Finite Group Databasebeta

← #15768248

Subgroups — #15768248

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719450C211yesmaximal, characteristic
2C2×#11718667C211yesmaximal, characteristic
3#13117424C211yesmaximal, characteristic
4#13114557C211yesmaximal, characteristic, complemented
5#13114556C211yesmaximal, characteristic, complemented
6C2×#11718123C211yesmaximal, characteristic, complemented
7C2×C13×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11719450—22no—
16#11719450—22no—
17#11719450—22no—
18#11719450C414yescomplemented
19C2×#88161—22no—
20C2×M16×D13—22no—
21C2×#88155—22no—
22#11718667—22no—
23#11718667C414yescomplemented
24#11718648—22no—
25#11718619—22no—
26C2×#88046—22no—
27#11718600C412yescomplemented
28#11718590C412yescomplemented
29C13×H(3,ℤ/4)—22no—
30#11718143—22no—
31#11718123—22no—
32#11718121—22no—
33C23×C4×C13C2311yescharacteristic
34C22×C22⋊D13D412yes—
35C23×Dic13—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—
46C2×#6127D412yes—
47C2×#6127Q812yes—
48C22×D52C2×C411yescharacteristic
49C22×C4×D13D412yes—
50C22×Dic26C2×C411yescharacteristic
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16C2×C412yes—
56C2×C13×M16D412yes—
57C22×C8×C13D412yes—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117—21no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—21no—
65C13×#117C2×C412yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4—21no—
70C2×C42×C13—21no—
71C2×C42×C13C2×C412yes—
72C2×C22⋊Dic13—21no—
73C2×#6103—24no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180C2×C412yes—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13C2×C412yes—
85C2×C4×Dic13—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099C2×C412yes—
91C2×#6099D412yes—
92C22×#1055D412yes—
93#88161—28no—
94#88161—28no—
95M16×D13—28no—
96M16×D13—28no—
97#88155—28no—
98#88155—28no—
99C2×#6094—24no—
100C2×C8×D13—24no—
101#88071—24no—
102#88046—28no—
103#10742—131nomaximal, Sylow
104C24×C13C2×D411yescharacteristic
105C23×D13C22⋊C412yes—
106C22×C4×C13—22no—
107C22×C4×C13—41no—
108C22×C4×C13C22×C411yescharacteristic
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×Q811yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C2×C22⋊D13—22no—
123C2×C22⋊D13—22no—
124C2×C22⋊D13—22no—
125C2×C22⋊D13—22no—
126C2×C22⋊D13C22⋊C414yes—
127C2×C22⋊D13C4⋊C414yes—
128C22×Dic13—22no—
129C22×Dic13—41no—
130C22×Dic13—41no—
131C22×Dic13—41no—
132C22×Dic13—82no—
133C22×Dic13C22⋊C412yes—
134#6127—22no—
135#6127—22no—
136#6127—22no—
137#6127—22no—
138#6127—22no—
139#6127—22no—
140#6127—22no—
141#6127—22no—
142#6127—22no—
143#6127—22no—
144#6127—22no—
145#6127—22no—
146#6127—22no—
147#6127—22no—
148#6127—22no—
149#6127—22no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52C4212yes—
155C2×D52C4⋊C412yes—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13C22⋊C414yes—
161C2×C4×D13C4⋊C414yes—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26C4212yes—
167C2×Dic26C4⋊C412yes—
168C13×M16—22no—
169C13×M16—22no—
170C13×M16—22no—
171C13×M16—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13C22⋊C414yescomplemented
175C13×C4⋊C4—22no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4—41no—
178C13×C4⋊C4—41no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—41no—
183C42×C13—22no—
