Finite Group Databasebeta

← #11865786

Subgroups — #11865786

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C2×#63822C212yesmaximal, complemented
4C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
5#10591083C212yesmaximal, complemented
6#10590384C211yesmaximal, characteristic, complemented
7#10590364C211yesmaximal, characteristic, complemented
8#10590363C211yesmaximal, characteristic, complemented
9#10590348C212yesmaximal, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590267C212yesmaximal, complemented
12#83296—31nomaximal
13#82525—31nomaximal
14C2×C3×#235C2212yes—
15C2×C3×#235C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2212yes—
18C3×#930—21no—
19C3×#930—21no—
20C3×C4×#67—21no—
21C3×C4×#67—21no—
22C3×#926C2211yescharacteristic
23C3×#875C2212yes—
24C3×#874C2211yescharacteristic
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×#872—21no—
30C3×C42×D3—21no—
31C3×#869C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C2×#3718C2212yes—
35C2×#3715C2212yes—
36C2×#3715C2212yes—
37#63822—28no—
38C2×#3713C2212yes—
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#63565C2212yes—
43#63565C2212yes—
44#63562C2212yes—
45#63562C2212yes—
46C3×#532—31no—
47C3×C4×#41—31no—
48C2×#950—32no—
49C2×#950—32no—
50#5477D311yescharacteristic, complemented
51C4×#235D311yescharacteristic, complemented
52#5233—32no—
53#5090—31no—
54#5083—31no—
55#5075—31no—
56#5072—31no—
57#5057—32no—
58#5054—32no—
59#5031—31no—
60#5028—32no—
61#5027—31no—
62#5019—31no—
63#5016—32no—
64#5015—31no—
65#5002—32no—
66C2×C4⋊(C3⋊C8)—31no—
67C2×C4⋊(C3⋊C8)—31no—
68C2×C4⋊(C3⋊C8)—61no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—21no—
73C2×C3×#67—22no—
74C3×#235—22no—
75C3×#235—24no—
76C3×#235—24no—
77C3×#235D414yescomplemented
78C2×C3×D12—21no—
79C2×C3×D12—21no—
80C2×C3×D12C2312yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—22no—
86C2×C3×Dic6C2312yes—
87C2×C3×Dic6C2311yescharacteristic
88C32×C42D411yescharacteristic
89C32×C42D411yescharacteristic
90C32×C42C2311yescharacteristic
91C32×C42C2311yescharacteristic
92C2×C3⋊(C3⋊C8)—24no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—22no—
99C3×(C2×D3)⋊C4—22no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3—21no—
102C3×C4⋊Dic3C2311yescharacteristic
103C3×C4⋊Dic3C2311yescharacteristic
104C3×Dic3⋊C4—21no—
105C3×Dic3⋊C4—21no—
106C3×C4×Dic3—21no—
107C3×C4×Dic3—21no—
108C3×C4×Dic3—21no—
109#3718—24no—
110#3715—24no—
111#3715—24no—
112#3713—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×C3×#41—32no—
116C2×#235C2×D312yes—
117C2×#235C2×D311yescharacteristic
118C3×C4⋊Q8—31no—
119C3×#127—31no—
120C3×#124—32no—
121C3×#121—61no—
122C3×#121—61no—
123C3×C4×Q8—31no—
124C3×C4×Q8—31no—
125C3×C4×D4—31no—
126C3×C4×D4—31no—
127C3×C4×D4—61no—
128C3×C4×D4—61no—
129C3×C4×D4—61no—
130C3×C4×D4—61no—
131C3×#117—31no—
132C3×#117—61no—
133C2×C3×C42—21no—
134C2×C3×C42—61no—
135C2×C3×C42C2×D311yescharacteristic
136C2×C3×C42C2×D311yescharacteristic
137#950—68no—
138#950—68no—
139C2×#216—32no—
140C2×#216—32no—
141C2×#215—32no—
142C2×#215—32no—
143C2×#214—32no—
144C2×#214—32no—
145C2×#213—32no—
146C2×#213—32no—
147#930—21no—
148#930—21no—
149C4×#67—21no—
150C4×#67—21no—
