Finite Group Databasebeta

← #11869655

Subgroups — #11869655

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5606C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591422C212yesmaximal, complemented
6#10591420C212yesmaximal, complemented
7D3×#830C211yesmaximal, characteristic, complemented
8#10591132C211yesmaximal, characteristic, complemented
9#10591126C211yesmaximal, characteristic, complemented
10#10590572C212yesmaximal, complemented
11#10590447C212yesmaximal, complemented
12#82913—31nomaximal
13#81324—31nomaximal
14C2×C3×#237C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C32×#121C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#938C2211yescharacteristic
19C3×#937—21no—
20C3×D4×Dic3—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C3×#897C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#883—21no—
26C3×#67⋊C4—21no—
27C2×(C2×D3)⋊Dic3—21no—
28C2×Dic32—21no—
29#63841—21no—
30#63841—21no—
31#63841C2212yes—
32#63841C2212yes—
33C2×D3×C3⋊C8C2212yes—
34#63659C2212yescomplemented
35#63657C2211yescharacteristic
36#63634C2212yescomplemented
37C3×#832C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#808C2212yescomplemented
40#63576C2212yescomplemented
41#63573C2212yescomplemented
42#63566C2212yescomplemented
43#63565C2212yescomplemented
44(C2×D3)⋊(C3⋊C8)C2212yes—
45C3×#525—31no—
46C2×#926—31no—
47#5606D311yescharacteristic
48C2×#892—31no—
49C3×#481—31no—
50#5233—32no—
51C2×#830—31no—
52#5045—32no—
53#5044—31no—
54#5043—31no—
55#5035—32no—
56#5034D311yescharacteristic, complemented
57#5033—31no—
58#5033—31no—
59#5033—61no—
60#4998—32no—
61#4970—31no—
62#4868—32no—
63#4860—32no—
64#4779—32no—
65#4772—32no—
66D3×C22⋊C8—31no—
67#4721—31no—
68C23×C3×D3D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3—21no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C3×#237—24no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×C4×D3C2311yescharacteristic
84C2×C3×Dic6C2311yescharacteristic
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)C2312yes—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×#217—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4⋊Dic3C2312yes—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C2×C3×C3⋊C8C2312yes—
101(C2×D3)⋊Dic3—22no—
102(C2×D3)⋊Dic3—22no—
103Dic32—22no—
104Dic32—22no—
105D3×C3⋊C8—24no—
106#3091—91noSylow
107C2×C3×#41—31no—
108C23×C3×C4—31no—
109C2×#237C2×D311yescharacteristic
110C22×C4×D3C2×D311yescharacteristic
111C3×#123—61no—
112C3×C22⋊Q8—31no—
113C3×C22⋊Q8—31no—
114C3×#121—21no—
115C3×#121—31no—
116C3×#121C2×D311yescharacteristic
117C3×#121C2×D311yescharacteristic
118C3×#120—61no—
119C3×C4×D4—61no—
120C3×C4×D4—61no—
121C3×#117—31no—
122C2×C3×C4⋊C4—31no—
123C2×#217—61no—
124#938C2×D311yescharacteristic
125#937—21no—
126D4×Dic3—21no—
127C2×(C2×D3)⋊C4—61no—
128#926—32no—
129#926—32no—
130#926—61no—
131#926—61no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136#924C2×D311yescharacteristic
137C2×C4×Dic3—61no—
138C2×C4×Dic3—61no—
139C22×C3⋊C8—32no—
140C2×D3×C8—32no—
141#897C2×D311yescharacteristic
142#892—32no—
143#892—32no—
144#892—61no—
145#892—61no—
146#892C2×D311yescharacteristic
147#883—21no—
148#67⋊C4—21no—
149C3×#106—32no—
150C3×#102—32no—
151C3×C22⋊C8—31no—
152#835—32no—
153#835—32no—
154#832—32no—
155#832—32no—
156#832—62no—
157#832C2×D312yescomplemented
158#830—31no—
159#830—31no—
160#830—32no—
161#830—61no—
162#830C2×D311yescharacteristic
163(C2×D3)⋊C8—32no—
164#817—32no—
165#816—32no—
166#810—32no—
167#808—32no—
168#808C2×D312yescomplemented
169#807—32no—
170#807—32no—
171#807—32no—
172#807—32no—
173#807—62no—
174C23×C32—21no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—41no—
179C22×C3×D3C2×D411yescharacteristic
