Finite Group Databasebeta

← #11864363

Subgroups — #11864363

Order 1152.

1653 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591463C214yesmaximal, complemented
7#10591459C214yesmaximal, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84105—31nomaximal
11#78929—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
14C22×C3×#67—22no—
15C3×#1004—24no—
16C3×#1004—24no—
17C2×C3×#237—21no—
18C2×C3×#237C2212yes—
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2212yes—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×#3754—24no—
24C2×#3754C2214yescomplemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#926C2211yescharacteristic, complemented
27C2×C3×#208C2211yescharacteristic, complemented
28#63962—22no—
29#63866—21no—
30#63860—21no—
31#63857C2214yescomplemented
32C2×#3719C2212yescomplemented
33#63831—24no—
34C2×#3716C2212yescomplemented
35C3×#832C2214yescomplemented
36#63565C2212yescomplemented
37#63562C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×H(5,𝔽2)—31no—
40C2×#1004D311yescharacteristic
41#5825—31no—
42C2×#951—31no—
43C22×#214—31no—
44C22×#214—31no—
45C22×#214—61no—
46C2×#909—31no—
47#5526—31no—
48C3×#418—31no—
49#5239—34no—
50#5234—31no—
51#5233—31no—
52#5218—34no—
53#5215D311yescharacteristic, complemented
54#5129—31no—
55#5002—31no—
56#4783—34no—
57#4776—34no—
58C24×C32—21no—
59C23×C3×D3—22no—
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yes—
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3—21no—
66C2×#634—22no—
67C2×#634—22no—
68C2×#634—21no—
69C2×#634C2312yes—
70C2×C3×#67—216no—
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C2×C3×#67D412yes—
75C22×C3×Dic3—22no—
76C3×#237—28no—
77C3×#237—24no—
78C3×#237—24no—
79C3×D3×D4—28no—
80C3×D3×D4—24no—
81C3×D3×D4—24no—
82C3×#235—22no—
83C3×#235—22no—
84C3×#235—22no—
85C3×#235D414yes—
86C2×C3×D12D411yescharacteristic
87C2×C3×D12C2311yescharacteristic
88C2×C3×C4×D3—21no—
89C2×C3×C4×D3C2312yes—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2311yescharacteristic
92#3754—28no—
93C2×C3⋊(C3⋊C8)—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4×Dic3—21no—
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102#3719—24no—
103#3716—24no—
104#3009—91noSylow
105C3×H(5,𝔽2)—64no—
106C3×H(5,𝔽2)—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—61no—
111C22×C3×D4—21no—
112C22×C3×D4—32no—
113C22×C3×D4—61no—
114C22×C3×D4—62no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C2×D311yescharacteristic
117C22×#67—22no—
118#1004—24no—
119#1004—24no—
120C2×#237—21no—
121C2×#237C2×D312yes—
122C2×D3×D4—21no—
123C2×D3×D4C2×D312yes—
124C2×#235C2×D311yescharacteristic
125C2×#235C2×D311yescharacteristic
126C22×Dic6—31no—
127C22×Dic6—31no—
128C22×Dic6—61no—
129C2×C3×M16—31no—
130C3×#117—31no—
131#951—64no—
132#944—61no—
133C2×#216—32no—
134#936—61no—
135#935—62no—
136C2×#214—34no—
137C2×#214—34no—
138C2×#214—32no—
139C2×#214—64no—
140C2×#214—68no—
141C2×#214—64no—
142C2×#214—64no—
143#926C2×D311yescharacteristic, complemented
144#924—34no—
145C2×#208C2×D311yescharacteristic, complemented
146C22×C3⋊C8—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—61no—
149#909—64no—
150C2×Dic12—32no—
151C2×#204—32no—
152#897—34no—
153#886—62no—
154#875—61no—
155#869—61no—
156C3×#102—34no—
157#835—32no—
158#832—32no—
159#832C2×D314yescomplemented
160#830—34no—
161(C2×D3)⋊C8—34no—
162#810—32no—
163#809—32no—
164C23×C32—22no—
165C23×C32—24no—
166C23×C32—82no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3—28no—
170C22×C3×D3—84no—
171C22×C3×D3C2×D412yes—
172C32×D4—24no—
173C32×D4—22no—
174C32×D4C2×D414yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—42no—
181#634—22no—
182#634—22no—
183#634—42no—
184C3×#67—28no—
185C3×#67—28no—
186C3×#67—24no—
187C3×#67—24no—
188C2×C3×Dic3—28no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D412yes—
192C3×D12—22no—
193C3×D12—21no—
194C3×D12C2×D412yes—
195C3×C4×D3—24no—
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198C3×Dic6—22no—
199C3×Dic6—21no—
200C3×Dic6C2×D412yes—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×H(5,𝔽2)—31no—
204C2×#137—91no—
205C22×SD16—91no—
206#536—91no—
207#452—94no—
208#450—94no—
209#418—31no—
