Finite Group Databasebeta

← #11870509

Subgroups — #11870509

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591467C212yesmaximal
6#10591445C212yesmaximal, complemented
7#10590529C212yesmaximal, complemented
8#10590483C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590256C211yesmaximal, characteristic, complemented
12#81044—31nomaximal
13#80408—31nomaximal
14C2×D4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×C4×D4C2211yescharacteristic
17D4×C3⋊Dic3C2211yescharacteristic
18C4×#638—21no—
19#64102C2211yescharacteristic
20C4⋊C4×C3⋊D3C2211yescharacteristic
21#64090—21no—
22C22⋊C4×C3⋊D3—21no—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C42×C3⋊D3C2211yescharacteristic
25C2×C3×#214C2212yes—
26C3×#869C2211yescharacteristic, complemented
27C3×#869C2211yescharacteristic, complemented
28#63872—21no—
29#63871—21no—
30#63871C2212yes—
31#63849—21no—
32#63843—21no—
33#63843C2212yescomplemented
34C2×#3717C2212yes—
35C3×#832C2212yes—
36C3×#810C2212yescomplemented
37C3×#808C2212yescomplemented
38C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63573C2212yescomplemented
41#63566C2212yescomplemented
42#63564C2212yes—
43#63557C2212yes—
44#63553C2212yescomplemented
45#5728—31no—
46#5728—31no—
47C4×D3×D4—31no—
48C4×D3×D4—31no—
49C4×D3×D4—61no—
50C3×#476—31no—
51C3×#461—31no—
52#5169—32no—
53Dic3×SD16—32no—
54#5084—31no—
55#5083—31no—
56#5019D311yescharacteristic, complemented
57#5008D311yescharacteristic, complemented
58#4862—32no—
59#4852—32no—
60#4842—31no—
61#4841—31no—
62#4833—31no—
63#4833—31no—
64#4805—32no—
65#4788—32no—
66#4776—32no—
67#4758—32no—
68C23×C3⋊D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#638—21no—
72C22×C3⋊Dic3—21no—
73D4×C3⋊D3—22no—
74D4×C3⋊D3—22no—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×C4×C3⋊D3—44no—
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×C3×Dic6—21no—
84C2×C3×Dic6C2312yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3757—21no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C3×#214—24no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3—21no—
100C3×C4⋊Dic3C2312yes—
101C2×C3×C3⋊C8C2312yes—
102C2×C3×C3⋊C8C2312yes—
103Dic3⋊Dic3—22no—
104Dic3⋊Dic3—22no—
105#3722—22no—
106Dic32—22no—
107#3717—24no—
108#3101—91noSylow
109C2×D3×D4—31no—
110C2×D3×D4—31no—
111C2×D3×D4—61no—
112C22×C4×D3—61no—
113C22×C4×D3—61no—
114C22×C4×D3—62no—
115C2×C3×SD16—32no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—31no—
118C3×C4×D4—21no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121#946—32no—
122#946—61no—
123Q8×Dic3—32no—
124Q8×Dic3—61no—
125C2×#215—32no—
126D4×Dic3—31no—
127D4×Dic3—31no—
128D4×Dic3—61no—
129C2×#214C2×D312yes—
130C4×#67—61no—
131C4×#67—61no—
132C4×#67—62no—
133C2×#204—32no—
134#897—32no—
135#897—61no—
136#893—31no—
137#893—31no—
138#893—61no—
139#892—61no—
140#892—61no—
141D3×C4⋊C4—31no—
142D3×C4⋊C4—31no—
143D3×C4⋊C4—61no—
144#890—61no—
145#890—61no—
146#887—32no—
147#887—61no—
148#67⋊C4—61no—
149#67⋊C4—61no—
150#67⋊C4—62no—
151D3×C22⋊C4—61no—
152D3×C22⋊C4—61no—
153D3×C22⋊C4—62no—
154C4×D12—31no—
155C4×D12—31no—
156C4×D12—61no—
157C42×D3—31no—
158C42×D3—31no—
159C42×D3—61no—
160#869C2×D311yescharacteristic, complemented
161#869C2×D311yescharacteristic, complemented
162C3×#106—32no—
163C3×C4⋊C8—31no—
164C3×C4⋊C8—31no—
165C3×#103—32no—
166C3×#102—32no—
167#835—32no—
168#832C2×D312yes—
169#821—32no—
