Finite Group Databasebeta

← #16799367

Subgroups — #16799367

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#423C211yesmaximal, characteristic
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3#13131016C214yesmaximal, complemented
4#13131015C212yesmaximal, complemented
5#13131014C212yesmaximal, complemented
6#13130525C214yesmaximal
7D13×#533C211yesmaximal, characteristic
8C22×C4⋊#261C2212yes—
9C22×C4×#261—21no—
10C2×D13⋊M16C2212yes—
11C13×#533C411yescharacteristic, complemented
12#11719433C411yescharacteristic, complemented
13#11719433C411yescharacteristic, complemented
14D13×C4⋊Q8C2211yescharacteristic
15D13×C4⋊Q8C2211yescharacteristic
16#11719393C412yescomplemented
17D13×#125C2212yes—
18D13×C22⋊Q8—21no—
19D13×C22⋊Q8—21no—
20#11719327—21no—
21#11719327—21no—
22#11719283—21no—
23#11719283—21no—
24C4×Q8×D13—21no—
25C4×Q8×D13—21no—
26D13×#117C2212yes—
27#11719222C412yescomplemented
28C2×C42×D13C2211yescharacteristic
29#11719175C411yescharacteristic, complemented
30C2×(C2×#261)⋊C4—21no—
31#11719129—21no—
32#11719129—21no—
33C4×C4⋊#261—21no—
34C4×C4⋊#261—21no—
35C4×C4⋊#261C2212yes—
36C4×C4⋊#261C2212yes—
37#11719053—21no—
38#11719052—21no—
39D13⋊(C4⋊C8)C2212yes—
40D13⋊(C4⋊C8)C2212yes—
41#11718246C2218yes—
42#11718246C2218yes—
43C23×#261—22no—
44C2×Q8×D13—21no—
45C2×Q8×D13—21no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C2×#6122—22no—
50C2×C4⋊#261—22no—
51C2×C4⋊#261—24no—
52C2×C4⋊#261Q818yescomplemented
53C2×C4⋊#261C2314yes—
54C2×C4×#261—22no—
55C2×C4×#261—22no—
56C2×C4×#261—44no—
57D13⋊M16—28no—
58C2×#6118—22no—
59C2×D13⋊C8C2314yes—
60C13×C4⋊Q8C2×C411yescharacteristic, complemented
61C13×C4⋊Q8C2×C411yescharacteristic, complemented
62C13×#125C2×C412yescomplemented
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C4×Q8×C13—21no—
66C4×Q8×C13—21no—
67C13×#117C2×C412yes—
68C2×C42×C13C2×C411yescharacteristic
69#88200—21no—
70#88200—21no—
71Q8×Dic13—21no—
72Q8×Dic13—21no—
73#88198—21no—
74#88198—21no—
75#88180C2×C412yes—
76#88178—21no—
77#88178—21no—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13D411yescharacteristic
81#88151—21no—
82#88151—21no—
83#88150—22no—
84#88150—22no—
85#88146C2×C412yes—
86#88146C2×C412yes—
87C4⋊C4×D13—21no—
88C4⋊C4×D13—21no—
89C4⋊C4×D13—22no—
90C4⋊C4×D13—22no—
91C4⋊C4×D13C2312yes—
92C4⋊C4×D13C2312yes—
93#88144C2×C412yescomplemented
94#88144C2×C412yescomplemented
95#88143—22no—
96#88143—22no—
97#88142—21no—
98#88142—21no—
99#88142C2×C412yescomplemented
100#88142C2×C412yescomplemented
101#88141—21no—
102#88141—21no—
103#88141—22no—
104#88141—22no—
105C22⋊C4×D13—22no—
106#88132—22no—
107#88132—22no—
108#88131—22no—
109#88126—22no—
110C42×D13—22no—
111C42×D13C2×C411yescharacteristic
112C42×D13C2×C411yescharacteristic
113C42×D13D411yescharacteristic
114C42×D13D411yescharacteristic
115C42×D13D411yescharacteristic
116C42×D13D411yescharacteristic
117C42×D13C2311yescharacteristic
118C42×D13C2311yescharacteristic
119#88124C2×C412yescomplemented
120#88123C2×C411yescharacteristic, complemented
121#88123C2×C411yescharacteristic, complemented
122C4×Dic26—21no—
123C4×Dic26—21no—
124C4×Dic26—22no—
125C4×Dic26—22no—
126(C2×#261)⋊C4—22no—
127(C2×#261)⋊C4—22no—
128#88112—22no—
129#88112—22no—
130C4⋊#1057—22no—
131C4⋊#1057—22no—
132#21312—131nomaximal, Sylow
133C23×D13C2×D411yescharacteristic
134C22×#261—28no—
135C22×#261—24no—
136C22×#261—44no—
