Finite Group Databasebeta

← #11860314

Subgroups — #11860314

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594958C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic
4M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5131C211yesmaximal, characteristic, complemented
7#10591139C211yesmaximal, characteristic, complemented
8#10590743C212yesmaximal, complemented
9#10590742C212yesmaximal, complemented
10#10590741C212yesmaximal, complemented
11#10590740C212yesmaximal, complemented
12#78914—31nomaximal
13#78866—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C2×C32×M16C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22#67⋊Dic3—21no—
23#67⋊Dic3—21no—
24C2×(C2×D3)⋊Dic3—21no—
25#63898—21no—
26#63898—21no—
27#63898C2212yes—
28#63898C2212yes—
29#63898C2211yescharacteristic, complemented
30#63898C2211yescharacteristic, complemented
31C4×D3×Dic3—21no—
32#63855—21no—
33#63843C2211yescharacteristic, complemented
34#63843C2211yescharacteristic, complemented
35C2×#3715C2212yes—
36#63823C418yescomplemented
37C2×#3713C2212yes—
38#63642C2212yescomplemented
39C8×C3⋊Dic3C2212yescomplemented
40C3×#821C2212yes—
41C3×#821C2212yes—
42C3×#821C2212yescomplemented
43C3×#816C2212yescomplemented
44#63576C2212yescomplemented
45#63574C2212yescomplemented
46Dic3×#41—31no—
47C2×#949—31no—
48C2×D4×Dic3—31no—
49C2×#932—31no—
50#5522—31no—
51C2×#893—31no—
52C3×#418—31no—
53C3×#417—31no—
54#5133D311yescharacteristic, complemented
55#5131D311yescharacteristic, complemented
56Dic3×M16—31no—
57Dic3×M16—31no—
58Dic3×M16—61no—
59#4995—31no—
60#4964—31no—
61#4817—32no—
62#4788—32no—
63#4785—32no—
64#4785—32no—
65#4758—32no—
66#4757—32no—
67#4756—32no—
68#4756—32no—
69C23×C3×D3—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C22×C3⋊Dic3D411yescharacteristic
73C2×C3×#67—21no—
74C22×C3×Dic3—21no—
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×Dic6C2311yescharacteristic
84C2×D3×Dic3—22no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—21no—
87C2×D3×Dic3—21no—
88C2×D3×Dic3—44no—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95#3748C2×C414yescomplemented
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#217—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4⋊Dic3C2311yescharacteristic
102C3×C4×Dic3—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—22no—
109Dic32—21no—
110Dic32—21no—
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—21no—
121C2×C3×M16C2×D311yescharacteristic
122C2×C3×M16C2×D311yescharacteristic
123C3×#117—31no—
124C2×C3×C4⋊C4—31no—
125C2×#217—61no—
126#949—38no—
127Q8×Dic3—31no—
128Q8×Dic3—31no—
129C2×#215—32no—
130D4×Dic3—31no—
131D4×Dic3—32no—
132D4×Dic3—32no—
133D4×Dic3—31no—
134D4×Dic3—61no—
135D4×Dic3—61no—
136D4×Dic3—61no—
137D4×Dic3—61no—
138C2×#214—32no—
139#932—38no—
140C2×#213—32no—
141C2×#213—32no—
142C2×(C2×D3)⋊C4—61no—
143#926—61no—
144#926C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148C2×C4×Dic3—61no—
149C2×C4×Dic3—61no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153#893—32no—
154#893—32no—
155#893—31no—
156#893—31no—
157#893—61no—
158#893—61no—
159#887—31no—
160#887—31no—
161#67⋊C4—61no—
162#67⋊C4—61no—
163#872—61no—
164C42×D3—61no—
165C3×#103—32no—
