Finite Group Databasebeta

← #15784745

Subgroups — #15784745

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718610C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718310C212yesmaximal, complemented
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic
5C2×C22⋊C4×Dic13C212yesmaximal
6#13113103C211yesmaximal, characteristic, complemented
7#13113102C212yesmaximal, complemented
8#13113099C211yesmaximal, characteristic, complemented
9#13113079C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic
12C24×Dic13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C4⋊C4×Dic13—24no—
36#11718610C418yescomplemented
37C22⋊C4×Dic13—28no—
38C22⋊C4×Dic13—24no—
39#11718310—28no—
40C25×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13—24no—
46C23×Dic13—22no—
47C23×Dic13—22no—
48C23×Dic13—24no—
49C23×Dic13Q814yes—
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—24no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4C2×C414yes—
64C2×C22⋊Dic13—22no—
65C2×C22⋊Dic13—22no—
66C2×C22⋊Dic13—24no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—24no—
69C2×C22⋊Dic13C2×C418yes—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13C2×C414yescomplemented
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101C2×C418yescomplemented
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—24no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13D418yes—
88C2×C4×Dic13D414yes—
89C13×#95—24no—
90C13×#95—22no—
91#88071—24no—
92#88071—24no—
93#88071—22no—
94#88071—22no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071C2×C414yescomplemented
99C4×#399—131nomaximal, Sylow
100C24×C13—22no—
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—22no—
106C24×C13—21no—
107C24×C13—22no—
108C24×C13C22×C412yes—
109C24×C13C2×Q812yes—
110C24×C13#4112yes—
111C24×C13C2411yescharacteristic
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D414yes—
133C22×C4×C13C2×D412yes—
134C22×C4×C13#4114yes—
135C22×C4×C13#4112yes—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—21no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—28no—
159C22×Dic13—216no—
160C22×Dic13—48no—
161C22×Dic13—44no—
162C22×Dic13—44no—
163C22×Dic13C22×C414yes—
164C22×Dic13C22×C414yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×D414yes—
167C22×Dic13C2×D414yes—
168C22×Dic13C2×D412yes—
169C22×Dic13C2×Q812yes—
170C22×Dic13C2×Q812yes—
171C22×Dic13#4112yes—
172C22×Dic13#4114yes—
173C22×Dic13#4112yes—
174C22×Dic13#4114yes—
175C13×C4⋊C4—28no—
176C13×C22⋊C4—216no—
177C13×C22⋊C4—28no—
178C22⋊Dic13—28no—
179C22⋊Dic13—216no—
180C4⋊Dic13—28no—
181#6101—216no—
182#6101—216no—
183C4×Dic13—216no—
184C4×Dic13—28no—
185C4×Dic13—44no—
186C4×Dic13—48no—
187C2×#399—131no—
188C2×C4×C4⋊C4—132no—
189C2×C4×C4⋊C4—131no—
190C2×C4×C22⋊C4—132no—
191C2×C4×C22⋊C4—131no—
192#1445—132no—
193#1445—131no—
194#1444—131no—
195#1439—132no—
196#1439D1311yescharacteristic
197C4×#95—131no—
198C23×C13—24no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—24no—
204C23×C13—22no—
205C23×C13—24no—
206C23×C13—22no—
207C23×C13—24no—
208C23×C13—22no—
209C23×C13—24no—
210C23×C13—42no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—42no—
214C23×C13—42no—
215C23×C13—42no—
216C23×C13—42no—
217C23×C13—41no—
218C23×C13—42no—
219C23×C13—41no—
220C23×C13C4×Q814yes—
221C23×C13C23×C411yescharacteristic
222C23×C13C22×D411yescharacteristic
223C23×C13C22×D412yes—
224C23×C13C22×Q811yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4112yes—
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4112yes—
230C23×C13C2×#4112yes—
231C23×C13C2×#4111yescharacteristic
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—41no—
255C2×C4×C13C4×D414yes—
