Finite Group Databasebeta

← #15917628

Subgroups — #15917628

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718669C211yesmaximal, characteristic, complemented
3#13119828C211yesmaximal, characteristic, complemented
4#13116022C212yesmaximal, complemented
5#13116015C212yesmaximal, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115635C211yesmaximal, characteristic, complemented
8#13115035C212yesmaximal, complemented
9#13115029C212yesmaximal, complemented
10#13114661C211yesmaximal, characteristic, complemented
11C2×C13×#553C211yesmaximal, characteristic
12C13×#553—24no—
13C13×#553—24no—
14C2×C13×#126—21no—
15C2×C13×#125C2211yescharacteristic
16C2×C13×#123—21no—
17C2×C13×#121—21no—
18C2×C13×#121C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×C4×D4×C13—21no—
21C2×C4×D4×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88190—21no—
26C2×#88123C2211yescharacteristic
27C2×#88072C2212yes—
28C2×#88072C2212yes—
29#11718873C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2212yes—
33#11718726—24no—
34#11718669—24no—
35#11718635—21no—
36C2×#88048C2212yes—
37C2×#88048C2212yes—
38C2×#88047C2212yes—
39#11718614—21no—
40#11718614—21no—
41C4×C4⋊Dic13C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13D411yescharacteristic
50C22×D4×C13C2311yescharacteristic
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C22×Dic26—21no—
56C13×#126—28no—
57C13×#125—22no—
58C13×#125D414yes—
59C13×#123—28no—
60C13×#121—28no—
61C13×#121—22no—
62C13×#121—22no—
63C13×#121—22no—
64C13×#121—22no—
65C4×D4×C13—28no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13D414yes—
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91#88190—44no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2312yes—
95C2×C4×Dic13—21no—
96C22×#1055C2312yes—
97C22×#1055C2312yes—
98#88123—22no—
99#88123—22no—
100#88072—24no—
101#88072—24no—
102#88071—21no—
103#88071—22no—
104#88071—22no—
105C22⋊#1055—24no—
106C22⋊#1055—24no—
107#88048—24no—
108#88048—24no—
109#88047—24no—
110C4⋊#1055—22no—
111#88043—22no—
112#25714—131nomaximal, Sylow
113C24×C13—21no—
114C24×C13C2×D411yescharacteristic
115C24×C13C2×D411yescharacteristic
116C2×D4×C13—24no—
117C2×D4×C13—22no—
118C2×D4×C13—24no—
119C2×D4×C13—22no—
120C2×D4×C13—21no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—41no—
124C2×D4×C13—42no—
125C2×D4×C13—42no—
126C2×D4×C13—82no—
127C2×D4×C13C2×D412yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—24no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—82no—
142C22×C4×C13—82no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—22no—
149C22×Dic13—22no—
150C2×Dic26—42no—
151C2×Dic26—42no—
152C2×Dic26—42no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4C2×D412yes—
161C13×C4⋊C4C2×D412yes—
162C13×C4⋊C4C2×D412yes—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C42×C13—24no—
170C42×C13C2×D412yes—
171C42×C13C2×D412yes—
172C22⋊Dic13—44no—
173C22⋊Dic13—44no—
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—42no—
179C4×Dic13—42no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055#4114yes—
186C2×#553D1311yescharacteristic
187C2×#501—131no—
188C2×#476—131no—
189#2547—131no—
190#2034—132no—
191#2033—132no—
192#1989—131no—
193#1955—131no—
194#1854—132no—
195#1853—132no—
196#1762—131no—
197C23×C13—21no—
198C23×C13—22no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13—21no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—22no—
207C23×C13—42no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13AGL(1,ℤ/8)12yes—
212C23×C13C22×D411yescharacteristic
213D4×C13—22no—
214D4×C13—22no—
215D4×C13—44no—
216D4×C13—48no—
217D4×C13—42no—
218D4×C13—84no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—84no—
240C2×C4×C13—84no—
241C2×C4×C13#12012yes—
242C2×C4×C13#12012yes—
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4112yes—
246C2×C4×C132−1+412yes—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253Dic26—84no—
254#1055—24no—
255#1055—42no—
256#553—24no—
257#553—24no—
258C2×C4⋊Q8—131no—
259C2×#126—21no—
260C2×#125C2×D1311yescharacteristic
261C2×#124—261no—
262C2×#123—21no—
263C2×#121—21no—
264C2×#121C2×D1311yescharacteristic
265C2×#121C2×D1311yescharacteristic
266C2×C4×D4—21no—
267C2×C4×D4C2×D1311yescharacteristic
268C2×C4×D4C2×D1311yescharacteristic
269C2×#117C2×D1311yescharacteristic
270C22×C4⋊C4C2×D1311yescharacteristic
271#501—264no—
272#476—264no—
273C2×#107—132no—
274C2×#106—132no—
275C2×#106—132no—
276C2×C4⋊C8—131no—
277C2×#102—132no—
278C2×#102—132no—
279C2×C22⋊C8—132no—
280C2×C22⋊C8—132no—
281C2×#97—131no—
282#397—261no—
283#397—261no—
284#391—261no—
285#380—132no—
286#380—132no—
287C4×C4⋊C4—131no—
288#340—132no—
289#340—132no—
290#340—132no—
291C22×C13—24no—
292C22×C13—22no—
