Finite Group Databasebeta

← #15770776

Subgroups — #15770776

Order 3328.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88045C211yesmaximal, characteristic
2C2×#11718627C211yesmaximal, characteristic
3#13117429C211yesmaximal, characteristic
4C2×#11718122C211yesmaximal, characteristic, complemented
5#13114555C211yesmaximal, characteristic, complemented
6C2×#11718115C211yesmaximal, characteristic, complemented
7C13×C4⋊#95C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C2×C13×#95—22no—
16#11718874—22no—
17#11718649—21no—
18#11718648—21no—
19#11718648—21no—
20#11718635—21no—
21C2×#88050—21no—
22#11718627—22no—
23#11718627C414yescomplemented
24C2×#88049—21no—
25C2×#88045—22no—
26C2×#88045—22no—
27C2×#88045—22no—
28#11718122—22no—
29#11718121—21no—
30#11718121—21no—
31#11718115—22no—
32C23×C4×C13—21no—
33C23×C4×C13—21no—
34C23×C4×C13D412yes—
35C23×C4×C13C2311yescharacteristic
36C22×C22⋊D13—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127C2×C412yes—
48C2×#6127D412yes—
49C22×D52D411yescharacteristic
50C22×C4×D13—21no—
51C22×Dic26D411yescharacteristic
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4C2×C412yes—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C2×C42×C13—21no—
69C2×C42×C13D412yes—
70C2×C22⋊Dic13—21no—
71C2×#6103—22no—
72C2×#6103—22no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77C2×C4⋊Dic13D411yescharacteristic
78C2×C4⋊Dic13D411yescharacteristic
79C2×C4×Dic13—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099C2×C412yes—
91C2×#6099D412yes—
92C22×#1055—21no—
93C22×#1055—21no—
94C13×#95—44no—
95#88071—22no—
96#88071—22no—
97#88050—24no—
98#88049—24no—
99#88045—28no—
100#11195—131nomaximal, Sylow
101C24×C13C2×D411yescharacteristic
102C23×D13—21no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13—42no—
115C22×C4×C13—42no—
116C22×C4×C13—42no—
117C22×C4×C13—42no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C22×C4×C13#4111yescharacteristic
128C22×C4×C13#4111yescharacteristic
129C22×C4×C13#4111yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C22×C4×C13#4111yescharacteristic
132C22×C4×C13#4111yescharacteristic
133C22×C4×C13#4111yescharacteristic
134C2×C22⋊D13—22no—
135C2×C22⋊D13—22no—
136C2×C22⋊D13—41no—
137C2×C22⋊D13—41no—
138C2×C22⋊D13—41no—
139C2×C22⋊D13—41no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143#6127—22no—
144#6127—22no—
145#6127—22no—
146#6127—22no—
147#6127—22no—
148#6127—22no—
149#6127—22no—
150#6127—22no—
151#6127—41no—
152#6127—41no—
153#6127—41no—
154#6127—41no—
155#6127—41no—
156#6127—41no—
157#6127—41no—
158#6127—41no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52C22⋊C412yes—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—41no—
168C2×C4×D13—41no—
169C2×C4×D13—41no—
170C2×C4×D13—41no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26C22⋊C412yes—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4—41no—
185C42×C13—22no—
186C42×C13—22no—
187C42×C13—41no—
188C42×C13—41no—
189C22⋊Dic13—41no—
190C22⋊Dic13—41no—
191#6103—82no—
192#6103—82no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4×Dic13—41no—
198C4×Dic13—41no—
199#6099—22no—
200#6099—22no—
201#6099—22no—
202#6099—22no—
203#6099—41no—
204#6099—41no—
205#6099—41no—
206#6099—41no—
207C2×#1055—22no—
208C2×#1055—22no—
209C2×#1055—41no—