137C22×#261—44no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C22⋊C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146Q8×D13—44no—
147Q8×D13—42no—
148Q8×D13—42no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—42no—
154C2×C4×D13C22⋊C411yescharacteristic
155C2×C4×D13C22⋊C411yescharacteristic
156C2×C4×D13C22⋊C411yescharacteristic
157C2×C4×D13C22⋊C411yescharacteristic
158C2×C4×D13C22×C411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13C2×D411yescharacteristic
165C2×C4×D13C2×Q814yes—
166C2×C4×D13#4114yes—
167C2×C4×D13C2411yescharacteristic
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—22no—
171C2×Dic26—22no—
172#6122—44no—
173C2×#1057—24no—
174C4⋊#261—28no—
175C4⋊#261—24no—
176C4⋊#261C2×Q818yes—
177C4×#261—44no—
178C4×#261—44no—
179#6118—44no—
180D13⋊C8—28no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4C22×C412yes—
186C13×C4⋊C4C22×C412yes—
187C13×C22⋊C4—22no—
188C42×C13—22no—
189C42×C13C22⋊C411yescharacteristic
190C42×C13C22⋊C411yescharacteristic
191C42×C13C22×C411yescharacteristic
192C42×C13C22×C411yescharacteristic
193C22⋊Dic13—22no—
194#6103—22no—
195#6103—22no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—22no—
199C4⋊Dic13—22no—
200C4⋊Dic13C22×C412yes—
201C4⋊Dic13C22×C412yes—
202#6101—22no—
203#6101—22no—
204#6101—22no—
205#6101—22no—
206#6101—22no—
207#6101—22no—
208#6101—22no—
209#6101—22no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13—22no—
213C4×Dic13C22⋊C411yescharacteristic
214C4×Dic13C22⋊C411yescharacteristic
215C4×Dic13C22⋊C411yescharacteristic
216C4×Dic13C22⋊C411yescharacteristic
217C4×Dic13C22⋊C411yescharacteristic
218C4×Dic13C22⋊C411yescharacteristic
219C4×Dic13C22×C411yescharacteristic
220C4×Dic13C22×C411yescharacteristic
221C4×Dic13C2×D411yescharacteristic
222C4×Dic13C2×D411yescharacteristic
223C4×Dic13C2×D411yescharacteristic
224C4×Dic13C2×D411yescharacteristic
225C2×#533—131no—
226C2×#423—131no—
227C2×C4×C4⋊C4—131no—
228#1989—134no—
229#1988—132no—
230#1987—132no—
231#1736—134no—
232C23×C13C2×C22⋊C411yescharacteristic
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—22no—
236C22×D13C2×C22⋊C411yescharacteristic
237C22×D13C22⋊Q814yes—
238C22×D13C22×D411yescharacteristic
239C2×#261—28no—
240C2×#261—416no—
241C2×#261—44no—
242C2×#261—44no—
243Q8×C13—42no—
244Q8×C13—42no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—41no—
249C2×C4×C13C2×C22⋊C411yescharacteristic
250C2×C4×C13C2×C22⋊C411yescharacteristic
251C2×C4×C13C2×C22⋊C411yescharacteristic
252C2×C4×C13C2×C22⋊C411yescharacteristic
253C2×C4×C13C2×C22⋊C411yescharacteristic
254C2×C4×C13C4×Q814yes—
255C2×C4×C13C23×C411yescharacteristic
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—41no—
260C2×Dic13C2×C22⋊C411yescharacteristic
261C2×Dic13C2×C22⋊C411yescharacteristic
262C2×Dic13C2×C22⋊C411yescharacteristic
263C2×Dic13C2×C22⋊C411yescharacteristic
264C2×Dic13C2×C22⋊C411yescharacteristic
265C2×Dic13#12412yes—
266C2×Dic13C4⋊Q812yes—
267C2×Dic13C22×D411yescharacteristic
268C4×D13—21no—
269C4×D13—21no—
270C4×D13—22no—
271C4×D13—22no—
272C4×D13—22no—
273C4×D13—22no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—42no—
277C4×D13—42no—
278C4×D13—44no—
279C4×D13C4×Q814yes—
280C4×D13C22⋊Q814yes—
281C4×D13#12412yes—
282C4×D13C4⋊Q812yes—
283C4×D13AGL(1,ℤ/8)12yes—
284C4×D13#13712yes—
285C4×D13C22×Q812yes—
286C4×D13C2×#4112yes—
287Dic26—44no—
288Dic26—42no—
289Dic26—42no—
290Dic26—44no—
291#1057—44no—
292C22×M16—132no—
293#533—131no—
294#533—131no—
295#533—132no—