293C22×C13—42no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—41no—
299C22×C13—42no—
300C22×C13—41no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—41no—
304C22×C13—82no—
305C22×C13—82no—
306C22×C13C2×#12011yescharacteristic
307C22×C13#54712yes—
308C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C13#57511yescharacteristic
310C22×C13#57712yes—
311C4×C13—22no—
312C4×C13—22no—
313C4×C13—41no—
314C4×C13—41no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13#53211yescharacteristic
319C4×C13#53611yescharacteristic
320C4×C13#54812yes—
321Dic13—82no—
322Dic13—82no—
323C22×Q8—261no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C22⋊D1311yescharacteristic
327C22×D4C22×D1311yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C22×D1311yescharacteristic
331C23×C4C22×D1311yescharacteristic
332C22×C8—132no—
333C22×C8—132no—
334C4⋊Q8—262no—
335C4⋊Q8—262no—
336#126—28no—
337#125—22no—
338#125C22⋊D1314yes—
339#124—524no—
340#123—28no—
341#121—28no—
342#121—22no—
343#121—22no—
344#121—22no—
345#121—22no—
346C4×D4—28no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4C22⋊D1314yes—
351#117—22no—
352#117—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—132no—
359C2×C4⋊C4—132no—
360C2×C4⋊C4—261no—
361C2×C4⋊C4C22⋊D1311yescharacteristic
362C2×C4⋊C4C22×D1311yescharacteristic
363C2×C4⋊C4C22×D1311yescharacteristic
364C2×C4⋊C4C22×D1311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—262no—
370C2×C22⋊C4—262no—
371C2×C22⋊C4C22⋊D1311yescharacteristic
372C2×C22⋊C4C22⋊D1311yescharacteristic
373C2×C42—21no—
374C2×C42—261no—
375C2×C42C22×D1311yescharacteristic
376#107—264no—
377#106—264no—
378#106—264no—
379C4⋊C8—262no—
380#102—264no—
381#102—264no—
382C22⋊C8—264no—
383C22⋊C8—264no—
384#97—262no—
385#95—261no—
386#95—262no—
387#95—262no—
388C2×C13—42no—
389C2×C13—81no—
390C2×C13—82no—
391C2×C13#243211yescharacteristic
392C2×C13#300611yescharacteristic
393C2×C13#300911yescharacteristic
394C2×C13#334512yes—
395C2×C13#335012yes—
396C24—21no—
397C24C2×C22⋊D1311yescharacteristic
398C24C2×C22⋊D1311yescharacteristic
399C2×Q8—522no—
400C2×Q8—522no—
401C2×Q8—522no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—82no—
413C2×D4C2×C22⋊D1312yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—82no—
428C22×C4—82no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C23×D1311yescharacteristic
436C2×C8—134no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C2×C8—262no—
441C2×C8—262no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—262no—
450C4⋊C4—262no—
451C4⋊C4—262no—
452C4⋊C4—262no—
453C4⋊C4—522no—
454C4⋊C4C2×C22⋊D1312yes—
455C4⋊C4C2×C22⋊D1312yes—
456C4⋊C4C2×C22⋊D1312yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—524no—
464C22⋊C4—524no—
465C42—24no—
466C42—522no—
467C42C2×C22⋊D1312yes—
468C42C2×C22⋊D1312yes—
469C13#2571411yescharacteristic, complemented, Sylow
470C23—21no—
471C23—22no—
472C23—22no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—22no—
477C23—22no—
478C23—21no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23#8820312yes—
485C23C22×C22⋊D1311yescharacteristic
486Q8—1044no—
487D4—22no—
488D4—22no—
489D4—44no—
490D4—48no—
491D4—42no—
492D4—84no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—84no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4#8820712yes—
522C2×C4#8820712yes—
523C2×C4#41×D1312yes—
524C2×C4#8825712yes—
525C2×C4C22×C22⋊D1311yescharacteristic
526C2×C4C22×C22⋊D1311yescharacteristic
527C8—264no—
528C8—522no—
529C22—24no—
530C22—22no—
531C22—41no—
532C22—42no—
533C22—41no—
534C22—42no—
535C22—41no—
536C22—42no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—42no—
542C22—82no—
543C22—82no—
544C22C2×#8820311yescharacteristic
545C22#1171952711yescharacteristic
546C22#1171952912yes—
547C22#1171954112yes—
548C22C2×#8820711yescharacteristic
549C4—22no—
550C4—22no—
551C4—42no—
552C4—42no—
553C4—42no—
554C4—41no—
555C4—41no—
556C4—1042no—
557C4—1042no—
558C4#1171953011yescharacteristic
559C4#1171953612yes—
560C4#1171953711yescharacteristic
561C2—42no—
562C2—81no—
563C2—82no—
564C2#1311846011yescharacteristic
565C2#1312408811yescharacteristic
566C2#1312411311yescharacteristic
567C2#1312730012yes—
568C2#1312737512yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
hypercenterC2×#553D13
hypocenterC13#25714
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718669C2semidirect
3. #13119828C2semidirect
4. #13116022C2semidirect
5. #13116015C2semidirect
6. #13115794C2semidirect
7. #13115635C2semidirect
8. #13115035C2semidirect
9. #13115029C2semidirect
10. #13114661C2semidirect
469. C13#25714semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117186692
#131198282
#131160222
#131160152
#131157942
#131156352
#131150352
#131150292
#131146612
C2×C13×#5532
#2571413