Finite Group Databasebeta

← #16792815

Subgroups — #16792815

Order 3328.

1314 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C212yesmaximal, complemented
2#13130078C212yesmaximal, complemented
3#13130075C212yesmaximal, complemented
4#13130073C212yesmaximal, complemented
5#13130071C212yesmaximal, complemented
6#13130069C212yesmaximal, complemented
7#13130067C212yesmaximal, complemented
8C2×C4×#6127C211yesmaximal, characteristic
9C22×#6127C411yescharacteristic
10C22×C42×C13C411yescharacteristic
11C2×C4×C22⋊D13C411yescharacteristic
12C2×C4×C22⋊D13C411yescharacteristic
13C2×C4×C22⋊D13C2211yescharacteristic
14C2×C4×C22⋊D13C2211yescharacteristic
15C2×#88180C2211yescharacteristic
16C4×#6127—22no—
17C4×#6127—22no—
18C4×#6127—22no—
19C4×#6127—22no—
20C2×C4×D52C411yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C2×#88126C411yescharacteristic
23C2×#88126C2211yescharacteristic
24C2×C42×D13C411yescharacteristic
25C2×C42×D13C2211yescharacteristic
26C2×C4×Dic26C411yescharacteristic
27C2×C4×Dic26C2211yescharacteristic
28#11719125C2214yes—
29D13⋊(C22⋊C8)C2214yes—
30#11719119C2214yes—
31#11719051—22no—
32D13⋊(C4⋊C8)—22no—
33#11719049—22no—
34C4×D13⋊C8—22no—
35#11718305C2214yes—
36#11718287C2214yes—
37#11718286C2214yes—
38#11718285C2214yes—
39C23×C4×C13C2×C411yescharacteristic
40C23×C4×C13C2×C411yescharacteristic
41C23×C4×C13C2×C411yescharacteristic
42C22×C22⋊D13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C2×#6127—22no—
45C2×#6127—22no—
46C2×#6127—24no—
47C2×#6127C818yescomplemented
48C22×D52C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic
50C22×C4×D13C2×C411yescharacteristic
51C22×C4×D13C2×C411yescharacteristic
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13C2×C411yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×Dic26C2×C411yescharacteristic
56C2×D13⋊C8—24no—
57C2×C42×C13—21no—
58C2×C42×C13—21no—
59C2×C42×C13—21no—
60C2×C42×C13—21no—
61C2×C42×C13C2×C411yescharacteristic
62C2×C42×C13C2×C411yescharacteristic
63C2×C42×C13C2×C411yescharacteristic
64C2×C42×C13C2×C411yescharacteristic
65C2×C22⋊Dic13C2×C411yescharacteristic
66C2×C22⋊Dic13C2311yescharacteristic
67C4×C22⋊D13—22no—
68C4×C22⋊D13—22no—
69C4×C22⋊D13—22no—
70C4×C22⋊D13—22no—
71C4×C22⋊D13—22no—
72C4×C22⋊D13—22no—
73C4×C22⋊D13—22no—
74C4×C22⋊D13—22no—
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2311yescharacteristic
79#88180—22no—
80#88180—22no—
81C2×C4⋊Dic13C2×C411yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2311yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C2×C4×Dic13C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C4×D52—22no—
94C4×D52—22no—
95C4×D52—22no—
96C4×D52—22no—
97#88126—22no—
98#88126—22no—
99#88126—22no—
100#88126—22no—
101C42×D13—21no—
102C42×D13—21no—
103C42×D13—21no—
104C42×D13—21no—
105C42×D13D412yes—
106C42×D13D412yes—
107C42×D13D412yes—
108C42×D13D412yes—
109C4×Dic26—22no—
110C4×Dic26—22no—
111C4×Dic26—22no—
112C4×Dic26—22no—
113C22⋊#1057C2318yes—
114#88112—24no—
115#88111—24no—
116C4⋊#1057—24no—
117C4×#1057—24no—
118C4×#1057—24no—
119#17349—131nomaximal, Sylow
120C24×C13C22×C411yescharacteristic
