Finite Group Databasebeta

← #11860959

Subgroups — #11860959

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3#10594986C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591582C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10591445C212yesmaximal, complemented
8#10591436C212yesmaximal, complemented
9C2×#63573C211yesmaximal, characteristic, complemented
10#10591088C211yesmaximal, characteristic, complemented
11#10591059C211yesmaximal, characteristic, complemented
12#83899—31nomaximal
13#78869—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16Q8×C3⋊Dic3C2212yes—
17D4×C3⋊Dic3—22no—
18D4×C3⋊Dic3C2212yes—
19#64135—21no—
20#64135C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#950C418yescomplemented
24C2×C3×#216C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31Dic3×#67—22no—
32#63898C2212yes—
33D3×C4⋊Dic3—21no—
34#63843C2212yes—
35#63841—21no—
36C3×#835C2212yes—
37C3×#832C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#63553C2212yes—
44C2×C3×#135—31no—
45#5827—31no—
46#5827—31no—
47#5827—31no—
48#5827—61no—
49C2×#950D311yescharacteristic
50#5504—31no—
51C3×#417—31no—
52#5232—31no—
53#5232D311yescharacteristic, complemented
54#5184—32no—
55Dic3×SD16—32no—
56Dic3×SD16—32no—
57#5152—32no—
58#5133—31no—
59#5122—31no—
60C2×#817—31no—
61#5101—31no—
62C2×#808—31no—
63#4789—32no—
64#4788—32no—
65#4785—32no—
66#4758—32no—
67C32×#41—22no—
68C32×#41C2×C414yescomplemented
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—21no—
75C22×C3⋊Dic3—22no—
76C2×C3×#67—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235C2×C414yescomplemented
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6C2311yescharacteristic
83C2×D3×Dic3—22no—
84#3757—22no—
85#3757D412yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)D411yescharacteristic
89C4⋊(C3⋊Dic3)D411yescharacteristic
90C4⋊(C3⋊Dic3)C2312yes—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3C2312yes—
93C3×#216C2×C414yescomplemented
94C3×#215C2×C414yescomplemented
95C3×#214C2×C414yescomplemented
96C3×#213C2×C414yescomplemented
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2312yes—
99C3×#208—22no—
100C2×C3×C3⋊C8C2×C414yescomplemented
101C2×C3×C3⋊C8C2312yes—
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107#2952—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#135—38no—
114C2×C3×Q16—31no—
115C2×C3×SD16—31no—
116C2×C3×SD16—31no—
117C2×C3×D8—31no—
118C2×C3×M16—31no—
119C22×C3×C8—31no—
120C2×C3×C4⋊C4—31no—
121#950Dic318yescomplemented
122Q8×Dic3—32no—
123Q8×Dic3—32no—
124Q8×Dic3—32no—
125Q8×Dic3—62no—
126C2×#216C2×D311yescharacteristic
127C2×#215C2×D311yescharacteristic
128D4×Dic3—32no—
129D4×Dic3—32no—
130D4×Dic3—32no—
131D4×Dic3—62no—
132D4×Dic3—62no—
133D4×Dic3—62no—
134D4×Dic3—62no—
135D4×Dic3—64no—
136C2×#214C2×D311yescharacteristic
137C2×#213C2×D311yescharacteristic
138C4×#67—62no—
139#926—31no—
140#926—31no—
141#926—61no—
142#926—61no—
143#926—61no—
144#926—61no—
145#926—62no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—61no—
149C2×C4⋊Dic3—61no—
150C2×C4⋊Dic3—61no—
151C2×C4⋊Dic3—61no—
152C2×C4⋊Dic3—62no—
