Finite Group Databasebeta

← #15769350

Subgroups — #15769350

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718666C211yesmaximal, characteristic
2C2×#11718627C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4C2×#11718125C211yesmaximal, characteristic, complemented
5#13114555C211yesmaximal, characteristic, complemented
6C2×#11718123C211yesmaximal, characteristic, complemented
7C13×#2274C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C2×C13×#117C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C4×C13×C4⋊C4—22no—
16C4×C13×C4⋊C4—22no—
17C4×C13×C22⋊C4—22no—
18#11718667—22no—
19#11718667C414yescomplemented
20#11718666—22no—
21#11718666C414yescomplemented
22C2×#88050C412yescomplemented
23#11718627—22no—
24#11718627—22no—
25C2×#88049C412yescomplemented
26C2×#88046—22no—
27C2×#88045—22no—
28#11718125—22no—
29#11718123—22no—
30#11718121—22no—
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C22×C22⋊D13—21no—
34C2×#6127—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127C2×C412yes—
45C2×#6127C2×C412yes—
46C22×D52C2×C411yescharacteristic
47C22×C4×D13—21no—
48C22×Dic26C2×C411yescharacteristic
49C13×#117—21no—
50C13×#117—21no—
51C13×#117—21no—
52C13×#117—21no—
53C13×#117C2×C412yes—
54C13×#117C2×C412yes—
55C13×#117D412yes—
56C13×#117D412yes—
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⋊C4C2×C412yes—
63C2×C13×C4⋊C4D412yes—
64C2×C13×C4⋊C4D412yes—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4D412yes—
67C2×C42×C13—21no—
68C2×C42×C13—24no—
69C2×C42×C13D412yes—
70C2×C22⋊Dic13—21no—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180C2×C412yes—
75C2×C4⋊Dic13—21no—
76C2×C4×Dic13—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—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×#6099C2×C412yes—
89C22×#1055—21no—
90C22×#1055C2×C412yes—
91C13×#95—24no—
92#88050—24no—
93#88049—24no—
94#88046—28no—
95#88045—28no—
96#10954—131nomaximal, Sylow
97C24×C13C2×D411yescharacteristic
98C23×D13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—82no—
105C22×C4×C13C22×C411yescharacteristic
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C22×C411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C2×C22⋊D13—22no—
120C2×C22⋊D13—22no—
121C2×C22⋊D13—41no—
122C2×C22⋊D13—41no—
123C2×C22⋊D13—41no—
124C2×C22⋊D13—41no—
125C22×Dic13—21no—
126C22×Dic13—41no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—22no—
133#6127—22no—
134#6127—22no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140#6127—41no—
141#6127—41no—
142#6127—41no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52C4212yescomplemented
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—41no—
152C2×C4×D13—41no—
153C2×C4×D13—41no—
154C2×C4×D13—41no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C4212yescomplemented
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4C22⋊C414yes—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4C22⋊C414yes—
173C42×C13—22no—
174C42×C13—22no—
175C42×C13—22no—
176C42×C13—84no—
177C42×C13C22⋊C414yes—
178C22⋊Dic13—22no—
179C22⋊Dic13—41no—
180C4⋊Dic13—22no—
181C4⋊Dic13—41no—
182C4×Dic13—22no—
183C4×Dic13—41no—
184#6099—22no—
185#6099—22no—
186#6099—41no—
187#6099—41no—
188#6099—41no—
189#6099—41no—
190#6099—41no—
191#6099—41no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#421—131no—
199C2×#417—131no—
200C2×#410—131no—
201#2274D1311yescharacteristic, complemented
202C2×#344—131no—
203#1736—131no—
204C2×H(3,ℤ/4)—131no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13C2×C22⋊C411yescharacteristic
208C23×C13C4×D411yescharacteristic
209C23×C13C4×D411yescharacteristic
210C23×C13#12011yescharacteristic
211C23×C13#12111yescharacteristic
212C23×C13#12111yescharacteristic
213C23×C13#12311yescharacteristic
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—81no—
218C22×D13—81no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—44no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—82no—
228C2×C4×C13—82no—
229C2×C4×C13C2×C4211yescharacteristic
230C2×C4×C13C2×C22⋊C411yescharacteristic
231C2×C4×C13C2×C22⋊C411yescharacteristic
232C2×C4×C13#11711yescharacteristic
