Finite Group Databasebeta

← #11860411

Subgroups — #11860411

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic
3#10594958C211yesmaximal, characteristic
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591582C212yesmaximal, complemented
6#10591581C212yesmaximal, complemented
7#10591572C212yesmaximal, complemented
8#10591571C212yesmaximal, complemented
9#10591131C211yesmaximal, characteristic, complemented
10#10591088C211yesmaximal, characteristic
11#10591060C211yesmaximal, characteristic, complemented
12Dic3×#137—31nomaximal
13#78946—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16Q8×C3⋊Dic3—21no—
17Q8×C3⋊Dic3—21no—
18Q8×C3⋊Dic3C2212yes—
19Q8×C3⋊Dic3C2212yes—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#216C2212yes—
25C3×#942C418yescomplemented
26C2×C3×#215C2212yes—
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30#67⋊Dic3—21no—
31#67⋊Dic3—21no—
32#63898C2211yescharacteristic
33#63898C2211yescharacteristic
34C4×D3×Dic3—21no—
35#63855—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38C3×#835C2212yes—
39C3×#835C2212yes—
40#63575C2212yes—
41#63573C2212yes—
42#63566C2212yes—
43#63563C2212yes—
44#63555C2212yes—
45#63553C2212yes—
46C2×C3×#137—31no—
47Dic3×#41—31no—
48C2×Q8×Dic3—31no—
49C2×Q8×Dic3—31no—
50C2×Q8×Dic3—61no—
51C2×#942D311yescharacteristic
52#5522—31no—
53C3×#419—31no—
54#5232—31no—
55#5225D311yescharacteristic, complemented
56#5184—32no—
57Dic3×Q16—32no—
58#5164—32no—
59Dic3×SD16—32no—
60#5133—31no—
61#5121—31no—
62Dic3×M16—31no—
63Dic3×M16—31no—
64#4995—31no—
65#4817—32no—
66#4790—32no—
67#4789—32no—
68#4788—32no—
69C2×C32×Q8—21no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2×C414yescomplemented
72C2×C32×Q8C2312yes—
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—21no—
76C22×C3⋊Dic3D411yescharacteristic
77C22×C3⋊Dic3D411yescharacteristic
78C2×C3×#67—21no—
79C3×#235—22no—
80C3×#235C2×C414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)—22no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C3×#217—21no—
97C3×#216C2×C418yescomplemented
98C3×#215C2×C418yescomplemented
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2311yescharacteristic
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C3×#208C2×C414yescomplemented
104C2×C3×C3⋊C8C2312yes—
105C2×C3×C3⋊C8C2312yes—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—21no—
108(C2×D3)⋊Dic3—21no—
109(C2×D3)⋊Dic3—21no—
110Dic32—21no—
111Dic32—21no—
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C22×C3×Q8—21no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117C2×#235C2×D311yescharacteristic
118C3×#137—38no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C3×#117—31no—
124Q8×Dic3—32no—
125Q8×Dic3—32no—
126Q8×Dic3—32no—
127Q8×Dic3—32no—
128Q8×Dic3—31no—
129Q8×Dic3—31no—
130Q8×Dic3—62no—
131Q8×Dic3—62no—
132Q8×Dic3—61no—
133Q8×Dic3—61no—
134Q8×Dic3—61no—
135Q8×Dic3—61no—
136Q8×Dic3—62no—
137Q8×Dic3—62no—
138C2×#216C2×D312yes—
139#942Dic318yescomplemented
140C2×#215C2×D312yes—
141D4×Dic3—31no—
142D4×Dic3—31no—
143D4×Dic3—61no—
144D4×Dic3—61no—
145#926—61no—
146#926C2×D311yescharacteristic
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—61no—
150C2×C4⋊Dic3—61no—
151C2×C4⋊Dic3—61no—
