Finite Group Databasebeta

← #15789932

Subgroups — #15789932

Order 3328.

1590 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718610C211yesmaximal, characteristic
2C2×#11718589C211yesmaximal, characteristic, complemented
3C2×#11718633C212yesmaximal, complemented
4C2×#11718606C212yesmaximal
5#13113105C211yesmaximal, characteristic, complemented
6#13113102C212yesmaximal, complemented
7#13113100C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C212yesmaximal
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#388C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×#6101C2212yes—
24C22×C4×Dic13C2212yes—
25C13×#388—24no—
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718633—28no—
37#11718610C418yescomplemented
38#11718606—28no—
39#11718589—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—24no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—42no—
59C2×C13×C22⋊C4C2×C414yes—
60C2×C42×C13—42no—
61C2×C42×C13D414yes—
62C2×C22⋊Dic13—24no—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—42no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13C2×C418yes—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—42no—
72C2×C4⋊Dic13C2×C414yes—
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×#6101C2×C418yes—
82C2×C4×Dic13—42no—
83C2×C4×Dic13—42no—
84C2×C4×Dic13D418yes—
85C13×#95—22no—
86C13×#95—22no—
87#88071—24no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071C2×C414yes—
95#14322—131nomaximal, Sylow
96C24×C13—22no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—21no—
100C24×C13—21no—
101C24×C13—22no—
102C24×C13—21no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—22no—
106C24×C13C22×C412yes—
107C24×C13C2411yescharacteristic
108C22×C4×C13—21no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C2×D414yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13#4112yes—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
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—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13C22×C414yes—
162C22×Dic13C22×C414yes—
163C22×Dic13C2×D414yes—
164C22×Dic13C2×D414yes—
165C22×Dic13#4114yes—
166C13×C4⋊C4—44no—
167C13×C22⋊C4—28no—
168C13×C22⋊C4—44no—
169C13×C22⋊C4—44no—
170C42×C13—44no—
171C22⋊Dic13—216no—
172C22⋊Dic13—48no—
173C4⋊Dic13—28no—
174C4⋊Dic13—44no—
175#6101—216no—
176#6101—48no—
177#6101—48no—
178C4×Dic13—48no—
179C2×#399—131no—
180C2×#389—131no—
181C2×#389—132no—
182C2×#388—132no—
183C2×#388D1311yescharacteristic
184#1445—132no—
185#1445—131no—
186#1444—131no—
187#1439—132no—
188#1439—131no—
189C4×#95—131no—
190C23×C13—24no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—24no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—42no—
202C23×C13—41no—
203C23×C13—42no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—41no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—42no—
213C23×C13C23×C411yescharacteristic
214C23×C13C22×D412yes—
215C23×C13C22×D411yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4112yes—
218C23×C13H(5,𝔽2)12yes—
219C23×C13H(5,𝔽2)11yescharacteristic
220C23×C132−1+411yescharacteristic
221C23×C132−1+411yescharacteristic
222C23×C132−1+411yescharacteristic
223C23×C132−1+412yes—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—41no—
238C2×C4×C13—42no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13C4×D414yes—
253C2×C4×C13#12714yes—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—24no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—42no—
280C2×Dic13—42no—
281C2×Dic13C4×D418yes—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4—132no—
285C22×C4⋊C4—132no—
286C22×C4⋊C4—131no—
287C22×C4⋊C4C2×D1311yescharacteristic
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4C2×D1311yescharacteristic
291C22×C22⋊C4C2×D1311yescharacteristic
292C22×C22⋊C4C2×D1311yescharacteristic
293C22×C42—132no—
294C22×C42C2×D1311yescharacteristic
295#399—138no—
296#389—268no—
297#389—264no—
298#388—24no—
299#388—268no—
300C2×#95—131no—
301C2×#95—132no—
302C2×#95—131no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95C2×D1311yescharacteristic
309C2×#95C2×D1311yescharacteristic
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—44no—
313C22×C13—44no—
314C22×C13—42no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13—82no—
319C22×C13—81no—
320C22×C13—82no—
321C22×C13C2×C4×D411yescharacteristic
322C22×C13C2×C4×D412yes—
323C22×C13#51911yescharacteristic
324C22×C13#52011yescharacteristic
325C22×C13#52012yes—
326C22×C13C2×#12711yescharacteristic
327C22×C13#53212yes—
328C22×C13#53211yescharacteristic
329C22×C13#53411yescharacteristic
330C22×C13#53412yes—
331C22×C13#53611yescharacteristic
332C22×C13#53611yescharacteristic
333C22×C13#53612yes—
334C22×C13#53612yes—
335C22×C13#53711yescharacteristic