210C2×#1055—41no—
211C2×#1055—41no—
212C2×#1055—41no—
213C22×#104—131no—
214C2×#417—131no—
215#2311—131no—
216C2×#343—131no—
217#1736—131no—
218C2×#339—131no—
219C4⋊#95D1311yescharacteristic, complemented
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13C4×D411yescharacteristic
225C23×C13#12011yescharacteristic
226C23×C13#12111yescharacteristic
227C23×C13#12111yescharacteristic
228C23×C13#12111yescharacteristic
229C23×C13#12311yescharacteristic
230C23×C13#12411yescharacteristic
231C22×D13—22no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C2×C4×C13—24no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—44no—
246C2×C4×C13—44no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—82no—
252C2×C4×C13—81no—
253C2×C4×C13—81no—
254C2×C4×C13—82no—
255C2×C4×C13C2×C22⋊C411yescharacteristic
256C2×C4×C13#11711yescharacteristic
257C2×C4×C13#11711yescharacteristic
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12111yescharacteristic
263C2×C4×C13#12111yescharacteristic
264C2×C4×C13#12111yescharacteristic
265C2×C4×C13#12111yescharacteristic
266C2×C4×C13#12111yescharacteristic
267C2×C4×C13#12311yescharacteristic
268C2×C4×C13#12311yescharacteristic
269C2×C4×C13#12311yescharacteristic
270C2×C4×C13#12311yescharacteristic
271C2×C4×C13#12311yescharacteristic
272C2×C4×C13#12311yescharacteristic
273C2×C4×C13#12311yescharacteristic
274C2×C4×C13#12311yescharacteristic
275C2×C4×C13#12311yescharacteristic
276C2×C4×C13#12411yescharacteristic
277C2×C4×C13#12411yescharacteristic
278C2×C4×C13#12411yescharacteristic
279C2×C4×C13#12611yescharacteristic
280C2×C4×C13#12611yescharacteristic
281C2×C4×C13#12611yescharacteristic
282C2×C4×C13#12611yescharacteristic
283C22⋊D13—42no—
284C22⋊D13—42no—
285C22⋊D13—42no—
286C22⋊D13—42no—
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296D52—22no—
297D52—22no—
298D52—41no—
299D52—41no—
300C4×D13—42no—
301C4×D13—42no—
302C4×D13—42no—
303C4×D13—42no—
304Dic26—22no—
305Dic26—22no—
306Dic26—41no—
307Dic26—41no—
308#1055—42no—
309#1055—42no—
310C22×#41—131no—
311C22×M16—131no—
312C22×M16—131no—
313C2×#117—131no—
314C22×C4⋊C4C2×D1311yescharacteristic
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C42C2×D1311yescharacteristic
317C2×#104—262no—
318C2×#104—262no—
319C2×#104—262no—
320#417—134no—
321#417—262no—
322C2×#103—261no—
323C2×#102—261no—
324#391—261no—
325#390—261no—
326#386—262no—
327#380—261no—
328#380—261no—
329C2×#95—22no—
330#343—262no—
331#340—261no—
332#340—261no—
333#339—262no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13#38611yescharacteristic
347C22×C13#38811yescharacteristic
348C22×C13#38811yescharacteristic
349C22×C13#39411yescharacteristic
350C22×C13#39411yescharacteristic
351C22×C13#39411yescharacteristic
352C22×C13#39711yescharacteristic
353C22×C13#45311yescharacteristic
354C22×C13#45411yescharacteristic
355C22×C13#45511yescharacteristic
356C22×C13#45611yescharacteristic
357C2×D13—42no—
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—81no—
361C2×D13—81no—
362C2×D13—81no—
363C2×D13—81no—
364C4×C13—44no—
365C4×C13—82no—
366C4×C13—82no—
367C4×C13#38111yescharacteristic
368C4×C13#38611yescharacteristic
369C4×C13#38811yescharacteristic
370C4×C13#38811yescharacteristic
371C4×C13#39411yescharacteristic
372C4×C13#39711yescharacteristic