153C2×C4⋊Dic3C2×D311yescharacteristic
154C2×#208C2×D311yescharacteristic
155C22×C3⋊C8C2×D311yescharacteristic
156#893—32no—
157#892—61no—
158D3×C4⋊C4—61no—
159#887—32no—
160C3×#103—32no—
161C3×#102—32no—
162#835—32no—
163#835C2×D312yes—
164#832—32no—
165#832C2×D312yes—
166#821—32no—
167#817—32no—
168#817—32no—
169#816—32no—
170#815—32no—
171#815—32no—
172C8×Dic3—32no—
173C8×Dic3—32no—
174#808—32no—
175#808—32no—
176C23×C32—21no—
177C23×C32C2×D411yescharacteristic
178C22×C3×D3—21no—
179C32×Q8—21no—
180C32×Q8C22×C412yes—
181C32×D4—24no—
182C32×D4—21no—
183C32×D4C22×C412yes—
184C2×C32×C4—21no—
185C2×C32×C4—24no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—82no—
192C2×C3⋊Dic3—81no—
193C2×C3⋊Dic3C2×D412yes—
194C2×C3⋊Dic3C2×D412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—81no—
199C3×D12—21no—
200C3×D12C22×C412yes—
201C3×C4×D3—24no—
202C3×Dic6—21no—
203C3×Dic6C22×C412yes—
204D3×Dic3—82no—
205C3×C3⋊C8—22no—
206C3×C3⋊C8C22×C412yes—
207C3×C3⋊C8C22×C412yes—
208C2×#135—31no—
209#520—91no—
210#520—91no—
211#442—92no—
212#441—92no—
213C4×SD16—92no—
214C4×SD16—92no—
215C2×#106—91no—
216#417—31no—
217#417—91no—
218#405—91no—
219C3×#41—24no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—24no—
223C3×#41—34no—
224C3×#41—62no—
225C3×#41C4×D314yescomplemented
226C3×#41C2×Dic314yescomplemented
227C2×C3×Q8—21no—
228C2×C3×Q8—31no—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—31no—
236C2×C3×D4—61no—
237C2×C3×D4C22×D311yescharacteristic
238C2×C3×D4C22×D311yescharacteristic
239C22×C3×C4—22no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—21no—
248C22×Dic3—21no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—64no—
253C22×Dic3—62no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256#235—22no—
257#235C2×Dic314yescomplemented
258C2×D12C22×D311yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—62no—
261C2×Dic6C22×D311yescharacteristic
262C3×Q16—34no—
263C3×SD16—34no—
264C3×SD16—34no—
265C3×D8—34no—
266C3×M16—62no—
267C2×C3×C8—34no—
268C2×C3×C8—31no—
269C2×C3×C8—31no—
270C2×C3×C8—32no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—61no—
273#217—32no—
274#217—32no—
275#217—62no—
276#217—62no—
277#217—62no—
278#217—62no—
279#217—64no—
280#216C2×Dic314yescomplemented
281#215C2×Dic314yescomplemented
282#214C2×Dic314yescomplemented
283#213C2×Dic314yescomplemented
284(C2×D3)⋊C4—62no—
285C4⋊Dic3—21no—
286C4⋊Dic3—31no—
287C4⋊Dic3—31no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—32no—
291C4⋊Dic3—32no—
292C4⋊Dic3—61no—
293C4⋊Dic3—62no—
294C4⋊Dic3—61no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3—64no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3C22×D312yes—
303Dic3⋊C4—62no—
304C4×Dic3—32no—
305C4×Dic3—32no—
306C4×Dic3—62no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3—62no—
310C4×Dic3—62no—
311C4×Dic3—64no—
312#208—22no—
313C2×C3⋊C8C2×Dic314yescomplemented
314C2×C3⋊C8C22×D312yes—
315C2×C3⋊C8C22×D311yescharacteristic
316C2×C3⋊C8C22×D311yescharacteristic
317C22×C32—22no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32C4×D412yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C32×C4—22no—
