Finite Group Databasebeta

← #11868120

Subgroups — #11868120

Order 1152.

1081 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic, complemented
3C3×#5819C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10591680C214yesmaximal, complemented
6#10591677C214yesmaximal, complemented
7#10591141C211yesmaximal, characteristic, complemented
8C2×#63559C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#84002—31nomaximal
11#83814—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15#64158—22no—
16#64158C2214yes—
17C2×#3755—21no—
18C2×#3753—21no—
19C2×#3748C2211yescharacteristic
20C3×#951C2212yescomplemented
21C3×#950—22no—
22C3×#949C2212yescomplemented
23C3×#948—22no—
24C3×#948C2214yescomplemented
25C3×#942—21no—
26C3×#932—21no—
27C2×C3×#208—22no—
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×C3×#208C2211yescharacteristic
31C2×#3717C2212yescomplemented
32#63825—22no—
33#63825—22no—
34C2×#3714C2212yescomplemented
35#63577C2214yescomplemented
36#63560C2212yescomplemented
37#63559C2214yescomplemented
38#63558C2212yescomplemented
39C3×#575—31no—
40C3×#568—31no—
41#5822D311yescharacteristic, complemented
42C2×#949—31no—
43C2×#949—31no—
44C2×#949—31no—
45C2×#949—61no—
46#5819D311yescharacteristic, complemented
47C2×#908—31no—
48#5237—31no—
49#5203—34no—
50#5199—34no—
51#5142—34no—
52#5141—34no—
53#5132—31no—
54C2×#823—31no—
55C2×#823—31no—
56#5125—31no—
57#5124—31no—
58C23×C3⋊D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41D412yes—
62C32×#41C2312yes—
63C2×C32×Q8D411yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4D411yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C3×#67—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82#3755—24no—
83#3753—24no—
84#3748—21no—
85#3748C2312yes—
86C2×C3⋊(C3⋊C8)—21no—
87C3×#216—22no—
88C3×#215—22no—
89C3×#214—22no—
90C3×#213—22no—
91C3×#208—21no—
92C3×#208—21no—
93C3×#208—24no—
94C3×#208D412yes—
95C3×#208D412yes—
96C3×#208C2312yes—
97C3×#208C2312yes—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8—21no—
100C2×C3×C3⋊C8—24no—
101C2×C3×C3⋊C8C2312yes—
102#3717—24no—
103#3714—24no—
104#3068—91noSylow
105C2×C3×#41—21no—
106C2×C3×#41—31no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C2×#235C2×D311yescharacteristic
110C22×D12—31no—
111C22×D12—31no—
112C22×D12—61no—
113C3×#137—32no—
114C3×#137—61no—
115C3×AGL(1,ℤ/8)—32no—
116C3×AGL(1,ℤ/8)—61no—
117C3×#135—62no—
118C3×#131—34no—
119C3×#131—62no—
120C2×C3×M16—31no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C2×C3×M16—62no—
124#951C2×D312yescomplemented
125#950—22no—
126#949—34no—
127#949—34no—
128#949—64no—
129#949—64no—
130#949—62no—
131#949—62no—
132#949—62no—
133#949—62no—
134#949C2×D312yescomplemented
135#948—22no—
136#948C2×D314yescomplemented
137#942—21no—
138C2×#215—32no—
139C2×#215—62no—
140C2×#215—61no—
141C2×#215—61no—
142#932—21no—
143C2×#213—32no—
144C2×#213—62no—
145C2×#213—61no—
146C2×#213—61no—
147C2×#208—22no—
148C2×#208—31no—
149C2×#208—31no—
150C2×#208—61no—
151C2×#208C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153C2×#208C2×D311yescharacteristic
154#908—62no—
155#908—62no—
156C2×D24—32no—
157C2×#204—32no—
158#836—32no—
159#833—32no—
160#824—32no—
161#823—32no—
