Finite Group Databasebeta

← #11868618

Subgroups — #11868618

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592720C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591556C212yesmaximal
6#10591545C212yesmaximal, complemented
7#10590572C212yesmaximal, complemented
8#10590545C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#82507—31nomaximal
13#81010—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×Q8×Dic3C2211yescharacteristic
18C3×#893—21no—
19C3×#893C2211yescharacteristic
20C3×#892—21no—
21C3×#892C2211yescharacteristic
22C3×C4×D12—21no—
23C3×C4×D12C2211yescharacteristic
24C3×C42×D3—21no—
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic
27#63869C2212yes—
28#63857—21no—
29#63856—21no—
30#63844—21no—
31Dic3×Dic6—21no—
32#63841C2212yes—
33C2×D3×C3⋊C8C2212yes—
34#63662C2212yes—
35#63634C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#835C2212yes—
38C3×#808C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63576C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63563C2212yes—
44#63562C2212yes—
45C3×C4×#41—31no—
46#5728—31no—
47C4×#239D311yescharacteristic
48#5470—31no—
49C3×#475—31no—
50#5233—32no—
51#5087—31no—
52#5022—32no—
53#5021—31no—
54#5021—31no—
55#5021—61no—
56#5020D311yescharacteristic, complemented
57#5009—32no—
58#5008—31no—
59#5007—31no—
60#4998—32no—
61C2×C4⋊(C3⋊C8)—31no—
62#4871—32no—
63#4860—32no—
64#4842—31no—
65D3×C4⋊C8—31no—
66#4804—32no—
67#4799—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634—21no—
70C3×#239—22no—
71C3×#239Q814yescomplemented
72C2×C3×D12—21no—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3—21no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6—21no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#3724—22no—
102Dic3⋊Dic3—22no—
103(C2×D3)⋊Dic3—22no—
104Dic32—22no—
105D3×C3⋊C8—24no—
106#3076—91noSylow
107C2×C3×#41—31no—
108C2×#239C2×D311yescharacteristic
109C3×C4⋊Q8—31no—
110C3×C4×Q8—21no—
111C3×C4×Q8—31no—
112C3×C4×Q8C2×D311yescharacteristic
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116C3×C4×D4—61no—
117C3×C4×D4—61no—
118C3×#117—31no—
119C3×#117—61no—
120C2×C3×C42—31no—
121C2×C3×C42—61no—
122#946—61no—
123Q8×Dic3—61no—
124Q8×Dic3C2×D311yescharacteristic
125#926—32no—
126#924—61no—
127#924—61no—
128C22×C3⋊C8—32no—
129C2×D3×C8—32no—
130#897—61no—
131#893—21no—
132#893C2×D311yescharacteristic
133#892—21no—
134#892—32no—
135#892C2×D311yescharacteristic
136#890—32no—
137#887—61no—
138C4×D12—21no—
139C4×D12C2×D311yescharacteristic
140C42×D3—21no—
141C42×D3C2×D311yescharacteristic
142#870—32no—
143#869—31no—
144#869—31no—
145#869—61no—
146#869C2×D311yescharacteristic
147C4×Dic6—61no—
148C4×Dic6—61no—
149C3×#106—32no—
150C3×C4⋊C8—31no—
151C3×#103—32no—
152#835—32no—
153#835—32no—
154#835—62no—
155#835C2×D312yes—
156#832—32no—
157#832—32no—
158#821—32no—
159#817—32no—
160Dic3⋊C8—32no—
161#809—32no—
162#808—32no—
163#808C2×D312yes—
164#807—32no—
165#807—32no—
166#807—32no—
167#807—32no—
168#807—62no—
169C4⋊(C3⋊C8)—31no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—32no—
172C4⋊(C3⋊C8)—61no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C22×C3×D3—21no—
175C22×C3×D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8C2×Q812yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184#634—42no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C3×D12—24no—
191C3×D12—21no—
192C3×D12C2×Q812yes—
193C3×C4×D3—22no—
194C3×C4×D3—24no—
195C3×C4×D3—41no—
196C3×C4×D3—42no—
197C3×C4×D3—42no—
198C3×C4×D3C2×Q812yes—
199C3×C4×D3#4112yes—
200C3×Dic6—42no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203#533—91no—