166C3×#102—32no—
167C3×#102—32no—
168C3×#102—32no—
169#821C2×D312yes—
170#821C2×D312yes—
171#821C2×D312yescomplemented
172#816C2×D312yescomplemented
173#815—32no—
174#815—32no—
175#815—62no—
176C8×Dic3—32no—
177C8×Dic3—32no—
178C8×Dic3—62no—
179#808—32no—
180#808—32no—
181#807—32no—
182#807—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×C4C22×C412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—41no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C3×#67—24no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—42no—
205C3×D12—24no—
206C3×D12—22no—
207C3×D12—21no—
208C3×D12C22×C414yes—
209C3×D12C22×C412yescomplemented
210C3×C4×D3—24no—
211C3×Dic6—21no—
212C3×Dic6C22×C412yescomplemented
213D3×Dic3—42no—
214D3×Dic3—44no—
215D3×Dic3—42no—
216D3×Dic3—44no—
217C32×C8—22no—
218C3⋊(C3⋊C8)C22×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—31no—
228#417—31no—
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—61no—
240C2×C3×D4—62no—
241C22×C3×C4—21no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—21no—
247C22×Dic3—21no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—31no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256C22×Dic3—62no—
257C22×Dic3—62no—
258C22×Dic3—124no—
259#235—22no—
260#235C4×D314yescomplemented
261C2×D12—21no—
262C2×D12—22no—
263C2×D12C4×D314yescomplemented
264C2×D12C22×D312yes—
265C2×D12C22×D311yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—124no—
272C2×Dic6C22×D311yescharacteristic
273C3×M16—24no—
274C3×M16—22no—
275C3×M16—22no—
276C2×C3×C8—22no—
277C2×C3×C8C22×D312yes—
278C2×C3×C8C22×D312yes—
279C3×C4⋊C4—31no—
280C3×C4⋊C4—32no—
281C3×C4⋊C4—31no—
282C3×C4⋊C4—61no—
283C3×C22⋊C4—61no—
284C3×C42—61no—
285#217—21no—
286#217—61no—
287#217—61no—
288#217—62no—
289#217—62no—
290#215—38no—
291#214—38no—
292#213—38no—
293#213—38no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—61no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298C4⋊Dic3—21no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3C22×D311yescharacteristic
302C4⋊Dic3C22×D312yes—
303C4⋊Dic3C22×D311yescharacteristic
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306C4×Dic3—21no—
307C4×Dic3—31no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—61no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—61no—
322C4×Dic3—61no—
323#208—34no—
324#208—34no—
325#208—64no—
326C2×C3⋊C8—32no—
327C2×C3⋊C8—32no—
328C2×C3⋊C8—62no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32C4×D412yes—
332C22×C32C22×D411yescharacteristic
333C2×C3×D3—22no—
334C2×C3×D3—24no—
335C2×C3×D3—48no—
336C2×C3×D3—42no—
337C2×C3×D3—41no—
338C2×C3×D3—41no—
339C2×C3×D3—42no—
340C32×C4C4×D412yes—
341C32×C4C23×C411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—21no—
344C3⋊Dic3—21no—
345C3⋊Dic3—21no—
346C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
347C3×Dic3—22no—
348C3×Dic3—42no—
349C3×Dic3—41no—
350C3×Dic3—41no—
351C2×#41—31no—
352C22×D4—31no—
353C23×C4—181no—
354AGL(1,ℤ/8)—98no—
355C2×SD16—92no—
356C2×D8—92no—
357C2×M16—91no—
358C2×M16D3211yescharacteristic
359C4×Q8—91no—
360C4×Q8—91no—
361C4×D4—92no—
362C4×D4—92no—
363C4×D4—91no—
364C4×D4—91no—
365C4×D4—181no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369#117—31no—