121C23×D13C22×C411yescharacteristic
122C23×D13C22×C411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13C2×C814yescomplemented
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C2×C22⋊D13—22no—
140C2×C22⋊D13—22no—
141C2×C22⋊D13—22no—
142C2×C22⋊D13—22no—
143C2×C22⋊D13C2×C814yes—
144C2×C22⋊D13C2×C814yescomplemented
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C2411yescharacteristic
151#6127—216no—
152#6127—216no—
153C2×D52—22no—
154C2×D52—22no—
155C2×D52C2×C814yes—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—22no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—42no—
164C2×C4×D13—42no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C4×D13C22⋊C412yes—
168C2×C4×D13C22⋊C412yes—
169C2×C4×D13C22⋊C412yes—
170C2×C4×D13C22⋊C412yes—
171C2×C4×D13C2×C814yes—
172C2×C4×D13C2×C814yescomplemented
173C2×C4×D13M1614yes—
174C2×C4×D13C2×D412yes—
175C2×C4×D13C2×D412yes—
176C2×Dic26—22no—
177C2×Dic26—22no—
178C2×Dic26C2×C814yescomplemented
179C2×#1057—28no—
180D13⋊C8—48no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13C22⋊C411yescharacteristic
188C42×C13C22⋊C411yescharacteristic
189C42×C13C22⋊C411yescharacteristic
190C42×C13C22⋊C411yescharacteristic
191C22⋊Dic13—22no—
192C22⋊Dic13—22no—
193#6103—22no—
194#6103—22no—
195#6103—22no—
196#6103—22no—
197C4⋊Dic13—22no—
198C4⋊Dic13—22no—
199#6101—22no—
200#6101—22no—
201#6101—22no—
202#6101—22no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13C22⋊C412yes—
210C4×Dic13C22⋊C412yes—
211C4×Dic13C2×D412yes—
212C4×Dic13C2×D412yes—
213C4×Dic13C2×D412yes—
214C4×Dic13C2×D412yes—
215C2×C4×#41—131no—
216C2×#431—132no—
217#1461—132no—
218#1460—132no—
219#1459—132no—
220#1459—132no—
221#1458—132no—
222#1458—132no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13C22×C812yes—
228C23×C13C23×C411yescharacteristic
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13C2×C22⋊C412yes—
236C22×D13C22×C812yes—
237C22×D13C22×C812yes—
238C22×D13C2×M1612yes—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C2×C22⋊C411yescharacteristic
254C2×C4×C13C2×C22⋊C411yescharacteristic
255C2×C4×C13C2×C22⋊C411yescharacteristic
256C2×C4×C13C2×C22⋊C411yescharacteristic
257C2×C4×C13C2×C22⋊C411yescharacteristic
258C2×C4×C13C2×C22⋊C411yescharacteristic
259C2×C4×C13C22×C812yes—
260C2×C4×C13C22×C812yes—
261C2×C4×C13C2×M1612yes—
262C22⋊D13—28no—
263C22⋊D13—28no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13C2×C22⋊C412yes—
273C2×Dic13C2×C22⋊C412yes—
274C2×Dic13C22×C812yes—
275C2×Dic13C22×C812yes—
276C2×Dic13C2×M1612yes—
277C2×Dic13C22×D412yes—
278D52—28no—
279C4×D13—24no—
280C4×D13—24no—
281C4×D13—24no—
282C4×D13—24no—
283C4×D13—42no—
284C4×D13—42no—
285C4×D13—42no—
286C4×D13—42no—
287C4×D13—42no—
288C4×D13—42no—
289C4×D13C22⋊C818yes—
290C4×D13C22⋊C818yes—
291Dic26—28no—
292#1057—48no—
293C22×#41—131no—
294C4×#41—262no—
295C4×#41—262no—
296C4×#41—262no—
297C4×#41—262no—
298C2×C4×Q8—131no—
299C2×C4×Q8—131no—
300C2×C4×D4—131no—
301C2×C4×D4—131no—
302C2×C4×D4—131no—
303C2×C4×D4—131no—
304C2×C4×D4—131no—
305C2×C4×D4—131no—
306C2×#117—131no—
307C2×#117—131no—
308C2×#117—131no—
309C22×C42—131no—
