Finite Group Databasebeta

← #15793589

Subgroups — #15793589

Order 3328.

1586 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#13113099C211yesmaximal, characteristic, complemented
4#13113086C211yesmaximal, characteristic, complemented
5#13113083C212yesmaximal, complemented
6#13113079C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113079C212yesmaximal, complemented
9#13113077C211yesmaximal, characteristic
10#13113063C211yesmaximal, 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×#6101C2212yes—
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—42no—
59C2×C13×C22⋊C4—42no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4—42no—
62C2×C42×C13—42no—
63C2×C42×C13D414yes—
64C2×C22⋊Dic13—42no—
65C2×C22⋊Dic13—42no—
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×#6101—42no—
81C2×#6101—42no—
82C2×#6101—42no—
83C2×#6101C2×C414yes—
84#88071—22no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88071—22no—
89#88071—42no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071C2×C414yes—
95#14624—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—22no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
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×C13—22no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13#4112yes—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—22no—
170C22×Dic13—21no—
171C22×Dic13—22no—
172C22×Dic13C22×C414yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C412yes—
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—
185#6101—48no—
186C2×#394—131no—
187C2×#390D1311yescharacteristic
188C2×#387—131no—
189#1444—131no—
190#1441—131no—
191#1440—132no—
192#1439—132no—
193#1439—132no—
194#1439—132no—
195#1438—131no—
196#1434—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×C13H(5,𝔽2)12yes—
236C23×C13H(5,𝔽2)12yes—
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)12yes—
241C23×C132−1+412yes—
242C23×C132−1+411yescharacteristic
243D4×C13—416no—
244C2×C4×C13—24no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—42no—
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×C13—42no—
265C2×C4×C13C4×D414yes—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—24no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—22no—
273C2×Dic13—24no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—42no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—42no—
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⋊C4—132no—
306C22×C4⋊C4C2×D1311yescharacteristic
307C22×C22⋊C4—132no—
308C22×C22⋊C4—132no—
309C22×C22⋊C4—132no—
310C22×C22⋊C4—132no—
311C22×C22⋊C4C2×D1312yes—
312C22×C22⋊C4C2×D1312yes—
313C22×C42C2×D1311yescharacteristic
314#394—138no—
315#390—24no—
316#387—264no—
317C2×#95—131no—
318C2×#95—131no—
319C2×#95—131no—
320C2×#95—131no—
321C2×#95—131no—
322C2×#95—131no—
323C2×#95—132no—
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×C13#51812yes—
345C22×C13#51811yescharacteristic
346C22×C13#52011yescharacteristic
347C22×C13#52012yes—
348C22×C13#53411yescharacteristic
349C22×C13#53511yescharacteristic
350C22×C13#53511yescharacteristic
351C22×C13#53511yescharacteristic
352C22×C13#53611yescharacteristic
353C22×C13#53711yescharacteristic
354C22×C13#53812yes—
355C22×C13#54011yescharacteristic
356C22×C13#54212yes—
357C22×C13#54211yescharacteristic
358C22×C13#56012yes—
359C22×C13#56012yes—
360C22×C13#56012yes—
361C22×C13#56212yes—
362C22×C13#56212yes—
363C22×C13#56212yes—
364C22×C13#56212yes—
365C22×C13#56312yes—
366C4×C13—24no—
367C4×C13—42no—
368C4×C13—42no—
369C4×C13—82no—
370Dic13—42no—
371Dic13—42no—
372Dic13—44no—
373Dic13—81no—
374Dic13—82no—
375Dic13—81no—
376C25C22×D1312yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C4×D1314yes—
382C23×C4—131no—
383C23×C4—132no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4—131no—
387C23×C4—132no—
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×C4⋊C4—522no—
400C2×C4⋊C4—522no—
401C2×C4⋊C4—522no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—138no—
