Finite Group Databasebeta

← #11864377

Subgroups — #11864377

Order 1152.

1583 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3#10594855C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591597C214yesmaximal, complemented
7#10591458C214yesmaximal, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84105—31nomaximal
11#83982—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1009—24no—
14C3×#1009—24no—
15C2×C3×#239C2212yes—
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C2212yes—
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12—21no—
21C22×C3×D12C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic, complemented
23#64135C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×#951—24no—
26C2×C3×#216C2212yescomplemented
27C2×C3×#214C2212yescomplemented
28C2×C3×#208C2211yescharacteristic, complemented
29#63961—22no—
30#63873—21no—
31#63863—21no—
32#63856C2214yescomplemented
33C2×#3715—24no—
34C2×#3715C2214yescomplemented
35#63662C2212yescomplemented
36#63659C2212yescomplemented
37#63563C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1009D311yescharacteristic
41C2×C3×#137—31no—
42#5825—31no—
43C2×#951D311yescharacteristic, complemented
44#5816—31no—
45C22×#215—31no—
46C22×#214—31no—
47#5239—34no—
48#5234—31no—
49#5233—31no—
50#5233—31no—
51#5233—61no—
52#5218—34no—
53#5215—31no—
54#5187—34no—
55#5169—34no—
56#5131—31no—
57#5129—31no—
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
67C2×C3×#67—22no—
68C2×C3×#67D412yes—
69C22×C3×Dic3—21no—
70C3×#239—24no—
71C3×#239—24no—
72C3×D3×D4—216no—
73C3×D3×D4—24no—
74C3×D3×D4—24no—
75C3×#235—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—28no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12—22no—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12D414yes—
84C2×C3×D12C2312yes—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6—21no—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2312yes—
92#3757—21no—
93C4⋊(C3⋊Dic3)C2312yes—
94C4×C3⋊Dic3—21no—
95C2×C3⋊(C3⋊C8)—22no—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#216—24no—
98C3×#214—24no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101#3724—24no—
102(C2×D3)⋊Dic3—24no—
103#3715—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×Q8—31no—
114C22×C3×D4—32no—
115C22×C3×D4—31no—
116C22×C3×D4—61no—
117C22×C3×D4—62no—
118#1009—24no—
119#1009—24no—
120C2×#239C2×D312yes—
121C2×D3×D4—22no—
122C2×D3×D4C2×D312yes—
123C2×#235—21no—
124C2×#235C2×D311yescharacteristic
125C22×D12—21no—
126C22×D12C2×D311yescharacteristic
127C22×Dic6C2×D311yescharacteristic, complemented
128C3×#137—64no—
129C2×C3×Q16—32no—
130C2×C3×SD16—32no—
131C2×C3×M16—31no—
132#951—24no—
133#947—61no—
134#946—34no—
135#944—61no—
136#944—61no—
137C2×#216C2×D312yescomplemented
138C2×#215—34no—
139C2×#215—64no—
140#936—61no—
141#935—62no—
142C2×#214—34no—
143C2×#214—64no—
144C2×#214C2×D312yescomplemented
145#929—62no—
146#926—31no—
147#926—31no—
148#926—61no—
149#924—34no—
150C2×#208C2×D311yescharacteristic, complemented
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—32no—
155#835—32no—
156#835—62no—
157#832—32no—
158#832—32no—
159#832—34no—
160#832—62no—
161#830—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—28no—
168C22×C3×D3—24no—
169C22×C3×D3—84no—
170C22×C3×D3—82no—
171C22×C3×D3C2×D412yes—
172C32×Q8—21no—
173C32×Q8C2×D412yes—
174C32×D4—24no—
175C32×D4—21no—
176C32×D4C2×D412yes—
177C2×C32×C4—21no—
178C2×C32×C4—24no—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184C3×#67—28no—
185C3×#67—24no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—42no—
188C2×C3×Dic3C2×D412yes—
189C3×D12—28no—
190C3×D12—22no—
191C3×D12—24no—
192C3×D12—22no—
193C3×D12C2×D414yes—
194C3×C4×D3—28no—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—22no—
198C3×Dic6—22no—
199C3×Dic6—22no—
200C3×Dic6—42no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×H(5,𝔽2)—31no—
204C2×#137—31no—
205C22×SD16—91no—
206#536—91no—
207#452—94no—
208#450—94no—
209#418—91no—
210#416—91no—
211#408—91no—
