Finite Group Databasebeta

← #11860306

Subgroups — #11860306

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic
4#10592694C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic, complemented
6#10591088C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590455C212yesmaximal, complemented
9#10590454C212yesmaximal, complemented
10#10590453C212yesmaximal, complemented
11#10590452C212yesmaximal, complemented
12C4×#949—31nomaximal
13#78914—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C32×#117C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#893C2211yescharacteristic, complemented
23C3×#893C2211yescharacteristic, complemented
24C3×#887C2211yescharacteristic, complemented
25C3×#887C2211yescharacteristic, complemented
26C3×#67⋊C4—21no—
27C3×#67⋊C4—21no—
28C3×#872—21no—
29C3×C42×D3—21no—
30C2×(C2×D3)⋊Dic3—21no—
31Dic3×D12—21no—
32Dic3×D12—21no—
33Dic3×D12C2212yes—
34Dic3×D12C2212yes—
35C2×#3715C2212yes—
36#63823C418yescomplemented
37C2×#3713C2212yes—
38#63635C2212yescomplemented
39#63634C2212yescomplemented
40C3×#809C2212yes—
41C3×#809C2212yes—
42#63566C2212yescomplemented
43#63563C2212yescomplemented
44#63554C2212yescomplemented
45Dic3×C3⋊C8C2212yescomplemented
46C3×C4×#41—31no—
47C2×#949—31no—
48C2×D4×Dic3—31no—
49C2×#932—31no—
50#5522D311yescharacteristic, complemented
51C2×C4×D12—31no—
52C3×#418—31no—
53#5232—31no—
54#5133—31no—
55Dic3×M16—31no—
56#5026—32no—
57C4×#215—32no—
58#5014—32no—
59C4×#213—32no—
60#5001D311yescharacteristic, complemented
61#4995—31no—
62#4995—31no—
63#4995—61no—
64C4×#208—31no—
65#4785—32no—
66#4758—32no—
67#4757—32no—
68#4756—32no—
69C23×C3×D3—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C3×#235—22no—
76C3×#235C2×C414yescomplemented
77C2×C3×D12—21no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yescomplemented
80C2×C3×D12C2312yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—21no—
85C2×C3×Dic6C2311yescharacteristic
86C2×D3×Dic3—22no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—44no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C4⋊C4C2311yescharacteristic
91C32×C22⋊C4—21no—
92C32×C42—21no—
93C4⋊(C3⋊Dic3)—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95#3748C2×C414yescomplemented
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—21no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C3×#208—22no—
108C2×C3×C3⋊C8C2312yes—
109(C2×D3)⋊Dic3—22no—
110(C2×D3)⋊Dic3—22no—
111#3715C2×C418yescomplemented
112#3713C2×C418yescomplemented
113C4×AGL(1,ℤ/8)—91noSylow
114C2×C3×#41—31no—
115C22×C3×D4—31no—
116C23×Dic3—61no—
117C2×#235C2×D311yescharacteristic
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—61no—
120C2×C3×M16—31no—
121C3×C4×Q8—31no—
122C3×C4×Q8—31no—
123C3×C4×D4—31no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C3×#117—21no—
128C3×#117—61no—
129C3×#117C2×D311yescharacteristic
130C3×#117C2×D311yescharacteristic
131C2×C3×C42—31no—
132C2×C3×C42—61no—
133C2×#217—61no—
134#949—38no—
135C2×#215—32no—
136D4×Dic3—32no—
137D4×Dic3—32no—
138D4×Dic3—61no—
139D4×Dic3—61no—
140C2×#214—32no—
141#932—38no—
142C2×#213—32no—
143C2×#213—32no—
144C2×(C2×D3)⋊C4—61no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—61no—
148C2×C4×Dic3C2×D311yescharacteristic
149C2×#208—31no—
150C2×#208—31no—
151C2×#208—61no—
152C2×#208C2×D311yescharacteristic
153#893C2×D311yescharacteristic, complemented
154#893C2×D311yescharacteristic, complemented
155#887C2×D311yescharacteristic, complemented