328C32×C4C4×D412yes—
329C32×C4C23×C411yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—22no—
332C3⋊Dic3—22no—
333C3⋊Dic3—42no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—31no—
337C2×#41D3211yescharacteristic
338#135—38no—
339C2×Q16—31no—
340C2×SD16—31no—
341C2×SD16—31no—
342C2×D8—31no—
343C2×M16—31no—
344C22×C8—31no—
345C4×Q8—92no—
346C4×Q8—92no—
347C4×D4—92no—
348C4×D4—92no—
349C4×D4—182no—
350C4×D4—182no—
351#117—91no—
352#117—181no—
353#117—181no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—181no—
357C2×C4⋊C4—181no—
358#106—92no—
359#106—92no—
360#103—32no—
361#103—92no—
362#102—32no—
363#102—92no—
364#97—92no—
365C4×C8—92no—
366C23×C3—22no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—61no—
371C23×C3D3×D411yescharacteristic
372C23×C3D3×D411yescharacteristic
373C22×D3—21no—
374C3×Q8—22no—
375C3×Q8—21no—
376C3×Q8—21no—
377C3×Q8—22no—
378C3×Q8—32no—
379C3×Q8—61no—
380C3×Q8C2×C4×D312yes—
381C3×Q8C22×Dic312yes—
382C3×D4—28no—
383C3×D4—22no—
384C3×D4—24no—
385C3×D4—24no—
386C3×D4—21no—
387C3×D4—21no—
388C3×D4—22no—
389C3×D4—32no—
390C3×D4—64no—
391C3×D4—61no—
392C3×D4C2×C4×D312yes—
393C3×D4C22×Dic312yes—
394C2×C3×C4—22no—
395C2×C3×C4—28no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—61no—
405C2×C3×C4—64no—
406C2×C3×C4—62no—
407C2×C3×C4—241no—
408C2×C3×C4C2×C4×D312yes—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4#23712yes—
412C2×C3×C4#23712yes—
413C2×C3×C4C22×Dic312yes—
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—24no—
417C2×Dic3—21no—
418C2×Dic3—22no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—81no—
429C2×Dic3—242no—
430C2×Dic3—242no—
431C2×Dic3—242no—
432C2×Dic3—241no—
433C2×Dic3—241no—
434C2×Dic3—244no—
435C2×Dic3—242no—
436D12—21no—
437D12C22×Dic312yes—
438C4×D3—24no—
439C4×D3—242no—
440Dic6—21no—
441Dic6C22×Dic312yes—
442C3×C8—32no—
443C3×C8—32no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8C22×Dic312yes—
447C3⋊C8C22×Dic312yes—
448C2×C32—22no—
449C2×C32—42no—
450C2×C32C2×C4×D411yescharacteristic
451C2×C32#57711yescharacteristic
452C2×C32#57711yescharacteristic
453C3×D3—42no—
454#41—22no—
455#41—34no—
456#41—62no—
457#41D3×Dic314yescomplemented
458C2×Q8—31no—
459C2×Q8C2×D3211yescharacteristic
460C2×D4—21no—
461C2×D4—31no—
462C2×D4—61no—
463C2×D4C2×D3211yescharacteristic
464C22×C4—21no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4—181no—
470C22×C4C2×D3211yescharacteristic
471Q16—34no—
472SD16—34no—
473SD16—34no—
474D8—34no—
475M16—62no—
476C2×C8—31no—
477C2×C8—31no—
478C2×C8—34no—
479C2×C8—32no—
480C4⋊C4—32no—
481C4⋊C4—61no—
482C4⋊C4—91no—
483C4⋊C4—91no—
484C4⋊C4—92no—
485C4⋊C4—182no—
486C4⋊C4—182no—
487C4⋊C4—181no—
488C22⋊C4—92no—
489C22⋊C4—182no—
490C22⋊C4—182no—
491C42—92no—
492C42—182no—
493C42—182no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—24no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—22no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—62no—
512C22×C3—121no—
513C22×C3—121no—
514C22×C3#67⋊C412yes—
515C22×C3D4×Dic312yes—
516C22×C3C2×D3×D411yescharacteristic
