Finite Group Databasebeta

← #15785802

Subgroups — #15785802

Order 3328.

2558 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D52C211yesmaximal, characteristic
2C2×#11718649C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718650C214yesmaximal, complemented
5C2×#11718637C211yesmaximal, characteristic, complemented
6#13113080C214yesmaximal, complemented
7#13113065C211yesmaximal, characteristic, complemented
8C4×#88071C211yesmaximal, characteristic, complemented
9C2×C13×#389C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2214yes—
18C22×#6103C2214yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101C2214yes—
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×C4×D52—24no—
24C2×C4×D52—24no—
25C2×C4×D52—24no—
26C13×#389—24no—
27C2×C13×#95C2212yes—
28C2×#88071C2214yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31#11718650—216no—
32#11718649—24no—
33#11718649C418yescomplemented
34#11718637—24no—
35C24×D13C2312yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
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—24no—
54C22×C4×D13—28no—
55C22×C4×D13—44no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—24no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—28no—
63C2×C13×C4⋊C4C2×C414yescomplemented
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13D414yes—
67C2×#6103—24no—
68C2×#6103—24no—
69C2×#6103—24no—
70C2×#6103—28no—
71C2×#6103—28no—
72C2×#6103—28no—
73C2×#6103—28no—
74C2×#6103—44no—
75C2×#6103C2×C4116yescomplemented
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13D414yes—
79C2×#6101—28no—
80C2×#6101—28no—
81C2×#6101—44no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13C2×C414yescomplemented
88C4×D52—232no—
89C13×#95—24no—
90#88071—28no—
91#88071—24no—
92#88071D418yescomplemented
93#13977—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C23×D13—24no—
96C23×D13—22no—
97C23×D13—22no—
98C23×D13—24no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—24no—
102C23×D13—24no—
103C23×D13C22×C414yes—
104C23×D13C2×D414yes—
105C23×D13C2×Q814yes—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—24no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—24no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—24no—
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×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×Q812yes—
131C22×C4×C13#4112yes—
132C22×C4×C13#4112yes—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—24no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—24no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13C22×C414yes—
148C22×Dic13C2×D414yes—
149C22×Dic13C2×D414yes—
150C22×Dic13C2×D414yes—
151C22×Dic13#4114yes—
152C2×D52—28no—
153C2×D52—28no—
154C2×D52—28no—
155C2×D52—28no—
156C2×D52—28no—
157C2×D52—28no—
158C2×D52C4⋊C4116yescomplemented
159C2×C4×D13—216no—
160C2×C4×D13—416no—
161C2×C4×D13—416no—
162C2×C4×D13—48no—
163C2×C4×D13—48no—
164C13×C4⋊C4—28no—
165C13×C4⋊C4—44no—
166C13×C4⋊C4—48no—
167C42×C13—28no—
168#6103—216no—
169#6103—232no—
170#6103—416no—
171C4⋊Dic13—28no—
172#6101—416no—
173C4×Dic13—28no—
174C4×Dic13—44no—
175C22×C4×D4—131no—
176C2×#390—131no—
177C2×#390—131no—
178C2×#389D1311yescharacteristic, complemented
179C2×#385—134no—
180C2×#384—131no—
181#1439—134no—
182C4⋊#95—131no—
183C4×#95—131no—
184C23×C13C23×C411yescharacteristic
185C23×C13C22×D411yescharacteristic
186C23×C13C22×D411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×D412yes—
189C23×C13C22×Q811yescharacteristic
190C23×C13C2×#4111yescharacteristic
191C23×C13C2×#4111yescharacteristic
192C23×C13C2×#4112yes—
193C23×C13H(5,𝔽2)12yes—
194C23×C132−1+412yes—
195C22×D13—28no—
196C22×D13—24no—
197C22×D13—24no—
198C22×D13—28no—
199C22×D13—24no—
200C22×D13—24no—
201C22×D13—24no—
202C22×D13—24no—
203C22×D13—28no—
204C22×D13—28no—
205C22×D13—28no—
206C22×D13—28no—
207C22×D13—42no—
208C22×D13—42no—
209C22×D13—44no—
210C22×D13—42no—
211C22×D13—42no—
212C22×D13—44no—
