Finite Group Databasebeta

← #11868123

Subgroups — #11868123

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
3C2×#63825C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5C3×#5237C211yesmaximal, characteristic, complemented
6#10591643C214yesmaximal, complemented
7#10591508C214yesmaximal, complemented
8#10591143C211yesmaximal, characteristic, complemented
9C2×#63559C211yesmaximal, characteristic, complemented
10#84002—31nomaximal
11#78720—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15#64158—22no—
16#64158—22no—
17C2×#3755C2212yescomplemented
18C2×#3753C2212yescomplemented
19C2×#3748C2211yescharacteristic
20C3×#951—21no—
21C3×#950—22no—
22C3×#949—21no—
23C3×#942C2212yescomplemented
24C3×#932C2212yescomplemented
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×#3717—21no—
29#63825—22no—
30#63825C2214yes—
31C2×#3714—21no—
32#63815C2214yescomplemented
33#63814—22no—
34D3×#208—22no—
35C3×#836C2212yescomplemented
36C3×#833C2212yescomplemented
37#63578C2214yescomplemented
38#63559C2214yescomplemented
39C3×#575—31no—
40#5822D311yescharacteristic, complemented
41C2×#949—31no—
42C2×#949—31no—
43C2×#949—31no—
44C2×#949—61no—
45#5819—31no—
46C2×#908—31no—
47#5745—31no—
48C3×#413—31no—
49#5237D311yescharacteristic, complemented
50#5203—34no—
51#5199—34no—
52C2×#823—31no—
53C2×#823—31no—
54#5124—31no—
55#5124—31no—
56#4754—34no—
57#4749—34no—
58C23×C3⋊D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41—21no—
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
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×#235D412yes—
78C3×#235C2312yes—
79C2×C3×D12D411yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6D411yescharacteristic
82#3755—24no—
83#3753—24no—
84#3748D412yes—
85#3748D412yes—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#216—22no—
88C3×#215—22no—
89C3×#214—22no—
90C3×#213—22no—
91C3×#208—21no—
92C3×#208—21no—
93C3×#208—21no—
94C3×#208C2312yes—
95C3×#208C2312yes—
96C3×#208C2312yes—
97C2×C3×C3⋊C8—21no—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8—21no—
100#3717—24no—
101#3714—24no—
102#3711—24no—
103D3×C3⋊C8—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—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120C2×C3×M16—31no—
121#951—21no—
122#950—22no—
123#949—21no—
124#949—34no—
125#949—62no—
126#949—62no—
127#949—62no—
128#949—62no—
129#949—62no—
130#949—64no—
131#949—64no—
132#948—34no—
133#948—62no—
134#942C2×D312yescomplemented
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—62no—
138C2×#215—61no—
139#932C2×D312yescomplemented
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—62no—
143C2×#213—61no—
144C2×#208—31no—
145C2×#208—31no—
146C2×#208—61no—
147C2×#208—62no—
148C2×#208C2×D311yescharacteristic
149C2×#208C2×D311yescharacteristic
150C2×#208C2×D311yescharacteristic
151#908—34no—
152#908—62no—
153#907—34no—
154D3×M16—62no—
155C2×D24—61no—
156C2×#204—61no—
157#901—62no—
158C3×#101—32no—
159C3×#100—32no—
160#836C2×D312yescomplemented
161#833C2×D312yescomplemented
162#823—34no—
163#823—34no—
164#822—34no—
165#822—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×Q8—21no—
175C32×D4—21no—
176C32×D4—21no—
177C32×D4—41no—
178C32×D4—41no—
179C2×C32×C4—21no—
180C2×C32×C4—41no—
181C2×C32×C4—41no—
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—22no—
193C3×#67—22no—
194C2×C3×Dic3—21no—
195C3×D12—21no—
196C3×D12C2×D412yes—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199C3×Dic6—21no—
200C3×Dic6C2×D412yes—
201C3⋊(C3⋊C8)C2×D414yes—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205#575—31no—
