Finite Group Databasebeta

← #11860960

Subgroups — #11860960

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic
2C3×#5827C211yesmaximal, characteristic, complemented
3#10594990C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic, complemented
5#10591541C212yesmaximal, complemented
6#10591536C212yesmaximal, complemented
7#10591404C212yesmaximal, complemented
8#10591401C212yesmaximal, complemented
9C2×#63574C211yesmaximal, characteristic, complemented
10#10591106C211yesmaximal, characteristic, complemented
11#10591057C211yesmaximal, characteristic, complemented
12#82558—31nomaximal
13#78869—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16#64159C418yescomplemented
17C2×#3756C2211yescharacteristic
18C2×#3755C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×Q8×Dic3C2212yes—
23C3×D4×Dic3—22no—
24C3×D4×Dic3C2212yes—
25C3×#926—21no—
26C3×#926C2211yescharacteristic
27C2×C3×C4⋊Dic3—21no—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31#63952—22no—
32#63900—21no—
33#63894C2212yes—
34#63849—21no—
35#63844C2212yes—
36C3×#835C2212yes—
37C3×#832C2212yes—
38#63574C2212yes—
39#63574C2212yes—
40#63567C2212yes—
41#63564C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45#5827D311yescharacteristic, complemented
46C2×#950—31no—
47C2×#950—31no—
48C2×#950—61no—
49#5523—31no—
50#5504—31no—
51C3×#417—31no—
52#5232D311yescharacteristic, complemented
53#5133—31no—
54#5122—31no—
55#5030—32no—
56C4×#215—32no—
57C4×#214—32no—
58#5014—32no—
59#4997—31no—
60#4966—31no—
61C2×#808—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
74C2×#638—21no—
75#3828—22no—
76#3828C2×C414yescomplemented
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—22no—
83C2×#624—22no—
84#3756C2×C414yescomplemented
85#3755C2×C414yescomplemented
86#3754C2×C414yescomplemented
87#3753C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)C2×C414yescomplemented
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90C2×C3⋊(C3⋊C8)C2311yescharacteristic
91C3×#217—22no—
92C3×#217D412yes—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3D411yescharacteristic
97C3×C4⋊Dic3D411yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2312yes—
100C3×C4×Dic3—22no—
101C3×C4×Dic3C2312yes—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3724—22no—
105#3722—22no—
106Dic32—22no—
107#2952—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41C2×D311yescharacteristic
110C2×C3×#41C2×D311yescharacteristic
111C2×#235—31no—
112C2×#235—31no—
113C2×#235—61no—
114C2×C3×M16—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C3×#117—31no—
119C3×#117—61no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—61no—
123#950—38no—
124#950—38no—
125#950—68no—
126Q8×Dic3C2×D312yes—
127C2×#216—31no—
128C2×#216—31no—
129C2×#216—61no—
130C2×#215—31no—
131C2×#215—31no—
132C2×#215—61no—
133D4×Dic3—22no—
134D4×Dic3C2×D312yes—
135C2×#214—31no—
136C2×#214—31no—
137C2×#214—61no—
138C2×#213—31no—
139C2×#213—31no—
140C2×#213—61no—
141C4×#67—62no—
142#926—21no—
143#926C2×D311yescharacteristic
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8—31no—
149C22×C3⋊C8—31no—
150C22×C3⋊C8—61no—
151#893—32no—
152#892—61no—
153#892—61no—
154D3×C4⋊C4—61no—
155D3×C4⋊C4—61no—
156#887—32no—
157#67⋊C4—62no—
158C4×D12—32no—
159C4×Dic6—32no—
160C3×#103—32no—
161C3×#102—32no—
162#835C2×D312yes—
163#832C2×D312yes—
164#821—32no—
165#816—32no—
166#815—32no—
167C8×Dic3—32no—
168#810—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172#808—32no—
173#808—32no—
174#803—32no—
175C4×C3⋊C8—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
190#638—24no—
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C22×C412yes—
194C4×C3⋊D3—24no—
195#634—21no—
196#634C22×C412yes—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—82no—
200C2×C3×Dic3—81no—
201C2×C3×Dic3—81no—
202C2×C3×Dic3C2×D412yes—
203C2×C3×Dic3C2×D412yes—
204#624—82no—
205C3⋊(C3⋊C8)C22×C412yes—
206C3⋊(C3⋊C8)C22×C412yes—