296#533—132no—
297#533—131no—
298#533—261no—
299#533—261no—
300#533—261no—
301#533—261no—
302#533#26111yescharacteristic, complemented
303C2×C4⋊Q8—131no—
304C2×C4⋊Q8—131no—
305C2×#125—132no—
306C2×C22⋊Q8—261no—
307C2×C22⋊Q8—261no—
308C2×C4×Q8—261no—
309C2×C4×Q8—261no—
310C2×#117—132no—
311C22×C4⋊C4—132no—
312C22×C42—131no—
313C22×C42—261no—
314#423—261no—
315#423—261no—
316#423—261no—
317#423—261no—
318C2×C4⋊C8—132no—
319C2×C4⋊C8—132no—
320C4×C4⋊C4—132no—
321C4×C4⋊C4—132no—
322C4×C4⋊C4—261no—
323C4×C4⋊C4—261no—
324C2×#95—261no—
325#340—138no—
326#340—138no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13#39112yes—
330C22×C13C22×C22⋊C411yescharacteristic
331C2×D13—21no—
332C2×D13—21no—
333C2×D13—24no—
334C2×D13—24no—
335C2×D13#39112yes—
336C2×D13C2×C22⋊Q812yes—
337C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
338C2×D13C2×#13711yescharacteristic
339C2×D13#57512yes—
340#261—48no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13#39112yes—
347C4×C13#41712yes—
348C4×C13C2×C4×Q812yes—
349Dic13—21no—
350Dic13—21no—
351Dic13—21no—
352Dic13—42no—
353Dic13—42no—
354Dic13#39112yes—
355Dic13#41712yes—
356Dic13C2×#12411yescharacteristic
357Dic13C2×C4⋊Q811yescharacteristic
358C22×Q8—261no—
359C22×Q8—261no—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—262no—
364C2×M16—262no—
365C2×M16—262no—
366C2×M16—268no—
367C22×C8—134no—
368C4⋊Q8—132no—
369C4⋊Q8—132no—
370C4⋊Q8—131no—
371C4⋊Q8—131no—
372C4⋊Q8—261no—
373C4⋊Q8—261no—
374C4⋊Q8—261no—
375C4⋊Q8—261no—
376C4⋊Q8C2×#26111yescharacteristic, complemented
377C4⋊Q8C2×#26111yescharacteristic, complemented
378#125—132no—
379#125—132no—
380#125—132no—
381#125—262no—
382#125—262no—
383#125C2×#26112yescomplemented
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—262no—
387C22⋊Q8—262no—
388C22⋊Q8—262no—
389C22⋊Q8—262no—
390C22⋊Q8—261no—
391C22⋊Q8—261no—
392C22⋊Q8—261no—
393C22⋊Q8—261no—
394C22⋊Q8—261no—
395C22⋊Q8—261no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—262no—
399C4×Q8—262no—
400C4×Q8—262no—
401C4×Q8—262no—
402C4×Q8—261no—
403C4×Q8—261no—
404C4×Q8—261no—
405C4×Q8—261no—
406C4×Q8—261no—
407C4×Q8—261no—
408#117—132no—
409#117—132no—
410#117—132no—
411#117—262no—
412#117—262no—
413#117C2×#26112yes—
414C2×C4⋊C4—134no—
415C2×C4⋊C4—138no—
416C2×C4⋊C4—132no—
417C2×C4⋊C4—132no—
418C2×C4⋊C4—262no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—262no—
423C2×C4⋊C4—264no—
424C2×C22⋊C4—262no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—262no—
437C2×C42—262no—
438C2×C42—262no—
439C2×C42—524no—
440C2×C42C2×#26111yescharacteristic
441C4⋊C8—262no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444C4⋊C8—262no—
445#95—262no—
446#95—262no—
447C2×C13—22no—
448C2×C13C2×#39111yescharacteristic
449C2×C13C2×#41711yescharacteristic
450C2×C13#289611yescharacteristic
451D13—22no—
452D13#307712yes—
453D13#307812yes—
454C24—131no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—262no—
458C2×Q8—262no—
459C2×Q8—261no—
460C2×Q8—261no—
461C2×Q8—522no—
462C2×Q8—522no—
463C2×Q8—524no—
464C22×C4—131no—
465C22×C4—134no—
466C22×C4—134no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—264no—
486C22×C4—268no—
487C22×C4—522no—
488C22×C4—524no—
489C22×C4—524no—
490C22×C4C22⋊#26111yescharacteristic
491C22×C4C22⋊#26111yescharacteristic
492C22×C4C22×#26111yescharacteristic
493M16—524no—
494M16—524no—
495C2×C8—264no—
496C2×C8—268no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—138no—
