Finite Group Databasebeta

← #11864366

Subgroups — #11864366

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2#10596296C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6#10591173C214yesmaximal, complemented
7#10591172C214yesmaximal, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#84105—31nomaximal
11#78671—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
14C3×#1009—24no—
15C3×#1009—24no—
16C2×C3×#239—21no—
17C2×C3×D3×D4—22no—
18C2×C3×D3×D4—21no—
19C2×C3×#235C2212yes—
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2212yes—
22C22×C3×D12C2211yescharacteristic
23#64153—21no—
24#64145—21no—
25#64144—22no—
26#64135C2211yescharacteristic, complemented
27#64133C2214yescomplemented
28C2×C3×#208C2211yescharacteristic, complemented
29C22×C3×C3⋊C8C2211yescharacteristic, complemented
30C2×#3719C2212yescomplemented
31#63831—24no—
32C2×#3716—24no—
33C2×#3716C2212yescomplemented
34C2×#3716C2214yescomplemented
35C3×#830C2214yescomplemented
36#63566C2212yescomplemented
37#63563C2212yescomplemented
38#63563C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1009D311yescharacteristic
41#5825—31no—
42#5825—31no—
43#5825—61no—
44C2×#951—31no—
45C22×#214—31no—
46C2×#909—31no—
47C22×#204—31no—
48C3×#408—31no—
49#5239—34no—
50#5234D311yescharacteristic, complemented
51#5233—31no—
52#5218—34no—
53#5215—31no—
54#5131—31no—
55#5113—31no—
56#4733—34no—
57#4731—34no—
58C23×C3×D3—22no—
59C23×C3×D3—21no—
60C32×#41—22no—
61C32×#41—22no—
62C2×C32×Q8D411yescharacteristic
63C2×C32×D4D412yes—
64C2×C32×D4D411yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3—21no—
68C2×#634—22no—
69C2×#634—22no—
70C2×#634—21no—
71C2×#634C2312yes—
72C2×C3×#67—22no—
73C2×C3×#67—21no—
74C3×#239—28no—
75C3×D3×D4—216no—
76C3×D3×D4—28no—
77C3×#235—22no—
78C3×#235—24no—
79C3×#235—24no—
80C3×#235D414yes—
81C2×C3×D12—22no—
82C2×C3×D12—21no—
83C2×C3×D12—22no—
84C2×C3×D12—24no—
85C2×C3×D12—24no—
86C2×C3×D12D414yes—
87C2×C3×D12C2311yescharacteristic
88C2×C3×D12C2312yes—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—21no—
91C2×C3×Dic6C2311yescharacteristic
92#3757—24no—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95#3750—24no—
96C4×C3⋊Dic3—21no—
97C3×#208—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101#3719—24no—
102#3716—28no—
103#3716—24no—
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—31no—
114C22×C3×D4—32no—
115C22×C3×D4—62no—
116C22×C3×D4—61no—
117#1009—24no—
118#1009—24no—
119C2×#239—21no—
120C2×D3×D4—22no—
121C2×D3×D4—21no—
122C2×#235C2×D312yes—
123C2×#235C2×D311yescharacteristic
124C22×D12C2×D312yes—
125C22×D12C2×D311yescharacteristic
126C22×Dic6—31no—
127C22×Dic6—31no—
128C22×Dic6—61no—
129C2×C3×M16—31no—
130C22×C3×C8—31no—
131#951—64no—
132#944—62no—
133#944—61no—
134#944—61no—
135C2×#216—32no—
136#936—62no—
137#936—61no—
138#936—61no—
139#935—64no—
140#935—62no—
141#935—62no—
142C2×#214—32no—
143C2×#214—34no—
144C2×#214—64no—
145#926—31no—
146#926—31no—
147#926—61no—
148#924—34no—
149#924—34no—
150#924—64no—
151C2×#208C2×D311yescharacteristic, complemented
152C22×C3⋊C8C2×D311yescharacteristic, complemented
153#909—64no—
