescharacteristic
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4C22⋊D1312yes—
333C2×C42—21no—
334C2×C42—22no—
335C2×C42C22×D1311yescharacteristic
336C4⋊C8—261no—
337C4⋊C8—261no—
338C22⋊C8—132no—
339C22⋊C8—132no—
340C22⋊C8—264no—
341C4×C8—261no—
342C4×C8—261no—
343#95—22no—
344#95—21no—
345#95C22×D1311yescharacteristic
346#95C22×D1312yes—
347#95C22×D1311yescharacteristic
348C2×C13—21no—
349C2×C13—21no—
350C2×C13—44no—
351C2×C13#288311yescharacteristic
352C2×C13C2×#41611yescharacteristic
353C2×C13#290111yescharacteristic
354D13—82no—
355C24C2×C22⋊D1312yes—
356#41—522no—
357#41—522no—
358#41—1044no—
359C2×Q8—132no—
360C2×Q8—261no—
361C2×Q8—261no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—132no—
365C2×D4—262no—
366C2×D4—264no—
367C2×D4—264no—
368C2×D4—261no—
369C2×D4—261no—
370C2×D4#610312yes—
371C2×D4#610312yes—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—82no—
376C22×C4—262no—
377C22×C4—264no—
378C22×C4C2×C4×D1314yes—
379C22×C4C2×D5214yes—
380C22×C4C2×C22⋊D1312yes—
381C22×C4C2×C22⋊D1311yescharacteristic
382C22×C4C2×C22⋊D1311yescharacteristic
383C22×C4C23×D1311yescharacteristic
384C2×C8—262no—
385C2×C8—262no—
386C2×C8—1044no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—132no—
390C4⋊C4—132no—
391C4⋊C4—261no—
392C4⋊C4—264no—
393C4⋊C4—261no—
394C4⋊C4—261no—
395C4⋊C4—262no—
396C4⋊C4—261no—
397C4⋊C4—262no—
398C4⋊C4#610312yes—
399C4⋊C4#610312yes—
400C22⋊C4—44no—
401C22⋊C4—82no—
402C22⋊C4—264no—
403C22⋊C4—264no—
404C22⋊C4—262no—
405C22⋊C4—264no—
406C22⋊C4—262no—
407C22⋊C4—262no—
408C22⋊C4#610314yes—
409C22⋊C4#610314yes—
410C42—42no—
411C42—82no—
412C42—264no—
413C42—262no—
414C42C2×C4×D1311yescharacteristic
415C42C2×C4×D1311yescharacteristic
416C42C2×D5211yescharacteristic
417C42C2×D5211yescharacteristic
418C13#1761711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—42no—
422C23—42no—
423C23—262no—
424C23C2×#610314yes—
425C23C22×C22⋊D1311yescharacteristic
426Q8—522no—
427Q8—522no—
428Q8—1041no—
429D4—24no—
430D4—24no—
431D4—522no—
432D4—522no—
433D4—522no—
434D4—522no—
435D4—1041no—
436D4—1044no—
437D4—1044no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—262no—
453C2×C4—262no—
454C2×C4—262no—
455C2×C4—524no—
456C2×C4—1044no—
457C2×C4C2×#610314yes—
458C2×C4C2×#610311yescharacteristic
459C2×C4C2×#610311yescharacteristic
460C2×C4C2×#610311yescharacteristic
461C2×C4C2×#610311yescharacteristic
462C2×C4#8820412yes—
463C2×C4#8820412yes—
464C2×C4C22×C4×D1311yescharacteristic
465C2×C4C22×D5211yescharacteristic
466C8—522no—
467C8—522no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—82no—
474C22—82no—
475C22—522no—
476C22—522no—
477C22—522no—
478C22C22×#610311yescharacteristic
479C22C2×#8820411yescharacteristic
480C22C2×#8820411yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—24no—
486C4—42no—
487C4—81no—
488C4—82no—
489C4—522no—
490C4—522no—
491C4—522no—
492C4#1171866312yes—
493C4#1171866312yes—
494C2—21no—
495C2—21no—
496C2—44no—
497C2—1042no—
498C2#1312329611yescharacteristic
499C2C2×#1171866311yescharacteristic
500C2#1312338411yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2357C2
socleC22×C13C22×C22⋊C4
prime radical#13128688C2
cosocleC22×C4×C13C24
hypercenter#2357D13
hypocenterC13#17617
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13123860C2semidirect
3. #13113399C2semidirect
4. #13113395C2semidirect
5. #13113390C2semidirect
6. #13113334C2semidirect
7. #13113330C2semidirect
8. #13113325C2semidirect
9. C13×#2357C2semidirect
13. #11719268C4semidirect
16. #11719258C4semidirect
17. #11719256C4semidirect
18. #11719247C4semidirect
171. #2357D13semidirect
418. C13#17617semidirect

Maximal subgroups

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

subgroupindex
#131286882
#131238602
#131133992
#131133952
#131133902
#131133342
#131133302
#131133252
C13×#23572
#1761713