Finite Group Databasebeta

← #11870882

Subgroups — #11870882

Order 1152.

1121 conjugacy classes of subgroups.

The subgroup lattice has 635 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10594965C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10591479C212yesmaximal, complemented
6#10591476C212yesmaximal, complemented
7#10591445C212yesmaximal, complemented
8#10591435C212yesmaximal, complemented
9#10591103C211yesmaximal, characteristic, complemented
10#10591092C211yesmaximal, characteristic, complemented
11#10591061C211yesmaximal, characteristic, complemented
12#80133—31nomaximal
13#79989—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3—21no—
16C2×#3757—21no—
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3—21no—
19D4×C3⋊Dic3C2212yes—
20D4×C3⋊Dic3C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#214C2212yes—
24C2×C3×#213C2212yes—
25C3×#930C2211yescharacteristic
26C3×#924C2211yescharacteristic
27#67⋊Dic3—21no—
28#63962—21no—
29#63898C2211yescharacteristic, complemented
30#63878—21no—
31#63872C2211yescharacteristic, complemented
32#63863C2211yescharacteristic, complemented
33#63862—21no—
34#63843C2211yescharacteristic, complemented
35C3×#832C2212yes—
36C3×#832C2212yes—
37C3×#830C2211yescharacteristic
38C3×#830C2211yescharacteristic
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41#63572C2212yescomplemented
42#63566C2212yescomplemented
43#63563C2212yescomplemented
44#63553C2212yescomplemented
45C2×D4×Dic3—31no—
46C2×D4×Dic3—31no—
47C2×D4×Dic3—61no—
48#5624—31no—
49#5600—31no—
50C3×#450—31no—
51C3×#447—31no—
52#5218D311yescharacteristic, complemented
53#5217D311yescharacteristic
54#5165—32no—
55Dic3×SD16—32no—
56#5153—32no—
57Dic3×D8—32no—
58#5044—31no—
59#5034—31no—
60#4766—32no—
61#4763—32no—
62#4758—32no—
63#4756—32no—
64#4735—31no—
65#4722—31no—
66#4718—31no—
67#4718—31no—
68C24×C32—21no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—22no—
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—44no—
77C22×C3⋊Dic3D411yescharacteristic
78C22×C3⋊Dic3D411yescharacteristic
79C2×C3×#67—21no—
80C2×C3×D12C2311yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×D3×Dic3—21no—
83#3757—22no—
84#3757—22no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C4×C3⋊Dic3D411yescharacteristic
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3C2311yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C3×#217—21no—
92C3×#214—24no—
93C3×#213—24no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103(C2×D3)⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106Dic32—21no—
107#3105—91noSylow
108C22×C3×D4—21no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C2×D311yescharacteristic
111C23×Dic3—61no—
112C23×Dic3—61no—
113C23×Dic3—62no—
114C2×C3×SD16—32no—
115C2×C3×D8—32no—
116C3×C22⋊Q8—31no—
117C3×#121—31no—
118C2×#217—61no—
119C2×#217—61no—
120C2×#217—62no—
121#947—31no—
122Q8×Dic3—31no—
123#936—31no—
124#935—61no—
125D4×Dic3—32no—
126D4×Dic3—32no—
127D4×Dic3—32no—
128D4×Dic3—32no—
129D4×Dic3—31no—
130D4×Dic3—62no—
131D4×Dic3—62no—
132D4×Dic3—61no—
133D4×Dic3—61no—
134D4×Dic3—61no—
135D4×Dic3—61no—
136D4×Dic3—61no—
137D4×Dic3—62no—
138D4×Dic3—62no—
139C2×#214C2×D312yes—
140C2×#213C2×D312yes—
141#930C2×D311yescharacteristic
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—61no—
145#924C2×D311yescharacteristic
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—61no—
149#898—61no—
150#893—31no—
151#892—61no—
152#890—31no—
153#890—31no—
154#887—31no—
155#886—61no—
156#67⋊C4—61no—
157#879—61no—
158#877—61no—
159C3×#102—32no—
160C3×#102—32no—
161C3×C22⋊C8—31no—
162C3×C22⋊C8—31no—
163#835—32no—
164#832—32no—
165#832C2×D312yes—
166#832C2×D312yes—
167#830C2×D311yescharacteristic
168#830C2×D311yescharacteristic
169#821—32no—
170#818—32no—
171#817—32no—
172#816—32no—
173Dic3⋊C8—32no—
174Dic3⋊C8—32no—
175C8×Dic3—32no—
176C8×Dic3—32no—
177#808—32no—
178#807—32no—
179C23×C32—24no—
180C23×C32—22no—
181C23×C32—42no—
182C23×C32—42no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—21no—
185C32×D4—24no—
