Finite Group Databasebeta

← #11865322

Subgroups — #11865322

Order 1152.

1937 conjugacy classes of subgroups.

The subgroup lattice has 677 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic, complemented
2C3×#5828C211yesmaximal, characteristic, complemented
3#10595023C212yesmaximal, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5#10591535C214yesmaximal, complemented
6#10591532C214yesmaximal, complemented
7#10591232C212yesmaximal, complemented
8#82936—31nomaximal
9#78690—31nomaximal
10C2×C32×#41C2211yescharacteristic
11#64367—22no—
12#64366—22no—
13#41×C3⋊D3—24no—
14#64364—21no—
15#64361—21no—
16#64361C2214yes—
17C2×#3828—22no—
18C2×#3828C2212yes—
19C22×C3×C4×D3C2211yescharacteristic, complemented
20C3×#946—21no—
21C3×#938—21no—
22C3×#937C2212yescomplemented
23C3×#935C2212yescomplemented
24C3×C4×#67—22no—
25C3×#926C2211yescharacteristic, complemented
26C3×#926C2212yescomplemented
27#63977C2214yescomplemented
28#63966C2214yescomplemented
29#63909—22no—
30C4×#626—24no—
31#63857—22no—
32C3×#834C2214yescomplemented
33#63581C2218yescomplemented
34#5964—31no—
35#5964—31no—
36#5964—61no—
37C3×#525—31no—
38#5828D311yescharacteristic, complemented
39#5791—32no—
40#5524—32no—
41C3×#410—31no—
42#5240D311yescharacteristic, complemented
43#5053—34no—
44#5032—34no—
45#5006—32no—
46#5006—32no—
47#4742—34no—
48#4741—34no—
49C23×C3×D3C2311yescharacteristic
50C32×#41—22no—
51C32×#41—22no—
52C2×C32×Q8D411yescharacteristic, complemented
53C2×C32×D4D411yescharacteristic, complemented
54C2×C32×D4C2312yes—
55C22×C32×C4D412yescomplemented
56C22×C32×C4C2311yescharacteristic
57C2×#638—24no—
58C2×#638C2314yes—
59#3832—24no—
60Q8×C3⋊D3—24no—
61#3830—24no—
62#3830—28no—
63D4×C3⋊D3—24no—
64D4×C3⋊D3—28no—
65#3828—24no—
66#3828—24no—
67#3828—22no—
68#3828—24no—
69#3828—22no—
70#3828—22no—
71#3828—22no—
72C2×C4⋊(C3⋊D3)—22no—
73C2×C4⋊(C3⋊D3)D412yescomplemented
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3D414yescomplemented
76C2×#634—22no—
77C2×#634D412yescomplemented
78C2×C3×#67—22no—
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—22no—
84C2×#626—24no—
85C3×#217—22no—
86C3×#217C2312yes—
87C3×#217C2314yes—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—21no—
93C3×C4×Dic3—22no—
94Dic3⋊Dic3—24no—
95#3722—24no—
96(C2×D3)⋊Dic3—24no—
97#3025—91noSylow
98C2×C3×#41—21no—
99C2×C3×#41C2×D311yescharacteristic
100C2×C3×#41C2×D311yescharacteristic
101C23×C3×C4—31no—
102#1010—62no—
103#1010—62no—
104#1010—64no—
105#1009—62no—
106#1009—62no—
107#1009—64no—
108D3×#41—64no—
109D3×#41—64no—
110D3×#41—68no—
111#1007—62no—
112#1007—61no—
113#1007—61no—
114#1004—34no—
115#1004—34no—
116#1004—64no—
117#1004—62no—
118#1004—61no—
119#1004—61no—
120C2×#235—32no—
121C2×#235—32no—
122C2×#235—62no—
123C2×#235—64no—
124C2×#235—62no—
125C2×#235—62no—
126C22×C4×D3C2×D311yescharacteristic, complemented
127C3×#123—32no—
128C3×C22⋊Q8—61no—
129C3×#121—61no—
130C3×#120—32no—
131C3×C4×D4—62no—
132C3×#117—31no—
133C3×#117—32no—
134#953—34no—
135#946—21no—
136#938—21no—
137#937C2×D312yescomplemented
138#935C2×D312yescomplemented
139#930—62no—
140#929—34no—
141C4×#67—22no—
142C4×#67—64no—
143#926C2×D312yescomplemented
144#926C2×D311yescharacteristic, complemented
145#924—62no—
146#897—62no—
147#895—62no—
148#886—34no—
149#882—34no—
150C4×D12—64no—
151C3×#99—34no—
152#834C2×D314yescomplemented
153#806—38no—
154#806—38no—
155C23×C32C2×D412yes—
156C23×C32C2411yescharacteristic
