Finite Group Databasebeta

← #15770773

Subgroups — #15770773

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×#88077C211yesmaximal, characteristic
2#13117428C211yesmaximal, characteristic
3C2×#11718146C211yesmaximal, characteristic, complemented
4#13114555C211yesmaximal, characteristic, complemented
5C2×#11718147C211yesmaximal, characteristic, complemented
6#13113065C211yesmaximal, characteristic, complemented
7C2×C13×#417C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C2×#88180C2211yescharacteristic
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C13×#417—22no—
16C13×#417C414yescomplemented
17C2×C13×#103—21no—
18C2×C13×#102—21no—
19C2×#88077—22no—
20C2×#88077—22no—
21C2×#88077—22no—
22#11718891—21no—
23#11718882—21no—
24#11718881—22no—
25#11718873—21no—
26#11718873—21no—
27C2×#88071—22no—
28#11718147—22no—
29#11718146—22no—
30#11718121—21no—
31#11718121—21no—
32C2×C13×#41—21no—
33C2×C13×#41—21no—
34C2×C13×#41—21no—
35C2×C13×#41—21no—
36C2×C13×#41—21no—
37C2×C13×#41—21no—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41C2×C412yes—
43C2×C13×#41D412yes—
44C22×Q8×C13D411yescharacteristic
45C22×D4×C13—21no—
46C22×D4×C13D411yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13—21no—
49C23×C4×C13C2311yescharacteristic
50C23×Dic13—21no—
51C23×Dic13D412yes—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16C2×C412yes—
58C22×C8×C13—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2×C412yes—
65C2×C22⋊Dic13—21no—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13—22no—
68#88180—21no—
69#88180—21no—
70#88180—21no—
71#88180—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13D411yescharacteristic
79C2×C4⋊Dic13D411yescharacteristic
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13D412yes—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099—21no—
91C2×#6099—21no—
92C2×#6099D412yes—
93C22×#1055—21no—
94C13×#103—24no—
95C13×#102—24no—
96#88077—28no—
97#88071—22no—
98#88071—22no—
99#88071—44no—
100#11195—131nomaximal, Sylow
101C24×C13—21no—
102C24×C13C2×D411yescharacteristic
103C13×#41—22no—
104C13×#41—22no—
105C13×#41—22no—
106C13×#41—22no—
107C13×#41—22no—
108C13×#41—22no—
109C13×#41—22no—
110C13×#41—22no—
111C13×#41—41no—
112C13×#41—41no—
113C13×#41—41no—
114C13×#41—41no—
115C13×#41—41no—
116C13×#41—41no—
117C13×#41—41no—
118C13×#41—41no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13—21no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13C22⋊C412yes—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13C22⋊C412yes—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C22×C4×C13#4111yescharacteristic
157C22×C4×C13#4111yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—41no—
172C22×Dic13—41no—
173C22×Dic13—41no—
174C22×Dic13—41no—
175C22×Dic13—42no—
176C22×Dic13—42no—
177C13×M16—22no—
178C13×M16—22no—
179C13×M16—41no—
180C13×M16—41no—
181C2×C8×C13—22no—
182C2×C8×C13—41no—
183C2×C8×C13—41no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C22⋊Dic13—41no—
189C22⋊Dic13—41no—
190C22⋊Dic13—82no—
191C22⋊Dic13—82no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—41no—
197C4⋊Dic13—41no—
198C4⋊Dic13—41no—
199C4⋊Dic13—41no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—41no—
203C4×Dic13—41no—
204C4×Dic13—41no—
205C4×Dic13—41no—
206#6099—22no—
207#6099—22no—
208#6099—41no—
209#6099—41no—
210C2×#1055—22no—
211C2×#1055—41no—
212C2×#1055—41no—
213C22×#104—131no—
214C2×#417D1311yescharacteristic
215#2311—131no—
216C2×#343—131no—
217#1736—131no—
218C2×#339—131no—
219C4⋊#95—131no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—22no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13C4×D411yescharacteristic
232C23×C13#12011yescharacteristic
233C23×C13#12111yescharacteristic
234C23×C13#12111yescharacteristic
235C23×C13#12111yescharacteristic
236C23×C13#12311yescharacteristic
237C23×C13#12411yescharacteristic
238Q8×C13—22no—
239Q8×C13—22no—
240Q8×C13—41no—
241Q8×C13—41no—
242D4×C13—22no—
243D4×C13—22no—
244D4×C13—42no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—42no—
248D4×C13—41no—
249D4×C13—41no—
250C2×C4×C13—22no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—44no—
258C2×C4×C13—42no—
259C2×C4×C13—82no—
260C2×C4×C13—81no—
261C2×C4×C13—81no—
262C2×C4×C13C2×C22⋊C411yescharacteristic
263C2×C4×C13#11711yescharacteristic
264C2×C4×C13#11711yescharacteristic
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C4×D411yescharacteristic