186C32×D4—22no—
187C32×D4#4114yes—
188C2×C32×C4—22no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—44no—
195C2×C3⋊Dic3—42no—
196C2×C3⋊Dic3—44no—
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C3×#67—42no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C3×D12—22no—
206C3×Dic6—22no—
207D3×Dic3—42no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210#529—91no—
211C2×C4×D4—91no—
212#484—91no—
213#481—91no—
214#478—92no—
215#463—92no—
216#450—31no—
217#447—31no—
218C4×SD16—92no—
219C4×D8—92no—
220#431—91no—
221C24×C3—22no—
222C24×C3—21no—
223C24×C3—21no—
224C2×C3×Q8—31no—
225C2×C3×D4—22no—
226C2×C3×D4—28no—
227C2×C3×D4—24no—
228C2×C3×D4—24no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—22no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C2×C3×D4C22×D312yes—
235C2×C3×D4C22×D312yes—
236C22×C3×C4—21no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—21no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—64no—
253C22×Dic3—64no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3—124no—
257C22×Dic3—124no—
258C22×Dic3—128no—
259C2×D12C22×D311yescharacteristic
260C2×C4×D3—61no—
261C2×Dic6C22×D311yescharacteristic
262C3×SD16—64no—
263C3×D8—64no—
264C2×C3×C8—32no—
265C2×C3×C8—32no—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271#217—21no—
272#217—61no—
273#217—61no—
274#217—61no—
275#217—62no—
276#217—62no—
277#217—62no—
278#217—62no—
279#217—64no—
280#217—64no—
281#214—24no—
282#213—24no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—61no—
287C4⋊Dic3—32no—
288C4⋊Dic3—32no—
289C4⋊Dic3—62no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—61no—
293C4⋊Dic3—62no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3C22×D311yescharacteristic
297C4⋊Dic3C22×D311yescharacteristic
298Dic3⋊C4—21no—
299Dic3⋊C4—61no—
300Dic3⋊C4—61no—
301Dic3⋊C4—61no—
302C4×Dic3—31no—
303C4×Dic3—31no—
304C4×Dic3—31no—
305C4×Dic3—31no—
306C4×Dic3—31no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—61no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C2×C3⋊C8C22×D312yes—
317C2×C3⋊C8C22×D312yes—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—24no—
321C22×C32—48no—
322C22×C32—42no—
323C22×C32—42no—
324C22×C32#13512yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4C2×#4112yes—
331C3⋊Dic3—21no—
332C3⋊Dic3—21no—
333C3⋊Dic3—21no—
334C3⋊Dic3—42no—
335C3⋊Dic3AGL(1,ℤ/8)12yes—
336C3×Dic3—41no—
337C3×Dic3—41no—
338C3×Dic3—41no—
339C22×D4D3211yescharacteristic
340C23×C4—181no—
341C2×SD16—32no—
342C2×D8—32no—
343#126—181no—
344#125—91no—
345#124—91no—
346#123—181no—
347C22⋊Q8—31no—
348#121—31no—
349C4×Q8—91no—
350C4×D4—91no—
351C4×D4—92no—
352C4×D4—92no—
353C4×D4—181no—
354C4×D4—181no—
355C4×D4—181no—
356#117—181no—
357C2×C4⋊C4—91no—
358C2×C22⋊C4—181no—
359C2×C42—91no—
360#107—92no—
361#106—92no—
362C4⋊C8—92no—
363#103—92no—
364#102—32no—
365#102—32no—
366#102—92no—
367C22⋊C8—31no—
368C22⋊C8—31no—
369C4×C8—92no—
370C23×C3—24no—
371C23×C3—28no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—44no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—44no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—61no—
384C23×C3D3×D411yescharacteristic
385C23×C3D3×D411yescharacteristic
386C22×D3—21no—
387C3×Q8—62no—
388C3×D4—28no—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—24no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—24no—
395C3×D4—62no—
396C3×D4—122no—
397C3×D4#23714yes—
398C3×D4#23714yes—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—42no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—31no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—31no—
421C2×Dic3—31no—
422C2×Dic3—31no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—64no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—64no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3—124no—
438C2×Dic3—124no—
439C2×Dic3—128no—
440C2×Dic3—128no—
441C2×Dic3—124no—
442C2×Dic3—124no—
443C2×Dic3—124no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446D12—22no—
447C4×D3—122no—
448Dic6—22no—
