Finite Group Databasebeta

← #15867522

Subgroups — #15867522

Order 3328.

1134 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719434C211yesmaximal, characteristic
2C2×#11718350C211yesmaximal, characteristic
3#13117457C211yesmaximal, characteristic
4#13115810C211yesmaximal, characteristic, complemented
5#13115807C211yesmaximal, characteristic, complemented
6#13115804C211yesmaximal, characteristic, complemented
7#13115803C211yesmaximal, characteristic, complemented
8#13115801C211yesmaximal, characteristic, complemented
9#13115799C211yesmaximal, characteristic, complemented
10#13115795C211yesmaximal, characteristic, complemented
11#13114554C211yesmaximal, characteristic
12#13114554C211yesmaximal, characteristic
13#13114551C211yesmaximal, characteristic
14D13×#340C211yesmaximal, characteristic
15C13×#1990C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×#88200—21no—
18C2×#88198—21no—
19C22×#6094C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21#11719434—24no—
22#11719434C418yescomplemented
23C2×#88150—21no—
24C2×#88146C2211yescharacteristic
25C2×#88146C2211yescharacteristic
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×#88144C2211yescharacteristic
29C2×#88143—21no—
30C2×#88142C2211yescharacteristic
31C2×#88126C2211yescharacteristic
32C2×#88124C2211yescharacteristic
33C2×C4×C8×C13C2211yescharacteristic
34C13×#384C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37#11718650—21no—
38#11718650—21no—
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41#11718633—21no—
42#11718633—21no—
43#11718597C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718350—24no—
46C13×#340C2211yescharacteristic
47C13×#340C2211yescharacteristic
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13—21no—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13C2311yescharacteristic
66C22×Dic26—21no—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8C2×C414yescomplemented
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79#88200—28no—
80#88198—28no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103D411yescharacteristic
84C2×#6103D411yescharacteristic
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101D411yescharacteristic
99C2×#6101D411yescharacteristic
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C2×#6094—22no—
106C2×#6094—22no—
107C2×#6094Q814yescomplemented
108C2×C8×D13—22no—
109C2×C8×D13—22no—
110C2×C8×D13Q814yescomplemented
111#88150—28no—
112#88146—22no—
113#88146—22no—
114#88146—22no—
115#88146C2×C414yes—
116C4⋊C4×D13—22no—
117C4⋊C4×D13—22no—
118C4⋊C4×D13—22no—
119C4⋊C4×D13C2×C414yes—
120#88144—22no—
121#88144C2×C414yescomplemented
122#88143—28no—
123#88142—22no—
124#88142C2×C414yescomplemented
125#88126C2×C414yes—
126#88126D414yes—
127#88124—22no—
128#88124C2×C414yescomplemented
129C4×C8×C13—22no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134#88055—22no—
135C8×Dic13—22no—
136#88043—22no—
137#21326—131nomaximal, Sylow
138C23×D13C2×D411yescharacteristic
139C2×Q8×C13—24no—
140C2×Q8×C13—81no—
141C2×Q8×C13—81no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C2×C4×D13—24no—
157C2×C4×D13—42no—
158C2×C4×D13—81no—
159C2×C4×D13—81no—
160C2×C4×D13—81no—
161C2×C4×D13—81no—
162C2×C4×D13C22×C412yes—
163C2×C4×D13C2×D412yes—
164C2×C4×D13C2×Q812yes—
165C2×C4×D13C2×Q812yes—
166C2×C4×D13#4112yes—
167C2×C4×D13#4112yes—
168C2×Dic26—24no—
169C2×Dic26—81no—
170C2×Dic26—81no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13C2×Q812yes—
176C2×C8×C13C2×Q812yes—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—81no—
185C13×C4⋊C4—81no—
186C13×C4⋊C4C22×C412yes—
187C13×C4⋊C4C22×C412yes—
188C42×C13C22×C412yes—
189C42×C13C2×D412yes—
190#6103—24no—
191#6103—42no—
192#6103C22⋊C414yes—
193#6103C22⋊C414yes—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—24no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C22×C412yes—
202C4⋊Dic13C22×C412yes—
203#6101—24no—
204#6101—24no—
205#6101—24no—
206#6101—24no—
207#6101—24no—
208#6101—42no—
209#6101—81no—