180C22×C3×D3C2×D411yescharacteristic
181C32×D4—22no—
182C32×D4—42no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189C3×#67—42no—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×C4×D3—22no—
202C3×C4×D3#4114yes—
203C3×Dic6—22no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#525—31no—
207C2×#117—91no—
208#485—92no—
209#484—91no—
210#483—91no—
211#482—92no—
212#481—31no—
213#480—91no—
214#427—92no—
215#416—92no—
216C2×C22⋊C8—91no—
217C24×C3—31no—
218C23×D3#6711yescharacteristic
219C3×#41—64no—
220C2×C3×Q8—31no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—41no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—64no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C2×#67—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—121no—
247C22×Dic3#6711yescharacteristic
248#237—24no—
249C2×C4×D3—24no—
250C2×C4×D3#6711yescharacteristic
251C2×C4×D3#6711yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×C4×D3C22×D311yescharacteristic
254C2×Dic6C22×D311yescharacteristic
255C2×C3×C8—32no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—41no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C42—61no—
272#217—21no—
273#217—21no—
274#217—62no—
275#217—62no—
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—21no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3C22×D311yescharacteristic
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—21no—
291C4×Dic3—21no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C2×C3⋊C8—32no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—64no—
300C2×C3⋊C8C22×D312yes—
301D3×C8—64no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32#13512yes—
308C22×C32C22×D411yescharacteristic
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—21no—
314C2×C3×D3—44no—
315C2×C3×D3#12312yes—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4C2×#4112yes—
319C3⋊Dic3—42no—
320C3×Dic3—21no—
321C3×Dic3—41no—
322C3×Dic3—42no—
323C3×Dic3—41no—
324C3×Dic3#12312yes—
325C2×#41—31no—
326C23×C4—31no—
327C22×C8—92no—
328#123—61no—
329C22⋊Q8—31no—
330C22⋊Q8—31no—
331#121—31no—
332#121D3211yescharacteristic
333#120—61no—
334C4×D4—61no—
335C4×D4—61no—
336#117—31no—
337#117—92no—
338#117—92no—
339#117—181no—
340#117—181no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—181no—
344C2×C42—181no—
345#107—92no—
346#107—92no—
347#106—32no—
348#106—92no—
349#103—92no—
350#103—92no—
351#102—32no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8—92no—
355C22⋊C8—91no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—31no—
360C23×C3—31no—
361C23×C3—41no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3—121no—
365C23×C3D3×D411yescharacteristic
366C23×C3C2×#6711yescharacteristic
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—41no—
370C22×D3C2×#6711yescharacteristic
371C22×D3C2×#6711yescharacteristic
372C3×Q8—62no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—82no—
379C3×D4—122no—
380C3×D4—122no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—31no—
388C2×C3×C4—34no—
389C2×C3×C4—31no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—122no—
400C2×C3×C4—122no—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—42no—
406#67—42no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—42no—
412C2×Dic3—42no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—242no—
419C2×Dic3C2×#6711yescharacteristic
420C2×Dic3C2×#6711yescharacteristic
421C4×D3—22no—
422C4×D3—22no—
423C4×D3—22no—
424C4×D3#23714yes—
425Dic6—22no—
426C3×C8—62no—
427C3⋊C8—22no—
428C3⋊C8—62no—
429C3⋊C8—62no—
430C3⋊C8—122no—
431C2×C32—22no—
432C2×C32—81no—
433C2×C32C2×#12311yescharacteristic
434C2×C32C2×#13511yescharacteristic
435C2×C32#57511yescharacteristic
436C3×D3—22no—
437C3×D3—41no—
438C24—31no—
439#41—64no—