212C24×C3—62no—
213C24×C3—61no—
214C23×D3—21no—
215C23×D3—22no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—24no—
219C3×#41—42no—
220C3×#41—68no—
221C3×#41—64no—
222C3×#41—64no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41#6714yes—
226C3×#41#6714yes—
227C2×C3×Q8—21no—
228C2×C3×Q8—31no—
229C2×C3×Q8—32no—
230C2×C3×Q8—61no—
231C2×C3×Q8—62no—
232C2×C3×Q8—62no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—32no—
239C2×C3×D4—34no—
240C2×C3×D4—31no—
241C2×C3×D4—32no—
242C2×C3×D4—41no—
243C2×C3×D4—62no—
244C2×C3×D4—68no—
245C2×C3×D4—62no—
246C2×C3×D4—64no—
247C2×C3×D4—616no—
248C2×C3×D4—64no—
249C2×C3×D4—61no—
250C2×C3×D4—62no—
251C2×C3×D4C22×D311yescharacteristic
252C2×C3×D4C22×D311yescharacteristic
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—32no—
257C22×C3×C4—41no—
258C22×C3×C4—62no—
259C22×C3×C4—61no—
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C2×#67—22no—
263C2×#67#6712yes—
264C22×Dic3—21no—
265#239—24no—
266#239—24no—
267D3×D4—216no—
268D3×D4—24no—
269D3×D4—24no—
270#235—28no—
271#235—22no—
272#235—22no—
273C2×D12—28no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12—22no—
277C2×D12#6711yescharacteristic
278C2×D12#6714yes—
279C2×D12C22×D312yes—
280C2×C4×D3—22no—
281C2×C4×D3C22×D312yes—
282C2×Dic6—22no—
283C2×Dic6—22no—
284C2×Dic6—21no—
285C2×Dic6#6711yescharacteristic
286C2×Dic6C22×D312yes—
287C3×Q16—64no—
288C3×SD16—64no—
289C3×M16—62no—
290C2×C3×C8—32no—
291#217—64no—
292#217—61no—
293#217—61no—
294#217—121no—
295#216—24no—
296#215—68no—
297#214—24no—
298#214—68no—
299(C2×D3)⋊C4—64no—
300C4⋊Dic3—32no—
301C4⋊Dic3—32no—
302C4⋊Dic3—62no—
303Dic3⋊C4—64no—
304Dic3⋊C4—64no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—121no—
308#208—22no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—122no—
315C2×C3⋊C8C22×D312yes—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—42no—
319C22×C32#12012yes—
320C22×C32C22×D411yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—24no—
324C2×C3×D3—44no—
325C2×C3×D3—84no—
326C2×C3×D3—88no—
327C32×C4—22no—
328C32×C4#12012yes—
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3—42no—
332C3×Dic3—22no—
333C3×Dic3—42no—
334H(5,𝔽2)—64no—
335H(5,𝔽2)—64no—
336C2×#41—31no—
337C2×#41—32no—
338C2×#41—61no—
339C2×#41D3211yescharacteristic
340C22×Q8—31no—
341C22×D4—32no—
342C22×D4—31no—
343C22×D4—61no—
344C22×D4—62no—
345#137—64no—
346C2×Q16—32no—
347C2×SD16—32no—
348C2×SD16—94no—
349C2×SD16—184no—
350C2×M16—31no—
351C22×C8—91no—
352C4⋊Q8—181no—
353#124—181no—
354#123—182no—
355C22⋊Q8—94no—
356#117—91no—
357#103—92no—
358#102—94no—
359#102—92no—
360C22⋊C8—94no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—41no—
366C23×C3—68no—
367C23×C3—62no—
368C23×C3—64no—
369C23×C3—242no—
370C23×C3—244no—
371C23×C3D3×D411yescharacteristic
372C23×C3C2×#6711yescharacteristic
373C22×D3—22no—
374C22×D3—28no—
375C22×D3—24no—
376C22×D3—84no—
377C22×D3—82no—
378C22×D3C2×#6712yes—
379C3×Q8—21no—
380C3×Q8—21no—
381C3×Q8—22no—
382C3×Q8—41no—
383C3×Q8—62no—
384C3×Q8—62no—
385C3×Q8—62no—
386C3×Q8—122no—
387C3×Q8C2×#6712yes—
388C3×Q8C2×#6712yes—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—22no—
394C3×D4—34no—
395C3×D4—41no—
396C3×D4—44no—
397C3×D4—68no—
398C3×D4—68no—
399C3×D4—64no—
400C3×D4—64no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4C2×#6712yes—
404C3×D4C2×#6712yes—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—32no—
414C2×C3×C4—44no—
415C2×C3×C4—41no—
416C2×C3×C4—68no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—122no—
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D412yes—
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—28no—
430#67—24no—
431C2×Dic3—22no—
432C2×Dic3—42no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3C2×#6712yes—
437D12—28no—
438D12—22no—
439D12—24no—
440D12—22no—
441D12C2×#6714yes—
442C4×D3—28no—
443C4×D3—22no—
444C4×D3—22no—
445Dic6—22no—
446Dic6—22no—
447Dic6—22no—
448Dic6—42no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—62no—
452C3⋊C8—62no—
453C3⋊C8—122no—
