Finite Group Databasebeta

← #15860325

Subgroups — #15860325

Order 3328.

2270 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D13C211yesmaximal, characteristic
2C22×#88146C211yesmaximal, characteristic
3C2×D13×#117C211yesmaximal, characteristic
4#13114557C211yesmaximal, characteristic, complemented
5#13114556C211yesmaximal, characteristic, complemented
6#13114555C211yesmaximal, characteristic, complemented
7#13114554C214yesmaximal, complemented
8#13114551C214yesmaximal, complemented
9C13×#1736C211yesmaximal, characteristic, complemented
10C23×C4×D13C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C2×#88180C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4×Dic13—21no—
18C22×#6099C2211yescharacteristic
19C2×M16×D13—24no—
20C2×M16×D13—24no—
21C2×M16×D13C418yescomplemented
22C22×#6094C2212yes—
23C22×C8×D13C2212yes—
24D13×#117—24no—
25D13×#117C418yescomplemented
26C2×#88146—21no—
27C2×#88146—21no—
28C2×#88146—24no—
29C2×#88146C418yescomplemented
30C2×#88146C2212yes—
31C2×#88146C2212yes—
32C2×#88146C2212yes—
33C2×C4⋊C4×D13C2212yes—
34C2×C22⋊C4×D13—21no—
35C2×#88131—21no—
36C2×#88126—21no—
37C2×C42×D13—21no—
38C13×#340C2214yescomplemented
39#11718143C2214yescomplemented
40#11718121C2214yescomplemented
41#11718121C2214yescomplemented
42C24×D13D411yescharacteristic
43C23×C4×C13—21no—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13—21no—
46C23×Dic13D411yescharacteristic
47C22×C4×D13—22no—
48C22×C4×D13C2×C414yes—
49C22×C4×D13C2×C414yes—
50C22×C4×D13C2×C414yes—
51C22×C4×D13D411yescharacteristic
52C22×C4×D13D411yescharacteristic
53C22×C4×D13D414yes—
54C22×C4×D13D414yes—
55C22×C4×D13Q814yes—
56C22×C4×D13C2311yescharacteristic
57C22×C4×D13C2311yescharacteristic
58C2×C13×M16—22no—
59C2×C13×M16—22no—
60C2×C13×M16C2×C414yescomplemented
61C22×C8×C13C2312yes—
62C13×#117—22no—
63C13×#117C2×C414yes—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4C2×C414yescomplemented
67C2×C13×C4⋊C4C2312yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C22⋊C4—21no—
70C2×C42×C13—21no—
71C2×C22⋊Dic13—21no—
72C2×#6103—28no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—22no—
76#88180—22no—
77#88180C2×C414yes—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13C2×C414yescomplemented
81C2×C4⋊Dic13C2312yes—
82C2×C4⋊Dic13C2312yes—
83C2×#6101—22no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—28no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×#6099—22no—
90C2×#6099—22no—
91C2×#6099C2×C414yescomplemented
92C22×#1055C2312yes—
93M16×D13—232no—
94C2×#6094—24no—
95C2×#6094—24no—
96C2×#6094C2×C418yescomplemented
97C2×C8×D13—24no—
98C2×C8×D13—24no—
99C2×C8×D13C2×C418yescomplemented
100#88146—28no—
101#88146—28no—
102#88146—24no—
103#88146—24no—
104#88146—24no—
105#88146C2×C418yes—
106#88146C2×C418yescomplemented
107#88146C2×C418yescomplemented
108C4⋊C4×D13—24no—
109C4⋊C4×D13C2×C418yescomplemented
110C22⋊C4×D13—28no—
111#88131—28no—
112#88126—28no—
113C42×D13—28no—
114#20347—131nomaximal, Sylow
115C24×C13C2×D411yescharacteristic
116C23×D13—42no—
117C23×D13—42no—
118C23×D13C22⋊C414yes—
119C23×D13C22⋊C414yes—
120C23×D13C4⋊C414yes—
121C23×D13C2×D411yescharacteristic
122C23×D13C2×D411yescharacteristic
123C22×C4×C13—24no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—44no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C412yes—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×Q812yes—
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—24no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—44no—
