Finite Group Databasebeta

← #11870441

Subgroups — #11870441

Order 1152.

1038 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic, complemented
5#10591447C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10590498C212yesmaximal, complemented
8#10590452C212yesmaximal, complemented
9#10590347C211yesmaximal, characteristic, complemented
10#10590272C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#82308—31nomaximal
13#80312—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×#3795—21no—
17C32×C4×D4C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C3×D4×Dic3C2211yescharacteristic
20C2×C3×#213C2212yes—
21C3×C4×#67—21no—
22C3×#893C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#67⋊C4—21no—
25C3×D3×C22⋊C4—21no—
26C3×#874C2211yescharacteristic, complemented
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29#63908—21no—
30#63908C2212yes—
31Dic3×D12—21no—
32Dic3×D12C2212yescomplemented
33#63860—21no—
34C2×#3713C2212yes—
35#63659C2212yes—
36#63634C2212yescomplemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×#809C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63575C2212yescomplemented
41#63563C2212yes—
42#63562C2212yescomplemented
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46#5716—31no—
47C4×D3×D4D311yescharacteristic, complemented
48#5477—31no—
49C3×#459—31no—
50#5217—32no—
51#5156—32no—
52Dic3×D8—32no—
53#5072—31no—
54#5015—31no—
55#5015D311yescharacteristic, complemented
56C4×#213—32no—
57C4×#213—32no—
58#5007—31no—
59#5007—31no—
60#5007—31no—
61#5007—61no—
62#4967—32no—
63#4925—31no—
64#4846—31no—
65#4833—31no—
66#4774—32no—
67#4756—32no—
68C23×C3×D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#634—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C3×D3×D4—22no—
75C3×D3×D4—22no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12C2312yes—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—44no—
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3C2311yescharacteristic
87C2×#625—22no—
88C2×D3×Dic3—22no—
89#3795—44no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C22⋊C4—21no—
92C32×C42C2311yescharacteristic
93C4⋊(C3⋊Dic3)—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×#213—24no—
98C3×(C2×D3)⋊C4—21no—
99C3×(C2×D3)⋊C4—21no—
100C3×C4⋊Dic3C2311yescharacteristic
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3713—24no—
109#3100—91noSylow
110C22×C3×D4—31no—
111C23×C3×C4—61no—
112C2×#237—61no—
113C2×D3×D4C2×D311yescharacteristic
114C2×#235—61no—
115C22×C4×D3—21no—
116C2×C3×D8—32no—
117C3×#127—31no—
118C3×C4×D4—21no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121C3×C4×D4—31no—
122C3×C4×D4—61no—
123C3×C4×D4—61no—
124C3×C4×D4C2×D311yescharacteristic
125C3×C4×D4C2×D311yescharacteristic
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—61no—
128C2×C3×C42—31no—
129#938—32no—
130#938—61no—
131#936—61no—
132D4×Dic3—32no—
133D4×Dic3—61no—
134D4×Dic3C2×D311yescharacteristic
135C2×#213—32no—
136C2×#213—32no—
137C2×#213C2×D312yes—
138#930—32no—
139#930—61no—
140C4×#67—21no—
141#893C2×D311yescharacteristic
142D3×C4⋊C4C2×D311yescharacteristic
143#67⋊C4—21no—
144D3×C22⋊C4—21no—
145#875—61no—
146#874C2×D311yescharacteristic, complemented
147C4×D12—32no—
148C4×D12—61no—
149C4×D12C2×D311yescharacteristic
150C42×D3C2×D311yescharacteristic
151#869—31no—
152#869—31no—
153#869—61no—
