Finite Group Databasebeta

← #15923016

Subgroups — #15923016

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718680C211yesmaximal, characteristic
2C2×C4×#6105C211yesmaximal, characteristic
3#13118612C211yesmaximal, characteristic, complemented
4#13116380C211yesmaximal, characteristic, complemented
5#13116337C211yesmaximal, characteristic, complemented
6#13116245C211yesmaximal, characteristic, complemented
7#13116082C211yesmaximal, characteristic, complemented
8#13115511C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115170C211yesmaximal, characteristic
13#13115103C211yesmaximal, characteristic, complemented
14#13115097C211yesmaximal, characteristic
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4—21no—
20C22×#6105C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C2×#88123C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#385—21no—
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33#11718680—24no—
34C4×#6105—24no—
35#11718645—21no—
36#11718642—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718321—21no—
52#11718316—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C22×Dic26C2311yescharacteristic
66C22×Dic26C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—41no—
72C4×D4×C13—41no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—44no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×#6105—22no—
90C2×#6105—22no—
91C2×#6105—22no—
92C2×#6105—22no—
93C2×#6105—22no—
94C2×#6105D414yes—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×#6101—21no—
101C2×C4×Dic13—21no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88123—22no—
107#88123—41no—
108C4×Dic26—22no—
109C4×Dic26—41no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88072—22no—
115#88072—22no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88050—22no—
128#88050—41no—
129#88048—22no—
130#88048—41no—
131C4⋊#1055—22no—
132C4×#1055—22no—
133#26166—131nomaximal, Sylow
134C24×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13C2×D412yes—
139C2×D4×C13#4112yes—
140C2×D4×C13#4112yes—
141C22×C4×C13—24no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—81no—
152C22×C4×C13—81no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26C2×D412yes—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4—81no—
186C13×C4⋊C4SD1614yescomplemented
187C13×C4⋊C4#4112yes—
188C13×C22⋊C4—24no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—42no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—21no—
197#6105—28no—
198#6105—44no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—42no—
204C4⋊Dic13—42no—
205#6101—42no—
206#6101—42no—
207C4×Dic13—42no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055C2×D412yes—
220C2×#461—131no—
221C2×C4×SD16—131no—
222#2446—131no—
223D4×C4⋊C4D1311yescharacteristic
224#2096—131no—
225#2088—131no—
226#2072—131no—
227#2043—131no—
228#1933—131no—
229#1916—131no—
230#1877—131no—
231#1877—131no—
232#1877—131no—
233#1865—131no—
234#1864—131no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C22×D411yescharacteristic
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—22no—
246D4×C13#12314yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—48no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—84no—
273C2×C4×C13—84no—
274C2×C4×C13C2×SD1612yes—
275C2×C4×C13C2×SD1612yes—
276C2×C4×C13C2×SD1612yes—
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C2×C4×C132−1+411yescharacteristic
283C2×Dic13—22no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295Dic26—22no—
296Dic26—22no—
297Dic26—41no—
298Dic26—41no—
299Dic26—41no—
300Dic26—41no—
301Dic26—41no—
302Dic26—41no—
303#1055—22no—
304#1055—41no—
305#1055—41no—
306#1055—41no—
307C22×SD16—131no—
308C22×SD16—131no—
309C2×C4⋊Q8—131no—
310C2×C4×Q8—131no—
311C2×C4×D4C2×D1311yescharacteristic
312C2×C4×D4C2×D1311yescharacteristic
313C2×C4×D4C2×D1311yescharacteristic
314C22×C4⋊C4—21no—
315#461—264no—
316C4×SD16—264no—
317C2×#106—131no—
318C2×#106—131no—
319C2×C4⋊C8—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#103—131no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#102—131no—
327C2×#102—131no—
328C2×C4×C8—131no—
329#400—261no—
330#398—261no—
331#391—131no—
332#391—131no—
333#391—131no—
334#389—131no—
335#389C2×D1311yescharacteristic
336#389C2×D1311yescharacteristic
337#387—261no—
338#387—261no—
339#385—21no—
340#385—21no—
341#384C2×D1311yescharacteristic
342#380—21no—
343C4×C4⋊C4C2×D1311yescharacteristic
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352C22×C13—24no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13#52511yescharacteristic
360C22×C13D4211yescharacteristic
361C22×C13#54811yescharacteristic
362C22×C13C22×SD1611yescharacteristic
