Finite Group Databasebeta

← #15903984

Subgroups — #15903984

Order 3328.

808 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic
3#13120027C211yesmaximal, characteristic, complemented
4#13116249C211yesmaximal, characteristic
5#13116239C211yesmaximal, characteristic
6#13116153C211yesmaximal, characteristic
7#13116153C211yesmaximal, characteristic
8#13115804C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115594C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115477C211yesmaximal, characteristic, complemented
13#13115470C211yesmaximal, characteristic, complemented
14#13114838C211yesmaximal, characteristic, complemented
15C13×#2354C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117—21no—
18C22×#6105C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C13×#390C2211yescharacteristic
22C13×#390C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#384C2211yescharacteristic
26C13×#380—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718679—24no—
34#11718670—24no—
35#11718644—21no—
36#11718644—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718597C2211yescharacteristic
44#11718596C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718314—21no—
52#11718314—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×Dic26C2311yescharacteristic
64C4×D4×C13—22no—
65C4×D4×C13D414yes—
66C13×#117—44no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×#6105—22no—
85C2×#6105—22no—
86C2×#6105—22no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100#88124—22no—
101#88124—22no—
102C4×Dic26—22no—
103C4×Dic26—22no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95D411yescharacteristic
107C13×#95D411yescharacteristic
108#88072—22no—
109#88072—22no—
110#88072—22no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88050—22no—
118#88050—22no—
119#88050—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123C4⋊#1055—22no—
124C4⋊#1055—22no—
125C4⋊#1055—22no—
126#88043—22no—
127#24690—131nomaximal, Sylow
128C24×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13C2×D412yes—
135C22×C4×C13—21no—
136C22×C4×C13—24no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26#4112yes—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—81no—
167C13×C4⋊C4C2×D412yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—81no—
172C13×C22⋊C4—81no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—42no—
178C42×C13—42no—
179C42×C13C2×D412yes—
180C42×C13#4112yes—
181#6105—28no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—42no—
189C4⋊Dic13—42no—
190#6101—42no—
191#6101—42no—
192#6101—42no—
193C4×Dic13—42no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055#4112yes—
206C2×#478—131no—
207C2×#440—131no—
208#2565—131no—
209#2354D1311yescharacteristic
210#2073—131no—
211#2071—131no—
212#2055—131no—
213#2055—131no—
214#1992—131no—
215#1949—131no—
216#1947—131no—
217#1940—131no—
218#1928—131no—
219#1927—131no—
220#1803—131no—
221C23×C13—22no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13C22×D411yescharacteristic
229D4×C13—22no—
230D4×C13—22no—
231D4×C13—41no—
232D4×C13—41no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—48no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13#12112yes—
259C2×C4×C13#12112yes—
260C2×C4×C13AGL(1,ℤ/8)12yes—
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279Dic26—22no—
280Dic26—22no—
281Dic26—41no—
282Dic26—41no—
283#1055—22no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C22×SD16—131no—
288C2×#125—131no—
289C2×C4×Q8—131no—
290C2×C4×D4C2×D1311yescharacteristic
291C2×#117—21no—
292#478—264no—
293#440—264no—
294C2×#107—131no—
295C2×#107—131no—
296C2×#106—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8—131no—
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#102—131no—
306C2×#97—131no—
307#398—261no—
308#398—261no—
309#391—131no—
310#391—131no—
311#390C2×D1311yescharacteristic
312#390C2×D1311yescharacteristic
313#388—21no—
314#388—21no—
315#387—261no—
316#387—261no—
317#384—131no—
318#384C2×D1311yescharacteristic
319#382—131no—
320#380—21no—
321C4×C4⋊C4C2×D1311yescharacteristic
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C4⋊C4C2×D1311yescharacteristic
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#336—131no—