151#926C2×D311yescharacteristic
152C22×C3⋊C8—32no—
153C22×C3⋊C8—32no—
154C22×C3⋊C8—62no—
155#875C2×D312yes—
156#874C2×D311yescharacteristic
157C4×D12—21no—
158C4×D12—21no—
159C4×D12C2×D311yescharacteristic
160C4×D12C2×D311yescharacteristic
161#872—21no—
162C42×D3—21no—
163#869C2×D311yescharacteristic
164C4×Dic6C2×D311yescharacteristic
165C4×Dic6C2×D311yescharacteristic
166#835—32no—
167#835—32no—
168#832—32no—
169#832—32no—
170#810—32no—
171#810—32no—
172#809—32no—
173#809—32no—
174C4⋊(C3⋊C8)—31no—
175C4⋊(C3⋊C8)—32no—
176C4⋊(C3⋊C8)—31no—
177C4⋊(C3⋊C8)—32no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—61no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)—62no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—21no—
185C22×C3×D3—22no—
186C2×C32×C4—22no—
187C2×C32×C4—41no—
188C2×C32×C4C2×D412yes—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4#4112yes—
195C2×C32×C4C2411yescharacteristic
196C3×#67—24no—
197C3×#67—44no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—22no—
202C3×D12—22no—
203C3×D12—21no—
204C3×D12—22no—
205C3×D12—42no—
206C3×D12—42no—
207C3×D12C2×D412yes—
208C3×C4×D3—24no—
209C3×C4×D3—42no—
210C3×C4×D3—44no—
211C3×C4×D3—42no—
212C3×Dic6—21no—
213C3×Dic6—22no—
214C3×Dic6—22no—
215C3×Dic6C2×D412yes—
216C3⋊(C3⋊C8)—22no—
217C3⋊(C3⋊C8)—22no—
218C2×#135—92no—
219#532—31no—
220C4×#41—31no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—91no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—34no—
230C3×#41—62no—
231C3×#41—64no—
232C3×#41—64no—
233C2×C3×Q8—31no—
234C2×C3×Q8—32no—
235C2×C3×D4—31no—
236C2×C3×D4—32no—
237C2×C3×D4—61no—
238C2×C3×D4—62no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—62no—
248C22×C3×C4#6711yescharacteristic
249C22×C3×C4#6711yescharacteristic
250C22×C3×C4#6711yescharacteristic
251C22×C3×C4#6711yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—21no—
255C2×#67—22no—
256#235—22no—
257#235—24no—
258#235—24no—
259#235D1214yescomplemented
260C2×D12—21no—
261C2×D12—21no—
262C2×D12C22×D312yes—
263C2×D12C22×D311yescharacteristic
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—22no—
268C2×Dic6C22×D312yes—
269C2×Dic6C22×D311yescharacteristic
270C3×C4⋊C4—31no—
271C3×C4⋊C4—31no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—61no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4—62no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—61no—
286C3×C42—61no—
287C3×C42—61no—
288C3×C42#6711yescharacteristic
289C3×C42#6711yescharacteristic
290C3×C42#6711yescharacteristic
291C3×C42#6711yescharacteristic
292C3×C42C22×D311yescharacteristic
293C3×C42C22×D311yescharacteristic
294C3×C42C22×D311yescharacteristic
295C3×C42C22×D311yescharacteristic
296#217—21no—
297#216—64no—
298#216—64no—
299#215—64no—
300#215—64no—
301#214—64no—
302#214—64no—
303#213—64no—
304#213—64no—
305(C2×D3)⋊C4—21no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—22no—
308(C2×D3)⋊C4—22no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C22×D311yescharacteristic
312C4⋊Dic3C22×D311yescharacteristic
313Dic3⋊C4—21no—
314Dic3⋊C4—21no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3—21no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—32no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8—62no—