267C2×C4×C13C4×D411yescharacteristic
268C2×C4×C13#12011yescharacteristic
269C2×C4×C13#12111yescharacteristic
270C2×C4×C13#12111yescharacteristic
271C2×C4×C13#12111yescharacteristic
272C2×C4×C13#12111yescharacteristic
273C2×C4×C13#12111yescharacteristic
274C2×C4×C13#12311yescharacteristic
275C2×C4×C13#12311yescharacteristic
276C2×C4×C13#12311yescharacteristic
277C2×C4×C13#12311yescharacteristic
278C2×C4×C13#12311yescharacteristic
279C2×C4×C13#12311yescharacteristic
280C2×C4×C13#12311yescharacteristic
281C2×C4×C13#12311yescharacteristic
282C2×C4×C13#12311yescharacteristic
283C2×C4×C13#12411yescharacteristic
284C2×C4×C13#12411yescharacteristic
285C2×C4×C13#12411yescharacteristic
286C2×C4×C13#12611yescharacteristic
287C2×C4×C13#12611yescharacteristic
288C2×C4×C13#12611yescharacteristic
289C2×C4×C13#12611yescharacteristic
290C2×Dic13—24no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—44no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—42no—
301C2×Dic13—41no—
302C2×Dic13—42no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—42no—
306C2×Dic13—41no—
307C2×Dic13—82no—
308C8×C13—42no—
309#1055—42no—
310C22×#41C2×D1311yescharacteristic
311C22×M16—131no—
312C22×M16C2×D1311yescharacteristic
313C2×#117—131no—
314C22×C4⋊C4—131no—
315C22×C4⋊C4C2×D1311yescharacteristic
316C22×C42—131no—
317C2×#104—262no—
318C2×#104—262no—
319C2×#104—262no—
320#417—22no—
321#417Dic1314yescomplemented
322C2×#103—21no—
323C2×#102—21no—
324#391—261no—
325#390—261no—
326#386—262no—
327#380—261no—
328#380—261no—
329C2×#95—262no—
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—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13#38611yescharacteristic
354C22×C13#38811yescharacteristic
355C22×C13#38811yescharacteristic
356C22×C13#39411yescharacteristic
357C22×C13#39411yescharacteristic
358C22×C13#39411yescharacteristic
359C22×C13#39711yescharacteristic
360C22×C13#45311yescharacteristic
361C22×C13#45411yescharacteristic
362C22×C13#45511yescharacteristic
363C22×C13#45611yescharacteristic
364C4×C13—42no—
365C4×C13—82no—
366C4×C13#38111yescharacteristic
367C4×C13#38611yescharacteristic
368C4×C13#38811yescharacteristic
369C4×C13#38811yescharacteristic
370C4×C13#39411yescharacteristic
371C4×C13#39711yescharacteristic
372C4×C13#39711yescharacteristic
373C4×C13#39711yescharacteristic
374Dic13—44no—
375Dic13—82no—
376Dic13—81no—
377Dic13—81no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41C2×Dic1312yes—
389C2×#41C22⋊D1312yes—
390C22×Q8C22⋊D1311yescharacteristic
391C22×D4—21no—
392C22×D4C22⋊D1311yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—132no—
396C23×C4—261no—
397C23×C4C22×D1311yescharacteristic
398C2×M16—21no—
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—132no—
404C2×M16—261no—
405C2×M16—261no—
406C2×M16—261no—
407C2×M16—261no—
408C2×M16—261no—
409C2×M16C2×Dic1312yes—
410C22×C8—21no—
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—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4C2×Dic1312yes—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—262no—
432C2×C22⋊C4—262no—
433C2×C42—132no—
434C2×C42—261no—
435C2×C42—261no—
436C2×C42—261no—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42—261no—
440#104—268no—
441#103—24no—
442#102—24no—
443#95—262no—
444#95—262no—
445#95—524no—
446C2×C13—21no—
447C2×C13—21no—
448C2×C13—21no—
449C2×C13—21no—
450C2×C13—82no—
451C2×C13#144011yescharacteristic
452C2×C13#188211yescharacteristic
453C2×C13#188311yescharacteristic
454C2×C13#203711yescharacteristic
455C2×C13#203811yescharacteristic
456C2×C13#203911yescharacteristic
457C2×C13#204011yescharacteristic
458C24—21no—
459C24D4×D1311yescharacteristic
460#41—22no—
461#41—22no—
462#41—22no—
463#41—22no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—22no—
468#41—41no—
469#41—41no—
470#41—41no—
471#41—41no—
472#41—41no—
473#41—41no—
474#41—41no—
475#41—41no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C22⋊Dic1312yes—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4C22⋊Dic1312yes—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—262no—
507C22×C4—262no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—521no—
515C22×C4—521no—
516C22×C4—521no—
517C22×C4—521no—
518C22×C4—522no—
519C22×C4—522no—
520C22×C4#612711yescharacteristic
521C22×C4#612711yescharacteristic
522C22×C4#612711yescharacteristic
523C22×C4#612711yescharacteristic
