Finite Group Databasebeta

← #15917285

Subgroups — #15917285

Order 3328.

1032 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic, complemented
2C2×#11718716C211yesmaximal, characteristic, complemented
3#13120657C211yesmaximal, characteristic, complemented
4#13116036C212yesmaximal, complemented
5#13116015C212yesmaximal
6#13115810C211yesmaximal, characteristic, complemented
7#13115648C211yesmaximal, characteristic, complemented
8#13115090C212yesmaximal, complemented
9#13115083C212yesmaximal, complemented
10#13114602C211yesmaximal, characteristic, complemented
11C2×C13×#542C211yesmaximal, characteristic
12C13×#542—24no—
13C13×#542—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—21no—
16C2×C13×#124—21no—
17C2×C13×#124C2211yescharacteristic
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88072C2212yes—
29C2×#88072C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32#11718739—24no—
33#11718716—24no—
34#11718647—21no—
35#11718640—21no—
36C2×#88047C2212yes—
37C2×#88047C2212yes—
38#11718610—21no—
39#11718608—21no—
40#11718597C2211yescharacteristic
41#11718589C2212yes—
42C2×#88043C2211yescharacteristic
43C2×C4×#1055C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13C2311yescharacteristic
49C22×D4×C13—21no—
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13C2311yescharacteristic
53C22×Dic26—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8D414yes—
56C13×#126—28no—
57C13×#124—28no—
58C13×#124—22no—
59C13×#124D414yes—
60C13×#123—28no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×#121—22no—
65C13×#121—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2312yes—
92C2×C4⋊Dic13C2312yes—
93C2×#6101—22no—
94C22×#1055C2312yes—
95C22×#1055C2312yes—
96#88123—22no—
97#88123—22no—
98#88075—24no—
99#88075—24no—
100#88072—24no—
101#88072—24no—
102#88071—22no—
103#88071—21no—
104#88071—21no—
105#88071—22no—
106C22⋊#1055—24no—
107#88047—24no—
108#88047—24no—
109#88043—22no—
110C4×#1055—22no—
111#25681—131nomaximal, Sylow
112C24×C13—21no—
113C24×C13C2×D411yescharacteristic
114C2×Q8×C13—24no—
115C2×Q8×C13—21no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—82no—
119C2×Q8×C13C2×D412yes—
120C2×D4×C13—24no—
121C2×D4×C13—21no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—82no—
125C2×D4×C13C2×D412yes—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—24no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—82no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C22×Dic13—22no—
143C2×Dic26—42no—
144C2×Dic26—82no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4C2×D412yes—
153C13×C4⋊C4C2×D412yes—
154C13×C22⋊C4—24no—
155C13×C22⋊C4—24no—
156C13×C22⋊C4—24no—
157C13×C22⋊C4—24no—
158C13×C22⋊C4—24no—
159C13×C22⋊C4—22no—
160C13×C22⋊C4—22no—
161C42×C13—24no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13C2×D412yes—
165C42×C13C2×D412yes—
166C22⋊Dic13—82no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—42no—
172#6101—82no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055#4114yes—
179C2×#542D1311yescharacteristic
180C2×#500—131no—
181C2×#489—131no—
182#2628—131no—
183#2036—132no—
184#2033—132no—
185#1993—131no—
186#1958—131no—
187#1863—132no—
188#1862—132no—
189#1750—131no—
190C23×C13—21no—
191C23×C13—22no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13C22×D411yescharacteristic
201Q8×C13—24no—
202Q8×C13—42no—
203Q8×C13—84no—
204D4×C13—24no—
205D4×C13—42no—
206D4×C13—84no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—21no—
210C2×C4×C13—22no—
211C2×C4×C13—21no—
212C2×C4×C13—22no—
213C2×C4×C13—21no—
214C2×C4×C13—22no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—84no—
226C2×C4×C13#12012yes—
227C2×C4×C13#12012yes—
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C2×#4112yes—
231C2×C4×C132−1+412yes—
232C2×Dic13—42no—
233C2×Dic13—42no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238Dic26—84no—
239#1055—24no—
240#1055—42no—
241#542—24no—
242#542—24no—
243C2×C4⋊Q8—131no—
244C2×C4⋊Q8C2×D1311yescharacteristic
245C2×#126—21no—
246C2×#124—21no—
247C2×#124C2×D1311yescharacteristic
248C2×#123—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C2×D1311yescharacteristic
251C2×#121C2×D1311yescharacteristic
252C2×C4×Q8C2×D1311yescharacteristic
253C2×C4×D4C2×D1311yescharacteristic
254C2×#117C2×D1311yescharacteristic
255#500—264no—
256#489—264no—
257C2×#107—132no—
258C2×#107—132no—
259C2×#103—132no—
260C2×#103—132no—
261C2×#102—132no—
262C2×#102—132no—
263C2×C22⋊C8—132no—
264C2×#97—131no—
265C2×C4×C8—131no—
266#400—261no—
267#399—261no—
268#395—261no—
269#393—261no—
270#389—132no—
271#382—131no—
272#380—132no—
273#340—132no—
274#340—132no—
275#336—132no—
276C22×C13—42no—
277C22×C13—41no—