331#336—131no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13C2×#12111yescharacteristic
340C22×C13#54711yescharacteristic
341C22×C13#54811yescharacteristic
342C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C13#57511yescharacteristic
344C22×C13#57711yescharacteristic
345C22×C13#57811yescharacteristic
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—22no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—42no—
353C4×C13—81no—
354C4×C13—81no—
355C4×C13#52511yescharacteristic
356C4×C13#53611yescharacteristic
357C4×C13#55211yescharacteristic
358C4×C13#55611yescharacteristic
359Dic13—42no—
360Dic13—81no—
361Dic13—81no—
362Dic13—81no—
363C22×Q8—131no—
364C22×D4C22×D1311yescharacteristic
365C23×C4—21no—
366C2×SD16—262no—
367C2×SD16—262no—
368C2×SD16—262no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—131no—
373#125—262no—
374#125—262no—
375C4×Q8—262no—
376C4×Q8—262no—
377C4×D4—22no—
378C4×D4D5214yes—
379#117—44no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4C22⋊D1311yescharacteristic
391C2×C4⋊C4C22⋊D1311yescharacteristic
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—261no—
403C2×C42C22×D1311yescharacteristic
404C2×C42C22×D1311yescharacteristic
405C2×C42C22×D1311yescharacteristic
406#107—262no—
407#107—262no—
408#106—262no—
409C4⋊C8—262no—
410C4⋊C8—262no—
411C4⋊C8—262no—
412#103—262no—
413#103—262no—
414#103—262no—
415#102—262no—
416#102—262no—
417#102—262no—
418#97—262no—
419#95—21no—
420#95—21no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95C22⋊D1311yescharacteristic
428#95C22⋊D1311yescharacteristic
429C2×C13—82no—
430C2×C13#241511yescharacteristic
431C2×C13#303611yescharacteristic
432C2×C13#304611yescharacteristic
433C2×C13#334311yescharacteristic
434C2×C13#334811yescharacteristic
435C2×C13#336811yescharacteristic
436C2×C13#337711yescharacteristic
437C24—21no—
438C2×Q8—132no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×D5212yes—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C23×D1311yescharacteristic
467SD16—268no—
468C2×C8—132no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4C2×D5212yes—
501C22⋊C4—24no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—42no—
512C42—522no—
513C42C2×D5212yes—
514C42#612712yes—
515C13#2469011yescharacteristic, complemented, Sylow
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×C22⋊D1311yescharacteristic
524Q8—262no—
525Q8—262no—
526Q8—521no—
527Q8—521no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—48no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—262no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4#8818412yes—
570C2×C4#8818412yes—
571C2×C4#8818612yes—
572C2×C4C22×D5211yescharacteristic
573C2×C4C2×#612711yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#41×D1311yescharacteristic
576C2×C4#8825711yescharacteristic
577C2×C4#8825711yescharacteristic
578C8—262no—
579C8—521no—
580C8—521no—
581C8—521no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C2×#8818411yescharacteristic
590C22C2×#8818611yescharacteristic
591C22#1171952711yescharacteristic
592C22#1171952911yescharacteristic
593C22#1171953611yescharacteristic
594C22#1171954111yescharacteristic
595C22#1171954311yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—522no—
606C4—1041no—
607C4—1041no—
608C4—1041no—
609C4#1171922911yescharacteristic
610C4#1171923111yescharacteristic
611C4#1171923411yescharacteristic
612C4#1171923811yescharacteristic
613C2—82no—
614C2#1311825911yescharacteristic
615C2#1312430011yescharacteristic
616C2#1312438611yescharacteristic
617C2#1312727011yescharacteristic
618C2#1312735111yescharacteristic
619C2#1312756111yescharacteristic
620C2#1312767211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2354C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2354D13
hypocenterC13#24690
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
3. #13120027C2semidirect
8. #13115804C2semidirect
9. #13115604C2semidirect
10. #13115594C2semidirect
11. #13115560C2semidirect
12. #13115477C2semidirect
13. #13115470C2semidirect
14. #13114838C2semidirect
515. C13#24690semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117186792
#131200272
#131162492
#131162392
#131161532
#131158042
#131156042
#131155942
#131155602
#131154772
#131154702
#131148382
C13×#23542
#2469013