Finite Group Databasebeta

← #11870439

Subgroups — #11870439

Order 1152.

1054 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591448C212yesmaximal, complemented
6#10591400C212yesmaximal, complemented
7#10590456C212yesmaximal, complemented
8#10590422C212yesmaximal, complemented
9#10590349C211yesmaximal, characteristic, complemented
10#10590269C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic, complemented
12#82308—31nomaximal
13#80948—31nomaximal
14C2×C3×D3×D4C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×#3799—21no—
17C32×C4×D4C2211yescharacteristic
18C2×#3753C2212yes—
19#64083C2211yescharacteristic, complemented
20C3×D4×Dic3C2211yescharacteristic
21C3×C4×#67—21no—
22C3×#893C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#67⋊C4—21no—
25C3×D3×C22⋊C4—21no—
26C3×C4×D12C2211yescharacteristic
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic, complemented
29#63909—21no—
30#63909C2212yes—
31#63894—21no—
32#63894C2212yescomplemented
33#63864—21no—
34C2×#3714C2212yes—
35#63636C2212yescomplemented
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
37C3×#832C2212yes—
38C3×#807C2212yescomplemented
39C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
40#63576C2212yescomplemented
41#63564C2212yescomplemented
42#63562C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×C4×D4—31no—
46#5725—31no—
47C4×D3×D4D311yescharacteristic, complemented
48#5477—31no—
49C3×#474—31no—
50#5217—32no—
51#5087—31no—
52#5015—31no—
53#5015—31no—
54#5015—31no—
55#5015—61no—
56C4×#213—32no—
57C4×#213—32no—
58#5007—31no—
59#5007D311yescharacteristic, complemented
60#4967—32no—
61#4925—31no—
62#4882—32no—
63#4872—32no—
64#4843—31no—
65#4833—31no—
66#4773—32no—
67#4756—32no—
68C23×C3×D3—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C3×D3×D4—22no—
77C3×D3×D4—22no—
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—44no—
83C2×C3×C4×D3D411yescharacteristic
84C2×C3×C4×D3D411yescharacteristic
85C2×C3×C4×D3C2311yescharacteristic
86C2×C3×Dic6—21no—
87C2×#626—22no—
88C2×#624—22no—
89#3799—44no—
90C32×C4⋊C4C2311yescharacteristic
91C32×C22⋊C4—21no—
92C32×C42C2311yescharacteristic
93#3753—24no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×C4⋊Dic3C2312yes—
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106#3722—22no—
107#3722—22no—
108#3714—24no—
109#3100—91noSylow
110C22×C3×D4—31no—
111C23×C3×C4—61no—
112C2×#239—61no—
113C2×D3×D4C2×D311yescharacteristic
114C2×#235—61no—
115C22×C4×D3—21no—
116C3×C4⋊Q8—31no—
117C3×C4×D4—21no—
118C3×C4×D4—31no—
119C3×C4×D4—31no—
120C3×C4×D4—31no—
121C3×C4×D4—61no—
122C3×C4×D4—61no—
123C3×C4×D4C2×D311yescharacteristic
124C3×C4×D4C2×D311yescharacteristic
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—61no—
127C2×C3×C42—31no—
128#947—61no—
129D4×Dic3C2×D311yescharacteristic
130C2×#213—32no—
131C2×#213—32no—
132C2×#213—32no—
133C2×#213—62no—
134#930—32no—
135#930—61no—
136C4×#67—21no—
137C2×D24—32no—
138#895—32no—
139#895—61no—
140#893—32no—
141#893—61no—
142#893C2×D311yescharacteristic
143D3×C4⋊C4C2×D311yescharacteristic
144#67⋊C4—21no—
145D3×C22⋊C4—21no—
146#875—61no—
147#874—31no—
148#874—31no—
149#874—61no—
150C4×D12—32no—
151C4×D12—61no—
152C4×D12C2×D311yescharacteristic
