Finite Group Databasebeta

← #11864454

Subgroups — #11864454

Order 1152.

1543 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3#10595040C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10591583C214yesmaximal, complemented
7#10591450C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#83948—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—24no—
14C3×#1010—24no—
15C2×C3×D3×Q8C2212yescomplemented
16C2×C3×#237—22no—
17C2×C3×#237C2212yescomplemented
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×Dic6—21no—
22C22×C3×Dic6C2211yescharacteristic
23#64135C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#949—24no—
26C2×C3×#215C2212yes—
27C2×C3×#213C2212yes—
28C2×C3×#208C2211yescharacteristic
29#63976—22no—
30#63914—21no—
31#63908C2214yes—
32#63863—21no—
33C2×#3715—24no—
34C2×#3715C2214yes—
35#63662C2212yescomplemented
36#63659C2212yescomplemented
37#63566C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42#5830—31no—
43C2×#949D311yescharacteristic, complemented
44C22×#215—31no—
45#5805—31no—
46C22×#214—31no—
47#5238—34no—
48#5234—31no—
49#5233—31no—
50#5233—31no—
51#5233—61no—
52#5227—34no—
53#5225—31no—
54#5170—34no—
55#5158—34no—
56#5129—31no—
57#5120—31no—
58C23×C3×D3—21no—
59C32×#41—22no—
60C32×#41D414yescomplemented
61C2×C32×Q8C2311yescharacteristic
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—22no—
67C2×C3×#67D412yes—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—22no—
70C3×D3×Q8—24no—
71C3×D3×Q8—24no—
72C3×#237—216no—
73C3×#237—24no—
74C3×#237—24no—
75C3×#235—28no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12D411yescharacteristic
82C2×C3×D12C2312yes—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6—28no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×C3×Dic6D411yescharacteristic
90C2×C3×Dic6D414yescomplemented
91C2×C3×Dic6C2312yes—
92C2×#625—24no—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4×C3⋊Dic3—21no—
96C2×C3⋊(C3⋊C8)—22no—
97C2×C3⋊(C3⋊C8)C2312yes—
98C3×#215—24no—
99C3×#213—24no—
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102(C2×D3)⋊Dic3—24no—
103#3715—28no—
104#3010—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—61no—
111C2×C3×#41—62no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—32no—
115C22×C3×Q8—31no—
116C22×C3×Q8—61no—
117C22×C3×D4—31no—
118#1010—24no—
119#1010—24no—
120C2×D3×Q8C2×D312yescomplemented
121C2×#237—22no—
122C2×#237C2×D312yescomplemented
123C2×#235—21no—
124C2×#235C2×D311yescharacteristic
125C22×D12C2×D311yescharacteristic
126C22×Dic6—21no—
127C22×Dic6C2×D311yescharacteristic
128C3×AGL(1,ℤ/8)—64no—
129C2×C3×SD16—32no—
130C2×C3×D8—32no—
131C2×C3×M16—31no—
132#953—62no—
133#949—24no—
134#947—61no—
135C2×#215—34no—
136C2×#215—64no—
137C2×#215C2×D312yes—
138#940—61no—
139#940—61no—
140#938—34no—
141#937—62no—
142#936—61no—
143C2×#214—34no—
144C2×#214—64no—
145C2×#213C2×D312yes—
146#930—34no—
147#926—31no—
148#926—31no—
149#926—61no—
150C2×#208C2×D311yescharacteristic
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—32no—
155#835—32no—
156#835—34no—
157#835—62no—
158#832—32no—
159#832—32no—
160#832—62no—
161#830—34no—
162(C2×D3)⋊C8—34no—
163#816—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—42no—
168C22×C3×D3—82no—
169C22×C3×D3C2×D412yes—
170C32×Q8—21no—
171C32×Q8C2×D412yes—
172C32×D4—24no—
173C32×D4—21no—
174C32×D4C2×D412yes—
175C2×C32×C4—21no—
176C2×C32×C4—24no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—22no—
182C3×#67—28no—
183C3×#67—24no—
184C2×C3×Dic3—28no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—22no—
191C3×D12—42no—
192C3×C4×D3—28no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6C2×D414yes—
200#625—84no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—31no—
204C2×AGL(1,ℤ/8)—31no—
205C22×SD16—91no—
206#535—91no—
207#449—94no—
208#448—94no—
209#419—91no—
210#416—91no—
211#408—91no—
212C24×C3—61no—
213C23×D3—21no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—24no—
