Finite Group Databasebeta

← #11860313

Subgroups — #11860313

Order 1152.

1191 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#235C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic
4#10592830C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×Dic3×M16C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590795C212yesmaximal, complemented
9#10590792C212yesmaximal, complemented
10#10590746C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#78866—31nomaximal
13C4×#908—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×#624—21no—
17C2×C32×M16C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22Dic3×#67—21no—
23Dic3×#67—21no—
24C2×#3722—21no—
25#63894—21no—
26#63894—21no—
27#63894C2212yes—
28#63894C2212yes—
29Dic3×D12C2211yescharacteristic, complemented
30Dic3×D12C2211yescharacteristic, complemented
31C4×D3×Dic3—21no—
32#63855—21no—
33Dic3×Dic6C2211yescharacteristic, complemented
34Dic3×Dic6C2211yescharacteristic, complemented
35C2×#3717C2212yes—
36#63825C418yescomplemented
37C2×#3714C2212yes—
38#63648C2212yes—
39#63648C2212yes—
40C3×#821C2212yescomplemented
41C3×#816C2212yescomplemented
42C3×#815C2212yescomplemented
43C3×C8×Dic3C2212yescomplemented
44#63575C2212yescomplemented
45#63573C2212yescomplemented
46Dic3×#41—31no—
47C2×#949—31no—
48C2×#908—31no—
49C2×#893—31no—
50C4×#235—31no—
51C2×C4×D12—31no—
52C3×#417—31no—
53C3×C4×M16—31no—
54#5133D311yescharacteristic, complemented
55#5131—31no—
56#5131—31no—
57#5131—61no—
58#5121—31no—
59Dic3×M16D311yescharacteristic, complemented
60#4964—31no—
61#4817—32no—
62#4788—32no—
63#4785—32no—
64#4756—32no—
65#4711—32no—
66#4710—32no—
67C4×D24—32no—
68C4×#204—32no—
69C23×C3⋊D3—21no—
70C22×C32×C4C2311yescharacteristic
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)C2×C414yescomplemented
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#235—22no—
80C3×#235C2×C414yescomplemented
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6C2311yescharacteristic
84C2×#624—22no—
85C2×#624—22no—
86C2×#624—44no—
87C2×D3×Dic3—21no—
88C2×D3×Dic3—21no—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91#3757—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C4×C3⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×#208C2×C414yescomplemented
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105#3722—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—21no—
108(C2×D3)⋊Dic3—21no—
109Dic32—21no—
110Dic32—21no—
111#3717C2×C418yescomplemented
112#3714C2×C418yescomplemented
113C4×AGL(1,ℤ/8)—91noSylow
114C2×C3×#41—31no—
115C2×#235C2×D311yescharacteristic
116C22×D12—31no—
117C22×D12—31no—
118C22×D12—61no—
119C22×C4×D3—61no—
120C22×C4×D3—61no—
121C2×C3×M16—21no—
122C2×C3×M16—31no—
123C2×C3×M16C2×D311yescharacteristic
124C2×C3×M16C2×D311yescharacteristic
125C2×C3×C4⋊C4—31no—
126C2×C3×C42—31no—
127#949—38no—
128Q8×Dic3—31no—
129Q8×Dic3—31no—
130C2×#215—32no—
131D4×Dic3—31no—
132D4×Dic3—31no—
133D4×Dic3—61no—
134D4×Dic3—61no—
135C2×#213—32no—
136C4×#67—61no—
137C4×#67—61no—
138C2×(C2×D3)⋊C4—61no—
139C2×(C2×D3)⋊C4—61no—
140#926—31no—
141#926—31no—
142#926—61no—
143#926—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×C4×Dic3—61no—
146C2×C4×Dic3C2×D311yescharacteristic
147C2×#208C2×D311yescharacteristic
148#908—38no—
149C2×D24—32no—
150C2×#204—32no—
151#893—32no—
152#893—32no—
153#893—61no—
154#893—61no—
155C4×D12—31no—
156C4×D12—31no—
157C4×D12—32no—
158C4×D12—32no—
159C4×D12—61no—
160C4×D12—61no—
161#872—61no—
162C42×D3—61no—
163C4×Dic6—31no—