373C4×C13#39711yescharacteristic
374C4×C13#39711yescharacteristic
375Dic13—42no—
376Dic13—81no—
377Dic13—81no—
378C2×#41—132no—
379C2×#41—132no—
380C2×#41—261no—
381C2×#41—261no—
382C2×#41—261no—
383C2×#41—261no—
384C2×#41—261no—
385C2×#41—261no—
386C2×#41—261no—
387C2×#41—261no—
388C2×#41—261no—
389C2×#41—261no—
390C22×Q8—131no—
391C22×D4—131no—
392C22×D4—261no—
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—261no—
396C23×C4C22⋊D1312yes—
397C23×C4C22×D1311yescharacteristic
398C2×M16—132no—
399C2×M16—132no—
400C2×M16—261no—
401C2×M16—261no—
402C2×M16—261no—
403C2×M16—261no—
404C2×M16—261no—
405C2×M16—261no—
406C2×M16—261no—
407C2×M16—261no—
408C2×M16—261no—
409C2×M16—261no—
410C22×C8—261no—
411C22×C8—261no—
412#117—261no—
413#117—261no—
414#117—261no—
415#117—261no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—131no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4C4×D1312yes—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—262no—
432C2×C22⋊C4—262no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—261no—
439C2×C42D5212yes—
440#104—268no—
441#103—264no—
442#102—264no—
443#95—44no—
444#95—262no—
445#95—262no—
446C2×C13—21no—
447C2×C13—21no—
448C2×C13—21no—
449C2×C13—21no—
450C2×C13#144011yescharacteristic
451C2×C13#188211yescharacteristic
452C2×C13#188311yescharacteristic
453C2×C13#203711yescharacteristic
454C2×C13#203811yescharacteristic
455C2×C13#203911yescharacteristic
456C2×C13#204011yescharacteristic
457D13—82no—
458C24—261no—
459C24C2×C22⋊D1311yescharacteristic
460#41—262no—
461#41—262no—
462#41—262no—
463#41—262no—
464#41—262no—
465#41—262no—
466#41—262no—
467#41—262no—
468#41—521no—
469#41—521no—
470#41—521no—
471#41—521no—
472#41—521no—
473#41—521no—
474#41—521no—
475#41—521no—
476C2×Q8—132no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×D4—132no—
483C2×D4—262no—
484C2×D4—262no—
485C2×D4—261no—
486C2×D4—261no—
487C2×D4—261no—
488C2×D4—261no—
489C2×D4—261no—
490C2×D4—521no—
491C2×D4—521no—
492C2×D4—521no—
493C2×D4—521no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—261no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—521no—
517C22×C4—521no—
518C22×C4—521no—
519C22×C4—521no—
520C22×C4C2×C4×D1311yescharacteristic
521C22×C4C2×D5211yescharacteristic
522C22×C4#612711yescharacteristic
523C22×C4#612711yescharacteristic
524C22×C4#612711yescharacteristic
525C22×C4#612711yescharacteristic
526C22×C4D4×D1311yescharacteristic
527C22×C4D4×D1311yescharacteristic
528C22×C4D4×D1311yescharacteristic
529C22×C4D4×D1311yescharacteristic
530C22×C4#612911yescharacteristic
531C22×C4#612911yescharacteristic
532C22×C4#613111yescharacteristic
533C22×C4#613111yescharacteristic
534M16—262no—
535M16—262no—
536M16—262no—
537M16—262no—
538M16—521no—
539M16—521no—
540M16—521no—
541M16—521no—
542C2×C8—262no—
543C2×C8—262no—
544C2×C8—521no—
545C2×C8—521no—
546C2×C8—521no—
547C2×C8—521no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C22⋊C4—521no—
561C22⋊C4—521no—
562C22⋊C4—1042no—
563C22⋊C4—1042no—
564C42—22no—
565C42—22no—
566C42—41no—
567C42—41no—
568C42—521no—
569C42—521no—
570C13#1119511yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—262no—
576C23—521no—
577C23—521no—
578C23—521no—
579C23—521no—
580C23—521no—
581C23—521no—
582C23C4×C22⋊D1311yescharacteristic