210#416—91no—
211#408—91no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—41no—
215C24×C3—62no—
216C23×D3—22no—
217C3×#41—34no—
218C3×#41—64no—
219C3×#41—68no—
220C3×#41—64no—
221C3×#41—62no—
222C3×#41—62no—
223C3×#41—62no—
224C2×C3×Q8—31no—
225C2×C3×Q8—31no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—21no—
229C2×C3×D4—22no—
230C2×C3×D4—24no—
231C2×C3×D4—22no—
232C2×C3×D4—32no—
233C2×C3×D4—31no—
234C2×C3×D4—31no—
235C2×C3×D4—41no—
236C2×C3×D4—42no—
237C2×C3×D4—62no—
238C2×C3×D4—64no—
239C2×C3×D4—68no—
240C2×C3×D4—62no—
241C2×C3×D4—616no—
242C2×C3×D4—61no—
243C2×C3×D4—64no—
244C2×C3×D4D1214yes—
245C2×C3×D4#6714yes—
246C2×C3×D4C22×D312yes—
247C2×C3×D4C22×D312yes—
248C22×C3×C4—21no—
249C22×C3×C4—32no—
250C22×C3×C4—62no—
251C22×C3×C4—61no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—216no—
255C2×#67—21no—
256C2×#67—22no—
257C2×#67—22no—
258C2×#67#6712yes—
259C22×Dic3—22no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—121no—
263#237—28no—
264#237—24no—
265#237—24no—
266D3×D4—28no—
267D3×D4—24no—
268D3×D4—24no—
269#235—22no—
270#235—22no—
271#235—22no—
272#235#6714yes—
273C2×D12#6711yescharacteristic
274C2×D12C22×D311yescharacteristic
275C2×C4×D3—21no—
276C2×C4×D3C22×D312yes—
277C2×Dic6—32no—
278C2×Dic6—32no—
279C2×Dic6—62no—
280C2×Dic6—64no—
281C2×Dic6—62no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—62no—
285C2×Dic6—61no—
286C2×Dic6—61no—
287C2×Dic6—121no—
288C2×Dic6—122no—
289C2×Dic6#6711yescharacteristic
290C2×Dic6C22×D311yescharacteristic
291C3×M16—62no—
292C2×C3×C8—32no—
293C3×C4⋊C4—32no—
294C3×C22⋊C4—61no—
295C3×C42—61no—
296#217—21no—
297#217—64no—
298#216—64no—
299#214—64no—
300#214—616no—
301#214—68no—
302#214—68no—
303(C2×D3)⋊C4—64no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D312yes—
306Dic3⋊C4—64no—
307C4×Dic3—21no—
308#208—22no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—64no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8C22×D312yes—
316Dic12—64no—
317#204—64no—
318C22×C32—22no—
319C22×C32—24no—
320C22×C32—44no—
321C22×C32—84no—
322C22×C32#12012yes—
323C22×C32C22×D411yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—42no—
328C2×C3×D3—88no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—42no—
333C3×Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336H(5,𝔽2)—64no—
337H(5,𝔽2)—64no—
338C2×#41—31no—
339C2×#41—32no—
340C2×#41—31no—
341C2×#41—61no—
342C22×Q8—91no—
343C22×D4—32no—
344C22×D4—61no—
345C22×D4—62no—
346C22×D4D3211yescharacteristic
347#137—184no—
348C2×Q16—92no—
349C2×SD16—92no—
350C2×SD16—94no—
351C2×SD16—184no—
352C2×M16—31no—
353C22×C8—91no—
354C4⋊Q8—181no—
355#124—181no—
356#123—182no—
357C22⋊Q8—94no—
358#117—31no—
359#103—92no—
360#102—34no—
361#102—92no—
362C22⋊C8—94no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—21no—
368C23×C3—32no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3—68no—
372C23×C3—61no—
373C23×C3—82no—
374C23×C3—82no—
375C23×C3—84no—
376C23×C3—244no—
377C23×C3D3×D411yescharacteristic
378C23×C3C2×#6711yescharacteristic
379C22×D3—21no—
380C22×D3—28no—
381C22×D3—84no—
382C22×D3C2×#6712yes—
383C3×Q8—32no—
384C3×Q8—62no—
385C3×Q8—61no—
386C3×D4—24no—
387C3×D4—24no—
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—24no—
391C3×D4—32no—
392C3×D4—42no—
393C3×D4—44no—
394C3×D4—68no—
395C3×D4—68no—
396C3×D4—64no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4—61no—
400C3×D4C2×D1214yes—
401C3×D4C2×#6714yes—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—32no—
407C2×C3×C4—68no—
408C2×C3×C4—61no—
409C2×C3×C4—64no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4C2×D1212yes—
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4D3×D412yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6712yes—
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—28no—
422#67—28no—
423#67—24no—
424#67—24no—
425C2×Dic3—28no—
426C2×Dic3—21no—
427C2×Dic3—22no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—122no—
431C2×Dic3—124no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3C2×#6712yes—
435D12—22no—
436D12—21no—
437D12C2×#6712yes—
438C4×D3—24no—
439C4×D3—22no—
440C4×D3—22no—
441Dic6—22no—
442Dic6—21no—
443Dic6—64no—
444Dic6—62no—
