Finite Group Databasebeta

← #15784423

Subgroups — #15784423

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718871C212yesmaximal
2C2×#11718310C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic13C212yesmaximal
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113071C212yesmaximal, complemented
6#13113067C212yesmaximal, complemented
7#13113064C211yesmaximal, characteristic, complemented
8#13113060C211yesmaximal, characteristic, complemented
9#13113059C211yesmaximal, characteristic
10#95×Dic13C211yesmaximal, characteristic, complemented
11C22×C13×#95C211yesmaximal, characteristic
12C24×C4×C13C2212yes—
13C24×C4×C13C2211yescharacteristic
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2212yes—
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×C13×#95—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2211yescharacteristic
27#11718871C4116yescomplemented
28C4×C22⋊Dic13—28no—
29C4×C22⋊Dic13C418yescomplemented
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39#11718310—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—24no—
42C23×C4×C13—24no—
43C23×C4×C13—24no—
44C23×C4×C13—22no—
45C23×C4×C13—24no—
46C23×C4×C13—22no—
47C23×C4×C13—24no—
48C23×C4×C13—42no—
49C23×C4×C13—42no—
50C23×C4×C13—42no—
51C23×C4×C13C2×C414yes—
52C23×C4×C13C2×C418yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×Dic13C2312yes—
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13C2×C418yes—
66C2×C22⋊Dic13C2×C414yes—
67C2×C22⋊Dic13C2×C418yes—
68C2×C22⋊Dic13C2×C414yes—
69C2×C22⋊Dic13D414yes—
70C2×C22⋊Dic13Q814yes—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—42no—
74C2×#6101—42no—
75C2×#6101C2×C418yescomplemented
76C2×#6101C2×C418yescomplemented
77C2×C4×Dic13—22no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13—24no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—42no—
84C2×C4×Dic13—42no—
85C2×C4×Dic13—42no—
86C2×C4×Dic13C2×C414yescomplemented
87C2×C4×Dic13C2×C414yescomplemented
88C13×#95—22no—
89C13×#95—24no—
90C13×#95D414yes—
91#88071—22no—
92#88071—22no—
93#88071—24no—
94#88071—24no—
95#88071—42no—
96#88071C2×C414yescomplemented
97#88071C2×C414yescomplemented
98#88071C2×C418yescomplemented
99#88071C2×C418yescomplemented
100#13814—131nomaximal, Sylow
101C24×C13—21no—
102C24×C13—22no—
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—22no—
106C24×C13—21no—
107C24×C13C22×C412yes—
108C24×C13C22×C414yes—
109C24×C13C2×D412yes—
110C24×C13C2×Q812yes—
111C24×C13#4114yes—
112C24×C13C2411yescharacteristic
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—28no—
120C22×C4×C13—216no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
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×C13—22no—
131C22×C4×C13—28no—
132C22×C4×C13—216no—
133C22×C4×C13—44no—
134C22×C4×C13—48no—
135C22×C4×C13—48no—
136C22×C4×C13—48no—
137C22×C4×C13—48no—
138C22×C4×C13—48no—
139C22×C4×C13—48no—
140C22×C4×C13—48no—
141C22×C4×C13C22×C412yes—
142C22×C4×C13C22×C414yes—
143C22×C4×C13C22×C414yes—
144C22×C4×C13C22×C412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13#4112yes—
148C22×C4×C13#4114yes—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13C22×C414yes—
174C22×Dic13C22×C414yes—
175C22×Dic13C22×C412yes—
176C22×Dic13C22×C412yes—
177C22×Dic13C22×C414yes—
178C22×Dic13C22×C414yes—
179C22×Dic13C22×C412yes—