210#6101—81no—
211#6101C22⋊C414yes—
212#6101C22⋊C414yes—
213C4×Dic13—24no—
214C4×Dic13—42no—
215C4×Dic13C22×C412yes—
216C4×Dic13C2×D412yes—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055C2×Q812yes—
222C2×#1055C2×Q812yes—
223#6094—28no—
224C8×D13—28no—
225C2×#544—131no—
226C2×#405—131no—
227#2317—131no—
228#1993—131no—
229#1993—131no—
230#1992—131no—
231#1992—131no—
232#1991—131no—
233#1991—131no—
234#1990—131no—
235#1990D1311yescharacteristic, complemented
236#1736—131no—
237#1736—131no—
238#1735—131no—
239C2×#340—131no—
240C23×C13C22×D411yescharacteristic
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13C2×C22⋊C412yes—
246C22×D13#12412yes—
247C22×D13C4⋊Q812yes—
248Q8×C13—84no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13C2×C22⋊C412yes—
266C2×C4×C13C2×C22⋊C412yes—
267C2×C4×C13C23×C411yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13C2×C22⋊C412yes—
290C2×Dic13C2×C22⋊C412yes—
291C2×Dic13C2×C22⋊C412yes—
292C2×Dic13#12412yes—
293C2×Dic13C4⋊Q812yes—
294C4×D13—84no—
295C4×D13—84no—
296C4×D13C4×Q814yes—
297C4×D13C4×Q814yes—
298C4×D13C22⋊Q814yes—
299C4×D13C22⋊Q814yes—
300Dic26—84no—
301C8×C13—22no—
302C8×C13—22no—
303#1055—22no—
304#1055—22no—
305C22×M16—131no—
306C23×C8—131no—
307#544—138no—
308#544—264no—
309C2×C4⋊Q8—131no—
310C2×C4⋊Q8—261no—
311C2×C4⋊Q8C2×D1311yescharacteristic
312C2×#125—131no—
313C2×#125—131no—
314C2×#125—261no—
315C2×C22⋊Q8—261no—
316C2×C22⋊Q8—261no—
317C2×#117—131no—
318C2×#117—131no—
319C2×#117—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322#405—264no—
323C2×#97—131no—
324C2×#97—131no—
325C2×C4×C8—131no—
326C2×C4×C8C2×D1311yescharacteristic
327#389—261no—
328#389—261no—
329#385—261no—
330#385—261no—
331#384—131no—
332#384C2×D1311yescharacteristic
333#382—131no—
334#382—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340C2×D1311yescharacteristic
348#340C2×D1311yescharacteristic
349#340C2×D1311yescharacteristic
350#340C2×D1311yescharacteristic
351C22×C13C22×C22⋊C411yescharacteristic
352C22×C13C2×#12411yescharacteristic
353C22×C13C2×C4⋊Q811yescharacteristic
354C22×C13#57611yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57711yescharacteristic
357C22×C13#57811yescharacteristic
358C2×D13—22no—
359C2×D13—22no—
360C2×D13—22no—
361C2×D13—22no—
362C2×D13—22no—
363C2×D13—22no—
364C2×D13#39114yes—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—42no—
368C4×C13—42no—
369C4×C13—81no—
370C4×C13—81no—
371C4×C13C2×C4×Q811yescharacteristic
372C4×C13C2×C4×Q811yescharacteristic
373C4×C13C2×C22⋊Q811yescharacteristic
374C4×C13C2×C22⋊Q811yescharacteristic
375Dic13—22no—
376Dic13—22no—
377Dic13—42no—
378Dic13—42no—
379Dic13—81no—
380Dic13—81no—
381Dic13#39114yes—
382C22×Q8—21no—
383C22×Q8—261no—
384C23×C4—131no—
385C23×C4—261no—
386C23×C4—261no—
387C2×M16—134no—
388C2×M16—262no—
389C2×M16—262no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—134no—
393C22×C8—262no—
394C22×C8—262no—
395C22×C8C22×D1311yescharacteristic
396C22×C8C22×D1311yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—134no—
399C4⋊Q8—262no—
400C4⋊Q8—268no—
401C4⋊Q8C4×D1314yescomplemented
402#125—134no—
403#125—134no—
404#125—262no—
405#125—268no—
406#125—262no—
407C22⋊Q8—268no—
408C22⋊Q8—268no—
409#117—134no—
410#117—134no—
411#117—134no—
412#117—262no—
413#117—262no—
414#117—262no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—134no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—131no—
425C2×C4⋊C4—262no—
426C2×C4⋊C4—262no—
427C2×C4⋊C4—262no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1311yescharacteristic
439C2×C4⋊C4C22×D1311yescharacteristic
440C2×C4⋊C4C22×D1311yescharacteristic
441C2×C22⋊C4—131no—
442C2×C22⋊C4—131no—
443C2×C22⋊C4—261no—
444C2×C22⋊C4—261no—
445C2×C42—131no—
446C2×C42—261no—
447C2×C42—261no—
448C2×C42C22×D1311yescharacteristic
449#97—262no—
450#97—262no—
451C4×C8—22no—
452C4×C8—262no—
453#95—261no—
454#95—261no—
455#95—261no—
456#95—261no—
457C2×C13C2×#39111yescharacteristic
458C2×C13#289711yescharacteristic