154C3×C4⋊C8—31no—
155C3×#102—32no—
156#832—32no—
157#832—32no—
158#832—32no—
159#832—32no—
160#832—62no—
161#830—32no—
162#821—32no—
163(C2×D3)⋊C8—32no—
164#818—32no—
165C8×Dic3—32no—
166#809—32no—
167#809C2×D312yescomplemented
168#807—32no—
169#807—32no—
170#807—32no—
171#807—62no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
176C4×C3⋊C8—32no—
177C23×C32—21no—
178C22×C3×D3—24no—
179C22×C3×D3—21no—
180C22×C3×D3—22no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C22×C3×D3C2×D411yescharacteristic
184C32×D4—21no—
185C32×D4#4112yescomplemented
186C2×C32×C4—21no—
187C2×C32×C4—42no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191C2×C3⋊Dic3—22no—
192#634—42no—
193C3×#67—24no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—21no—
200C3×D12—22no—
201C3×D12—22no—
202C3×D12—42no—
203C3×D12—42no—
204C3×D12#4112yescomplemented
205C3×C4×D3—21no—
206C3×C4×D3—21no—
207C3×C4×D3—41no—
208C3×C4×D3—42no—
209C3×C4×D3—42no—
210C3×C4×D3—42no—
211C3×C4×D3D814yescomplemented
212#625—44no—
213D3×Dic3—44no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#532—91no—
217C2×C4×D4—31no—
218#480—92no—
219#474—91no—
220#474—91no—
221#459—31no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—91no—
227C24×C3—61no—
228C23×D3—21no—
229C2×C3×D4—21no—
230C2×C3×D4—31no—
231C2×C3×D4—32no—
232C2×C3×D4—61no—
233C2×C3×D4—62no—
234C2×C3×D4—62no—
235C2×C3×D4—61no—
236C2×C3×D4—61no—
237C2×C3×D4C22×D311yescharacteristic
238C2×C3×D4C22×D311yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—41no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—61no—
248C22×C3×C4—61no—
249C22×C3×C4—124no—
250C2×#67—21no—
251C2×#67—62no—
252C2×#67—62no—
253C22×Dic3—21no—
254C22×Dic3—62no—
255#237—124no—
256D3×D4—22no—
257D3×D4—22no—
258#235—124no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C22×D312yes—
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—44no—
267C2×C4×D3—62no—
268C2×C4×D3#6711yescharacteristic
269C2×C4×D3#6711yescharacteristic
270C2×C4×D3C22×D311yescharacteristic
271C2×Dic6—61no—
272C2×Dic6—61no—
273C2×Dic6—121no—
274C3×D8—64no—
275C2×C3×C8—32no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4C22×D311yescharacteristic
280C3×C4⋊C4C22×D311yescharacteristic
281C3×C22⋊C4—21no—
282C3×C22⋊C4—21no—
283C3×C22⋊C4—41no—
284C3×C22⋊C4—61no—
285C3×C22⋊C4—61no—
286C3×C22⋊C4—61no—
287C3×C42—21no—
288C3×C42—31no—
289C3×C42—31no—
290C3×C42—31no—
291C3×C42C22×D311yescharacteristic
292C3×C42C22×D311yescharacteristic
293#217—21no—
294#217—62no—
295#217—62no—
296#213—24no—
297#213—64no—
298#213—64no—
299(C2×D3)⋊C4—21no—
300(C2×D3)⋊C4—21no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—32no—
304C4⋊Dic3—32no—
305C4⋊Dic3—62no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—121no—
309C4⋊Dic3C22×D311yescharacteristic
310Dic3⋊C4—21no—
311C4×Dic3#6711yescharacteristic
312C4×Dic3#6711yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314C2×C3⋊C8—32no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318C22×C32—22no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—21no—
323C2×C3×D3—21no—
324C2×C3×D3—22no—
325C2×C3×D3—48no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—42no—
329C2×C3×D3—42no—
330C2×C3×D3—42no—
331C2×C3×D3C2×D812yes—
332C32×C4—21no—
333C32×C4—41no—
334C32×C4C2×D812yes—
