Finite Group Databasebeta

← #15907755

Subgroups — #15907755

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119749C211yesmaximal, characteristic
2#13116273C212yesmaximal, complemented
3#13116025C212yesmaximal, complemented
4#13115631C211yesmaximal, characteristic, complemented
5#13115599C211yesmaximal, characteristic, complemented
6#13115153C212yesmaximal, complemented
7#13114963C211yesmaximal, characteristic, complemented
8#13114926C212yesmaximal, complemented
9#13114833C211yesmaximal, characteristic, complemented
10C4×#88049C211yesmaximal, characteristic, complemented
11D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13—21no—
13C2×C4×D4×C13C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C2×#88192—21no—
16C2×#88184C2212yes—
17C2×C4×D52C2211yescharacteristic
18C13×#389—21no—
19C13×#385—22no—
20C13×#384C2211yescharacteristic
21C13×#380C2212yes—
22C4×C13×C4⋊C4C2211yescharacteristic
23#11718873C2212yes—
24C2×C22⋊#1055C2212yes—
25C2×C22⋊#1055C2212yes—
26#11718648—21no—
27C2×#88049C2211yescharacteristic
28C2×#88049C2211yescharacteristic
29C2×#88049C2212yes—
30C2×#88048C2212yes—
31#11718622—22no—
32#11718596C2211yescharacteristic
33C2×C4⋊#1055C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718121C2212yes—
36#11718121C2212yes—
37#11718121C2211yescharacteristic
38#11718121C2211yescharacteristic
39#11718121C2212yes—
40#11718121C2212yes—
41C22×D4×C13D411yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13C2312yes—
44C22×C22⋊D13—22no—
45C22×D52C2311yescharacteristic
46C22×C4×D13—21no—
47C4×D4×C13—22no—
48C4×D4×C13—22no—
49C4×D4×C13—44no—
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4D411yescharacteristic
56C2×C13×C4⋊C4C2311yescharacteristic
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4D412yes—
61C2×C42×C13—21no—
62C2×C42×C13C2311yescharacteristic
63C2×C22⋊Dic13—22no—
64#88192—44no—
65#88184—24no—
66#88184—42no—
67C2×#6103—21no—
68C2×#6103—22no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13C2311yescharacteristic
72C2×C4⋊Dic13C2312yes—
73C22×#1055C2311yescharacteristic
74C22×#1055C2311yescharacteristic
75C22×#1055C2312yes—
76C4×D52—22no—
77C4×D52—22no—
78C13×#95—21no—
79C13×#95—22no—
80#88071—22no—
81C22⋊#1055—42no—
82C22⋊#1055—42no—
83#88049—22no—
84#88049—22no—
85#88049—42no—
86#88048—42no—
87C4⋊#1055—22no—
88C4×#1055—22no—
89#24967—131nomaximal, Sylow
90C24×C13C2×D412yes—
91C23×D13—21no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13SD1614yes—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—44no—
105C22×C4×C13—44no—
106C22×C4×C13—82no—
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2411yescharacteristic
111C2×C22⋊D13—44no—
112C2×C22⋊D13—44no—
113C2×C22⋊D13—82no—
114C22×Dic13—21no—
115C22×Dic13—22no—
116C2×D52—21no—
117C2×D52—21no—
118C2×D52—21no—
119C2×D52—21no—
120C2×D52—21no—
121C2×D52#4112yes—
122C2×C4×D13—42no—
123C2×C4×D13—42no—
124C2×C4×D13—42no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—44no—
132C13×C4⋊C4—42no—
133C13×C4⋊C4—81no—
134C13×C4⋊C4#4112yes—
135C13×C22⋊C4—24no—
136C13×C22⋊C4—44no—
137C42×C13—42no—
138C42×C13#4112yes—
139C42×C13#4112yes—
140C22⋊Dic13—44no—
141#6103—44no—
142#6103—42no—
143C4⋊Dic13—21no—
144C4⋊Dic13—21no—
145C4⋊Dic13—22no—
146C4⋊Dic13—22no—
147C4⋊Dic13—42no—
148C4⋊Dic13—81no—
149C2×#1055—21no—
150C2×#1055—21no—
151C2×#1055—22no—
152C2×#1055—21no—
153C2×#1055—21no—
154C2×#1055—21no—
155C2×#1055—21no—
156C2×#1055—22no—
157C2×#1055—22no—
158#2537—131no—