207C3×C3⋊C8—22no—
208C2×#135—91no—
209#520—31no—
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—22no—
220C3×#41—22no—
221C3×#41—24no—
222C3×#41—42no—
223C3×#41C4×D314yescomplemented
224C3×#41C4×D314yescomplemented
225C2×C3×Q8—21no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—41no—
232C2×C3×D4C22×D311yescharacteristic
233C2×C3×D4C22×D311yescharacteristic
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—41no—
238C22×C3×C4—62no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—61no—
244C2×#67—61no—
245C2×#67—121no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249#235—34no—
250#235—34no—
251#235—64no—
252#235—62no—
253#235—62no—
254#235—122no—
255C2×D12—31no—
256C2×D12—31no—
257C2×D12—61no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—121no—
263C2×Dic6—31no—
264C2×Dic6—31no—
265C2×Dic6—61no—
266C3×M16—62no—
267C2×C3×C8—32no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—32no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C22⋊C4—32no—
276C3×C22⋊C4—62no—
277C3×C42—32no—
278C3×C42—62no—
279#217—22no—
280#217#6712yes—
281#216—34no—
282#216—34no—
283#216—64no—
284#215—34no—
285#215—34no—
286#215—64no—
287#214—34no—
288#214—34no—
289#214—64no—
290#213—34no—
291#213—34no—
292#213—64no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—22no—
298C4⋊Dic3#6711yescharacteristic
299C4⋊Dic3#6711yescharacteristic
300C4⋊Dic3C22×D312yes—
301C4⋊Dic3C22×D312yes—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304C4×Dic3—22no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3C22×D312yes—
308#208—22no—
309C2×C3⋊C8—34no—
310C2×C3⋊C8—34no—
311C2×C3⋊C8—31no—
312C2×C3⋊C8—31no—
313C2×C3⋊C8—31no—
314C2×C3⋊C8—31no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8—64no—
317C2×C3⋊C8—61no—
318C2×C3⋊C8C22×D312yes—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—22no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32C4×D412yes—
325C22×C32C22×D411yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C32×C4—22no—
330C32×C4C4×D412yes—
331C32×C4C23×C411yescharacteristic
332C32×C4C2×#4111yescharacteristic
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C3×Dic3—42no—
338C2×#41—91no—
339C2×#41D3211yescharacteristic
340#135—98no—
341C2×Q16—91no—
342C2×SD16—91no—
343C2×SD16—91no—
344C2×D8—91no—
345C2×M16—31no—
346C22×C8—91no—
347C4×Q8—32no—
348C4×Q8—92no—
349C4×D4—32no—
350C4×D4—62no—
351C4×D4—92no—
352C4×D4—182no—
353#117—31no—
354#117—61no—
355#117—181no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—181no—
360#106—92no—
361#106—92no—
362#103—32no—
363#103—92no—
364#102—32no—
365#102—92no—
366#97—92no—
367C4×C8—92no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—41no—
372C23×C3D3×D411yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—121no—
377C3×Q8—21no—
378C3×Q8—21no—
379C3×Q8—22no—
380C3×Q8—41no—
381C3×Q8C2×C4×D312yes—
382C3×Q8C2×C4×D312yes—
383C3×D4—24no—
384C3×D4—24no—
385C3×D4—21no—
386C3×D4—21no—
387C3×D4—22no—
388C3×D4—41no—
389C3×D4—44no—
390C3×D4C2×C4×D312yes—
391C3×D4C2×C4×D312yes—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—32no—
401C2×C3×C4—32no—
402C2×C3×C4—44no—
403C2×C3×C4—41no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—242no—
407C2×C3×C4—241no—
408C2×C3×C4—241no—
409C2×C3×C4C2×C4×D312yes—
410C2×C3×C4C2×C4×D312yes—
411C2×C3×C4#23512yes—
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4#23712yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—64no—
418#67—64no—
419#67—124no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—82no—
425C2×Dic3—81no—
426C2×Dic3—81no—
427C2×Dic3—121no—
428C2×Dic3C2×#6712yes—
429C2×Dic3C2×#6712yes—
430D12—32no—
431D12—32no—
432D12—62no—
433D12—61no—
434D12—61no—
435D12—121no—
436C4×D3—64no—
437C4×D3—64no—
438C4×D3—124no—
439C4×D3—242no—
440C4×D3—242no—
441Dic6—32no—
442Dic6—32no—
443Dic6—62no—
444Dic6—61no—
445Dic6—61no—
446Dic6—121no—
447C3×C8—62no—
448C3⋊C8—22no—
449C3⋊C8—32no—
450C3⋊C8—32no—