409C2×C22⋊C4—138no—
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×C22⋊C4—522no—
418C2×C22⋊C4—522no—
419C2×C22⋊C4—522no—
420C2×C42—42no—
421C2×C42C22⋊D1314yes—
422#95—134no—
423#95—262no—
424#95—262no—
425#95—262no—
426#95—262no—
427#95—262no—
428#95—522no—
429#95—522no—
430#95—522no—
431#95—522no—
432#95—522no—
433C2×C13—84no—
434C2×C13#232111yescharacteristic
435C2×C13#232411yescharacteristic
436C2×C13#232611yescharacteristic
437C2×C13#237612yes—
438C2×C13#237712yes—
439C2×C13#281311yescharacteristic
440C2×C13#281611yescharacteristic
441C2×C13#281811yescharacteristic
442C2×C13#282011yescharacteristic
443C2×C13#282912yes—
444C2×C13#283012yes—
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—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—134no—
484C22×C4—132no—
485C22×C4—132no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—262no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—262no—
507C22×C4—261no—
508C22×C4—262no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—261no—
513C22×C4—262no—
514C22×C4—261no—
515C22×C4—262no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4C2×C4×D1312yes—
520C22×C4#612712yes—
521C22×C4C2×C22⋊D1312yes—
522C22×C4C2×C22⋊D1312yes—
523C22×C4C2×C22⋊D1312yes—
524C4⋊C4—44no—
525C4⋊C4—268no—
526C4⋊C4—524no—
527C4⋊C4—528no—
528C22⋊C4—48no—
529C22⋊C4—48no—
530C22⋊C4—528no—
531C22⋊C4—528no—
532C22⋊C4—528no—
533C22⋊C4—528no—
534C42—44no—
535C13#1462411yescharacteristic, 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
573C23#8825112yes—
574C23#8825111yescharacteristic
575C23#8825112yes—
576C23#8825111yescharacteristic
577C23#8825112yes—
578C23#8825611yescharacteristic
579C23#8825712yes—
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—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—42no—
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—42no—
604C2×C4—264no—
605C2×C4—264no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—264no—
610C2×C4—264no—
611C2×C4—262no—
612C2×C4—522no—
613C2×C4—522no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—522no—
621C2×C4—522no—
622C2×C4—522no—
623C2×C4—522no—
624C2×C4—522no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—522no—
633C2×C4—522no—
634C2×C4—521no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4C4×C22⋊D1314yes—
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—
658C22#1171925011yescharacteristic
659C22#1171925111yescharacteristic
660C22#1171925112yes—
661C22#1171926611yescharacteristic
662C22#1171926612yes—
663C22#1171926711yescharacteristic
664C22#1171932512yes—
665C22#1171932612yes—
666C22#1171932612yes—
667C22#1171932612yes—
668C22#1171937712yes—
669C22#1171938912yes—
670C22#1171942512yes—
671C22#1171942512yes—
672C22C2×C4×C22⋊D1311yescharacteristic
673C22#1171950911yescharacteristic
674C22#1171951011yescharacteristic
675C22#1171951011yescharacteristic
676C22#1171951011yescharacteristic
677C22#1171953011yescharacteristic
678C22#1171953811yescharacteristic
679C4—24no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—524no—
684C4—522no—
685C4—522no—
686C4—1041no—
687C4—1041no—
688C4—1042no—
689C2—84no—
690C2#1311749411yescharacteristic
691C2#1311752311yescharacteristic
692C2#1311754811yescharacteristic
693C2#1311798612yes—
694C2#1311798712yes—
695C2#1312283611yescharacteristic
696C2#1312286411yescharacteristic
697C2#1312287711yescharacteristic
698C2#1312288711yescharacteristic
699C2#1312296412yes—
700C2#1312297912yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14624
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. #13113099C2semidirect
4. #13113086C2semidirect
5. #13113083C2semidirect
6. #13113079C2semidirect
7. #13113079C2semidirect
8. #13113079C2semidirect
10. #13113063C2semidirect
25. #11718883C4semidirect
535. C13#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#117188832
C2×#117185942
#131130992
#131130862
#131130832
#131130792
#131130772
#131130632
C2×C13×#3902
#1462413