156#887C2×D311yescharacteristic, complemented
157#67⋊C4—21no—
158#67⋊C4—21no—
159C4×D12—32no—
160C4×D12—32no—
161C4×D12—61no—
162C4×D12—61no—
163#872—21no—
164C42×D3—21no—
165C3×#102—32no—
166C3×#102—32no—
167#835—32no—
168#832—32no—
169#821—32no—
170#816—32no—
171#815—32no—
172C8×Dic3—32no—
173#809C2×D312yes—
174#809C2×D312yes—
175#808—32no—
176#808—32no—
177#808—62no—
178#807—32no—
179#807—32no—
180#807—62no—
181#803—32no—
182C4×C3⋊C8—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—24no—
185C22×C3×D3—22no—
186C22×C3×D3—21no—
187C22×C3×D3—42no—
188C22×C3×D3—42no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4#4112yes—
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—42no—
197C3×#67—24no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—41no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—24no—
206C3×D12—22no—
207C3×D12—21no—
208C3×D12C22×C414yes—
209C3×D12C22×C412yescomplemented
210C3×C4×D3—24no—
211C3×C4×D3—42no—
212C3×C4×D3—42no—
213C3×Dic6—21no—
214C3×Dic6C22×C412yescomplemented
215D3×Dic3—44no—
216D3×Dic3—44no—
217C3⋊(C3⋊C8)C22×C414yescomplemented
218C3×C3⋊C8—22no—
219C2×AGL(1,ℤ/8)—91no—
220C4×#41—31no—
221C2×C4×D4—91no—
222#442—92no—
223#440—92no—
224C4×SD16—92no—
225C4×D8—92no—
226#428—91no—
227#418—31no—
228#417—91no—
229C4×M16—91no—
230C24×C3—61no—
231C23×D3—21no—
232C3×#41—34no—
233C3×#41—62no—
234C2×C3×Q8—31no—
235C2×C3×D4—34no—
236C2×C3×D4—31no—
237C2×C3×D4—32no—
238C2×C3×D4—61no—
239C2×C3×D4—62no—
240C2×C3×D4—61no—
241C22×C3×C4—21no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—21no—
250C22×Dic3—61no—
251C22×Dic3—61no—
252C22×Dic3—62no—
253C22×Dic3—62no—
254C22×Dic3—121no—
255C22×Dic3—124no—
256C22×Dic3#6711yescharacteristic
257C22×Dic3#6711yescharacteristic
258#235—22no—
259#235C4×D314yescomplemented
260C2×D12—21no—
261C2×D12—22no—
262C2×D12C4×D314yescomplemented
263C2×D12C22×D312yes—
264C2×D12C22×D311yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—124no—
271C2×Dic6C22×D311yescharacteristic
272C3×M16—62no—
273C2×C3×C8—32no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—61no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4C22×D311yescharacteristic
279C3×C4⋊C4C22×D311yescharacteristic
280C3×C4⋊C4C22×D311yescharacteristic
281C3×C4⋊C4C22×D311yescharacteristic
282C3×C22⋊C4—21no—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—41no—
285C3×C22⋊C4—61no—
286C3×C22⋊C4—61no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—31no—
290C3×C42—31no—
291C3×C42—31no—
292C3×C42—31no—
293C3×C42—41no—
294C3×C42—61no—
295C3×C42—61no—
296#217—62no—
297#217—62no—
298#215—38no—
299#214—38no—
300#213—38no—
301#213—38no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—21no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—62no—
306C4⋊Dic3—32no—
307C4⋊Dic3—32no—
308C4⋊Dic3—62no—
309C4⋊Dic3—61no—
310C4⋊Dic3—61no—
311C4⋊Dic3—121no—
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3#6711yescharacteristic
317C4×Dic3#6711yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320#208—22no—
321#208—34no—
322#208—34no—
323#208—64no—
324C2×C3⋊C8—32no—
325C2×C3⋊C8—32no—
326C2×C3⋊C8—62no—
327C2×C3⋊C8C22×D312yes—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32C4×D412yes—
331C22×C32C22×D411yescharacteristic
332C2×C3×D3—22no—
333C2×C3×D3—24no—
334C2×C3×D3—48no—
335C2×C3×D3—42no—
336C2×C3×D3—41no—
337C2×C3×D3—41no—
338C2×C3×D3—42no—
339C32×C4—41no—
340C32×C4—41no—
341C32×C4C4×D412yes—