153C42×D3C2×D311yescharacteristic
154#869C2×D311yescharacteristic, complemented
155C3×#107—32no—
156C3×C4⋊C8—31no—
157C3×#102—32no—
158#832—32no—
159#832C2×D312yes—
160#830—32no—
161#821—32no—
162(C2×D3)⋊C8—32no—
163C8×Dic3—32no—
164#809—32no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#807—32no—
170#807—32no—
171#807C2×D312yescomplemented
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—22no—
179C22×C3×D3—24no—
180C22×C3×D3—21no—
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
191C4⋊(C3⋊D3)—22no—
192C4⋊(C3⋊D3)—22no—
193C4⋊(C3⋊D3)—42no—
194C4⋊(C3⋊D3)—42no—
195C3×#67—24no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—21no—
203C3×D12#4112yescomplemented
204C3×C4×D3—21no—
205C3×C4×D3—21no—
206C3×C4×D3—41no—
207C3×C4×D3—42no—
208C3×C4×D3—42no—
209C3×C4×D3—42no—
210C3×C4×D3D814yescomplemented
211C3×Dic6—42no—
212#626—44no—
213#624—44no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#532—91no—
217C2×C4×D4—31no—
218#480—92no—
219#474—31no—
220#474—91no—
221#459—91no—
222#459—91no—
223#447—92no—
224C4×D8—92no—
225C4×D8—92no—
226#431—91no—
227C24×C3—61no—
228C23×D3—21no—
229C2×C3×Q8—61no—
230C2×C3×D4—21no—
231C2×C3×D4—31no—
232C2×C3×D4—61no—
233C2×C3×D4—62no—
234C2×C3×D4—62no—
235C2×C3×D4C22×D311yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—41no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C22×C3×C4—124no—
248C2×#67—21no—
249C2×#67—62no—
250C22×Dic3—21no—
251#239—124no—
252D3×D4—22no—
253D3×D4—22no—
254#235—124no—
255C2×D12—32no—
256C2×D12—32no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—61no—
262C2×D12—61no—
263C2×D12—121no—
264C2×D12—121no—
265C2×D12C22×D311yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—44no—
270C2×C4×D3—62no—
271C2×C4×D3—62no—
272C2×C4×D3#6711yescharacteristic
273C2×C4×D3#6711yescharacteristic
274C2×C4×D3C22×D311yescharacteristic
275C2×Dic6—21no—
276C2×C3×C8—32no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—61no—
281C3×C4⋊C4—61no—
282C3×C4⋊C4C22×D311yescharacteristic
283C3×C4⋊C4C22×D311yescharacteristic
284C3×C22⋊C4—21no—
285C3×C22⋊C4—21no—
286C3×C22⋊C4—41no—
287C3×C22⋊C4—61no—
288C3×C22⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C42—21no—
291C3×C42—31no—
292C3×C42—31no—
293C3×C42—31no—
294C3×C42C22×D311yescharacteristic
295C3×C42C22×D311yescharacteristic
296#217—21no—
297#213—64no—
298#213—64no—
299#213—64no—
300#213—124no—
301(C2×D3)⋊C4—21no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—62no—
306(C2×D3)⋊C4—62no—
307C4⋊Dic3—21no—
308C4⋊Dic3C22×D311yescharacteristic
309C4⋊Dic3C22×D312yes—
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—
318D24—64no—
319C22×C32—22no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32C22×D411yescharacteristic
323C2×C3⋊D3—42no—
324C2×C3⋊D3—42no—
325C2×C3⋊D3—42no—
326C2×C3×D3—21no—
327C2×C3×D3—21no—
328C2×C3×D3—22no—
329C2×C3×D3—48no—
330C2×C3×D3—41no—
331C2×C3×D3—41no—
332C2×C3×D3C2×D812yes—
333C32×C4—21no—
334C32×C4—41no—
335C32×C4C2×D812yes—
336C32×C4C2×#4111yescharacteristic
337C32×C4C2×#4111yescharacteristic
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—42no—
341C3×Dic3—41no—
342C3×Dic3C2×D812yes—
343C2×#41—181no—
344C22×D4—31no—
345C23×C4—61no—
346C2×D8—92no—
347C2×D8—92no—
348C4⋊Q8—31no—
349#127—91no—
