Finite Group Databasebeta

← #15921114

Subgroups — #15921114

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119857C211yesmaximal, characteristic, complemented
2#13116224C211yesmaximal, characteristic
3#13116210C211yesmaximal, characteristic
4#13115982C211yesmaximal, characteristic
5#13115972C211yesmaximal, characteristic
6#13115793C211yesmaximal, characteristic, complemented
7#13115784C211yesmaximal, characteristic, complemented
8#13115602C211yesmaximal, characteristic, complemented
9#13115555C211yesmaximal, characteristic, complemented
10#13115414C211yesmaximal, characteristic, complemented
11#13115407C211yesmaximal, characteristic, complemented
12#13114966C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C13×#2357C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88124C2211yescharacteristic
18C2×#88123C2211yescharacteristic
19C13×#390C2211yescharacteristic
20C13×#390C2211yescharacteristic
21C13×#388—21no—
22C13×#388—21no—
23C13×#382C2211yescharacteristic
24C13×#381—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718645—21no—
34#11718640—21no—
35C2×#88048C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718308—21no—
46#11718307—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C22×Dic26—21no—
62C4×D4×C13—22no—
63C4×D4×C13Q814yescomplemented
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C42×C13—21no—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93#88124—22no—
94#88124—41no—
95#88123—22no—
96#88123—41no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95D411yescharacteristic
102C13×#95D411yescharacteristic
103#88072—22no—
104#88072—22no—
105#88072—41no—
106#88072—41no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88048—22no—
113#88047—22no—
114C4⋊#1055—22no—
115C4⋊#1055—41no—
116C4⋊#1055—41no—
117C4×#1055—22no—
118#26030—131nomaximal, Sylow
119C24×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13C2×Q812yes—
126C22×C4×C13—21no—
127C22×C4×C13—24no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—81no—
131C22×C4×C13—81no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C2×Dic26—42no—
144C2×Dic26—42no—
145C2×Dic26—81no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4C2×Q812yes—
154C13×C22⋊C4—24no—
155C13×C22⋊C4—42no—
156C13×C22⋊C4—42no—
157C13×C22⋊C4—81no—
158C13×C22⋊C4—81no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—81no—
164C42×C13—81no—
165C42×C13C2×Q812yes—
166C42×C13#4112yes—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—42no—
174C4⋊Dic13#4112yes—
175C4⋊Dic13#4112yes—
176#6101—42no—
177#6101—42no—
178#6101—42no—
179#6101—81no—
180C4×Dic13—81no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193#2550—131no—
194#2357D1311yescharacteristic
195#2067—131no—
196#2065—131no—
197#2025—131no—
198#2023—131no—
199#1989—131no—
200#1987—131no—
201#1949—131no—
202#1939—131no—
203#1919—131no—
204#1918—131no—
205#1835—131no—
206#1804—131no—
207C4×#102—131no—
208C23×C13—22no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13C22×D411yescharacteristic
216D4×C13—22no—
217D4×C13—22no—
218D4×C13—41no—
219D4×C13—41no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—84no—
245C2×C4×C13C22⋊Q812yes—
246C2×C4×C13C22⋊Q812yes—
247C2×C4×C13#13512yes—
248C2×C4×C13C22×Q811yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13H(5,𝔽2)11yescharacteristic
253C2×C4×C132−1+411yescharacteristic
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266Dic26—84no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271C2×C4⋊Q8—131no—
272C2×#125—131no—
273C2×C4×D4C2×D1311yescharacteristic
274C2×#107—131no—
275C2×#106—131no—
276C2×C4⋊C8—131no—
277C2×C4⋊C8—131no—
278C2×C4⋊C8—131no—
279C2×#102—131no—
280C2×#102—131no—
281C2×#102—131no—
282C2×#102—131no—
283C2×C4×C8—131no—
284#398—261no—
285#395—261no—
286#391—261no—
287#390C2×D1311yescharacteristic
288#390C2×D1311yescharacteristic
289#389—131no—
290#389—131no—
291#389—261no—
292#388—21no—
293#388—21no—
294#382—131no—
295#382C2×D1311yescharacteristic
296#381—21no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4C2×D1311yescharacteristic
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C4⋊C4C2×D1311yescharacteristic
301C4×C22⋊C4—21no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340—131no—
312#336—131no—
313#336—131no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—81no—
318C22×C13—81no—
319C22×C13—81no—
320C22×C13—81no—