139C22×Dic13C22⋊C414yes—
140C22×Dic13C22⋊C414yes—
141C22×Dic13C4⋊C414yes—
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C2×C4×D13—28no—
145C2×C4×D13—44no—
146C2×C4×D13—44no—
147C2×C4×D13C42116yes—
148C2×C4×D13C22⋊C414yes—
149C2×C4×D13C22⋊C414yes—
150C2×C4×D13C22⋊C414yes—
151C2×C4×D13C22⋊C414yes—
152C2×C4×D13C22⋊C4116yes—
153C2×C4×D13C4⋊C414yes—
154C2×C4×D13C4⋊C414yes—
155C2×C4×D13C4⋊C4116yes—
156C2×C4×D13C4⋊C4116yes—
157C2×C4×D13C22×C412yes—
158C2×C4×D13C22×C412yes—
159C2×C4×D13C22×C412yes—
160C2×C4×D13C22×C412yes—
161C2×C4×D13C22×C412yes—
162C2×C4×D13C22×C412yes—
163C2×C4×D13C2×D412yes—
164C2×C4×D13C2×D412yes—
165C2×C4×D13C2×D412yes—
166C2×C4×D13C2×D412yes—
167C2×C4×D13C2×Q812yes—
168C2×C4×D13C2×Q812yes—
169C13×M16—28no—
170C2×C8×C13—22no—
171C2×C8×C13—22no—
172C2×C8×C13C22×C414yes—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—22no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4C22×C414yes—
177C13×C4⋊C4C22×C414yes—
178C13×C22⋊C4—24no—
179C42×C13—24no—
180C22⋊Dic13—24no—
181#6103—28no—
182#6103—28no—
183#6103—28no—
184C4⋊Dic13—24no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13C22×C414yes—
188C4⋊Dic13C22×C414yes—
189#6101—28no—
190C4×Dic13—24no—
191C4×Dic13—28no—
192C4×Dic13—28no—
193C4×Dic13—28no—
194#6099—28no—
195C2×#1055—22no—
196C2×#1055—22no—
197C2×#1055C22×C414yes—
198#6094—216no—
199C8×D13—216no—
200C23×M16—131no—
201C22×#117—131no—
202C22×#117—131no—
203#1736—134no—
204#1736—131no—
205#1736—131no—
206#1736—131no—
207#1736D1311yescharacteristic, complemented
208#1735—134no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13C2×C22⋊C412yes—
212C23×C13C2×C22⋊C412yes—
213C23×C13C2×C4⋊C412yes—
214C23×C13C22×D411yescharacteristic
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—48no—
220C22×D13—44no—
221C22×D13—44no—
222C22×D13—48no—
223C22×D13#95116yes—
224C22×D13C2×C22⋊C412yes—
225C22×D13C2×C22⋊C412yes—
226C22×D13C2×C22⋊C412yes—
227C22×D13C2×C22⋊C412yes—
228C22×D13C2×C4⋊C412yes—
229C22×D13C2×C4⋊C412yes—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—48no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—44no—
236C2×C4×C13C2×C4214yes—
237C2×C4×C13C2×C22⋊C414yes—
238C2×C4×C13C2×C22⋊C412yes—
239C2×C4×C13C2×C22⋊C412yes—
240C2×C4×C13C2×C4⋊C414yes—
241C2×C4×C13C2×C4⋊C414yes—
242C2×C4×C13C2×C4⋊C412yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C22×Q811yescharacteristic
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—48no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—44no—
255C2×Dic13#95116yes—
256C2×Dic13C2×C22⋊C412yes—
257C2×Dic13C2×C22⋊C412yes—
258C2×Dic13C2×C22⋊C412yes—
259C2×Dic13C2×C22⋊C412yes—
260C2×Dic13C2×C4⋊C412yes—
261C2×Dic13C2×C4⋊C412yes—
262C4×D13—416no—
263C4×D13#95116yes—
264C4×D13#95116yes—
265C4×D13C2×C4214yes—
266C4×D13C2×C4214yes—
267C4×D13C2×C22⋊C414yes—
268C4×D13C2×C22⋊C414yes—
269C4×D13C2×C4⋊C414yes—
270C4×D13C2×C4⋊C414yes—
271C4×D13C2×C4⋊C414yes—
272C4×D13C2×C4⋊C414yes—
273C8×C13—24no—
274#1055—24no—
275C24×C4—131no—
276C22×M16—131no—
277C22×M16—138no—
278C22×M16—132no—
279C22×M16—264no—
280C22×M16—264no—
281C22×M16C2×D1311yescharacteristic
282C23×C8—132no—
283C2×#117—131no—
284C2×#117—138no—
285C2×#117—138no—
286C2×#117—132no—
287C2×#117—132no—
288C2×#117—132no—
289C2×#117—261no—
290C2×#117—261no—
291C2×#117—261no—
292C2×#117—264no—
293C2×#117—261no—
294C2×#117—264no—
295C2×#117C2×D1311yescharacteristic
296C22×C4⋊C4—131no—
297C22×C4⋊C4—132no—
298C22×C4⋊C4C2×D1311yescharacteristic
299C22×C22⋊C4—261no—