162#823—34no—
163#823—34no—
164#822—34no—
165#819—34no—
166C23×C32—21no—
167C23×C32#4111yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—41no—
170C22×C3⋊D3—41no—
171C22×C3⋊D3—82no—
172C22×C3×D3—21no—
173C32×Q8—21no—
174C32×Q8C2×D412yes—
175C32×D4—22no—
176C32×D4—22no—
177C32×D4—21no—
178C32×D4C2×D412yes—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4#4111yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)—22no—
190C4⋊(C3⋊D3)—41no—
191C4⋊(C3⋊D3)—41no—
192C3×#67—41no—
193C3×#67—41no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12—21no—
197C3×C4×D3—41no—
198C3×C4×D3—41no—
199C3×Dic6—21no—
200C3×Dic6—21no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8C2×D414yes—
205#575—31no—
206C2×AGL(1,ℤ/8)—91no—
207C2×AGL(1,ℤ/8)—91no—
208#568—31no—
209#472—94no—
210#471—94no—
211#430—91no—
212#413—91no—
213C2×#100—91no—
214C23×D3—61no—
215C23×D3—61no—
216C23×D3—121no—
217C3×#41—21no—
218C3×#41—21no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—22no—
222C3×#41—22no—
223C3×#41—41no—
224C3×#41—41no—
225C3×#41—61no—
226C3×#41—61no—
227C3×#41—61no—
228C3×#41—61no—
229C3×#41D1212yes—
230C3×#41#6712yes—
231C3×#41C22×D312yes—
232C3×#41C22×D312yes—
233C2×C3×Q8—21no—
234C2×C3×Q8—31no—
235C2×C3×Q8D1211yescharacteristic
236C2×C3×Q8#6711yescharacteristic
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—31no—
241C2×C3×D4—41no—
242C2×C3×D4—61no—
243C2×C3×D4D1211yescharacteristic
244C2×C3×D4#6711yescharacteristic
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—41no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—21no—
253#235—21no—
254#235—21no—
255#235—21no—
256#235—21no—
257C2×D12—32no—
258C2×D12—32no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—61no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12—61no—
267C2×D12—61no—
268C2×D12—61no—
269C2×D12—61no—
270C2×D12—61no—
271C2×D12—61no—
272C2×D12—121no—
273C2×D12—121no—
274C2×D12—121no—
275C2×D12C22×D311yescharacteristic
276C2×C4×D3—21no—
277C2×Dic6C22×D311yescharacteristic
278C3×Q16—62no—
279C3×SD16—62no—
280C3×SD16—62no—
281C3×D8—62no—
282C3×M16—32no—
283C3×M16—32no—
284C3×M16—32no—
285C3×M16—32no—
286C3×M16—64no—
287C3×M16—61no—
288C3×M16—61no—
289C2×C3×C8—32no—
290C2×C3×C8—64no—
291C2×C3×C8—61no—
292C2×C3×C8—61no—
293#216—22no—
294#215—22no—
295#215—68no—
296#215—64no—
297#215—64no—
298#215—64no—
299#214—22no—
300#213—22no—
301#213—68no—
302#213—64no—
303#213—64no—
304#213—64no—
305#208—21no—
306#208—21no—
307#208—24no—
308#208—32no—
309#208—32no—
310#208—62no—
311#208—62no—
312#208—61no—
313#208—61no—
314#208#6712yes—
315#208#6712yes—
316#208C22×D312yes—
317#208C22×D312yes—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—24no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8—61no—
323C2×C3⋊C8—61no—
324C2×C3⋊C8C22×D312yes—
325D24—64no—
326#204—64no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—81no—
330C22×C32#12111yescharacteristic
331C22×C32#12111yescharacteristic
332C22×C32C2×#4111yescharacteristic
333C2×C3⋊D3—42no—
334C2×C3⋊D3—82no—
335C2×C3⋊D3—82no—
336C2×C3⋊D3—82no—
337C2×C3×D3—41no—
338C2×C3×D3—81no—
339C32×C4—22no—
340C32×C4#12111yescharacteristic
341C32×C4#12111yescharacteristic