370#117—181no—
371C2×C4⋊C4—31no—
372C2×C22⋊C4—181no—
373C2×C42—91no—
374C2×C42—181no—
375#107—92no—
376#106—92no—
377#103—32no—
378#102—32no—
379#102—32no—
380#102—32no—
381#97—92no—
382C4×C8—92no—
383C23×C3—21no—
384C23×C3—64no—
385C23×C3—61no—
386C23×C3—62no—
387C23×C3—122no—
388C23×C3—122no—
389C23×C3D3×D411yescharacteristic
390C23×C3D3×D411yescharacteristic
391C22×D3—24no—
392C22×D3—21no—
393C22×D3—22no—
394C22×D3—42no—
395C22×D3—42no—
396C3×Q8—32no—
397C3×Q8—61no—
398C3×D4—34no—
399C3×D4—32no—
400C3×D4—64no—
401C3×D4—64no—
402C3×D4—62no—
403C3×D4—61no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—61no—
409C2×C3×C4—64no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—122no—
414C2×C3×C4C2×C4×D312yes—
415C2×C3×C4C2×C4×D312yes—
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4#23712yes—
419C2×C3×C4#23712yes—
420C2×C3×C4C23×D311yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422#67—24no—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—22no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—31no—
434C2×Dic3—31no—
435C2×Dic3—42no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—122no—
443C2×Dic3—122no—
444C2×Dic3—124no—
445C2×Dic3—122no—
446C2×Dic3—124no—
447C2×Dic3—121no—
448C2×Dic3—121no—
449C2×Dic3—122no—
450D12—24no—
451D12—22no—
452D12—21no—
453D12C2×C4×D314yes—
454D12C2×C4×D312yescomplemented
455C4×D3—24no—
456C4×D3—122no—
457C4×D3—124no—
458C4×D3—122no—
459C4×D3—124no—
460Dic6—21no—
461Dic6C2×C4×D312yescomplemented
462C3×C8—24no—
463C3×C8—22no—
464C3×C8—22no—
465C3⋊C8—34no—
466C3⋊C8—34no—
467C3⋊C8—64no—
468C2×C32—22no—
469C2×C32C2×C4×D411yescharacteristic
470C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
471C2×C32#57511yescharacteristic
472C3×D3—42no—
473C3×D3—44no—
474C24—61no—
475#41—34no—
476#41—62no—
477C2×Q8—31no—
478C2×D4—31no—
479C2×D4—32no—
480C2×D4—34no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—62no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—181no—
489C22×C4—181no—
490C22×C4—182no—
491C22×C4—182no—
492C22×C4—364no—
493C22×C4C2×D3211yescharacteristic
494SD16—98no—
495D8—98no—
496M16—22no—
497M16—94no—
498C2×C8—92no—
499C2×C8C2×D3212yes—
500C4⋊C4—31no—
501C4⋊C4—31no—
502C4⋊C4—32no—
503C4⋊C4—61no—
504C4⋊C4—181no—
505C4⋊C4—181no—
506C22⋊C4—61no—
507C22⋊C4—182no—
508C22⋊C4—182no—
509C22⋊C4—181no—
510C22⋊C4—181no—
511C42—61no—
512C42—91no—
513C42—91no—
514C42—91no—
515C42—91no—
516C42—181no—
517C42—181no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—22no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—62no—
527C22×C3—64no—
528C22×C3—128no—
529C22×C3—122no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3—122no—
533C22×C3#67⋊C412yes—
534C22×C3#67⋊C412yes—
535C22×C3C2×D3×D411yescharacteristic
536C22×C3C2×D3×D411yescharacteristic
537C2×D3—22no—
538C2×D3—24no—
539C2×D3—48no—
540C2×D3—42no—
541C2×D3—41no—
542C2×D3—42no—
543C2×D3—41no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—62no—
548C3×C4—122no—
549C3×C4—121no—
550C3×C4—121no—
551C3×C4#67⋊C412yes—
552C3×C4#67⋊C412yes—
553C3×C4C22×C4×D311yescharacteristic
554C3×C4C22×C4×D311yescharacteristic
555C3×C4C2×#23711yescharacteristic
556C3×C4C2×#23711yescharacteristic
