Finite Group Databasebeta

← #11864375

Subgroups — #11864375

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591599C214yesmaximal, complemented
7#10591459C214yesmaximal, complemented
8#10591085C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84105—31nomaximal
11#78835—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
14C3×#1009—24no—
15C3×#1009—24no—
16C2×C3×#239C2212yes—
17C2×C3×D3×D4—22no—
18C2×C3×D3×D4C2212yes—
19C2×C3×#235—21no—
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12—21no—
22C22×C3×D12C2211yescharacteristic
23#64160—24no—
24C2×#3756C2212yescomplemented
25C2×#3754C2212yescomplemented
26C2×#3748C2211yescharacteristic, complemented
27C3×#926C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29#63962—22no—
30#63866—21no—
31#63860—21no—
32#63857C2214yescomplemented
33C2×#3716—24no—
34C2×#3716C2214yescomplemented
35C3×#835C2212yescomplemented
36C3×#832C2212yescomplemented
37#63562C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1009D311yescharacteristic
41#5825—31no—
42C2×#951—31no—
43C2×#951—31no—
44C2×#951—61no—
45C22×#214—31no—
46C22×#204—31no—
47#5526—31no—
48C3×#416—31no—
49#5239—34no—
50#5234—31no—
51#5233D311yescharacteristic, complemented
52#5218—34no—
53#5215—31no—
54#5110—31no—
55#5001—31no—
56#4808—34no—
57#4776—34no—
58C23×C3×D3—21no—
59C23×C3×D3—22no—
60C32×#41—22no—
61C32×#41D414yes—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—21no—
68C2×#634—22no—
69C2×#634—22no—
70C2×#634—21no—
71C2×#634C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67D412yes—
74C3×#239—24no—
75C3×#239—24no—
76C3×D3×D4—216no—
77C3×D3×D4—24no—
78C3×D3×D4—24no—
79C3×#235—28no—
80C3×#235—22no—
81C3×#235—22no—
82C2×C3×D12—28no—
83C2×C3×D12—22no—
84C2×C3×D12—21no—
85C2×C3×D12—22no—
86C2×C3×D12D411yescharacteristic
87C2×C3×D12D414yes—
88C2×C3×D12C2312yes—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3C2312yes—
91C2×C3×Dic6D411yescharacteristic
92#3756—24no—
93#3754—24no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—24no—
102(C2×D3)⋊Dic3—24no—
103#3716—28no—
104#3009—91noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41C2×D311yescharacteristic
112C2×C3×#41C2×D311yescharacteristic
113C22×C3×D4—32no—
114C22×C3×D4—31no—
115C22×C3×D4—61no—
116C22×C3×D4—62no—
117#1009—24no—
118#1009—24no—
119C2×#239C2×D312yes—
120C2×D3×D4—22no—
121C2×D3×D4C2×D312yes—
122C2×#235—21no—
123C2×#235C2×D311yescharacteristic
124C22×D12—21no—
125C22×D12C2×D311yescharacteristic
126C22×Dic6—31no—
127C22×Dic6—31no—
128C22×Dic6—61no—
129C22×C3×C8—31no—
130C3×#117—31no—
131#951—68no—
132#951—64no—
133#951—64no—
134#944—61no—
135C2×#216—32no—
136C2×#216—32no—
137C2×#216—62no—
138#936—61no—
139#935—62no—
140C2×#214—32no—
141C2×#214—32no—
142C2×#214—34no—
143C2×#214—62no—
144C2×#214—64no—
145#926C2×D311yescharacteristic, complemented
146#924—34no—
147C2×#208—31no—
148C2×#208—31no—
149C2×#208—61no—
150C22×C3⋊C8C2×D311yescharacteristic, complemented
151C2×#204—34no—
152C2×#204—64no—
153#897—34no—
154#886—62no—
155#875—61no—
156#869—61no—
157C3×#103—32no—
158C3×#102—32no—
