Finite Group Databasebeta

← #11887032

Subgroups — #11887032

Order 1152.

1202 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591168C212yesmaximal, complemented
5#10591164C212yesmaximal, complemented
6#10591133C212yesmaximal, complemented
7C2×#63564C212yesmaximal, complemented
8#10590349C211yesmaximal, characteristic, complemented
9C4×#3714C211yesmaximal, characteristic, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#83525—31nomaximal
13#79438—31nomaximal
14C2×D4×C3⋊D3—21no—
15C22×C4⋊(C3⋊D3)C2212yes—
16C2×C3×#237—21no—
17C32×C4×D4C2211yescharacteristic
18#64139C2212yes—
19#64104—21no—
20#64091—22no—
21#64083C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#930C2212yescomplemented
24C2×C3×C4⋊Dic3C2212yescomplemented
25C22×C3×C3⋊C8C2212yescomplemented
26C3×#897—21no—
27C3×#886—22no—
28C3×C4×D12C2211yescharacteristic, complemented
29C3×#869C2211yescharacteristic, complemented
30C2×#3714C2211yescharacteristic
31C2×#3714C2212yescomplemented
32C3×#830C2212yescomplemented
33C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×C4×C3⋊C8C2211yescharacteristic, complemented
35#63575C2212yescomplemented
36#63575C2211yescharacteristic, complemented
37#63564C2212yes—
38#63564C2211yescharacteristic
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63564C2212yescomplemented
42#63563C2211yescharacteristic, complemented
43C3×#547—31no—
44#5555D311yescharacteristic, complemented
45D4×D12—31no—
46D4×D12—31no—
47D4×D12—61no—
48C3×C8×D4—31no—
49#5115—32no—
50C2×#821—32no—
51#5088—31no—
52#5087—31no—
53#5038—32no—
54#5036—32no—
55#5015—31no—
56C4×#213—31no—
57D4×C3⋊C8D311yescharacteristic, complemented
58#4967—32no—
59C2×#809—32no—
60#4846—31no—
61#4843—31no—
62#4736—32no—
63#4732—32no—
64#4694—31no—
65C4×D24—31no—
66C23×C3⋊D3—22no—
67C2×C32×D4D411yescharacteristic
68C22×C32×C4C2312yes—
69C2×#638—22no—
70D4×C3⋊D3—44no—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—22no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)—42no—
76C2×C4⋊(C3⋊D3)C2312yes—
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×C3×#67—22no—
80C22×C3×Dic3—22no—
81C3×#237—44no—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×Dic6—21no—
85C32×C4⋊C4D411yescharacteristic
86C32×C22⋊C4D412yes—
87C32×C42C2311yescharacteristic
88#3752—21no—
89#3752—22no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3714—22no—
102#3714—42no—
103#3294—91noSylow
104C2×C3×#41—61no—
105C2×#237—21no—
106C2×D3×D4—62no—
107C2×D3×D4—61no—
108C2×D3×D4—61no—
109C22×D12—32no—
110C22×D12—32no—
111C22×D12—62no—
112C22×C3×C8—32no—
113C3×C4⋊Q8—31no—
114C3×#123—62no—
115C3×C22⋊Q8—61no—
116C3×#121—32no—
117C3×C4×D4—21no—
118C3×C4×D4—31no—
119C3×C4×D4C2×D311yescharacteristic
120C3×C4×D4C2×D311yescharacteristic
121C2×C3×C4⋊C4—32no—
122C2×#213—31no—
123C2×#213—32no—
124#930—32no—
125#930—32no—
126#930—62no—
127#930C2×D312yescomplemented
128C2×C4⋊Dic3C2×D312yescomplemented
129C22×C3⋊C8C2×D312yescomplemented
130C2×D24—31no—
131C2×D24—32no—
132#897—21no—
133#895—62no—
134#895—61no—
135#895—61no—
136#886—22no—
137#882—64no—
138#882—62no—
139#882—62no—
140#874—31no—
141#874—31no—
142#874—61no—
143C4×D12—31no—
144C4×D12—31no—
145C4×D12—61no—
146C4×D12C2×D311yescharacteristic, complemented
147#869C2×D311yescharacteristic, complemented
148C3×C4⋊C8—31no—
149C3×C22⋊C8—32no—
150C3×C4×C8—31no—