204C4×#41—31no—
205#479—92no—
206#478—92no—
207#477—91no—
208#476—91no—
209#475—31no—
210#474—91no—
211#427—92no—
212C2×C4⋊C8—91no—
213#416—92no—
214C3×#41—34no—
215C3×#41—62no—
216C2×C3×Q8—21no—
217C2×C3×Q8—61no—
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C2×C3×D4—31no—
221C2×C3×D4—61no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228#239—22no—
229#239Dic614yescomplemented
230C2×D12—21no—
231C2×D12C22×D311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3#6711yescharacteristic
236C2×C4×D3#6711yescharacteristic
237C2×C4×D3C22×D311yescharacteristic
238C2×Dic6—21no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—121no—
242C2×C3×C8—32no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—41no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C22⋊C4—61no—
254C3×C22⋊C4—61no—
255C3×C22⋊C4—61no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—21no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—41no—
263C3×C42—61no—
264C3×C42—61no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—62no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—21no—
270(C2×D3)⋊C4—21no—
271(C2×D3)⋊C4—62no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—32no—
275C4⋊Dic3—32no—
276C4⋊Dic3—62no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—121no—
281C4⋊Dic3C22×D311yescharacteristic
282C4⋊Dic3C22×D312yes—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286C4×Dic3—21no—
287C4×Dic3—21no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3#6711yescharacteristic
291C4×Dic3#6711yescharacteristic
292C4×Dic3C22×D311yescharacteristic
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—62no—
296C2×C3⋊C8—64no—
297C2×C3⋊C8C22×D312yes—
298D3×C8—64no—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—21no—
301C2×C3×D3—21no—
302C2×C3×D3—22no—
303C2×C3×D3—41no—
304C2×C3×D3—41no—
305C2×C3×D3C22⋊Q812yes—
306C32×C4—22no—
307C32×C4—21no—
308C32×C4—41no—
309C32×C4#13512yes—
310C32×C4C22×Q811yescharacteristic
311C32×C4C2×#4111yescharacteristic
312C3⋊Dic3—42no—
313C3×Dic3—21no—
314C3×Dic3—21no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3C22⋊Q812yes—
318C2×#41—31no—
319C22×C8—92no—
320C4⋊Q8—31no—
321C4⋊Q8—91no—
322#125—92no—
323C22⋊Q8—181no—
324C22⋊Q8—181no—
325C4×Q8—31no—
326C4×Q8—181no—
327C4×Q8—181no—
328C4×Q8D3211yescharacteristic
329C4×D4—31no—
330C4×D4—31no—
331C4×D4—61no—
332C4×D4—61no—
333#117—31no—
334#117—61no—
335#117—92no—
336C2×C42—31no—
337C2×C42—61no—
338#107—92no—
339#107—92no—
340#106—32no—
341#106—92no—
342C4⋊C8—31no—
343C4⋊C8—92no—
344C4⋊C8—91no—
345#103—32no—
346#103—92no—
347#102—92no—
348#102—92no—
349C23×C3—31no—
350C23×C3—61no—
351C22×D3—21no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—22no—
356C3×Q8—41no—
357C3×Q8—122no—
358C3×Q8C2×Dic612yes—
359C3×Q8D3×Q812yes—
360C3×D4—32no—
361C3×D4—64no—
362C3×D4—61no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—31no—
371C2×C3×C4—32no—
372C2×C3×C4—32no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—121no—
382C2×C3×C4—122no—
383C2×C3×C4—122no—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3C2×#6711yescharacteristic
396C2×Dic3C2×#6711yescharacteristic
397C2×Dic3C2×#6711yescharacteristic
398D12—24no—
399D12—21no—
400D12C2×Dic612yes—
401C4×D3—22no—
402C4×D3—24no—
403C4×D3—41no—
404C4×D3—42no—
405C4×D3—42no—
406C4×D3C2×Dic612yes—
407C4×D3#23512yes—
408Dic6—42no—
409Dic6—122no—
410Dic6—122no—
411Dic6—242no—
412C3×C8—62no—
413C3⋊C8—22no—
414C3⋊C8—62no—
415C3⋊C8—62no—
416C3⋊C8—122no—
417C2×C32C2×C22⋊Q811yescharacteristic
