Finite Group Databasebeta

← #15785163

Subgroups — #15785163

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88147C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718637C211yesmaximal, characteristic, complemented
5C2×#11718328C214yesmaximal, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113080C214yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6103C2214yes—
16C22×#6103C2214yes—
17C22×#6103C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C2×#88147—24no—
25C2×#88147—24no—
26C2×#88147C418yescomplemented
27C2×C13×#95C2214yes—
28C2×#88071C2214yes—
29C2×#88071C2212yes—
30#11718649—24no—
31#11718637—24no—
32#11718600—24no—
33C4×#6101—24no—
34#11718328—216no—
35C24×D13C2312yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13C2312yes—
41C23×Dic13C2312yes—
42C23×Dic13C2311yescharacteristic
43C23×Dic13C2311yescharacteristic
44C22×D52—22no—
45C22×D52—22no—
46C22×D52—22no—
47C22×D52—22no—
48C22×D52C2×C414yes—
49C22×D52D414yes—
50C22×D52Q814yes—
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—28no—
54C22×C4×D13—28no—
55C22×C4×D13C2×C418yes—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4C2×C414yes—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13—22no—
65C2×#6103—24no—
66C2×#6103—24no—
67C2×#6103—28no—
68C2×#6103—28no—
69C2×#6103—28no—
70C2×#6103—28no—
71C2×#6103—44no—
72C2×#6103—44no—
73C2×#6103C2×C418yes—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—22no—
76C2×C4⋊Dic13—22no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—28no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—44no—
83C2×#6101D418yescomplemented
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13C2×C414yes—
88C2×C4×Dic13D414yes—
89C2×C4×Dic13D414yes—
90#88147—232no—
91C13×#95—28no—
92#88071—28no—
93#88071—24no—
94#13906—131nomaximal, Sylow
95C24×C13C2411yescharacteristic
96C23×D13—24no—
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—24no—
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—24no—
103C23×D13—24no—
104C23×D13C22×C414yes—
105C23×D13C2×D414yes—
106C23×D13C2×Q814yes—
107C22×C4×C13—24no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—24no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—24no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—24no—
122C22×C4×C13C22×C414yes—
123C22×C4×C13C22×C412yes—
124C22×C4×C13C2×D414yes—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×Q812yes—
129C22×C4×C13#4112yes—
130C22×C4×C13#4112yes—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—24no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—24no—
144C22×Dic13C22×C412yes—
145C22×Dic13C22×C412yes—
146C22×Dic13C2×D414yes—
147C22×Dic13C2×D412yes—
148C22×Dic13C2×D412yes—
149C22×Dic13C2×D412yes—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D414yes—
152C22×Dic13#4114yes—
153C2×D52—28no—
154C2×D52—28no—
155C2×D52—28no—
156C2×D52—28no—
157C2×D52—28no—
158C2×D52—28no—
159C2×D52C4⋊C4116yescomplemented
160C2×C4×D13—216no—
161C2×C4×D13—232no—
162C2×C4×D13—416no—
163C2×C4×D13—48no—
164C2×C4×D13—48no—
165C13×C4⋊C4—28no—
166C13×C4⋊C4—44no—
167C42×C13—44no—
168#6103—216no—
169#6103—416no—
170#6103—416no—
171C4⋊Dic13—44no—
172#6101—216no—
173#6101—48no—
174#6101—48no—
175C4×Dic13—44no—
176C4×Dic13C22⋊C4116yescomplemented
177C22×C4×D4—131no—
178C2×#390—131no—
179C2×#390—131no—
180C2×#384—131no—
181C2×#380—134no—
182C2×C4×C4⋊C4—131no—
183#1439—134no—
184C4⋊#95—131no—
185C4⋊#95D1311yescharacteristic, complemented
186C23×C13C23×C411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×D411yescharacteristic
189C23×C13C22×D411yescharacteristic
190C23×C13C22×D412yes—
191C23×C13C22×Q811yescharacteristic
192C23×C13C2×#4111yescharacteristic
193C23×C13C2×#4111yescharacteristic
194C23×C13C2×#4112yes—
195C23×C13H(5,𝔽2)12yes—
196C23×C132−1+412yes—
197C22×D13—24no—
198C22×D13—24no—
199C22×D13—28no—
200C22×D13—28no—
201C22×D13—24no—
202C22×D13—24no—
203C22×D13—24no—
204C22×D13—24no—
205C22×D13—28no—
206C22×D13—28no—
207C22×D13—28no—
208C22×D13—28no—
209C22×D13—44no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—42no—
