Finite Group Databasebeta

← #11784977

Subgroups — #11784977

Order 1152.

1271 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64308C211yesmaximal, characteristic
2#10592830C211yesmaximal, characteristic, complemented
3C3×#5139C211yesmaximal, characteristic, complemented
4C3×#5132C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10591110C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#70414—31nomaximal
9#70139—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C2×#3811—22no—
14#64308—22no—
15#64308—22no—
16#64308—22no—
17#64308—22no—
18C2×D3×D12—21no—
19C2×D3×D12C412yescomplemented
20C2×#3799—21no—
21C2×#3799C412yescomplemented
22C2×C32×M16C2211yescharacteristic, complemented
23#64135C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic, complemented
25C2×C3×#208C2211yescharacteristic, complemented
26#63648—22no—
27C3×#825—22no—
28C3×#824—21no—
29C3×#823—21no—
30#63580—22no—
31#63568—22no—
32#63564—22no—
33C2×#1009—31no—
34C2×#1009—31no—
35C3×#421—31no—
36C3×#413—31no—
37#5240—31no—
38#5236—31no—
39#5139—31no—
40#5139D311yescharacteristic, complemented
41#5132D311yescharacteristic, complemented
42#5131—31no—
43#5131—31no—
44#5131—31no—
45#5131—61no—
46#5006—31no—
47#5001—31no—
48C23×C3⋊D3—21no—
49C22×D32—22no—
50C22×C32×C4C2311yescharacteristic
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2×C412yes—
55C2×C4⋊(C3⋊D3)D412yes—
56C2×C4⋊(C3⋊D3)D412yes—
57C2×C3×#67—21no—
58C2×C3×#67D412yes—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235D412yes—
66C3×#235D412yes—
67C2×C3×D12C2×C411yescharacteristic
68C2×C3×D12D411yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3C2×C412yes—
71C2×C3×Dic6C2×C411yescharacteristic
72C2×C3×Dic6D411yescharacteristic
73#3811—28no—
74#3811—28no—
75C2×#626—22no—
76C2×#626—22no—
77C2×#624—22no—
78D3×D12—24no—
79D3×D12—24no—
80D3×D12—24no—
81D3×D12—24no—
82#3799—24no—
83#3799—24no—
84#3799—24no—
85#3799—24no—
86C32×M16—21no—
87C32×M16—21no—
88C2×C32×C8—21no—
89#3757—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4×C3⋊Dic3—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4×Dic3—21no—
95C3×#208—21no—
96C3×#208—21no—
97C2×C3×C3⋊C8—21no—
98#1795—91noSylow
99C2×C3×#41—31no—
100C2×C3×#41—31no—
101#1009—62no—
102#1009—62no—
103#1009—62no—
104#1009—62no—
105#1009—62no—
106#1009—62no—
107#1009—62no—
108#1009—62no—
109C2×#239—32no—
110C2×#239—61no—
111C2×D3×D4—32no—
112C2×D3×D4—61no—
113C2×D3×D4—62no—
114C2×D3×D4—62no—
115C2×#235—32no—
116C2×#235—61no—
117C2×#235C2×D311yescharacteristic
118C2×#235C2×D311yescharacteristic
119C22×D12—31no—
120C22×D12—31no—
121C22×D12—32no—
122C22×D12—61no—
123C22×D12—61no—
124C2×C3×M16—21no—
125C2×C3×M16—31no—
126C2×C3×M16C2×D311yescharacteristic, complemented
127C2×C3×M16C2×D311yescharacteristic, complemented
128C3×#117—31no—
129#926—31no—
130#926—31no—
131#926—61no—
132#926C2×D311yescharacteristic, complemented
133C2×#208C2×D311yescharacteristic, complemented
134C3×#104—62no—
135C3×#101—61no—
136C3×#100—61no—
137#837—62no—
138#834—62no—
139#825—22no—
140#825—62no—
141#824—21no—
142#823—21no—
143#821—62no—
144#821—62no—
145#821—62no—
146#821—64no—
147#809—62no—
148#806—62no—