335C32×C4C2×#4111yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—42no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—41no—
341C3×Dic3C2×D812yes—
342C2×#41—181no—
343C22×D4—31no—
344C23×C4—61no—
345C2×D8—32no—
346C2×D8—92no—
347C4⋊Q8—91no—
348#127—31no—
349#124—181no—
350#121—92no—
351#121—181no—
352C4×D4—31no—
353C4×D4—31no—
354C4×D4—31no—
355C4×D4—61no—
356C4×D4—61no—
357C4×D4—92no—
358C4×D4—181no—
359C4×D4D3211yescharacteristic
360C2×C4⋊C4—31no—
361C2×C22⋊C4—61no—
362C2×C42—31no—
363#107—92no—
364#107—92no—
365C4⋊C8—31no—
366C4⋊C8—91no—
367#102—32no—
368#102—92no—
369#102—92no—
370#102—92no—
371C22⋊C8—92no—
372C4×C8—92no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—31no—
376C23×C3—41no—
377C23×C3—64no—
378C23×C3—61no—
379C23×C3—62no—
380C23×C3—122no—
381C23×C3—122no—
382C22×D3—24no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3—42no—
386C22×D3—42no—
387C22×D3C2×#6711yescharacteristic
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—22no—
391C3×D4—32no—
392C3×D4—41no—
393C3×D4—64no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—61no—
397C3×D4—122no—
398C3×D4—122no—
399C3×D4#23512yescomplemented
400C3×D4#23712yescomplemented
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—31no—
407C2×C3×C4—34no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—82no—
417C2×C3×C4—121no—
418C2×C3×C4—122no—
419C2×C3×C4—122no—
420C2×C3×C4—122no—
421C2×C3×C4—122no—
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428#67—24no—
429#67—124no—
430#67—124no—
431C2×Dic3—21no—
432C2×Dic3—42no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—124no—
437C2×Dic3C2×#6711yescharacteristic
438C2×Dic3C2×#6711yescharacteristic
439C2×Dic3C2×#6711yescharacteristic
440D12—21no—
441D12—22no—
442D12—22no—
443D12—42no—
444D12—42no—
445D12#23512yescomplemented
446C4×D3—21no—
447C4×D3—21no—
448C4×D3—41no—
449C4×D3—42no—
450C4×D3—42no—
451C4×D3—42no—
452C4×D3—124no—
453C4×D3#21314yescomplemented
454Dic6—122no—
455Dic6—122no—
456Dic6—242no—
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—62no—
460C3⋊C8—62no—
461C3⋊C8—122no—
462C2×C32—42no—
463C2×C32#52511yescharacteristic
464C2×C32C22×D811yescharacteristic
465C2×C32#57511yescharacteristic
466C3×D3—22no—
467C3×D3—42no—
468C3×D3—82no—
469C24—61no—
470#41—364no—
471C2×Q8—181no—
472C2×D4—31no—
473C2×D4—32no—
474C2×D4—61no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—182no—
480C2×D4C2×D3211yescharacteristic
481C22×C4—21no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—124no—
490C22×C4—182no—
491D8—64no—
492D8—184no—
493C2×C8—32no—
494C2×C8—92no—
495C4⋊C4—31no—
496C4⋊C4—61no—
497C4⋊C4—92no—
498C4⋊C4—181no—
499C4⋊C4C2×D3211yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—61no—
502C22⋊C4—61no—
503C22⋊C4—61no—
504C22⋊C4—182no—
505C22⋊C4—182no—
506C42—31no—
507C42—31no—
508C42—31no—
509C42C2×D3211yescharacteristic
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—32no—
514C22×C3—42no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—61no—
520C22×C3—61no—
521C22×C3—62no—
522C22×C3—81no—
523C22×C3—81no—
524C22×C3—128no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3C2×D3×D411yescharacteristic
531C22×C3C22×#6711yescharacteristic
532C2×D3—21no—
533C2×D3—21no—
534C2×D3—22no—
535C2×D3—48no—
536C2×D3—41no—
537C2×D3—41no—
538C2×D3—42no—
539C2×D3—42no—
540C2×D3—42no—
