Finite Group Databasebeta

← #11860315

Subgroups — #11860315

Order 1152.

1177 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
1#10594954C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4#10592832C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×Dic3×M16C211yesmaximal, characteristic, complemented
7#10591131C211yesmaximal, characteristic, complemented
8#10590747C212yesmaximal, complemented
9#10590746C212yesmaximal, complemented
10#10590745C212yesmaximal, complemented
11#10590744C212yesmaximal, complemented
12#78914—31nomaximal
13C4×#908—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C2×C32×M16C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23#63952—21no—
24#63952—21no—
25#63894C2211yescharacteristic, complemented
26#63894C2211yescharacteristic, complemented
27Dic3×D12—21no—
28Dic3×D12—21no—
29Dic3×D12C2212yes—
30Dic3×D12C2212yes—
31C4×#624—21no—
32#63874—21no—
33#63844C2211yescharacteristic, complemented
34#63844C2211yescharacteristic, complemented
35#63830C418yescomplemented
36C2×#3716C2212yes—
37C2×#3714C2212yes—
38#63648C2212yescomplemented
39#63643C2212yescomplemented
40C3×#821C2212yes—
41C3×#821C2212yes—
42C3×#815C2212yescomplemented
43C3×C8×Dic3C2212yescomplemented
44#63575C2212yescomplemented
45#63573C2212yescomplemented
46C2×D4×Dic3—31no—
47C2×#932—31no—
48C2×#908—31no—
49#5522—31no—
50C4×#235—31no—
51C2×C4×D12—31no—
52C3×#418—31no—
53C3×C4×M16—31no—
54#5133—31no—
55#5133—31no—
56#5133—61no—
57#5131D311yescharacteristic, complemented
58#5121—31no—
59Dic3×M16D311yescharacteristic, complemented
60#4995—31no—
61#4785—32no—
62#4758—32no—
63#4757—32no—
64#4756—32no—
65#4711—32no—
66#4710—32no—
67C4×D24—32no—
68C4×#204—32no—
69C23×C3×D3—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C22×C3⋊Dic3—21no—
73#3828—22no—
74#3828C2×C414yescomplemented
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×#634C2311yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C22×C3×Dic3D411yescharacteristic
80C2×C3×D12—21no—
81C2×C3×D12—22no—
82C2×C3×D12C2×C414yescomplemented
83C2×C3×D12C2312yes—
84C2×#624—21no—
85C2×#624—21no—
86C2×D3×Dic3—22no—
87C2×D3×Dic3—22no—
88C2×D3×Dic3—44no—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C3×#217—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4×Dic3—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×#208C2×C414yescomplemented
102C2×C3×C3⋊C8C2312yes—
103#3724—21no—
104#3724—21no—
105#3722—21no—
106#3722—21no—
107(C2×D3)⋊Dic3—22no—
108(C2×D3)⋊Dic3—22no—
109Dic32—21no—
110Dic32—21no—
111#3716C2×C418yescomplemented
112#3714C2×C418yescomplemented
113C4×AGL(1,ℤ/8)—91noSylow
114C22×C3×D4—31no—
115C23×Dic3—61no—
116C2×#235—31no—
117C2×#235—31no—
118C2×#235—61no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—61no—
121C2×C3×M16—21no—
122C2×C3×M16—31no—
123C2×C3×M16C2×D311yescharacteristic
124C2×C3×M16C2×D311yescharacteristic
125C3×#117—31no—
126C2×C3×C42—31no—
127C2×#217—61no—
128D4×Dic3—32no—
129D4×Dic3—32no—
130D4×Dic3—61no—
131D4×Dic3—61no—
132C2×#214—32no—
133#932—38no—
134C2×#213—32no—
135C4×#67—61no—
136C4×#67—61no—
137C2×(C2×D3)⋊C4—61no—
138#926C2×D311yescharacteristic
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—61no—
142C2×C4×Dic3C2×D311yescharacteristic
143C2×#208C2×D311yescharacteristic
144#908—38no—
145C2×D24—32no—