159D4×C4⋊C4D1311yescharacteristic, complemented
160#2077—132no—
161#2034—132no—
162#1954—131no—
163#1948—131no—
164#1874—132no—
165#1834—131no—
166#1824—132no—
167#1802—131no—
168C4×#102—131no—
169C23×C13—22no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13C2×SD1614yes—
176C23×C13C22×D411yescharacteristic
177C22×D13—22no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181C22×D13—41no—
182C22×D13—41no—
183C22×D13—41no—
184D4×C13—28no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—88no—
204C2×C4×C13#12312yes—
205C2×C4×C13#12312yes—
206C2×C4×C13C2×SD1612yes—
207C2×C4×C13AGL(1,ℤ/8)12yes—
208C2×C4×C13C2×#4111yescharacteristic
209C2×C4×C13C2×#4111yescharacteristic
210C2×C4×C13C2×#4111yescharacteristic
211C2×C4×C13C2×#4111yescharacteristic
212C2×C4×C13H(5,𝔽2)11yescharacteristic
213C2×C4×C13H(5,𝔽2)11yescharacteristic
214C22⋊D13—88no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—42no—
221D52—22no—
222D52—22no—
223D52—41no—
224D52—41no—
225C4×D13—84no—
226#1055—42no—
227#1055—41no—
228#1055—41no—
229C2×#121—132no—
230C2×#121—261no—
231C2×C4×D4—21no—
232C2×C4×D4—131no—
233C2×C4×D4C2×D1311yescharacteristic
234C22×C4⋊C4C2×D1312yes—
235C2×#106—132no—
236C2×C4⋊C8—131no—
237C2×#102—131no—
238C2×#102—131no—
239C2×#102—132no—
240C2×C22⋊C8—132no—
241C2×C22⋊C8—132no—
242C2×C4×C8—131no—
243#394—262no—
244#389—21no—
245#385—22no—
246#384—131no—
247#384C2×D1311yescharacteristic
248#380—132no—
249#380—261no—
250#380C2×D1312yes—
251C4×C4⋊C4C2×D1311yescharacteristic
252#340—132no—
253#340—131no—
254#340—132no—
255#340—131no—
256#340—132no—
257#340—132no—
258C22×C13—24no—
259C22×C13—24no—
260C22×C13—24no—
261C22×C13—42no—
262C22×C13—42no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13C2×#12311yescharacteristic
266C22×C13#54611yescharacteristic
267C22×C13#54611yescharacteristic
268C22×C13C22×SD1611yescharacteristic
269C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C13#57611yescharacteristic
271C22×C13#57811yescharacteristic
272C2×D13—42no—
273C2×D13—42no—
274C2×D13—42no—
275C2×D13—81no—
276C2×D13—81no—
277C2×D13—81no—
278C2×D13—81no—
279C4×C13—22no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—81no—
283C4×C13—82no—
284C4×C13#48114yes—
285C4×C13#52911yescharacteristic
286C4×C13#54011yescharacteristic
287C4×C13#55311yescharacteristic
288C4×C13#55511yescharacteristic
289Dic13—81no—
290Dic13—82no—
291C22×D4—131no—
292C22×D4—262no—
293C22×D4C22⋊D1311yescharacteristic
294C23×C4—22no—
295C23×C4—261no—
296C23×C4C22×D1312yes—
297C22×C8—131no—
298C22×C8—131no—
299C22×C8—132no—
300#121—264no—
301#121—522no—
302#121—524no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—44no—
306C4×D4—262no—
307C4×D4—262no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—131no—
314C2×C4⋊C4—132no—
315C2×C4⋊C4—261no—
316C2×C4⋊C4—261no—
317C2×C4⋊C4C22⋊D1311yescharacteristic
318C2×C4⋊C4C22×D1312yes—
319C2×C4⋊C4C22×D1311yescharacteristic
320C2×C4⋊C4C22×D1311yescharacteristic
321C2×C22⋊C4—22no—
322C2×C22⋊C4—262no—
323C2×C22⋊C4—261no—
324C2×C22⋊C4—262no—
325C2×C22⋊C4C22⋊D1312yes—
326C2×C42—21no—
327C2×C42C22×D1311yescharacteristic
328#106—522no—
329C4⋊C8—262no—
330#102—262no—
331#102—262no—
332#102—522no—
333C22⋊C8—522no—
334C22⋊C8—522no—
335C4×C8—262no—
336#95—21no—
337#95—22no—
338#95—262no—
339C2×C13—44no—
340C2×C13#242011yescharacteristic
341C2×C13C2×#48111yescharacteristic
342C2×C13#309811yescharacteristic
343C2×C13#329511yescharacteristic
344C2×C13#329811yescharacteristic
345C2×C13#332511yescharacteristic