213C22×D13—42no—
214C22×D13—44no—
215C22×D13—44no—
216C22×D13—44no—
217C22×D13—44no—
218C22×D13—44no—
219C22×D13C2×C4⋊C418yes—
220C2×C4×C13—24no—
221C2×C4×C13—28no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—42no—
226C2×C4×C13—44no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—44no—
236C2×C4×C13—44no—
237C2×C4×C13C2×C22⋊C414yes—
238C2×C4×C13C2×C4⋊C414yes—
239C2×C4×C13#11714yes—
240C2×C4×C13#12114yes—
241C2×C4×C13#12114yes—
242C2×C4×C13C22⋊Q814yes—
243C2×C4×C13C22⋊Q814yes—
244C2×Dic13—24no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—44no—
259C2×Dic13—44no—
260C2×Dic13C2×C22⋊C414yes—
261C2×Dic13C2×C22⋊C414yes—
262C2×Dic13C4×D418yes—
263C2×Dic13#12118yes—
264C2×Dic13#12414yes—
265C2×Dic13#12714yes—
266D52—232no—
267C4×D13—432no—
268C23×D4—131no—
269C24×C4—132no—
270C2×C4×D4—138no—
271C2×C4×D4—264no—
272C2×C4×D4—264no—
273C22×C4⋊C4—132no—
274C22×C4⋊C4—132no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—132no—
277C22×C4⋊C4C2×D1311yescharacteristic
278C22×C4⋊C4C2×D1311yescharacteristic
279C22×C22⋊C4—132no—
280C22×C22⋊C4—134no—
281C22×C22⋊C4—134no—
282C22×C42—131no—
283C22×C42—131no—
284C22×C42C2×D1311yescharacteristic
285#390—264no—
286#390—264no—
287#384—264no—
288#380—2616no—
289C4×C4⋊C4—264no—
290C2×#95—134no—
291C2×#95—132no—
292C2×#95C2×D1314yes—
293C22×C13C22×C22⋊C411yescharacteristic
294C22×C13C22×C4⋊C411yescharacteristic
295C22×C13C2×#11711yescharacteristic
296C22×C13C2×C4×D412yes—
297C22×C13#52012yes—
298C22×C13C2×#12111yescharacteristic
299C22×C13C2×#12111yescharacteristic
300C22×C13C2×#12112yes—
301C22×C13C2×C22⋊Q811yescharacteristic
302C22×C13C2×C22⋊Q811yescharacteristic
303C22×C13C2×#12411yescharacteristic
304C22×C13C2×#12711yescharacteristic
305C22×C13#53511yescharacteristic
306C22×C13#53611yescharacteristic
307C22×C13#53712yes—
308C22×C13D4212yes—
309C22×C13#54712yes—
310C22×C13#54712yes—
311C22×C13D4×Q812yes—
312C22×C13#55012yes—
313C22×C13#55412yes—
314C22×C13#55512yes—
315C22×C13#55612yes—
316C2×D13—216no—
317C2×D13—28no—
318C2×D13—44no—
319C2×D13—44no—
320C2×D13—48no—
321C2×D13—48no—
322C2×D13—48no—
323C2×D13—44no—
324C2×D13—44no—
325C2×D13—44no—
326C2×D13—44no—
327C4×C13—44no—
328C4×C13—44no—
329C4×C13—82no—
330C4×C13#38018yescomplemented
331Dic13—24no—
332Dic13—44no—
333Dic13—82no—
334Dic13#39018yescomplemented
335C25—132no—
336C22×D4—134no—
337C22×D4—134no—
338C22×D4—134no—
339C22×D4—262no—
340C22×D4—262no—
341C22×D4—262no—
342C22×D4—262no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—132no—
346C23×C4—138no—
347C23×C4—132no—
348C23×C4—264no—
349C23×C4—264no—
350C23×C4—268no—
351C23×C4—268no—
352C23×C4C22×D1312yes—
353C23×C4C22×D1312yes—
354C23×C4C22×D1312yes—
355C23×C4C22×D1311yescharacteristic
356C4×D4—2632no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—138no—
363C2×C4⋊C4—264no—
364C2×C4⋊C4—264no—
365C2×C4⋊C4—268no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—264no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—524no—
372C2×C4⋊C4C4×D1314yes—
373C2×C22⋊C4—138no—
374C2×C22⋊C4—264no—
375C2×C22⋊C4—264no—
376C2×C22⋊C4—268no—
377C2×C22⋊C4—268no—
378C2×C22⋊C4—268no—
379C2×C22⋊C4—268no—
380C2×C22⋊C4—524no—
381C2×C22⋊C4—524no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—134no—
386C2×C42—134no—
387C2×C42—134no—
388C2×C42—262no—
389C2×C42—262no—
390C2×C42—262no—
391#95—28no—
392#95—264no—
393#95—268no—
394C2×C13C2×#38011yescharacteristic
395C2×C13C2×#39011yescharacteristic
396C2×C13#231111yescharacteristic
397C2×C13D4×C4⋊C412yes—
398C2×C13#235412yes—
399C2×C13#253712yes—
400C2×C13#253812yes—
401C2×C13#254111yescharacteristic
402C2×C13#254211yescharacteristic
403C2×C13#254711yescharacteristic
404C2×C13#256311yescharacteristic
405D13—48no—
406C24—134no—
407C24—134no—
408C24—134no—
409C24—262no—
410C24—262no—
411C24—264no—
412C24—262no—
413C24—262no—
414C24—264no—
415C24—264no—
416C24—264no—
417C24C23×D1311yescharacteristic
418C2×D4—1316no—
419C2×D4—268no—
420C2×D4—268no—
421C2×D4—268no—
422C2×D4—268no—
423C2×D4—268no—
424C2×D4—268no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—132no—
