Finite Group Databasebeta

← #11868683

Subgroups — #11868683

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2#10595049C211yesmaximal, characteristic, complemented
3#10592914C211yesmaximal, characteristic
4C3×#5215C211yesmaximal, characteristic
5#10591411C212yesmaximal, complemented
6#10591410C212yesmaximal, complemented
7#10591409C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9#10591139C211yesmaximal, characteristic, complemented
10#10591130C211yesmaximal, characteristic, complemented
11#10591115C211yesmaximal, characteristic, complemented
12#82296—31nomaximal
13#78917—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3—21no—
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2212yes—
22C3×D4×Dic3C2212yes—
23C3×#926C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63964—21no—
28#63964—21no—
29#63918C2211yescharacteristic, complemented
30#63918C2211yescharacteristic, complemented
31C4×#627—21no—
32C4×#627—21no—
33#63869C2211yescharacteristic, complemented
34#63869C2211yescharacteristic, complemented
35#63659C2212yes—
36#63659C2212yes—
37C3×#832C2212yes—
38C3×#832C2212yes—
39#63576C2212yescomplemented
40#63575C2212yescomplemented
41#63574C2212yescomplemented
42#63573C2212yescomplemented
43Dic3⋊(C3⋊C8)C2212yescomplemented
44Dic3⋊(C3⋊C8)C2212yescomplemented
45C2×C3×C4×D4—31no—
46C2×D4×Dic3D311yescharacteristic
47#5517—31no—
48#5470—31no—
49C3×#418—31no—
50#5215—31no—
51#5215—31no—
52#5215—61no—
53#5215D311yescharacteristic
54#5121—31no—
55#5118—31no—
56#5009—32no—
57#5009—32no—
58#5008—32no—
59#5007—32no—
60#4995—31no—
61#4964—31no—
62#4964—31no—
63#4924—31no—
64#4766—32no—
65#4763—32no—
66#4761—32no—
67#4759—32no—
68C24×C32—21no—
69C2×C32×D4—21no—
70C2×C32×D4—22no—
71C2×C32×D4Q814yescomplemented
72C2×C32×D4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—21no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—22no—
77C22×C3×Dic3—44no—
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×#627—21no—
81C2×#627—21no—
82#3757—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4×C3⋊Dic3—21no—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×#217—22no—
90C3×#217—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3—21no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102#3724—21no—
103#3724—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—21no—
108#3077—91noSylow
109C22×C3×D4—21no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—61no—
113C23×Dic3—21no—
114C2×C3×M16—31no—
115C3×C4×D4—32no—
116C3×C4×D4—32no—
117C3×C4×D4—61no—
118C3×C4×D4—61no—
119C3×#117—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C22⋊C4—61no—
122C2×C3×C42—31no—
123C2×#217—21no—
124D4×Dic3—21no—
125D4×Dic3—21no—
126D4×Dic3C2×D312yes—
127D4×Dic3C2×D312yes—
128#926—31no—
129#926—31no—
130#926—61no—
131#926C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D311yescharacteristic
133#924—61no—
134#924—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136C2×#208—31no—
137C2×#208—31no—
138C2×#208—61no—
139C2×#208C2×D311yescharacteristic
140#890—31no—
141#890—31no—
142#888—31no—
143#888—31no—
144#878—61no—
145#878—61no—
146#870—31no—
147#870—31no—
148#869—31no—
149#869—31no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C3×#102—32no—
155C3×#102—32no—
156#832—32no—
157#832—32no—
158#832—32no—
159#832—32no—
160#832—62no—
161#832—62no—
162#832C2×D312yes—
163#832C2×D312yes—
164#818—32no—
165#817—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—32no—
168#808—32no—
169#808—32no—
170#808—32no—
171#807—32no—
172#807—32no—
173#807—32no—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32—24no—
177C23×C32—22no—
178C23×C32—42no—
179C23×C32—42no—
180C23×C32C2×D411yescharacteristic
181C32×D4—24no—
182C32×D4—22no—
