Finite Group Databasebeta

← #16799600

Subgroups — #16799600

Order 3328.

1258 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3#13131014C212yesmaximal, complemented
4#13131002C212yesmaximal, complemented
5#13130821C214yesmaximal
6C4×#88117C214yesmaximal, complemented
7D13×#533C211yesmaximal, characteristic
8C22×C4⋊#261C2212yes—
9C22×C4×#261—21no—
10C13×#533C411yescharacteristic, complemented
11#11719433C411yescharacteristic, complemented
12#11719433C411yescharacteristic, complemented
13D13×C4⋊Q8C2211yescharacteristic
14D13×C4⋊Q8C2211yescharacteristic
15#11719393—21no—
16D13×#125—21no—
17D13×C22⋊Q8—21no—
18D13×C22⋊Q8C2212yes—
19#11719327—21no—
20#11719327C412yescomplemented
21#11719283—21no—
22#11719283C412yescomplemented
23C4×Q8×D13—21no—
24C4×Q8×D13C2212yes—
25D13×#117—21no—
26#11719222—21no—
27C2×C42×D13C2211yescharacteristic
28#11719175C411yescharacteristic, complemented
29C2×#88117C2218yes—
30C2×(C2×#261)⋊C4—21no—
31#11719125—21no—
32D13⋊(C22⋊C8)C2212yes—
33#11719119—21no—
34C4×C4⋊#261—21no—
35C4×C4⋊#261—21no—
36C4×C4⋊#261C2212yes—
37C4×C4⋊#261C2212yes—
38#11719051—21no—
39D13⋊(C4⋊C8)C2212yes—
40#11719049—21no—
41C4×D13⋊C8C2212yes—
42#11718246C2218yes—
43C23×#261—22no—
44C2×Q8×D13—21no—
45C2×Q8×D13C2312yes—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C2×C4⋊#261—22no—
50C2×C4⋊#261—28no—
51C2×C4⋊#261C2314yes—
52C2×C4×#261—22no—
53C2×C4×#261—22no—
54C2×C4×#261—44no—
55C2×D13⋊C8C2314yes—
56C13×C4⋊Q8C2×C411yescharacteristic, complemented
57C13×C4⋊Q8C2×C411yescharacteristic, complemented
58C13×#125—21no—
59C13×C22⋊Q8—21no—
60C13×C22⋊Q8C2×C412yes—
61C4×Q8×C13—21no—
62C4×Q8×C13C2×C412yescomplemented
63C13×#117—21no—
64C2×C42×C13C2×C411yescharacteristic
65#88200—21no—
66#88200C2×C412yes—
67Q8×Dic13—21no—
68Q8×Dic13C2×C412yescomplemented
69#88198—21no—
70#88198C2×C412yescomplemented
71#88180—21no—
72#88178—21no—
73#88178C2×C412yes—
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77#88151—21no—
78#88151C2×C412yes—
79#88150—22no—
80#88150—22no—
81#88146—21no—
82#88146—21no—
83C4⋊C4×D13—21no—
84C4⋊C4×D13—21no—
85C4⋊C4×D13—21no—
86C4⋊C4×D13—22no—
87C4⋊C4×D13—22no—
88C4⋊C4×D13C2312yes—
89#88144—21no—
90#88144—21no—
91#88143—22no—
92#88143—22no—
93#88142—21no—
94#88142—21no—
95#88142—21no—
96#88142C2×C412yescomplemented
97#88141—21no—
98#88141—22no—
99#88141—22no—
100#88141C2×C412yescomplemented
101C22⋊C4×D13—22no—
102#88132—22no—
103#88132—22no—
104#88131—22no—
105#88126—22no—
106C42×D13—22no—
107C42×D13C2×C411yescharacteristic
108C42×D13C2×C411yescharacteristic
109C42×D13D411yescharacteristic
110C42×D13D411yescharacteristic
111C42×D13D411yescharacteristic
112C42×D13D411yescharacteristic
113C42×D13C2311yescharacteristic
114C42×D13C2311yescharacteristic
115#88124—21no—
116#88123C2×C411yescharacteristic, complemented
117#88123C2×C411yescharacteristic, complemented
118C4×Dic26—21no—
119C4×Dic26—22no—
120C4×Dic26—22no—
121C4×Dic26C2×C412yescomplemented
122C22⋊#1057—22no—
123#88117—216no—
124(C2×#261)⋊C4—22no—
125(C2×#261)⋊C4—22no—
126#88112—22no—
127#88111—22no—
128C4⋊#1057—22no—
129C4×#1057—22no—
130C4×#1057—22no—
131#21385—131nomaximal, Sylow
132C23×D13C2×D411yescharacteristic
133C22×#261—28no—
134C22×#261—24no—
135C22×#261—44no—
136C22×#261—44no—
137C2×Q8×C13—21no—
138C2×Q8×C13C22×C412yes—
139C22×C4×C13C22⋊C411yescharacteristic
