Finite Group Databasebeta

← #11788851

Subgroups — #11788851

Order 1152.

831 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595518C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic, complemented
3C2×C3×#806C211yesmaximal, characteristic, complemented
4C2×C3×#806C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6#10589392C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#70034—31nomaximal
9#70024—31nomaximal
10C22×C3×#67C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17#63980—22no—
18#63976—21no—
19#63976C412yescomplemented
20#67⋊Dic3—22no—
21Dic3×#67—22no—
22D3×#217—21no—
23#63961—21no—
24#63961C412yescomplemented
25#63955—21no—
26C3×#806—22no—
27C3×#806—22no—
28#63580—22no—
29#5804—31no—
30#5804—31no—
31#5798—31no—
32#5486—31no—
33C2×C3×#99—31no—
34C2×C3×#99—31no—
35C2×#834—31no—
36C2×#806—31no—
37C2×#806D311yescharacteristic, complemented
38C2×#806D311yescharacteristic, complemented
39#4527—31no—
40#4526—31no—
41#4526—31no—
42#4526—31no—
43#4526—61no—
44C24×C32C2311yescharacteristic
45C23×C3×D3C2×C411yescharacteristic, complemented
46C23×C3×D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C2×C3×#67—21no—
55C2×C3×#67—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67C2×C412yes—
61C2×C3×#67D412yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3C2×C411yescharacteristic, complemented
65C22×C3×Dic3D411yescharacteristic
66C2×#625—22no—
67C2×D3×Dic3—22no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4—21no—
70#3757—21no—
71#3757—21no—
72#3757C2×C412yescomplemented
73#3757D412yescomplemented
74C3×#217—21no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217D412yescomplemented
78#3724—22no—
79Dic3⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1913—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C22×#67C2×D311yescharacteristic
88C22×#67C2×D311yescharacteristic
89C2×C3×C22⋊C4—21no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C22⋊C4C2×D311yescharacteristic
93C2×C3×C22⋊C4C2×D311yescharacteristic
94#953—32no—
95#953—61no—
96C2×#217—31no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—31no—
100C2×#217—61no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217C2×D311yescharacteristic
104C2×#217C2×D311yescharacteristic
105#939—62no—
106#939—62no—
107#937—32no—
108#937—61no—
109#935—32no—
110#935—61no—
111D4×Dic3—62no—
112D4×Dic3—62no—
113#929—32no—
114#929—61no—
115C4×#67—62no—
116#926—61no—
117#67⋊C4—62no—
118D3×C22⋊C4—61no—
119#877—61no—
120C3×#99—62no—
121C3×#99—62no—
122#834—62no—
123#806—22no—
124#806—22no—
125#806—62no—
126C23×C32—81no—
127C23×C32C22×C411yescharacteristic
128C23×C32C2×D411yescharacteristic
129C23×C32C2×D411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×D411yescharacteristic
132C23×C32#4111yescharacteristic
133C23×C32#4111yescharacteristic
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—81no—
140C22×C3×D3—81no—
141C22×C3×D3C22⋊C412yes—
142C2×C32×C4—41no—
143C2×C32×C4—81no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—81no—
147C2×C3⋊Dic3—81no—
148C3×#67—22no—
149C3×#67—22no—
150C3×#67—22no—
151C3×#67—22no—
152C3×#67—41no—
153C3×#67—41no—
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—81no—
164C2×C3×Dic3—81no—
165C2×C3×Dic3C22⋊C412yes—
166#625—82no—
167D3×Dic3—82no—
168#534—91no—
169#518—91no—
170C2×#99—31no—
171C2×#99—31no—
172C2×#99—91no—
173#342—91no—
174#342—91no—
175C24×C3—21no—
176C24×C3—31no—
177C24×C3—31no—
178C24×C3C22×D311yescharacteristic
179C24×C3C22×D311yescharacteristic
180C23×D3C4×D311yescharacteristic, complemented
181C23×D3D1211yescharacteristic
182C2×C3×D4—32no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—21no—
204C2×#67—21no—
205C2×#67—21no—
206C2×#67—21no—
207C2×#67—21no—
208C2×#67—21no—
209C2×#67—21no—
210C2×#67—21no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67C4×D312yes—