451C3⋊C8—32no—
452C3⋊C8—32no—
453C3⋊C8—62no—
454C3⋊C8—62no—
455C2×C32—22no—
456C2×C32—42no—
457C2×C32C2×C4×D411yescharacteristic
458C2×C32#57711yescharacteristic
459C2×C32#57711yescharacteristic
460C3⋊D3—42no—
461#41—22no—
462#41—94no—
463#41—182no—
464#41#62414yescomplemented
465C2×Q8—91no—
466C2×Q8C2×D3211yescharacteristic
467C2×D4—21no—
468C2×D4—91no—
469C2×D4—181no—
470C2×D4C2×D3211yescharacteristic
471C22×C4—21no—
472C22×C4—62no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—182no—
476C22×C4—181no—
477C22×C4C2×D3211yescharacteristic
478Q16—94no—
479SD16—94no—
480SD16—94no—
481D8—94no—
482M16—62no—
483C2×C8—32no—
484C2×C8—91no—
485C2×C8—91no—
486C2×C8—94no—
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—32no—
490C4⋊C4—32no—
491C4⋊C4—62no—
492C4⋊C4—61no—
493C4⋊C4—61no—
494C4⋊C4—182no—
495C22⋊C4—32no—
496C22⋊C4—62no—
497C22⋊C4—182no—
498C42—32no—
499C42—62no—
500C42—182no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—42no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3#67⋊C412yes—
519C22×C3C4×#6712yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—241no—
530C2×D3—241no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—42no—
537C3×C4—62no—
538C3×C4—62no—
539C3×C4—122no—
540C3×C4—122no—
541C3×C4#67⋊C412yes—
542C3×C4C4×#6712yes—
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C2×#23511yescharacteristic
546C3×C4C2×#23711yescharacteristic
547Dic3—22no—
548Dic3—22no—
549Dic3—42no—
550Dic3—42no—
551Dic3—62no—
552Dic3—62no—
553Dic3—122no—
554C32#295211yescharacteristic, complemented, Sylow
555C23—21no—
556C23—181no—
557C23D3×#6711yescharacteristic
558Q8—21no—
559Q8—92no—
560Q8—181no—
561Q8C2×#62412yes—
562D4—24no—
563D4—21no—
564D4—92no—
565D4—184no—
566D4—181no—
567D4C2×#62412yes—
568C2×C4—21no—
569C2×C4—24no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—181no—
575C2×C4—184no—
576C2×C4—242no—
577C2×C4—241no—
578C2×C4—241no—
579C2×C4—722no—
580C2×C4#380412yes—
581C2×C4C2×#62412yes—
582C2×C4D3×#6711yescharacteristic
583C2×C4C22×D3211yescharacteristic
584C8—62no—
585C8—92no—
586C8—92no—
587C2×C3—22no—
588C2×C3—22no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—42no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—82no—
596C2×C3C2×#67⋊C411yescharacteristic
597C2×C3#577511yescharacteristic
598C2×C3#577811yescharacteristic
599C2×C3C2×C4×#6711yescharacteristic
600C2×C3#583611yescharacteristic
601C2×C3#583711yescharacteristic
602D3—122no—
603D3—122no—
604D3—242no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—182no—
611C22—361no—
612C22—361no—
613C22#6395212yes—
614C22C2×D3×#6711yescharacteristic
615C4—22no—
616C4—62no—
617C4—62no—
618C4—122no—
619C4—122no—
620C4—182no—
621C4#6395212yes—
622C4C2×#380411yescharacteristic
623C4C22×#62411yescharacteristic
624C3—21no—
625C3#7886911yescharacteristic, complemented
626C3#8255811yescharacteristic, complemented
627C2—22no—
628C2—42no—
629C2—362no—
630C2#1059545511yescharacteristic
631C2#1059546411yescharacteristic
632C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×#64159C2
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
2. C3×#5827C2semidirect
3. #10594990C2semidirect
4. C3×#5232C2semidirect
5. #10591541C2semidirect
6. #10591536C2semidirect
7. #10591404C2semidirect
8. #10591401C2semidirect
9. C2×#63574C2semidirect
10. #10591106C2semidirect
11. #10591057C2semidirect
16. #64159C4semidirect
45. #5827D3semidirect
52. #5232D3semidirect
68. C32×#41C2×C4semidirect
76. #3828C2×C4semidirect
84. #3756C2×C4semidirect
85. #3755C2×C4semidirect
86. #3754C2×C4semidirect
87. #3753C2×C4semidirect
88. C2×C3⋊(C3⋊C8)C2×C4semidirect
223. C3×#41C4×D3semidirect
224. C3×#41C4×D3semidirect
464. #41#624semidirect
554. C32#2952semidirect
625. C3#78869semidirect
626. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58272
#105949902
C3×#52322
#105915412
#105915362
#105914042
#105914012
C2×#635742
#105911062
#105910572
#825583
#788693