184C42×C13—22no—
185C42×C13—22no—
186C42×C13—41no—
187C22⋊Dic13—22no—
188C22⋊Dic13—41no—
189#6103—84no—
190C4⋊Dic13—22no—
191C4⋊Dic13—22no—
192C4⋊Dic13—22no—
193C4⋊Dic13—41no—
194C4⋊Dic13—41no—
195C4⋊Dic13—41no—
196C4×Dic13—22no—
197C4×Dic13—41no—
198#6099—22no—
199#6099—22no—
200#6099—22no—
201#6099—22no—
202C2×#1055—22no—
203C2×#1055—22no—
204C2×#1055C22⋊C414yescomplemented
205#6094—216no—
206C8×D13—216no—
207C2×#568—131no—
208C2×#410—131no—
209#2311—131no—
210#1736—131no—
211#1736—131no—
212C2×H(3,ℤ/4)—131no—
213C2×H(3,ℤ/4)D1311yescharacteristic, complemented
214C23×C13—41no—
215C23×C13—41no—
216C23×C13C2×C22⋊C411yescharacteristic
217C23×C13C2×C22⋊C411yescharacteristic
218C23×C13C2×C4⋊C411yescharacteristic
219C23×C13#12111yescharacteristic
220C23×C13#12111yescharacteristic
221C23×C13#12111yescharacteristic
222C23×C13#12111yescharacteristic
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13#9514yes—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—81no—
233C2×C4×C13—81no—
234C2×C4×C13C2×C4211yescharacteristic
235C2×C4×C13C2×C22⋊C411yescharacteristic
236C2×C4×C13C2×C22⋊C411yescharacteristic
237C2×C4×C13C2×C22⋊C411yescharacteristic
238C2×C4×C13C2×C4⋊C411yescharacteristic
239C2×C4×C13C2×C4⋊C411yescharacteristic
240C2×C4×C13#11711yescharacteristic
241C2×C4×C13#11711yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13#12011yescharacteristic
251C2×C4×C13#12011yescharacteristic
252C2×C4×C13#12011yescharacteristic
253C2×C4×C13#12011yescharacteristic
254C2×C4×C13C22⋊Q811yescharacteristic
255C2×C4×C13C22⋊Q811yescharacteristic
256C2×C4×C13C22⋊Q811yescharacteristic
257C2×C4×C13C22⋊Q811yescharacteristic
258C2×C4×C13#12311yescharacteristic
259C2×C4×C13#12311yescharacteristic
260C2×C4×C13#12311yescharacteristic
261C2×C4×C13#12311yescharacteristic
262C22⋊D13—24no—
263C22⋊D13—24no—
264C22⋊D13—24no—
265C22⋊D13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—44no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—81no—
272C2×Dic13—81no—
273C2×Dic13—82no—
274C2×Dic13—82no—
275C2×Dic13#9514yes—
276D52—22no—
277D52—22no—
278D52—22no—
279D52—22no—
280C4×D13—24no—
281C4×D13—24no—
282C4×D13—24no—
283C4×D13—24no—
284Dic26—22no—
285Dic26—22no—
286Dic26—22no—
287Dic26—22no—
288C8×C13—24no—
289#1055—24no—
290C22×#41—131no—
291#568—134no—
292#568—262no—
293#568—262no—
294#568—262no—
295C2×#131—262no—
296C2×#131—262no—
297C22×M16—131no—
298C22×M16—262no—
299C22×M16C2×D1311yescharacteristic
300C2×#117—131no—
301C2×#117C2×D1311yescharacteristic
302C2×#117C2×D1311yescharacteristic
303C22×C4⋊C4—131no—
304#410—134no—
305#410—262no—
306C2×#99—262no—
307#391—132no—
308#390—132no—
309#386—262no—
310#380—262no—
311#340—262no—
312#340—262no—
313H(3,ℤ/4)—22no—
314H(3,ℤ/4)—262no—
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×#9511yescharacteristic
326C22×C13#38011yescharacteristic
327C22×C13#38011yescharacteristic
328C22×C13#38611yescharacteristic
329C22×C13#38611yescharacteristic
330C22×C13#38611yescharacteristic
331C22×C13#38611yescharacteristic
332C2×D13—24no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—44no—
336C2×D13—82no—
337C4×C13—82no—
338C4×C13—82no—
339C4×C13C4×C22⋊C411yescharacteristic
340C4×C13C4×C22⋊C411yescharacteristic
341C4×C13#37911yescharacteristic