214C2×#67#6712yes—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—62no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—121no—
223C22×Dic3—121no—
224C22×Dic3C4×D311yescharacteristic, complemented
225C22×Dic3D1211yescharacteristic
226C2×C4×D3—62no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C22⋊C4—21no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—41no—
233C3×C22⋊C4—41no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—61no—
237#217—21no—
238#217—21no—
239#217—21no—
240#217—32no—
241#217—32no—
242#217—32no—
243#217—32no—
244#217—62no—
245#217—62no—
246#217—62no—
247#217—62no—
248#217—61no—
249#217—61no—
250#217—61no—
251#217—61no—
252#217—62no—
253#217—121no—
254#217—121no—
255#217#6712yescomplemented
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259C4⋊Dic3—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C22×C32—41no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32C2×C22⋊C411yescharacteristic
273C22×C32C4×D411yescharacteristic
274C22×C32C4×D411yescharacteristic
275C22×C32#12011yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32#12111yescharacteristic
278C22×C32#12311yescharacteristic
279C2×C3×D3—22no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—41no—
284C2×C3×D3—81no—
285C2×C3×D3—81no—
286C2×C3×D3—81no—
287C32×C4—81no—
288C3⋊Dic3—42no—
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C3×Dic3—81no—
294C22×D4—31no—
295C22×D4—31no—
296#123—92no—
297#123—181no—
298#121—182no—
299#120—92no—
300#120—181no—
301C4×D4—182no—
302C4×D4—182no—
303#117—181no—
304C2×C22⋊C4—31no—
305C2×C22⋊C4—31no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—181no—
309C2×C22⋊C4D3211yescharacteristic
310#99—62no—
311#99—62no—
312#99—182no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—21no—
316C23×C3—21no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—32no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—81no—
327C23×C3—81no—
328C23×C3—82no—
329C23×C3—241no—
330C23×C3—241no—
331C23×C3C2×C4×D311yescharacteristic
332C23×C3C2×C4×D311yescharacteristic
333C23×C3C2×D1211yescharacteristic
334C23×C3#23511yescharacteristic
335C23×C3D3×D411yescharacteristic
336C23×C3D3×D411yescharacteristic
337C23×C3D3×D411yescharacteristic
338C23×C3D3×D411yescharacteristic
339C23×C3D3×D411yescharacteristic
340C23×C3#23711yescharacteristic
341C23×C3#23711yescharacteristic
342C23×C3#23711yescharacteristic
343C23×C3C2×#6711yescharacteristic
344C23×C3C2×#6711yescharacteristic
345C22×D3—21no—
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3—81no—
351C22×D3—81no—
352C22×D3(C2×D3)⋊C412yes—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—62no—
356C3×D4—62no—
357C3×D4—121no—
358C3×D4—121no—
359C3×D4—121no—
360C3×D4—121no—
361C2×C3×C4—32no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—81no—
372C2×C3×C4—81no—
373C2×C3×C4—82no—
374C2×C3×C4—121no—
375C2×C3×C4—241no—
376C2×C3×C4—241no—
377#67—22no—
378#67—22no—
379#67—22no—
380#67—22no—
381#67—41no—
382#67—41no—
383#67—41no—
384#67—41no—
385#67—242no—
386#67—242no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—41no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—81no—
399C2×Dic3—81no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—242no—
403C2×Dic3—241no—
404C2×Dic3—241no—
405C2×Dic3—241no—
406C2×Dic3—241no—
407C2×Dic3—242no—
408C2×Dic3—242no—
409C2×Dic3(C2×D3)⋊C412yes—
410C4×D3—242no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32—21no—
418C2×C32#38611yescharacteristic
419C3×D3—42no—
420C3×D3—81no—
421C24—31no—
422C24—31no—
423C24C2×D3211yescharacteristic
424C2×D4—32no—
425C2×D4—32no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—182no—
437C22×C4—21no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—182no—
443C22×C4—181no—
444C22×C4—181no—
445C4⋊C4—182no—
446C4⋊C4—182no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—32no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—92no—