524C22×C4D4×D1311yescharacteristic
525C22×C4D4×D1311yescharacteristic
526C22×C4D4×D1311yescharacteristic
527C22×C4#612911yescharacteristic
528C22×C4#612911yescharacteristic
529C22×C4#612911yescharacteristic
530C22×C4#612911yescharacteristic
531C22×C4C22×Dic1311yescharacteristic
532C22×C4C2×C22⋊D1311yescharacteristic
533C22×C4C2×C22⋊D1311yescharacteristic
534M16—22no—
535M16—22no—
536M16—41no—
537M16—41no—
538M16—262no—
539M16—262no—
540M16—521no—
541M16—521no—
542C2×C8—22no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—262no—
546C2×C8—521no—
547C2×C8—521no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—521no—
557C4⋊C4—521no—
558C4⋊C4—521no—
559C4⋊C4—521no—
560C22⋊C4—521no—
561C22⋊C4—521no—
562C22⋊C4—1042no—
563C22⋊C4—1042no—
564C42—262no—
565C42—262no—
566C42—521no—
567C42—521no—
568C42—521no—
569C42—521no—
570C13#1119511yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23#8813711yescharacteristic
583C23#8813811yescharacteristic
584C23#8813811yescharacteristic
585C23#8813911yescharacteristic
586C23D4×Dic1311yescharacteristic
587C23#8819111yescharacteristic
588C23#8819311yescharacteristic
589Q8—22no—
590Q8—22no—
591Q8—41no—
592Q8—41no—
593D4—22no—
594D4—22no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—42no—
599D4—41no—
600D4—41no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—44no—
609C2×C4—42no—
610C2×C4—82no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—264no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—524no—
621C2×C4—521no—
622C2×C4—522no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—522no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—522no—
630C2×C4—1042no—
631C2×C4#8813311yescharacteristic
632C2×C4#8813311yescharacteristic
633C2×C4#8813311yescharacteristic
634C2×C4#8813311yescharacteristic
635C2×C4#8813711yescharacteristic
636C2×C4#8813711yescharacteristic
637C2×C4#8813711yescharacteristic
638C2×C4#8813811yescharacteristic
639C2×C4#8813811yescharacteristic
640C2×C4#8813911yescharacteristic
641C2×C4#8813911yescharacteristic
642C2×C4#8813911yescharacteristic
643C2×C4#8818011yescharacteristic
644C2×C4#8818011yescharacteristic
645C2×C4#8818311yescharacteristic
646C2×C4#8818311yescharacteristic
647C2×C4#8818311yescharacteristic
648C2×C4#8818311yescharacteristic
649C2×C4D4×Dic1311yescharacteristic
650C2×C4D4×Dic1311yescharacteristic
651C2×C4D4×Dic1311yescharacteristic
652C2×C4#8818911yescharacteristic
653C2×C4#8818911yescharacteristic
654C2×C4#8819111yescharacteristic
655C2×C4#8819311yescharacteristic
656C2×C4#8819311yescharacteristic
657C2×C4#8819311yescharacteristic
658C2×C4C2×C22⋊Dic1311yescharacteristic
659C8—42no—
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—42no—
674C22—42no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22#1171861211yescharacteristic
681C22#1171861211yescharacteristic
682C22#1171861311yescharacteristic
683C22#1171862011yescharacteristic
684C22#1171862011yescharacteristic
685C22#1171862011yescharacteristic
686C22#1171885911yescharacteristic
687C22#1171886211yescharacteristic
688C22#1171886311yescharacteristic
689C22#1171886611yescharacteristic
690C22#1171888111yescharacteristic
691C4—42no—
692C4—82no—
693C4—524no—
694C4—1042no—
695C4—1041no—
696C4—1041no—
697C4#1171861211yescharacteristic
698C4#1171861211yescharacteristic
699C4#1171861311yescharacteristic
700C4#1171861311yescharacteristic
701C4#1171861311yescharacteristic
702C4#1171862011yescharacteristic
703C4#1171887211yescharacteristic
704C4#1171888111yescharacteristic
705C2—21no—
706C2—21no—
707C2—21no—
708C2—21no—
709C2—82no—
710C2#1311308511yescharacteristic
711C2#1311520711yescharacteristic
712C2#1311521411yescharacteristic
713C2#1311604411yescharacteristic
714C2#1311605111yescharacteristic
715C2#1311605811yescharacteristic
716C2#1311606311yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#417C2
socleC23×C13#120
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenterC2×#417D13
hypocenterC13#11195
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
3. C2×#11718146C2semidirect
4. #13114555C2semidirect
5. C2×#11718147C2semidirect
6. #13113065C2semidirect
16. C13×#417C4semidirect
321. #417Dic13semidirect
570. C13#11195semidirect

Maximal subgroups

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

subgroupindex
C22×#880772
#131174282
C2×#117181462
#131145552
C2×#117181472
#131130652
C2×C13×#4172
#1119513