342C4×C13#38111yescharacteristic
343C4×C13#38511yescharacteristic
344C4×C13#38511yescharacteristic
345C4×C13#38511yescharacteristic
346C4×C13#38511yescharacteristic
347Dic13—24no—
348Dic13—82no—
349Dic13—82no—
350C2×#41—132no—
351C2×#41—132no—
352C2×#41—132no—
353C2×#41—132no—
354C2×#41—261no—
355C2×#41—261no—
356C2×#41—261no—
357C2×#41—261no—
358C2×#41—261no—
359C2×#41—261no—
360C2×#41—261no—
361C2×#41—261no—
362C22×Q8—131no—
363C22×D4—132no—
364C22×D4—131no—
365C23×C4—132no—
366C23×C4—261no—
367C23×C4C22×D1311yescharacteristic
368#131—268no—
369#131—268no—
370#131—268no—
371#131—268no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—132no—
377C2×M16—132no—
378C2×M16—264no—
379C2×M16—268no—
380C2×M16—268no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C2×M16—261no—
385C2×M16C4×D1312yes—
386C2×M16C22⋊D1312yes—
387C22×C8—132no—
388C22×C8—264no—
389C22×C8D5212yes—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—132no—
398#117—261no—
399#117—261no—
400#117—261no—
401#117C4×D1312yes—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—264no—
415C2×C42—21no—
416C2×C42—261no—
417C2×C42C4×D1312yes—
418#99—268no—
419#95—264no—
420C2×C13—21no—
421C2×C13—21no—
422C2×C13—21no—
423C2×C13—21no—
424C2×C13—21no—
425C2×C13—21no—
426C2×C13C22⋊#9511yescharacteristic
427C2×C13#190911yescharacteristic
428C2×C13#191011yescharacteristic
429D13—44no—
430C24—132no—
431C24D4×D1311yescharacteristic
432#41—262no—
433#41—262no—
434#41—262no—
435#41—262no—
436#41—262no—
437#41—262no—
438#41—262no—
439#41—262no—
440#41—262no—
441#41—262no—
442#41—262no—
443#41—262no—
444#41—262no—
445#41—262no—
446#41—262no—
447#41—262no—
448C2×Q8—132no—
449C2×Q8—132no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×D4—134no—
455C2×D4—134no—
456C2×D4—132no—
457C2×D4—132no—
458C2×D4—262no—
459C2×D4—262no—
460C2×D4—262no—
461C2×D4—262no—
462C2×D4—261no—
463C2×D4—261no—
464C2×D4—261no—
465C2×D4—261no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—132no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—521no—
477C22×C4—521no—
478C22×C4—521no—
479C22×C4—1042no—
480C22×C4C2×C4×D1311yescharacteristic
481C22×C4C2×C4×D1311yescharacteristic
482C22×C4C2×C4×D1311yescharacteristic
483C22×C4C2×D5211yescharacteristic
484C22×C4#612711yescharacteristic
485C22×C4#612711yescharacteristic
486C22×C4D4×D1311yescharacteristic
487C22×C4D4×D1311yescharacteristic
488C22×C4D4×D1311yescharacteristic
489C22×C4D4×D1311yescharacteristic
490C22×C4#612911yescharacteristic
491C22×C4Q8×D1311yescharacteristic
492C22×C4#613111yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494M16—22no—
495M16—22no—
496M16—22no—
497M16—22no—
498M16—2616no—
499M16—262no—
500M16—262no—
501M16—262no—
502M16—262no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—134no—
506C2×C8—2616no—
507C2×C8—262no—
508C2×C8—262no—
509C2×C8#610314yescomplemented
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—262no—
515C4⋊C4—262no—
516C4⋊C4—262no—
517C4⋊C4—521no—
518C4⋊C4—521no—
519C4⋊C4—521no—
520C22⋊C4—22no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—262no—
525C22⋊C4—521no—
526C22⋊C4—1044no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—41no—
531C42—262no—
532C42—521no—
533C13#1074211yescharacteristic, complemented, Sylow
534C23—41no—
535C23—41no—