152C2×C4⋊Dic3—62no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—61no—
156C2×C4×Dic3—61no—
157C2×C4×Dic3—61no—
158C2×C4×Dic3—61no—
159C2×C4×Dic3—62no—
160C2×#208C2×D311yescharacteristic
161C2×#208C2×D311yescharacteristic
162#893—31no—
163#893—31no—
164#887—31no—
165#887—31no—
166#67⋊C4—61no—
167#67⋊C4—61no—
168#872—61no—
169C42×D3—61no—
170C3×#103—32no—
171C3×#103—32no—
172#835—32no—
173#835C2×D312yes—
174#835C2×D312yes—
175#832—32no—
176#821—32no—
177#818—32no—
178#817—32no—
179#816—32no—
180#815—32no—
181#815—32no—
182C8×Dic3—32no—
183C8×Dic3—32no—
184#808—32no—
185#807—32no—
186C23×C32C2×D411yescharacteristic
187C22×C3×D3—21no—
188C32×Q8—24no—
189C32×Q8—22no—
190C32×Q8C22×C414yes—
191C2×C32×C4—24no—
192C2×C32×C4—22no—
193C2×C32×C4C22×C412yes—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4#4112yes—
196C2×C32×C4C2411yescharacteristic
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—41no—
200C2×C3⋊Dic3—42no—
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C2×C3⋊Dic3C2×D411yescharacteristic
204C2×C3⋊Dic3C2×D411yescharacteristic
205C3×#67—24no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C3×D12—21no—
210C3×D12C22×C412yes—
211C3×C4×D3—24no—
212C3×Dic6—21no—
213C3×Dic6C22×C412yes—
214D3×Dic3—42no—
215D3×Dic3—42no—
216C3×C3⋊C8—22no—
217C3×C3⋊C8C22×C414yes—
218C2×#137—31no—
219C4×#41—91no—
220C2×C4×Q8—91no—
221#441—92no—
222#440—92no—
223C4×Q16—92no—
224C4×SD16—92no—
225#428—91no—
226#419—31no—
227#417—91no—
228C4×M16—91no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—22no—
232C2×C3×Q8—24no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—22no—
236C2×C3×Q8—22no—
237C2×C3×Q8—24no—
238C2×C3×Q8—22no—
239C2×C3×Q8—31no—
240C2×C3×Q8C4×D314yescomplemented
241C2×C3×Q8C2×Dic314yescomplemented
242C2×C3×Q8C22×D312yes—
243C2×C3×Q8C22×D312yes—
244C2×C3×D4—31no—
245C2×C3×D4—61no—
246C22×C3×C4—22no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—61no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C2×#67—21no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—62no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265#235—22no—
266#235C2×Dic314yes—
267C2×D12C22×D311yescharacteristic
268C2×C4×D3—21no—
269C2×C4×D3—61no—
270C2×C4×D3—61no—
271C2×Dic6C22×D311yescharacteristic
272C3×Q16—38no—
273C3×SD16—38no—
274C3×M16—34no—
275C3×M16—62no—
276C2×C3×C8—32no—
277C2×C3×C8—32no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—31no—
280C3×C22⋊C4—61no—
281C3×C42—61no—
282#217—21no—
283#217—61no—
284#217—61no—
285#216C2×Dic318yescomplemented
286#215C2×Dic318yescomplemented
287(C2×D3)⋊C4—61no—
288(C2×D3)⋊C4—61no—
289C4⋊Dic3—32no—
290C4⋊Dic3—32no—
291C4⋊Dic3—62no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—62no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3—64no—
299C4⋊Dic3—64no—
300C4⋊Dic3—62no—
301C4⋊Dic3—61no—
302C4⋊Dic3—61no—
303C4⋊Dic3C22×D311yescharacteristic
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307C4×Dic3—21no—
308C4×Dic3—31no—
309C4×Dic3—31no—
310C4×Dic3—31no—
311C4×Dic3—31no—
312C4×Dic3—31no—
313C4×Dic3—31no—
314C4×Dic3—31no—
315C4×Dic3—31no—
316C4×Dic3—61no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C4×Dic3—61no—
322C4×Dic3—61no—
