Finite Group Databasebeta

← #15962663

Subgroups — #15962663

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88129C211yesmaximal, characteristic
2#13116404C212yesmaximal, complemented
3#13116077C212yesmaximal
4#13115532C212yesmaximal
5#13115525C212yesmaximal, complemented
6#13114838C211yesmaximal, characteristic, complemented
7#13114838C211yesmaximal, characteristic, complemented
8#13114833C211yesmaximal, characteristic
9#13114833C211yesmaximal, characteristic
10#13114689C211yesmaximal, characteristic, complemented
11C13×#2859C211yesmaximal, characteristic, complemented
12C2×C13×#125—21no—
13C2×#88129C2211yescharacteristic
14C2×C4×D52C2211yescharacteristic
15C2×C4×Dic26C2211yescharacteristic
16C13×#389—21no—
17C13×#389—21no—
18C13×#389C2212yes—
19C13×#389C2212yes—
20C13×#384C2211yescharacteristic
21C13×#384C2211yescharacteristic
22C13×#382—21no—
23C43×C13C2211yescharacteristic
24C2×#88050C2212yes—
25C2×#88050C2212yes—
26C2×#88049C2212yes—
27C2×#88049C2212yes—
28#11718601—21no—
29#11718601—21no—
30#11718600C2211yescharacteristic
31C4×#6103—21no—
32C4×#6103—21no—
33#11718597C2211yescharacteristic
34#11718590C2211yescharacteristic
35C2×C4⋊#1055C2211yescharacteristic
36C2×C4⋊#1055C2211yescharacteristic
37C2×#88043C2212yes—
38#11718121C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718116C2212yes—
43C22×D52C2311yescharacteristic
44C22×C4×D13—21no—
45C22×Dic26C2311yescharacteristic
46C13×#125—44no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4C2312yes—
54C2×C13×C4⋊C4C2312yes—
55C2×C42×C13D411yescharacteristic
56C2×C42×C13D411yescharacteristic
57C2×C42×C13D411yescharacteristic
58C2×C42×C13D411yescharacteristic
59C2×C42×C13C2311yescharacteristic
60C2×C42×C13C2311yescharacteristic
61C2×C42×C13C2311yescharacteristic
62C2×#6103—21no—
63C2×#6103—21no—
64C2×#6103—21no—
65C2×#6103—21no—
66C2×#6103—21no—
67C2×C4⋊Dic13C2311yescharacteristic
68C2×C4⋊Dic13C2311yescharacteristic
69C2×#6101—21no—
70C2×C4×Dic13—21no—
71C22×#1055C2312yes—
72C22×#1055C2312yes—
73#88129—22no—
74#88129—22no—
75C4×D52—22no—
76C4×D52—22no—
77C4×Dic26—22no—
78C4×Dic26—22no—
79C13×#95—22no—
80C13×#95—22no—
81#88071—21no—
82#88071—21no—
83#88071—21no—
84#88071—21no—
85#88050—24no—
86#88050—42no—
87#88049—24no—
88#88049—42no—
89C4⋊#1055—22no—
90C4⋊#1055—22no—
91#88043—42no—
92#29131—131nomaximal, Sylow
93C23×D13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—21no—
106C2×D52—21no—
107C2×D52—21no—
108C2×D52—21no—
109C2×D52—21no—
110C2×D52—21no—
111C2×D52#4112yes—
112C2×C4×D13—42no—
113C2×C4×D13—42no—
114C2×C4×D13—42no—
115C2×Dic26—21no—
116C2×Dic26—21no—
117C2×Dic26—21no—
118C2×Dic26—21no—
119C2×Dic26—21no—
120C2×Dic26#4112yes—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—42no—
126C13×C4⋊C4—42no—
127C13×C4⋊C4—44no—
128C13×C4⋊C4—44no—
129C13×C4⋊C4—42no—
130C13×C4⋊C4—42no—
131C42×C13—22no—
132C42×C13—22no—
133C42×C13—21no—
134C42×C13—21no—
135C42×C13—21no—
136C42×C13—21no—
137C42×C13—41no—
138C42×C13—41no—
139C42×C13#4112yes—
140C42×C13#4112yes—
141#6103—24no—
142#6103—24no—
143#6103—42no—
144#6103—42no—
145#6103—42no—
146C4⋊Dic13—21no—
147C4⋊Dic13—21no—
148C4⋊Dic13—21no—
149C4⋊Dic13—21no—
150#6101—42no—
151C4×Dic13—42no—
152C2×#1055—22no—
153C2×#1055—22no—
154C2×#1055—22no—
155C2×#1055—22no—
156C2×#1055—22no—
157C2×#1055—22no—
158#2859D1311yescharacteristic, complemented