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—82no—
154C22×C3×D3—21no—
155C22×C3×D3C22⋊C412yes—
156C2×D32—28no—
157C2×D32—84no—
158C2×C32×C4C22×C411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C3⋊Dic3—41no—
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)C22⋊C414yes—
169C3×#67—22no—
170C3×#67—22no—
171C3×#67—22no—
172C3×#67—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—41no—
175C2×C3×Dic3C22⋊C412yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—21no—
179C3×D12C22⋊C412yes—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187C3×Dic6C22⋊C412yes—
188#626—28no—
189#626—28no—
190#624—28no—
191C32×C8—41no—
192C3×C3⋊C8—41no—
193C2×H(5,𝔽2)—91no—
194#421—31no—
195#421—91no—
196#418—91no—
197#418—91no—
198#413—31no—
199#410—91no—
200C23×D3—62no—
201C23×D3—61no—
202C23×D3—61no—
203C23×D3—62no—
204C23×D3—121no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—61no—
212C3×#41—61no—
213C2×C3×Q8—31no—
214C2×C3×Q8—31no—
215C2×C3×D4—32no—
216C2×C3×D4—31no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—32no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C2×#67—62no—
226C2×#67—62no—
227C2×#67D1212yes—
228#239—64no—
229#239—64no—
230#239—64no—
231#239—64no—
232D3×D4—64no—
233D3×D4—64no—
234D3×D4—64no—
235D3×D4—64no—
236D3×D4—68no—
237D3×D4—68no—
238D3×D4—68no—
239D3×D4—68no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246#235—64no—
247#235—64no—
248#235—64no—
249#235—64no—
250#235D1212yes—
251#235#6712yes—
252C2×D12—32no—
253C2×D12—32no—
254C2×D12—32no—
255C2×D12—32no—
256C2×D12—32no—
257C2×D12—32no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—64no—
262C2×D12—64no—
263C2×D12—64no—
264C2×D12—62no—
265C2×D12—62no—
266C2×D12—61no—
267C2×D12—61no—
268C2×D12—61no—
269C2×D12—61no—
270C2×D12—61no—
271C2×D12—61no—
272C2×D12—64no—
273C2×D12—121no—
274C2×D12—121no—
275C2×D12—121no—
276C2×D12C4×D311yescharacteristic
277C2×D12#6711yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3C4×D312yes—
282C2×Dic6C4×D311yescharacteristic
283C2×Dic6#6711yescharacteristic
284C3×M16—21no—
285C3×M16—21no—
286C3×M16—21no—
287C3×M16—21no—
288C3×M16—41no—
289C3×M16—41no—
290C3×M16—61no—
291C3×M16—61no—
292C2×C3×C8—22no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—61no—
296C3×C4⋊C4—61no—
297C3×C22⋊C4—61no—
298C3×C42—61no—
299#217—21no—
300#217—61no—
301#217—61no—
302#217—121no—
303C4⋊Dic3—21no—
304C4⋊Dic3—62no—
305C4⋊Dic3—61no—
306C4⋊Dic3—61no—
307C4×Dic3—21no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—121no—
311#208—21no—
312#208—21no—
313C2×C3⋊C8—21no—
314C22×C32—41no—
315C22×C32C2×C22⋊C411yescharacteristic
316C22×C32#12011yescharacteristic
317C22×C32#12011yescharacteristic
318C2×C3⋊D3—24no—
319C2×C3⋊D3—44no—
320C2×C3⋊D3—82no—
321C2×C3⋊D3—82no—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326D32—88no—
327C32×C4C2×C22⋊C411yescharacteristic
328C32×C4C2×C22⋊C411yescharacteristic
329C32×C4#12011yescharacteristic
330C32×C4#12011yescharacteristic
331C3⋊Dic3—81no—
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—81no—
335H(5,𝔽2)—182no—
336H(5,𝔽2)—182no—
337H(5,𝔽2)—182no—
338H(5,𝔽2)—182no—
339C2×#41—31no—
340C2×#41—31no—