217C3×#41—42no—
218C3×#41—68no—
219C3×#41—64no—
220C3×#41—616no—
221C3×#41—64no—
222C3×#41—62no—
223C3×#41—62no—
224C3×#41#6714yescomplemented
225C3×#41#6714yescomplemented
226C2×C3×Q8—21no—
227C2×C3×Q8—31no—
228C2×C3×Q8—34no—
229C2×C3×Q8—32no—
230C2×C3×Q8—62no—
231C2×C3×Q8—68no—
232C2×C3×Q8—64no—
233C2×C3×Q8—64no—
234C2×C3×Q8—61no—
235C2×C3×Q8—62no—
236C2×C3×Q8C22×D311yescharacteristic
237C2×C3×Q8C22×D311yescharacteristic
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—32no—
242C2×C3×D4—31no—
243C2×C3×D4—32no—
244C2×C3×D4—41no—
245C2×C3×D4—62no—
246C2×C3×D4—62no—
247C2×C3×D4—62no—
248C2×C3×D4—61no—
249C2×C3×D4C22×D311yescharacteristic
250C2×C3×D4C22×D311yescharacteristic
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—32no—
255C22×C3×C4—41no—
256C22×C3×C4—62no—
257C22×C3×C4—62no—
258C22×C3×C4—61no—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—22no—
262C2×#67—64no—
263C2×#67—64no—
264C2×#67#6712yes—
265C22×Dic3—21no—
266C22×Dic3—22no—
267D3×Q8—24no—
268D3×Q8—24no—
269#237—216no—
270#237—24no—
271#237—24no—
272#235—28no—
273#235—22no—
274#235—22no—
275C2×D12—22no—
276C2×D12—22no—
277C2×D12—21no—
278C2×D12#6711yescharacteristic
279C2×D12C22×D312yes—
280C2×C4×D3—22no—
281C2×C4×D3C22×D312yes—
282C2×Dic6—28no—
283C2×Dic6—21no—
284C2×Dic6—22no—
285C2×Dic6—22no—
286C2×Dic6#6711yescharacteristic
287C2×Dic6#6714yescomplemented
288C2×Dic6C22×D312yes—
289C3×SD16—64no—
290C3×D8—64no—
291C3×M16—62no—
292C2×C3×C8—32no—
293#217—61no—
294#217—61no—
295#217—64no—
296#217—121no—
297#215—24no—
298#215—68no—
299#214—68no—
300#213—24no—
301(C2×D3)⋊C4—64no—
302C4⋊Dic3—32no—
303C4⋊Dic3—32no—
304C4⋊Dic3—62no—
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—42no—
324C2×C3×D3—44no—
325C2×C3×D3—84no—
326C32×C4—22no—
327C32×C4#12012yes—
328C32×C4C22×D411yescharacteristic
329C32×C4C22×D411yescharacteristic
330C3⋊Dic3—42no—
331C3×Dic3—22no—
332C3×Dic3—24no—
3332−1+4—64no—
3342−1+4—64no—
335C2×#41—31no—
336C2×#41—32no—
337C2×#41—61no—
338C2×#41—62no—
339C2×#41D3211yescharacteristic
340C22×Q8—32no—
341C22×Q8—31no—
342C22×Q8—61no—
343C22×D4—31no—
344AGL(1,ℤ/8)—64no—
345C2×SD16—32no—
346C2×SD16—94no—
347C2×SD16—184no—
348C2×D8—32no—
349C2×M16—31no—
350C22×C8—91no—
351#127—181no—
352#124—181no—
353#121—94no—
354#120—182no—
355#117—91no—
356#103—94no—
357#103—92no—
358#102—92no—
359C22⋊C8—94no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—32no—
364C23×C3—41no—
365C23×C3—62no—
366C23×C3—122no—
367C23×C3—242no—
368C23×C3D3×D411yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—22no—
371C22×D3—42no—
372C22×D3—82no—
373C22×D3C2×#6712yes—
374C3×Q8—21no—
375C3×Q8—21no—
376C3×Q8—22no—
377C3×Q8—34no—
378C3×Q8—41no—
379C3×Q8—68no—
380C3×Q8—62no—
381C3×Q8—64no—
382C3×Q8—62no—
383C3×Q8C2×#6712yes—
384C3×Q8C2×#6712yes—
385C3×D4—24no—
386C3×D4—24no—
387C3×D4—21no—
388C3×D4—21no—
389C3×D4—22no—
390C3×D4—41no—
391C3×D4—44no—
392C3×D4—68no—
393C3×D4—64no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—62no—
397C3×D4—122no—
398C3×D4C2×#6712yes—
399C3×D4C2×#6712yes—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—32no—
409C2×C3×C4—44no—
410C2×C3×C4—41no—
411C2×C3×C4—68no—
412C2×C3×C4—68no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D412yes—
419C2×C3×C4C2×#6712yes—
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6712yes—
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—28no—
426#67—24no—
427#67—244no—
428#67—244no—
429C2×Dic3—28no—
430C2×Dic3—24no—
431C2×Dic3—22no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3C2×#6712yes—
436D12—22no—
437D12—22no—
438D12—22no—
439D12—42no—
440C4×D3—28no—
441C4×D3—22no—
442C4×D3—22no—
443Dic6—28no—
444Dic6—22no—
445Dic6—24no—
446Dic6—22no—
447Dic6C2×#6714yes—
448C3×C8—62no—
449C3⋊C8—22no—
450C3⋊C8—62no—
451C3⋊C8—62no—
452C3⋊C8—122no—
453C2×C32—22no—
454C2×C32—42no—
455C2×C32C2×#12011yescharacteristic
456C2×C32#57712yes—