557Dic3—22no—
558Dic3—32no—
559Dic3—32no—
560Dic3—42no—
561Dic3—41no—
562Dic3—41no—
563Dic3—62no—
564Dic3—62no—
565Dic3—61no—
566Dic3—61no—
567Dic3—61no—
568Dic3—61no—
569Dic3—61no—
570Dic3—61no—
571Dic3—121no—
572Dic3—121no—
573C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
574C23—61no—
575C23—62no—
576C23—64no—
577C23—122no—
578C23—122no—
579C23#380211yescharacteristic
580Q8—32no—
581Q8—61no—
582D4—32no—
583D4—34no—
584D4—64no—
585D4—62no—
586D4—61no—
587D4—64no—
588C2×C4—61no—
589C2×C4—64no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—122no—
598C2×C4—182no—
599C2×C4—364no—
600C2×C4—362no—
601C2×C4—364no—
602C2×C4—362no—
603C2×C4—361no—
604C2×C4C4×D3212yes—
605C2×C4#380211yescharacteristic
606C2×C4#380512yes—
607C2×C4C22×D3211yescharacteristic
608C8—22no—
609C8—94no—
610C2×C3—22no—
611C2×C3—22no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—42no—
616C2×C3—124no—
617C2×C3—122no—
618C2×C3C2×#67⋊C411yescharacteristic
619C2×C3C2×#67⋊C411yescharacteristic
620C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
621C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
622C2×C3#577311yescharacteristic
623C2×C3#577711yescharacteristic
624D3—42no—
625D3—44no—
626C22—21no—
627C22—21no—
628C22—62no—
629C22—64no—
630C22—128no—
631C22—122no—
632C22—121no—
633C22—121no—
634C22—122no—
635C22#6390212yes—
636C22C2×#380211yescharacteristic
637C4—62no—
638C4—92no—
639C4—122no—
640C4—121no—
641C4—121no—
642C4—181no—
643C4—181no—
644C4—181no—
645C4#6390212yes—
646C4C2×C4×D3211yescharacteristic
647C4C2×#380511yescharacteristic
648C3—21no—
649C3#7886611yescharacteristic, complemented
650C3#7891411yescharacteristic, complemented
651C2—22no—
652C2—124no—
653C2—122no—
654C2#1059471611yescharacteristic
655C2#1059471811yescharacteristic
656C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63823C2
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. #10594958C2semidirect
2. C2×#63898C2semidirect
4. M16×C3⋊Dic3C2semidirect
5. C3×#5133C2semidirect
6. C3×#5131C2semidirect
7. #10591139C2semidirect
8. #10590743C2semidirect
9. #10590742C2semidirect
10. #10590741C2semidirect
11. #10590740C2semidirect
29. #63898C22semidirect
30. #63898C22semidirect
33. #63843C22semidirect
34. #63843C22semidirect
36. #63823C4semidirect
38. #63642C22semidirect
39. C8×C3⋊Dic3C22semidirect
42. C3×#821C22semidirect
43. C3×#816C22semidirect
44. #63576C22semidirect
45. #63574C22semidirect
54. #5133D3semidirect
55. #5131D3semidirect
76. C3×#235C2×C4semidirect
79. C2×C3×D12C2×C4semidirect
95. #3748C2×C4semidirect
111. #3715C2×C4semidirect
112. #3713C2×C4semidirect
171. #821C2×D3semidirect
172. #816C2×D3semidirect
209. C3×D12C22×C4semidirect
212. C3×Dic6C22×C4semidirect
218. C3⋊(C3⋊C8)C22×C4semidirect
260. #235C4×D3semidirect
263. C2×D12C4×D3semidirect
346. C3⋊Dic3AGL(1,ℤ/8)semidirect
454. D12C2×C4×D3semidirect
461. Dic6C2×C4×D3semidirect
573. C32C4×AGL(1,ℤ/8)semidirect
649. C3#78866semidirect
650. C3#78914semidirect

Maximal subgroups

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

subgroupindex
#105949582
C2×#638982
C2×#638232
M16×C3⋊Dic32
C3×#51332
C3×#51312
#105911392
#105907432
#105907422
#105907412
#105907402
#789143
#788663