336C22×C13#53712yes—
337C22×C13#53912yes—
338C22×C13#53912yes—
339C22×C13#53912yes—
340C22×C13#54111yescharacteristic
341C22×C13#54112yes—
342C22×C13#54211yescharacteristic
343C22×C13#54212yes—
344C4×C13—24no—
345C4×C13—24no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—81no—
349C4×C13—81no—
350Dic13—28no—
351Dic13—44no—
352Dic13—44no—
353Dic13—82no—
354C25C22×D1311yescharacteristic
355C23×C4—132no—
356C23×C4—132no—
357C23×C4—132no—
358C23×C4—132no—
359C23×C4C22×D1311yescharacteristic
360C23×C4C22×D1311yescharacteristic
361C23×C4C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C23×C4C22×D1311yescharacteristic
364C23×C4C22×D1311yescharacteristic
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—138no—
368C2×C4⋊C4—134no—
369C2×C4⋊C4—264no—
370C2×C4⋊C4—264no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—264no—
374C2×C4⋊C4—264no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—522no—
379C2×C4⋊C4—522no—
380C2×C4⋊C4—522no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—522no—
392C2×C22⋊C4—522no—
393C2×C22⋊C4C4×D1314yes—
394C2×C42—42no—
395C2×C42—138no—
396C2×C42—522no—
397C2×C42—522no—
398C2×C42C22⋊D1314yes—
399#95—22no—
400#95—22no—
401#95—134no—
402#95—264no—
403#95—264no—
404#95—264no—
405#95—264no—
406#95—264no—
407#95—262no—
408#95—264no—
409C2×C13—82no—
410C2×C13C4×#12711yescharacteristic
411C2×C13#232211yescharacteristic
412C2×C13#232212yes—
413C2×C13#232312yes—
414C2×C13#232311yescharacteristic
415C2×C13#265611yescharacteristic
416C2×C13#265811yescharacteristic
417C2×C13#266311yescharacteristic
418C2×C13#266312yes—
419C2×C13#266411yescharacteristic
420C2×C13#266412yes—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24C2×C4×D1312yes—
432C24C23×D1311yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—134no—
457C22×C4—134no—
458C22×C4—134no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4C2×C4×D1312yes—
485C22×C4C2×C4×D1312yes—
486C22×C4#612712yes—
487C22×C4D4×D1314yes—
488C22×C4C2×C22⋊D1312yes—
489C22×C4C2×C22⋊D1312yes—
490C22×C4C2×C22⋊D1312yes—
491C4⋊C4—44no—
492C4⋊C4—2616no—
493C4⋊C4—268no—
494C4⋊C4—524no—
495C4⋊C4—528no—
496C4⋊C4—528no—
497C22⋊C4—28no—
498C22⋊C4—44no—
499C22⋊C4—44no—
500C22⋊C4—2616no—
501C22⋊C4—528no—
502C42—44no—
503C42—528no—
504C13#1432211yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C22×C4×D1311yescharacteristic
529C23C2×#612711yescharacteristic
530C23C2×D4×D1312yes—
531C23#8825112yes—
532C23#41×D1312yes—
533C23#8825611yescharacteristic
534C23#8825711yescharacteristic
535C23#8825711yescharacteristic
536C23#8825711yescharacteristic
537C23#8825712yes—
538C23C22×C22⋊D1311yescharacteristic
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—138no—
568C2×C4—264no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—264no—
577C2×C4—264no—
578C2×C4—264no—
579C2×C4—264no—
580C2×C4—522no—
581C2×C4—522no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4C4×C22⋊D1314yes—
596C2×C4#8819414yes—
597C22—42no—
598C22—44no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—82no—
606C22—81no—
607C22—82no—
608C22#1171922111yescharacteristic
609C22#1171922311yescharacteristic
610C22#1171922811yescharacteristic
611C22#1171923911yescharacteristic
612C22C4×D4×D1312yes—
613C22#1171925112yes—
614C22#1171925312yes—
615C22#1171926912yes—
616C22#1171930212yes—
617C22#1171931012yes—
618C22#1171936512yes—
619C22#1171936712yes—
620C22#1171938012yes—
621C22#1171938012yes—
622C22#1171940612yes—
623C22#1171941212yes—
624C22C2×C4×C22⋊D1311yescharacteristic
625C22C2×#8819411yescharacteristic
626C22#1171950911yescharacteristic
627C22#1171953011yescharacteristic
628C22#1171953011yescharacteristic
629C22#1171953711yescharacteristic
630C22#1171953811yescharacteristic
631C4—24no—
632C4—24no—
633C4—42no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—268no—
638C4—524no—
639C4—524no—
640C4—1042no—
641C2—82no—
642C2C4×#8819411yescharacteristic
643C2#1311750111yescharacteristic
644C2#1311750612yes—
645C2#1311751112yes—
646C2#1311751811yescharacteristic
647C2#1312094011yescharacteristic
648C2#1312094711yescharacteristic
649C2#1312098611yescharacteristic
650C2#1312098812yes—
651C2#1312099811yescharacteristic
652C2#1312100112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14322
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#11718589C2semidirect
3. C2×#11718633C2semidirect
5. #13113105C2semidirect
6. #13113102C2semidirect
7. #13113100C2semidirect
10. C4×#88071C2semidirect
37. #11718610C4semidirect
504. C13#14322semidirect

Maximal subgroups

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

subgroupindex
C2×#117186102
C2×#117185892
C2×#117186332
C2×#117186062
#131131052
#131131022
#131131002
#131130812
#131130792
C4×#880712
C2×C13×#3882
#1432213