445Dic6—62no—
446Dic6—62no—
447Dic6—62no—
448Dic6—122no—
449Dic6—124no—
450Dic6—122no—
451Dic6—122no—
452Dic6C2×#6712yes—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—64no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C2×C32—22no—
459C2×C32—44no—
460C2×C32C2×#12011yescharacteristic
461C2×C32#57712yes—
462C3×D3—42no—
463C3×D3—42no—
464C24—21no—
465C24—62no—
466#41—34no—
467#41—64no—
468#41—68no—
469#41—64no—
470#41—62no—
471#41—62no—
472#41—62no—
473C2×Q8—31no—
474C2×Q8—31no—
475C2×Q8—92no—
476C2×Q8—181no—
477C2×Q8—182no—
478C2×Q8—182no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—32no—
482C2×D4—31no—
483C2×D4—31no—
484C2×D4—62no—
485C2×D4—64no—
486C2×D4—68no—
487C2×D4—62no—
488C2×D4—616no—
489C2×D4—61no—
490C2×D4—64no—
491C2×D4#62614yes—
492C2×D4C2×D3212yes—
493C22×C4—32no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—181no—
497C22×C4C2×D3211yescharacteristic
498Q16—184no—
499SD16—184no—
500SD16—188no—
501M16—62no—
502C2×C8—32no—
503C2×C8—92no—
504C2×C8—182no—
505C4⋊C4—32no—
506C4⋊C4—184no—
507C22⋊C4—61no—
508C22⋊C4—184no—
509C42—61no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—64no—
523C22×C3—84no—
524C22×C3—84no—
525C22×C3—84no—
526C22×C3—88no—
527C22×C3—122no—
528C22×C3—248no—
529C22×C3#88212yes—
530C22×C3#95312yes—
531C22×C3C2×D3×D411yescharacteristic
532C22×C3C22×#6711yescharacteristic
533C2×D3—24no—
534C2×D3—22no—
535C2×D3—22no—
536C2×D3—42no—
537C2×D3—88no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—62no—
542C3×C4—62no—
543C3×C4—122no—
544C3×C4#88212yes—
545C3×C4#95312yes—
546C3×C4C22×D1211yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C22×#6711yescharacteristic
549C3×C4C22×#6711yescharacteristic
550Dic3—22no—
551Dic3—22no—
552Dic3—42no—
553Dic3—124no—
554Dic3—122no—
555Dic3—122no—
556C32#300911yescharacteristic, complemented, Sylow
557C23—22no—
558C23—24no—
559C23—32no—
560C23—68no—
561C23—61no—
562C23—82no—
563C23—244no—
564C23D3×#6711yescharacteristic
565Q8—32no—
566Q8—61no—
567Q8—62no—
568Q8—182no—
569Q8—182no—
570Q8—362no—
571D4—22no—
572D4—24no—
573D4—32no—
574D4—68no—
575D4—68no—
576D4—64no—
577D4—64no—
578D4—61no—
579D4—62no—
580D4C2×#62614yes—
581C2×C4—32no—
582C2×C4—68no—
583C2×C4—61no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—182no—
589C2×C4—362no—
590C2×C4C2×#62612yes—
591C2×C4D3×#6712yes—
592C2×C4D3×#6711yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—62no—
595C8—182no—
596C2×C3—24no—
597C2×C3—22no—
598C2×C3—22no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—44no—
602C2×C3—44no—
603C2×C3—84no—
604C2×C3—122no—
605C2×C3—122no—
606C2×C3C2×#88211yescharacteristic
607C2×C3#577512yes—
608C2×C3#583612yes—
609C2×C3C2×#95311yescharacteristic
610D3—42no—
611D3—42no—
612C22—22no—
613C22—24no—
614C22—44no—
615C22—64no—
616C22—62no—
617C22—62no—
618C22—84no—
619C22—122no—
620C22—248no—
621C22#6397712yes—
622C22C2×D3×#6711yescharacteristic
623C4—62no—
624C4—62no—
625C4—122no—
626C4—362no—
627C4#6397712yes—
628C4C22×#62611yescharacteristic
629C4C2×D3×#6711yescharacteristic
630C3—21no—
631C3#7892911yescharacteristic, complemented
632C3#8410511yescharacteristic, complemented
633C2—22no—
634C2—44no—
635C2—122no—
636C2—122no—
637C2#1059510612yes—
638C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#1004C2
hypercenterC22×D4D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3754C2semidirect
3. #10594856C2semidirect
4. C2×#63831C2semidirect
5. C3×#5215C2semidirect
6. #10591463C2semidirect
7. #10591459C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
13. C22×#634C22semidirect
24. C2×#3754C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
26. C3×#926C22semidirect
27. C2×C3×#208C22semidirect
31. #63857C22semidirect
32. C2×#3719C22semidirect
34. C2×#3716C22semidirect
35. C3×#832C22semidirect
36. #63565C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
53. #5215D3semidirect
143. #926C2×D3semidirect
145. C2×#208C2×D3semidirect
159. #832C2×D3semidirect
556. C32#3009semidirect
631. C3#78929semidirect
632. C3#84105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×#37542
#105948562
C2×#638312
C3×#52152
#105914632
#105914592
#105910832
#105910712
#841053
#789293