146C2×#204—32no—
147#893—31no—
148#893—31no—
149#887—31no—
150#887—31no—
151#67⋊C4—61no—
152#67⋊C4—61no—
153C4×D12—32no—
154C4×D12—32no—
155C4×D12—31no—
156C4×D12—31no—
157C4×D12—61no—
158C4×D12—61no—
159#872—61no—
160#872—61no—
161C42×D3—61no—
162C42×D3—61no—
163C4×Dic6—31no—
164C4×Dic6—31no—
165C3×#102—32no—
166C3×#102—32no—
167C3×#97—32no—
168C3×C4×C8—32no—
169#821—32no—
170#821—32no—
171#821—62no—
172#821C2×D312yes—
173#821C2×D312yes—
174#818—32no—
175#817—32no—
176#816—32no—
177#816—32no—
178#816—62no—
179#815C2×D312yescomplemented
180C8×Dic3C2×D312yescomplemented
181#808—32no—
182#807—32no—
183C23×C32C2×D411yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3×D3—24no—
186C22×C3×D3—22no—
187C22×C3×D3—42no—
188C22×C3×D3—42no—
189C2×C32×C4C22×C412yes—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4#4112yes—
192C2×C32×C4C2411yescharacteristic
193#638—24no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—42no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)C22×C412yescomplemented
199C4×C3⋊D3—24no—
200#634—21no—
201#634C22×C412yescomplemented
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—41no—
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C2×C3×Dic3C2×D411yescharacteristic
210C3×D12—24no—
211C3×D12—22no—
212C3×D12C22×C414yes—
213#624—42no—
214#624—42no—
215D3×Dic3—44no—
216D3×Dic3—44no—
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—31no—
228#417—91no—
229C4×M16—31no—
230C24×C3—61no—
231C23×D3—21no—
232C2×C3×D4—34no—
233C2×C3×D4—32no—
234C2×C3×D4—61no—
235C2×C3×D4—62no—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—61no—
242C2×#67—61no—
243C2×#67—121no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—62no—
247C22×Dic3—62no—
248C22×Dic3—121no—
249C22×Dic3—124no—
250C22×Dic3D1211yescharacteristic
251C22×Dic3D1211yescharacteristic
252#235—34no—
253#235—34no—
254#235—64no—
255#235—62no—
256#235—62no—
257#235—122no—
258C2×D12—21no—
259C2×D12—22no—
260C2×D12—31no—
261C2×D12—31no—
262C2×D12—61no—
263C2×D12C4×D314yescomplemented
264C2×D12C22×D312yes—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—61no—
272C2×C4×D3—61no—
273C2×C4×D3—121no—
274C2×C4×D3—124no—
275C2×Dic6—31no—
276C2×Dic6—31no—
277C2×Dic6—61no—
278C3×M16—22no—
279C3×M16—22no—
280C3×M16—34no—
281C3×M16—42no—
282C2×C3×C8—22no—
283C2×C3×C8—32no—
284C2×C3×C8C22×D312yes—
285C2×C3×C8C22×D312yes—
286C3×C4⋊C4—31no—
287C3×C4⋊C4—31no—
288C3×C22⋊C4—61no—
289C3×C42—31no—
290C3×C42—31no—
291C3×C42—31no—
292C3×C42—31no—
293C3×C42—61no—
294#217—21no—
295#217—62no—
296#217—62no—
297#214—38no—
298#213—38no—
299(C2×D3)⋊C4—61no—
300(C2×D3)⋊C4—61no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—61no—
304(C2×D3)⋊C4—61no—
305C4⋊Dic3—32no—
306C4⋊Dic3—32no—
307C4⋊Dic3—62no—
308C4⋊Dic3—61no—
309C4⋊Dic3—61no—
310C4⋊Dic3—121no—
311C4⋊Dic3C22×D311yescharacteristic
312C4⋊Dic3C22×D311yescharacteristic
313Dic3⋊C4—61no—
314Dic3⋊C4—61no—
315Dic3⋊C4—61no—
316Dic3⋊C4—61no—
317C4×Dic3—21no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—61no—
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—22no—
335C2×C3⋊D3—41no—
336C2×C3⋊D3—41no—
337C2×C3×D3—24no—
338C2×C3×D3—48no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C32×C4C4×D412yes—
342C32×C4C23×C411yescharacteristic
343C32×C4C2×#4111yescharacteristic
344C3⋊Dic3—22no—
345C3⋊Dic3—42no—
