Finite Group Databasebeta

← #15879591

Subgroups — #15879591

Order 3328.

1066 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
1C2×#11719244C211yesmaximal, characteristic
2C2×#11718362C211yesmaximal, characteristic, complemented
3#13117791C211yesmaximal, characteristic, complemented
4#13115807C211yesmaximal, characteristic, complemented
5#13115805C211yesmaximal, characteristic, complemented
6#13115799C211yesmaximal, characteristic, complemented
7#13115793C211yesmaximal, characteristic, complemented
8#13115790C211yesmaximal, characteristic, complemented
9#13115786C211yesmaximal, characteristic, complemented
10#13114844C211yesmaximal, characteristic
11#13114844C211yesmaximal, characteristic
12#13114836C211yesmaximal, characteristic
13#13114663C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C13×#1762C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×#88178—21no—
20C22×#6101—21no—
21#11719244—24no—
22#11719244C418yescomplemented
23C2×#88144C2211yescharacteristic
24C2×#88142C2211yescharacteristic
25C2×#88132—21no—
26C2×#88132—21no—
27C2×#88124C2211yescharacteristic
28C2×C4×Dic26C2211yescharacteristic
29C2×C13×#102C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×#97C2211yescharacteristic
32C4×C13×C4⋊C4C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718638C2211yescharacteristic
40#11718638C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43#11718596C2211yescharacteristic
44C4×C4⋊Dic13—21no—
45#11718590—21no—
46C2×C4⋊#1055C2211yescharacteristic
47#11718362—24no—
48#11718316—21no—
49#11718316—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C22×Dic26—21no—
67C22×Dic26D411yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C4×D4×C13—22no—
71C4×D4×C13C2×C414yes—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80D4×Dic13—22no—
81D4×Dic13—22no—
82D4×Dic13C2×C414yes—
83D4×Dic13C2×C414yes—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13D411yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92#88178—28no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—28no—
98C2×#6101D411yescharacteristic
99C2×#6101D411yescharacteristic
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88144—22no—
107#88144C2×C414yes—
108#88142—22no—
109#88142C2×C414yes—
110#88132—28no—
111#88132—28no—
112#88124—22no—
113#88124C2×C414yes—
114C4×Dic26C2×C414yes—
115C4×Dic26D414yes—
116C13×#102—22no—
117C13×#102Q814yescomplemented
118C13×#97—22no—
119C13×#95—21no—
120#88072—22no—
121#88072—22no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88055—22no—
129#88054—22no—
130#88054—22no—
131C8×Dic13—22no—
132C4⋊#1055—22no—
133#22526—131nomaximal, Sylow
134C24×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C22×C412yes—
139C2×D4×C13C2×Q812yes—
140C2×D4×C13#4112yes—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—24no—
144C22×C4×C13—21no—
145C22×C4×C13—81no—
146C22×C4×C13—81no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—42no—
157C22×Dic13—42no—
158C22×Dic13—81no—
159C22×Dic13—81no—
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C2×Dic26—24no—
165C2×Dic26—41no—
166C2×Dic26—41no—
167C2×Dic26—81no—
168C2×Dic26—81no—
169C2×Dic26C22⋊C414yes—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13C2×Q812yes—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C412yes—
181C13×C4⋊C4C2×Q812yes—
182C13×C22⋊C4—24no—
183C42×C13—42no—
184C42×C13C22×C412yes—
185C42×C13C2×D412yes—
186C22⋊Dic13—24no—
187C22⋊Dic13—24no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—24no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—42no—
196C4⋊Dic13—81no—
197C4⋊Dic13C22⋊C414yes—
198C4⋊Dic13C22×C412yes—
199C4⋊Dic13C22×C412yes—
200#6101—24no—
201#6101—24no—
202#6101—24no—
203#6101—24no—