363C22×C13#57511yescharacteristic
364C22×C13#57711yescharacteristic
365C22×C13#57811yescharacteristic
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—22no—
369C4×C13—42no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13C2×#12311yescharacteristic
376C4×C13#53911yescharacteristic
377C4×C13#54711yescharacteristic
378C4×C13#55311yescharacteristic
379Dic13—42no—
380Dic13—81no—
381Dic13—81no—
382Dic13—81no—
383C22×Q8—131no—
384C22×Q8—131no—
385C22×D4C22×D1311yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—21no—
389C2×SD16—134no—
390C2×SD16—262no—
391C2×SD16—262no—
392C2×SD16—262no—
393C2×SD16—262no—
394C2×SD16—262no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C4⋊Q8—262no—
400C4⋊Q8—521no—
401C4×Q8—262no—
402C4×Q8—521no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—41no—
408C4×D4—41no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4C22⋊D1311yescharacteristic
421C2×C4⋊C4C22⋊D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C2×C42C22×D1311yescharacteristic
431C2×C42C22×D1311yescharacteristic
432#106—262no—
433#106—521no—
434C4⋊C8—262no—
435#103—262no—
436#103—262no—
437#103—262no—
438#103—262no—
439#103—262no—
440#103—521no—
441#102—262no—
442#102—262no—
443C4×C8—262no—
444#95—21no—
445#95—21no—
446#95—261no—
447#95—261no—
448#95—261no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95C22⋊D1311yescharacteristic
454#95C22⋊D1311yescharacteristic
455C2×C13—44no—
456C2×C13#244311yescharacteristic
457C2×C13#310111yescharacteristic
458C2×C13#312011yescharacteristic
459C2×C13#326911yescharacteristic
460C2×C13D4×SD1611yescharacteristic
461C2×C13#335911yescharacteristic
462C2×C13#337611yescharacteristic
463C24—21no—
464C2×Q8—132no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×Q8—261no—
472C2×Q8—261no—
473C2×Q8—261no—
474C2×Q8—261no—
475C2×Q8—261no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4#612712yes—
480C2×D4D4×D1312yes—
481C2×D4#613112yes—
482C22×C4—24no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C23×D1311yescharacteristic
505SD16—268no—
506SD16—524no—
507C2×C8—132no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—41no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—81no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—522no—
534C4⋊C4—522no—
535C4⋊C4—522no—
536C4⋊C4—522no—
537C4⋊C4#610514yescomplemented
538C4⋊C4#612712yes—
539C22⋊C4—24no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—522no—
549C13#2616611yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C22×C22⋊D1311yescharacteristic
558Q8—262no—
559Q8—262no—
560Q8—521no—
561Q8—521no—
562Q8—521no—
563Q8—521no—
564Q8—521no—
565Q8—521no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4#8814814yes—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—48no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4—262no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4C2×#610512yes—
610C2×C4C2×#610512yes—
611C2×C4C2×#610512yes—
612C2×C4C2×#612711yescharacteristic
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×D4×D1311yescharacteristic
615C2×C4#8825111yescharacteristic
616C2×C4C2×#613111yescharacteristic
617C2×C4#8825411yescharacteristic
618C8—262no—
619C8—521no—
620C8—521no—
621C8—521no—
622C22—24no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22#1171949611yescharacteristic
630C22C22×#610511yescharacteristic
631C22D4×C22⋊D1311yescharacteristic
632C22#1171952211yescharacteristic
633C22#1171952711yescharacteristic
634C22#1171954111yescharacteristic
635C22#1171954311yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—522no—
646C4—1041no—
647C4—1041no—
648C4—1041no—
649C4C2×#8814811yescharacteristic
650C4#1171921211yescharacteristic
651C4#1171921911yescharacteristic
652C4#1171922011yescharacteristic
653C2—44no—
654C2#1311857111yescharacteristic
655C2#1312484411yescharacteristic
656C2#1312505011yescharacteristic
657C2#1312638711yescharacteristic
658C2D4×#610511yescharacteristic
659C2#1312747811yescharacteristic
660C2#1312766311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterD4×C4⋊C4D13
hypocenterC13#26166
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13118612C2semidirect
4. #13116380C2semidirect
5. #13116337C2semidirect
6. #13116245C2semidirect
7. #13116082C2semidirect
8. #13115511C2semidirect
9. #13115395C2semidirect
13. #13115103C2semidirect
186. C13×C4⋊C4SD16semidirect
537. C4⋊C4#6105semidirect
549. C13#26166semidirect

Maximal subgroups

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

subgroupindex
C2×#117186802
C2×C4×#61052
#131186122
#131163802
#131163372
#131162452
#131160822
#131155112
#131153952
#131151702
#131151032
#131150972
D4×C13×C4⋊C42
#2616613