346C3×Dic3—21no—
347C3×Dic3—21no—
348C3×Dic3—21no—
349C3×Dic3—41no—
350C3×Dic3—41no—
351C3×Dic3AGL(1,ℤ/8)12yescomplemented
352C2×#41—91no—
353C22×D4—31no—
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—91no—
363C4×D4—91no—
364C4×D4—92no—
365C4×D4—92no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4—181no—
369C4×D4—181no—
370#117—31no—
371#117—181no—
372C2×C4⋊C4—91no—
373C2×C22⋊C4—181no—
374C2×C42—31no—
375C2×C42—181no—
376#107—92no—
377#106—92no—
378#103—92no—
379#102—32no—
380#102—32no—
381#102—92no—
382#97—32no—
383C4×C8—32no—
384C23×C3—21no—
385C23×C3—64no—
386C23×C3—62no—
387C23×C3—122no—
388C23×C3—122no—
389C23×C3C2×D1211yescharacteristic
390C23×C3D3×D411yescharacteristic
391C22×D3—24no—
392C22×D3—22no—
393C22×D3—42no—
394C22×D3—42no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—121no—
398C3×D4—34no—
399C3×D4—64no—
400C3×D4—62no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—121no—
413C2×C3×C4C2×C4×D312yes—
414C2×C3×C4C2×C4×D312yes—
415C2×C3×C4C2×D1211yescharacteristic
416C2×C3×C4#23512yes—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4#23712yes—
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—64no—
422#67—64no—
423#67—124no—
424C2×Dic3—22no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—41no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—121no—
433C2×Dic3—122no—
434C2×Dic3—124no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3—124no—
438C2×Dic3—242no—
439C2×Dic3C2×D1211yescharacteristic
440C2×Dic3C2×D1211yescharacteristic
441C2×Dic3C2×D1211yescharacteristic
442C2×Dic3C2×D1211yescharacteristic
443D12—24no—
444D12—22no—
445D12—32no—
446D12—32no—
447D12—62no—
448D12—61no—
449D12—61no—
450D12—121no—
451D12C2×C4×D314yes—
452C4×D3—64no—
453C4×D3—64no—
454C4×D3—124no—
455C4×D3—122no—
456C4×D3—122no—
457C4×D3—122no—
458C4×D3—124no—
459C4×D3—124no—
460C4×D3—122no—
461Dic6—32no—
462Dic6—32no—
463Dic6—62no—
464Dic6—61no—
465Dic6—61no—
466Dic6—121no—
467C3×C8—22no—
468C3×C8—22no—
469C3×C8—34no—
470C3×C8—42no—
471C3⋊C8C2×C4×D314yescomplemented
472C2×C32—22no—
473C2×C32C2×C4×D411yescharacteristic
474C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
475C2×C32#57511yescharacteristic
476C3⋊D3—42no—
477C3×D3—44no—
478C24—61no—
479#41—94no—
480#41—182no—
481C2×Q8—91no—
482C2×D4—32no—
483C2×D4—34no—
484C2×D4—61no—
485C2×D4—62no—
486C2×D4—91no—
487C2×D4—181no—
488C22×C4—31no—
489C22×C4—31no—
490C22×C4—181no—
491C22×C4—181no—
492C22×C4—182no—
493C22×C4—182no—
494C22×C4—181no—
495C22×C4—181no—
496C22×C4—364no—
497C22×C4C2×D3211yescharacteristic
498SD16—98no—
499D8—98no—
500M16—22no—
501M16—34no—
502C2×C8—32no—
503C2×C8C2×D3212yes—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—92no—
507C4⋊C4—181no—
508C4⋊C4—181no—
509C4⋊C4—181no—
510C22⋊C4—61no—
511C22⋊C4—181no—
512C22⋊C4—181no—
513C22⋊C4—182no—
514C22⋊C4—182no—
515C42—31no—
516C42—31no—
517C42—31no—
518C42—31no—
519C42—61no—
520C42—181no—
521C42—181no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—64no—
531C22×C3—128no—
532C22×C3—122no—
533C22×C3—122no—
534C22×C3C4×D1212yes—
535C22×C3#67⋊C412yes—
536C22×C3C22×D1211yescharacteristic
537C22×C3C2×D3×D411yescharacteristic
538C2×D3—24no—
539C2×D3—48no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—122no—
545C2×D3—121no—
546C2×D3—121no—
547C2×D3—121no—