341C2×#41—92no—
342C2×#41—181no—
343C22×D4—92no—
344C22×D4—91no—
345C22×D4—181no—
346C22×D4—182no—
347C2×M16—31no—
348C2×M16D3211yescharacteristic, complemented
349#117—31no—
350#117—91no—
351#104—62no—
352#104—182no—
353#102—182no—
354#102—182no—
355#101—61no—
356#100—61no—
357#99—182no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3C2×D1211yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—21no—
364C22×D3—68no—
365C22×D3—68no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—244no—
376C22×D3—244no—
377C22×D3—242no—
378C22×D3—242no—
379C22×D3—244no—
380C22×D3(C2×D3)⋊C412yes—
381C3×Q8—32no—
382C3×Q8—61no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×D4—32no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—62no—
389C3×D4—62no—
390C3×D4—61no—
391C3×D4—61no—
392C3×D4—61no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—32no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—121no—
406C2×C3×C4C2×C4×D311yescharacteristic
407C2×C3×C4C2×C4×D311yescharacteristic
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418#67—22no—
419#67—22no—
420#67—22no—
421#67—22no—
422#67—68no—
423#67—68no—
424C2×Dic3—21no—
425C2×Dic3—41no—
426C2×Dic3—122no—
427C2×Dic3—121no—
428C2×Dic3—121no—
429C2×Dic3(C2×D3)⋊C412yes—
430D12—21no—
431D12—21no—
432D12—21no—
433D12—34no—
434D12—34no—
435D12—64no—
436D12—68no—
437D12—68no—
438D12—62no—
439D12—62no—
440D12—62no—
441D12—62no—
442D12—62no—
443D12—62no—
444D12—122no—
445D12—122no—
446D12—122no—
447D12(C2×D3)⋊C412yes—
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—68no—
453C4×D3—68no—
454Dic6—21no—
455Dic6—21no—
456Dic6—21no—
457Dic6(C2×D3)⋊C412yes—
458C3×C8—42no—
459C3×C8—41no—
460C3×C8—41no—
461C3×C8—121no—
462C3⋊C8—41no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32#37911yescharacteristic
467C3⋊D3—44no—
468C3×D3—42no—
469C3×D3—42no—
470C24—182no—
471C24—181no—
472#41—32no—
473#41—32no—
474#41—61no—
475#41—61no—
476#41—61no—
477#41—61no—
478#41—61no—
479#41—61no—
480#41—184no—
481#41—184no—
482#41—184no—
483#41—184no—
484C2×Q8—31no—
485C2×Q8—31no—
486C2×D4—32no—
487C2×D4—31no—
488C2×D4—31no—
489C2×D4—61no—
490C2×D4—92no—
491C2×D4—92no—
492C2×D4—92no—
493C2×D4—182no—
494C2×D4—184no—
495C2×D4—184no—
496C2×D4—184no—
497C2×D4—184no—
498C2×D4—182no—
499C2×D4—188no—
500C2×D4—188no—
501C2×D4—181no—
502C2×D4—181no—
503C2×D4—181no—
504C22×C4—32no—
505C22×C4—61no—
506C22×C4—182no—
507C22×C4C2×D3211yescharacteristic
508M16—21no—
509M16—21no—
510M16—61no—
511M16—61no—
512C2×C8—21no—
513C2×C8—61no—
514C4⋊C4—61no—
515C4⋊C4—181no—
516C22⋊C4—61no—
517C22⋊C4—181no—
518C42—61no—
519C42—181no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—62no—
527C22×C3—62no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3D3×C22⋊C411yescharacteristic
531C22×C3#88211yescharacteristic
532C22×C3#88211yescharacteristic
533C22×C3#88211yescharacteristic
534C22×C3C2×(C2×D3)⋊C411yescharacteristic
535C22×C3#93711yescharacteristic
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—42no—
539C2×D3—42no—
540C2×D3—64no—
541C2×D3—64no—
542C2×D3—124no—
543C2×D3—124no—
544C2×D3—124no—
545C2×D3—244no—
546C2×D3—248no—
547C2×D3—248no—
548C2×D3—242no—