300C22×C22⋊C4—261no—
301C22×C42—261no—
302C22×C42—261no—
303#340—134no—
304#340—134no—
305#340—134no—
306#340C2×D1314yescomplemented
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—24no—
310C22×C13—24no—
311C22×C13C2×#9514yes—
312C22×C13C22×C22⋊C411yescharacteristic
313C22×C13C22×C22⋊C411yescharacteristic
314C22×C13C22×C4⋊C411yescharacteristic
315C22×C13#57512yes—
316C22×C13#57512yes—
317C2×D13—24no—
318C2×D13—22no—
319C2×D13—22no—
320C2×D13—24no—
321C2×D13—22no—
322C2×D13—22no—
323C2×D13—24no—
324C2×D13—24no—
325C2×D13—416no—
326C2×D13C2×#9514yes—
327C2×D13C2×#9514yes—
328C4×C13—44no—
329C4×C13—44no—
330C4×C13C2×#9514yes—
331C4×C13C22×C4211yescharacteristic
332C4×C13C22×C22⋊C411yescharacteristic
333C4×C13C22×C4⋊C411yescharacteristic
334C4×C13C22×C4⋊C411yescharacteristic
335Dic13—44no—
336Dic13—44no—
337Dic13C2×#9514yes—
338Dic13C2×#9514yes—
339C25—131no—
340C23×C4—21no—
341C23×C4—131no—
342C23×C4—134no—
343C23×C4—134no—
344C23×C4—134no—
345C23×C4—131no—
346C23×C4—134no—
347C23×C4—134no—
348C23×C4—131no—
349C23×C4—134no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—262no—
353C23×C4—261no—
354C23×C4C22×D1311yescharacteristic
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—134no—
358C2×M16—138no—
359C2×M16—264no—
360C2×M16—264no—
361C2×M16—2632no—
362C2×M16—262no—
363C2×M16—262no—
364C2×M16C4×D1314yescomplemented
365C22×C8—132no—
366C22×C8—138no—
367C22×C8—264no—
368C22×C8—264no—
369C22×C8C22×D1312yes—
370#117—22no—
371#117—134no—
372#117—138no—
373#117—138no—
374#117—138no—
375#117—268no—
376#117—268no—
377#117—268no—
378#117—268no—
379#117—264no—
380#117—264no—
381#117—264no—
382#117—262no—
383#117C4×D1314yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—134no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—132no—
389C2×C4⋊C4—138no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—262no—
394C2×C4⋊C4C4×D1314yescomplemented
395C2×C4⋊C4C22×D1312yes—
396C2×C4⋊C4C22×D1312yes—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—268no—
399C2×C22⋊C4—268no—
400C2×C22⋊C4—262no—
401C2×C22⋊C4—262no—
402C2×C22⋊C4—262no—
403C2×C22⋊C4—261no—
404C2×C42—21no—
405C2×C42—268no—
406C2×C42—268no—
407C2×C42—262no—
408C2×C42—262no—
409C2×C42—262no—
410C2×C42—261no—
411C2×C13—24no—
412C2×C13C22×#9511yescharacteristic
413C2×C13#289611yescharacteristic
414C2×C13#289612yes—
415C2×C13#289611yescharacteristic
416C2×C13#291112yes—
417D13—24no—
418D13—24no—
419C24—131no—
420C24—131no—
421C24—134no—
422C24—134no—
423C24—134no—
424C24—522no—
425C24—522no—
426C24D4×D1311yescharacteristic
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—44no—
431C22×C4—134no—
432C22×C4—134no—
433C22×C4—134no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—1316no—
437C22×C4—134no—
438C22×C4—134no—
439C22×C4—134no—
440C22×C4—134no—
441C22×C4—1316no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—1316no—
445C22×C4—1316no—
446C22×C4—132no—
447C22×C4—132no—
448C22×C4—132no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—132no—
456C22×C4—132no—
457C22×C4—132no—
458C22×C4—268no—
459C22×C4—264no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—524no—
463C22×C4—524no—
464C22×C4—524no—
465C22×C4C2×C4×D1312yes—
466C22×C4C2×C4×D1312yes—
467C22×C4C2×C4×D1312yes—
468C22×C4D4×D1311yescharacteristic
469C22×C4D4×D1312yes—
470C22×C4D4×D1312yes—
471C22×C4Q8×D1312yes—
472C22×C4C23×D1311yescharacteristic
473M16—28no—
474M16—2616no—
475M16—268no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—134no—