233C2×C4×C13#11711yescharacteristic
234C2×C4×C13#11711yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13#12111yescharacteristic
246C2×C4×C13#12111yescharacteristic
247C2×C4×C13#12111yescharacteristic
248C2×C4×C13#12111yescharacteristic
249C2×C4×C13#12311yescharacteristic
250C2×C4×C13#12311yescharacteristic
251C2×C4×C13#12411yescharacteristic
252C2×C4×C13#12411yescharacteristic
253C2×C4×C13#12411yescharacteristic
254C2×C4×C13#12611yescharacteristic
255C2×C4×C13#12611yescharacteristic
256C2×C4×C13#12711yescharacteristic
257C22⋊D13—42no—
258C22⋊D13—42no—
259C22⋊D13—42no—
260C22⋊D13—42no—
261C2×Dic13—22no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—42no—
265C2×Dic13—81no—
266C2×Dic13—81no—
267D52—22no—
268D52—22no—
269D52—41no—
270D52—41no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—42no—
275Dic26—22no—
276Dic26—22no—
277Dic26—41no—
278Dic26—41no—
279#1055—42no—
280#1055—42no—
281C22×#41—131no—
282C22×M16—131no—
283C22×M16—131no—
284C2×#117—131no—
285C2×#117C2×D1311yescharacteristic
286C2×#117C2×D1311yescharacteristic
287C22×C4⋊C4C2×D1311yescharacteristic
288#421—134no—
289#421—262no—
290C2×#104—262no—
291#417—262no—
292#417—262no—
293C2×#103—132no—
294C2×#102—132no—
295#410—134no—
296#410—262no—
297C2×#99—262no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C22⋊C4—22no—
301#344—262no—
302#340—262no—
303H(3,ℤ/4)—262no—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—41no—
311C22×C13—41no—
312C22×C13—41no—
313C22×C13—41no—
314C22×C13C4×C22⋊C411yescharacteristic
315C22×C13#38611yescharacteristic
316C22×C13#38611yescharacteristic
317C22×C13#38611yescharacteristic
318C22×C13#38811yescharacteristic
319C22×C13#38811yescharacteristic
320C22×C13#39011yescharacteristic
321C2×D13—42no—
322C2×D13—82no—
323C2×D13—81no—
324C2×D13—81no—
325C2×D13—82no—
326C4×C13—44no—
327C4×C13—44no—
328C4×C13—44no—
329C4×C13C4×C22⋊C411yescharacteristic
330C4×C13C4×C22⋊C411yescharacteristic
331C4×C13#38811yescharacteristic
332C4×C13#38811yescharacteristic
333C4×C13#38811yescharacteristic
334C4×C13#38811yescharacteristic
335C4×C13#39011yescharacteristic
336C4×C13#39011yescharacteristic
337Dic13—42no—
338Dic13—82no—
339C2×#41—132no—
340C2×#41—132no—
341C2×#41—261no—
342C2×#41—261no—
343C2×#41—261no—
344C2×#41—261no—
345C2×#41—261no—
346C2×#41—261no—
347C2×#41—261no—
348C2×#41—261no—
349C2×#41—261no—
350C2×#41—261no—
351C22×Q8—131no—
352C22×D4—131no—
353C22×D4—261no—
354C23×C4—21no—
355C23×C4—261no—
356C23×C4C22×D1311yescharacteristic
357C2×M16—132no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16—261no—
362C2×M16—261no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—132no—
370C22×C8—261no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—132no—
376#117—261no—
377#117—261no—
378#117—261no—
379#117C4×D1312yes—
380#117C4×D1312yes—
381#117D5212yes—
382#117D5212yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4C4×D1312yes—
390C2×C4⋊C4D5212yes—
391C2×C4⋊C4C22⋊D1312yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4C22⋊D1312yes—
395C2×C42—21no—
396C2×C42—24no—
397C2×C42—261no—
398C2×C42C22⋊D1312yes—
399#104—268no—
400#103—264no—
401#102—264no—
402#99—268no—
403#95—24no—
404C2×C13—21no—
405C2×C13—21no—
406C2×C13—21no—
407C2×C13—21no—
408C2×C13—21no—
409C2×C13—21no—
410C2×C13#143711yescharacteristic
411C2×C13#190411yescharacteristic
412C2×C13#190511yescharacteristic
413D13—82no—
414C24—261no—
415C24C2×C22⋊D1311yescharacteristic
416#41—262no—
417#41—262no—
418#41—262no—
419#41—262no—
420#41—262no—
421#41—262no—
422#41—262no—
423#41—262no—
424#41—521no—
425#41—521no—
426#41—521no—
427#41—521no—
428#41—521no—
429#41—521no—
430#41—521no—
431#41—521no—
432C2×Q8—132no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×D4—132no—
439C2×D4—262no—
440C2×D4—262no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C2×D4—261no—
446C2×D4—521no—
447C2×D4—521no—
448C2×D4—521no—
449C2×D4—521no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—82no—
456C22×C4—261no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—521no—
460C22×C4—521no—
461C22×C4—521no—
462C22×C4—521no—
463C22×C4—521no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×C4×D1311yescharacteristic
