Finite Group Databasebeta

← #15789961

Subgroups — #15789961

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718883C211yesmaximal, characteristic
2C2×#11718594C211yesmaximal, characteristic, complemented
3#13113095C211yesmaximal, characteristic, complemented
4#13113086C211yesmaximal, characteristic, complemented
5#13113083C212yesmaximal, complemented
6#13113079C212yesmaximal, complemented
7#13113077C211yesmaximal, characteristic
8#13113073C212yesmaximal, complemented
9#13113073C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×#6101C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×C4×Dic13C2212yes—
24C13×#390—24no—
25#11718883C418yescomplemented
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37#11718594—24no—
38C25×C13C2312yes—
39C22×D4×C13—22no—
40C22×D4×C13—22no—
41C22×D4×C13—42no—
42C22×D4×C13—42no—
43C22×D4×C13C2×C414yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2312yes—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—42no—
56C2×C13×C22⋊C4—24no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4—42no—
62C2×C42×C13—42no—
63C2×C42×C13D414yes—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C22⋊Dic13—42no—
69C2×C22⋊Dic13—42no—
70C2×C22⋊Dic13—42no—
71C2×C22⋊Dic13—42no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—42no—
74C2×C22⋊Dic13C2×C418yes—
75C2×C22⋊Dic13C2×C418yes—
76C2×#6101—22no—
77C2×#6101—22no—
78C2×#6101—22no—
79C2×#6101—42no—
80C2×#6101C2×C414yes—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—42no—
83C2×C4×Dic13—42no—
84#88071—22no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88071—22no—
89#88071—24no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071C2×C414yes—
95#14325—131nomaximal, Sylow
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13—22no—
106C24×C13—22no—
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13C22×C414yes—
111C24×C13C2411yescharacteristic
112C2×D4×C13—28no—
113C2×D4×C13—48no—
114C2×D4×C13—44no—
115C2×D4×C13—44no—
116C2×D4×C13—48no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13#4112yes—
138C22×C4×C13#4114yes—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13C22×C414yes—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C412yes—
174C22×Dic13#4114yes—
175C13×C4⋊C4—44no—
176C13×C22⋊C4—48no—
177C13×C22⋊C4—48no—
178C42×C13—44no—
179C22⋊Dic13—48no—
180C22⋊Dic13—48no—
181C22⋊Dic13—48no—
182C22⋊Dic13—48no—
183#6101—28no—
184#6101—44no—
185C4×Dic13—48no—
186C2×#394—131no—
187C2×#390D1311yescharacteristic
188C2×#387—131no—
189#1442—131no—
190#1441—131no—
191#1440—132no—
192#1439—132no—
193#1438—131no—
194#1437—132no—
195#1437—132no—
196C4×#95—131no—
197C23×C13—24no—
198C23×C13—24no—
199C23×C13—24no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—24no—
203C23×C13—24no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—42no—
218C23×C13—42no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—42no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13C23×C411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13H(5,𝔽2)12yes—
238C23×C13H(5,𝔽2)12yes—
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)11yescharacteristic
241C23×C13H(5,𝔽2)11yescharacteristic
242C23×C132−1+411yescharacteristic
243D4×C13—416no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13C4×D414yes—
265C2×C4×C13#12414yes—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—24no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—42no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C23×D4C2×D1311yescharacteristic
303C22×C4⋊C4—131no—
304C22×C4⋊C4—131no—
305C22×C4⋊C4C2×D1311yescharacteristic
306C22×C22⋊C4—132no—
307C22×C22⋊C4—132no—
308C22×C22⋊C4—132no—
309C22×C22⋊C4—132no—
310C22×C22⋊C4C2×D1312yes—
311C22×C22⋊C4C2×D1312yes—
312C22×C42—132no—
313C22×C42C2×D1311yescharacteristic
314#394—138no—
315#390—24no—
316#387—264no—
317C2×#95—131no—
318C2×#95—131no—
319C2×#95—132no—
320C2×#95—131no—
321C2×#95—131no—
322C2×#95—131no—
323C2×#95—131no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C2×#95—132no—
328C22×C13—44no—
329C22×C13—44no—
330C22×C13—44no—
331C22×C13—44no—
332C22×C13—44no—
333C22×C13—44no—
334C22×C13—44no—
335C22×C13—82no—
336C22×C13—82no—
337C22×C13—82no—
338C22×C13—82no—
339C22×C13—82no—
340C22×C13—82no—
341C22×C13—82no—
342C22×C13—82no—
343C22×C13C2×C4×D411yescharacteristic
344C22×C13C4×#4112yes—
345C22×C13#51812yes—
346C22×C13#51811yescharacteristic
347C22×C13#52011yescharacteristic
348C22×C13C2×#12411yescharacteristic
349C22×C13#52912yes—
350C22×C13#53211yescharacteristic
351C22×C13#53411yescharacteristic
352C22×C13#53511yescharacteristic
353C22×C13#53511yescharacteristic
354C22×C13#53711yescharacteristic
355C22×C13#53812yes—
356C22×C13#53812yes—
357C22×C13#53812yes—
358C22×C13#53812yes—