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—22no—
266C2×Dic13—24no—
267C2×Dic13—22no—
268C2×Dic13—24no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—42no—
273C2×Dic13—41no—
274C2×Dic13—42no—
275C2×Dic13—41no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—42no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—416no—
285C2×Dic13C4×D418yes—
286C2×Dic13C22⋊Q814yes—
287C2×Dic13C22⋊Q818yes—
288C2×Dic13#12318yes—
289C2×Dic13#12314yes—
290C2×Dic13#12714yes—
291C24×C4—131no—
292C22×C4⋊C4—132no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4C2×D1311yescharacteristic
296C22×C22⋊C4—132no—
297C22×C22⋊C4—131no—
298C22×C22⋊C4C2×D1312yes—
299C22×C22⋊C4C2×D1311yescharacteristic
300C22×C42—132no—
301C22×C42—131no—
302C22×C42—131no—
303C22×C42—132no—
304#399—138no—
305C4×C4⋊C4—268no—
306C4×C4⋊C4—264no—
307C4×C22⋊C4—268no—
308C4×C22⋊C4—264no—
309C2×#95—131no—
310C2×#95—132no—
311C2×#95—132no—
312C2×#95—132no—
313C2×#95—132no—
314C2×#95—131no—
315C2×#95—131no—
316C2×#95—132no—
317C2×#95C2×D1311yescharacteristic
318C2×#95C2×D1312yes—
319C22×C13—24no—
320C22×C13—28no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—44no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—44no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—44no—
330C22×C13C2×C4×D411yescharacteristic
331C22×C13C2×C4×D412yes—
332C22×C13C2×C4×Q811yescharacteristic
333C22×C13C4×#4111yescharacteristic
334C22×C13C4×#4112yes—
335C22×C13C2×C22⋊Q811yescharacteristic
336C22×C13C2×C22⋊Q812yes—
337C22×C13C2×#12312yes—
338C22×C13C2×#12311yescharacteristic
339C22×C13#52512yes—
340C22×C13#52511yescharacteristic
341C22×C13#52511yescharacteristic
342C22×C13#52512yes—
343C22×C13#52911yescharacteristic
344C22×C13#52912yes—
345C22×C13#52912yes—
346C22×C13#52912yes—
347C22×C13#52912yes—
348C22×C13C2×#12711yescharacteristic
349C22×C13#53212yes—
350C22×C13#53211yescharacteristic
351C22×C13#53312yes—
352C22×C13#53311yescharacteristic
353C4×C13—24no—
354C4×C13—42no—
355C4×C13—44no—
356C4×C13—44no—
357Dic13—28no—
358Dic13—44no—
359Dic13—42no—
360Dic13—42no—
361Dic13—42no—
362Dic13#39918yescomplemented
363C25C22×D1311yescharacteristic
364C23×C4—131no—
365C23×C4—132no—
366C23×C4—134no—
367C23×C4—132no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—262no—
372C23×C4—264no—
373C23×C4—262no—
374C23×C4—264no—
375C23×C4C22×D1311yescharacteristic
376C23×C4C22×D1312yes—
377C23×C4C22×D1312yes—
378C23×C4C22×D1311yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—138no—
382C2×C4⋊C4—134no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—264no—
385C2×C4⋊C4—264no—
386C2×C4⋊C4—264no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—264no—
389C2×C4⋊C4—262no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—138no—
396C2×C22⋊C4—264no—
397C2×C22⋊C4—262no—
398C2×C22⋊C4—264no—
399C2×C22⋊C4—262no—
400C2×C22⋊C4—262no—
401C2×C22⋊C4C4×D1314yes—
402C2×C42—138no—
403C2×C42—134no—
404C2×C42—264no—
405C2×C42—264no—
406C2×C42—264no—
407C2×C42—262no—
408C2×C42—264no—
409C2×C42—264no—
410C2×C42—264no—
411C2×C42—264no—
412#95—24no—
413#95—22no—
414#95—134no—
415#95—264no—
416#95—264no—
417#95—262no—
418#95—264no—
419#95—264no—
420#95—262no—
421#95—264no—
422C2×C13—44no—
423C2×C13C4×#12311yescharacteristic
424C2×C13C4×#12312yes—
425C2×C13C4×C22⋊Q811yescharacteristic
426C2×C13C4×C22⋊Q812yes—
427C2×C13C4×#12711yescharacteristic
428C2×C13C2×#39911yescharacteristic
429C2×C13#239512yes—
430C2×C13#239511yescharacteristic
431C2×C13#239611yescharacteristic
432C2×C13#239612yes—
433C2×C13#239711yescharacteristic
434C24—21no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24C2×C4×D1312yes—
443C24#612912yes—
444C24Q8×D1312yes—
445C24C23×D1311yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—132no—