159#835C2×D312yescomplemented
160#832—34no—
161#832C2×D312yescomplemented
162#830—34no—
163(C2×D3)⋊C8—34no—
164#809—34no—
165C23×C32—21no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—28no—
169C22×C3×D3—24no—
170C22×C3×D3—84no—
171C22×C3×D3—82no—
172C22×C3×D3C2×D412yes—
173C32×Q8—21no—
174C32×Q8C2×D412yes—
175C32×D4—24no—
176C32×D4—21no—
177C32×D4C2×D412yes—
178C2×C32×C4—21no—
179C2×C32×C4—24no—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—42no—
186#634—22no—
187#634—22no—
188#634—42no—
189C3×#67—28no—
190C3×#67—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C2×D412yes—
193C3×D12—28no—
194C3×D12—22no—
195C3×D12—24no—
196C3×D12—22no—
197C3×D12C2×D414yes—
198C3×C4×D3—28no—
199C3×C4×D3—22no—
200C3×C4×D3—22no—
201C3×Dic6—22no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204C2×H(5,𝔽2)—31no—
205C2×#137—91no—
206C22×SD16—91no—
207#536—91no—
208#452—94no—
209#450—94no—
210#418—91no—
211#416—31no—
212#408—91no—
213C24×C3—62no—
214C24×C3—61no—
215C23×D3—21no—
216C23×D3—22no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—24no—
220C3×#41—42no—
221C3×#41—68no—
222C3×#41—64no—
223C3×#41—64no—
224C3×#41—62no—
225C3×#41—62no—
226C3×#41D1214yes—
227C3×#41#6714yes—
228C2×C3×Q8—21no—
229C2×C3×Q8—31no—
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—32no—
236C2×C3×D4—34no—
237C2×C3×D4—31no—
238C2×C3×D4—32no—
239C2×C3×D4—41no—
240C2×C3×D4—62no—
241C2×C3×D4—68no—
242C2×C3×D4—62no—
243C2×C3×D4—64no—
244C2×C3×D4—616no—
245C2×C3×D4—64no—
246C2×C3×D4—62no—
247C2×C3×D4—61no—
248C2×C3×D4C22×D311yescharacteristic
249C2×C3×D4C22×D311yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—41no—
255C22×C3×C4—62no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—22no—
259C2×#67#6712yes—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—121no—
263#239—24no—
264#239—24no—
265D3×D4—216no—
266D3×D4—24no—
267D3×D4—24no—
268#235—28no—
269#235—22no—
270#235—22no—
271C2×D12—28no—
272C2×D12—22no—
273C2×D12—21no—
274C2×D12—22no—
275C2×D12#6711yescharacteristic
276C2×D12#6714yes—
277C2×D12C22×D312yes—
278C2×C4×D3—22no—
279C2×C4×D3C22×D312yes—
280C2×Dic6—32no—
281C2×Dic6—32no—
282C2×Dic6—62no—
283C2×Dic6—64no—
284C2×Dic6—62no—
285C2×Dic6—62no—
286C2×Dic6—62no—
287C2×Dic6—62no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6—121no—
291C2×Dic6—122no—
292C2×Dic6#6711yescharacteristic
293C2×C3×C8—32no—
294C2×C3×C8—62no—
295C3×C4⋊C4—32no—
296C3×C22⋊C4—61no—
297C3×C42—61no—
298#217—21no—
299#217—64no—
300#216—68no—
301#216—64no—
302#216—64no—
303#214—68no—
304#214—68no—
305#214—64no—
306#214—64no—
307(C2×D3)⋊C4—64no—
308C4⋊Dic3—64no—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—64no—
311C4×Dic3—21no—
312#208—64no—
313#208—62no—
314#208—62no—
315C2×C3⋊C8—22no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—62no—
319C2×C3⋊C8C22×D312yes—
320#204—68no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—42no—
324C22×C32#12012yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—22no—
327C2×C3×D3—24no—
328C2×C3×D3—24no—
329C2×C3×D3—44no—
330C2×C3×D3—84no—