350#124—181no—
351#121—92no—
352#121—181no—
353C4×D4—31no—
354C4×D4—31no—
355C4×D4—31no—
356C4×D4—61no—
357C4×D4—61no—
358C4×D4—92no—
359C4×D4—181no—
360C4×D4D3211yescharacteristic
361C2×C4⋊C4—31no—
362C2×C22⋊C4—61no—
363C2×C42—31no—
364#107—32no—
365#107—92no—
366C4⋊C8—31no—
367C4⋊C8—91no—
368#102—32no—
369#102—92no—
370#102—92no—
371#102—92no—
372C22⋊C8—92no—
373C4×C8—92no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—31no—
377C23×C3—41no—
378C23×C3—64no—
379C23×C3—61no—
380C23×C3—122no—
381C23×C3—122no—
382C22×D3—24no—
383C22×D3—21no—
384C22×D3—42no—
385C22×D3—42no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—122no—
389C22×D3C2×#6711yescharacteristic
390C3×Q8—122no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—22no—
394C3×D4—32no—
395C3×D4—41no—
396C3×D4—64no—
397C3×D4—61no—
398C3×D4#23512yescomplemented
399C3×D4#23912yescomplemented
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—31no—
406C2×C3×C4—34no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
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—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—42no—
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435C2×Dic3C2×#6711yescharacteristic
436D12—21no—
437D12—62no—
438D12—62no—
439D12—62no—
440D12—62no—
441D12—122no—
442D12—122no—
443D12—122no—
444D12—122no—
445D12—124no—
446D12—122no—
447D12—122no—
448D12—242no—
449D12—242no—
450D12#23512yescomplemented
451C4×D3—21no—
452C4×D3—21no—
453C4×D3—41no—
454C4×D3—42no—
455C4×D3—42no—
456C4×D3—42no—
457C4×D3—124no—
458C4×D3—124no—
459C4×D3#21314yescomplemented
460Dic6—42no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—62no—
464C3⋊C8—62no—
465C3⋊C8—122no—
466C2×C32—42no—
467C2×C32#52511yescharacteristic
468C2×C32C22×D811yescharacteristic
469C2×C32#57511yescharacteristic
470C3⋊D3—82no—
471C3×D3—22no—
472C3×D3—42no—
473C24—61no—
474#41—364no—
475C2×Q8—61no—
476C2×D4—31no—
477C2×D4—61no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—92no—
481C2×D4—182no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4C2×D3211yescharacteristic
485C22×C4—21no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—124no—
494C22×C4—182no—
495D8—184no—
496D8—184no—
497C2×C8—32no—
498C2×C8—92no—
499C4⋊C4—32no—
500C4⋊C4—31no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C4⋊C4C2×D3211yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—61no—
506C22⋊C4—61no—
507C22⋊C4—61no—
508C22⋊C4—182no—
509C22⋊C4—182no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42C2×D3211yescharacteristic
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—32no—
518C22×C3—42no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—61no—
524C22×C3—61no—
525C22×C3—62no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—128no—
529C22×C3—121no—
530C22×C3—121no—
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C22×#6711yescharacteristic
533C2×D3—21no—
534C2×D3—21no—
535C2×D3—22no—
536C2×D3—48no—
537C2×D3—41no—
538C2×D3—41no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—122no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—242no—
546C2×D3—242no—
547C2×D3—242no—
548C2×D3C2×#21312yes—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—32no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—61no—