157C22×C3⋊D3—24no—
158C22×C3⋊D3C2×D414yes—
159C22×C3×D3—22no—
160C22×C3×D3—21no—
161C22×C3×D3—42no—
162C32×Q8—22no—
163C32×D4—24no—
164C32×D4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D412yes—
172#638—28no—
173#638—24no—
174#638—24no—
175C2×C3⋊Dic3—24no—
176C2×C3⋊Dic3C2×D414yes—
177C4⋊(C3⋊D3)—24no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4×C3⋊D3—28no—
181C4×C3⋊D3—24no—
182C4×C3⋊D3—24no—
183#634—24no—
184#634—22no—
185#634—22no—
186C3×#67—44no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C3×C4×D3—41no—
192C3×C4×D3—42no—
193C3×C4×D3—41no—
194#626—48no—
195#585—91no—
196#525—31no—
197#525—92no—
198#458—94no—
199B(4,𝔽2)—94no—
200#410—31no—
201#410—92no—
202C24×C3—31no—
203C23×D3C22×D311yescharacteristic
204C3×#41—24no—
205C3×#41—24no—
206C3×#41—22no—
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—22no—
210C2×C3×Q8—21no—
211C2×C3×Q8D1211yescharacteristic, complemented
212C2×C3×Q8#6711yescharacteristic, complemented
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—62no—
216C2×C3×D4D1211yescharacteristic, complemented
217C2×C3×D4#6711yescharacteristic, complemented
218C2×C3×D4C22×D312yes—
219C2×C3×D4C22×D312yes—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C22×C3×C4—62no—
226C22×C3×C4—62no—
227C22×C3×C4D1212yescomplemented
228C22×C3×C4#6712yescomplemented
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—22no—
232C2×#67—34no—
233C2×#67—34no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—68no—
237C2×#67—64no—
238C2×#67—64no—
239C22×Dic3C22×D311yescharacteristic
240#239—68no—
241#239—64no—
242#239—64no—
243D3×Q8—68no—
244D3×Q8—64no—
245D3×Q8—64no—
246#237—68no—
247#237—68no—
248#237—616no—
249#237—68no—
250#237—64no—
251#237—64no—
252D3×D4—68no—
253D3×D4—68no—
254D3×D4—616no—
255D3×D4—68no—
256D3×D4—64no—
257D3×D4—64no—
258#235—64no—
259#235—64no—
260#235—68no—
261#235—68no—
262#235—64no—
263#235—64no—
264#235—64no—
265#235—68no—
266#235—64no—
267#235—64no—
268#235—64no—
269#235—62no—
270#235—62no—
271#235—64no—
272#235—62no—
273#235—62no—
274#235—62no—
275#235—62no—
276#235—62no—
277#235—62no—
278#235—64no—
279C2×D12—32no—
280C2×D12—32no—
281C2×D12—62no—
282C2×D12—64no—
283C2×D12—62no—
284C2×D12—62no—
285C2×D12—64no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—34no—
291C2×C4×D3—34no—
292C2×C4×D3—64no—
293C2×C4×D3—68no—
294C2×C4×D3—64no—
295C2×C4×D3—64no—
296C2×Dic6—32no—
297C2×Dic6—32no—
298C2×Dic6—62no—
299C2×Dic6—64no—
300C2×Dic6—62no—
301C2×Dic6—62no—
302C3×C4⋊C4—62no—
303C3×C4⋊C4—61no—
304C3×C4⋊C4—62no—
305C3×C22⋊C4—32no—
306C3×C22⋊C4—34no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—62no—
309C3×C42—61no—
310C3×C42—62no—
311#217—22no—
312#217—64no—
313#217C22×D312yes—
314#217C22×D314yes—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—64no—
317(C2×D3)⋊C4—64no—
318(C2×D3)⋊C4—64no—
319C4⋊Dic3—22no—
320C4⋊Dic3—21no—
321C4⋊Dic3—64no—
322Dic3⋊C4—22no—
323Dic3⋊C4—64no—
324C4×Dic3—22no—
325C4×Dic3—21no—
326C22×C32—22no—
327C22×C32—41no—
328C22×C32—42no—
329C22×C32C22×D411yescharacteristic
330C22×C32C22×D412yes—
331C2×C3⋊D3—24no—
332C2×C3⋊D3—44no—
333C2×C3⋊D3—84no—
334C2×C3×D3—24no—
335C2×C3×D3—22no—
336C2×C3×D3—42no—
337C2×C3×D3—41no—
338C2×C3×D3—41no—
339C32×C4—22no—
340C32×C4#12011yescharacteristic
341C32×C4#12012yes—
342C32×C4#12011yescharacteristic
343C3⋊Dic3—24no—
344C3×Dic3—44no—
345C3×Dic3—42no—
346C3×Dic3—41no—
3472−1+4—182no—
3482−1+4—181no—