418C2×C32C2×#13511yescharacteristic
419C2×C32#57511yescharacteristic
420C3×D3—22no—
421C3×D3—42no—
422#41—34no—
423#41—62no—
424C2×Q8—61no—
425C2×Q8—181no—
426C2×Q8C2×D3211yescharacteristic
427C2×D4—31no—
428C2×D4—61no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C2×C8—32no—
436C2×C8—92no—
437C2×C8—184no—
438C4⋊C4—21no—
439C4⋊C4—32no—
440C4⋊C4—31no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—92no—
444C4⋊C4—182no—
445C4⋊C4—182no—
446C4⋊C4—181no—
447C4⋊C4C2×D3211yescharacteristic
448C22⋊C4—61no—
449C22⋊C4—61no—
450C22⋊C4—61no—
451C22⋊C4—182no—
452C42—21no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—61no—
457C42—61no—
458C42—182no—
459C42C2×D3211yescharacteristic
460C22×C3—21no—
461C22×C3—32no—
462C22×C3—61no—
463C22×C3—61no—
464C22×C3—62no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3C2×D3×D411yescharacteristic
468C22×C3C22×#6711yescharacteristic
469C2×D3—21no—
470C2×D3—21no—
471C2×D3—22no—
472C2×D3—41no—
473C2×D3—41no—
474C2×D3#92412yes—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—22no—
482C3×C4—32no—
483C3×C4—41no—
484C3×C4—42no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—61no—
488C3×C4—61no—
489C3×C4—81no—
490C3×C4—121no—
491C3×C4—122no—
492C3×C4#91612yes—
493C3×C4#95012yes—
494C3×C4C22×Dic611yescharacteristic
495C3×C4C2×#23511yescharacteristic
496C3×C4C2×D3×Q811yescharacteristic
497C3×C4D3×#4111yescharacteristic
498Dic3—21no—
499Dic3—21no—
500Dic3—42no—
501Dic3—41no—
502Dic3—122no—
503Dic3—122no—
504Dic3—242no—
505Dic3#92412yes—
506C32#307611yescharacteristic, complemented, Sylow
507C23—31no—
508C23—61no—
509Q8—21no—
510Q8—122no—
511Q8—362no—
512Q8D3×Dic612yes—
513D4—32no—
514D4—64no—
515D4—61no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—31no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—31no—
522C2×C4—31no—
523C2×C4—64no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—121no—
528C2×C4—122no—
529C2×C4—122no—
530C2×C4—182no—
531C2×C4D3×#6711yescharacteristic
532C2×C4D3×#6711yescharacteristic
533C2×C4C22×D3211yescharacteristic
534C8—62no—
535C8—182no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—62no—
540C2×C3—122no—
541C2×C3D3×C22⋊Q811yescharacteristic
542C2×C3C2×#91611yescharacteristic
543C2×C3#577711yescharacteristic
544C2×C3C2×#92411yescharacteristic
545C2×C3C2×#95011yescharacteristic
546C2×C3#582211yescharacteristic
547D3—22no—
548D3—42no—
549C22—32no—
550C22—61no—
551C22—61no—
552C22—62no—
553C22—121no—
554C22—121no—
555C22C2×D3×#6711yescharacteristic
556C4—22no—
557C4—21no—
558C4—32no—
559C4—41no—
560C4—61no—
561C4—61no—
562C4—121no—
563C4—122no—
564C4—362no—
565C4#6394712yes—
566C4C2×D3×Dic611yescharacteristic
567C4D3×#23511yescharacteristic
568C3—21no—
569C3#8101011yescharacteristic, complemented
570C3#8250711yescharacteristic, complemented
571C2—62no—
572C2—122no—
573C2D3×#92411yescharacteristic
574C2C2×#6394711yescharacteristic
575C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
hypercenterC4×Q8D32
hypocenterC32#3076
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592720C2semidirect
4. C3×#5020C2semidirect
6. #10591545C2semidirect
7. #10590572C2semidirect
8. #10590545C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590269C2semidirect
11. #10590268C2semidirect
56. #5020D3semidirect
71. C3×#239Q8semidirect
229. #239Dic6semidirect
506. C32#3076semidirect
569. C3#81010semidirect
570. C3#82507semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
#105938592
#105927202
C3×#50202
#105915562
#105915452
#105905722
#105905452
D3×C4⋊(C3⋊C8)2
#105902692
#105902682
#825073
#810103