541C2×D3C2×#21312yes—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—32no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—41no—
551C3×C4—61no—
552C3×C4—61no—
553C3×C4—81no—
554C3×C4—121no—
555C3×C4D3×D812yes—
556C3×C4C2×#21312yes—
557C3×C4C2×#23511yescharacteristic
558C3×C4C2×#23511yescharacteristic
559C3×C4C2×#23711yescharacteristic
560C3×C4D3×#4111yescharacteristic
561Dic3—21no—
562Dic3—21no—
563Dic3—41no—
564Dic3—122no—
565Dic3—122no—
566Dic3—242no—
567Dic3C2×#21312yes—
568C32#310011yescharacteristic, complemented, Sylow
569C23—21no—
570C23—31no—
571C23—64no—
572C23—61no—
573C23—62no—
574C23—122no—
575C23—122no—
576Q8—362no—
577D4—21no—
578D4—32no—
579D4—64no—
580D4—61no—
581D4—62no—
582D4—62no—
583D4—122no—
584D4—122no—
585D4—364no—
586D4#379512yescomplemented
587C2×C4—21no—
588C2×C4—31no—
589C2×C4—34no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—42no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—121no—
597C2×C4—122no—
598C2×C4—122no—
599C2×C4—122no—
600C2×C4—122no—
601C2×C4—182no—
602C2×C4—364no—
603C2×C4D3×#6711yescharacteristic
604C2×C4D3×#6711yescharacteristic
605C2×C4C22×D3211yescharacteristic
606C8—62no—
607C8—182no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—62no—
614C2×C3—82no—
615C2×C3—122no—
616C2×C3—242no—
617C2×C3#560611yescharacteristic
618C2×C3C2×D3×D811yescharacteristic
619C2×C3#577311yescharacteristic
620C2×C3#579111yescharacteristic
621C2×C3C22×#21311yescharacteristic
622C2×C3#582211yescharacteristic
623D3—22no—
624D3—42no—
625D3—82no—
626C22—22no—
627C22—32no—
628C22—41no—
629C22—41no—
630C22—61no—
631C22—61no—
632C22—62no—
633C22—128no—
634C22—121no—
635C22—121no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22C2×D3×#6711yescharacteristic
640C4—21no—
641C4—32no—
642C4—41no—
643C4—61no—
644C4—61no—
645C4—121no—
646C4—362no—
647C4D3×#21312yes—
648C4C2×#379511yescharacteristic
649C4D3×#23511yescharacteristic
650C3—21no—
651C3#8031211yescharacteristic, complemented
652C3#8230811yescharacteristic, complemented
653C2—42no—
654C2—62no—
655C2—122no—
656C2—242no—
657C2#1059489211yescharacteristic
658C2C2×D3×#21311yescharacteristic
659C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3100
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
1. C3×C4×D3×D4C2semidirect
2. #10593897C2semidirect
3. #10592706C2semidirect
4. C3×#5015C2semidirect
5. #10591447C2semidirect
6. Dic3×#213C2semidirect
7. #10590498C2semidirect
8. #10590452C2semidirect
9. #10590347C2semidirect
10. #10590272C2semidirect
11. #10590248C2semidirect
18. #64078C22semidirect
26. C3×#874C22semidirect
32. Dic3×D12C22semidirect
36. #63634C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×#809C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63575C22semidirect
42. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. C4×D3×D4D3semidirect
55. #5015D3semidirect
146. #874C2×D3semidirect
167. #809C2×D3semidirect
175. C4⋊(C3⋊C8)C2×D3semidirect
185. C32×D4#41semidirect
204. C3×D12#41semidirect
211. C3×C4×D3D8semidirect
399. C3×D4#235semidirect
400. C3×D4#237semidirect
445. D12#235semidirect
453. C4×D3#213semidirect
568. C32#3100semidirect
586. D4#3795semidirect
651. C3#80312semidirect
652. C3#82308semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105938972
#105927062
C3×#50152
#105914472
Dic3×#2132
#105904982
#105904522
#105903472
#105902722
#105902482
#823083
#803123