467C22×C4—132no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—134no—
471C22×C4—134no—
472C22×C4—134no—
473C22×C4—132no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—268no—
477C22×C4—2616no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—261no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—261no—
499C22×C4—262no—
500C22×C4—528no—
501C22×C4—524no—
502C22×C4—524no—
503C22×C4C2×C4×D1312yes—
504C22×C4C2×C4×D1312yes—
505C22×C4D4×D1314yes—
506C22×C4D4×D1312yes—
507C22×C4#612914yes—
508C22×C4#612912yes—
509C4⋊C4—28no—
510C4⋊C4—2616no—
511C4⋊C4—2616no—
512C4⋊C4—268no—
513C22⋊C4—216no—
514C22⋊C4—28no—
515C22⋊C4—2616no—
516C22⋊C4—268no—
517C42—268no—
518C42—2616no—
519C42—528no—
520C42—524no—
521C13C4×#39911yescharacteristic, complemented, Sylow
522C23—22no—
523C23—22no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—22no—
532C23—24no—
533C23—24no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23#8814114yes—
545C23C22×C4×D1311yescharacteristic
546C23C2×D4×D1311yescharacteristic
547C23C2×D4×D1312yes—
548C23C2×#612911yescharacteristic
549C23C2×#612911yescharacteristic
550C23C2×#612912yes—
551C23C2×Q8×D1311yescharacteristic
552C23#41×D1311yescharacteristic
553C23#41×D1311yescharacteristic
554C23#41×D1312yes—
555C23#41×D1312yes—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—134no—
580C2×C4—138no—
581C2×C4—138no—
582C2×C4—134no—
583C2×C4—134no—
584C2×C4—138no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—264no—
597C2×C4—262no—
598C2×C4—264no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—5216no—
602C2×C4—522no—
603C2×C4—521no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—522no—
607C2×C4—522no—
608C2×C4—521no—
609C2×C4—522no—
610C2×C4—522no—
611C2×C4—521no—
612C2×C4—522no—
613C2×C4—521no—
614C2×C4#8813514yes—
615C22—24no—
616C22—28no—
617C22—42no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—44no—
625C22—42no—
626C22C2×#8813511yescharacteristic
627C22C2×#8814111yescharacteristic
628C22#1171922711yescharacteristic
629C22C4×#612912yes—
630C22C4×D4×D1312yes—
631C22#1171929112yes—
632C22#1171929111yescharacteristic
633C22#1171930112yes—
634C22#1171930511yescharacteristic
635C22#1171930512yes—
636C22#1171931111yescharacteristic
637C22#1171931112yes—
638C22#1171932712yes—
639C22#1171932711yescharacteristic
640C22D13×C22⋊Q811yescharacteristic
641C22D13×C22⋊Q812yes—
642C22#1171935412yes—
643C22D13×#12312yes—
644C22D13×#12311yescharacteristic
645C22#1171937311yescharacteristic
646C22#1171938512yes—
647C22#1171941112yes—
648C22D13×#12711yescharacteristic
649C4—24no—
650C4—44no—
651C4—44no—
652C4—42no—
653C4—138no—
654C4—268no—
655C4—522no—
656C4—522no—
657C4—522no—
658C4—524no—
659C2—44no—
660C2#1311736111yescharacteristic
661C2#1311736312yes—
662C2#1311736411yescharacteristic
663C2#1311736812yes—
664C2#1311740011yescharacteristic
665C2D13×#39911yescharacteristic
666C2#1311809212yes—
667C2#1311809811yescharacteristic
668C2#1311810311yescharacteristic
669C2#1311811112yes—
670C2#1311811411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13C4×#399
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic13C2semidirect
3. C2×#11718310C2semidirect
6. #13113103C2semidirect
7. #13113102C2semidirect
8. #13113099C2semidirect
10. #95×Dic13C2semidirect
36. #11718610C4semidirect
72. C2×C4⋊Dic13C2×C4semidirect
78. C2×#6101C2×C4semidirect
98. #88071C2×C4semidirect
362. Dic13#399semidirect
521. C13C4×#399semidirect

Maximal subgroups

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

subgroupindex
C2×#117186102
C2×C4⋊C4×Dic132
C2×#117183102
C2×C22⋊C4×Dic132
#131131032
#131131022
#131130992
#131130792
#95×Dic132
C13×#14392
C4×#39913