359C22×C13#53912yes—
360C22×C13#54012yes—
361C22×C13#54012yes—
362C22×C13#54011yescharacteristic
363C22×C13#54012yes—
364C22×C13#54211yescharacteristic
365C22×C13#54212yes—
366C4×C13—24no—
367C4×C13—24no—
368C4×C13—42no—
369C4×C13—82no—
370Dic13—42no—
371Dic13—42no—
372Dic13—44no—
373Dic13—44no—
374Dic13—81no—
375Dic13—81no—
376C25C22×D1312yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C4×D1314yes—
382C23×C4—131no—
383C23×C4—131no—
384C23×C4—132no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4C22×D1312yes—
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—522no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—138no—
406C2×C22⋊C4—138no—
407C2×C22⋊C4—264no—
408C2×C22⋊C4—264no—
409C2×C22⋊C4—522no—
410C2×C22⋊C4—522no—
411C2×C22⋊C4—522no—
412C2×C22⋊C4—522no—
413C2×C22⋊C4—522no—
414C2×C22⋊C4—522no—
415C2×C22⋊C4—522no—
416C2×C22⋊C4—522no—
417C2×C42—42no—
418C2×C42—264no—
419C2×C42—522no—
420C2×C42—522no—
421C2×C42C22⋊D1314yes—
422#95—134no—
423#95—264no—
424#95—262no—
425#95—262no—
426#95—262no—
427#95—262no—
428#95—262no—
429#95—522no—
430#95—522no—
431#95—522no—
432#95—522no—
433C2×C13—84no—
434C2×C13C4×#12411yescharacteristic
435C2×C13#232111yescharacteristic
436C2×C13#232411yescharacteristic
437C2×C13#233312yes—
438C2×C13#233512yes—
439C2×C13#263911yescharacteristic
440C2×C13#264111yescharacteristic
441C2×C13#264812yes—
442C2×C13#265112yes—
443C2×C13#266111yescharacteristic
444C2×C13#266211yescharacteristic
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C2×C4×D1314yes—
460C24C23×D1311yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—44no—
465C2×D4—44no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—134no—
483C22×C4—132no—
484C22×C4—132no—
485C22×C4—134no—
486C22×C4—262no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—261no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4—261no—
508C22×C4—261no—
509C22×C4—262no—
510C22×C4—261no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4C2×C4×D1312yes—
519C22×C4#612712yes—
520C22×C4#612914yes—
521C22×C4C2×C22⋊D1312yes—
522C22×C4C2×C22⋊D1312yes—
523C22×C4C2×C22⋊D1312yes—
524C4⋊C4—44no—
525C4⋊C4—268no—
526C4⋊C4—524no—
527C22⋊C4—48no—
528C22⋊C4—48no—
529C22⋊C4—528no—
530C22⋊C4—528no—
531C22⋊C4—528no—
532C22⋊C4—528no—
533C42—44no—
534C42—528no—
535C13#1432511yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C22×C4×D1311yescharacteristic
572C23C2×#612711yescharacteristic
573C23C2×#612912yes—
574C23#8825112yes—
575C23#8825111yescharacteristic
576C23#8825111yescharacteristic
577C23#8825112yes—
578C23#41×D1312yes—
579C23#8825611yescharacteristic
580C23#8825711yescharacteristic
581C23C22×C22⋊D1311yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—264no—
604C2×C4—264no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—264no—
608C2×C4—262no—
609C2×C4—264no—
610C2×C4—262no—
611C2×C4—264no—
612C2×C4—264no—
613C2×C4—264no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—522no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4C4×C22⋊D1314yes—
640C2×C4#8819014yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#1171919112yes—
657C22#1171919912yes—
658C22C4×#612912yes—
659C22#1171925011yescharacteristic
660C22#1171925111yescharacteristic
661C22#1171926212yes—
662C22#1171926611yescharacteristic
663C22#1171926711yescharacteristic
664C22#1171930712yes—
665C22#1171931812yes—
666C22#1171932012yes—
667C22#1171932212yes—
668C22#1171937412yes—
669C22#1171938312yes—
670C22#1171942412yes—
671C22#1171942412yes—
672C22C2×C4×C22⋊D1311yescharacteristic
673C22C2×#8819011yescharacteristic
674C22#1171950911yescharacteristic
675C22#1171951011yescharacteristic
676C22#1171951011yescharacteristic
677C22#1171953711yescharacteristic
678C22#1171953811yescharacteristic
679C4—24no—
680C4—24no—
681C4—42no—
682C4—82no—
683C4—522no—
684C4—524no—
685C4—522no—
686C4—524no—
687C4—1041no—
688C4—1041no—
689C2—84no—
690C2C4×#8819011yescharacteristic
691C2#1311749411yescharacteristic
692C2#1311752311yescharacteristic
693C2#1311759512yes—
694C2#1311762312yes—
695C2#1312076911yescharacteristic
696C2#1312078111yescharacteristic
697C2#1312082812yes—
698C2#1312087312yes—
699C2#1312096511yescharacteristic
700C2#1312097511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14325
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#11718594C2semidirect
3. #13113095C2semidirect
4. #13113086C2semidirect
5. #13113083C2semidirect
6. #13113079C2semidirect
8. #13113073C2semidirect
9. #13113073C2semidirect
10. C4×#88071C2semidirect
25. #11718883C4semidirect
535. C13#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#117188832
C2×#117185942
#131130952
#131130862
#131130832
#131130792
#131130772
#131130732
C4×#880712
C2×C13×#3902
#1432513