449C3×C8—62no—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—22no—
453C2×C32—22no—
454C2×C32—44no—
455C2×C32#52511yescharacteristic
456C2×C32C2×#13511yescharacteristic
457C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
458C3×D3—81no—
459C24—21no—
460C2×Q8—31no—
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4C2×D3212yes—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—181no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4—181no—
472C22×C4—364no—
473C22×C4C2×D3211yescharacteristic
474SD16—64no—
475D8—64no—
476C2×C8—32no—
477C2×C8—32no—
478C4⋊C4—31no—
479C4⋊C4—31no—
480C4⋊C4—61no—
481C4⋊C4—92no—
482C4⋊C4—181no—
483C4⋊C4—181no—
484C4⋊C4—181no—
485C4⋊C4—181no—
486C22⋊C4—61no—
487C22⋊C4—61no—
488C22⋊C4—181no—
489C22⋊C4—181no—
490C22⋊C4—181no—
491C22⋊C4—182no—
492C22⋊C4—182no—
493C42—91no—
494C42—91no—
495C42—91no—
496C42—91no—
497C42—181no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—28no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—44no—
510C22×C3—416no—
511C22×C3—48no—
512C22×C3—48no—
513C22×C3—44no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—121no—
519C22×C3—121no—
520C22×C3—121no—
521C22×C3#91212yes—
522C22×C3#91612yes—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C2×D3×D411yescharacteristic
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—41no—
528C3×C4—22no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—121no—
533C3×C4—121no—
534C3×C4—121no—
535C3×C4C2×#23712yes—
536C3×C4C2×#23712yes—
537Dic3—32no—
538Dic3—32no—
539Dic3—41no—
540Dic3—41no—
541Dic3—41no—
542Dic3—62no—
543Dic3—62no—
544Dic3—61no—
545Dic3—61no—
546Dic3—61no—
547Dic3—61no—
548Dic3—61no—
549Dic3—61no—
550Dic3—121no—
551Dic3—121no—
552Dic3—124no—
553Dic3—122no—
554Dic3—122no—
555C32#310511yescharacteristic, complemented, Sylow
556C23—24no—
557C23—22no—
558C23—42no—
559C23—42no—
560C23—61no—
561C23#381111yescharacteristic
562Q8—62no—
563D4—24no—
564D4—22no—
565D4—62no—
566D4—122no—
567D4#380514yes—
568C2×C4—22no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—91no—
573C2×C4—91no—
574C2×C4—91no—
575C2×C4—91no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—362no—
580C2×C4—364no—
581C2×C4—364no—
582C2×C4—362no—
583C2×C4#381111yescharacteristic
584C2×C4C22×D3211yescharacteristic
585C8—62no—
586C8—62no—
587C2×C3—24no—
588C2×C3—22no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—48no—
594C2×C3—44no—
595C2×C3—44no—
596C2×C3—241no—
597C2×C3#558611yescharacteristic
598C2×C3#558611yescharacteristic
599C2×C3C2×#91211yescharacteristic
600C2×C3C2×#91611yescharacteristic
601C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
602C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
603D3—81no—
604C22—21no—
605C22—21no—
606C22—24no—
607C22—48no—
608C22—42no—
609C22—42no—
610C22—121no—
611C22—121no—
612C22—121no—
613C22#6393612yes—
614C22C2×#381111yescharacteristic
615C4—21no—
616C4—92no—
617C4—121no—
618C4—121no—
619C4—121no—
620C4—181no—
621C4—181no—
622C4—181no—
623C4—362no—
624C4C2×#380512yes—
625C3—21no—
626C3#7998911yescharacteristic, complemented
627C3#8013311yescharacteristic, complemented
628C2—22no—
629C2—44no—
630C2—241no—
631C2#1059510011yescharacteristic
632C2C2×#6393611yescharacteristic
633C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC22×D4D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. #10594965C2semidirect
3. C3×#5218C2semidirect
5. #10591479C2semidirect
6. #10591476C2semidirect
7. #10591445C2semidirect
8. #10591435C2semidirect
9. #10591103C2semidirect
10. #10591092C2semidirect
11. #10591061C2semidirect
29. #63898C22semidirect
31. #63872C22semidirect
32. #63863C22semidirect
34. #63843C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
41. #63572C22semidirect
42. #63566C22semidirect
43. #63563C22semidirect
44. #63553C22semidirect
52. #5218D3semidirect
555. C32#3105semidirect
626. C3#79989semidirect
627. C3#80133semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
#105949652
C3×#52182
C3×#52172
#105914792
#105914762
#105914452
#105914352
#105911032
#105910922
#105910612
#801333
#799893