159C4×#124—131no—
160#2101—132no—
161#2042—132no—
162#1936—132no—
163#1935—132no—
164#1803—131no—
165#1803—131no—
166#1802—131no—
167#1802—131no—
168#1767—131no—
169C23×C13C22×D411yescharacteristic
170C22×D13—22no—
171C22×D13—41no—
172C22×D13—41no—
173C22×D13—41no—
174C22×D13—41no—
175C22×D13—41no—
176C22×D13—41no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13#12412yes—
198C2×C4×C13#12412yes—
199C2×C4×C13AGL(1,ℤ/8)12yes—
200C2×C4×C13#13712yes—
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13C2×#4111yescharacteristic
204C2×C4×C13C2×#4111yescharacteristic
205C2×C4×C13H(5,𝔽2)11yescharacteristic
206C2×C4×C132−1+411yescharacteristic
207C2×Dic13—22no—
208C2×Dic13—41no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216D52—22no—
217D52—22no—
218D52—41no—
219D52—41no—
220C4×D13—84no—
221Dic26—22no—
222Dic26—22no—
223Dic26—41no—
224Dic26—41no—
225#1055—42no—
226#1055—42no—
227C2×#125—21no—
228C2×#124—131no—
229C2×C4×Q8—131no—
230C2×C4×D4—131no—
231C2×C4⋊C8—131no—
232C2×C4⋊C8—131no—
233C2×#103—132no—
234C2×#103—132no—
235C2×#102—132no—
236C2×#102—132no—
237C2×#97—132no—
238#391—131no—
239#390—131no—
240#389—21no—
241#389—21no—
242#389C2×D1312yes—
243#389C2×D1312yes—
244#388—261no—
245#388—261no—
246#384C2×D1311yescharacteristic
247#384C2×D1311yescharacteristic
248#382—21no—
249#382—131no—
250C4×C22⋊C4—261no—
251C4×C22⋊C4—261no—
252C43C2×D1311yescharacteristic
253#340—132no—
254#340—132no—
255#340—132no—
256#340—132no—
257#336—132no—
258C22×C13#52511yescharacteristic
259C22×C13C2×#12411yescharacteristic
260C22×C13#53711yescharacteristic
261C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C13C2×#13711yescharacteristic
263C22×C13#57511yescharacteristic
264C22×C13#57511yescharacteristic
265C2×D13—42no—
266C2×D13—42no—
267C2×D13—42no—
268C2×D13—81no—
269C2×D13—81no—
270C2×D13—81no—
271C2×D13—81no—
272C4×C13—22no—
273C4×C13—41no—
274C4×C13—41no—
275C4×C13—41no—
276C4×C13—41no—
277C4×C13—82no—
278C4×C13—82no—
279C4×C13#48914yes—
280C4×C13#55211yescharacteristic
281C4×C13#55211yescharacteristic
282C4×C13#55311yescharacteristic
283C4×C13#55311yescharacteristic
284Dic13—42no—
285Dic13—81no—
286Dic13—81no—
287C22×Q8—131no—
288C22×D4—131no—
289C23×C4—261no—
290C22×C8—132no—
291C22×C8—132no—
292#125—44no—
293#124—262no—
294#124—262no—
295C4×Q8—262no—
296C4×Q8—262no—
297C4×D4—262no—
298C4×D4—262no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—131no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4C22×D1312yes—
309C2×C4⋊C4C22×D1312yes—
310C2×C22⋊C4—261no—
311C2×C22⋊C4—261no—
312C2×C22⋊C4—261no—
313C2×C22⋊C4—261no—
314C2×C22⋊C4—261no—
315C2×C42—261no—
316C2×C42C22⋊D1311yescharacteristic
317C2×C42C22⋊D1311yescharacteristic
318C2×C42C22⋊D1311yescharacteristic
319C2×C42C22⋊D1311yescharacteristic
320C2×C42C22×D1311yescharacteristic
321C2×C42C22×D1311yescharacteristic
322C2×C42C22×D1311yescharacteristic
323C4⋊C8—262no—
324C4⋊C8—262no—
325#103—264no—
326#103—522no—
327#102—264no—
328#102—522no—
329#97—522no—
330#95—22no—
331#95—22no—
332#95—261no—
333#95—261no—
334#95—261no—
335#95—261no—
336C2×C13#256211yescharacteristic
337C2×C13#311511yescharacteristic
338C2×C13#311611yescharacteristic
339C2×C13C2×#48911yescharacteristic
340C2×C13#314211yescharacteristic
341C2×C13#325111yescharacteristic
342C2×C13#325211yescharacteristic