164C4×Dic6—31no—
165C3×#103—32no—
166C3×#102—32no—
167C3×#97—32no—
168C3×C4×C8—32no—
169#821—32no—
170#821—32no—
171#821—32no—
172#821—32no—
173#821—62no—
174#821—62no—
175#821C2×D312yescomplemented
176#818—32no—
177#817—32no—
178#816C2×D312yescomplemented
179#815C2×D312yescomplemented
180C8×Dic3C2×D312yescomplemented
181#808—32no—
182#807—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—24no—
185C22×C3⋊D3—22no—
186C22×C3⋊D3—42no—
187C22×C3⋊D3—42no—
188C22×C3×D3—21no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C4⋊(C3⋊D3)—24no—
196C4⋊(C3⋊D3)—22no—
197C4⋊(C3⋊D3)C22×C414yes—
198C3×#67—24no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—41no—
203C2×C3×Dic3—42no—
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C3×D12—21no—
209C3×D12C22×C412yescomplemented
210C3×C4×D3—24no—
211C3×Dic6—21no—
212C3×Dic6C22×C412yescomplemented
213#624—44no—
214#624—44no—
215D3×Dic3—42no—
216D3×Dic3—42no—
217C32×C8—22no—
218C3×C3⋊C8C22×C414yescomplemented
219C2×AGL(1,ℤ/8)—91no—
220C4×#41—91no—
221C2×C4×D4—91no—
222#442—92no—
223#440—92no—
224C4×SD16—92no—
225C4×D8—92no—
226#428—91no—
227#418—91no—
228#417—31no—
229C4×M16—31no—
230C23×D3—61no—
231C23×D3—61no—
232C23×D3—121no—
233C3×#41—34no—
234C3×#41—62no—
235C2×C3×Q8—31no—
236C2×C3×D4—31no—
237C2×C3×D4—61no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—21no—
246C22×Dic3—21no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3D1211yescharacteristic
250C22×Dic3D1211yescharacteristic
251#235—22no—
252#235C4×D314yescomplemented
253C2×D12—34no—
254C2×D12—34no—
255C2×D12—32no—
256C2×D12—32no—
257C2×D12—62no—
258C2×D12—64no—
259C2×D12—61no—
260C2×D12—62no—
261C2×D12—61no—
262C2×D12—62no—
263C2×D12—121no—
264C2×D12—122no—
265C2×D12C22×D311yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—61no—
270C2×C4×D3—61no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3—124no—
274C2×C4×D3—124no—
275C2×Dic6C22×D311yescharacteristic
276C3×M16—22no—
277C3×M16—22no—
278C3×M16—34no—
279C3×M16—42no—
280C2×C3×C8—22no—
281C2×C3×C8—32no—
282C2×C3×C8C22×D312yes—
283C2×C3×C8C22×D312yes—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—61no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42—31no—
290#217—61no—
291#217—61no—
292#217—61no—
293#217—61no—
294#217—121no—
295#215—38no—
296#213—38no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—21no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—31no—
307C4⋊Dic3—31no—
308C4⋊Dic3—61no—
309C4⋊Dic3—61no—
310C4⋊Dic3—61no—
311C4⋊Dic3—61no—
312C4⋊Dic3C22×D312yes—
313Dic3⋊C4—61no—
314Dic3⋊C4—61no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—121no—
322C4×Dic3D1211yescharacteristic
323C4×Dic3D1211yescharacteristic
324C4×Dic3C22×D311yescharacteristic
325C4×Dic3C22×D311yescharacteristic
326#208C4×D314yescomplemented
327C2×C3⋊C8C22×D312yes—
328D24—38no—
329#204—38no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32C4×D412yes—
333C22×C32C22×D411yescharacteristic
334C2×C3⋊D3—24no—
335C2×C3⋊D3—48no—
336C2×C3⋊D3—42no—
337C2×C3⋊D3—42no—
338C2×C3×D3—22no—
339C2×C3×D3—41no—
340C2×C3×D3—41no—
341C32×C4C4×D412yes—
342C32×C4C23×C411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3⋊Dic3—41no—
345C3⋊Dic3—41no—
346C3×Dic3—22no—
347C3×Dic3—21no—
348C3×Dic3—21no—
349C3×Dic3—21no—
350C3×Dic3—42no—
351C3×Dic3AGL(1,ℤ/8)12yescomplemented
352C2×#41—31no—
353C22×D4—91no—
354C23×C4—181no—
355AGL(1,ℤ/8)—98no—
356C2×SD16—92no—
357C2×D8—92no—
358C2×M16—31no—
359C2×M16D3211yescharacteristic
360C4×Q8—91no—
361C4×Q8—91no—