549C2×D3—242no—
550C2×D3—242no—
551C2×D3—242no—
552C2×D3—244no—
553C2×D3—244no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—62no—
559C3×C4—62no—
560C3×C4—241no—
561C3×C4D3×C22⋊C411yescharacteristic
562C3×C4D3×C22⋊C411yescharacteristic
563C3×C4D3×C22⋊C411yescharacteristic
564C3×C4#88211yescharacteristic
565C3×C4C2×(C2×D3)⋊C411yescharacteristic
566C3×C4#93711yescharacteristic
567C3×C4#93711yescharacteristic
568C3×C4#93711yescharacteristic
569Dic3—22no—
570Dic3—22no—
571Dic3—81no—
572Dic3—242no—
573Dic3—241no—
574Dic3—241no—
575C32#179511yescharacteristic, complemented, Sylow
576C23—32no—
577C23—61no—
578C23—188no—
579C23—182no—
580C23—182no—
581C23—182no—
582C23—722no—
583C23—724no—
584C23D3×D1211yescharacteristic
585Q8—32no—
586Q8—61no—
587Q8—61no—
588Q8—61no—
589D4—32no—
590D4—62no—
591D4—62no—
592D4—62no—
593D4—62no—
594D4—61no—
595D4—61no—
596D4—61no—
597D4—94no—
598D4—188no—
599D4—188no—
600D4—182no—
601D4—182no—
602D4—182no—
603C2×C4—32no—
604C2×C4—61no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—121no—
610C2×C4—188no—
611C2×C4—361no—
612C2×C4C4×D3211yescharacteristic
613C2×C4D3×D1211yescharacteristic
614C2×C4#380211yescharacteristic
615C2×C4D3×#6711yescharacteristic
616C2×C4D3×#6711yescharacteristic
617C2×C4#381111yescharacteristic
618C8—41no—
619C8—121no—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—41no—
629C2×C3—41no—
630C2×C3—122no—
631C2×C3—122no—
632C2×C3#495511yescharacteristic
633C2×C3#495511yescharacteristic
634D3—42no—
635D3—42no—
636D3—124no—
637D3—124no—
638D3—244no—
639C22—41no—
640C22—62no—
641C22—62no—
642C22—122no—
643C22—122no—
644C22—184no—
645C22—364no—
646C22—722no—
647C22—722no—
648C22—728no—
649C22D3×(C2×D3)⋊C411yescharacteristic
650C22#6392211yescharacteristic
651C22#6392311yescharacteristic
652C4—62no—
653C4—62no—
654C4—241no—
655C4—721no—
656C4D3×(C2×D3)⋊C411yescharacteristic
657C4#6392111yescharacteristic
658C4#6392211yescharacteristic
659C4#6398311yescharacteristic
660C3—21no—
661C3#7013911yescharacteristic, complemented
662C3#7041411yescharacteristic, complemented
663C2—21no—
664C2—21no—
665C2—21no—
666C2—122no—
667C2—122no—
668C2—364no—
669C2#1059139911yescharacteristic
subgroupG/H
centerC2#10591399
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#379
prime radicalC2×#64308C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1795
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592830C2semidirect
3. C3×#5139C2semidirect
4. C3×#5132C2semidirect
5. #10591231C2semidirect
6. #10591110C2semidirect
7. #10591096C2semidirect
19. C2×D3×D12C4semidirect
21. C2×#3799C4semidirect
22. C2×C32×M16C22semidirect
23. #64135C22semidirect
24. C3×#926C22semidirect
25. C2×C3×#208C22semidirect
40. #5139D3semidirect
41. #5132D3semidirect
126. C2×C3×M16C2×D3semidirect
127. C2×C3×M16C2×D3semidirect
132. #926C2×D3semidirect
133. C2×#208C2×D3semidirect
348. C2×M16D32semidirect
575. C32#1795semidirect
661. C3#70139semidirect
662. C3#70414semidirect

Maximal subgroups

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

subgroupindex
C2×#643082
#105928302
C3×#51392
C3×#51322
#105912312
#105911102
#105910962
#704143
#701393