349H(5,𝔽2)—94no—
350H(5,𝔽2)—182no—
351H(5,𝔽2)—181no—
352C2×#41—92no—
353C2×#41—184no—
354C2×#41—182no—
355C2×#41D3211yescharacteristic
356C23×C4—31no—
357#123—32no—
358#123—94no—
359C22⋊Q8—61no—
360C22⋊Q8—182no—
361#121—61no—
362#121—182no—
363#120—32no—
364#120—94no—
365C4×D4—62no—
366C4×D4—184no—
367#117—31no—
368#117—32no—
369#99—34no—
370#99—98no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—61no—
374C23×C3—62no—
375C23×C3—122no—
376C23×C3C2×D1212yes—
377C23×C3C2×#6712yes—
378C23×C3C23×D311yescharacteristic
379C23×C3C23×D311yescharacteristic
380C22×D3—22no—
381C22×D3—21no—
382C22×D3—34no—
383C22×D3—34no—
384C22×D3—42no—
385C22×D3—64no—
386C22×D3—68no—
387C22×D3—64no—
388C22×D3—64no—
389C3×Q8—24no—
390C3×Q8—22no—
391C3×Q8—22no—
392C3×D4—28no—
393C3×D4—24no—
394C3×D4—24no—
395C3×D4—24no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—124no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—62no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—64no—
414C2×C3×C4—121no—
415C2×C3×C4—122no—
416C2×C3×C4—121no—
417C2×C3×C4C2×D1212yes—
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4D3×D412yes—
421C2×C3×C4D3×D412yes—
422C2×C3×C4D3×D412yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427#67—44no—
428#67—68no—
429#67—616no—
430#67—68no—
431#67—68no—
432#67—68no—
433#67—64no—
434#67—64no—
435#67—64no—
436#67—64no—
437#67—128no—
438C2×Dic3—24no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—34no—
443C2×Dic3—34no—
444C2×Dic3—64no—
445C2×Dic3—68no—
446C2×Dic3—64no—
447C2×Dic3—64no—
448D12—64no—
449D12—68no—
450D12—64no—
451D12—64no—
452D12—64no—
453D12—62no—
454D12—62no—
455D12—62no—
456D12—62no—
457D12—128no—
458C4×D3—41no—
459C4×D3—42no—
460C4×D3—41no—
461C4×D3—68no—
462C4×D3—616no—
463C4×D3—68no—
464C4×D3—68no—
465C4×D3—68no—
466C4×D3—64no—
467C4×D3—64no—
468C4×D3—64no—
469C4×D3—64no—
470Dic6—64no—
471Dic6—68no—
472Dic6—64no—
473Dic6—64no—
474Dic6—64no—
475Dic6—62no—
476Dic6—62no—
477Dic6—62no—
478Dic6—62no—
479C2×C32—22no—
480C2×C32—21no—
481C2×C32—42no—
482C2×C32C2×#12011yescharacteristic
483C3⋊D3—44no—
484C3×D3—42no—
485C24—31no—
486#41—22no—
487#41—22no—
488#41—184no—
489#41—184no—
490#41—188no—
491#41—184no—
492#41—184no—
493#41—182no—
494#41—182no—
495#41—184no—
496#41—182no—
497#41—182no—
498C2×Q8—92no—
499C2×Q8—182no—
500C2×Q8—184no—
501C2×Q8#62611yescharacteristic, complemented
502C2×D4—62no—
503C2×D4—94no—
504C2×D4—92no—
505C2×D4—182no—
506C2×D4—184no—
507C2×D4—188no—
508C2×D4—184no—
509C2×D4—184no—
510C2×D4#62611yescharacteristic, complemented
511C2×D4C2×D3212yes—
512C22×C4—31no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—94no—
518C22×C4—184no—
519C22×C4#62612yescomplemented
520C22×C4C2×D3211yescharacteristic
521C4⋊C4—61no—
522C4⋊C4—62no—
523C4⋊C4—62no—
524C4⋊C4—184no—
525C22⋊C4—34no—
526C22⋊C4—32no—
527C22⋊C4—62no—
528C22⋊C4—62no—
529C22⋊C4—184no—
530C22⋊C4—184no—
531C42—61no—
532C42—62no—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—21no—
537C22×C3—22no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—64no—
543C22×C3—62no—
544C22×C3—81no—
545C22×C3—82no—
546C22×C3—122no—
547C22×C3—121no—
548C22×C3—121no—
549C22×C3C22×D1211yescharacteristic
550C22×C3C2×D3×D412yes—
551C22×C3C2×D3×D412yes—
552C22×C3C22×#6711yescharacteristic
553C2×D3—24no—
554C2×D3—22no—
555C2×D3—41no—
556C2×D3—42no—
557C2×D3—41no—
558C2×D3—68no—
559C2×D3—64no—
560C2×D3—64no—
561C2×D3—124no—
562C2×D3—124no—