180C22×Dic13C22×C412yes—
181C22×Dic13C2×D412yes—
182C22×Dic13C2×D412yes—
183C22×Dic13C2×Q812yes—
184C22×Dic13C2×Q812yes—
185C22⋊Dic13—216no—
186C22⋊Dic13C42116yescomplemented
187C22⋊Dic13C4⋊C4116yescomplemented
188#6101—216no—
189#6101—48no—
190C4×Dic13—28no—
191C4×Dic13—44no—
192C4×Dic13—48no—
193C4×Dic13—48no—
194C2×#385—132no—
195C2×C4×C4⋊C4—131no—
196C2×C4×C22⋊C4—131no—
197C2×C4×C22⋊C4—132no—
198C22×#95D1311yescharacteristic
199#1436—132no—
200#1436—132no—
201C4⋊#95—131no—
202#1434—131no—
203C22⋊#95—131no—
204C4×#95—131no—
205C23×C13—22no—
206C23×C13—24no—
207C23×C13—22no—
208C23×C13—24no—
209C23×C13—22no—
210C23×C13—24no—
211C23×C13—22no—
212C23×C13—24no—
213C23×C13—22no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—24no—
219C23×C13—24no—
220C23×C13—24no—
221C23×C13—22no—
222C23×C13—24no—
223C23×C13C2×C4214yes—
224C23×C13C2×C4⋊C414yes—
225C23×C13#11714yes—
226C23×C13C4×D418yes—
227C23×C13C4×Q818yes—
228C23×C13C23×C411yescharacteristic
229C23×C13C23×C412yes—
230C23×C13C22×D411yescharacteristic
231C23×C13C22×D411yescharacteristic
232C23×C13C22×Q811yescharacteristic
233C23×C13C2×#4112yes—
234C23×C13C2×#4112yes—
235C23×C13C2×#4111yescharacteristic
236C23×C13H(5,𝔽2)11yescharacteristic
237C23×C13H(5,𝔽2)12yes—
238C23×C132−1+411yescharacteristic
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—22no—
255C2×C4×C13—416no—
256C2×C4×C13—432no—
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×C13C4×D414yes—
264C2×C4×C13C4×D418yes—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—24no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—24no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—24no—
277C2×Dic13—22no—
278C2×Dic13—24no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13C2×C4214yes—
298C2×Dic13C2×C4214yes—
299C2×Dic13C2×C4⋊C414yes—
300C2×Dic13C2×C4⋊C414yes—
301C24×C4C2×D1311yescharacteristic
302C24×C4C2×D1312yes—
303C22×C4⋊C4—132no—
304C22×C4⋊C4—132no—
305C22×C22⋊C4—131no—
306C22×C22⋊C4—131no—
307C22×C22⋊C4—132no—
308C22×C42—131no—
309C22×C42—131no—
310C22×C42—132no—
311C22×C42—132no—
312#385—1316no—
313C4×C4⋊C4—264no—
314C4×C22⋊C4—138no—
315C4×C22⋊C4—268no—
316C2×#95—24no—
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—131no—
320C2×#95—131no—
321C2×#95—131no—
322C2×#95—131no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95C2×D1311yescharacteristic
327C2×#95C2×D1312yes—
328C2×#95C2×D1311yescharacteristic
329C22×C13—24no—
330C22×C13—24no—
331C22×C13—24no—
332C22×C13—24no—
333C22×C13—28no—
334C22×C13—28no—
335C22×C13—28no—
336C22×C13—28no—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13C4×C4⋊C418yescomplemented
340C22×C13C22×C4211yescharacteristic
341C22×C13C22×C4⋊C411yescharacteristic
342C22×C13C2×#11711yescharacteristic
343C22×C13C2×C4×D412yes—
344C22×C13C2×C4×D411yescharacteristic
345C22×C13C2×C4×D412yes—
346C22×C13C2×C4×Q812yes—
347C22×C13C4×#4111yescharacteristic
348C22×C13C4×#4112yes—
349C22×C13#51811yescharacteristic
350C22×C13#51812yes—
351C22×C13#52011yescharacteristic
352C22×C13#52012yes—
353C22×C13D4211yescharacteristic
354C22×C13#54612yes—
355C22×C13#54612yes—
356C22×C13#54711yescharacteristic
357C22×C13D4×Q811yescharacteristic
358C22×C13#55112yes—
359C22×C13#55112yes—
360C22×C13#55212yes—
361C22×C13#55411yescharacteristic
362C22×C13#55412yes—
363C4×C13—24no—
364C4×C13—28no—