323C4×Dic3—61no—
324C4×Dic3—62no—
325C4×Dic3—62no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3—64no—
329C4×Dic3—64no—
330#208—22no—
331#208C2×Dic314yescomplemented
332C2×C3⋊C8C22×D312yes—
333C2×C3⋊C8C22×D312yes—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32C4×D412yes—
337C22×C32C22×D411yescharacteristic
338C2×C3×D3—22no—
339C2×C3×D3—41no—
340C2×C3×D3—41no—
341C32×C4—24no—
342C32×C4C4×D412yes—
343C32×C4C23×C411yescharacteristic
344C32×C4C2×#4111yescharacteristic
345C3⋊Dic3—21no—
346C3⋊Dic3—21no—
347C3⋊Dic3—21no—
348C3⋊Dic3—42no—
349C3⋊Dic3#13712yescomplemented
350C3×Dic3—22no—
351C3×Dic3—41no—
352C3×Dic3—41no—
353C2×#41—31no—
354C22×Q8D3211yescharacteristic
355#137—38no—
356C2×Q16—32no—
357C2×SD16—32no—
358C2×M16—31no—
359C2×M16—31no—
360C4×Q8—91no—
361C4×Q8—91no—
362C4×Q8—92no—
363C4×Q8—92no—
364C4×Q8—181no—
365C4×Q8—181no—
366C4×D4—91no—
367C4×D4—91no—
368C4×D4—181no—
369C4×D4—181no—
370#117—31no—
371#117—181no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—181no—
374C2×C42—91no—
375C2×C42—181no—
376C2×C42—181no—
377#107—92no—
378#106—92no—
379#103—32no—
380#103—32no—
381#103—92no—
382#102—92no—
383#97—92no—
384C4×C8—92no—
385C23×C3—21no—
386C23×C3—61no—
387C23×C3D3×D411yescharacteristic
388C23×C3D3×D411yescharacteristic
389C22×D3—21no—
390C3×Q8—24no—
391C3×Q8—28no—
392C3×Q8—24no—
393C3×Q8—24no—
394C3×Q8—22no—
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8—32no—
398C3×Q8—61no—
399C3×Q8C2×C4×D314yes—
400C3×Q8C22×Dic314yes—
401C3×D4—32no—
402C3×D4—64no—
403C3×D4—61no—
404C2×C3×C4—24no—
405C2×C3×C4—28no—
406C2×C3×C4—24no—
407C2×C3×C4—24no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—61no—
415C2×C3×C4—64no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4#23712yes—
422C2×C3×C4#23712yes—
423C2×C3×C4C22×Dic312yes—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—24no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—31no—
433C2×Dic3—31no—
434C2×Dic3—31no—
435C2×Dic3—31no—
436C2×Dic3—31no—
437C2×Dic3—31no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—64no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—121no—
451C2×Dic3—121no—
452C2×Dic3—122no—
453C2×Dic3—124no—
454C2×Dic3—122no—
455C2×Dic3—122no—
456D12—21no—
457D12C22×Dic312yes—
458C4×D3—24no—
459C4×D3—122no—
460C4×D3—122no—
461Dic6—21no—
462Dic6C22×Dic312yes—
463C3×C8—34no—
464C3×C8—62no—
465C3⋊C8—22no—
466C3⋊C8C22×Dic314yes—
467C2×C32—22no—
468C2×C32C2×C4×D411yescharacteristic
469C2×C32C2×#13711yescharacteristic
470C2×C32#57511yescharacteristic
471C3×D3—42no—
472#41—34no—
473#41—62no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—31no—
477C2×Q8D3×Dic314yescomplemented
478C2×Q8C2×D3212yes—
479C2×D4—31no—
480C2×D4—61no—
481C22×C4—21no—
482C22×C4—61no—
483C22×C4—91no—
484C22×C4—91no—
485C22×C4—181no—
486C22×C4—181no—
487C22×C4—181no—
488C22×C4C2×D3211yescharacteristic
489Q16—38no—
490SD16—38no—
491M16—34no—
492M16—62no—
493C2×C8—32no—
494C2×C8—32no—
495C4⋊C4—31no—
496C4⋊C4—31no—
497C4⋊C4—92no—
498C4⋊C4—182no—
499C4⋊C4—182no—
500C4⋊C4—181no—
501C4⋊C4—181no—
502C4⋊C4—181no—
503C22⋊C4—61no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C42—61no—
507C42—91no—
508C42—91no—
509C42—91no—