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×Dic13C22⋊C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145Q8×D13—28no—
146Q8×D13—44no—
147C2×C4×D13—24no—
148C2×C4×D13—22no—
149C2×C4×D13—22no—
150C2×C4×D13—42no—
151C2×C4×D13C22⋊C411yescharacteristic
152C2×C4×D13C22⋊C411yescharacteristic
153C2×C4×D13C22⋊C411yescharacteristic
154C2×C4×D13C22⋊C411yescharacteristic
155C2×C4×D13SD1614yes—
156C2×C4×D13Q1614yes—
157C2×C4×D13C22×C411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13C2411yescharacteristic
165C2×Dic26—21no—
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26C22×C412yes—
169C2×#1057—24no—
170C4⋊#261—28no—
171C4⋊#261—24no—
172C4⋊#261#4118yes—
173C4×#261—44no—
174C4×#261—44no—
175D13⋊C8—28no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4C22×C412yes—
182C13×C22⋊C4—22no—
183C42×C13—22no—
184C42×C13C22⋊C411yescharacteristic
185C42×C13C22⋊C411yescharacteristic
186C42×C13C22×C411yescharacteristic
187C42×C13C22×C411yescharacteristic
188C22⋊Dic13—22no—
189#6103—22no—
190#6103—22no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—22no—
195C4⋊Dic13—22no—
196C4⋊Dic13C22×C412yes—
197#6101—22no—
198#6101—22no—
199#6101—22no—
200#6101—22no—
201#6101—22no—
202#6101—22no—
203#6101—22no—
204#6101—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—22no—
208C4×Dic13C22⋊C411yescharacteristic
209C4×Dic13C22⋊C411yescharacteristic
210C4×Dic13C22⋊C411yescharacteristic
211C4×Dic13C22⋊C411yescharacteristic
212C4×Dic13C22⋊C411yescharacteristic
213C4×Dic13C22⋊C411yescharacteristic
214C4×Dic13C22×C411yescharacteristic
215C4×Dic13C22×C411yescharacteristic
216C4×Dic13C2×D411yescharacteristic
217C4×Dic13C2×D411yescharacteristic
218C4×Dic13C2×D411yescharacteristic
219C4×Dic13C2×D411yescharacteristic
220C2×#533—131no—
221C2×#431—131no—
222C2×C4×C4⋊C4—131no—
223#1987—132no—
224#1981—132no—
225#1872—134no—
226C4×#103—134no—
227C23×C13C2×C22⋊C411yescharacteristic
228C22×D13—22no—
229C22×D13—22no—
230C22×D13C2×C22⋊C411yescharacteristic
231C22×D13C2×SD1612yes—
232C22×D13C2×Q1612yes—
233C22×D13C22×D411yescharacteristic
234C2×#261—28no—
235C2×#261—416no—
236C2×#261—44no—
237C2×#261—44no—
238Q8×C13—24no—
239Q8×C13—42no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—41no—
244C2×C4×C13#10314yescomplemented
245C2×C4×C13C2×C22⋊C411yescharacteristic
246C2×C4×C13C2×C22⋊C411yescharacteristic
247C2×C4×C13C2×C22⋊C411yescharacteristic
248C2×C4×C13C2×C22⋊C411yescharacteristic
249C2×C4×C13C2×C22⋊C411yescharacteristic
250C2×C4×C13C23×C411yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—41no—
255C2×Dic13#10314yescomplemented
256C2×Dic13C2×C22⋊C411yescharacteristic
257C2×Dic13C2×C22⋊C411yescharacteristic
258C2×Dic13C2×C22⋊C411yescharacteristic
259C2×Dic13C2×C22⋊C411yescharacteristic
260C2×Dic13C2×C22⋊C411yescharacteristic
261C2×Dic13C22×D411yescharacteristic
262C4×D13—22no—
263C4×D13—22no—
264C4×D13—22no—
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—44no—
270C4×D13—44no—
271C4×D13#10314yescomplemented
272C4×D13#10314yescomplemented
273C4×D13C2×SD1612yes—
274C4×D13C2×SD1612yes—
275C4×D13C2×Q1612yes—
276C4×D13C2×Q1612yes—
277C4×D13C2×#4114yes—
278Dic26—24no—
279Dic26—44no—
280Dic26—42no—
281Dic26—44no—
282#1057—44no—
283#533—131no—
284#533—131no—
285#533—132no—
286#533—132no—
287#533—131no—
288#533—261no—
289#533—261no—
290#533—261no—
291#533—261no—
292#533#26111yescharacteristic, complemented