365C4×C13—42no—
366C4×C13—44no—
367Dic13—24no—
368Dic13—24no—
369Dic13—24no—
370Dic13—24no—
371Dic13—44no—
372Dic13—44no—
373C25C22×D1311yescharacteristic
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—131no—
385C23×C4—131no—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—132no—
389C23×C4—132no—
390C23×C4C4×D1314yes—
391C23×C4C4×D1318yes—
392C23×C4C22×D1312yes—
393C23×C4C22×D1311yescharacteristic
394C23×C4C22×D1312yes—
395C23×C4C22×D1311yescharacteristic
396C2×C4⋊C4—138no—
397C2×C4⋊C4—138no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4—264no—
400C2×C4⋊C4—522no—
401C2×C4⋊C4—522no—
402C2×C22⋊C4—134no—
403C2×C22⋊C4—134no—
404C2×C22⋊C4—138no—
405C2×C22⋊C4—134no—
406C2×C22⋊C4—134no—
407C2×C22⋊C4—138no—
408C2×C22⋊C4—264no—
409C2×C22⋊C4—264no—
410C2×C42—134no—
411C2×C42—134no—
412C2×C42—262no—
413C2×C42—262no—
414C2×C42—264no—
415C2×C42—264no—
416C2×C42—264no—
417C2×C42—264no—
418C2×C42—522no—
419C2×C42—522no—
420C2×C42—522no—
421#95—22no—
422#95—24no—
423#95—134no—
424#95—134no—
425#95—138no—
426#95—138no—
427#95—264no—
428#95—264no—
429#95—262no—
430#95—262no—
431#95—522no—
432#95C22⋊D1314yes—
433C2×C13—28no—
434C2×C13C2×C4×C4⋊C411yescharacteristic
435C2×C13C42×D411yescharacteristic
436C2×C13#227511yescharacteristic
437C2×C13#234211yescharacteristic
438C2×C13#234311yescharacteristic
439C2×C13D4×C4⋊C411yescharacteristic
440C2×C13#234911yescharacteristic
441C2×C13#235812yes—
442C2×C13#235912yes—
443C2×C13#236012yes—
444C2×C13#236812yes—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24C2×C4×D1312yes—
452C24C2×C4×D1314yes—
453C24D4×D1312yes—
454C24#612914yes—
455C24Q8×D1312yes—
456C24C23×D1311yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—28no—
464C22×C4—216no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—28no—
476C22×C4—216no—
477C22×C4—44no—
478C22×C4—48no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—48no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—132no—
488C22×C4—132no—
489C22×C4—134no—
490C22×C4—134no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—132no—
494C22×C4—132no—
495C22×C4—134no—
496C22×C4—134no—
497C22×C4—261no—
498C22×C4—262no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4—261no—
503C22×C4—262no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—261no—
507C22×C4—261no—
508C22×C4—261no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—262no—
512C22×C4—262no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—262no—
516C22×C4—262no—
517C22×C4—262no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4C2×C4×D1312yes—
522C22×C4C2×C4×D1314yes—
523C22×C4C2×C4×D1314yes—
524C22×C4C2×C4×D1312yes—
525C22×C4#612712yes—
526C22×C4#612714yes—
527C22×C4C2×C22⋊D1312yes—
528C22×C4C2×C22⋊D1314yes—
529C4⋊C4—2616no—
530C4⋊C4—528no—
531C22⋊C4—1316no—
532C22⋊C4—1316no—
533C22⋊C4—2616no—
534C42—268no—
535C42—524no—
536C42—528no—
537C42—528no—
538C13#1381411yescharacteristic, complemented, Sylow
539C23—22no—
540C23—24no—
541C23—22no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—22no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—24no—
554C23—22no—
555C23—24no—
556C23—22no—
557C23C42×D1314yes—
558C23#8813114yes—
559C23#8813518yes—
560C23#8814118yes—
561C23C4⋊C4×D1314yes—
562C23C22×C4×D1311yescharacteristic
563C23C22×C4×D1312yes—
564C23C2×#612712yes—