170(C2×D3)⋊C8—32no—
171(C2×D3)⋊C8—32no—
172#817—32no—
173#816—32no—
174C8×Dic3—32no—
175C8×Dic3—32no—
176#810C2×D312yescomplemented
177#809—32no—
178#808—32no—
179#808C2×D312yescomplemented
180C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
181C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
182C23×C32—21no—
183C22×C3⋊D3—24no—
184C22×C3⋊D3—21no—
185C22×C3⋊D3—42no—
186C22×C3⋊D3—42no—
187C22×C3⋊D3C2×D411yescharacteristic
188C32×D4—21no—
189C32×D4#4112yes—
190C2×C32×C4—21no—
191C2×C32×C4—42no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195#638—24no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—42no—
198C2×C3⋊Dic3C2×D411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C4⋊(C3⋊D3)—21no—
202C4⋊(C3⋊D3)#4112yes—
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205C4×C3⋊D3—41no—
206C4×C3⋊D3—42no—
207C4×C3⋊D3—42no—
208C4×C3⋊D3—42no—
209C4×C3⋊D3SD1614yescomplemented
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C3×Dic6—22no—
213C3×Dic6—22no—
214C3×Dic6—42no—
215C3×C3⋊C8—22no—
216C3×C3⋊C8—22no—
217#533—91no—
218C2×C4×D4—91no—
219#483—92no—
220#476—31no—
221#476—91no—
222#461—31no—
223#461—91no—
224#450—92no—
225C4×SD16—92no—
226C4×SD16—92no—
227#431—91no—
228C23×D3—61no—
229C23×D3—61no—
230C23×D3—62no—
231C2×C3×Q8—32no—
232C2×C3×Q8—61no—
233C2×C3×D4—21no—
234C2×C3×D4C22×D311yescharacteristic
235C2×C3×D4C22×D311yescharacteristic
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C2×#67—61no—
240C2×#67—61no—
241C2×#67—62no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245D3×D4—62no—
246D3×D4—62no—
247D3×D4—64no—
248D3×D4—64no—
249D3×D4—62no—
250D3×D4—62no—
251C2×D12—31no—
252C2×D12—31no—
253C2×D12—61no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—61no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×C4×D3—61no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—61no—
271C2×C4×D3—61no—
272C2×C4×D3—124no—
273C2×C4×D3—124no—
274C2×C4×D3—128no—
275C2×Dic6—21no—
276C2×Dic6C22×D312yes—
277C3×SD16—64no—
278C2×C3×C8—32no—
279C2×C3×C8—32no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—32no—
282C3×C4⋊C4—61no—
283C3×C4⋊C4—61no—
284C3×C4⋊C4—61no—
285C3×C4⋊C4C22×D311yescharacteristic
286C3×C4⋊C4C22×D311yescharacteristic
287C3×C22⋊C4—22no—
288C3×C22⋊C4—21no—
289C3×C22⋊C4—21no—
290C3×C42—21no—
291C3×C42C22×D311yescharacteristic
292C3×C42C22×D311yescharacteristic
293#217—61no—
294#217—61no—
295#217—62no—
296#215—64no—
297#214—24no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—61no—
301(C2×D3)⋊C4—61no—
302(C2×D3)⋊C4—62no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—61no—
305(C2×D3)⋊C4—61no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—31no—
310C4⋊Dic3—31no—
311C4⋊Dic3—61no—
312C4⋊Dic3—62no—
313C4⋊Dic3—62no—
314C4⋊Dic3C22×D312yes—
315Dic3⋊C4—62no—
316Dic3⋊C4—62no—
317Dic3⋊C4—61no—
318Dic3⋊C4—61no—
319Dic3⋊C4—62no—
320C4×Dic3—31no—
321C4×Dic3—31no—
322C4×Dic3—31no—
323C4×Dic3—31no—
324C4×Dic3—31no—
325C4×Dic3—31no—
326C4×Dic3—61no—
327C4×Dic3—61no—
328C4×Dic3—61no—
329C4×Dic3—62no—
330C4×Dic3—62no—
331C2×C3⋊C8C22×D312yes—
332C2×C3⋊C8C22×D312yes—
333#204—64no—
334C22×C32—22no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32C22×D411yescharacteristic
338C2×C3⋊D3—21no—
339C2×C3⋊D3—21no—
340C2×C3⋊D3—22no—
341C2×C3⋊D3—48no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3⋊D3C2×SD1612yes—
345C32×C4—21no—
346C32×C4—41no—