151#832—31no—
152#830C2×D312yescomplemented
153#821—31no—
154#821—31no—
155#821—32no—
156#821—32no—
157#821—32no—
158#821—32no—
159#818—31no—
160#818—32no—
161#809—31no—
162#809—32no—
163#809—32no—
164#809—32no—
165#809—32no—
166#807—31no—
167#807—32no—
168C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
169C4×C3⋊C8C2×D311yescharacteristic, complemented
170C23×C32C2×D412yes—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—44no—
174C22×C3⋊D3—44no—
175C22×C3⋊D3—82no—
176C22×C3×D3—21no—
177C32×D4D814yescomplemented
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—44no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)—22no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—44no—
190C4⋊(C3⋊D3)—42no—
191C4⋊(C3⋊D3)—81no—
192C4⋊(C3⋊D3)#4112yescomplemented
193C4×C3⋊D3—42no—
194C3×#67—44no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—44no—
198C3×D12—21no—
199C3×D12—21no—
200C3×C4×D3—42no—
201C3×Dic6—42no—
202C3×C3⋊C8—21no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—21no—
205#547—31no—
206D42—91no—
207#486—91no—
208#480—92no—
209#474—91no—
210#466—92no—
211#459—91no—
212#447—92no—
213C4×D8—91no—
214C8×D4—31no—
215C2×#102—92no—
216C23×D3—64no—
217C23×D3—62no—
218C23×D3—62no—
219C3×#41—124no—
220C2×C3×Q8—61no—
221C2×C3×D4—21no—
222C2×C3×D4—31no—
223C2×C3×D4—62no—
224C2×C3×D4D1211yescharacteristic
225C2×C3×D4#6711yescharacteristic
226C22×C3×C4—22no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D312yes—
231C2×#67—22no—
232C2×#67—64no—
233C2×#67—62no—
234C2×#67—62no—
235C22×Dic3—22no—
236#237—44no—
237D3×D4—128no—
238D3×D4—124no—
239D3×D4—124no—
240C2×D12—31no—
241C2×D12—31no—
242C2×D12—32no—
243C2×D12—32no—
244C2×D12—61no—
245C2×D12—62no—
246C2×D12—64no—
247C2×D12—64no—
248C2×D12—62no—
249C2×D12—64no—
250C2×D12—61no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—124no—
258C2×D12—122no—
259C2×D12—122no—
260C2×D12—124no—
261C2×D12C22×D311yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—62no—
264C2×C4×D3—61no—
265C2×C4×D3—61no—
266C2×Dic6—21no—
267C2×C3×C8—31no—
268C2×C3×C8—32no—
269C2×C3×C8—31no—
270C2×C3×C8—122no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—61no—
276C3×C4⋊C4D1211yescharacteristic
277C3×C4⋊C4#6711yescharacteristic
278C3×C22⋊C4—22no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—62no—
281C3×C22⋊C4D1212yes—
282C3×C22⋊C4#6712yes—
283C3×C42—21no—
284C3×C42C22×D311yescharacteristic
285C3×C42C22×D311yescharacteristic
286#213—62no—
287#213—122no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—61no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—61no—
295(C2×D3)⋊C4—62no—
296C4⋊Dic3—21no—
297C4⋊Dic3—22no—
298C4⋊Dic3—31no—
299C4⋊Dic3—31no—
300C4⋊Dic3—61no—
301C4⋊Dic3C22×D312yes—
302C4⋊Dic3C22×D311yescharacteristic
303C2×C3⋊C8—42no—
304C2×C3⋊C8C22×D311yescharacteristic
305C2×C3⋊C8C22×D311yescharacteristic
306C2×C3⋊C8C22×D312yes—
307D24—62no—
308D24—122no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32C2×D814yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—41no—
315C2×C3⋊D3—41no—
316C2×C3⋊D3—42no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3—42no—
319C2×C3⋊D3—88no—
320C2×C3×D3—41no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C32×C4—22no—
324C32×C4—21no—
325C32×C4C2×D812yes—
326C32×C4C2×#4111yescharacteristic