310C22×C42—131no—
311C22×C42#26111yescharacteristic
312#431—134no—
313#431—134no—
314#431—262no—
315#431—262no—
316C2×C4⋊C8—262no—
317C2×C22⋊C8—134no—
318C2×C4×C8—262no—
319#324—134no—
320#324—134no—
321#323—134no—
322#323—134no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—22no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13C22×C22⋊C411yescharacteristic
331C22×C13C23×C811yescharacteristic
332C22×C13C22×M1611yescharacteristic
333C2×D13—22no—
334C2×D13—22no—
335C2×D13—22no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—42no—
342C2×D13C2×C22⋊C814yes—
343C4×C13—22no—
344C4×C13—21no—
345C4×C13—21no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C2×C22⋊C812yes—
349C4×C13C2×C22⋊C812yes—
350C4×C13#41012yes—
351C4×C13#41312yes—
352Dic13—22no—
353Dic13—22no—
354Dic13—22no—
355Dic13—41no—
356Dic13—41no—
357Dic13C2×C22⋊C814yes—
358C2×#41—138no—
359C2×#41—262no—
360C2×#41—262no—
361C2×#41—264no—
362C22×Q8—131no—
363C22×D4—131no—
364C22×D4—131no—
365C22×D4—131no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4C2×#26111yescharacteristic
373C23×C4C2×#26111yescharacteristic
374C23×C4C2×#26111yescharacteristic
375C22×C8—264no—
376C4×Q8—262no—
377C4×Q8—262no—
378C4×Q8—262no—
379C4×Q8—262no—
380C4×D4—262no—
381C4×D4—262no—
382C4×D4—262no—
383C4×D4—262no—
384C4×D4—262no—
385C4×D4—262no—
386C4×D4—262no—
387C4×D4—262no—
388C4×D4—262no—
389C4×D4—262no—
390C4×D4—262no—
391C4×D4—262no—
392#117—262no—
393#117—262no—
394#117—262no—
395#117—262no—
396#117—262no—
397#117—262no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C22⋊C4—131no—
405C2×C22⋊C4—131no—
406C2×C22⋊C4—131no—
407C2×C22⋊C4—131no—
408C2×C22⋊C4—131no—
409C2×C22⋊C4—131no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—132no—
418C2×C42—132no—
419C2×C42—132no—
420C2×C42—132no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42—261no—
428C2×C42C2×#26111yescharacteristic
429C2×C42C2×#26111yescharacteristic
430C2×C42C2×#26111yescharacteristic
431C2×C42C2×#26111yescharacteristic
432C4⋊C8—264no—
433C4⋊C8—264no—
434C22⋊C8—138no—
435C22⋊C8—264no—
436C4×C8—264no—
437C4×C8—264no—
438C2×C13—21no—
439C2×C13—21no—
440C2×C13—42no—
441C2×C13C22×C22⋊C811yescharacteristic
442C2×C13C2×#41011yescharacteristic
443C2×C13C2×#41311yescharacteristic
444D13—24no—
445D13—42no—
446C24—131no—
447C24—131no—
448C24C22×#26111yescharacteristic
449#41—2616no—
450#41—2616no—
451C2×Q8—134no—
452C2×Q8—262no—
453C2×Q8—262no—
454C2×D4—134no—
455C2×D4—134no—
456C2×D4—134no—
457C2×D4—262no—
458C2×D4—262no—
459C2×D4—262no—
460C2×D4—262no—
461C2×D4—262no—
462C2×D4—262no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—131no—
473C22×C4—134no—
474C22×C4—134no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—134no—
481C22×C4—132no—
482C22×C4—132no—
483C22×C4—132no—
484C22×C4—132no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—262no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—522no—
495C22×C4—522no—
496C22×C4—522no—
497C22×C4—522no—
498C22×C4D13⋊C814yescomplemented
499C22×C4C22×#26111yescharacteristic
500C22×C4C22×#26111yescharacteristic
501C22×C4C22×#26111yescharacteristic
