Finite Group Databasebeta

← #11870456

Subgroups — #11870456

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic, complemented
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590595C212yesmaximal, complemented
6#10590456C212yesmaximal, complemented
7#10590452C212yesmaximal, complemented
8#10590438C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#83298—31nomaximal
13#80948—31nomaximal
14C2×C3×#239—21no—
15C2×D3×D12C2211yescharacteristic
16C2×C4×D32—21no—
17C32×C4⋊Q8C2211yescharacteristic, complemented
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C3×#947—21no—
20C3×#895—21no—
21C3×#895C2212yes—
22C3×#893—21no—
23C3×#893C2212yescomplemented
24C3×#874C2211yescharacteristic, complemented
25C3×C4×D12C2211yescharacteristic
26C3×C42×D3C2211yescharacteristic
27D3×(C2×D3)⋊C4—21no—
28C4×#626—21no—
29#63894C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63880—21no—
33C2×#3714C2212yes—
34C2×#3713C2212yes—
35#63636C2212yes—
36#63634C2212yescomplemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×#809C2212yes—
39C3×#807C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63563C2212yescomplemented
42#63562C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#532—31no—
46#5725D311yescharacteristic, complemented
47C4×D3×D4—31no—
48C2×C4×D12—31no—
49C3×#474—31no—
50#5087—31no—
51#5087—31no—
52#5087—61no—
53#5087D311yescharacteristic, complemented
54#5072—31no—
55#5072—31no—
56#5036—32no—
57#5033—32no—
58#5015—31no—
59C4×#213—32no—
60C4×#213—32no—
61#4925—31no—
62#4882—32no—
63#4872—32no—
64#4843—31no—
65#4833—31no—
66#4773—32no—
67#4756—32no—
68C22×D32—21no—
69C2×C32×Q8—21no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C3×#239—44no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×#626—21no—
84C2×#624—21no—
85C2×D3×Dic3—21no—
86C2×D3×Dic3—21no—
87D3×D12—22no—
88D3×D12—22no—
89C4×D32—44no—
90C32×C4⋊C4—21no—
91C32×C4⋊C4C2312yes—
92C32×C42C2311yescharacteristic
93#3752—21no—
94C4⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—22no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—21no—
105#3722—21no—
106(C2×D3)⋊Dic3—21no—
107#3714—24no—
108#3713—24no—
109#3100—91noSylow
110C2×C3×#41—61no—
111C2×#239—21no—
112C2×D3×D4—31no—
113C22×D12—31no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C3×C4⋊Q8—21no—
117C3×C4⋊Q8C2×D311yescharacteristic, complemented
118C3×C4⋊Q8C2×D311yescharacteristic, complemented
119C3×#127—31no—
120C3×#124—61no—
121C3×#121—32no—
122C3×#121—61no—
123C3×C4×D4—32no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C2×C3×C42—31no—
127#947—21no—
128D4×Dic3—31no—
129C2×#213—32no—
130C2×#213—32no—
131C2×#213—32no—
132C4×#67—61no—
133C2×(C2×D3)⋊C4—61no—
134C2×C4⋊Dic3—31no—
135C2×D24—32no—
136#895—21no—
137#895C2×D312yes—
138#893—21no—
139#893—31no—
140#893C2×D312yescomplemented
141D3×C4⋊C4—31no—
142#67⋊C4—61no—
143D3×C22⋊C4—61no—
144#874C2×D311yescharacteristic, complemented
145C4×D12—31no—
146C4×D12—31no—
147C4×D12—31no—
148C4×D12—31no—
149C4×D12—61no—
150C4×D12—61no—
151C4×D12—61no—
152C4×D12C2×D311yescharacteristic
153C42×D3C2×D311yescharacteristic
154C3×#107—32no—
155C3×C4⋊C8—31no—
156C3×#102—32no—
157#832—32no—
158#832—32no—
159#830—32no—
160#821—32no—
161(C2×D3)⋊C8—32no—
162C8×Dic3—32no—
163#809—32no—
164#809—32no—
165#809—32no—
166#809—62no—
167#809C2×D312yes—
168#807—32no—
169#807—32no—
170#807—62no—
171#807C2×D312yescomplemented
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
176C4×C3⋊C8—32no—
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C22×C3×D3—22no—
180C22×C3×D3C2×D411yescharacteristic
181C2×D32—24no—
182C2×D32—42no—
183C2×D32—42no—
184C32×Q8—42no—
185C2×C32×C4—22no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3—21no—
190C4⋊(C3⋊D3)—21no—
191C4⋊(C3⋊D3)#4112yescomplemented
192C4×C3⋊D3—42no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—21no—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12—42no—
201C3×D12—44no—
202C3×D12—42no—
203C3×D12#4112yescomplemented
204C3×C4×D3—21no—
205C3×C4×D3—21no—
206C3×C4×D3—41no—
207C3×C4×D3—42no—
208C3×C4×D3—44no—
209C3×C4×D3D814yescomplemented
210#626—24no—
211#624—42no—
212D3×Dic3—42no—
213D3×Dic3—42no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#532—31no—
217C2×C4×D4—91no—
218#480—92no—
219#474—31no—
220#474—91no—