293C2×C4⋊Q8—131no—
294C2×C4⋊Q8—131no—
295C2×#125—261no—
296C2×C22⋊Q8—132no—
297C2×C22⋊Q8—261no—
298C2×C4×Q8—132no—
299C2×C4×Q8—261no—
300C2×#117—261no—
301C22×C4⋊C4—132no—
302C22×C42—131no—
303C22×C42—261no—
304#431—261no—
305#431—261no—
306#431—261no—
307#431—261no—
308C2×C4⋊C8—132no—
309C2×#103—138no—
310C2×C22⋊C8—132no—
311C2×C4×C8—132no—
312C4×C4⋊C4—132no—
313C4×C4⋊C4—132no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4—261no—
316C2×#95—261no—
317#340—138no—
318C22×C13—21no—
319C22×C13—21no—
320C22×C13C2×#10312yes—
321C22×C13C22×C22⋊C411yescharacteristic
322C2×D13—21no—
323C2×D13—21no—
324C2×D13—24no—
325C2×D13—24no—
326C2×D13C2×#10312yes—
327C2×D13#52512yes—
328C2×D13C22×SD1611yescharacteristic
329C2×D13C22×Q1611yescharacteristic
330C2×D13#57512yes—
331#261—48no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—42no—
336C4×C13—42no—
337C4×C13C2×#10312yes—
338C4×C13C2×#10312yes—
339C4×C13C4×#4112yes—
340Dic13—21no—
341Dic13—21no—
342Dic13—21no—
343Dic13—42no—
344Dic13—42no—
345Dic13C2×#10312yes—
346Dic13C2×#10312yes—
347Dic13#53212yes—
348C22×Q8—132no—
349C22×Q8—261no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—262no—
354C22×C8—134no—
355C4⋊Q8—132no—
356C4⋊Q8—132no—
357C4⋊Q8—131no—
358C4⋊Q8—131no—
359C4⋊Q8—261no—
360C4⋊Q8—261no—
361C4⋊Q8—261no—
362C4⋊Q8—261no—
363C4⋊Q8C2×#26111yescharacteristic, complemented
364C4⋊Q8C2×#26111yescharacteristic, complemented
365#125—21no—
366#125—262no—
367#125—262no—
368#125—261no—
369#125—261no—
370#125—261no—
371C22⋊Q8—21no—
372C22⋊Q8—132no—
373C22⋊Q8—132no—
374C22⋊Q8—132no—
375C22⋊Q8—262no—
376C22⋊Q8—262no—
377C22⋊Q8—262no—
378C22⋊Q8—262no—
379C22⋊Q8—261no—
380C22⋊Q8—261no—
381C22⋊Q8—261no—
382C22⋊Q8C2×#26112yes—
383C4×Q8—21no—
384C4×Q8—132no—
385C4×Q8—132no—
386C4×Q8—132no—
387C4×Q8—262no—
388C4×Q8—262no—
389C4×Q8—262no—
390C4×Q8—261no—
391C4×Q8—262no—
392C4×Q8—261no—
393C4×Q8—261no—
394C4×Q8C2×#26112yescomplemented
395#117—21no—
396#117—262no—
397#117—262no—
398#117—261no—
399#117—261no—
400#117—261no—
401C2×C4⋊C4—134no—
402C2×C4⋊C4—132no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—262no—
406C2×C4⋊C4—262no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—268no—
409C2×C4⋊C4—262no—
410C2×C22⋊C4—262no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—131no—
419C2×C42—131no—
420C2×C42—131no—
421C2×C42—131no—
422C2×C42—262no—
423C2×C42—262no—
424C2×C42—262no—
425C2×C42—524no—
426C2×C42C2×#26111yescharacteristic
427C4⋊C8—262no—
428C4⋊C8—262no—
429#103—2616no—
430C22⋊C8—262no—
431C22⋊C8—262no—
432C4×C8—262no—
433C4×C8—262no—
434#95—262no—
435#95—262no—
436C2×C13—22no—
437C2×C13#229711yescharacteristic
438C2×C13C22×#10311yescharacteristic
439C2×C13#289611yescharacteristic
440D13—22no—
441D13#310112yes—
442D13#310412yes—
443C24—131no—
444C2×Q8—21no—
445C2×Q8—132no—
446C2×Q8—262no—
447C2×Q8—262no—
448C2×Q8—268no—
449C2×Q8—261no—
450C2×Q8—524no—
451C2×Q8C22×#26112yes—
452C22×C4—131no—
453C22×C4—134no—
454C22×C4—134no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—264no—
473C22×C4—268no—
474C22×C4—522no—
475C22×C4—524no—
476C22×C4—524no—
477C22×C4C22⋊#26111yescharacteristic
478C22×C4C22⋊#26111yescharacteristic
479C22×C4C22×#26111yescharacteristic
480C2×C8—264no—
481C2×C8—268no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—138no—
488C4⋊C4—132no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—262no—