454C22⋊C4—92no—
455C22⋊C4—182no—
456C22⋊C4—182no—
457C22⋊C4—182no—
458C22⋊C4—181no—
459C22⋊C4—181no—
460C42—182no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—62no—
486C22×C3—81no—
487C22×C3—81no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—121no—
494C22×C3—241no—
495C22×C3—241no—
496C22×C3—241no—
497C22×C3D3×C22⋊C411yescharacteristic
498C22×C3#67⋊C411yescharacteristic
499C22×C3#67⋊C411yescharacteristic
500C22×C3#67⋊C411yescharacteristic
501C22×C3#88211yescharacteristic
502C22×C3#88311yescharacteristic
503C22×C3#88411yescharacteristic
504C22×C3#88611yescharacteristic
505C22×C3C2×(C2×D3)⋊C411yescharacteristic
506C22×C3C4×#6711yescharacteristic
507C22×C3#93711yescharacteristic
508C22×C3#93811yescharacteristic
509C22×C3#93911yescharacteristic
510C22×C3#93911yescharacteristic
511C2×D3—22no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—41no—
516C2×D3—81no—
517C2×D3—81no—
518C2×D3—81no—
519C3×C4—62no—
520C3×C4—82no—
521C3×C4—81no—
522C3×C4—81no—
523C3×C4—122no—
524C3×C4—121no—
525C3×C4—241no—
526Dic3—22no—
527Dic3—42no—
528Dic3—41no—
529Dic3—81no—
530Dic3—122no—
531Dic3—122no—
532Dic3—122no—
533Dic3—122no—
534Dic3—242no—
535Dic3—242no—
536C32#191311yescharacteristic, complemented, Sylow
537C23—32no—
538C23—61no—
539C23—61no—
540C23—61no—
541C23—61no—
542C23—61no—
543C23—81no—
544C23—241no—
545C23—241no—
546C23#379511yescharacteristic
547C23C4×D3211yescharacteristic
548C23D3×D1211yescharacteristic
549C23#380211yescharacteristic
550C23#380511yescharacteristic
551C23D3×#6711yescharacteristic
552C23D3×#6711yescharacteristic
553D4—62no—
554D4—62no—
555D4—62no—
556D4—62no—
557D4—121no—
558D4—121no—
559D4—121no—
560D4—121no—
561D4—722no—
562C2×C4—32no—
563C2×C4—41no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—62no—
570C2×C4—81no—
571C2×C4—121no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4—241no—
575C2×C4—241no—
576C2×C4—722no—
577C2×C4—721no—
578C2×C4—721no—
579C2×C3—22no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—41no—
596C2×C3—41no—
597C2×C3—41no—
598C2×C3—41no—
599C2×C3—41no—
600C2×C3—41no—
601C2×C3—122no—
602C2×C3—241no—
603C2×C3#495611yescharacteristic
604C2×C3#495811yescharacteristic
605D3—42no—
606D3—81no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—62no—
615C22—122no—
616C22—122no—
617C22—122no—
618C22—121no—
619C22—241no—
620C22—241no—
621C22—241no—
622C22#6387911yescharacteristic
623C22#6388511yescharacteristic
624C22#6389111yescharacteristic
625C22#6390211yescharacteristic
626C22D3×(C2×D3)⋊C411yescharacteristic
627C22#6392211yescharacteristic
628C22#6397011yescharacteristic
629C4—62no—
630C4—81no—
631C4—122no—
632C4—121no—
633C4—241no—
634C4—362no—
635C4—362no—
636C3—21no—
637C3#7002411yescharacteristic, complemented
638C3#7003411yescharacteristic, complemented
639C2—21no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—122no—
647C2—241no—
648C2#1059136311yescharacteristic
subgroupG/H
centerC2#10591363
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#386
prime radical#10595518C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10595506C2semidirect
3. C2×C3×#806C2semidirect
4. C2×C3×#806C2semidirect
5. C2×#63580C2semidirect
6. #10589392C2semidirect
7. #10589186C2semidirect
19. #63976C4semidirect
24. #63961C4semidirect
37. C2×#806D3semidirect
38. C2×#806D3semidirect
45. C23×C3×D3C2×C4semidirect
64. C22×C3×Dic3C2×C4semidirect
72. #3757C2×C4semidirect
73. #3757D4semidirect
77. C3×#217D4semidirect
180. C23×D3C4×D3semidirect
224. C22×Dic3C4×D3semidirect
255. #217#67semidirect
536. C32#1913semidirect
637. C3#70024semidirect
638. C3#70034semidirect

Maximal subgroups

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

subgroupindex
#105955182
#105955062
C2×C3×#8062
C2×#635802
#105893922
#105891862
#700343
#700243