342C32×C4C23×C411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3⋊Dic3—42no—
345C3×Dic3—22no—
346C3×Dic3—21no—
347C3×Dic3—21no—
348C3×Dic3—21no—
349C3×Dic3AGL(1,ℤ/8)12yescomplemented
350C2×#41—31no—
351C22×D4—31no—
352C23×C4—181no—
353AGL(1,ℤ/8)—98no—
354C2×SD16—92no—
355C2×D8—92no—
356C2×M16—31no—
357C2×M16—91no—
358C4×Q8—31no—
359C4×Q8—31no—
360C4×D4—31no—
361C4×D4—31no—
362C4×D4—61no—
363C4×D4—61no—
364C4×D4—92no—
365C4×D4—92no—
366C4×D4—181no—
367C4×D4—181no—
368#117—61no—
369#117D3211yescharacteristic
370C2×C4⋊C4—91no—
371C2×C22⋊C4—181no—
372C2×C42—31no—
373C2×C42—61no—
374#107—92no—
375#106—92no—
376#103—92no—
377#102—32no—
378#102—32no—
379#102—92no—
380#97—92no—
381C4×C8—92no—
382C23×C3—21no—
383C23×C3—64no—
384C23×C3—61no—
385C23×C3—62no—
386C23×C3—122no—
387C23×C3—122no—
388C23×C3D3×D411yescharacteristic
389C23×C3C2×#6711yescharacteristic
390C22×D3—24no—
391C22×D3—22no—
392C22×D3—21no—
393C22×D3—42no—
394C22×D3—42no—
395C3×Q8—32no—
396C3×Q8—61no—
397C3×D4—34no—
398C3×D4—32no—
399C3×D4—64no—
400C3×D4—64no—
401C3×D4—62no—
402C3×D4—61no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—31no—
414C2×C3×C4—31no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—62no—
418C2×C3×C4—61no—
419C2×C3×C4—64no—
420C2×C3×C4—122no—
421C2×C3×C4—122no—
422C2×C3×C4—121no—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4#23512yes—
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4#23712yes—
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—24no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—41no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—122no—
438C2×Dic3—124no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—124no—
442C2×Dic3—242no—
443C2×Dic3C2×#6711yescharacteristic
444C2×Dic3C2×#6711yescharacteristic
445C2×Dic3C2×#6711yescharacteristic
446C2×Dic3C2×#6711yescharacteristic
447D12—24no—
448D12—21no—
449D12—22no—
450D12C2×C4×D314yes—
451D12C2×C4×D312yescomplemented
452C4×D3—24no—
453C4×D3—42no—
454C4×D3—42no—
455C4×D3—124no—
456C4×D3—124no—
457Dic6—21no—
458Dic6C2×C4×D312yescomplemented
459C3×C8—62no—
460C3⋊C8—22no—
461C3⋊C8—34no—
462C3⋊C8—34no—
463C3⋊C8—64no—
464C2×C32—22no—
465C2×C32C2×C4×D411yescharacteristic
466C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
467C2×C32#57511yescharacteristic
468C3×D3—42no—
469C3×D3—44no—
470C24—61no—
471#41—34no—
472#41—62no—
473C2×Q8—31no—
474C2×D4—32no—
475C2×D4—31no—
476C2×D4—34no—
477C2×D4—61no—
478C2×D4—62no—
479C2×D4—61no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—182no—
486C22×C4—182no—
487C22×C4—181no—
488C22×C4—364no—
489C22×C4C2×D3211yescharacteristic
490SD16—98no—
491D8—98no—
492M16—62no—
493M16—94no—
494C2×C8—32no—
495C2×C8—92no—
496C4⋊C4—61no—
497C4⋊C4—61no—
498C4⋊C4—92no—
499C4⋊C4—181no—
500C4⋊C4C2×D3211yescharacteristic
501C4⋊C4C2×D3211yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—61no—
504C22⋊C4—61no—
505C22⋊C4—182no—
506C22⋊C4—182no—
507C42—21no—
508C42—31no—
509C42—31no—
510C42—31no—
511C42—31no—
512C42—61no—
513C42—61no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—62no—
523C22×C3—64no—
524C22×C3—128no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3#67⋊C412yes—
530C22×C3C4×#6712yes—
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C22×#6711yescharacteristic
533C2×D3—24no—
534C2×D3—22no—
535C2×D3—48no—
536C2×D3—42no—
537C2×D3—42no—
538C2×D3—41no—
539C2×D3—41no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—22no—