347C32×C4C2×SD1612yes—
348C32×C4C2×#4111yescharacteristic
349C32×C4C2×#4111yescharacteristic
350C3⋊Dic3—21no—
351C3⋊Dic3—21no—
352C3⋊Dic3—41no—
353C3⋊Dic3C2×SD1612yes—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C22×D4—91no—
357C23×C4—181no—
358C2×SD16—32no—
359C2×SD16—92no—
360C4⋊Q8—31no—
361C4⋊Q8—31no—
362#125—181no—
363C22⋊Q8—92no—
364C22⋊Q8—181no—
365C4×Q8—92no—
366C4×Q8—181no—
367C4×D4—91no—
368C4×D4—91no—
369C4×D4—91no—
370C4×D4—181no—
371C4×D4—181no—
372C4×D4D3211yescharacteristic
373#117—181no—
374C2×C4⋊C4—91no—
375C2×C22⋊C4—181no—
376C2×C42—91no—
377#106—32no—
378#106—92no—
379C4⋊C8—31no—
380C4⋊C8—31no—
381#103—32no—
382#103—92no—
383#102—32no—
384#102—92no—
385C22⋊C8—92no—
386C4×C8—92no—
387C23×C3—22no—
388C23×C3—21no—
389C23×C3—21no—
390C22×D3—31no—
391C22×D3—31no—
392C22×D3—61no—
393C22×D3—62no—
394C22×D3—68no—
395C22×D3—64no—
396C22×D3—64no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—122no—
400C22×D3—122no—
401C22×D3—124no—
402C22×D3—124no—
403C22×D3—122no—
404C22×D3—122no—
405C3×Q8—62no—
406C3×Q8—62no—
407C3×Q8—122no—
408C3×D4—22no—
409C3×D4—21no—
410C3×D4—21no—
411C3×D4—22no—
412C3×D4#23712yes—
413C3×D4#23912yes—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—44no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4D3×D411yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—68no—
432#67—64no—
433#67—64no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—31no—
437C2×Dic3—31no—
438C2×Dic3—31no—
439C2×Dic3—31no—
440C2×Dic3—31no—
441C2×Dic3—31no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—62no—
446C2×Dic3—61no—
447C2×Dic3—61no—
448C2×Dic3—122no—
449C2×Dic3—122no—
450C2×Dic3—124no—
451D12—32no—
452D12—32no—
453D12—62no—
454D12—62no—
455D12—61no—
456D12—61no—
457C4×D3—34no—
458C4×D3—34no—
459C4×D3—64no—
460C4×D3—62no—
461C4×D3—62no—
462C4×D3—61no—
463C4×D3—61no—
464C4×D3—61no—
465C4×D3—61no—
466C4×D3—122no—
467C4×D3—122no—
468C4×D3—121no—
469C4×D3—121no—
470C4×D3—124no—
471C4×D3—124no—
472C4×D3—122no—
473C4×D3—122no—
474C4×D3—122no—
475C4×D3—124no—
476C4×D3—122no—
477C4×D3—122no—
478Dic6—22no—
479Dic6—22no—
480Dic6—42no—
481C3×C8—62no—
482C3×C8—62no—
483C3⋊C8—22no—
484C3⋊C8—22no—
485C2×C32—42no—
486C2×C32#52511yescharacteristic
487C2×C32C22×SD1611yescharacteristic
488C2×C32#57511yescharacteristic
489C3⋊D3—22no—
490C3⋊D3—42no—
491C24—181no—
492C2×Q8—32no—
493C2×Q8—61no—
494C2×D4—91no—
495C2×D4—181no—
496C2×D4—182no—
497C2×D4—182no—
498C2×D4C2×D3211yescharacteristic
499C22×C4—21no—
500C22×C4—91no—
501C22×C4—91no—
502C22×C4—91no—
503C22×C4—181no—
504C22×C4—181no—
505C22×C4—181no—
506C22×C4—181no—
507C22×C4—364no—
508SD16—64no—
509SD16—184no—
510C2×C8—32no—
511C2×C8—32no—
512C4⋊C4—32no—
513C4⋊C4—61no—
514C4⋊C4—61no—
515C4⋊C4—61no—
516C4⋊C4—91no—
517C4⋊C4—181no—
518C4⋊C4—182no—
519C4⋊C4—182no—
520C4⋊C4C2×D3211yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—181no—
523C22⋊C4—182no—
524C22⋊C4—181no—
525C22⋊C4—181no—
526C42—91no—
527C42—91no—
528C42—91no—
529C42—182no—
530C42C2×D3211yescharacteristic
531C22×C3—24no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—21no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3C2×D3×D411yescharacteristic
542C22×C3C2×D3×D411yescharacteristic
543C2×D3—32no—
544C2×D3—32no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—61no—
549C2×D3—61no—
550C2×D3—61no—
551C2×D3—61no—