563C2×D3—244no—
564C2×D3—248no—
565C2×D3—244no—
566C2×D3—244no—
567C3×C4—24no—
568C3×C4—22no—
569C3×C4—22no—
570C3×C4—21no—
571C3×C4—22no—
572C3×C4—21no—
573C3×C4—124no—
574C3×C4—122no—
575C3×C4—121no—
576C3×C4#88211yescharacteristic
577C3×C4#88212yes—
578C3×C4#88211yescharacteristic
579C3×C4#93711yescharacteristic
580C3×C4#93712yes—
581C3×C4#93711yescharacteristic
582Dic3—42no—
583Dic3—44no—
584Dic3—41no—
585Dic3—68no—
586Dic3—64no—
587Dic3—64no—
588C32#302511yescharacteristic, complemented, Sylow
589C23—61no—
590C23—62no—
591C23—94no—
592C23—122no—
593C23—184no—
594C23C2×#62612yes—
595C23C22×D3211yescharacteristic
596Q8—22no—
597Q8—184no—
598Q8—182no—
599Q8—182no—
600D4—24no—
601D4—22no—
602D4—124no—
603D4—184no—
604D4—188no—
605D4—184no—
606D4—184no—
607D4—182no—
608D4—182no—
609D4—368no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—62no—
613C2×C4—61no—
614C2×C4—64no—
615C2×C4—62no—
616C2×C4—94no—
617C2×C4—121no—
618C2×C4—122no—
619C2×C4—121no—
620C2×C4—188no—
621C2×C4—184no—
622C2×C4—184no—
623C2×C4—184no—
624C2×C4C2×#62612yes—
625C2×C4C2×#62611yescharacteristic
626C2×C4C2×#62611yescharacteristic
627C2×C4#381112yes—
628C2×C4#381112yes—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—22no—
633C2×C3—21no—
634C2×C3—42no—
635C2×C3—41no—
636C2×C3—44no—
637C2×C3—42no—
638C2×C3—42no—
639C2×C3—122no—
640C2×C3C2×#88211yescharacteristic
641C2×C3C2×#93711yescharacteristic
642D3—42no—
643D3—128no—
644D3—124no—
645D3—124no—
646C22—22no—
647C22—41no—
648C22—42no—
649C22—62no—
650C22—64no—
651C22—121no—
652C22—122no—
653C22—121no—
654C22—184no—
655C22—364no—
656C22—724no—
657C22C22×#62611yescharacteristic
658C22C2×#381112yes—
659C4—22no—
660C4—122no—
661C4—124no—
662C4—121no—
663C4—184no—
664C4#6398111yescharacteristic
665C4#6398112yes—
666C4#6398111yescharacteristic
667C3—21no—
668C3#7869011yescharacteristic, complemented
669C3#8293611yescharacteristic, complemented
670C2—21no—
671C2—22no—
672C2—42no—
673C2—122no—
674C2—364no—
675C2C2×#6398111yescharacteristic
subgroupG/H
centerC4#63981
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3025
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596756C2semidirect
2. C3×#5828C2semidirect
3. #10595023C2semidirect
4. C3×#5240C2semidirect
5. #10591535C2semidirect
6. #10591532C2semidirect
7. #10591232C2semidirect
19. C22×C3×C4×D3C22semidirect
22. C3×#937C22semidirect
23. C3×#935C22semidirect
25. C3×#926C22semidirect
26. C3×#926C22semidirect
27. #63977C22semidirect
28. #63966C22semidirect
32. C3×#834C22semidirect
33. #63581C22semidirect
38. #5828D3semidirect
42. #5240D3semidirect
52. C2×C32×Q8D4semidirect
53. C2×C32×D4D4semidirect
55. C22×C32×C4D4semidirect
73. C2×C4⋊(C3⋊D3)D4semidirect
75. C2×C4×C3⋊D3D4semidirect
77. C2×#634D4semidirect
126. C22×C4×D3C2×D3semidirect
137. #937C2×D3semidirect
138. #935C2×D3semidirect
143. #926C2×D3semidirect
144. #926C2×D3semidirect
152. #834C2×D3semidirect
211. C2×C3×Q8D12semidirect
212. C2×C3×Q8#67semidirect
216. C2×C3×D4D12semidirect
217. C2×C3×D4#67semidirect
227. C22×C3×C4D12semidirect
228. C22×C3×C4#67semidirect
501. C2×Q8#626semidirect
510. C2×D4#626semidirect
519. C22×C4#626semidirect
588. C32#3025semidirect
668. C3#78690semidirect
669. C3#82936semidirect

Maximal subgroups

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

subgroupindex
#105967562
C3×#58282
#105950232
C3×#52402
#105915352
#105915322
#105912322
#829363
#786903