Finite Group Databasebeta

← #15920666

Subgroups — #15920666

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118560C211yesmaximal, characteristic
2#13116404C211yesmaximal, characteristic, complemented
3#13116338C211yesmaximal, characteristic, complemented
4#13116332C211yesmaximal, characteristic, complemented
5#13116174C211yesmaximal, characteristic, complemented
6#13115793C211yesmaximal, characteristic, complemented
7#13115604C211yesmaximal, characteristic, complemented
8#13115428C211yesmaximal, characteristic, complemented
9#13115414C211yesmaximal, characteristic, complemented
10#13115023C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114922C211yesmaximal, characteristic
13#13114859C211yesmaximal, characteristic
14C2×#11718121C211yesmaximal, characteristic
15C13×#2344C211yesmaximal, characteristic
16C2×C13×#117—21no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C2×#88124C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C13×#381—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88048C2211yescharacteristic
33C2×#88048C2211yescharacteristic
34C2×#88047C2211yescharacteristic
35C2×#88047C2211yescharacteristic
36#11718607—21no—
37#11718603—21no—
38#11718597C2211yescharacteristic
39#11718589C2211yescharacteristic
40#11718589C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718321—21no—
44#11718318—21no—
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C13×#117—44no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4Q814yes—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C13×C22⋊C4D411yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13—21no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—41no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C22×#1055—22no—
92C22×#1055—22no—
93C22×#1055—41no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98#88124—22no—
99#88124—41no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112C22⋊#1055—22no—
113#88048—22no—
114#88048—41no—
115#88047—22no—
116#88047—41no—
117C4⋊#1055—22no—
118C4⋊#1055—41no—
119#25998—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—24no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×Q812yes—
138C22×C4×C13#4112yes—
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—42no—
145C22×Dic13—42no—
146C22×Dic13—81no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—42no—
156C13×C4⋊C4C2×Q812yes—
157C13×C4⋊C4C2×Q812yes—
158C13×C22⋊C4—22no—
159C13×C22⋊C4—22no—
160C13×C22⋊C4—42no—
161C42×C13—21no—
162C42×C13—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13—42no—
166C42×C13—42no—
167C22⋊Dic13—42no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—42no—
176C4⋊Dic13#4112yes—
177#6101—42no—
178#6101—42no—
179#6101—81no—
180#6101—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—44no—
193C2×#1055#4112yes—
194#2442—131no—
195#2344D1311yescharacteristic
196#2101—131no—
197#2088—131no—
198#2087—131no—
199#2059—131no—
200#1989—131no—
201#1949—131no—
202#1921—131no—
203#1919—131no—
204#1852—131no—
205#1850—131no—
206#1823—131no—
207#1807—131no—
208C2×#340—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C22⋊Q812yes—
214C23×C13#13512yes—
215C23×C13AGL(1,ℤ/8)12yes—
216C23×C13C22×D411yescharacteristic
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
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—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—48no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C22⋊Q812yes—
249C2×C4×C13C22×Q811yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C132−1+411yescharacteristic
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—
266C2×Dic13—41no—
267C2×Dic13—84no—
268#1055—22no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272C23×C8—131no—
273C2×#125—131no—
274C2×#117—21no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4C2×D1311yescharacteristic
277C2×#107—131no—
278C2×#107—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×C4⋊C8—131no—
282C2×C4⋊C8—131no—
283C2×C22⋊C8—131no—
284#400—261no—
285#398—261no—
286#389—131no—
287#389—131no—
288#389C2×D1311yescharacteristic
289#389C2×D1311yescharacteristic
290#387—21no—
291#387—21no—
292#385—261no—
293#382—131no—
294#381—21no—
295#380—131no—
296#380—261no—
297#380C2×D1311yescharacteristic
298C4×C4⋊C4C2×D1311yescharacteristic
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C22⋊C4C2×D1311yescharacteristic
301#340—131no—
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#340—131no—