441C22×C4—132no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—134no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—134no—
449C22×C4—2616no—
450C22×C4—2632no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—264no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—264no—
464C22×C4—5216no—
465C22×C4—528no—
466C22×C4—528no—
467C22×C4C2×C4×D1314yes—
468C22×C4C2×C4×D1312yes—
469C22×C4#612712yes—
470C22×C4#612712yes—
471C22×C4D4×D1314yes—
472C22×C4D4×D1312yes—
473C22×C4D4×D1312yes—
474C22×C4D4×D1312yes—
475C22×C4Q8×D1312yes—
476C4⋊C4—28no—
477C4⋊C4—44no—
478C4⋊C4—2616no—
479C4⋊C4—528no—
480C4⋊C4—528no—
481C4⋊C4—524no—
482C22⋊C4—2616no—
483C22⋊C4—5216no—
484C22⋊C4—5216no—
485C42—44no—
486C42—1316no—
487C42—524no—
488C13#1390611yescharacteristic, complemented, Sylow
489C23—138no—
490C23—268no—
491C23—264no—
492C23—264no—
493C23—264no—
494C23—264no—
495C23—264no—
496C23—264no—
497C23—268no—
498C23—268no—
499C23—268no—
500C23—268no—
501C23—268no—
502C23—522no—
503C23—524no—
504C23—524no—
505C23—524no—
506C23—524no—
507C23—524no—
508C23—524no—
509C23—522no—
510C23—522no—
511C23—522no—
512C23C22×C4×D1311yescharacteristic
513C23C2×#612711yescharacteristic
514C23C2×#612711yescharacteristic
515C23C2×D4×D1311yescharacteristic
516C23C2×D4×D1312yes—
517C23C2×D4×D1311yescharacteristic
518C23C2×D4×D1311yescharacteristic
519C23C2×Q8×D1311yescharacteristic
520C23#8825412yes—
521C23#41×D1312yes—
522C23#8825612yes—
523D4—2632no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—28no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—134no—
542C2×C4—138no—
543C2×C4—138no—
544C2×C4—134no—
545C2×C4—134no—
546C2×C4—134no—
547C2×C4—262no—
548C2×C4—264no—
549C2×C4—264no—
550C2×C4—262no—
551C2×C4—264no—
552C2×C4—264no—
553C2×C4—264no—
554C2×C4—5232no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—524no—
561C2×C4—524no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4#8812614yes—
565C2×C4C22⋊C4×D1314yes—
566C2×C4#8813814yes—
567C2×C4#8813814yes—
568C2×C4C4⋊C4×D1314yes—
569C2×C4#8815014yes—
570C2×C4#8815014yes—
571C22—268no—
572C22—2616no—
573C22—528no—
574C22—524no—
575C22—528no—
576C22—524no—
577C22—524no—
578C22—528no—
579C22—524no—
580C22—524no—
581C22—524no—
582C22C2×#8812611yescharacteristic
583C22C2×C22⋊C4×D1311yescharacteristic
584C22C2×#8813811yescharacteristic
585C22C2×#8813811yescharacteristic
586C22C2×C4⋊C4×D1311yescharacteristic
587C22#1171921212yes—
588C22C2×#8815011yescharacteristic
589C22C2×#8815011yescharacteristic
590C22#1171923712yes—
591C22C4×D4×D1312yes—
592C22#1171925812yes—
593C22#1171927312yes—
594C22#1171927912yes—
595C22D13×#12112yes—
596C22#1171931412yes—
597C22#1171933412yes—
598C22#1171933612yes—
599C22D13×#12411yescharacteristic
600C22#1171937911yescharacteristic
601C22#1171939512yes—
602C22D13×#12711yescharacteristic
603C22#1171942911yescharacteristic
604C22#1171943212yes—
605C4—44no—
606C4—44no—
607C4—82no—
608C4—138no—
609C4—264no—
610C4—524no—
611C4—1042no—
612C4#1171832818yescomplemented
613C2—528no—
614C2C2×#1171832811yescharacteristic
615C2D13×#39011yescharacteristic
616C2#1311742711yescharacteristic
617C2#1311773712yes—
618C2#1311778112yes—
619C2#1311975112yes—
620C2#1311975712yes—
621C2#1311978111yescharacteristic
622C2#1311978811yescharacteristic
623C2#1311983311yescharacteristic
624C2#1312000811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#13906
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718637C2semidirect
5. C2×#11718328C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113080C2semidirect
8. #13113065C2semidirect
9. C13×C4⋊#95C2semidirect
26. C2×#88147C4semidirect
83. C2×#6101D4semidirect
159. C2×D52C4⋊C4semidirect
176. C4×Dic13C22⋊C4semidirect
185. C4⋊#95D13semidirect
330. C4×C13#380semidirect
334. Dic13#390semidirect
488. C13#13906semidirect
612. C4#11718328semidirect

Maximal subgroups

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

subgroupindex
C22×#881472
C2×#117186002
C2×#117186492
C2×#117186372
C2×#117183282
C2×C4×#61012
#131130802
#131130652
C13×C4⋊#952
#1390613