362C4×D4—92no—
363C4×D4—92no—
364C4×D4—91no—
365C4×D4—91no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369C4×D4—181no—
370#117—91no—
371#117—181no—
372C2×C4⋊C4—31no—
373C2×C22⋊C4—181no—
374C2×C42—31no—
375C2×C42—181no—
376#107—92no—
377#106—92no—
378#103—32no—
379#102—32no—
380#102—92no—
381#102—92no—
382#97—32no—
383C4×C8—32no—
384C23×C3—21no—
385C23×C3—61no—
386C23×C3C2×D1211yescharacteristic
387C23×C3D3×D411yescharacteristic
388C22×D3—21no—
389C22×D3—64no—
390C22×D3—64no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—122no—
394C22×D3—124no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—242no—
400C22×D3—242no—
401C3×Q8—32no—
402C3×Q8—61no—
403C3×D4—32no—
404C3×D4—64no—
405C3×D4—61no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—31no—
411C2×C3×C4—31no—
412C2×C3×C4—31no—
413C2×C3×C4—31no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—64no—
417C2×C3×C4—62no—
418C2×C3×C4—121no—
419C2×C3×C4—122no—
420C2×C3×C4C2×C4×D312yes—
421C2×C3×C4C2×C4×D312yes—
422C2×C3×C4C2×D1211yescharacteristic
423C2×C3×C4#23512yes—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4#23712yes—
426C2×C3×C4C23×D311yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428#67—24no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—41no—
433C2×Dic3—42no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—121no—
439C2×Dic3—121no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3C2×D1211yescharacteristic
443C2×Dic3C2×D1211yescharacteristic
444C2×Dic3C2×D1211yescharacteristic
445C2×Dic3C2×D1211yescharacteristic
446D12—21no—
447D12—34no—
448D12—34no—
449D12—64no—
450D12—64no—
451D12—64no—
452D12—62no—
453D12—62no—
454D12—122no—
455D12—124no—
456D12C2×C4×D312yescomplemented
457C4×D3—24no—
458C4×D3—124no—
459C4×D3—124no—
460C4×D3—124no—
461C4×D3—122no—
462C4×D3—122no—
463C4×D3—124no—
464Dic6—21no—
465Dic6C2×C4×D312yescomplemented
466C3×C8—22no—
467C3×C8—22no—
468C3×C8—34no—
469C3×C8—42no—
470C3⋊C8C2×C4×D314yescomplemented
471C2×C32—22no—
472C2×C32C2×C4×D411yescharacteristic
473C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
474C2×C32#57511yescharacteristic
475C3⋊D3—44no—
476C3×D3—42no—
477C24—181no—
478#41—34no—
479#41—62no—
480C2×Q8—31no—
481C2×D4—31no—
482C2×D4—61no—
483C2×D4—92no—
484C2×D4—94no—
485C2×D4—181no—
486C2×D4—182no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—182no—
492C22×C4—182no—
493C22×C4—181no—
494C22×C4—181no—
495C22×C4—364no—
496C22×C4C2×D3211yescharacteristic
497SD16—98no—
498D8—98no—
499M16—22no—
500M16—34no—
501C2×C8—32no—
502C2×C8C2×D3212yes—
503C4⋊C4—32no—
504C4⋊C4—61no—
505C4⋊C4—91no—
506C4⋊C4—91no—
507C4⋊C4—181no—
508C4⋊C4—181no—
509C22⋊C4—182no—
510C22⋊C4—182no—
511C22⋊C4—181no—
512C22⋊C4—181no—
513C22⋊C4—181no—
514C42—31no—
515C42—31no—
516C42—31no—
517C42—31no—
518C42—181no—
519C42—181no—
520C42—181no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—22no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—62no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3C4×D1212yes—
533C22×C3#67⋊C412yes—
534C22×C3C22×D1211yescharacteristic
535C22×C3C2×D3×D411yescharacteristic
536C2×D3—22no—
537C2×D3—41no—
538C2×D3—41no—
539C2×D3—64no—
540C2×D3—64no—
541C2×D3—124no—
542C2×D3—128no—
543C2×D3—128no—
544C2×D3—122no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—242no—
549C2×D3—242no—
550C2×D3—248no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—32no—
555C3×C4—62no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—61no—
559C3×C4—122no—
560C3×C4C4×D1212yes—