543C3×C4—32no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—62no—
549C3×C4—61no—
550C3×C4—61no—
551C3×C4—61no—
552C3×C4—81no—
553C3×C4—81no—
554C3×C4#67⋊C412yes—
555C3×C4C4×#6712yes—
556C3×C4C22×C4×D311yescharacteristic
557C3×C4C22×C4×D311yescharacteristic
558C3×C4C2×#23511yescharacteristic
559C3×C4C2×#23711yescharacteristic
560Dic3—22no—
561Dic3—21no—
562Dic3—21no—
563Dic3—21no—
564Dic3—122no—
565Dic3—122no—
566Dic3—242no—
567Dic3#94912yescomplemented
568C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
569C23—61no—
570C23—62no—
571C23—64no—
572C23—122no—
573C23—122no—
574C23D3×#6711yescharacteristic
575Q8—32no—
576Q8—61no—
577D4—32no—
578D4—34no—
579D4—64no—
580D4—62no—
581D4—61no—
582D4—64no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—31no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—64no—
592C2×C4—122no—
593C2×C4—122no—
594C2×C4—121no—
595C2×C4—182no—
596C2×C4—364no—
597C2×C4—364no—
598C2×C4—362no—
599C2×C4#379512yes—
600C2×C4C4×D3212yes—
601C2×C4D3×#6711yescharacteristic
602C2×C4C22×D3211yescharacteristic
603C8—62no—
604C8—94no—
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—42no—
611C2×C3—122no—
612C2×C3—124no—
613C2×C3C2×#67⋊C411yescharacteristic
614C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
615C2×C3#577311yescharacteristic
616C2×C3C2×C4×#6711yescharacteristic
617C2×C3C2×#94911yescharacteristic
618C2×C3#582211yescharacteristic
619D3—44no—
620D3—42no—
621C22—21no—
622C22—21no—
623C22—62no—
624C22—64no—
625C22—128no—
626C22—121no—
627C22—122no—
628C22—121no—
629C22—122no—
630C22#6387912yes—
631C22C2×D3×#6711yescharacteristic
632C4—32no—
633C4—41no—
634C4—41no—
635C4—62no—
636C4—61no—
637C4—61no—
638C4—61no—
639C4—362no—
640C4#6387912yes—
641C4C2×#379511yescharacteristic
642C4C2×C4×D3211yescharacteristic
643C3—21no—
644C3#7891411yescharacteristic, complemented
645C3C4×#94911yescharacteristic, complemented
646C2—22no—
647C2—124no—
648C2—122no—
649C2C2×#6387911yescharacteristic
650C2D3×#94911yescharacteristic
651C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63823C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5522C2semidirect
2. C2×Dic3×D12C2semidirect
4. #10592694C2semidirect
5. C3×#5001C2semidirect
6. #10591088C2semidirect
7. Dic3×#208C2semidirect
8. #10590455C2semidirect
9. #10590454C2semidirect
10. #10590453C2semidirect
11. #10590452C2semidirect
22. C3×#893C22semidirect
23. C3×#893C22semidirect
24. C3×#887C22semidirect
25. C3×#887C22semidirect
36. #63823C4semidirect
38. #63635C22semidirect
39. #63634C22semidirect
42. #63566C22semidirect
43. #63563C22semidirect
44. #63554C22semidirect
45. Dic3×C3⋊C8C22semidirect
50. #5522D3semidirect
60. #5001D3semidirect
76. C3×#235C2×C4semidirect
79. C2×C3×D12C2×C4semidirect
95. #3748C2×C4semidirect
111. #3715C2×C4semidirect
112. #3713C2×C4semidirect
153. #893C2×D3semidirect
154. #893C2×D3semidirect
155. #887C2×D3semidirect
156. #887C2×D3semidirect
209. C3×D12C22×C4semidirect
214. C3×Dic6C22×C4semidirect
217. C3⋊(C3⋊C8)C22×C4semidirect
259. #235C4×D3semidirect
262. C2×D12C4×D3semidirect
349. C3×Dic3AGL(1,ℤ/8)semidirect
451. D12C2×C4×D3semidirect
458. Dic6C2×C4×D3semidirect
567. Dic3#949semidirect
568. C32C4×AGL(1,ℤ/8)semidirect
644. C3#78914semidirect
645. C3C4×#949semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×Dic3×D122
C2×#638232
#105926942
C3×#50012
#105910882
Dic3×#2082
#105904552
#105904542
#105904532
#105904522
C4×#9493
#789143