Finite Group Databasebeta

← #11870883

Subgroups — #11870883

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
2#10594949C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10591468C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10591411C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9#10591135C211yesmaximal, characteristic, complemented
10#10591091C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#82309—31nomaximal
13#79989—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16C2×#3754C2212yes—
17#64133C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×D4×Dic3C2212yes—
23C2×C3×#213C2212yes—
24C3×#930C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27Dic3×#67—21no—
28#63961—21no—
29Dic3×D12C2211yescharacteristic, complemented
30#63877—21no—
31#63869C2211yescharacteristic, complemented
32#63860C2211yescharacteristic, complemented
33#63859—21no—
34#63844C2211yescharacteristic, complemented
35#63659C2212yes—
36#63657C2211yescharacteristic
37C3×#832C2212yes—
38C3×#830C2211yescharacteristic
39#63575C2212yescomplemented
40#63574C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63567C2212yescomplemented
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46C2×D4×Dic3D311yescharacteristic, complemented
47#5600—31no—
48#5479—31no—
49C3×#447—31no—
50#5218—31no—
51#5218—31no—
52#5218—61no—
53#5217D311yescharacteristic
54#5153—32no—
55Dic3×D8—32no—
56#5034—31no—
57C4×#214—32no—
58#5016—32no—
59C4×#213—32no—
60#5009—32no—
61#4970—31no—
62#4968—31no—
63#4925—31no—
64#4766—32no—
65#4758—32no—
66#4722—31no—
67#4718—31no—
68C24×C32—21no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C2×#634C2311yescharacteristic
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—22no—
78C22×C3×Dic3—44no—
79C22×C3×Dic3D411yescharacteristic
80C22×C3×Dic3D411yescharacteristic
81C2×C3×D12C2311yescharacteristic
82C2×D3×Dic3—21no—
83#3757—21no—
84#3754—24no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—22no—
89C3×#217—22no—
90C3×#213—24no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101#3724—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×C3×C4—61no—
112C23×Dic3—21no—
113C2×C3×D8—32no—
114C3×#121—31no—
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—61no—
118C3×C4×D4—61no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C22⋊C4—61no—
121C2×C3×C42—31no—
122C2×#217—21no—
123#936—31no—
124#935—61no—
125D4×Dic3—21no—
126D4×Dic3—21no—
127D4×Dic3—31no—
128D4×Dic3—61no—
129D4×Dic3C2×D312yes—
130D4×Dic3C2×D312yes—
131C2×#214—32no—
132C2×#214—32no—
133C2×#214—62no—
134C2×#213C2×D312yes—
135#930C2×D311yescharacteristic
136#929—61no—
137C4×#67—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139#924—31no—
140#924—31no—
141#924—61no—
142C2×C4×Dic3C2×D311yescharacteristic
143#890—31no—
144#887—31no—
145#879—61no—
146#877—61no—
147#876—61no—
148#875—31no—
149C4×D12—31no—
150#872—61no—
151#870—31no—
152C4×Dic6—31no—
153C3×#102—32no—
154C3×C22⋊C8—31no—
155#832—32no—
156#832—32no—
157#832—32no—
158#832—62no—
159#832C2×D312yes—
160#830—31no—
161#830—31no—
162#830—61no—
163#830C2×D311yescharacteristic
164#818—32no—
165#816—32no—
166Dic3⋊C8—32no—
167C8×Dic3—32no—
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172#807—32no—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32—24no—
176C23×C32—22no—
177C23×C32—42no—
178C23×C32—42no—
179C23×C32C2×D411yescharacteristic
180C22×C3×D3—21no—
181C32×D4—24no—
182C32×D4—22no—
183C32×D4#4114yes—
184C2×C32×C4—22no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189#634—22no—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—44no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3—44no—
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203D3×Dic3—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#529—91no—
207C2×C4×D4—31no—
208#484—91no—
209#481—91no—
210#478—92no—
211#463—92no—
212#450—91no—
213#447—31no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—91no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—41no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—31no—
226C2×C3×D4—41no—
227C2×C3×D4—44no—
228C2×C3×D4—61no—
229C2×C3×D4C22×D312yes—
230C2×C3×D4C22×D312yes—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4—61no—
237C22×C3×C4—124no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—44no—
245C22×Dic3—61no—
246C22×Dic3#6711yescharacteristic
247C22×Dic3#6711yescharacteristic
248C2×D12C22×D311yescharacteristic
249C2×C4×D3—61no—
250C2×Dic6—31no—
251C2×Dic6—31no—
252C2×Dic6—61no—
253C3×D8—64no—
254C2×C3×C8—32no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260C3×C22⋊C4—61no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—31no—
265#217—22no—
266#217—22no—
267#217—61no—
268#217—61no—
269#217—61no—
270#217—61no—
271#217—61no—
272#217—121no—
273#214—64no—
274#214—64no—
275#214—124no—
276#213—24no—
277(C2×D3)⋊C4—21no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281C4⋊Dic3—21no—
282C4⋊Dic3—31no—
283C4⋊Dic3—31no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D312yes—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295Dic3⋊C4—121no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8C22×D312yes—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—24no—
309C22×C32—48no—
310C22×C32—42no—