561C3×C4#67⋊C412yes—
562C3×C4C22×C4×D311yescharacteristic
563C3×C4C22×C4×D311yescharacteristic
564C3×C4C2×#23511yescharacteristic
565C3×C4C2×#23711yescharacteristic
566Dic3—22no—
567Dic3—21no—
568Dic3—21no—
569Dic3—21no—
570Dic3—42no—
571Dic3—121no—
572Dic3—121no—
573Dic3—121no—
574Dic3—121no—
575Dic3—241no—
576Dic3—241no—
577Dic3#90812yescomplemented
578C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
579C23—61no—
580C23—182no—
581C23—184no—
582C23—362no—
583C23—362no—
584C23D3×D1211yescharacteristic
585Q8—32no—
586Q8—61no—
587D4—32no—
588D4—64no—
589D4—61no—
590D4—94no—
591D4—182no—
592D4—184no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—62no—
598C2×C4—61no—
599C2×C4—64no—
600C2×C4—62no—
601C2×C4—121no—
602C2×C4—122no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4—364no—
606C2×C4—362no—
607C2×C4—364no—
608C2×C4—362no—
609C2×C4C4×D3212yes—
610C2×C4D3×D1211yescharacteristic
611C2×C4#380412yes—
612C2×C4C22×D3211yescharacteristic
613C8—22no—
614C8—34no—
615C2×C3—22no—
616C2×C3—22no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—42no—
621C2×C3—122no—
622C2×C3C2×C4×D1211yescharacteristic
623C2×C3C2×#67⋊C411yescharacteristic
624C2×C3C2×#90811yescharacteristic
625C2×C3#574811yescharacteristic
626C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
627C2×C3#577711yescharacteristic
628D3—42no—
629D3—124no—
630D3—124no—
631D3—244no—
632C22—21no—
633C22—21no—
634C22—62no—
635C22—121no—
636C22—121no—
637C22—184no—
638C22—368no—
639C22—362no—
640C22—362no—
641C22#6388012yes—
642C22C2×D3×D1211yescharacteristic
643C4—32no—
644C4—62no—
645C4—61no—
646C4—61no—
647C4—61no—
648C4—122no—
649C4—361no—
650C4—361no—
651C4#6388012yes—
652C4C2×C4×D3211yescharacteristic
653C4C2×#380411yescharacteristic
654C3—21no—
655C3C4×#90811yescharacteristic, complemented
656C3#7886611yescharacteristic, complemented
657C2—22no—
658C2—122no—
659C2—364no—
660C2D3×#90811yescharacteristic
661C2#1059471111yescharacteristic
662C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63825C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. Dic3×#235C2semidirect
2. C2×#63894C2semidirect
4. #10592830C2semidirect
5. C3×#5133C2semidirect
6. C3×Dic3×M16C2semidirect
7. #10591130C2semidirect
8. #10590795C2semidirect
9. #10590792C2semidirect
10. #10590746C2semidirect
11. #10590745C2semidirect
29. Dic3×D12C22semidirect
30. Dic3×D12C22semidirect
33. Dic3×Dic6C22semidirect
34. Dic3×Dic6C22semidirect
36. #63825C4semidirect
40. C3×#821C22semidirect
41. C3×#816C22semidirect
42. C3×#815C22semidirect
43. C3×C8×Dic3C22semidirect
44. #63575C22semidirect
45. #63573C22semidirect
54. #5133D3semidirect
59. Dic3×M16D3semidirect
73. C2×C4⋊(C3⋊D3)C2×C4semidirect
80. C3×#235C2×C4semidirect
101. C3×#208C2×C4semidirect
111. #3717C2×C4semidirect
112. #3714C2×C4semidirect
175. #821C2×D3semidirect
178. #816C2×D3semidirect
179. #815C2×D3semidirect
180. C8×Dic3C2×D3semidirect
209. C3×D12C22×C4semidirect
212. C3×Dic6C22×C4semidirect
218. C3×C3⋊C8C22×C4semidirect
252. #235C4×D3semidirect
326. #208C4×D3semidirect
351. C3×Dic3AGL(1,ℤ/8)semidirect
456. D12C2×C4×D3semidirect
465. Dic6C2×C4×D3semidirect
470. C3⋊C8C2×C4×D3semidirect
577. Dic3#908semidirect
578. C32C4×AGL(1,ℤ/8)semidirect
655. C3C4×#908semidirect
656. C3#78866semidirect

Maximal subgroups

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

subgroupindex
Dic3×#2352
C2×#638942
C2×#638252
#105928302
C3×#51332
C3×Dic3×M162
#105911302
#105907952
#105907922
#105907462
#105907452
#788663
C4×#9083