548C2×D3—121no—
549C2×D3—241no—
550C2×D3—241no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—32no—
555C3×C4—61no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—121no—
559C3×C4—121no—
560C3×C4C4×D1212yes—
561C3×C4#67⋊C412yes—
562C3×C4C22×C4×D311yescharacteristic
563C3×C4C22×C4×D311yescharacteristic
564C3×C4C2×#23511yescharacteristic
565C3×C4C2×#23711yescharacteristic
566Dic3—21no—
567Dic3—21no—
568Dic3—21no—
569Dic3—41no—
570Dic3—41no—
571Dic3—62no—
572Dic3—62no—
573Dic3—122no—
574Dic3—122no—
575Dic3—122no—
576Dic3—242no—
577Dic3#90812yescomplemented
578C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
579C23—62no—
580C23—64no—
581C23—122no—
582C23—122no—
583C23—181no—
584C23D3×D1211yescharacteristic
585Q8—92no—
586Q8—181no—
587D4—34no—
588D4—62no—
589D4—64no—
590D4—92no—
591D4—184no—
592D4—181no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—62no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—121no—
601C2×C4—181no—
602C2×C4—184no—
603C2×C4—182no—
604C2×C4—362no—
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—124no—
622C2×C3C2×C4×D1211yescharacteristic
623C2×C3C2×#67⋊C411yescharacteristic
624C2×C3C2×#90811yescharacteristic
625C2×C3#574811yescharacteristic
626C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
627C2×C3#577311yescharacteristic
628D3—44no—
629D3—122no—
630D3—122no—
631D3—242no—
632C22—21no—
633C22—21no—
634C22—64no—
635C22—128no—
636C22—122no—
637C22—122no—
638C22—182no—
639C22—361no—
640C22—361no—
641C22#6388012yes—
642C22C2×D3×D1211yescharacteristic
643C4—32no—
644C4—61no—
645C4—61no—
646C4—61no—
647C4—121no—
648C4—121no—
649C4—182no—
650C4—362no—
651C4#6388012yes—
652C4C2×C4×D3211yescharacteristic
653C4C2×#380411yescharacteristic
654C3—21no—
655C3C4×#90811yescharacteristic, complemented
656C3#7891411yescharacteristic, complemented
657C2—22no—
658C2—124no—
659C2—362no—
660C2D3×#90811yescharacteristic
661C2#1059471211yescharacteristic
662C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
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. #10594954C2semidirect
2. C2×Dic3×D12C2semidirect
4. #10592832C2semidirect
5. C3×#5131C2semidirect
6. C3×Dic3×M16C2semidirect
7. #10591131C2semidirect
8. #10590747C2semidirect
9. #10590746C2semidirect
10. #10590745C2semidirect
11. #10590744C2semidirect
25. #63894C22semidirect
26. #63894C22semidirect
33. #63844C22semidirect
34. #63844C22semidirect
35. #63830C4semidirect
38. #63648C22semidirect
39. #63643C22semidirect
42. C3×#815C22semidirect
43. C3×C8×Dic3C22semidirect
44. #63575C22semidirect
45. #63573C22semidirect
57. #5131D3semidirect
59. Dic3×M16D3semidirect
74. #3828C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
101. C3×#208C2×C4semidirect
111. #3716C2×C4semidirect
112. #3714C2×C4semidirect
179. #815C2×D3semidirect
180. C8×Dic3C2×D3semidirect
198. C4⋊(C3⋊D3)C22×C4semidirect
201. #634C22×C4semidirect
218. C3×C3⋊C8C22×C4semidirect
263. C2×D12C4×D3semidirect
326. #208C4×D3semidirect
351. C3×Dic3AGL(1,ℤ/8)semidirect
471. C3⋊C8C2×C4×D3semidirect
577. Dic3#908semidirect
578. C32C4×AGL(1,ℤ/8)semidirect
655. C3C4×#908semidirect
656. C3#78914semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×Dic3×D122
C2×#638302
#105928322
C3×#51312
C3×Dic3×M162
#105911312
#105907472
#105907462
#105907452
#105907442
#789143
C4×#9083