311C22×C32—42no—
312C22×C32#13512yes—
313C22×C32C22×D411yescharacteristic
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4C2×#4112yes—
319C3⋊Dic3—41no—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4D3211yescharacteristic
328C23×C4—61no—
329C2×SD16—92no—
330C2×D8—32no—
331#126—181no—
332#125—91no—
333#124—91no—
334#123—181no—
335C22⋊Q8—91no—
336#121—31no—
337C4×Q8—91no—
338C4×D4—32no—
339C4×D4—32no—
340C4×D4—61no—
341C4×D4—61no—
342C4×D4—91no—
343C4×D4—181no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—61no—
347C2×C42—31no—
348#107—92no—
349#106—92no—
350C4⋊C8—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8—91no—
357C4×C8—92no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—42no—
364C23×C3—44no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—61no—
370C23×C3—82no—
371C23×C3—82no—
372C23×C3D3×D411yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C22×D3—21no—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4—42no—
381C3×D4—44no—
382C3×D4—62no—
383C3×D4—122no—
384C3×D4#23514yes—
385C3×D4#23714yes—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—42no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—124no—
400C2×C3×C4—124no—
401C2×C3×C4—122no—
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—42no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—22no—
411C2×Dic3—44no—
412C2×Dic3—42no—
413C2×Dic3—44no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—122no—
421C2×Dic3C2×#6711yescharacteristic
422C2×Dic3C2×#6711yescharacteristic
423C2×Dic3C2×#6711yescharacteristic
424C2×Dic3C2×#6711yescharacteristic
425D12—22no—
426C4×D3—122no—
427Dic6—62no—
428Dic6—62no—
429Dic6—122no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C2×C32—22no—
436C2×C32—44no—
437C2×C32#52511yescharacteristic
438C2×C32C2×#13511yescharacteristic
439C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
440C3×D3—81no—
441C24—21no—
442C2×Q8—91no—
443C2×D4—24no—
444C2×D4—21no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4C2×D3212yes—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—61no—
453C22×C4—124no—
454C22×C4—181no—
455C22×C4C2×D3211yescharacteristic
456SD16—184no—
457D8—64no—
458C2×C8—32no—
459C2×C8—92no—
460C4⋊C4—31no—
461C4⋊C4—32no—
462C4⋊C4—61no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C22⋊C4—62no—
469C22⋊C4—62no—
470C22⋊C4—61no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—181no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—44no—
491C22×C3—48no—
492C22×C3—48no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—88no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3#91212yes—
504C22×C3#95012yes—
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C22×#6711yescharacteristic
507C2×D3—41no—
508C2×D3—41no—
509C2×D3—41no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—41no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—122no—
519C3×C4—121no—
520C3×C4C2×#23512yes—
521C3×C4C2×#23712yes—
522Dic3—21no—
523Dic3—21no—
524Dic3—21no—
525Dic3—41no—
526Dic3—42no—
527Dic3—121no—
528Dic3—121no—
529Dic3—121no—
530Dic3—121no—
531Dic3—241no—
532Dic3—241no—
533Dic3#93212yes—
534C32#310511yescharacteristic, complemented, Sylow
535C23—24no—
536C23—22no—
537C23—42no—
538C23—42no—
539C23—61no—
540C23D3×#6711yescharacteristic
541Q8—182no—
542D4—24no—
543D4—22no—
544D4—62no—
545D4—122no—
546D4#380414yes—
547C2×C4—22no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—124no—
557C2×C4—124no—
558C2×C4—122no—
559C2×C4—181no—
560C2×C4—181no—
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—44no—
573C2×C3—44no—
574C2×C3—84no—
575C2×C3—241no—
576C2×C3#558611yescharacteristic
577C2×C3C2×#91211yescharacteristic
578C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#579111yescharacteristic
580C2×C3C2×#93211yescharacteristic
581C2×C3C2×#95011yescharacteristic
582D3—81no—
583C22—21no—
584C22—21no—
585C22—24no—
586C22—48no—
587C22—42no—
588C22—42no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22#6393312yes—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—32no—
596C4—61no—
597C4—61no—
598C4—61no—
599C4—122no—
600C4—121no—
601C4—361no—
602C4—361no—
603C4C2×#380412yes—
604C3—21no—
605C3#7998911yescharacteristic, complemented
606C3#8230911yescharacteristic, complemented
607C2—22no—
608C2—44no—
609C2—241no—
610C2D3×#93211yescharacteristic
611C2C2×#6393311yescharacteristic
612C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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×C3×D4×Dic3C2semidirect
2. #10594949C2semidirect
3. #10592917C2semidirect
5. #10591468C2semidirect
6. Dic3×#213C2semidirect
7. #10591411C2semidirect
8. #10591401C2semidirect
9. #10591135C2semidirect
10. #10591091C2semidirect
11. #10591053C2semidirect
29. Dic3×D12C22semidirect
31. #63869C22semidirect
32. #63860C22semidirect
34. #63844C22semidirect
39. #63575C22semidirect
40. #63574C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63567C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. C2×D4×Dic3D3semidirect
534. C32#3105semidirect
605. C3#79989semidirect
606. C3#82309semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105949492
#105929172
C3×#52172
#105914682
Dic3×#2132
#105914112
#105914012
#105911352
#105910912
#105910532
#823093
#799893