183C32×D4C2×Q814yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×Q812yes—
186C2×C32×C4#4112yes—
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—41no—
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
202#627—42no—
203#627—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207C2×C4×D4—31no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—91no—
213#428—91no—
214#423—91no—
215#418—31no—
216#418—91no—
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—41no—
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—22no—
223C2×C3×D4—21no—
224C2×C3×D4—24no—
225C2×C3×D4—22no—
226C2×C3×D4—42no—
227C2×C3×D4—41no—
228C2×C3×D4Dic614yescomplemented
229C2×C3×D4Dic614yescomplemented
230C2×C3×D4C22×D312yes—
231C2×C3×D4C22×D312yes—
232C22×C3×C4—21no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—62no—
236C22×C3×C4—62no—
237C22×C3×C4—61no—
238C22×C3×C4—124no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—44no—
245C22×Dic3#6711yescharacteristic
246C22×Dic3#6711yescharacteristic
247C2×Dic6—61no—
248C2×Dic6—61no—
249C2×Dic6—61no—
250C2×Dic6—61no—
251C3×M16—62no—
252C2×C3×C8—32no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—61no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—61no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263C3×C42—31no—
264C3×C42—61no—
265#217—21no—
266#217—22no—
267#217—22no—
268#217—61no—
269#217—61no—
270#217—121no—
271C4⋊Dic3—21no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—31no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3C22×D311yescharacteristic
283C4⋊Dic3C22×D312yes—
284C4⋊Dic3C22×D311yescharacteristic
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293C4×Dic3—21no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—121no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301#208—22no—
302#208—62no—
303#208—62no—
304#208—122no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8C22×D312yes—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—24no—
312C22×C32—48no—
313C22×C32—42no—
314C22×C32—42no—
315C22×C32C22⋊Q812yes—
316C22×C32C22×D411yescharacteristic
317C32×C4C22⋊Q812yes—
318C32×C4C22×Q811yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—41no—
321C3⋊Dic3—41no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C3×Dic3—41no—
328C3×Dic3AGL(1,ℤ/8)12yes—
329C22×D4D3211yescharacteristic
330C23×C4—61no—
331C2×M16—31no—
332C2×M16—91no—
333C4⋊Q8—91no—
334C4⋊Q8—91no—
335#125—91no—
336#125—91no—
337C22⋊Q8—181no—
338C22⋊Q8—181no—
339C4×Q8—181no—
340C4×Q8—181no—
341C4×D4—32no—
342C4×D4—32no—
343C4×D4—61no—
344C4×D4—61no—
345#117—31no—
346#117—91no—
347C2×C4⋊C4—31no—
348C2×C22⋊C4—61no—
349C2×C42—31no—
350#107—92no—
351#107—92no—
352#106—92no—
353#106—92no—
354C4⋊C8—92no—
355C4⋊C8—92no—
356#102—32no—
357#102—32no—
358#102—92no—
359#102—92no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—42no—
366C23×C3—44no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—82no—
372C23×C3—82no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4—42no—
381C3×D4—44no—
382C3×D4C2×Dic614yes—
383C3×D4C2×Dic614yes—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—124no—
397C2×C3×C4—121no—
398C2×C3×C4—124no—
399C2×C3×C4—122no—
400C2×C3×C4C2×Dic612yes—
401C2×C3×C4C2×Dic612yes—
402C2×C3×C4#23512yes—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4#23712yes—
405C2×C3×C4C2×#6711yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—41no—
413C2×Dic3—44no—
414C2×Dic3—42no—
415C2×Dic3—44no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3C2×#6711yescharacteristic
423C2×Dic3C2×#6711yescharacteristic
424C2×Dic3C2×#6711yescharacteristic
425C2×Dic3C2×#6711yescharacteristic
426Dic6—122no—
427Dic6—122no—
428Dic6—122no—
429Dic6—122no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C2×C32—22no—
436C2×C32—44no—