493C4⋊C4—262no—
494C4⋊C4—262no—
495C4⋊C4—262no—
496C4⋊C4—262no—
497C4⋊C4—264no—
498C4⋊C4—268no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—262no—
502C4⋊C4—262no—
503C4⋊C4—261no—
504C4⋊C4C22×#26112yes—
505C22⋊C4—22no—
506C22⋊C4—262no—
507C22⋊C4—262no—
508C22⋊C4—262no—
509C42—22no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42—131no—
514C42—131no—
515C42—131no—
516C42—131no—
517C42—131no—
518C42—131no—
519C42—131no—
520C42—131no—
521C42—131no—
522C42—262no—
523C42—262no—
524C42—262no—
525C42—524no—
526C42—524no—
527C42C22⋊#26111yescharacteristic
528C42C22⋊#26111yescharacteristic
529C42C22×#26111yescharacteristic
530C42C22×#26111yescharacteristic
531C13#2138511yescharacteristic, complemented, Sylow
532C23—131no—
533C23—131no—
534C23—132no—
535C23—132no—
536C23—262no—
537C23—262no—
538C23C2×C22⋊#26111yescharacteristic
539Q8—24no—
540Q8—42no—
541Q8—264no—
542Q8—522no—
543Q8—524no—
544Q8—524no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—131no—
550C2×C4—131no—
551C2×C4—131no—
552C2×C4—134no—
553C2×C4—134no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—134no—
557C2×C4—134no—
558C2×C4—132no—
559C2×C4—132no—
560C2×C4—131no—
561C2×C4—131no—
562C2×C4—131no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—268no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—524no—
575C2×C4—524no—
576C2×C4—521no—
577C2×C4—524no—
578C2×C4—524no—
579C2×C4—5216no—
580C2×C4#8811714yescomplemented
581C2×C4C2×C22⋊#26111yescharacteristic
582C2×C4C2×C22⋊#26111yescharacteristic
583C2×C4C2×C22⋊#26111yescharacteristic
584C2×C4C2×C22⋊#26111yescharacteristic
585C2×C4C2×C22⋊#26111yescharacteristic
586C2×C4C23×#26111yescharacteristic
587C8—524no—
588C22—21no—
589C22—21no—
590C22—132no—
591C22—131no—
592C22—131no—
593C22—132no—
594C22—132no—
595C22—264no—
596C22—264no—
597C22—261no—
598C22—261no—
599C22C2×#8811712yes—
600C22C22×C22⋊#26111yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—132no—
607C4—132no—
608C4—132no—
609C4—261no—
610C4—261no—
611C4—261no—
612C4—528no—
613C4—522no—
614C4—522no—
615C4C2×#8811712yes—
616C4C2×#8811712yes—
617C4#41×#26112yes—
618C2—22no—
619C2—132no—
620C2—132no—
621C2—262no—
622C2#1313129711yescharacteristic
623C2C22×#8811711yescharacteristic
624C2#1313145611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#533C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenter#533#261
hypocenterC13#21385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #13131014C2semidirect
4. #13131002C2semidirect
6. C4×#88117C2semidirect
10. C13×#533C4semidirect
11. #11719433C4semidirect
12. #11719433C4semidirect
20. #11719327C4semidirect
22. #11719283C4semidirect
28. #11719175C4semidirect
56. C13×C4⋊Q8C2×C4semidirect
57. C13×C4⋊Q8C2×C4semidirect
62. C4×Q8×C13C2×C4semidirect
68. Q8×Dic13C2×C4semidirect
70. #88198C2×C4semidirect
96. #88142C2×C4semidirect
100. #88141C2×C4semidirect
116. #88123C2×C4semidirect
117. #88123C2×C4semidirect
121. C4×Dic26C2×C4semidirect
244. C2×C4×C13#103semidirect
255. C2×Dic13#103semidirect
271. C4×D13#103semidirect
272. C4×D13#103semidirect
292. #533#261semidirect
363. C4⋊Q8C2×#261semidirect
364. C4⋊Q8C2×#261semidirect
394. C4×Q8C2×#261semidirect
531. C13#21385semidirect
580. C2×C4#88117semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
C2×C4×C4⋊#2612
#131310142
#131310022
#131308212
C4×#881172
D13×#5332
#2138513