324C2×C3⋊C8—64no—
325C2×C3⋊C8—64no—
326C2×C3⋊C8—124no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32#12112yes—
330C22×C32C22×D411yescharacteristic
331C2×C3×D3—22no—
332C2×C3×D3—41no—
333C2×C3×D3—41no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3—42no—
337C32×C4—21no—
338C32×C4—21no—
339C32×C4—21no—
340C32×C4#12112yes—
341C32×C4#13512yescomplemented
342C32×C4C22×D411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3×Dic3—22no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3—41no—
348C2×#41—31no—
349C2×#41—32no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8—31no—
357#127—31no—
358#124—32no—
359#121—61no—
360#121—61no—
361C4×Q8—31no—
362C4×Q8—31no—
363C4×D4—31no—
364C4×D4—31no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—61no—
368C4×D4—61no—
369#117—31no—
370#117—61no—
371C2×C42—61no—
372C2×C42D3211yescharacteristic
373C4⋊C8—91no—
374C4⋊C8—91no—
375C4⋊C8—92no—
376#103—92no—
377#103—92no—
378#102—92no—
379#102—92no—
380C23×C3—21no—
381C23×C3—61no—
382C23×C3—62no—
383C23×C3C2×#6711yescharacteristic
384C23×C3C2×#6711yescharacteristic
385C22×D3—21no—
386C22×D3—22no—
387C3×Q8—32no—
388C3×Q8—61no—
389C3×Q8—62no—
390C3×Q8—62no—
391C3×D4—32no—
392C3×D4—64no—
393C3×D4—62no—
394C3×D4—62no—
395C3×D4—61no—
396C3×D4—122no—
397C3×D4—124no—
398C3×D4—122no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—42no—
413C2×C3×C4—61no—
414C2×C3×C4—64no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—62no—
418C2×C3×C4—122no—
419C2×C3×C4—124no—
420C2×C3×C4—122no—
421C2×C3×C4C2×D1212yes—
422C2×C3×C4#23512yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4#23712yes—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×#6711yescharacteristic
435C2×C3×C4C23×D311yescharacteristic
436C2×C3×C4C23×D311yescharacteristic
437#67—24no—
438#67—44no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—22no—
443D12—21no—
444D12—22no—
445D12—22no—
446D12—42no—
447D12—42no—
448D12C2×D1212yes—
449C4×D3—24no—
450C4×D3—42no—
451C4×D3—44no—
452C4×D3—42no—
453Dic6—21no—
454Dic6—22no—
455Dic6—22no—
456Dic6C2×D1212yes—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C3⋊C8—62no—
460C3⋊C8—62no—
461C3⋊C8—122no—
462C3⋊C8—122no—
463C2×C32—22no—
464C2×C32C2×#12111yescharacteristic
465C2×C32C2×#13511yescharacteristic
466C2×C32#57511yescharacteristic
467C3×D3—42no—
468C3×D3—82no—
469#41—34no—
470#41—62no—
471#41—64no—
472#41—64no—
473C2×Q8—31no—
474C2×Q8—32no—
475C2×D4—31no—
476C2×D4—32no—
477C2×D4—61no—
478C2×D4—62no—
479C2×D4—61no—
480C2×D4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—62no—
485C22×C4#62511yescharacteristic
486C22×C4#62511yescharacteristic
487C22×C4C2×D3211yescharacteristic
488Q16—184no—
489SD16—184no—
490SD16—184no—
491D8—184no—
492C2×C8—92no—
493C2×C8—92no—
494C2×C8—184no—
495C4⋊C4—31no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4—61no—
501C22⋊C4—61no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C22⋊C4—62no—
505C22⋊C4—62no—
506C42—61no—
507C42—61no—
508C42—61no—
509C42#62511yescharacteristic
510C42#62511yescharacteristic
511C42C2×D3211yescharacteristic
512C42C2×D3211yescharacteristic