517C22×C3C2×D3×D411yescharacteristic
518C2×D3—22no—
519C2×D3—41no—
520C2×D3—41no—
521C3×C4—24no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—22no—
527C3×C4—62no—
528C3×C4—122no—
529C3×C4#67⋊C412yes—
530C3×C4D4×Dic312yes—
531C3×C4C22×C4×D311yescharacteristic
532C3×C4C2×#23711yescharacteristic
533C3×C4C2×#23711yescharacteristic
534C3×C4C23×Dic311yescharacteristic
535Dic3—22no—
536Dic3—42no—
537Dic3—62no—
538Dic3—62no—
539Dic3—62no—
540Dic3—62no—
541Dic3—122no—
542Dic3—122no—
543Dic3—124no—
544Dic3—122no—
545Dic3—122no—
546C32#295211yescharacteristic, complemented, Sylow
547C23—21no—
548C23—61no—
549C23#381111yescharacteristic
550Q8—21no—
551Q8—32no—
552Q8—61no—
553Q8C2×D3×Dic312yes—
554D4—24no—
555D4—21no—
556D4—32no—
557D4—64no—
558D4—61no—
559D4C2×D3×Dic312yes—
560C2×C4—21no—
561C2×C4—24no—
562C2×C4—61no—
563C2×C4—64no—
564C2×C4—62no—
565C2×C4—92no—
566C2×C4—92no—
567C2×C4—182no—
568C2×C4—241no—
569C2×C4—722no—
570C2×C4—722no—
571C2×C4—721no—
572C2×C4C2×D3×Dic312yes—
573C2×C4#380512yes—
574C2×C4#381111yescharacteristic
575C2×C4C22×D3211yescharacteristic
576C8—32no—
577C8—32no—
578C8—62no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—42no—
585C2×C3—44no—
586C2×C3—42no—
587C2×C3—42no—
588C2×C3—122no—
589C2×C3C2×#67⋊C411yescharacteristic
590C2×C3#577011yescharacteristic
591C2×C3#577011yescharacteristic
592C2×C3#577511yescharacteristic
593C2×C3#577811yescharacteristic
594C2×C3C2×D4×Dic311yescharacteristic
595D3—42no—
596C22—21no—
597C22—21no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—62no—
602C22—121no—
603C22—121no—
604C22#67⋊Dic312yes—
605C22C2×#381111yescharacteristic
606C4—22no—
607C4—62no—
608C4—122no—
609C4—182no—
610C4—182no—
611C4—362no—
612C4#67⋊Dic312yes—
613C4C22×D3×Dic311yescharacteristic
614C4C2×#380511yescharacteristic
615C3—21no—
616C3#7886911yescharacteristic, complemented
617C3#8389911yescharacteristic, complemented
618C2—22no—
619C2—42no—
620C2—122no—
621C2#1059546211yescharacteristic
622C2#1059547311yescharacteristic
623C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
3. #10594986C2semidirect
4. C3×#5232C2semidirect
5. #10591582C2semidirect
6. #10591571C2semidirect
7. #10591445C2semidirect
8. #10591436C2semidirect
9. C2×#63573C2semidirect
10. #10591088C2semidirect
11. #10591059C2semidirect
23. C3×#950C4semidirect
53. #5232D3semidirect
68. C32×#41C2×C4semidirect
79. C3×#235C2×C4semidirect
93. C3×#216C2×C4semidirect
94. C3×#215C2×C4semidirect
95. C3×#214C2×C4semidirect
96. C3×#213C2×C4semidirect
100. C2×C3×C3⋊C8C2×C4semidirect
121. #950Dic3semidirect
225. C3×#41C4×D3semidirect
226. C3×#41C2×Dic3semidirect
257. #235C2×Dic3semidirect
280. #216C2×Dic3semidirect
281. #215C2×Dic3semidirect
282. #214C2×Dic3semidirect
283. #213C2×Dic3semidirect
313. C2×C3⋊C8C2×Dic3semidirect
457. #41D3×Dic3semidirect
546. C32#2952semidirect
616. C3#78869semidirect
617. C3#83899semidirect

Maximal subgroups

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

subgroupindex
#105962982
C2×C3×#9502
#105949862
C3×#52322
#105915822
#105915712
#105914452
#105914362
C2×#635732
#105910882
#105910592
#838993
#788693