346C2×C13#333011yescharacteristic
347D13—82no—
348C24—261no—
349C24C2×C22⋊D1312yes—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—132no—
353C2×D4—261no—
354C2×D4—261no—
355C2×D4—261no—
356C2×D4—261no—
357C2×D4—261no—
358C2×D4—524no—
359C2×D4—524no—
360C2×D4—1042no—
361C2×D4#610614yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—82no—
374C22×C4—261no—
375C22×C4—262no—
376C22×C4—522no—
377C22×C4—522no—
378C22×C4—522no—
379C22×C4C2×C22⋊D1312yes—
380C22×C4C2×C22⋊D1311yescharacteristic
381C22×C4C2×C22⋊D1311yescharacteristic
382C22×C4C23×D1311yescharacteristic
383C2×C8—261no—
384C2×C8—261no—
385C2×C8—262no—
386C2×C8—261no—
387C2×C8—261no—
388C2×C8—262no—
389C2×C8—261no—
390C2×C8—261no—
391C2×C8—262no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—44no—
399C4⋊C4—42no—
400C4⋊C4—81no—
401C4⋊C4—261no—
402C4⋊C4—261no—
403C4⋊C4—262no—
404C4⋊C4—262no—
405C4⋊C4—522no—
406C4⋊C4—1041no—
407C4⋊C4#612912yes—
408C22⋊C4—24no—
409C22⋊C4—44no—
410C22⋊C4—524no—
411C22⋊C4—524no—
412C22⋊C4—522no—
413C42—42no—
414C42#612712yes—
415C42#612712yes—
416C13#2496711yescharacteristic, complemented, Sylow
417C23—22no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—262no—
424C23—521no—
425C23—521no—
426C23—521no—
427C23—521no—
428C23—521no—
429C23—521no—
430C23C2×#610614yes—
431C23C22×C22⋊D1311yescharacteristic
432D4—28no—
433D4—262no—
434D4—262no—
435D4—521no—
436D4—521no—
437D4—1048no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—88no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—1044no—
464C2×C4#8818312yes—
465C2×C4#8818312yes—
466C2×C4#8818612yes—
467C2×C4C2×#610612yes—
468C2×C4C2×#612711yescharacteristic
469C2×C4C2×#612711yescharacteristic
470C2×C4C2×#612911yescharacteristic
471C2×C4#8825111yescharacteristic
472C2×C4#41×D1311yescharacteristic
473C2×C4#8825611yescharacteristic
474C8—521no—
475C8—522no—
476C8—521no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—522no—
485C22—522no—
486C22—522no—
487C22—1041no—
488C22—1041no—
489C22—1041no—
490C22—1041no—
491C22C2×#8818311yescharacteristic
492C22C2×#8818611yescharacteristic
493C22#1171951111yescharacteristic
494C22C22×#610611yescharacteristic
495C22#1171953411yescharacteristic
496C22#1171954011yescharacteristic
497C22#1171954311yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—82no—
502C4—81no—
503C4—1041no—
504C4—1042no—
505C4#1171862914yes—
506C4#1171926211yescharacteristic
507C4#1171926311yescharacteristic
508C4#1171926711yescharacteristic
509C4#1171926811yescharacteristic
510C2—44no—
511C2—1042no—
512C2#1311832211yescharacteristic
513C2C2×#1171862911yescharacteristic
514C2#1312481411yescharacteristic
515C2#1312665411yescharacteristic
516C2#1312670111yescharacteristic
517C2#1312707811yescharacteristic
518C2#1312713511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radical#13119749C2
hypercenterD4×C4⋊C4D13
hypocenterC13#24967
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13116273C2semidirect
3. #13116025C2semidirect
4. #13115631C2semidirect
5. #13115599C2semidirect
6. #13115153C2semidirect
7. #13114963C2semidirect
8. #13114926C2semidirect
9. #13114833C2semidirect
10. C4×#88049C2semidirect
11. D4×C13×C4⋊C4C2semidirect
159. D4×C4⋊C4D13semidirect
416. C13#24967semidirect

Maximal subgroups

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

subgroupindex
#131197492
#131162732
#131160252
#131156312
#131155992
#131151532
#131149632
#131149262
#131148332
C4×#880492
D4×C13×C4⋊C42
#2496713