154C2×Dic12—32no—
155C2×#204—34no—
156C2×#204—32no—
157C2×#204—64no—
158C3×C22⋊C8—34no—
159#835—32no—
160#832—34no—
161#832—32no—
162#830C2×D314yescomplemented
163#821—34no—
164#821—32no—
165#816—32no—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—28no—
171C22×C3×D3—24no—
172C22×C3×D3—82no—
173C22×C3×D3—84no—
174C32×Q8—22no—
175C32×D4—24no—
176C32×D4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—42no—
187#634—22no—
188#634—22no—
189#634—42no—
190C3×#67—28no—
191C3×#67—24no—
192C2×C3×Dic3—21no—
193C3×D12—28no—
194C3×D12—24no—
195C3×D12—21no—
196C3×D12—22no—
197C3×D12C2×D412yes—
198C3×D12C2×D414yes—
199C3×C4×D3—28no—
200C3×C4×D3—24no—
201C3×Dic6—21no—
202C3×Dic6C2×D412yes—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C2×H(5,𝔽2)—31no—
206C2×#137—91no—
207C22×SD16—91no—
208#536—91no—
209#452—94no—
210#450—94no—
211#418—91no—
212#416—91no—
213#408—31no—
214C24×C3—62no—
215C24×C3—61no—
216C23×D3—22no—
217C23×D3—21no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—34no—
223C3×#41—42no—
224C3×#41—42no—
225C3×#41—64no—
226C3×#41—64no—
227C3×#41—68no—
228C3×#41—62no—
229C2×C3×Q8—21no—
230C2×C3×Q8—31no—
231C2×C3×Q8D1211yescharacteristic
232C2×C3×Q8#6711yescharacteristic
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—34no—
236C2×C3×D4—32no—
237C2×C3×D4—31no—
238C2×C3×D4—64no—
239C2×C3×D4—64no—
240C2×C3×D4—616no—
241C2×C3×D4—68no—
242C2×C3×D4—62no—
243C2×C3×D4—61no—
244C2×C3×D4—62no—
245C2×C3×D4—61no—
246C2×C3×D4—62no—
247C2×C3×D4D1212yes—
248C2×C3×D4D1211yescharacteristic
249C2×C3×D4#6712yes—
250C2×C3×D4#6711yescharacteristic
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4C22×D312yes—
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—22no—
260C2×#67—21no—
261C22×Dic3—62no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264#239—28no—
265D3×D4—216no—
266D3×D4—28no—
267#235—22no—
268#235—24no—
269#235—24no—
270#235#6714yes—
271C2×D12—22no—
272C2×D12—21no—
273C2×D12—22no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12#6714yes—
277C2×D12C22×D311yescharacteristic
278C2×D12C22×D312yes—
279C2×C4×D3—22no—
280C2×C4×D3—21no—
281C2×Dic6—32no—
282C2×Dic6—32no—
283C2×Dic6—62no—
284C2×Dic6—62no—
285C2×Dic6—62no—
286C2×Dic6—62no—
287C2×Dic6—62no—
288C2×Dic6—62no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—122no—
292C2×Dic6—122no—
293C2×Dic6C22×D311yescharacteristic
294C3×M16—62no—
295C2×C3×C8—32no—
296C2×C3×C8—32no—
297C2×C3×C8—62no—
298#217—68no—
299#217—62no—
300#217—64no—
301#217—61no—
302#217—64no—
303#217—61no—
304#216—64no—
305#214—68no—
306#214—64no—
307C4⋊Dic3—32no—
308C4⋊Dic3—32no—
309C4⋊Dic3—62no—
310Dic3⋊C4—68no—
311Dic3⋊C4—64no—
312Dic3⋊C4—64no—
313C4×Dic3—62no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316#208—22no—
317C2×C3⋊C8—22no—
318C2×C3⋊C8C22×D312yes—
319C2×C3⋊C8C22×D312yes—
320Dic12—64no—
321#204—68no—
322#204—64no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—24no—
326C22×C32#12012yes—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—24no—
329C2×C3×D3—22no—
330C2×C3×D3—44no—
331C2×C3×D3—42no—
332C2×C3×D3—84no—
333C2×C3×D3—88no—
334C32×C4—22no—
335C32×C4#12012yes—