502C4⋊C4—132no—
503C4⋊C4—132no—
504C4⋊C4—262no—
505C4⋊C4—262no—
506C4⋊C4—262no—
507C4⋊C4—262no—
508C4⋊C4—262no—
509C4⋊C4—262no—
510C4⋊C4—262no—
511C4⋊C4—262no—
512C4⋊C4—264no—
513C4⋊C4—268no—
514C4⋊C4—262no—
515C4⋊C4—262no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4C22×#26112yes—
519C4⋊C4C22×#26112yes—
520C22⋊C4—22no—
521C22⋊C4—262no—
522C22⋊C4—262no—
523C22⋊C4—262no—
524C42—22no—
525C42—131no—
526C42—131no—
527C42—131no—
528C42—131no—
529C42—131no—
530C42—131no—
531C42—131no—
532C42—131no—
533C42—131no—
534C42—131no—
535C42—131no—
536C42—131no—
537C42—262no—
538C42—262no—
539C42—262no—
540C42—524no—
541C42—524no—
542C42C22⋊#26111yescharacteristic
543C42C22⋊#26111yescharacteristic
544C42C22×#26111yescharacteristic
545C42C22×#26111yescharacteristic
546C13#2131211yescharacteristic, complemented, Sylow
547C23—131no—
548C23—131no—
549C23—134no—
550C23—261no—
551C23—261no—
552C23—262no—
553C23C2×C22⋊#26111yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—522no—
557Q8—524no—
558Q8—524no—
559Q8—522no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—131no—
565C2×C4—131no—
566C2×C4—131no—
567C2×C4—132no—
568C2×C4—132no—
569C2×C4—132no—
570C2×C4—132no—
571C2×C4—134no—
572C2×C4—134no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—132no—
576C2×C4—132no—
577C2×C4—131no—
578C2×C4—131no—
579C2×C4—131no—
580C2×C4—262no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—268no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—524no—
595C2×C4—521no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4—5216no—
599C2×C4Q8×#26114yes—
600C2×C4C2×C22⋊#26111yescharacteristic
601C2×C4C2×C22⋊#26111yescharacteristic
602C2×C4C2×C22⋊#26111yescharacteristic
603C2×C4C2×C22⋊#26111yescharacteristic
604C2×C4C2×C22⋊#26111yescharacteristic
605C2×C4C23×#26111yescharacteristic
606C8—524no—
607C22—21no—
608C22—21no—
609C22—132no—
610C22—131no—
611C22—131no—
612C22—132no—
613C22—132no—
614C22—264no—
615C22—264no—
616C22—261no—
617C22—261no—
618C22(C2×#261)⋊Q812yes—
619C22C22×C22⋊#26111yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—42no—
624C4—42no—
625C4—131no—
626C4—131no—
627C4—132no—
628C4—132no—
629C4—261no—
630C4—261no—
631C4—261no—
632C4—528no—
633C4—522no—
634C4—522no—
635C4(C2×#261)⋊Q812yes—
636C4#1171916412yes—
637C4C2×Q8×#26112yes—
638C2—22no—
639C2—132no—
640C2—132no—
641C2—262no—
642C2C2×(C2×#261)⋊Q811yescharacteristic
643C2C2×#1171916411yescharacteristic
644C2#1313145611yescharacteristic
subgroupG/H
centerC22C22×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#21312
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #13131016C2semidirect
4. #13131015C2semidirect
5. #13131014C2semidirect
11. C13×#533C4semidirect
12. #11719433C4semidirect
13. #11719433C4semidirect
16. #11719393C4semidirect
27. #11719222C4semidirect
29. #11719175C4semidirect
52. C2×C4⋊#261Q8semidirect
60. C13×C4⋊Q8C2×C4semidirect
61. C13×C4⋊Q8C2×C4semidirect
62. C13×#125C2×C4semidirect
93. #88144C2×C4semidirect
94. #88144C2×C4semidirect
99. #88142C2×C4semidirect
100. #88142C2×C4semidirect
119. #88124C2×C4semidirect
120. #88123C2×C4semidirect
121. #88123C2×C4semidirect
302. #533#261semidirect
376. C4⋊Q8C2×#261semidirect
377. C4⋊Q8C2×#261semidirect
383. #125C2×#261semidirect
546. C13#21312semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4232
C2×C4×C4⋊#2612
#131310162
#131310152
#131310142
#131305252
D13×#5332
#2131213