459C2×C13#289811yescharacteristic
460C2×C13#313611yescharacteristic
461C2×C13#313711yescharacteristic
462C2×C13#316311yescharacteristic
463C2×C13#316411yescharacteristic
464D13—24no—
465C24—131no—
466C2×Q8—24no—
467C2×Q8—81no—
468C2×Q8—81no—
469C2×Q8—264no—
470C2×Q8—1041no—
471C2×Q8—1041no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—131no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—132no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—264no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—522no—
491C22×C4—1041no—
492C22×C4—1041no—
493C22×C4—1041no—
494C22×C4—1041no—
495C22×C4D4×D1311yescharacteristic
496C22×C4D4×D1311yescharacteristic
497C22×C4C23×D1311yescharacteristic
498M16—268no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—268no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8Q8×D1312yes—
511C2×C8Q8×D1312yes—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—81no—
520C4⋊C4—81no—
521C4⋊C4—134no—
522C4⋊C4—134no—
523C4⋊C4—132no—
524C4⋊C4—132no—
525C4⋊C4—264no—
526C4⋊C4—264no—
527C4⋊C4—264no—
528C4⋊C4—264no—
529C4⋊C4—264no—
530C4⋊C4—264no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—522no—
538C4⋊C4—1041no—
539C4⋊C4—1041no—
540C4⋊C4C2×C4×D1312yes—
541C4⋊C4C2×C4×D1312yes—
542C22⋊C4—134no—
543C22⋊C4—134no—
544C22⋊C4—264no—
545C22⋊C4—522no—
546C42—132no—
547C42—132no—
548C42—264no—
549C42—522no—
550C42C2×C4×D1312yes—
551C42D4×D1312yes—
552C13#2132611yescharacteristic, complemented, Sylow
553C23—132no—
554C23—132no—
555C23—132no—
556C23—261no—
557C23—261no—
558C23—261no—
559C23—261no—
560C23C2×D4×D1311yescharacteristic
561Q8—84no—
562Q8—1044no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—132no—
582C2×C4—134no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—134no—
586C2×C4—132no—
587C2×C4—132no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—1044no—
605C2×C4—1044no—
606C2×C4C22⋊C4×D1312yes—
607C2×C4C22⋊C4×D1312yes—
608C2×C4C22×C4×D1311yescharacteristic
609C2×C4C2×D4×D1311yescharacteristic
610C2×C4C2×Q8×D1311yescharacteristic
611C2×C4C2×Q8×D1311yescharacteristic
612C2×C4#41×D1311yescharacteristic
613C2×C4#41×D1311yescharacteristic
614C8—22no—
615C8—22no—
616C8—262no—
617C8—262no—
618C22—134no—
619C22—262no—
620C22—262no—
621C22—262no—
622C22—262no—
623C22—262no—
624C22—262no—
625C22C2×C22⋊C4×D1311yescharacteristic
626C22D13×#12411yescharacteristic
627C22D13×C4⋊Q811yescharacteristic
628C22#1171946211yescharacteristic
629C22#1171946711yescharacteristic
630C22#1171946711yescharacteristic
631C22#1171947111yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—81no—
637C4—81no—
638C4—134no—
639C4—262no—
640C4—262no—
641C4—522no—
642C4—522no—
643C4—1041no—
644C4—1041no—
645C4C4×Q8×D1311yescharacteristic
646C4C4×Q8×D1311yescharacteristic
647C4D13×C22⋊Q811yescharacteristic
648C4D13×C22⋊Q811yescharacteristic
649C2—264no—
650C2D13×#39111yescharacteristic
651C2#1312335711yescharacteristic
652C2#1312336411yescharacteristic
653C2#1312518511yescharacteristic
654C2#1312519611yescharacteristic
655C2#1312536111yescharacteristic
656C2#1312536911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1990C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1990D13
hypocenterC13#21326
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13115810C2semidirect
5. #13115807C2semidirect
6. #13115804C2semidirect
7. #13115803C2semidirect
8. #13115801C2semidirect
9. #13115799C2semidirect
10. #13115795C2semidirect
15. C13×#1990C2semidirect
22. #11719434C4semidirect
70. C13×C4⋊Q8C2×C4semidirect
107. C2×#6094Q8semidirect
110. C2×C8×D13Q8semidirect
121. #88144C2×C4semidirect
124. #88142C2×C4semidirect
128. #88124C2×C4semidirect
235. #1990D13semidirect
401. C4⋊Q8C4×D13semidirect
552. C13#21326semidirect

Maximal subgroups

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

subgroupindex
C2×#117194342
C2×#117183502
#131174572
#131158102
#131158072
#131158042
#131158032
#131158012
#131157992
#131157952
#131145542
#131145512
D13×#3402
C13×#19902
#2132613