206C2×AGL(1,ℤ/8)—91no—
207C2×AGL(1,ℤ/8)—91no—
208#568—91no—
209#472—94no—
210#471—94no—
211#430—91no—
212#413—31no—
213C2×#100—91no—
214C23×D3—61no—
215C23×D3—61no—
216C23×D3—121no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—21no—
226C3×#41—21no—
227C3×#41—32no—
228C3×#41—32no—
229C3×#41—41no—
230C3×#41—41no—
231C3×#41—61no—
232C3×#41—61no—
233C2×C3×Q8—21no—
234C2×C3×Q8—31no—
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×Q8C22×D311yescharacteristic
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×D4C22×D311yescharacteristic
244C2×C3×D4C22×D311yescharacteristic
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#6712yes—
256#235C22×D312yes—
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×D12#6711yescharacteristic
276C2×C4×D3—21no—
277C2×Dic6#6711yescharacteristic
278C3×Q16—62no—
279C3×SD16—62no—
280C3×SD16—62no—
281C3×D8—62no—
282C3×M16—32no—
283C3×M16—32no—
284C3×M16—32no—
285C3×M16—61no—
286C3×M16—61no—
287C3×M16—61no—
288C2×C3×C8—61no—
289C2×C3×C8—61no—
290C2×C3×C8—61no—
291#216—22no—
292#215—22no—
293#215—64no—
294#215—64no—
295#215—64no—
296#215—68no—
297#214—22no—
298#213—22no—
299#213—64no—
300#213—64no—
301#213—64no—
302#213—68no—
303#208—21no—
304#208—21no—
305#208—21no—
306#208—32no—
307#208—32no—
308#208—32no—
309#208—32no—
310#208—62no—
311#208—62no—
312#208—64no—
313#208C22×D312yes—
314#208C22×D312yes—
315#208C22×D312yes—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8—64no—
323D24—64no—
324#204—64no—
325ΓL(1,𝔽25)—64no—
326D3×C8—64no—
327C22×C32—41no—
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—22no—
338C2×C3×D3—81no—
339C32×C4—41no—
340C32×C4#12111yescharacteristic
341C32×C4#12111yescharacteristic
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—22no—
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—94no—
362#131—182no—
363C2×M16—31no—
364C2×M16—31no—
365C2×M16—31no—
366C2×M16—91no—
367C2×M16—182no—
368#108—94no—
369#101—32no—
370#100—32no—
371#100—94no—
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—22no—
393C3×Q8—21no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×Q8—21no—
397C3×Q8—32no—
398C3×Q8—41no—
399C3×Q8—61no—
400C3×D4—22no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—21no—
405C3×D4—32no—
406C3×D4—41no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—41no—
410C3×D4—41no—
411C3×D4—41no—
412C3×D4—41no—
413C3×D4—62no—
414C3×D4—62no—
415C3×D4—61no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—61no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4#23511yescharacteristic
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4D3×D411yescharacteristic
438C2×C3×C4D3×D411yescharacteristic
439C2×C3×C4D3×D411yescharacteristic
440C2×C3×C4D3×D411yescharacteristic
441C2×C3×C4#23711yescharacteristic
442C2×C3×C4C2×#6711yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C23×D311yescharacteristic
445C2×C3×C4C23×D311yescharacteristic
446#67—22no—
447#67—22no—
448C2×Dic3—21no—
449D12—21no—
450D12—64no—
451D12—62no—
452D12—62no—
453D12—62no—
454D12—62no—
455D12—122no—
456D12—122no—
457D12—122no—
458D12—121no—
459D12—121no—
460D12—121no—
461D12—121no—
462D12C2×#6712yes—
463C4×D3—22no—
464C4×D3—22no—
465Dic6—21no—
466Dic6C2×#6712yes—
467C3×C8—62no—
468C3×C8—62no—
469C3×C8—62no—
470C3⋊C8—22no—
471C3⋊C8—22no—
472C3⋊C8—22no—
473C3⋊C8—34no—
474C3⋊C8—34no—
475C3⋊C8—64no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—81no—
480C2×C32C2×#12111yescharacteristic
481C3⋊D3—82no—
482C3×D3—42no—
483C24—181no—
484#41—21no—
485#41—21no—
486#41—21no—