454C2×C32—22no—
455C2×C32—42no—
456C2×C32C2×#12011yescharacteristic
457C2×C32#57712yes—
458C3×D3—42no—
459C3×D3—44no—
460C24—62no—
461C24—61no—
462#41—22no—
463#41—68no—
464#41—64no—
465#41—64no—
466#41—62no—
467#41—62no—
468#41#62514yes—
469C2×Q8—31no—
470C2×Q8—32no—
471C2×Q8—61no—
472C2×Q8—62no—
473C2×Q8—62no—
474C2×Q8C2×D3211yescharacteristic
475C2×D4—21no—
476C2×D4—32no—
477C2×D4—32no—
478C2×D4—34no—
479C2×D4—31no—
480C2×D4—62no—
481C2×D4—68no—
482C2×D4—62no—
483C2×D4—64no—
484C2×D4—616no—
485C2×D4—64no—
486C2×D4—62no—
487C2×D4—61no—
488C2×D4C2×D3211yescharacteristic
489C22×C4—21no—
490C22×C4—32no—
491C22×C4—62no—
492C22×C4—61no—
493C22×C4C2×D3211yescharacteristic
494Q16—64no—
495SD16—64no—
496SD16—188no—
497M16—62no—
498C2×C8—32no—
499C2×C8—92no—
500C2×C8—182no—
501C4⋊C4—92no—
502C4⋊C4—184no—
503C22⋊C4—184no—
504C22⋊C4—181no—
505C42—181no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—64no—
517C22×C3—64no—
518C22×C3—62no—
519C22×C3—82no—
520C22×C3—124no—
521C22×C3—244no—
522C22×C3—248no—
523C22×C3#93712yes—
524C22×C3#95312yes—
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C22×#6711yescharacteristic
527C2×D3—24no—
528C2×D3—22no—
529C2×D3—24no—
530C2×D3—44no—
531C2×D3—84no—
532C2×D3—88no—
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—22no—
538C3×C4—42no—
539C3×C4—62no—
540C3×C4—122no—
541C3×C4#93712yes—
542C3×C4#95312yes—
543C3×C4C2×D3×D411yescharacteristic
544C3×C4C22×#6711yescharacteristic
545C3×C4C22×#6711yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—22no—
548Dic3—42no—
549Dic3—122no—
550Dic3—122no—
551Dic3—242no—
552C32#300911yescharacteristic, complemented, Sylow
553C23—21no—
554C23—32no—
555C23—68no—
556C23—62no—
557C23—64no—
558C23—242no—
559C23—244no—
560C23D3×#6711yescharacteristic
561Q8—21no—
562Q8—62no—
563Q8—62no—
564Q8—62no—
565Q8—122no—
566Q8C2×#62512yes—
567D4—24no—
568D4—21no—
569D4—34no—
570D4—68no—
571D4—68no—
572D4—64no—
573D4—62no—
574D4—64no—
575D4—62no—
576D4C2×#62512yes—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—32no—
580C2×C4—68no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—122no—
585C2×C4—182no—
586C2×C4C2×#62512yes—
587C2×C4D3×#6712yes—
588C2×C4D3×#6711yescharacteristic
589C2×C4C22×D3211yescharacteristic
590C8—62no—
591C8—182no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—42no—
597C2×C3—42no—
598C2×C3—42no—
599C2×C3—82no—
600C2×C3—122no—
601C2×C3—124no—
602C2×C3#577812yes—
603C2×C3C2×#93711yescharacteristic
604C2×C3#583612yes—
605C2×C3C2×#95311yescharacteristic
606D3—42no—
607D3—44no—
608C22—22no—
609C22—22no—
610C22—42no—
611C22—64no—
612C22—64no—
613C22—62no—
614C22—124no—
615C22—244no—
616C22—248no—
617C22#6397612yes—
618C22C2×D3×#6711yescharacteristic
619C4—22no—
620C4—62no—
621C4—122no—
622C4—362no—
623C4#6397612yes—
624C4C22×#62511yescharacteristic
625C4C2×D3×#6711yescharacteristic
626C3—21no—
627C3#8398211yescharacteristic, complemented
628C3#8410511yescharacteristic, complemented
629C2—22no—
630C2—42no—
631C2—122no—
632C2—124no—
633C2#1059546412yes—
634C2C2×#6397611yescharacteristic
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×C3×#951C2semidirect
3. #10594855C2semidirect
4. C22×#3715C2semidirect
5. #10592932C2semidirect
6. #10591597C2semidirect
7. #10591458C2semidirect
8. #10591086C2semidirect
9. #10591071C2semidirect
22. C22×C3×Dic6C22semidirect
23. #64135C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
26. C2×C3×#216C22semidirect
27. C2×C3×#214C22semidirect
28. C2×C3×#208C22semidirect
32. #63856C22semidirect
34. C2×#3715C22semidirect
35. #63662C22semidirect
36. #63659C22semidirect
37. #63563C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. C2×#951D3semidirect
127. C22×Dic6C2×D3semidirect
137. C2×#216C2×D3semidirect
144. C2×#214C2×D3semidirect
150. C2×#208C2×D3semidirect
552. C32#3009semidirect
627. C3#83982semidirect
628. 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×C3×#9512
#105948552
C22×#37152
#105929322
#105915972
#105914582
#105910862
#105910712
#841053
#839823