502C22×C4C22×#26111yescharacteristic
503C22×C4C22×#26111yescharacteristic
504C22×C4C22×#26111yescharacteristic
505C2×C8—268no—
506C2×C8—528no—
507C4⋊C4—262no—
508C4⋊C4—262no—
509C4⋊C4—262no—
510C4⋊C4—262no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C22⋊C4—262no—
514C22⋊C4—262no—
515C22⋊C4—262no—
516C22⋊C4—262no—
517C22⋊C4—262no—
518C22⋊C4—262no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—132no—
526C42—132no—
527C42—132no—
528C42—132no—
529C42—132no—
530C42—132no—
531C42—261no—
532C42—261no—
533C42—261no—
534C42—261no—
535C42—261no—
536C42—261no—
537C42C22⋊#26111yescharacteristic
538C42C22⋊#26111yescharacteristic
539C42C22⋊#26111yescharacteristic
540C42C22⋊#26111yescharacteristic
541C13#1734911yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—132no—
547C23—132no—
548C23—132no—
549C23—132no—
550C23—261no—
551C23—261no—
552C23—521no—
553C23—521no—
554C23—521no—
555C23—521no—
556C23C2×D13⋊C812yes—
557C23C23×#26111yescharacteristic
558Q8—268no—
559D4—268no—
560D4—268no—
561D4—268no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—132no—
577C2×C4—132no—
578C2×C4—132no—
579C2×C4—138no—
580C2×C4—138no—
581C2×C4—132no—
582C2×C4—132no—
583C2×C4—132no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4C2×D13⋊C812yes—
603C2×C4C2×D13⋊C812yes—
604C2×C4D13⋊M1612yes—
605C2×C4C2×C22⋊#26111yescharacteristic
606C2×C4C2×C22⋊#26111yescharacteristic
607C2×C4C2×C22⋊#26111yescharacteristic
608C2×C4C2×C22⋊#26111yescharacteristic
609C2×C4C2×C22⋊#26111yescharacteristic
610C2×C4C2×C22⋊#26111yescharacteristic
611C8—528no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—42no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—134no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22—522no—
624C22—522no—
625C22—522no—
626C22—522no—
627C22—521no—
628C22—521no—
629C22C22×D13⋊C811yescharacteristic
630C22C2×D13⋊M1611yescharacteristic
631C22C22×C22⋊#26111yescharacteristic
632C4—22no—
633C4—21no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—134no—
638C4—262no—
639C4—262no—
640C4—262no—
641C4—521no—
642C4—521no—
643C4#1171911612yes—
644C4D13⋊(C22⋊C8)12yes—
645C4D13⋊(C22⋊C8)12yes—
646C4#1171913212yes—
647C2—21no—
648C2—21no—
649C2—42no—
650C2—264no—
651C2—522no—
652C2C2×D13⋊(C22⋊C8)11yescharacteristic
653C2C2×#1171911611yescharacteristic
654C2C2×#1171913211yescharacteristic
subgroupG/H
centerC42C22⋊#261
commutatorC22×C13C23×C8
FrattiniC23C23×#261
FittingC22×C42×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC22×#6127C4
cosocleC22×Dic13C24
hypercenterC22×C42#261
hypocenterC13#17349
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. D13⋊#431C2semidirect
2. #13130078C2semidirect
3. #13130075C2semidirect
4. #13130073C2semidirect
5. #13130071C2semidirect
6. #13130069C2semidirect
7. #13130067C2semidirect
47. C2×#6127C8semidirect
132. C22×C4×C13C2×C8semidirect
144. C2×C22⋊D13C2×C8semidirect
172. C2×C4×D13C2×C8semidirect
178. C2×Dic26C2×C8semidirect
498. C22×C4D13⋊C8semidirect
541. C13#17349semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131300782
#131300752
#131300732
#131300712
#131300692
#131300672
C2×C4×#61272
#1734913