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—41no—
345C2×#41—31no—
346C2×#41D3211yescharacteristic
347C22×D4—91no—
348#137—32no—
349#137—61no—
350AGL(1,ℤ/8)—32no—
351AGL(1,ℤ/8)—61no—
352AGL(1,ℤ/8)—94no—
353AGL(1,ℤ/8)—182no—
354AGL(1,ℤ/8)—182no—
355AGL(1,ℤ/8)—182no—
356#135—62no—
357C2×SD16—92no—
358C2×SD16—181no—
359C2×D8—92no—
360C2×D8—181no—
361#131—34no—
362#131—62no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—62no—
367C2×M16—91no—
368#108—94no—
369#101—92no—
370#100—94no—
371#100—92no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—41no—
376C23×C3—61no—
377C23×C3#23511yescharacteristic
378C23×C3#23711yescharacteristic
379C22×D3—21no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—121no—
386C22×D3—121no—
387C22×D3—121no—
388C22×D3—121no—
389C22×D3—244no—
390C22×D3—242no—
391C22×D3—242no—
392C3×Q8—21no—
393C3×Q8—21no—
394C3×Q8—22no—
395C3×Q8—41no—
396C3×Q8—61no—
397C3×Q8—61no—
398C3×Q8C2×D1212yes—
399C3×Q8C2×#6712yes—
400C3×D4—22no—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—22no—
407C3×D4—41no—
408C3×D4—42no—
409C3×D4—42no—
410C3×D4—61no—
411C3×D4—61no—
412C3×D4—121no—
413C3×D4—121no—
414C3×D4C2×D1212yes—
415C3×D4C2×#6712yes—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—61no—
432C2×C3×C4—121no—
433C2×C3×C4—121no—
434C2×C3×C4C2×D1211yescharacteristic
435C2×C3×C4C2×D1211yescharacteristic
436C2×C3×C4#23511yescharacteristic
437C2×C3×C4D3×D411yescharacteristic
438C2×C3×C4D3×D411yescharacteristic
439C2×C3×C4#23711yescharacteristic
440C2×C3×C4C2×#6711yescharacteristic
441C2×C3×C4C2×#6711yescharacteristic
442C2×C3×C4C2×#6711yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C23×D311yescharacteristic
445C2×C3×C4C23×D311yescharacteristic
446#67—41no—
447#67—41no—
448C2×Dic3—21no—
449D12—21no—
450D12—21no—
451D12—64no—
452D12—62no—
453D12—62no—
454D12—62no—
455D12—62no—
456D12—122no—
457D12—122no—
458D12—122no—
459D12—121no—
460D12—121no—
461D12—121no—
462D12—121no—
463C4×D3—41no—
464C4×D3—41no—
465Dic6—21no—
466Dic6—21no—
467C3×C8—34no—
468C3×C8—62no—
469C3×C8—62no—
470C3⋊C8—22no—
471C3⋊C8—22no—
472C3⋊C8—64no—
473C3⋊C8—62no—
474C3⋊C8—62no—
475C3⋊C8C2×#6714yes—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—42no—
480C2×C32C2×#12111yescharacteristic
481C3⋊D3—82no—
482C3×D3—81no—
483C24—181no—
484#41—21no—
485#41—21no—
486#41—61no—
487#41—61no—
488#41—61no—
489#41—61no—
490#41#62612yes—
491#41C2×D3212yes—
492C2×Q8—31no—
493C2×Q8#62611yescharacteristic
494C2×D4—21no—
495C2×D4—31no—
496C2×D4—61no—
497C2×D4—92no—
498C2×D4—181no—
499C2×D4—181no—
500C2×D4—181no—
501C2×D4—181no—
502C2×D4—181no—
503C2×D4#62611yescharacteristic
504C22×C4—21no—
505C22×C4—61no—
506C22×C4C2×D3211yescharacteristic
507Q16—62no—
508SD16—62no—
509SD16—62no—
510SD16—184no—
511SD16—184no—
512D8—62no—
513D8—184no—
514D8—184no—
515M16—32no—
516M16—32no—
517M16—32no—
518M16—32no—
519M16—64no—
520M16—61no—
521M16—61no—
522M16—92no—
523M16—181no—
524C2×C8—32no—
525C2×C8—64no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—181no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—42no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3—82no—
541C22×C3—121no—
542C22×C3—241no—
543C22×C3#93011yescharacteristic