479C2×C8—2616no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8C2×C4×D1314yes—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—134no—
487C4⋊C4—134no—
488C4⋊C4—268no—
489C4⋊C4—264no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4C2×C4×D1314yes—
493C4⋊C4C2×C4×D1314yes—
494C22⋊C4—24no—
495C22⋊C4—268no—
496C22⋊C4—268no—
497C22⋊C4—268no—
498C22⋊C4—264no—
499C42—24no—
500C42—268no—
501C42—268no—
502C42—268no—
503C42—264no—
504C13#2034711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—132no—
508C23—132no—
509C23—132no—
510C23—132no—
511C23—132no—
512C23—132no—
513C23—1316no—
514C23—262no—
515C23—262no—
516C23—262no—
517C23—262no—
518C23—524no—
519C23—528no—
520C23—524no—
521C23—528no—
522C23C22⋊C4×D1312yes—
523C23C22⋊C4×D1312yes—
524C23C4⋊C4×D1312yes—
525C23C2×D4×D1311yescharacteristic
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—1316no—
539C2×C4—134no—
540C2×C4—134no—
541C2×C4—134no—
542C2×C4—134no—
543C2×C4—134no—
544C2×C4—134no—
545C2×C4—134no—
546C2×C4—134no—
547C2×C4—1316no—
548C2×C4—1316no—
549C2×C4—264no—
550C2×C4—264no—
551C2×C4—5216no—
552C2×C4—528no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—524no—
556C2×C4C42×D1314yes—
557C2×C4C22⋊C4×D1314yes—
558C2×C4C22⋊C4×D1312yes—
559C2×C4C22⋊C4×D1312yes—
560C2×C4C4⋊C4×D1314yes—
561C2×C4C4⋊C4×D1314yes—
562C2×C4C4⋊C4×D1312yes—
563C2×C4C22×C4×D1311yescharacteristic
564C2×C4C22×C4×D1311yescharacteristic
565C2×C4C22×C4×D1311yescharacteristic
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×D4×D1311yescharacteristic
568C2×C4C2×Q8×D1311yescharacteristic
569C8—24no—
570C8—264no—
571C22—22no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—134no—
576C22—134no—
577C22—262no—
578C22—262no—
579C22—264no—
580C22—264no—
581C22—262no—
582C22—262no—
583C22—264no—
584C22—264no—
585C22—5216no—
586C22D13×#9514yes—
587C22C2×C22⋊C4×D1311yescharacteristic
588C22C2×C22⋊C4×D1311yescharacteristic
589C22C2×C4⋊C4×D1311yescharacteristic
590C22#1171947812yes—
591C22#1171948212yes—
592C4—44no—
593C4—44no—
594C4—134no—
595C4—134no—
596C4—524no—
597C4—524no—
598C4D13×#9514yes—
599C4C2×C42×D1311yescharacteristic
600C4C2×C22⋊C4×D1311yescharacteristic
601C4C2×C4⋊C4×D1311yescharacteristic
602C4C2×C4⋊C4×D1311yescharacteristic
603C2—24no—
604C2—264no—
605C2—264no—
606C2C2×D13×#9511yescharacteristic
607C2#1312335011yescharacteristic
608C2#1312335212yes—
609C2#1312335411yescharacteristic
610C2#1312342312yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1736C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1736D13
hypocenterC13#20347
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13114557C2semidirect
5. #13114556C2semidirect
6. #13114555C2semidirect
7. #13114554C2semidirect
8. #13114551C2semidirect
9. C13×#1736C2semidirect
21. C2×M16×D13C4semidirect
25. D13×#117C4semidirect
29. C2×#88146C4semidirect
38. C13×#340C22semidirect
39. #11718143C22semidirect
40. #11718121C22semidirect
41. #11718121C22semidirect
60. C2×C13×M16C2×C4semidirect
66. C2×C13×C4⋊C4C2×C4semidirect
80. C2×C4⋊Dic13C2×C4semidirect
91. C2×#6099C2×C4semidirect
96. C2×#6094C2×C4semidirect
99. C2×C8×D13C2×C4semidirect
106. #88146C2×C4semidirect
107. #88146C2×C4semidirect
109. C4⋊C4×D13C2×C4semidirect
207. #1736D13semidirect
306. #340C2×D13semidirect
364. C2×M16C4×D13semidirect
394. C2×C4⋊C4C4×D13semidirect
504. C13#20347semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D132
C22×#881462
C2×D13×#1172
#131145572
#131145562
#131145552
#131145542
#131145512
C13×#17362
#2034713