321C22×C13C2×C22⋊Q811yescharacteristic
322C22×C13#54611yescharacteristic
323C22×C13#54811yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13#57511yescharacteristic
326C22×C13#57611yescharacteristic
327C22×C13#57711yescharacteristic
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13#53311yescharacteristic
338C4×C13#54411yescharacteristic
339C4×C13#55511yescharacteristic
340C4×C13#55611yescharacteristic
341Dic13—42no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—261no—
346C22×D4C22×D1311yescharacteristic
347C23×C4—21no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C4⋊Q8—262no—
353C4⋊Q8—521no—
354#125—262no—
355#125—521no—
356C4×D4—22no—
357C4×D4Dic2614yescomplemented
358C2×C4⋊C4—131no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C22⋊D1311yescharacteristic
368C2×C4⋊C4C22⋊D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—261no—
380C2×C42C22×D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—262no—
384#106—262no—
385C4⋊C8—262no—
386C4⋊C8—521no—
387C4⋊C8—521no—
388#102—262no—
389#102—262no—
390#102—521no—
391#102—521no—
392C4×C8—262no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95C22⋊D1311yescharacteristic
403#95C22⋊D1311yescharacteristic
404C2×C13—82no—
405C2×C13#243911yescharacteristic
406C2×C13#307611yescharacteristic
407C2×C13#308111yescharacteristic
408C2×C13#330111yescharacteristic
409C2×C13#332211yescharacteristic
410C2×C13#336111yescharacteristic
411C2×C13#337111yescharacteristic
412C24—21no—
413C2×Q8—522no—
414C2×Q8—522no—
415C2×Q8—1041no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×Dic2612yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4C2×C22⋊D1311yescharacteristic
433C22×C4C2×C22⋊D1311yescharacteristic
434C22×C4C2×C22⋊D1311yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C23×D1311yescharacteristic
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—261no—
445C2×C8—261no—
446C2×C8—261no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—41no—
458C4⋊C4—132no—
459C4⋊C4—132no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—522no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4—522no—
470C4⋊C4—1041no—
471C4⋊C4C2×Dic2612yes—
472C22⋊C4—24no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—81no—
482C42—81no—
483C42—1041no—
484C42C2×Dic2612yes—
485C42#612712yes—
486C13#2603011yescharacteristic, complemented, Sylow
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×C22⋊D1311yescharacteristic
495Q8—1044no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—84no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4#8817812yes—
538C2×C4#8817812yes—
539C2×C4#8820412yes—
540C2×C4C22×Dic2611yescharacteristic
541C2×C4C2×#612711yescharacteristic
542C2×C4#41×D1311yescharacteristic
543C2×C4#41×D1311yescharacteristic
544C2×C4#8825611yescharacteristic
545C2×C4#8825711yescharacteristic
546C8—521no—
547C8—521no—
548C8—521no—
549C8—521no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#8817811yescharacteristic
558C22C2×#8820411yescharacteristic
559C22#1171952711yescharacteristic
560C22#1171953411yescharacteristic
561C22#1171953611yescharacteristic
562C22#1171954011yescharacteristic
563C22#1171954111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—522no—
574C4—522no—
575C4—1041no—
576C4—1041no—
577C4#1171922211yescharacteristic
578C4#1171922411yescharacteristic
579C4#1171923711yescharacteristic
580C4#1171923811yescharacteristic
581C2—82no—
582C2#1311852111yescharacteristic
583C2#1312462411yescharacteristic
584C2#1312466711yescharacteristic
585C2#1312673211yescharacteristic
586C2#1312703111yescharacteristic
587C2#1312749211yescharacteristic
588C2#1312759811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2357C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2357D13
hypocenterC13#26030
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #13119857C2semidirect
6. #13115793C2semidirect
7. #13115784C2semidirect
8. #13115602C2semidirect
9. #13115555C2semidirect
10. #13115414C2semidirect
11. #13115407C2semidirect
12. #13114966C2semidirect
63. C4×D4×C13Q8semidirect
357. C4×D4Dic26semidirect
486. C13#26030semidirect

Maximal subgroups

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

subgroupindex
#131198572
#131162242
#131162102
#131159822
#131159722
#131157932
#131157842
#131156022
#131155552
#131154142
#131154072
#131149662
#131148462
C4×#880722
C13×#23572
#2603013