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—62no—
522C22×C3—121no—
523C22×C3—121no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3#93012yes—
528C22×C3#93812yes—
529C22×C3C22×#6711yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—22no—
532C2×D3—41no—
533C2×D3—41no—
534C2×D3—42no—
535C2×D3—42no—
536C2×D3—42no—
537C3×C4—22no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—62no—
551C3×C4—122no—
552C3×C4—121no—
553C3×C4—121no—
554C3×C4#93012yes—
555C3×C4#93812yes—
556C3×C4#95012yescomplemented
557C3×C4#95012yescomplemented
558C3×C4C22×D1211yescharacteristic
559C3×C4C2×#23511yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4C2×#23711yescharacteristic
562Dic3—22no—
563Dic3—42no—
564Dic3—41no—
565Dic3—41no—
566C32#303511yescharacteristic, complemented, Sylow
567C23—61no—
568C23—62no—
569C23C2×#62511yescharacteristic
570Q8—32no—
571Q8—61no—
572Q8—62no—
573Q8—62no—
574D4—32no—
575D4—64no—
576D4—61no—
577D4—62no—
578D4—62no—
579D4—122no—
580D4—124no—
581D4—122no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—61no—
585C2×C4—64no—
586C2×C4—61no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—122no—
590C2×C4—122no—
591C2×C4—124no—
592C2×C4#379512yes—
593C2×C4D3×D1212yes—
594C2×C4C2×#62511yescharacteristic
595C2×C4C2×#62511yescharacteristic
596C2×C4C2×#62511yescharacteristic
597C2×C4C2×#62511yescharacteristic
598C2×C4C2×#62511yescharacteristic
599C2×C4C22×D3211yescharacteristic
600C8—182no—
601C8—182no—
602C2×C3—24no—
603C2×C3—22no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—122no—
609C2×C3—242no—
610C2×C3C2×#93011yescharacteristic
611C2×C3C2×#93811yescharacteristic
612C2×C3C2×#95011yescharacteristic
613C2×C3C2×#95011yescharacteristic
614C2×C3#582211yescharacteristic
615C2×C3#582211yescharacteristic
616D3—42no—
617D3—82no—
618C22—21no—
619C22—21no—
620C22—62no—
621C22—121no—
622C22—121no—
623C22—122no—
624C22—122no—
625C22—122no—
626C22#6390812yes—
627C22C22×#62511yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—62no—
632C4—122no—
633C4—121no—
634C4—121no—
635C4#6382212yescomplemented
636C4#6390812yes—
637C4C2×#379511yescharacteristic
638C4C2×D3×D1211yescharacteristic
639C3—21no—
640C3#8252511yescharacteristic, complemented
641C3#8329611yescharacteristic, complemented
642C2—22no—
643C2—122no—
644C2—242no—
645C2C2×#6382211yescharacteristic
646C2#1059478611yescharacteristic
647C2C2×#6390811yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5477C2semidirect
2. C3×C4×#235C2semidirect
3. C2×#63822C2semidirect
4. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
5. #10591083C2semidirect
6. #10590384C2semidirect
7. #10590364C2semidirect
8. #10590363C2semidirect
9. #10590348C2semidirect
10. #10590347C2semidirect
11. #10590267C2semidirect
50. #5477D3semidirect
51. C4×#235D3semidirect
77. C3×#235D4semidirect
259. #235D12semidirect
341. C32×C4#135semidirect
556. C3×C4#950semidirect
557. C3×C4#950semidirect
566. C32#3035semidirect
635. C4#63822semidirect
640. C3#82525semidirect
641. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C3×C4×#2352
C2×#638222
C2×C4⋊(C3⋊(C3⋊C8))2
#105910832
#105903842
#105903642
#105903632
#105903482
#105903472
#105902672
#832963
#825253