221#459—91no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—91no—
227C23×D3—61no—
228C23×D3—61no—
229C3×#41—124no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—41no—
233C2×C3×D4—31no—
234C2×C3×D4—32no—
235C2×C3×D4—62no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—62no—
242C22×C3×C4—61no—
243C2×#67—61no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246#239—44no—
247D3×D4—62no—
248D3×D4—62no—
249C2×D12—22no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—31no—
253C2×D12—31no—
254C2×D12—61no—
255C2×D12—62no—
256C2×D12—61no—
257C2×D12—62no—
258C2×D12C22×D312yes—
259C2×D12C22×D311yescharacteristic
260C2×C4×D3—21no—
261C2×C4×D3—22no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—121no—
269C2×C4×D3—124no—
270C2×C4×D3—124no—
271C2×C4×D3#6711yescharacteristic
272C2×C4×D3#6711yescharacteristic
273C2×C4×D3C22×D311yescharacteristic
274C2×C3×C8—32no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—41no—
280C3×C4⋊C4C22×D312yes—
281C3×C4⋊C4C22×D312yes—
282C3×C22⋊C4—62no—
283C3×C22⋊C4—62no—
284C3×C22⋊C4—61no—
285C3×C42—21no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42C22×D311yescharacteristic
290C3×C42C22×D311yescharacteristic
291#217—61no—
292#213—64no—
293#213—64no—
294#213—64no—
295(C2×D3)⋊C4—21no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
301(C2×D3)⋊C4—61no—
302(C2×D3)⋊C4—61no—
303(C2×D3)⋊C4—121no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3C22×D311yescharacteristic
309Dic3⋊C4—61no—
310C4×Dic3#6711yescharacteristic
311C4×Dic3#6711yescharacteristic
312C4×Dic3C22×D311yescharacteristic
313C2×C3⋊C8—32no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8C22×D312yes—
317D24—64no—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—22no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3×D3—21no—
323C2×C3×D3—21no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—42no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3C2×D812yes—
331D32—48no—
332C32×C4—21no—
333C32×C4—42no—
334C32×C4C2×D812yes—
335C32×C4C2×#4111yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—41no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—41no—
341C3×Dic3C2×D812yes—
342C2×#41—61no—
343C22×D4—91no—
344C23×C4—181no—
345C2×D8—92no—
346C2×D8—92no—
347C4⋊Q8D3211yescharacteristic, complemented
348#127—31no—
349#124—61no—
350#121—32no—
351#121—61no—
352C4×D4—32no—
353C4×D4—31no—
354C4×D4—61no—
355C4×D4—91no—
356C4×D4—91no—
357C4×D4—91no—
358C4×D4—181no—
359C4×D4—181no—
360C2×C4⋊C4—91no—
361C2×C22⋊C4—181no—
362C2×C42—31no—
363#107—32no—
364#107—92no—
365C4⋊C8—31no—
366C4⋊C8—91no—
367#102—32no—
368#102—92no—
369#102—92no—
370#102—92no—
371C22⋊C8—92no—
372C4×C8—92no—
373C23×C3—31no—
374C23×C3—61no—
375C23×C3—62no—
376C22×D3—21no—
377C22×D3—22no—
378C22×D3—64no—
379C22×D3—64no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—121no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3C2×#6711yescharacteristic
388C3×Q8—42no—
389C3×Q8—42no—
390C3×Q8—82no—
391C3×D4—32no—
392C3×D4—62no—
393C3×D4—61no—
394C3×D4—62no—
395C3×D4—122no—
396C3×D4—124no—
397C3×D4—122no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—31no—
404C2×C3×C4—34no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—42no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—121no—
412C2×C3×C4—124no—
413C2×C3×C4—122no—
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420#67—64no—
421C2×Dic3—21no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—121no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3C2×#6711yescharacteristic
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430D12—21no—
431D12—22no—
432D12—22no—
433D12—32no—
434D12—32no—
435D12—42no—
436D12—44no—
437D12—42no—
438D12—62no—
439D12—64no—
440D12—61no—
441D12—61no—
442D12—121no—
443D12#23912yescomplemented
444C4×D3—21no—
445C4×D3—21no—
446C4×D3—41no—
447C4×D3—42no—
448C4×D3—44no—
449C4×D3—122no—
450C4×D3—122no—
451C4×D3—122no—
452C4×D3—122no—
453C4×D3—122no—
454C4×D3—122no—
455C4×D3—242no—
456C4×D3#21314yescomplemented
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—62no—
460C3⋊C8—62no—
461C3⋊C8—122no—
462C2×C32#52511yescharacteristic
463C2×C32C22×D811yescharacteristic
464C2×C32#57511yescharacteristic
465C3⋊D3—42no—
466C3×D3—22no—
467C3×D3—42no—
468C3×D3—82no—
469C24—181no—
470#41—124no—
471C2×Q8—21no—
472C2×D4—31no—
473C2×D4—32no—