327C32×C4H(5,𝔽2)11yescharacteristic
328C3⋊Dic3—41no—
329C3×Dic3—42no—
330C3×Dic3—41no—
331C2×#41—61no—
332C22×D4—92no—
333C22×D4—181no—
334C2×D8—91no—
335C2×D8—92no—
336C22×C8—32no—
337C4⋊Q8—31no—
338#127—91no—
339#123—62no—
340C22⋊Q8—61no—
341#121—32no—
342#121—92no—
343#121—181no—
344#120—182no—
345C4×D4—31no—
346C4×D4—91no—
347C4×D4D3211yescharacteristic
348C2×C4⋊C4—32no—
349#107—91no—
350#107—92no—
351C4⋊C8—31no—
352#102—91no—
353#102—92no—
354#102—92no—
355#102—92no—
356#102—92no—
357#102—91no—
358C22⋊C8—32no—
359C4×C8—31no—
360C23×C3—22no—
361C23×C3—61no—
362C23×C3C2×D1212yes—
363C23×C3C2×#6712yes—
364C22×D3—21no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—64no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—124no—
372C22×D3—124no—
373C22×D3—128no—
374C22×D3—128no—
375C22×D3—124no—
376C22×D3—124no—
377C22×D3—242no—
378C22×D3—242no—
379C22×D3—244no—
380C3×Q8—122no—
381C3×D4—24no—
382C3×D4—61no—
383C3×D4—61no—
384C3×D4—124no—
385C3×D4D2414yescomplemented
386C3×D4#21314yescomplemented
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—22no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—124no—
400C2×C3×C4—122no—
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1212yes—
403C2×C3×C4C2×D1211yescharacteristic
404C2×C3×C4C2×#6711yescharacteristic
405C2×C3×C4C2×#6712yes—
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—44no—
410#67—128no—
411#67—124no—
412#67—124no—
413C2×Dic3—22no—
414C2×Dic3—21no—
415C2×Dic3—44no—
416C2×Dic3—62no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419D12—21no—
420D12—21no—
421D12—32no—
422D12—32no—
423D12—62no—
424D12—62no—
425D12—61no—
426D12—62no—
427D12—62no—
428D12—62no—
429D12—61no—
430D12—62no—
431D12—122no—
432D12—122no—
433D12—124no—
434D12—124no—
435D12—124no—
436D12—128no—
437D12—122no—
438D12—122no—
439D12—241no—
440D12—241no—
441D12—242no—
442C4×D3—42no—
443C4×D3—124no—
444C4×D3—122no—
445C4×D3—122no—
446Dic6—42no—
447C3×C8—61no—
448C3×C8—62no—
449C3×C8—61no—
450C3⋊C8—21no—
451C3⋊C8—22no—
452C3⋊C8—21no—
453C2×C32—24no—
454C2×C32#54611yescharacteristic
455C2×C32C22×D811yescharacteristic
456C2×C32#57711yescharacteristic
457C3⋊D3—42no—
458C3⋊D3—82no—
459C3×D3—81no—
460C24—182no—
461#41—124no—
462C2×Q8—61no—
463C2×D4—31no—
464C2×D4—62no—
465C2×D4—91no—
466C2×D4—92no—
467C2×D4—184no—
468C2×D4—182no—
469C2×D4—182no—
470C2×D4—181no—
471C2×D4—181no—
472C2×D4—362no—
473C2×D4—364no—
474C2×D4#62611yescharacteristic
475C22×C4—62no—
476C22×C4—61no—
477C22×C4—181no—
478C22×C4C2×D3212yes—
479D8—182no—
480D8—362no—
481C2×C8—31no—
482C2×C8—31no—
483C2×C8—32no—
484C2×C8—122no—
485C4⋊C4—31no—
486C4⋊C4—32no—
487C4⋊C4—62no—
488C4⋊C4—61no—
489C4⋊C4—91no—
490C4⋊C4#62611yescharacteristic
491C22⋊C4—61no—
492C22⋊C4—62no—
493C22⋊C4—181no—
494C22⋊C4—182no—
495C22⋊C4#62612yes—
496C42C2×D3211yescharacteristic
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—21no—
502C22×C3—24no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—121no—
506C22×C3—121no—
507C22×C3—121no—
508C22×C3C2×D2414yes—
509C22×C3C2×#21314yes—
510C22×C3C22×D1211yescharacteristic
511C22×C3C22×#6711yescharacteristic
512C2×D3—41no—
513C2×D3—41no—
514C2×D3—41no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—248no—
534C2×D3—248no—
535C2×D3—2416no—
536C3×C4—21no—
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—22no—