457C3×D3—42no—
458C3×D3—82no—
459C24—61no—
460#41—22no—
461#41—68no—
462#41—64no—
463#41—616no—
464#41—64no—
465#41—62no—
466#41—62no—
467#41#62514yescomplemented
468C2×Q8—31no—
469C2×Q8—32no—
470C2×Q8—34no—
471C2×Q8—62no—
472C2×Q8—68no—
473C2×Q8—64no—
474C2×Q8—64no—
475C2×Q8—62no—
476C2×Q8—61no—
477C2×Q8C2×D3211yescharacteristic
478C2×D4—21no—
479C2×D4—32no—
480C2×D4—32no—
481C2×D4—31no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—61no—
486C2×D4—184no—
487C2×D4C2×D3211yescharacteristic
488C22×C4—21no—
489C22×C4—32no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—61no—
493C22×C4C2×D3211yescharacteristic
494SD16—64no—
495SD16—188no—
496D8—64no—
497M16—62no—
498C2×C8—32no—
499C2×C8—92no—
500C2×C8—182no—
501C4⋊C4—92no—
502C22⋊C4—184no—
503C22⋊C4—181no—
504C42—181no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—64no—
516C22×C3—62no—
517C22×C3—82no—
518C22×C3—124no—
519C22×C3—122no—
520C22×C3—244no—
521C22×C3#93712yes—
522C22×C3#95312yes—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C22×#6711yescharacteristic
525C2×D3—24no—
526C2×D3—22no—
527C2×D3—44no—
528C2×D3—42no—
529C2×D3—84no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—22no—
535C3×C4—42no—
536C3×C4—62no—
537C3×C4—64no—
538C3×C4#93712yes—
539C3×C4#95312yes—
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C22×#6711yescharacteristic
542C3×C4C22×#6711yescharacteristic
543C3×C4C22×#6711yescharacteristic
544Dic3—22no—
545Dic3—24no—
546Dic3—122no—
547Dic3—122no—
548Dic3—242no—
549C32#301011yescharacteristic, complemented, Sylow
550C23—21no—
551C23—32no—
552C23—62no—
553C23—122no—
554C23—242no—
555C23D3×#6711yescharacteristic
556Q8—21no—
557Q8—34no—
558Q8—68no—
559Q8—62no—
560Q8—62no—
561Q8—64no—
562Q8C2×#62512yes—
563D4—24no—
564D4—21no—
565D4—68no—
566D4—64no—
567D4—62no—
568D4—62no—
569D4—62no—
570D4—122no—
571D4—724no—
572D4C2×#62512yes—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—32no—
576C2×C4—68no—
577C2×C4—68no—
578C2×C4—62no—
579C2×C4—64no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—182no—
583C2×C4C2×#62512yes—
584C2×C4D3×#6712yes—
585C2×C4D3×#6711yescharacteristic
586C2×C4C22×D3211yescharacteristic
587C8—62no—
588C8—182no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—42no—
594C2×C3—42no—
595C2×C3—42no—
596C2×C3—82no—
597C2×C3—122no—
598C2×C3—242no—
599C2×C3#577512yes—
600C2×C3C2×#93711yescharacteristic
601C2×C3#583712yes—
602C2×C3C2×#95311yescharacteristic
603D3—42no—
604D3—82no—
605C22—22no—
606C22—22no—
607C22—42no—
608C22—64no—
609C22—62no—
610C22—124no—
611C22—122no—
612C22—244no—
613C22#6397612yes—
614C22C2×D3×#6711yescharacteristic
615C4—22no—
616C4—62no—
617C4—64no—
618C4—362no—
619C4#6397612yes—
620C4C22×#62511yescharacteristic
621C4C2×D3×#6711yescharacteristic
622C3—21no—
623C3#8394811yescharacteristic, complemented
624C3#8411311yescharacteristic, complemented
625C2—22no—
626C2—42no—
627C2—122no—
628C2—242no—
629C2#1059545512yes—
630C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3010
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
1. C2×C3×#1010C2semidirect
2. C2×C3×#949C2semidirect
3. #10595040C2semidirect
4. C22×#3715C2semidirect
5. #10592932C2semidirect
6. #10591583C2semidirect
7. #10591450C2semidirect
8. #10591100C2semidirect
9. #10591071C2semidirect
15. C2×C3×D3×Q8C22semidirect
17. C2×C3×#237C22semidirect
35. #63662C22semidirect
36. #63659C22semidirect
37. #63566C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C2×#1010D3semidirect
43. C2×#949D3semidirect
60. C32×#41D4semidirect
90. C2×C3×Dic6D4semidirect
120. C2×D3×Q8C2×D3semidirect
122. C2×#237C2×D3semidirect
224. C3×#41#67semidirect
225. C3×#41#67semidirect
287. C2×Dic6#67semidirect
467. #41#625semidirect
549. C32#3010semidirect
623. C3#83948semidirect
624. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#9492
#105950402
C22×#37152
#105929322
#105915832
#105914502
#105911002
#105910712
#841133
#839483