510C42—91no—
511C42—182no—
512C42—182no—
513C42—181no—
514C42—181no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—62no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3#67⋊C412yes—
527C22×C3D4×Dic312yes—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C2×D3—22no—
531C2×D3—41no—
532C2×D3—41no—
533C3×C4—28no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—62no—
540C3×C4—121no—
541C3×C4—121no—
542C3×C4#67⋊C412yes—
543C3×C4D4×Dic312yes—
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C2×#23711yescharacteristic
546C3×C4C2×#23711yescharacteristic
547C3×C4C23×Dic311yescharacteristic
548Dic3—22no—
549Dic3—32no—
550Dic3—32no—
551Dic3—41no—
552Dic3—41no—
553Dic3—62no—
554Dic3—62no—
555Dic3—61no—
556Dic3—61no—
557Dic3—61no—
558Dic3—61no—
559Dic3—61no—
560Dic3—61no—
561Dic3—121no—
562Dic3—121no—
563Dic3—124no—
564Dic3—122no—
565Dic3—122no—
566C32C4×#13711yescharacteristic, complemented, Sylow
567C23—61no—
568C23#381111yescharacteristic
569Q8—22no—
570Q8—24no—
571Q8—32no—
572Q8—61no—
573Q8C2×D3×Dic314yes—
574D4—32no—
575D4—64no—
576D4—61no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—61no—
580C2×C4—64no—
581C2×C4—61no—
582C2×C4—61no—
583C2×C4—91no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—91no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—362no—
590C2×C4—362no—
591C2×C4—361no—
592C2×C4—362no—
593C2×C4C2×D3×Dic312yes—
594C2×C4#380512yes—
595C2×C4#381111yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—34no—
598C8—62no—
599C2×C3—24no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—122no—
606C2×C3C2×#67⋊C411yescharacteristic
607C2×C3D3×#13711yescharacteristic
608C2×C3D3×#13711yescharacteristic
609C2×C3#577711yescharacteristic
610C2×C3#577711yescharacteristic
611C2×C3C2×D4×Dic311yescharacteristic
612D3—42no—
613C22—21no—
614C22—21no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22#67⋊Dic312yes—
619C22C2×#381111yescharacteristic
620C4—24no—
621C4—62no—
622C4—92no—
623C4—121no—
624C4—121no—
625C4—181no—
626C4—181no—
627C4—181no—
628C4—362no—
629C4#67⋊Dic312yes—
630C4C22×D3×Dic311yescharacteristic
631C4C2×#380511yescharacteristic
632C3—21no—
633C3#7894611yescharacteristic, complemented
634C3Dic3×#13711yescharacteristic, complemented
635C2—22no—
636C2—122no—
637C2#1059532211yescharacteristic
638C2#1059532311yescharacteristic
639C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
4. C3×#5225C2semidirect
5. #10591582C2semidirect
6. #10591581C2semidirect
7. #10591572C2semidirect
8. #10591571C2semidirect
9. #10591131C2semidirect
11. #10591060C2semidirect
25. C3×#942C4semidirect
55. #5225D3semidirect
71. C2×C32×Q8C2×C4semidirect
97. C3×#216C2×C4semidirect
98. C3×#215C2×C4semidirect
103. C3×#208C2×C4semidirect
139. #942Dic3semidirect
240. C2×C3×Q8C4×D3semidirect
241. C2×C3×Q8C2×Dic3semidirect
285. #216C2×Dic3semidirect
286. #215C2×Dic3semidirect
331. #208C2×Dic3semidirect
349. C3⋊Dic3#137semidirect
477. C2×Q8D3×Dic3semidirect
566. C32C4×#137semidirect
633. C3#78946semidirect
634. C3Dic3×#137semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×C3×#9422
#105949582
C3×#52252
#105915822
#105915812
#105915722
#105915712
#105911312
#105910882
#105910602
Dic3×#1373
#789463