204#6101C22⋊C414yes—
205#6101C22⋊C414yes—
206C4×Dic13—81no—
207C4×Dic13—81no—
208C4×Dic13C22×C412yes—
209C4×Dic13C22×C412yes—
210C4×Dic13C2×D412yes—
211C4×Dic13C2×D412yes—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#554—131no—
219C2×#446—131no—
220#2355—131no—
221#1993—131no—
222#1992—131no—
223#1991—131no—
224#1989—131no—
225#1989—131no—
226#1988—131no—
227#1804—131no—
228#1804—131no—
229#1802—131no—
230#1762—131no—
231#1762D1311yescharacteristic
232C4×#102—131no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13C22×D411yescharacteristic
241D4×C13—22no—
242D4×C13—22no—
243D4×C13—22no—
244D4×C13C4×Q814yes—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—84no—
259C2×C4×C13C2×C22⋊C412yes—
260C2×C4×C13C2×C22⋊C412yes—
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C22×Q811yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—48no—
278C2×Dic13—41no—
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—84no—
289C2×Dic13C2×C22⋊C412yes—
290C2×Dic13C2×C22⋊C412yes—
291C2×Dic13C2×C22⋊C412yes—
292C2×Dic13C2×C22⋊C412yes—
293Dic26—44no—
294Dic26—84no—
295C8×C13—22no—
296C8×C13—41no—
297#1055—41no—
298#1055—41no—
299#554—138no—
300#554—264no—
301C2×C4⋊Q8—131no—
302C2×#125—131no—
303C2×#125—131no—
304C2×C22⋊Q8—261no—
305C2×C22⋊Q8—261no—
306C2×C22⋊Q8—261no—
307C2×C4×Q8—131no—
308C2×C4×D4—131no—
309C2×C4×D4—131no—
310C2×C4×D4C2×D1311yescharacteristic
311C22×C4⋊C4—261no—
312#446—264no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×#102C2×D1311yescharacteristic
319C2×#102C2×D1311yescharacteristic
320C2×#97—131no—
321C2×#97C2×D1311yescharacteristic
322C2×C4×C8—131no—
323#391—261no—
324#387—261no—
325#387—261no—
326#384—131no—
327#382—131no—
328#382—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331C4×C4⋊C4—261no—
332C4×C4⋊C4C2×D1311yescharacteristic
333#340—131no—
334#340—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#340C2×D1311yescharacteristic
344#340C2×D1311yescharacteristic
345C22×C13—24no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13C22×C22⋊C411yescharacteristic
353C22×C13#54811yescharacteristic
354C22×C13D4×Q811yescharacteristic
355C22×C13#57511yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57611yescharacteristic
358C22×C13#57711yescharacteristic
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—42no—
362C4×C13—42no—
363C4×C13—81no—
364C4×C13C2×C4×Q811yescharacteristic
365C4×C13#51911yescharacteristic
366C4×C13#54811yescharacteristic
367C4×C13D4×Q811yescharacteristic
368Dic13—22no—
369Dic13—22no—
370Dic13—22no—
371Dic13—22no—
372Dic13—42no—
373Dic13—42no—
374Dic13—81no—
375Dic13—81no—
376C22×Q8—131no—
377C22×Q8—261no—
378C22×D4C22×D1311yescharacteristic
379C23×C4—21no—
380C23×C4—261no—
381C23×C4—261no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8C22×D1311yescharacteristic
385C22×C8C22×D1311yescharacteristic
386C4⋊Q8—134no—
387C4⋊Q8—262no—
388#125—134no—
389#125—134no—
390#125—262no—
391#125—262no—
392C22⋊Q8—268no—
393C22⋊Q8—268no—
394C22⋊Q8—268no—
395C4×Q8—134no—
396C4×Q8—134no—
397C4×D4—22no—
398C4×D4—134no—
399C4×D4—134no—
400C4×D4—262no—
401C4×D4—262no—
402C4×D4C4×D1314yes—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—268no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4C22×D1311yescharacteristic
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C42—21no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—261no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C4⋊C8—262no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433#102—22no—
434#102—262no—
435#102—262no—
436#102Dic2614yescomplemented
437#97—22no—
438#97—262no—
439C4×C8—262no—
440#95—21no—
441#95—261no—
442#95—261no—
443#95—261no—
444#95—261no—
445#95—261no—