313#336—131no—
314#336—131no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13#47814yes—
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13#54611yescharacteristic
324C22×C13#54711yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57811yescharacteristic
329C4×C13—22no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13#53311yescharacteristic
339C4×C13#54411yescharacteristic
340C4×C13#55111yescharacteristic
341C4×C13#55211yescharacteristic
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345Dic13—81no—
346C23×C4—21no—
347C23×C4—261no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8—131no—
353C22×C8—262no—
354C22×C8—262no—
355C22×C8—521no—
356#125—262no—
357#125—521no—
358#117—44no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—521no—
374C2×C4⋊C4Dic2614yes—
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4C22⋊D1311yescharacteristic
382C2×C22⋊C4C22⋊D1311yescharacteristic
383C2×C42—21no—
384C2×C42—21no—
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#107—262no—
388#107—521no—
389#106—262no—
390#106—521no—
391C4⋊C8—262no—
392C4⋊C8—521no—
393C22⋊C8—262no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95C22⋊D1311yescharacteristic
405#95C22⋊D1311yescharacteristic
406C2×C13—24no—
407C2×C13#243811yescharacteristic
408C2×C13C2×#47811yescharacteristic
409C2×C13#308211yescharacteristic
410C2×C13#330011yescharacteristic
411C2×C13#330611yescharacteristic
412C2×C13#333711yescharacteristic
413C2×C13#334311yescharacteristic
414C24C2×C22⋊D1311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—522no—
431C22×C4—522no—
432C22×C4—1041no—
433C22×C4C2×Dic2612yes—
434C22×C4#612712yes—
435C22×C4C2×C22⋊D1311yescharacteristic
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441C2×C8—132no—
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—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—524no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—132no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—522no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C4⋊C4—1041no—
475C4⋊C4—1041no—
476C4⋊C4C2×Dic2612yes—
477C4⋊C4C2×Dic2612yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—42no—
481C22⋊C4—522no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—42no—
488C13#2599811yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23#8817812yes—
494C23#8818612yes—
495C23#8820412yes—
496C23C22×C22⋊D1311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
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—21no—
517C2×C4—48no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—262no—
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—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1044no—
541C2×C4#8817812yes—
542C2×C4C22×Dic2611yescharacteristic
543C2×C4C2×#612711yescharacteristic
544C2×C4#41×D1311yescharacteristic
545C2×C4#41×D1311yescharacteristic
546C2×C4#8825611yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—262no—
549C8—521no—
550C8—521no—
551C8—521no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22#1171867014yes—
559C22C2×#8817811yescharacteristic
560C22C2×#8818611yescharacteristic
561C22C2×#8820411yescharacteristic
562C22#1171952911yescharacteristic
563C22#1171953411yescharacteristic
564C22#1171954211yescharacteristic
565C22#1171954311yescharacteristic
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—522no—
576C4—1041no—
577C4—1041no—
578C4—1041no—
579C4#1171922211yescharacteristic
580C4#1171922411yescharacteristic
581C4#1171923211yescharacteristic
582C4#1171923611yescharacteristic
583C2—24no—
584C2#1311850611yescharacteristic
585C2C2×#1171867011yescharacteristic
586C2#1312467811yescharacteristic
587C2#1312671711yescharacteristic
588C2#1312679111yescharacteristic
589C2#1312721511yescharacteristic
590C2#1312727011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2344C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2344D13
hypocenterC13#25998
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
3. #13116338C2semidirect
4. #13116332C2semidirect
5. #13116174C2semidirect
6. #13115793C2semidirect
7. #13115604C2semidirect
8. #13115428C2semidirect
9. #13115414C2semidirect
488. C13#25998semidirect

Maximal subgroups

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

subgroupindex
#131185602
#131164042
#131163382
#131163322
#131161742
#131157932
#131156042
#131154282
#131154142
#131150232
#131150162
#131149222
#131148592
C2×#117181212
C13×#23442
#2599813