336C32×C4C22×D411yescharacteristic
337C32×C4C22×D411yescharacteristic
338C3⋊Dic3—42no—
339C3⋊Dic3—42no—
340C3×Dic3—22no—
341H(5,𝔽2)—64no—
342H(5,𝔽2)—64no—
343C2×#41—31no—
344C2×#41—32no—
345C2×#41—61no—
346C2×#41D3211yescharacteristic
347C22×Q8—91no—
348C22×D4—31no—
349C22×D4—32no—
350C22×D4—62no—
351C22×D4—61no—
352#137—184no—
353C2×Q16—92no—
354C2×SD16—94no—
355C2×SD16—92no—
356C2×SD16—184no—
357C2×M16—31no—
358C22×C8—31no—
359C4⋊Q8—181no—
360#124—181no—
361#123—182no—
362C22⋊Q8—94no—
363#117—91no—
364#103—92no—
365#102—92no—
366#102—94no—
367C22⋊C8—34no—
368C23×C3—21no—
369C23×C3—22no—
370C23×C3—68no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—64no—
374C23×C3—242no—
375C23×C3—244no—
376C23×C3C2×D1212yes—
377C23×C3C2×D1211yescharacteristic
378C23×C3C2×#6712yes—
379C23×C3C2×#6711yescharacteristic
380C22×D3—22no—
381C22×D3—21no—
382C22×D3—28no—
383C22×D3—24no—
384C22×D3—82no—
385C22×D3—84no—
386C3×Q8—22no—
387C3×Q8—22no—
388C3×Q8—32no—
389C3×Q8—42no—
390C3×Q8—61no—
391C3×D4—24no—
392C3×D4—24no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—34no—
396C3×D4—32no—
397C3×D4—42no—
398C3×D4—44no—
399C3×D4—68no—
400C3×D4—68no—
401C3×D4—64no—
402C3×D4—64no—
403C3×D4—61no—
404C3×D4—62no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—68no—
417C2×C3×C4—61no—
418C2×C3×C4—64no—
419C2×C3×C4C2×D1212yes—
420C2×C3×C4C2×D1211yescharacteristic
421C2×C3×C4D3×D412yes—
422C2×C3×C4D3×D412yes—
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6712yes—
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—28no—
430#67—24no—
431C2×Dic3—21no—
432C2×Dic3—64no—
433C2×Dic3—64no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—124no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441D12—28no—
442D12—24no—
443D12—21no—
444D12—22no—
445D12C2×#6712yes—
446D12C2×#6714yes—
447C4×D3—28no—
448C4×D3—24no—
449Dic6—21no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—122no—
455Dic6—122no—
456Dic6—124no—
457Dic6—122no—
458Dic6—122no—
459Dic6C2×#6712yes—
460C3×C8—62no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—22no—
464C2×C32—22no—
465C2×C32—42no—
466C2×C32C2×#12011yescharacteristic
467C2×C32#57712yes—
468C3×D3—44no—
469C3×D3—42no—
470C24—62no—
471C24—61no—
472#41—22no—
473#41—22no—
474#41—34no—
475#41—64no—
476#41—64no—
477#41—68no—
478#41—62no—
479C2×Q8—31no—
480C2×Q8—92no—
481C2×Q8—181no—
482C2×Q8—182no—
483C2×Q8—182no—
484C2×Q8#62611yescharacteristic
485C2×D4—32no—
486C2×D4—31no—
487C2×D4—34no—
488C2×D4—64no—
489C2×D4—64no—
490C2×D4—616no—
491C2×D4—68no—
492C2×D4—62no—
493C2×D4—61no—
494C2×D4—62no—
495C2×D4—61no—
496C2×D4—62no—
497C2×D4#62612yes—
498C2×D4#62611yescharacteristic
499C22×C4—62no—
500C22×C4—61no—
501C22×C4—181no—
502C22×C4C2×D3212yes—
503C22×C4C2×D3211yescharacteristic
504Q16—184no—
505SD16—188no—
506SD16—184no—
507M16—62no—
508C2×C8—32no—
509C2×C8—32no—
510C2×C8—62no—
511C4⋊C4—92no—
512C4⋊C4—184no—
513C22⋊C4—181no—
514C22⋊C4—184no—
515C42—181no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—22no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—44no—
527C22×C3—64no—
528C22×C3—62no—
529C22×C3—124no—