440C2×Q8—31no—
441C2×D4—21no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4C2×D3211yescharacteristic
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—64no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—181no—
454C22×C4C2×D3211yescharacteristic
455C2×C8—32no—
456C2×C8—92no—
457C2×C8—184no—
458C4⋊C4—32no—
459C4⋊C4—31no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4—92no—
464C4⋊C4—181no—
465C4⋊C4C2×D3211yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—182no—
472C22⋊C4—182no—
473C42—61no—
474C42—182no—
475C42—182no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—22no—
482C22×C3—32no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—61no—
494C22×C3—61no—
495C22×C3—61no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3—81no—
499C22×C3—124no—
500C22×C3#91612yes—
501C22×C3#95012yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C2×D3—21no—
505C2×D3—21no—
506C2×D3—21no—
507C2×D3—21no—
508C2×D3—21no—
509C2×D3—44no—
510C2×D3#93512yes—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—22no—
514C3×C4—32no—
515C3×C4—41no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—61no—
519C3×C4—81no—
520C3×C4—121no—
521C3×C4—121no—
522C3×C4—122no—
523C3×C4C2×#23712yes—
524C3×C4D3×#4112yes—
525Dic3—21no—
526Dic3—42no—
527Dic3—41no—
528Dic3—41no—
529Dic3—122no—
530Dic3—122no—
531Dic3—242no—
532Dic3#93512yes—
533C32#309111yescharacteristic, complemented, Sylow
534C23—21no—
535C23—31no—
536C23—31no—
537C23—62no—
538C23—62no—
539C23—121no—
540C23D3×#6711yescharacteristic
541Q8—62no—
542D4—22no—
543D4—42no—
544D4—122no—
545D4—122no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—31no—
549C2×C4—34no—
550C2×C4—31no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—122no—
559C2×C4—122no—
560C2×C4—182no—
561C2×C4—362no—
562C2×C4D3×#6711yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—62no—
565C8—182no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—62no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—121no—
576C2×C3—161no—
577C2×C3D3×#12311yescharacteristic
578C2×C3C2×#91611yescharacteristic
579C2×C3#577311yescharacteristic
580C2×C3C2×#93511yescharacteristic
581C2×C3C2×#95011yescharacteristic
582C2×C3#582211yescharacteristic
583D3—22no—
584D3—41no—
585C22—21no—
586C22—21no—
587C22—32no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—61no—
592C22—61no—
593C22—61no—
594C22—61no—
595C22—61no—
596C22—124no—
597C22#6393512yes—
598C22C2×D3×#6711yescharacteristic
599C4—21no—
600C4—32no—
601C4—41no—
602C4—61no—
603C4—121no—
604C4—122no—
605C4—121no—
606C4—362no—
607C4D3×#23712yes—
608C3—21no—
609C3#8132411yescharacteristic, complemented
610C3#8291311yescharacteristic, complemented
611C2—22no—
612C2—62no—
613C2—81no—
614C2—121no—
615C2C2×#6393511yescharacteristic
616C2D3×#93511yescharacteristic
617C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5606C2
hypercenter#121D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. #10592732C2semidirect
4. C3×#5034C2semidirect
5. #10591422C2semidirect
6. #10591420C2semidirect
7. D3×#830C2semidirect
8. #10591132C2semidirect
9. #10591126C2semidirect
10. #10590572C2semidirect
11. #10590447C2semidirect
34. #63659C22semidirect
36. #63634C22semidirect
37. C3×#832C22semidirect
39. C3×#808C22semidirect
40. #63576C22semidirect
41. #63573C22semidirect
42. #63566C22semidirect
43. #63565C22semidirect
56. #5034D3semidirect
157. #832C2×D3semidirect
168. #808C2×D3semidirect
533. C32#3091semidirect
609. C3#81324semidirect
610. C3#82913semidirect

Maximal subgroups

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

subgroupindex
C3×#56062
C2×#638412
#105927322
C3×#50342
#105914222
#105914202
D3×#8302
#105911322
#105911262
#105905722
#105904472
#829133
#813243