Finite Group Databasebeta

← #15917595

Subgroups — #15917595

Order 3328.

1016 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718741C211yesmaximal, characteristic, complemented
2C2×#11718683C211yesmaximal, characteristic, complemented
3#13120002C211yesmaximal, characteristic
4#13116036C212yesmaximal, complemented
5#13116029C212yesmaximal, complemented
6#13115785C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic
8#13115035C212yesmaximal, complemented
9#13115035C212yesmaximal, complemented
10#13114666C211yesmaximal, characteristic, complemented
11C2×C13×#556C211yesmaximal, characteristic
12C13×#556—24no—
13C13×#556—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—22no—
16C2×C13×#124—21no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C4×Q8×C13—21no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C2×C13×#117C2212yes—
22C2×#88124C2211yescharacteristic
23C2×#88075C2211yescharacteristic
24C2×#88075C2211yescharacteristic
25C2×#88075C2212yes—
26#11718883—21no—
27#11718873C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718741—24no—
32#11718683—24no—
33#11718643—21no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2212yes—
36C2×#88047C2211yescharacteristic
37C2×#88047C2212yes—
38#11718606—22no—
39C4×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13C2311yescharacteristic
47C22×D4×C13D411yescharacteristic
48C23×C4×C13C2312yes—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8D414yes—
51C13×#126—216no—
52C13×#124—28no—
53C13×C22⋊Q8—24no—
54C13×C22⋊Q8—24no—
55C4×Q8×C13—28no—
56C4×Q8×C13—22no—
57C4×Q8×C13D414yes—
58C4×D4×C13—22no—
59C4×D4×C13—22no—
60C13×#117—24no—
61C13×#117—24no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4D412yes—
71C2×C42×C13—22no—
72C2×C42×C13—21no—
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13—22no—
75C2×C22⋊Dic13—22no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2312yes—
79C2×#6101—21no—
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2312yes—
85#88124—22no—
86#88124—22no—
87#88075—22no—
88#88075—22no—
89#88075—24no—
90#88071—21no—
91#88071—22no—
92#88071—22no—
93C22⋊#1055—24no—
94C22⋊#1055—24no—
95#88048—22no—
96#88048—24no—
97#88047—22no—
98#88047—24no—
99C4⋊#1055—22no—
100#88043—22no—
101#25711—131nomaximal, Sylow
102C24×C13C2×D412yes—
103C2×Q8×C13—24no—
104C2×Q8×C13—21no—
105C2×Q8×C13—22no—
106C2×Q8×C13—22no—
107C2×Q8×C13—44no—
108C2×Q8×C13C2×D412yes—
109C2×D4×C13—22no—
110C2×D4×C13—42no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2411yescharacteristic
124C22×Dic13—22no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C13×C4⋊C4—28no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—24no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4C2×D412yes—
134C13×C4⋊C4C2×D414yes—
135C13×C22⋊C4—28no—
136C13×C22⋊C4—28no—
137C13×C22⋊C4—24no—
138C42×C13—28no—
139C42×C13—24no—
140C42×C13C2×D412yes—
141C42×C13C2×D412yes—
142C22⋊Dic13—44no—
143C22⋊Dic13—82no—
144C4⋊Dic13—21no—
145C4⋊Dic13—21no—
146C4⋊Dic13—21no—
147C4⋊Dic13—21no—
148C4⋊Dic13—22no—
149C4⋊Dic13—22no—
150#6101—42no—
151#6101—42no—
152C4×Dic13—81no—
153C2×#1055—22no—
154C2×#1055—22no—
155C2×#1055—21no—
156C2×#1055—21no—
157C2×#1055—22no—
158C2×#1055—22no—
159C2×#1055#4114yes—
160C2×#556D1311yescharacteristic
161C2×#501—131no—
162C2×#479—131no—
163#2562—131no—
164#2036—132no—
165#2035—132no—
166#1987—131no—
167#1955—131no—
168#1854—132no—
169#1854—132no—
170#1763—131no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—22no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—22no—
178C23×C13C22×D411yescharacteristic
179Q8×C13—22no—
180Q8×C13—22no—
181Q8×C13—48no—
182Q8×C13—42no—
183D4×C13—44no—
184C2×C4×C13—22no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—22no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—42no—
194C2×C4×C13—44no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13#12012yes—
202C2×C4×C13#12012yes—
203C2×C4×C13C22×D411yescharacteristic
204C2×C4×C13C22×D411yescharacteristic
205C2×C4×C13C2×#4112yes—
206C2×C4×C132−1+412yes—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—41no—
214C2×Dic13—41no—
215#1055—24no—
216#1055—41no—
217#1055—41no—
218#556—24no—
219#556—24no—
220C2×C4⋊Q8C2×D1311yescharacteristic
221C2×#126—22no—
222C2×#125—131no—
223C2×#124—21no—
224C2×C22⋊Q8C2×D1312yes—
225C2×C4×Q8—21no—
226C2×C4×Q8C2×D1311yescharacteristic
227C2×C4×D4C2×D1311yescharacteristic
228C2×#117C2×D1312yes—
229#501—264no—
230#479—264no—
231C2×#107—131no—
232C2×#107—132no—
233C2×#106—131no—