536C23—134no—
537C23—262no—
538C23—262no—
539C23—522no—
540C23—522no—
541C23C22⋊C4×D1311yescharacteristic
542C23C22⋊C4×D1311yescharacteristic
543C23#8813811yescharacteristic
544C23#8813811yescharacteristic
545C23C4⋊C4×D1311yescharacteristic
546C23#8814911yescharacteristic
547C23#8819211yescharacteristic
548Q8—262no—
549Q8—262no—
550Q8—262no—
551Q8—262no—
552D4—264no—
553D4—264no—
554D4—264no—
555D4—264no—
556D4—262no—
557D4—262no—
558D4—262no—
559D4—262no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—134no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—524no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—1041no—
577C2×C4—1041no—
578C2×C4—1042no—
579C2×C4—1042no—
580C2×C4C42×D1311yescharacteristic
581C2×C4#8812611yescharacteristic
582C2×C4C4×D5211yescharacteristic
583C2×C4C4×D5211yescharacteristic
584C2×C4C22⋊C4×D1311yescharacteristic
585C2×C4C22⋊C4×D1311yescharacteristic
586C2×C4#8813511yescharacteristic
587C2×C4#8813511yescharacteristic
588C2×C4#8813611yescharacteristic
589C2×C4#8813611yescharacteristic
590C2×C4#8813711yescharacteristic
591C2×C4#8813711yescharacteristic
592C2×C4C4⋊C4×D1311yescharacteristic
593C2×C4C4⋊C4×D1311yescharacteristic
594C2×C4#8814611yescharacteristic
595C2×C4#8814711yescharacteristic
596C2×C4#8814711yescharacteristic
597C2×C4#8814811yescharacteristic
598C2×C4#8814811yescharacteristic
599C2×C4#8815011yescharacteristic
600C2×C4#8815011yescharacteristic
601C2×C4#8815111yescharacteristic
602C2×C4C2×#610311yescharacteristic
603C2×C4C4×C22⋊D1311yescharacteristic
604C2×C4C4×C22⋊D1311yescharacteristic
605C2×C4#8819111yescharacteristic
606C2×C4#8819111yescharacteristic
607C2×C4#8820011yescharacteristic
608C8—24no—
609C8—264no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—264no—
621C22—524no—
622C22—522no—
623C22—522no—
624C22—1042no—
625C22D13×#9511yescharacteristic
626C22#1171832611yescharacteristic
627C22#1171832611yescharacteristic
628C22#1171832811yescharacteristic
629C22#1171861711yescharacteristic
630C22#1171861711yescharacteristic
631C22#1171864811yescharacteristic
632C4—82no—
633C4—82no—
634C4—264no—
635C4—1042no—
636C4—1042no—
637C4#1171832511yescharacteristic
638C4#1171832711yescharacteristic
639C4#1171832911yescharacteristic
640C4#1171832911yescharacteristic
641C4C4×#610311yescharacteristic
642C4#1171861611yescharacteristic
643C4#1171865011yescharacteristic
644C4#1171865011yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—524no—
652C2#1311305711yescharacteristic
653C2#1311535711yescharacteristic
654C2#1311536211yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#386
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13#10742
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #13114557C2semidirect
5. #13114556C2semidirect
6. C2×#11718123C2semidirect
7. C2×C13×H(3,ℤ/4)C2semidirect
18. #11719450C4semidirect
23. #11718667C4semidirect
27. #11718600C4semidirect
28. #11718590C4semidirect
174. C2×C8×C13C22⋊C4semidirect
204. C2×#1055C22⋊C4semidirect
213. C2×H(3,ℤ/4)D13semidirect
509. C2×C8#6103semidirect
533. C13#10742semidirect

Maximal subgroups

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

subgroupindex
C2×#117194502
C2×#117186672
#131174242
#131145572
#131145562
C2×#117181232
C2×C13×H(3,ℤ/4)2
#1074213