544C22×C3#93011yescharacteristic
545C22×C3#93911yescharacteristic
546C22×C3#93911yescharacteristic
547C22×C3C2×#23511yescharacteristic
548C22×C3C2×#23711yescharacteristic
549C2×D3—41no—
550C2×D3—81no—
551C2×D3—124no—
552C2×D3—122no—
553C2×D3—122no—
554C2×D3—244no—
555C2×D3—242no—
556C2×D3—242no—
557C2×D3—242no—
558C2×D3—242no—
559C2×D3—244no—
560C2×D3—244no—
561C2×D3—242no—
562C2×D3—242no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—42no—
570C3×C4—121no—
571C3×C4#93011yescharacteristic
572C3×C4#93011yescharacteristic
573C3×C4#93911yescharacteristic
574C3×C4#93911yescharacteristic
575C3×C4C22×D1211yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577C3×C4C22×#6711yescharacteristic
578C3×C4C22×#6711yescharacteristic
579Dic3—41no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—21no—
582C23—61no—
583C23—182no—
584C23—361no—
585C23—361no—
586C23—722no—
587C23#380411yescharacteristic
588Q8—21no—
589Q8—61no—
590Q8—61no—
591Q8C2×#62612yes—
592D4—22no—
593D4—22no—
594D4—21no—
595D4—61no—
596D4—61no—
597D4—121no—
598D4—121no—
599D4—182no—
600D4—182no—
601D4—361no—
602D4—361no—
603D4C2×#62612yes—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—61no—
608C2×C4—121no—
609C2×C4—121no—
610C2×C4#380411yescharacteristic
611C2×C4C2×#62611yescharacteristic
612C2×C4C2×#62611yescharacteristic
613C2×C4D3×#6711yescharacteristic
614C2×C4D3×#6711yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C8—34no—
617C8—62no—
618C8—62no—
619C8—182no—
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—42no—
631C2×C3—42no—
632C2×C3—82no—
633C2×C3—241no—
634C2×C3C2×#93011yescharacteristic
635C2×C3C2×#93911yescharacteristic
636D3—81no—
637D3—244no—
638D3—242no—
639D3—242no—
640C22—22no—
641C22—41no—
642C22—81no—
643C22—121no—
644C22—241no—
645C22—362no—
646C22—722no—
647C22—722no—
648C22—722no—
649C22#6397811yescharacteristic
650C22#6397811yescharacteristic
651C22C2×#380411yescharacteristic
652C4—22no—
653C4—121no—
654C4#6397811yescharacteristic
655C4#6397811yescharacteristic
656C4C22×#62611yescharacteristic
657C4C2×D3×#6711yescharacteristic
658C3—21no—
659C3#8381411yescharacteristic, complemented
660C3#8400211yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—42no—
665C2—241no—
666C2—722no—
667C2C2×#6397811yescharacteristic
subgroupG/H
centerC2C2×#63978
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#121
hypercenterC2×#41D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64158C2semidirect
2. C3×#5822C2semidirect
3. C3×#5819C2semidirect
4. C2×#63825C2semidirect
5. #10591680C2semidirect
6. #10591677C2semidirect
7. #10591141C2semidirect
8. C2×#63559C2semidirect
9. #10591076C2semidirect
20. C3×#951C22semidirect
22. C3×#949C22semidirect
24. C3×#948C22semidirect
31. C2×#3717C22semidirect
34. C2×#3714C22semidirect
35. #63577C22semidirect
36. #63560C22semidirect
37. #63559C22semidirect
38. #63558C22semidirect
41. #5822D3semidirect
46. #5819D3semidirect
124. #951C2×D3semidirect
134. #949C2×D3semidirect
136. #948C2×D3semidirect
580. C32#3068semidirect
659. C3#83814semidirect
660. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58222
C3×#58192
C2×#638252
#105916802
#105916772
#105911412
C2×#635592
#105910762
#840023
#838143