234C2×#106—132no—
235C2×C4⋊C8—131no—
236C2×#103—131no—
237C2×#103—131no—
238C2×#103—132no—
239C2×C22⋊C8—132no—
240C2×C22⋊C8—132no—
241C2×#97—131no—
242#400—261no—
243#394—261no—
244#388—262no—
245#380—132no—
246#380—132no—
247C4×C4⋊C4—131no—
248#340—132no—
249#340—132no—
250#340—132no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13—42no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—42no—
258C22×C13C2×#12011yescharacteristic
259C22×C13#54712yes—
260C22×C13#57512yes—
261C22×C13#57711yescharacteristic
262C22×C13#57811yescharacteristic
263C4×C13—22no—
264C4×C13—22no—
265C4×C13—42no—
266C4×C13—42no—
267C4×C13—44no—
268C4×C13—42no—
269C4×C13#53211yescharacteristic
270C4×C13#53611yescharacteristic
271C4×C13#54812yes—
272Dic13—82no—
273Dic13—81no—
274Dic13—81no—
275C22×Q8—21no—
276C22×Q8C22×D1311yescharacteristic
277C22×D4C22⋊D1311yescharacteristic
278C23×C4C22×D1312yes—
279C22×C8—132no—
280C22×C8—131no—
281C22×C8—131no—
282C4⋊Q8—22no—
283C4⋊Q8C22⋊D1314yes—
284#126—216no—
285#125—262no—
286#125—262no—
287#124—28no—
288C22⋊Q8—24no—
289C22⋊Q8—24no—
290C4×Q8—28no—
291C4×Q8—22no—
292C4×Q8C22⋊D1314yes—
293C4×D4—22no—
294C4×D4—22no—
295#117—24no—
296#117—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4—131no—
302C2×C4⋊C4—132no—
303C2×C4⋊C4—261no—
304C2×C4⋊C4—261no—
305C2×C4⋊C4C22⋊D1311yescharacteristic
306C2×C4⋊C4C22×D1311yescharacteristic
307C2×C4⋊C4C22×D1312yes—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—262no—
311C2×C22⋊C4—262no—
312C2×C22⋊C4C22⋊D1312yes—
313C2×C42—22no—
314C2×C42—21no—
315C2×C42—261no—
316C2×C42C22×D1311yescharacteristic
317#107—262no—
318#107—264no—
319#106—262no—
320#106—264no—
321C4⋊C8—262no—
322#103—264no—
323#103—262no—
324#103—262no—
325C22⋊C8—264no—
326C22⋊C8—264no—
327#97—262no—
328#95—261no—
329#95—262no—
330#95—262no—
331C2×C13—82no—
332C2×C13#243211yescharacteristic
333C2×C13#300511yescharacteristic
334C2×C13#301311yescharacteristic
335C2×C13#334912yes—
336C2×C13#335012yes—
337C24C2×C22⋊D1312yes—
338C2×Q8—24no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—44no—
343C2×Q8C2×C22⋊D1312yes—
344C2×D4—22no—
345C2×D4—42no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—262no—
356C22×C4—261no—
357C22×C4—261no—
358C22×C4C2×C22⋊D1312yes—
359C22×C4C2×C22⋊D1311yescharacteristic
360C22×C4C2×C22⋊D1311yescharacteristic
361C22×C4C23×D1311yescharacteristic
362C2×C8—134no—
363C2×C8—262no—
364C2×C8—262no—
365C2×C8—262no—
366C2×C8—262no—
367C2×C8—261no—
368C2×C8—261no—
369C4⋊C4—28no—
370C4⋊C4—24no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—262no—
376C4⋊C4—262no—
377C4⋊C4—261no—
378C4⋊C4—261no—
379C4⋊C4—261no—
380C4⋊C4—261no—
381C4⋊C4—522no—
382C4⋊C4—522no—
383C4⋊C4C2×C22⋊D1312yes—
384C4⋊C4C2×C22⋊D1314yes—
385C22⋊C4—28no—
386C22⋊C4—28no—
387C22⋊C4—24no—
388C22⋊C4—524no—
389C22⋊C4—1042no—
390C42—28no—
391C42—24no—
392C42—1041no—
393C42C2×C22⋊D1312yes—
394C42C2×C22⋊D1312yes—
395C13#2571111yescharacteristic, complemented, Sylow
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23C22×C22⋊D1311yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—48no—
407Q8—42no—
408D4—44no—
409C2×C4—22no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—522no—
430C2×C4—521no—
431C2×C4—521no—
432C2×C4—521no—
433C2×C4—521no—
434C2×C4#8820712yes—
435C2×C4#8820712yes—
436C2×C4#41×D1312yes—
437C2×C4#8825712yes—
438C2×C4C22×C22⋊D1311yescharacteristic
439C2×C4C22×C22⋊D1311yescharacteristic
440C8—264no—
441C8—521no—
442C8—521no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22#1171952712yes—
451C22#1171952912yes—
452C22#1171954211yescharacteristic
453C22#1171954311yescharacteristic
454C22C2×#8820711yescharacteristic
455C4—22no—
456C4—22no—
457C4—42no—
458C4—44no—
459C4—42no—
460C4—42no—
461C4—1041no—
462C4—1042no—
463C4—1041no—
464C4#1171953011yescharacteristic
465C4#1171953612yes—
466C4#1171953711yescharacteristic
467C2—82no—
468C2#1311846011yescharacteristic
469C2#1312407811yescharacteristic
470C2#1312415111yescharacteristic
471C2#1312736012yes—
472C2#1312738112yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#556D13
hypocenterC13#25711
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
2. C2×#11718683C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115785C2semidirect
8. #13115035C2semidirect
9. #13115035C2semidirect
10. #13114666C2semidirect
395. C13#25711semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
C2×#117186832
#131200022
#131160362
#131160292
#131157852
#131156352
#131150352
#131146662
C2×C13×#5562
#2571113