543C3×C4—42no—
544C3×C4—41no—
545C3×C4—121no—
546C3×C4—122no—
547C3×C4C2×D2412yes—
548C3×C4C2×#21312yes—
549C3×C4#100411yescharacteristic
550C3×C4D3×#4111yescharacteristic
551C3×C4D3×#4111yescharacteristic
552C3×C4#100911yescharacteristic
553Dic3—42no—
554Dic3—41no—
555Dic3—122no—
556Dic3—121no—
557Dic3—121no—
558C32#329411yescharacteristic, complemented, Sylow
559C23—61no—
560C23—181no—
561C23—182no—
562C23—364no—
563C23—364no—
564C23—722no—
565C23C2×#62612yes—
566Q8—122no—
567D4—61no—
568D4—61no—
569D4—92no—
570D4—124no—
571D4—182no—
572D4—181no—
573D4—182no—
574D4—364no—
575D4—364no—
576D4—362no—
577D4—721no—
578D4#371414yescomplemented
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—124no—
584C2×C4—122no—
585C2×C4—181no—
586C2×C4—362no—
587C2×C4C2×#62611yescharacteristic
588C2×C4C2×#62612yes—
589C2×C4C2×#62611yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—61no—
592C8—61no—
593C8—62no—
594C2×C3—24no—
595C2×C3—24no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—44no—
600C2×C3—241no—
601C2×C3#555411yescharacteristic
602C2×C3C22×D2411yescharacteristic
603C2×C3#575111yescharacteristic
604C2×C3C22×#21311yescharacteristic
605C2×C3#582911yescharacteristic
606C2×C3#583711yescharacteristic
607D3—81no—
608D3—124no—
609D3—122no—
610D3—122no—
611D3—244no—
612D3—242no—
613D3—242no—
614C22—22no—
615C22—22no—
616C22—121no—
617C22—121no—
618C22—121no—
619C22—182no—
620C22—361no—
621C22—361no—
622C22—362no—
623C22—362no—
624C22—362no—
625C22—728no—
626C22C2×#371414yes—
627C22C22×#62611yescharacteristic
628C4—21no—
629C4—22no—
630C4—121no—
631C4—122no—
632C4—361no—
633C4C2×#371412yes—
634C4#6431211yescharacteristic
635C4#6431411yescharacteristic
636C3—21no—
637C3#7943811yescharacteristic, complemented
638C3#8352511yescharacteristic, complemented
639C2—24no—
640C2—241no—
641C2—362no—
642C2—722no—
643C2C22×#371411yescharacteristic
644C2#1059525411yescharacteristic
645C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×C4⋊(C3⋊D3)C2semidirect
2. C3×#5555C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10591168C2semidirect
5. #10591164C2semidirect
6. #10591133C2semidirect
7. C2×#63564C2semidirect
8. #10590349C2semidirect
9. C4×#3714C2semidirect
10. #10590313C2semidirect
11. #10590281C2semidirect
23. C3×#930C22semidirect
24. C2×C3×C4⋊Dic3C22semidirect
25. C22×C3×C3⋊C8C22semidirect
28. C3×C4×D12C22semidirect
29. C3×#869C22semidirect
31. C2×#3714C22semidirect
32. C3×#830C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. C3×C4×C3⋊C8C22semidirect
35. #63575C22semidirect
36. #63575C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
41. #63564C22semidirect
42. #63563C22semidirect
44. #5555D3semidirect
57. D4×C3⋊C8D3semidirect
127. #930C2×D3semidirect
128. C2×C4⋊Dic3C2×D3semidirect
129. C22×C3⋊C8C2×D3semidirect
146. C4×D12C2×D3semidirect
147. #869C2×D3semidirect
152. #830C2×D3semidirect
168. C4⋊(C3⋊C8)C2×D3semidirect
169. C4×C3⋊C8C2×D3semidirect
177. C32×D4D8semidirect
192. C4⋊(C3⋊D3)#41semidirect
385. C3×D4D24semidirect
386. C3×D4#213semidirect
558. C32#3294semidirect
578. D4#3714semidirect
637. C3#79438semidirect
638. C3#83525semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
C3×#55552
C3×D4×C3⋊C82
#105911682
#105911642
#105911332
C2×#635642
#105903492
C4×#37142
#105903132
#105902812
#835253
#794383