559C3×C4—61no—
560C3×C4—81no—
561C3×C4—121no—
562C3×C4—122no—
563C3×C4D3×D812yes—
564C3×C4C2×#21312yes—
565C3×C4C2×#23511yescharacteristic
566C3×C4C2×#23511yescharacteristic
567C3×C4C2×#23911yescharacteristic
568C3×C4D3×#4111yescharacteristic
569Dic3—21no—
570Dic3—21no—
571Dic3—42no—
572Dic3—41no—
573Dic3C2×#21312yes—
574C32#310011yescharacteristic, complemented, Sylow
575C23—21no—
576C23—31no—
577C23—64no—
578C23—61no—
579C23—122no—
580C23—122no—
581C23—182no—
582Q8—122no—
583D4—21no—
584D4—32no—
585D4—64no—
586D4—61no—
587D4—182no—
588D4—182no—
589D4—362no—
590D4—364no—
591D4—362no—
592D4#379912yescomplemented
593C2×C4—21no—
594C2×C4—31no—
595C2×C4—34no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—42no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—62no—
603C2×C4—121no—
604C2×C4—122no—
605C2×C4—122no—
606C2×C4—122no—
607C2×C4—122no—
608C2×C4—364no—
609C2×C4D3×#6711yescharacteristic
610C2×C4D3×#6711yescharacteristic
611C2×C4C22×D3211yescharacteristic
612C8—62no—
613C8—182no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3—42no—
619C2×C3—62no—
620C2×C3—82no—
621C2×C3—122no—
622C2×C3#562711yescharacteristic
623C2×C3C2×D3×D811yescharacteristic
624C2×C3#577711yescharacteristic
625C2×C3#579111yescharacteristic
626C2×C3C22×#21311yescharacteristic
627C2×C3#582211yescharacteristic
628D3—22no—
629D3—42no—
630D3—242no—
631D3—242no—
632D3—482no—
633C22—22no—
634C22—32no—
635C22—41no—
636C22—41no—
637C22—61no—
638C22—61no—
639C22—62no—
640C22—128no—
641C22—121no—
642C22—121no—
643C22—362no—
644C22—362no—
645C22—362no—
646C22C2×D3×#6711yescharacteristic
647C4—21no—
648C4—32no—
649C4—41no—
650C4—61no—
651C4—61no—
652C4—121no—
653C4—122no—
654C4D3×#21312yes—
655C4C2×#379911yescharacteristic
656C4D3×#23511yescharacteristic
657C3—21no—
658C3#8094811yescharacteristic, complemented
659C3#8230811yescharacteristic, complemented
660C2—42no—
661C2—62no—
662C2—122no—
663C2—722no—
664C2#1059500511yescharacteristic
665C2C2×D3×#21311yescharacteristic
666C2#1059547011yescharacteristic
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. #10593970C2semidirect
3. #10592714C2semidirect
4. C3×#5007C2semidirect
5. #10591448C2semidirect
6. #10591400C2semidirect
7. #10590456C2semidirect
8. #10590422C2semidirect
9. #10590349C2semidirect
10. #10590269C2semidirect
11. #10590248C2semidirect
19. #64083C22semidirect
28. C3×#869C22semidirect
32. #63894C22semidirect
35. #63636C22semidirect
36. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×#807C22semidirect
39. C3×C4⋊(C3⋊C8)C22semidirect
40. #63576C22semidirect
41. #63564C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. C4×D3×D4D3semidirect
59. #5007D3semidirect
154. #869C2×D3semidirect
171. #807C2×D3semidirect
175. C4⋊(C3⋊C8)C2×D3semidirect
185. C32×D4#41semidirect
203. C3×D12#41semidirect
210. C3×C4×D3D8semidirect
398. C3×D4#235semidirect
399. C3×D4#239semidirect
450. D12#235semidirect
459. C4×D3#213semidirect
574. C32#3100semidirect
592. D4#3799semidirect
658. C3#80948semidirect
659. 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
#105939702
#105927142
C3×#50072
#105914482
#105914002
#105904562
#105904222
#105903492
#105902692
#105902482
#823083
#809483