552C2×D3—64no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—1216no—
556C2×D3—128no—
557C2×D3—128no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—121no—
561C2×D3—121no—
562C2×D3—121no—
563C2×D3—121no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—22no—
569C3×C4—41no—
570C3×C4—42no—
571C3×C4—41no—
572C3×C4—41no—
573C3×C4—122no—
574C3×C4—122no—
575C3×C4D3×SD1612yes—
576C3×C4D3×SD1612yes—
577C3×C4C2×#23711yescharacteristic
578C3×C4C2×#23911yescharacteristic
579C3×C4D3×#4111yescharacteristic
580C3×C4D3×#4111yescharacteristic
581Dic3—32no—
582Dic3—32no—
583Dic3—42no—
584Dic3—42no—
585Dic3—62no—
586Dic3—62no—
587Dic3—61no—
588Dic3—61no—
589Dic3—61no—
590Dic3—61no—
591Dic3—121no—
592Dic3—122no—
593Dic3—121no—
594Dic3—121no—
595C32#310111yescharacteristic, complemented, Sylow
596C23—21no—
597C23—91no—
598C23—184no—
599C23—181no—
600C23—362no—
601C23—362no—
602Q8—62no—
603Q8—62no—
604Q8—122no—
605D4—21no—
606D4—92no—
607D4—184no—
608D4—181no—
609D4#379612yes—
610C2×C4—21no—
611C2×C4—42no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—91no—
615C2×C4—94no—
616C2×C4—91no—
617C2×C4—91no—
618C2×C4—181no—
619C2×C4—181no—
620C2×C4—181no—
621C2×C4—361no—
622C2×C4—362no—
623C2×C4—362no—
624C2×C4—362no—
625C2×C4—362no—
626C2×C4#381111yescharacteristic
627C2×C4#381111yescharacteristic
628C2×C4C22×D3211yescharacteristic
629C8—62no—
630C8—62no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—44no—
635C2×C3—42no—
636C2×C3—42no—
637C2×C3#560611yescharacteristic
638C2×C3#562711yescharacteristic
639C2×C3C2×D3×SD1611yescharacteristic
640C2×C3C2×D3×SD1611yescharacteristic
641C2×C3#577311yescharacteristic
642C2×C3#577711yescharacteristic
643D3—64no—
644D3—62no—
645D3—62no—
646D3—124no—
647D3—122no—
648D3—122no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—92no—
653C22—181no—
654C22—181no—
655C22—182no—
656C22—368no—
657C22—361no—
658C22—361no—
659C22C2×#381111yescharacteristic
660C4—21no—
661C4—41no—
662C4—92no—
663C4—122no—
664C4—122no—
665C4—181no—
666C4—181no—
667C4—361no—
668C4#6393012yes—
669C4C2×#379611yescharacteristic
670C4#6430611yescharacteristic
671C3—21no—
672C3#8040811yescharacteristic, complemented
673C3#8104411yescharacteristic, complemented
674C2—42no—
675C2—182no—
676C2—362no—
677C2#1059492211yescharacteristic
678C2C2×#6393011yescharacteristic
679C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3101
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593866C2semidirect
3. C3×#5019C2semidirect
4. C3×#5008C2semidirect
6. #10591445C2semidirect
7. #10590529C2semidirect
8. #10590483C2semidirect
9. #10590379C2semidirect
10. #10590300C2semidirect
11. #10590256C2semidirect
26. C3×#869C22semidirect
27. C3×#869C22semidirect
33. #63843C22semidirect
36. C3×#810C22semidirect
37. C3×#808C22semidirect
38. C3×C4⋊(C3⋊C8)C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63573C22semidirect
41. #63566C22semidirect
44. #63553C22semidirect
56. #5019D3semidirect
57. #5008D3semidirect
160. #869C2×D3semidirect
161. #869C2×D3semidirect
176. #810C2×D3semidirect
179. #808C2×D3semidirect
180. C4⋊(C3⋊C8)C2×D3semidirect
181. C4⋊(C3⋊C8)C2×D3semidirect
209. C4×C3⋊D3SD16semidirect
595. C32#3101semidirect
672. C3#80408semidirect
673. C3#81044semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938662
C3×#50192
C3×#50082
#105914672
#105914452
#105905292
#105904832
#105903792
#105903002
#105902562
#810443
#804083