466C22×C4C2×C4×D1311yescharacteristic
467C22×C4C2×D5211yescharacteristic
468C22×C4C2×D5211yescharacteristic
469C22×C4C2×D5211yescharacteristic
470C22×C4#612711yescharacteristic
471C22×C4#612711yescharacteristic
472C22×C4#612711yescharacteristic
473C22×C4#612711yescharacteristic
474C22×C4#612711yescharacteristic
475C22×C4#612711yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478M16—262no—
479M16—262no—
480M16—521no—
481M16—521no—
482M16—521no—
483M16—521no—
484M16—521no—
485M16—521no—
486C2×C8—262no—
487C2×C8—262no—
488C2×C8—262no—
489C2×C8—262no—
490C2×C8—521no—
491C2×C8—521no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—262no—
500C4⋊C4—521no—
501C4⋊C4#610314yes—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—262no—
506C22⋊C4—521no—
507C22⋊C4#610314yes—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—84no—
512C42—262no—
513C42—521no—
514C42#610314yes—
515C13#1095411yescharacteristic, complemented, Sylow
516C23—41no—
517C23—41no—
518C23—262no—
519C23—521no—
520C23—521no—
521C23—1041no—
522C23—1041no—
523C23C2×#610311yescharacteristic
524C23C4×C22⋊D1311yescharacteristic
525C23C4×C22⋊D1311yescharacteristic
526C23#8818311yescharacteristic
527C23#8818411yescharacteristic
528C23#8818411yescharacteristic
529C23#8820711yescharacteristic
530Q8—262no—
531Q8—262no—
532Q8—521no—
533Q8—521no—
534D4—262no—
535D4—262no—
536D4—522no—
537D4—522no—
538D4—522no—
539D4—522no—
540D4—521no—
541D4—521no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—262no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—1041no—
561C2×C4—1041no—
562C2×C4C42×D1311yescharacteristic
563C2×C4#8812611yescharacteristic
564C2×C4#8812611yescharacteristic
565C2×C4#8812611yescharacteristic
566C2×C4C4×D5211yescharacteristic
567C2×C4C4×D5211yescharacteristic
568C2×C4C4×D5211yescharacteristic
569C2×C4C4×D5211yescharacteristic
570C2×C4C4×D5211yescharacteristic
571C2×C4C4×D5211yescharacteristic
572C2×C4#8812811yescharacteristic
573C2×C4#8812911yescharacteristic
574C2×C4#8812911yescharacteristic
575C2×C4#8812911yescharacteristic
576C2×C4#8813011yescharacteristic
577C2×C4#8813011yescharacteristic
578C2×C4C2×#610311yescharacteristic
579C2×C4C2×#610311yescharacteristic
580C2×C4C4×C22⋊D1311yescharacteristic
581C2×C4C4×C22⋊D1311yescharacteristic
582C2×C4C4×C22⋊D1311yescharacteristic
583C2×C4C4×C22⋊D1311yescharacteristic
584C2×C4#8818311yescharacteristic
585C2×C4#8818311yescharacteristic
586C2×C4#8818411yescharacteristic
587C2×C4#8818411yescharacteristic
588C2×C4#8818411yescharacteristic
589C2×C4#8818411yescharacteristic
590C8—522no—
591C8—522no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—522no—
603C22—1042no—
604C22—1042no—
605C22—1041no—
606C22—1041no—
607C22C4×#610311yescharacteristic
608C22#1171860011yescharacteristic
609C22#1171860111yescharacteristic
610C22#1171860111yescharacteristic
611C22#1171887411yescharacteristic
612C22#1171887411yescharacteristic
613C22#1171887411yescharacteristic
614C4—44no—
615C4—44no—
616C4—44no—
617C4—522no—
618C4—1042no—
619C4C4×#610311yescharacteristic
620C4C4×#610311yescharacteristic
621C4#1171860011yescharacteristic
622C4#1171860011yescharacteristic
623C4#1171860111yescharacteristic
624C4#1171860111yescharacteristic
625C4#1171860111yescharacteristic
626C4#1171860111yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—1042no—
634C2#1311307411yescharacteristic
635C2#1311532311yescharacteristic
636C2#1311533011yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC13×#2274C2
socleC22×C13#386
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenter#2274D13
hypocenterC13#10954
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
4. C2×#11718125C2semidirect
5. #13114555C2semidirect
6. C2×#11718123C2semidirect
7. C13×#2274C2semidirect
19. #11718667C4semidirect
21. #11718666C4semidirect
22. C2×#88050C4semidirect
25. C2×#88049C4semidirect
148. C2×D52C42semidirect
160. C2×Dic26C42semidirect
201. #2274D13semidirect
515. C13#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#117186662
C2×#117186272
C2×#117186672
C2×#117181252
#131145552
C2×#117181232
C13×#22742
#1095413