213C22×D13—44no—
214C22×D13—44no—
215C22×D13—44no—
216C22×D13—44no—
217C22×D13C2×C4⋊C418yes—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—28no—
223C2×C4×C13—24no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—42no—
228C2×C4×C13—44no—
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×C4⋊C414yes—
238C2×C4×C13C4×D414yes—
239C2×C4×C13C4×D414yes—
240C2×C4×C13#12014yes—
241C2×C4×C13C22⋊Q814yes—
242C2×C4×C13C22⋊Q814yes—
243C2×C4×C13#12314yes—
244C2×C4×C13#12714yes—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—28no—
254C2×Dic13—24no—
255C2×Dic13—24no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—44no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13C4×D418yescomplemented
264D52—232no—
265C4×D13—432no—
266C23×D4—131no—
267C24×C4—132no—
268C2×C4×D4—264no—
269C2×C4×D4—264no—
270C2×C4×D4—264no—
271C22×C4⋊C4—131no—
272C22×C4⋊C4—134no—
273C22×C4⋊C4C2×D1311yescharacteristic
274C22×C4⋊C4C2×D1312yes—
275C22×C4⋊C4C2×D1311yescharacteristic
276C22×C22⋊C4—134no—
277C22×C22⋊C4—132no—
278C22×C22⋊C4—134no—
279C22×C42—131no—
280C22×C42—131no—
281C22×C42C2×D1311yescharacteristic
282#390—138no—
283#390—264no—
284#389—24no—
285#385—2616no—
286#384—264no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95—134no—
290C2×#95C2×D1312yes—
291C22×C13C22×C4⋊C411yescharacteristic
292C22×C13C2×C4×D411yescharacteristic
293C22×C13C2×C4×D411yescharacteristic
294C22×C13C2×C4×D412yes—
295C22×C13#52012yes—
296C22×C13C2×#12011yescharacteristic
297C22×C13C2×C22⋊Q811yescharacteristic
298C22×C13C2×C22⋊Q811yescharacteristic
299C22×C13C2×#12311yescharacteristic
300C22×C13C2×#12711yescharacteristic
301C22×C13#53212yes—
302C22×C13#53211yescharacteristic
303C22×C13#53511yescharacteristic
304C22×C13#53611yescharacteristic
305C22×C13#54212yes—
306C22×C13D4212yes—
307C22×C13D4212yes—
308C22×C13#54712yes—
309C22×C13#54712yes—
310C22×C13#54812yes—
311C22×C13D4×Q812yes—
312C22×C13#55312yes—
313C22×C13#55412yes—
314C2×D13—216no—
315C2×D13—28no—
316C2×D13—44no—
317C2×D13—44no—
318C2×D13—44no—
319C2×D13—48no—
320C2×D13—48no—
321C2×D13—44no—
322C2×D13—44no—
323C2×D13—48no—
324C2×D13—44no—
325C4×C13—24no—
326C4×C13—44no—
327C4×C13—42no—
328C4×C13—82no—
329C4×C13#38518yescomplemented
330Dic13—28no—
331Dic13—44no—
332Dic13—44no—
333C25—132no—
334C22×D4—134no—
335C22×D4—134no—
336C22×D4—134no—
337C22×D4—262no—
338C22×D4—262no—
339C22×D4—262no—
340C22×D4—262no—
341C23×C4—132no—
342C23×C4—132no—
343C23×C4—132no—
344C23×C4—264no—
345C23×C4—264no—
346C23×C4—264no—
347C23×C4—268no—
348C23×C4—524no—
349C23×C4C22×D1312yes—
350C23×C4C22×D1312yes—
351C23×C4C22×D1311yescharacteristic
352C23×C4C22×D1311yescharacteristic
353C23×C4C22×D1311yescharacteristic
354C4×D4—2632no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—134no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—268no—
366C2×C4⋊C4—268no—
367C2×C4⋊C4—524no—
368C2×C4⋊C4C4×D1314yescomplemented
369C2×C22⋊C4—1316no—
370C2×C22⋊C4—264no—
371C2×C22⋊C4—268no—
372C2×C22⋊C4—268no—
373C2×C22⋊C4—264no—
374C2×C22⋊C4—264no—
375C2×C22⋊C4—268no—
376C2×C22⋊C4—268no—
377C2×C22⋊C4—524no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—134no—
381C2×C42—262no—
382C2×C42—262no—
383C2×C42—262no—
384C2×C42—262no—
385C2×C42—262no—
386C2×C42C22⋊D1314yes—
387#95—24no—
388#95—138no—
389#95—264no—
390#95—268no—
391C2×C13C2×#38511yescharacteristic
392C2×C13C4×#12711yescharacteristic
393C2×C13#232611yescharacteristic
394C2×C13D4×C4⋊C412yes—
395C2×C13#236112yes—
396C2×C13#242212yes—
397C2×C13#243211yescharacteristic
398C2×C13#243311yescharacteristic
399C2×C13#245212yes—
400C2×C13#254211yescharacteristic
401C2×C13#256611yescharacteristic
402D13—48no—
403C24—134no—
404C24—134no—
405C24—134no—
406C24—262no—
407C24—264no—
408C24—262no—
409C24—262no—
410C24—264no—
411C24—264no—
412C24—264no—
413C24—262no—
414C24C23×D1311yescharacteristic
415C2×D4—1316no—
416C2×D4—268no—
417C2×D4—268no—
418C2×D4—268no—
419C2×D4—268no—