278C22×C13—42no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—42no—
284C22×C13—82no—
285C22×C13—82no—
286C22×C13C2×#12011yescharacteristic
287C22×C13#53211yescharacteristic
288C22×C13#53611yescharacteristic
289C22×C13#57612yes—
290C22×C13#57812yes—
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—41no—
294C4×C13—42no—
295C4×C13—41no—
296C4×C13—42no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13#54712yes—
300C4×C13#54812yes—
301Dic13—82no—
302Dic13—82no—
303C22×Q8—21no—
304C22×Q8—261no—
305C22×Q8C22×D1311yescharacteristic
306C22×D4—21no—
307C22×D4C22×D1311yescharacteristic
308C23×C4—21no—
309C23×C4C22×D1311yescharacteristic
310C22×C8—132no—
311C22×C8—132no—
312C4⋊Q8—22no—
313C4⋊Q8—262no—
314C4⋊Q8—262no—
315C4⋊Q8C22⋊D1314yes—
316#126—28no—
317#124—28no—
318#124—22no—
319#124C22⋊D1314yes—
320#123—28no—
321C22⋊Q8—28no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324#121—22no—
325#121—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×D4—22no—
329C4×D4—22no—
330#117—22no—
331#117—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—132no—
336C2×C4⋊C4—132no—
337C2×C4⋊C4—261no—
338C2×C4⋊C4—262no—
339C2×C4⋊C4C22⋊D1311yescharacteristic
340C2×C4⋊C4C22⋊D1311yescharacteristic
341C2×C4⋊C4C22×D1311yescharacteristic
342C2×C4⋊C4C22×D1311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—262no—
349C2×C22⋊C4C22⋊D1311yescharacteristic
350C2×C22⋊C4C22⋊D1311yescharacteristic
351C2×C42—21no—
352C2×C42C22×D1311yescharacteristic
353C2×C42C22×D1311yescharacteristic
354#107—264no—
355#107—264no—
356#103—264no—
357#103—264no—
358#102—264no—
359#102—264no—
360C22⋊C8—264no—
361#97—262no—
362C4×C8—262no—
363#95—262no—
364#95—261no—
365#95—261no—
366#95—262no—
367C2×C13—81no—
368C2×C13—82no—
369C2×C13#243211yescharacteristic
370C2×C13#300811yescharacteristic
371C2×C13#301111yescharacteristic
372C2×C13#317512yes—
373C2×C13#324312yes—
374C24—21no—
375C24C2×C22⋊D1311yescharacteristic
376C2×Q8—24no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—82no—
381C2×Q8—522no—
382C2×Q8—1042no—
383C2×Q8C2×C22⋊D1312yes—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—82no—
389C2×D4C2×C22⋊D1312yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—82no—
399C22×C4—262no—
400C22×C4—262no—
401C22×C4C2×C22⋊D1311yescharacteristic
402C22×C4C2×C22⋊D1311yescharacteristic
403C22×C4C2×C22⋊D1311yescharacteristic
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406C22×C4C23×D1311yescharacteristic
407C2×C8—134no—
408C2×C8—262no—
409C2×C8—262no—
410C2×C8—262no—
411C2×C8—262no—
412C2×C8—262no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—262no—
421C4⋊C4—262no—
422C4⋊C4—262no—
423C4⋊C4—262no—
424C4⋊C4—522no—
425C4⋊C4—1042no—
426C4⋊C4C2×C22⋊D1312yes—
427C4⋊C4C2×C22⋊D1312yes—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—1042no—
436C42—24no—
437C42—21no—
438C42—21no—
439C42C2×C22⋊D1312yes—
440C42C2×C22⋊D1312yes—
441C13#2568111yescharacteristic, complemented, Sylow
442C23—21no—
443C23—21no—
444C23—22no—
445C23—22no—
446C23—21no—
447C23—22no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—42no—
452C23C22×C22⋊D1311yescharacteristic
453Q8—24no—
454Q8—42no—
455Q8—84no—
456Q8—1044no—
457D4—24no—
458D4—42no—
459D4—84no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—84no—
479C2×C4—522no—
480C2×C4—522no—
481C2×C4—522no—
482C2×C4—522no—
483C2×C4—522no—
484C2×C4—522no—
485C2×C4#8820712yes—
486C2×C4#8820712yes—
487C2×C4#41×D1312yes—
488C2×C4#8825712yes—
489C2×C4C22×C22⋊D1311yescharacteristic
490C2×C4C22×C22⋊D1311yescharacteristic
491C8—264no—
492C8—522no—
493C22—42no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—41no—
500C22—42no—
501C22—82no—
502C22—82no—
503C22#1171953011yescharacteristic
504C22#1171953711yescharacteristic
505C22#1171954012yes—
506C22#1171954312yes—
507C22C2×#8820711yescharacteristic
508C4—22no—
509C4—22no—
510C4—41no—
511C4—42no—
512C4—42no—
513C4—41no—
514C4—41no—
515C4—42no—
516C4—1042no—
517C4—1042no—
518C4#1171952912yes—
519C4#1171953612yes—
520C2—81no—
521C2—82no—
522C2#1311846011yescharacteristic
523C2#1312410411yescharacteristic
524C2#1312413111yescharacteristic
525C2#1312546912yes—
526C2#1312611312yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#542D13
hypocenterC13#25681
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11718739C2semidirect
2. C2×#11718716C2semidirect
3. #13120657C2semidirect
4. #13116036C2semidirect
6. #13115810C2semidirect
7. #13115648C2semidirect
8. #13115090C2semidirect
9. #13115083C2semidirect
10. #13114602C2semidirect
441. C13#25681semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117187162
#131206572
#131160362
#131160152
#131158102
#131156482
#131150902
#131150832
#131146022
C2×C13×#5422
#2568113