437C2×C32C2×C22⋊Q811yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C2×C32#57511yescharacteristic
440C24—21no—
441C2×Q8—181no—
442C2×Q8—181no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4#62714yescomplemented
446C2×D4C2×D3212yes—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—61no—
452C22×C4—124no—
453C22×C4C2×D3211yescharacteristic
454M16—62no—
455M16—182no—
456C2×C8—32no—
457C2×C8—92no—
458C4⋊C4—31no—
459C4⋊C4—31no—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—91no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C4⋊C4—181no—
470C22⋊C4—62no—
471C22⋊C4—62no—
472C22⋊C4—61no—
473C22⋊C4—181no—
474C42—31no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—61no—
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#87812yes—
501C22×C3#92412yes—
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C22×#6711yescharacteristic
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—32no—
508C3×C4—61no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—122no—
512C3×C4—121no—
513C3×C4—121no—
514C3×C4#87812yes—
515C3×C4#92412yes—
516C3×C4C22×Dic611yescharacteristic
517C3×C4C22×Dic611yescharacteristic
518C3×C4C2×#23511yescharacteristic
519C3×C4C2×#23711yescharacteristic
520Dic3—21no—
521Dic3—21no—
522Dic3—21no—
523Dic3—41no—
524Dic3—41no—
525Dic3—42no—
526Dic3—121no—
527Dic3—121no—
528Dic3—121no—
529Dic3—121no—
530Dic3—241no—
531Dic3—241no—
532Dic3#93212yes—
533C32#307711yescharacteristic, complemented, Sylow
534C23—22no—
535C23—24no—
536C23—42no—
537C23—42no—
538C23D3×#6711yescharacteristic
539Q8—362no—
540Q8—362no—
541D4—22no—
542D4—24no—
543D4C2×#62714yes—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—31no—
547C2×C4—31no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—124no—
553C2×C4—121no—
554C2×C4—124no—
555C2×C4—122no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4#380412yes—
559C2×C4C2×#62712yes—
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—62no—
563C8—182no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—42no—
570C2×C3—44no—
571C2×C3—44no—
572C2×C3—84no—
573C2×C3C2×#87811yescharacteristic
574C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
575C2×C3#577311yescharacteristic
576C2×C3C2×#92411yescharacteristic
577C2×C3C2×#93211yescharacteristic
578C2×C3#582211yescharacteristic
579C22—21no—
580C22—21no—
581C22—24no—
582C22—48no—
583C22—42no—
584C22—42no—
585C22#6396412yes—
586C22C2×D3×#6711yescharacteristic
587C4—32no—
588C4—61no—
589C4—61no—
590C4—61no—
591C4—122no—
592C4—121no—
593C4—121no—
594C4—361no—
595C4—361no—
596C4#6396412yes—
597C4C2×#380411yescharacteristic
598C4C22×#62711yescharacteristic
599C3—21no—
600C3#7891711yescharacteristic, complemented
601C3#8229611yescharacteristic, complemented
602C2—22no—
603C2—44no—
604C2D3×#93211yescharacteristic
605C2#1059509511yescharacteristic
606C2C2×#6396411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3077
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
2. #10595049C2semidirect
5. #10591411C2semidirect
6. #10591410C2semidirect
7. #10591409C2semidirect
8. #10591408C2semidirect
9. #10591139C2semidirect
10. #10591130C2semidirect
11. #10591115C2semidirect
29. #63918C22semidirect
30. #63918C22semidirect
33. #63869C22semidirect
34. #63869C22semidirect
39. #63576C22semidirect
40. #63575C22semidirect
41. #63574C22semidirect
42. #63573C22semidirect
43. Dic3⋊(C3⋊C8)C22semidirect
44. Dic3⋊(C3⋊C8)C22semidirect
71. C2×C32×D4Q8semidirect
228. C2×C3×D4Dic6semidirect
229. C2×C3×D4Dic6semidirect
445. C2×D4#627semidirect
533. C32#3077semidirect
600. C3#78917semidirect
601. C3#82296semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
#105950492
#105929142
C3×#52152
#105914112
#105914102
#105914092
#105914082
#105911392
#105911302
#105911152
#822963
#789173