420C2×D4—268no—
421C2×D4—268no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—2616no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—264no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—264no—
457C22×C4—262no—
458C22×C4—5216no—
459C22×C4—5216no—
460C22×C4—528no—
461C22×C4—528no—
462C22×C4C2×C4×D1314yes—
463C22×C4C2×C4×D1312yes—
464C22×C4#612712yes—
465C22×C4D4×D1314yes—
466C22×C4D4×D1312yes—
467C22×C4D4×D1312yes—
468C22×C4Q8×D1312yes—
469C22×C4#613112yes—
470C22×C4C2×C22⋊D1312yes—
471C22×C4C2×C22⋊D1312yes—
472C22×C4C2×C22⋊D1312yes—
473C4⋊C4—28no—
474C4⋊C4—44no—
475C4⋊C4—48no—
476C4⋊C4—268no—
477C4⋊C4—5216no—
478C22⋊C4—2632no—
479C22⋊C4—2616no—
480C22⋊C4—5216no—
481C42—28no—
482C42—268no—
483C42—524no—
484C13#1397711yescharacteristic, complemented, Sylow
485C23—138no—
486C23—268no—
487C23—264no—
488C23—264no—
489C23—264no—
490C23—264no—
491C23—264no—
492C23—268no—
493C23—264no—
494C23—268no—
495C23—268no—
496C23—268no—
497C23—268no—
498C23—524no—
499C23—522no—
500C23—524no—
501C23—522no—
502C23—522no—
503C23—522no—
504C23—524no—
505C23—524no—
506C23—524no—
507C23—524no—
508C23C22×C4×D1311yescharacteristic
509C23C2×#612711yescharacteristic
510C23C2×D4×D1312yes—
511C23C2×D4×D1311yescharacteristic
512C23C2×D4×D1311yescharacteristic
513C23C2×Q8×D1311yescharacteristic
514C23C2×#613111yescharacteristic
515C23#8825412yes—
516C23#41×D1312yes—
517C23#8825612yes—
518C23C22×C22⋊D1311yescharacteristic
519D4—2632no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—138no—
540C2×C4—264no—
541C2×C4—264no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—264no—
550C2×C4—268no—
551C2×C4—5232no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—524no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4C4⋊C4×D1314yes—
560C2×C4#8814714yes—
561C2×C4#8814814yes—
562C2×C4#8815014yes—
563C2×C4C4×C22⋊D1314yes—
564C2×C4#8819114yes—
565C2×C4#8819414yes—
566C2×C4#8820014yes—
567C22—2616no—
568C22—268no—
569C22—524no—
570C22—524no—
571C22—524no—
572C22—524no—
573C22—524no—
574C22—528no—
575C22—528no—
576C22—524no—
577C22—528no—
578C22C2×C4⋊C4×D1311yescharacteristic
579C22C2×#8814711yescharacteristic
580C22C2×#8814811yescharacteristic
581C22C2×#8815011yescharacteristic
582C22C4×D4×D1312yes—
583C22#1171925312yes—
584C22#1171927912yes—
585C22#1171928712yes—
586C22#1171931412yes—
587C22#1171931412yes—
588C22#1171933612yes—
589C22#1171933812yes—
590C22#1171939512yes—
591C22#1171940012yes—
592C22#1171943112yes—
593C22#1171943212yes—
594C22C2×C4×C22⋊D1311yescharacteristic
595C22C2×#8819111yescharacteristic
596C22C2×#8819411yescharacteristic
597C22C2×#8820011yescharacteristic
598C22#1171952111yescharacteristic
599C22#1171953511yescharacteristic
600C22#1171953711yescharacteristic
601C4—24no—
602C4—42no—
603C4—44no—
604C4—82no—
605C4—268no—
606C4—524no—
607C4—524no—
608C4#1171865018yescomplemented
609C2—528no—
610C2C2×#1171865011yescharacteristic
611C2C4×#8819411yescharacteristic
612C2#1311754311yescharacteristic
613C2#1311773712yes—
614C2#1311785112yes—
615C2#1311835112yes—
616C2#1311846511yescharacteristic
617C2#1311847411yescharacteristic
618C2#1311868712yes—
619C2#1311979011yescharacteristic
620C2#1312003711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#13977
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#11718650C2semidirect
5. C2×#11718637C2semidirect
6. #13113080C2semidirect
7. #13113065C2semidirect
8. C4×#88071C2semidirect
9. C2×C13×#389C2semidirect
33. #11718649C4semidirect
63. C2×C13×C4⋊C4C2×C4semidirect
75. C2×#6103C2×C4semidirect
87. C2×C4×Dic13C2×C4semidirect
92. #88071D4semidirect
158. C2×D52C4⋊C4semidirect
178. C2×#389D13semidirect
263. C2×Dic13C4×D4semidirect
329. C4×C13#385semidirect
368. C2×C4⋊C4C4×D13semidirect
484. C13#13977semidirect
608. C4#11718650semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D522
C2×#117186492
C2×#117186502
C2×#117186372
#131130802
#131130652
C4×#880712
C2×C13×#3892
#1397713