343D13—82no—
344C24—261no—
345C2×Q8—132no—
346C2×Q8—261no—
347C2×Q8—261no—
348C2×Q8—261no—
349C2×Q8—261no—
350C2×Q8—261no—
351C2×D4—132no—
352C2×D4—261no—
353C2×D4—261no—
354C2×D4—261no—
355C2×D4—261no—
356C2×D4—261no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—261no—
360C22×C4—261no—
361C22×C4—261no—
362C22×C4—522no—
363C22×C4—522no—
364C22×C4—522no—
365C22×C4C2×C22⋊D1311yescharacteristic
366C22×C4C2×C22⋊D1311yescharacteristic
367C22×C4C2×C22⋊D1311yescharacteristic
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C22×C4C2×C22⋊D1311yescharacteristic
371C22×C4C23×D1311yescharacteristic
372C2×C8—262no—
373C2×C8—262no—
374C2×C8—262no—
375C2×C8—262no—
376C2×C8—262no—
377C2×C8—262no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—261no—
389C4⋊C4—261no—
390C4⋊C4—261no—
391C4⋊C4—261no—
392C4⋊C4—522no—
393C22⋊C4—264no—
394C22⋊C4—264no—
395C22⋊C4—522no—
396C22⋊C4—522no—
397C22⋊C4—522no—
398C42—22no—
399C42—22no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—41no—
405C42—41no—
406C42—522no—
407C42#613112yes—
408C42#613112yes—
409C13#2913111yescharacteristic, complemented, Sylow
410C23—262no—
411C23—521no—
412C23—521no—
413C23—521no—
414C23—521no—
415C23—521no—
416C23—521no—
417C23C22×C22⋊D1311yescharacteristic
418Q8—262no—
419Q8—262no—
420Q8—521no—
421Q8—521no—
422D4—262no—
423D4—262no—
424D4—521no—
425D4—521no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—262no—
447C2×C4—521no—
448C2×C4—521no—
449C2×C4—521no—
450C2×C4—521no—
451C2×C4—521no—
452C2×C4—521no—
453C2×C4—521no—
454C2×C4—521no—
455C2×C4—1044no—
456C2×C4#8818612yes—
457C2×C4#8819612yes—
458C2×C4#8820112yes—
459C2×C4#8820112yes—
460C2×C4C2×#613111yescharacteristic
461C2×C4C2×#613111yescharacteristic
462C2×C4#41×D1311yescharacteristic
463C2×C4#41×D1311yescharacteristic
464C2×C4#8825611yescharacteristic
465C2×C4#8825711yescharacteristic
466C8—522no—
467C8—522no—
468C22—522no—
469C22—522no—
470C22—522no—
471C22—1041no—
472C22—1041no—
473C22—1041no—
474C22—1041no—
475C22C2×#8818611yescharacteristic
476C22C2×#8819611yescharacteristic
477C22C2×#8820111yescharacteristic
478C22#1171952711yescharacteristic
479C22#1171952711yescharacteristic
480C22#1171953311yescharacteristic
481C22#1171953811yescharacteristic
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—82no—
489C4—522no—
490C4—1041no—
491C4—1041no—
492C4#1171875014yes—
493C4#1171939911yescharacteristic
494C4#1171939911yescharacteristic
495C4#1171940011yescharacteristic
496C4#1171940011yescharacteristic
497C2—1042no—
498C2#1312000311yescharacteristic
499C2#1312498111yescharacteristic
500C2#1312499211yescharacteristic
501C2C2×#1171875011yescharacteristic
502C2#1312523911yescharacteristic
503C2#1312619211yescharacteristic
504C2#1312620311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2859C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2859D13
hypocenterC13#29131
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
5. #13115525C2semidirect
6. #13114838C2semidirect
7. #13114838C2semidirect
10. #13114689C2semidirect
11. C13×#2859C2semidirect
158. #2859D13semidirect
409. C13#29131semidirect

Maximal subgroups

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

subgroupindex
C4×#881292
#131164042
#131160772
#131155322
#131155252
#131148382
#131148332
#131146892
C13×#28592
#2913113