474C2×D4—62no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—91no—
478C2×D4—181no—
479C2×D4—182no—
480C2×D4—182no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4—181no—
487C22×C4—181no—
488C22×C4—181no—
489C22×C4—181no—
490C22×C4—364no—
491D8—184no—
492D8—184no—
493C2×C8—32no—
494C2×C8—92no—
495C4⋊C4—21no—
496C4⋊C4—31no—
497C4⋊C4—91no—
498C4⋊C4—181no—
499C4⋊C4C2×D3212yes—
500C22⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—61no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—31no—
507C42—31no—
508C42—31no—
509C42C2×D3211yescharacteristic
510C22×C3—21no—
511C22×C3—32no—
512C22×C3—61no—
513C22×C3—61no—
514C22×C3—62no—
515C22×C3—121no—
516C22×C3—121no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—21no—
523C2×D3—21no—
524C2×D3—22no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—122no—
533C2×D3—128no—
534C2×D3—128no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3C2×#21312yes—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—32no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—61no—
552C3×C4—61no—
553C3×C4—82no—
554C3×C4—121no—
555C3×C4D3×D812yes—
556C3×C4C2×#21312yes—
557C3×C4C2×#23911yescharacteristic
558C3×C4D3×#4111yescharacteristic
559C3×C4D3×#4111yescharacteristic
560C3×C4D3×#4111yescharacteristic
561Dic3—21no—
562Dic3—21no—
563Dic3—41no—
564Dic3—121no—
565Dic3—121no—
566Dic3—241no—
567Dic3C2×#21312yes—
568C32#310011yescharacteristic, complemented, Sylow
569C23—31no—
570C23—61no—
571C23—62no—
572C23—184no—
573C23—181no—
574C23—362no—
575C23—362no—
576Q8—42no—
577D4—32no—
578D4—62no—
579D4—61no—
580D4—62no—
581D4—92no—
582D4—122no—
583D4—124no—
584D4—122no—
585D4—184no—
586D4—181no—
587C2×C4—22no—
588C2×C4—31no—
589C2×C4—34no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—121no—
596C2×C4—124no—
597C2×C4—122no—
598C2×C4—181no—
599C2×C4—362no—
600C2×C4—362no—
601C2×C4—362no—
602C2×C4—362no—
603C2×C4D3×#6711yescharacteristic
604C2×C4D3×#6711yescharacteristic
605C2×C4C22×D3211yescharacteristic
606C8—62no—
607C8—182no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—62no—
612C2×C3—122no—
613C2×C3—242no—
614C2×C3#562711yescharacteristic
615C2×C3C2×D3×D811yescharacteristic
616C2×C3#577711yescharacteristic
617C2×C3C22×#21311yescharacteristic
618C2×C3#582211yescharacteristic
619C2×C3#582811yescharacteristic
620D3—22no—
621D3—42no—
622D3—82no—
623D3—122no—
624D3—122no—
625D3—242no—
626C22—32no—
627C22—61no—
628C22—61no—
629C22—62no—
630C22—121no—
631C22—121no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—182no—
636C22—368no—
637C22—361no—
638C22—361no—
639C22C2×D3×#6711yescharacteristic
640C4—21no—
641C4—32no—
642C4—42no—
643C4—61no—
644C4—61no—
645C4—121no—
646C4—361no—
647C4D3×#21312yes—
648C4D3×#23911yescharacteristic
649C4#6431911yescharacteristic
650C3—21no—
651C3#8094811yescharacteristic, complemented
652C3#8329811yescharacteristic, complemented
653C2—62no—
654C2—122no—
655C2—242no—
656C2—362no—
657C2C2×D3×#21311yescharacteristic
658C2#1059531711yescharacteristic
659C2#1059542411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3100
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
1. C3×#5725C2semidirect
2. C4×D3×D12C2semidirect
3. #10592786C2semidirect
4. C3×#5087C2semidirect
5. #10590595C2semidirect
6. #10590456C2semidirect
7. #10590452C2semidirect
8. #10590438C2semidirect
9. #10590355C2semidirect
10. #10590347C2semidirect
11. #10590248C2semidirect
17. C32×C4⋊Q8C22semidirect
23. C3×#893C22semidirect
24. C3×#874C22semidirect
36. #63634C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
39. C3×#807C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63563C22semidirect
42. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5725D3semidirect
53. #5087D3semidirect
117. C3×C4⋊Q8C2×D3semidirect
118. C3×C4⋊Q8C2×D3semidirect
140. #893C2×D3semidirect
144. #874C2×D3semidirect
171. #807C2×D3semidirect
175. C4⋊(C3⋊C8)C2×D3semidirect
191. C4⋊(C3⋊D3)#41semidirect
203. C3×D12#41semidirect
209. C3×C4×D3D8semidirect
347. C4⋊Q8D32semidirect
443. D12#239semidirect
456. C4×D3#213semidirect
568. C32#3100semidirect
651. C3#80948semidirect
652. C3#83298semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
C4×D3×D122
#105927862
C3×#50872
#105905952
#105904562
#105904522
#105904382
#105903552
#105903472
#105902482
#832983
#809483