565C23C2×#612711yescharacteristic
566C23C2×D4×D1311yescharacteristic
567C23C2×#612912yes—
568C23#8825112yes—
569C23#8825111yescharacteristic
570C23C2×Q8×D1311yescharacteristic
571C23#8825411yescharacteristic
572C23C22×C22⋊D1311yescharacteristic
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—432no—
590C2×C4—416no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—134no—
598C2×C4—134no—
599C2×C4—134no—
600C2×C4—134no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—264no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—264no—
607C2×C4—264no—
608C2×C4—262no—
609C2×C4—264no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—262no—
613C2×C4—264no—
614C2×C4—262no—
615C2×C4—262no—
616C2×C4—264no—
617C2×C4—262no—
618C2×C4—262no—
619C2×C4—264no—
620C2×C4—264no—
621C2×C4—264no—
622C2×C4—264no—
623C2×C4—264no—
624C2×C4—264no—
625C2×C4—522no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4—522no—
630C2×C4—522no—
631C2×C4—522no—
632C2×C4—522no—
633C2×C4C4×C22⋊D1314yes—
634C2×C4C4×C22⋊D1318yes—
635C22—24no—
636C22—24no—
637C22—24no—
638C22—28no—
639C22—28no—
640C22—28no—
641C22—28no—
642C22—24no—
643C22—24no—
644C22—24no—
645C22#1171831018yescomplemented
646C22C2×C42×D1311yescharacteristic
647C22C4×#612711yescharacteristic
648C22C4×#612712yes—
649C22C2×#8813111yescharacteristic
650C22C2×#8813512yes—
651C22#1171919111yescharacteristic
652C22#1171919112yes—
653C22#1171919512yes—
654C22#1171920012yes—
655C22#1171920012yes—
656C22C2×#8814112yes—
657C22C2×C4⋊C4×D1311yescharacteristic
658C22#1171920911yescharacteristic
659C22#1171920912yes—
660C22#1171921211yescharacteristic
661C22#1171921611yescharacteristic
662C22#1171921612yes—
663C22#1171921812yes—
664C22C2×C4×C22⋊D1311yescharacteristic
665C22C2×C4×C22⋊D1312yes—
666C22D4×C22⋊D1311yescharacteristic
667C22#1171951112yes—
668C22Q8×C22⋊D1311yescharacteristic
669C4—28no—
670C4—24no—
671C4—44no—
672C4—42no—
673C4—264no—
674C4—264no—
675C4—264no—
676C4—264no—
677C4—524no—
678C4—524no—
679C2—28no—
680C2C2×#1171831011yescharacteristic
681C2C42×C22⋊D1311yescharacteristic
682C2#1311719411yescharacteristic
683C2#1311768111yescharacteristic
684C2#1311769211yescharacteristic
685C2C4⋊C4×C22⋊D1311yescharacteristic
686C2#1311774311yescharacteristic
687C2#1311781512yes—
688C2#1311782412yes—
689C2#1311784112yes—
690C2#1311791612yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC22×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×#95D13
hypocenterC13#13814
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718310C2semidirect
5. #13113071C2semidirect
6. #13113067C2semidirect
7. #13113064C2semidirect
8. #13113060C2semidirect
10. #95×Dic13C2semidirect
27. #11718871C4semidirect
29. C4×C22⋊Dic13C4semidirect
75. C2×#6101C2×C4semidirect
76. C2×#6101C2×C4semidirect
86. C2×C4×Dic13C2×C4semidirect
87. C2×C4×Dic13C2×C4semidirect
96. #88071C2×C4semidirect
97. #88071C2×C4semidirect
98. #88071C2×C4semidirect
99. #88071C2×C4semidirect
186. C22⋊Dic13C42semidirect
187. C22⋊Dic13C4⋊C4semidirect
339. C22×C13C4×C4⋊C4semidirect
538. C13#13814semidirect
645. C22#11718310semidirect

Maximal subgroups

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

subgroupindex
C2×#117188712
C2×#117183102
C2×C4×C22⋊Dic132
#131130712
#131130672
#131130642
#131130602
#131130592
#95×Dic132
C22×C13×#952
#1381413