331C2×C3×D3—88no—
332C32×C4—22no—
333C32×C4#12012yes—
334C32×C4C22×D411yescharacteristic
335C32×C4C22×D411yescharacteristic
336C3⋊Dic3—42no—
337C3×Dic3—22no—
338C3×Dic3—42no—
339H(5,𝔽2)—64no—
340H(5,𝔽2)—64no—
341C2×#41—31no—
342C2×#41—32no—
343C2×#41—61no—
344C2×#41D3211yescharacteristic
345C22×Q8—91no—
346C22×D4—32no—
347C22×D4—31no—
348C22×D4—61no—
349C22×D4—62no—
350#137—184no—
351C2×Q16—92no—
352C2×SD16—94no—
353C2×SD16—92no—
354C2×SD16—184no—
355C2×M16—91no—
356C22×C8—31no—
357C4⋊Q8—181no—
358#124—181no—
359#123—182no—
360C22⋊Q8—94no—
361#117—31no—
362#103—32no—
363#102—32no—
364#102—94no—
365C22⋊C8—94no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—32no—
370C23×C3—41no—
371C23×C3—68no—
372C23×C3—62no—
373C23×C3—64no—
374C23×C3—242no—
375C23×C3—244no—
376C23×C3D3×D411yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—22no—
379C22×D3—28no—
380C22×D3—24no—
381C22×D3—84no—
382C22×D3—82no—
383C22×D3C2×#6712yes—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—22no—
387C3×Q8—41no—
388C3×Q8—62no—
389C3×Q8C2×D1212yes—
390C3×Q8C2×#6712yes—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—21no—
394C3×D4—21no—
395C3×D4—22no—
396C3×D4—34no—
397C3×D4—41no—
398C3×D4—44no—
399C3×D4—68no—
400C3×D4—68no—
401C3×D4—64no—
402C3×D4—64no—
403C3×D4—62no—
404C3×D4—62no—
405C3×D4C2×D1212yes—
406C3×D4C2×#6712yes—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—44no—
417C2×C3×C4—41no—
418C2×C3×C4—68no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4C2×D1212yes—
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4D3×D412yes—
425C2×C3×C4C2×#6712yes—
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—28no—
431#67—24no—
432C2×Dic3—22no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—124no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3C2×#6712yes—
440D12—28no—
441D12—22no—
442D12—24no—
443D12—22no—
444D12C2×#6714yes—
445C4×D3—28no—
446C4×D3—22no—
447C4×D3—22no—
448Dic6—22no—
449Dic6—64no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—122no—
455Dic6—124no—
456Dic6—122no—
457Dic6—122no—
458C3×C8—62no—
459C3⋊C8—22no—
460C3⋊C8—64no—
461C3⋊C8—62no—
462C3⋊C8—62no—
463C2×C32—22no—
464C2×C32—42no—
465C2×C32C2×#12011yescharacteristic
466C2×C32#57712yes—
467C3×D3—42no—
468C3×D3—44no—
469C24—62no—
470C24—61no—
471#41—22no—
472#41—68no—
473#41—64no—
474#41—64no—
475#41—62no—
476#41—62no—
477#41#62614yes—
478C2×Q8—31no—
479C2×Q8—92no—
480C2×Q8—181no—
481C2×Q8—182no—
482C2×Q8—182no—
483C2×Q8C2×D3211yescharacteristic
484C2×D4—21no—
485C2×D4—32no—
486C2×D4—32no—
487C2×D4—34no—
488C2×D4—31no—
489C2×D4—62no—
490C2×D4—68no—
491C2×D4—62no—
492C2×D4—64no—
493C2×D4—616no—
494C2×D4—64no—
495C2×D4—62no—
496C2×D4—61no—
497C2×D4C2×D3211yescharacteristic
498C22×C4—21no—
499C22×C4—32no—
500C22×C4—62no—
501C22×C4—181no—
502C22×C4C2×D3211yescharacteristic
503Q16—184no—
504SD16—188no—
505SD16—184no—
506M16—182no—
507C2×C8—32no—
508C2×C8—62no—
509C2×C8—92no—
510C4⋊C4—32no—
511C4⋊C4—184no—
512C22⋊C4—61no—
513C22⋊C4—184no—
514C42—61no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—64no—