583C23#8818311yescharacteristic
584C23#8818411yescharacteristic
585C23#8819111yescharacteristic
586C23#8819211yescharacteristic
587C23#8819311yescharacteristic
588C23#8820111yescharacteristic
589Q8—262no—
590Q8—262no—
591Q8—521no—
592Q8—521no—
593D4—262no—
594D4—262no—
595D4—522no—
596D4—522no—
597D4—522no—
598D4—522no—
599D4—521no—
600D4—521no—
601C2×C4—24no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—82no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—82no—
618C2×C4—262no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4#8812611yescharacteristic
632C2×C4C4×D5211yescharacteristic
633C2×C4#8812911yescharacteristic
634C2×C4#8813011yescharacteristic
635C2×C4C22⋊C4×D1311yescharacteristic
636C2×C4#8813511yescharacteristic
637C2×C4#8813611yescharacteristic
638C2×C4#8813711yescharacteristic
639C2×C4#8813711yescharacteristic
640C2×C4#8813711yescharacteristic
641C2×C4#8813811yescharacteristic
642C2×C4#8813811yescharacteristic
643C2×C4#8813811yescharacteristic
644C2×C4#8813911yescharacteristic
645C2×C4#8813911yescharacteristic
646C2×C4#8814011yescharacteristic
647C2×C4#8814611yescharacteristic
648C2×C4#8814711yescharacteristic
649C2×C4#8814811yescharacteristic
650C2×C4#8814811yescharacteristic
651C2×C4#8814811yescharacteristic
652C2×C4#8814811yescharacteristic
653C2×C4#8814811yescharacteristic
654C2×C4#8814911yescharacteristic
655C2×C4#8814911yescharacteristic
656C2×C4#8815211yescharacteristic
657C2×C4#8815211yescharacteristic
658C2×C4#8815211yescharacteristic
659C8—522no—
660C8—522no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—522no—
674C22—522no—
675C22—522no—
676C22—1041no—
677C22—1041no—
678C22—1041no—
679C22—1041no—
680C22#1171860111yescharacteristic
681C22#1171861711yescharacteristic
682C22#1171862011yescharacteristic
683C22#1171862211yescharacteristic
684C22#1171865111yescharacteristic
685C22#1171865211yescharacteristic
686C22#1171865411yescharacteristic
687C22#1171872211yescharacteristic
688C22#1171872311yescharacteristic
689C22#1171873811yescharacteristic
690C22#1171875611yescharacteristic
691C4—44no—
692C4—82no—
693C4—82no—
694C4—522no—
695C4—1041no—
696C4—1041no—
697C4#1171832511yescharacteristic
698C4#1171832611yescharacteristic
699C4#1171833011yescharacteristic
700C4#1171833111yescharacteristic
701C4#1171833311yescharacteristic
702C4#1171833511yescharacteristic
703C4#1171833611yescharacteristic
704C4#1171833611yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—1042no—
710C2#1311308411yescharacteristic
711C2#1311520811yescharacteristic
712C2#1311521511yescharacteristic
713C2#1311604611yescharacteristic
714C2#1311605311yescharacteristic
715C2#1311606011yescharacteristic
716C2#1311606511yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×C4⋊#95C2
socleC23×C13#120
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC4⋊#95D13
hypocenterC13#11195
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718122C2semidirect
5. #13114555C2semidirect
6. C2×#11718115C2semidirect
7. C13×C4⋊#95C2semidirect
23. #11718627C4semidirect
219. C4⋊#95D13semidirect
570. C13#11195semidirect

Maximal subgroups

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

subgroupindex
C22×#880452
C2×#117186272
#131174292
C2×#117181222
#131145552
C2×#117181152
C13×C4⋊#952
#1119513