530C22×C3—122no—
531C22×C3—244no—
532C22×C3—248no—
533C22×C3#88212yes—
534C22×C3#95312yes—
535C22×C3C22×D1211yescharacteristic
536C22×C3C22×#6711yescharacteristic
537C2×D3—24no—
538C2×D3—22no—
539C2×D3—44no—
540C2×D3—42no—
541C2×D3—84no—
542C2×D3—88no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—22no—
548C3×C4—42no—
549C3×C4—62no—
550C3×C4#88212yes—
551C3×C4#95312yes—
552C3×C4C2×D3×D411yescharacteristic
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C22×#6711yescharacteristic
555C3×C4C22×#6711yescharacteristic
556Dic3—22no—
557Dic3—124no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561Dic3—122no—
562Dic3—122no—
563C32#300911yescharacteristic, complemented, Sylow
564C23—68no—
565C23—62no—
566C23—61no—
567C23—64no—
568C23—242no—
569C23—244no—
570C23C2×#62612yes—
571C23C2×#62611yescharacteristic
572Q8—22no—
573Q8—32no—
574Q8—61no—
575Q8—182no—
576Q8—182no—
577Q8—362no—
578D4—24no—
579D4—22no—
580D4—34no—
581D4—32no—
582D4—68no—
583D4—68no—
584D4—64no—
585D4—61no—
586D4—62no—
587D4—64no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—68no—
591C2×C4—61no—
592C2×C4—64no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—362no—
596C2×C4C2×#62612yes—
597C2×C4C2×#62611yescharacteristic
598C2×C4D3×#6712yes—
599C2×C4D3×#6712yes—
600C2×C4C22×D3211yescharacteristic
601C8—62no—
602C8—62no—
603C2×C3—22no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—42no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3—82no—
611C2×C3—124no—
612C2×C3—122no—
613C2×C3C2×#88211yescharacteristic
614C2×C3#575112yes—
615C2×C3#583612yes—
616C2×C3C2×#95311yescharacteristic
617D3—44no—
618D3—42no—
619C22—22no—
620C22—24no—
621C22—22no—
622C22—64no—
623C22—62no—
624C22—124no—
625C22—122no—
626C22—244no—
627C22—248no—
628C22#6397712yes—
629C22C22×#62611yescharacteristic
630C4—22no—
631C4—62no—
632C4—362no—
633C4—362no—
634C4#6397712yes—
635C4C2×D3×#6711yescharacteristic
636C4C2×D3×#6711yescharacteristic
637C3—21no—
638C3#7867111yescharacteristic, complemented
639C3#8410511yescharacteristic, complemented
640C2—22no—
641C2—42no—
642C2—124no—
643C2—122no—
644C2#1059544712yes—
645C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C22×#626
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 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10596296C2semidirect
3. C2×#63831C2semidirect
4. C22×#3716C2semidirect
5. C3×#5234C2semidirect
6. #10591173C2semidirect
7. #10591172C2semidirect
8. #10591086C2semidirect
9. #10591084C2semidirect
13. C22×#634C22semidirect
26. #64135C22semidirect
27. #64133C22semidirect
28. C2×C3×#208C22semidirect
29. C22×C3×C3⋊C8C22semidirect
30. C2×#3719C22semidirect
33. C2×#3716C22semidirect
34. C2×#3716C22semidirect
35. C3×#830C22semidirect
36. #63566C22semidirect
37. #63563C22semidirect
38. #63563C22semidirect
50. #5234D3semidirect
151. C2×#208C2×D3semidirect
152. C22×C3⋊C8C2×D3semidirect
162. #830C2×D3semidirect
563. C32#3009semidirect
638. C3#78671semidirect
639. 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
#105962962
C2×#638312
C22×#37162
C3×#52342
#105911732
#105911722
#105910862
#105910842
#841053
#786713