526C22×C3—62no—
527C22×C3—64no—
528C22×C3—82no—
529C22×C3—124no—
530C22×C3—244no—
531C22×C3—248no—
532C22×C3#88212yes—
533C22×C3#95312yes—
534C22×C3C2×D3×D411yescharacteristic
535C22×C3C22×#6711yescharacteristic
536C2×D3—24no—
537C2×D3—22no—
538C2×D3—24no—
539C2×D3—44no—
540C2×D3—84no—
541C2×D3—88no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—22no—
547C3×C4—42no—
548C3×C4—62no—
549C3×C4—122no—
550C3×C4#88212yes—
551C3×C4#95312yes—
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C22×#6711yescharacteristic
555C3×C4C22×#6711yescharacteristic
556Dic3—22no—
557Dic3—42no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561C32#300911yescharacteristic, complemented, Sylow
562C23—21no—
563C23—32no—
564C23—68no—
565C23—62no—
566C23—64no—
567C23—242no—
568C23—244no—
569C23D3×#6711yescharacteristic
570Q8—21no—
571Q8—62no—
572Q8—182no—
573Q8—182no—
574Q8—362no—
575Q8C2×#62612yes—
576D4—24no—
577D4—21no—
578D4—34no—
579D4—68no—
580D4—68no—
581D4—64no—
582D4—62no—
583D4—64no—
584D4—62no—
585D4C2×#62612yes—
586C2×C4—21no—
587C2×C4—24no—
588C2×C4—32no—
589C2×C4—68no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—182no—
594C2×C4—362no—
595C2×C4C2×#62612yes—
596C2×C4D3×#6712yes—
597C2×C4D3×#6711yescharacteristic
598C2×C4C22×D3211yescharacteristic
599C8—62no—
600C8—182no—
601C2×C3—22no—
602C2×C3—22no—
603C2×C3—22no—
604C2×C3—21no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3—42no—
608C2×C3—82no—
609C2×C3—122no—
610C2×C3—124no—
611C2×C3C2×#88211yescharacteristic
612C2×C3#577012yes—
613C2×C3#583612yes—
614C2×C3C2×#95311yescharacteristic
615D3—42no—
616D3—44no—
617C22—22no—
618C22—22no—
619C22—42no—
620C22—64no—
621C22—64no—
622C22—62no—
623C22—124no—
624C22—244no—
625C22—248no—
626C22#6397712yes—
627C22C2×D3×#6711yescharacteristic
628C4—22no—
629C4—62no—
630C4—122no—
631C4—362no—
632C4#6397712yes—
633C4C22×#62611yescharacteristic
634C4C2×D3×#6711yescharacteristic
635C3—21no—
636C3#7883511yescharacteristic, complemented
637C3#8410511yescharacteristic, complemented
638C2—22no—
639C2—42no—
640C2—122no—
641C2—124no—
642C2#1059546612yes—
643C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1009C2
hypercenterC2×#41D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. #10594856C2semidirect
4. C22×#3716C2semidirect
5. C3×#5233C2semidirect
6. #10591599C2semidirect
7. #10591459C2semidirect
8. #10591085C2semidirect
9. #10591070C2semidirect
13. C22×#634C22semidirect
24. C2×#3756C22semidirect
25. C2×#3754C22semidirect
26. C2×#3748C22semidirect
27. C3×#926C22semidirect
28. C22×C3×C3⋊C8C22semidirect
32. #63857C22semidirect
34. C2×#3716C22semidirect
35. C3×#835C22semidirect
36. C3×#832C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
51. #5233D3semidirect
145. #926C2×D3semidirect
150. C22×C3⋊C8C2×D3semidirect
159. #835C2×D3semidirect
161. #832C2×D3semidirect
561. C32#3009semidirect
636. C3#78835semidirect
637. C3#84105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#641602
#105948562
C22×#37162
C3×#52332
#105915992
#105914592
#105910852
#105910702
#841053
#788353