487#41—21no—
488#41—32no—
489#41—32no—
490#41—61no—
491#41—61no—
492C2×Q8—31no—
493C2×Q8C2×D3211yescharacteristic
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×D4C2×D3211yescharacteristic
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—61no—
519M16—61no—
520M16—61no—
521M16—92no—
522M16—92no—
523M16—184no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—92no—
528C2×C8—184no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—62no—
539C22×C3—81no—
540C22×C3—81no—
541C22×C3—82no—
542C22×C3—241no—
543C22×C3#88411yescharacteristic
544C22×C3#88411yescharacteristic
545C22×C3#93911yescharacteristic
546C22×C3#93911yescharacteristic
547C22×C3C2×#23511yescharacteristic
548C22×C3C2×#23711yescharacteristic
549C2×D3—22no—
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—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—42no—
568C3×C4—41no—
569C3×C4—41no—
570C3×C4—62no—
571C3×C4#88411yescharacteristic
572C3×C4#88411yescharacteristic
573C3×C4#93911yescharacteristic
574C3×C4#93911yescharacteristic
575C3×C4C2×D3×D411yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577C3×C4C2×D3×D411yescharacteristic
578C3×C4C22×#6711yescharacteristic
579Dic3—22no—
580C32#306811yescharacteristic, complemented, Sylow
581C23—21no—
582C23—61no—
583C23—182no—
584C23—361no—
585C23—361no—
586C23—722no—
587C23#380411yescharacteristic
588Q8—21no—
589Q8—21no—
590Q8—32no—
591Q8—61no—
592D4—21no—
593D4—21no—
594D4—32no—
595D4—41no—
596D4—41no—
597D4—62no—
598D4—62no—
599D4—61no—
600D4—182no—
601D4—182no—
602D4—361no—
603D4—361no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—61no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4#380411yescharacteristic
611C2×C4D3×#6711yescharacteristic
612C2×C4D3×#6711yescharacteristic
613C2×C4#381111yescharacteristic
614C2×C4#381111yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C8—62no—
617C8—62no—
618C8—62no—
619C8—94no—
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—82no—
631C2×C3—81no—
632C2×C3—81no—
633C2×C3—122no—
634C2×C3C2×#88411yescharacteristic
635C2×C3C2×#93911yescharacteristic
636D3—42no—
637D3—244no—
638D3—242no—
639D3—242no—
640C22—41no—
641C22—41no—
642C22—62no—
643C22—81no—
644C22—241no—
645C22—362no—
646C22—722no—
647C22—722no—
648C22—722no—
649C22#6397111yescharacteristic
650C22#6397111yescharacteristic
651C22C2×#380411yescharacteristic
652C4—41no—
653C4—62no—
654C4#6397111yescharacteristic
655C4#6397111yescharacteristic
656C4C2×D3×#6711yescharacteristic
657C4C2×#381111yescharacteristic
658C3—21no—
659C3#7872011yescharacteristic, complemented
660C3#8400211yescharacteristic, complemented
661C2—21no—
662C2—21no—
663C2—21no—
664C2—81no—
665C2—122no—
666C2—722no—
667C2C2×#6397111yescharacteristic
subgroupG/H
centerC2C2×#63971
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. C2×#63825C2semidirect
4. #10594776C2semidirect
5. C3×#5237C2semidirect
6. #10591643C2semidirect
7. #10591508C2semidirect
8. #10591143C2semidirect
9. C2×#63559C2semidirect
17. C2×#3755C22semidirect
18. C2×#3753C22semidirect
23. C3×#942C22semidirect
24. C3×#932C22semidirect
32. #63815C22semidirect
35. C3×#836C22semidirect
36. C3×#833C22semidirect
37. #63578C22semidirect
38. #63559C22semidirect
40. #5822D3semidirect
49. #5237D3semidirect
134. #942C2×D3semidirect
139. #932C2×D3semidirect
160. #836C2×D3semidirect
161. #833C2×D3semidirect
580. C32#3068semidirect
659. C3#78720semidirect
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
C2×#638252
#105947762
C3×#52372
#105916432
#105915082
#105911432
C2×#635592
#840023
#787203