446#95—261no—
447C2×C13—44no—
448C2×C13Q8×C22⋊C411yescharacteristic
449C2×C13#289611yescharacteristic
450C2×C13#289711yescharacteristic
451C2×C13#337011yescharacteristic
452C2×C13#337611yescharacteristic
453C2×C13#338811yescharacteristic
454C2×C13#338911yescharacteristic
455C24—21no—
456C2×Q8—134no—
457C2×Q8—264no—
458C2×Q8—521no—
459C2×Q8—521no—
460C2×Q8—1041no—
461C2×Q8—1041no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C2×Dic2612yes—
466C2×D4C2×C4×D1312yes—
467C2×D4#612712yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—131no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—264no—
479C22×C4—264no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—522no—
485C22×C4—522no—
486C22×C4—1041no—
487C22×C4—1041no—
488C22×C4D4×D1311yescharacteristic
489C22×C4D4×D1311yescharacteristic
490C22×C4C23×D1311yescharacteristic
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8C2×Dic2612yes—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—134no—
508C4⋊C4—134no—
509C4⋊C4—134no—
510C4⋊C4—132no—
511C4⋊C4—132no—
512C4⋊C4—264no—
513C4⋊C4—264no—
514C4⋊C4—264no—
515C4⋊C4—264no—
516C4⋊C4—264no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—522no—
524C4⋊C4—1041no—
525C4⋊C4C2×Dic2612yes—
526C4⋊C4C2×C4×D1312yes—
527C22⋊C4—24no—
528C22⋊C4—264no—
529C22⋊C4—264no—
530C42—42no—
531C42—132no—
532C42—132no—
533C42—132no—
534C42—132no—
535C42—1041no—
536C42—1041no—
537C42C2×C4×D1312yes—
538C42D4×D1312yes—
539C13#2252611yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C2×D4×D1311yescharacteristic
548Q8—524no—
549Q8—1044no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4C4×Dic2614yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—132no—
569C2×C4—132no—
570C2×C4—132no—
571C2×C4—132no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—528no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—1044no—
594C2×C4C22⋊C4×D1312yes—
595C2×C4C22⋊C4×D1312yes—
596C2×C4C22×Dic2611yescharacteristic
597C2×C4C22×C4×D1311yescharacteristic
598C2×C4C2×#612711yescharacteristic
599C2×C4C2×D4×D1311yescharacteristic
600C2×C4#8825711yescharacteristic
601C2×C4#8825711yescharacteristic
602C8—22no—
603C8—41no—
604C8—521no—
605C8—521no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C2×C22⋊C4×D1311yescharacteristic
614C22D4×Dic2611yescharacteristic
615C22#1171925711yescharacteristic
616C22#1171947811yescharacteristic
617C22#1171947911yescharacteristic
618C22#1171948011yescharacteristic
619C22#1171948211yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—262no—
626C4—262no—
627C4—262no—
628C4—262no—
629C4—522no—
630C4—522no—
631C4—1041no—
632C4—1041no—
633C4C2×C4×Dic2611yescharacteristic
634C4#1171922111yescharacteristic
635C4D4×Dic2611yescharacteristic
636C4#1171925711yescharacteristic
637C2—44no—
638C2C22⋊C4×Dic2611yescharacteristic
639C2#1312335211yescharacteristic
640C2#1312336111yescharacteristic
641C2#1312759011yescharacteristic
642C2#1312766411yescharacteristic
643C2#1312778211yescharacteristic
644C2#1312779511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1762C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1762D13
hypocenterC13#22526
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#11718362C2semidirect
3. #13117791C2semidirect
4. #13115807C2semidirect
5. #13115805C2semidirect
6. #13115799C2semidirect
7. #13115793C2semidirect
8. #13115790C2semidirect
9. #13115786C2semidirect
22. #11719244C4semidirect
117. C13×#102Q8semidirect
436. #102Dic26semidirect
539. C13#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#117192442
C2×#117183622
#131177912
#131158072
#131158052
#131157992
#131157932
#131157902
#131157862
#131148442
#131148362
#131146632
#102×Dic132
C13×#17622
#2252613