Finite Group Databasebeta

← #11864437

Subgroups — #11864437

Order 1152.

1613 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×#64298C211yesmaximal, characteristic, complemented
2C22×#3754C211yesmaximal, characteristic, complemented
3C3×#5805C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5#10591519C214yesmaximal, complemented
6#10591517C214yesmaximal, complemented
7#10591107C211yesmaximal, characteristic, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#83948—31nomaximal
11#83390—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×#3805—22no—
17#64298—24no—
18#64298—24no—
19C2×#3795—21no—
20C2×#3795C2212yescomplemented
21C2×D3×Dic6—21no—
22C2×D3×Dic6C2212yescomplemented
23C2×#3754—24no—
24C2×#3754C2214yes—
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#953—22no—
27C3×#940—21no—
28C3×#938C2214yes—
29C3×#936—21no—
30C2×C3×#214C2212yes—
31C3×#932—24no—
32C2×C3×#213C2212yes—
33C3×#926C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35#63567C2214yescomplemented
36#63565C2212yescomplemented
37#63562C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×#1010—31no—
40C2×#1010—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C3×#535—31no—
43#5805D311yescharacteristic, complemented
44C22×#214—31no—
45C22×#214—31no—
46C22×#214—61no—
47C2×#932D311yescharacteristic, complemented
48#5234—31no—
49#5233—31no—
50#5170—34no—
51#5158—34no—
52#5129—31no—
53#5120—31no—
54#5040—34no—
55#5037—34no—
56#5004—31no—
57#5002—31no—
58C24×C32—21no—
59C2×C32×D4—22no—
60C2×C32×D4—22no—
61C2×C32×D4—21no—
62C2×C32×D4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C2×#634—21no—
66C2×#634—22no—
67C2×#634D414yescomplemented
68C2×#634C2312yes—
69C2×C3×#67—21no—
70C2×C3×#67—24no—
71C2×C3×#67D412yes—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235—22no—
75C3×#235D414yescomplemented
76C2×C3×D12D411yescharacteristic
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×#627—22no—
83C2×#625—22no—
84#3805—216no—
85C2×D3×Dic3—22no—
86C2×D3×Dic3—22no—
87#3795—28no—
88#3795—24no—
89#3795—24no—
90D3×Dic6—28no—
91D3×Dic6—24no—
92D3×Dic6—24no—
93#3754—28no—
94C2×C3⋊(C3⋊C8)—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×#217—24no—
98C3×#214—24no—
99C3×#213—24no—
100C3×C4⋊Dic3C2312yes—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3010—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×D4—21no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C2×D311yescharacteristic
110#1010—64no—
111#1010—64no—
112#1010—64no—
113#1010—64no—
114C2×D3×Q8—32no—
115C2×D3×Q8—61no—
116C2×#237—32no—
117C2×#237—61no—
118C2×#237—62no—
119C2×#237—62no—
120C2×#235—32no—
121C2×#235—61no—
122C2×#235C2×D311yescharacteristic
123C2×#235C2×D311yescharacteristic
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—32no—
127C22×Dic6—61no—
128C22×Dic6—61no—
129C3×AGL(1,ℤ/8)—64no—
130C2×C3×SD16—32no—
131C2×C3×D8—32no—
132C2×C3×M16—31no—
133C3×#127—61no—
134C3×#124—61no—
135C3×#121—34no—
136C3×#120—62no—
137C3×#117—31no—
138#953—22no—
139#940—21no—
140#938C2×D314yes—
141#936—21no—
142C2×#214—34no—
143C2×#214—34no—
144C2×#214—64no—
145C2×#214—64no—
146C2×#214—64no—
147C2×#214—68no—
148C2×#214C2×D312yes—
149#932—24no—
150C2×#213C2×D312yes—
151#926C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—61no—
156#835—32no—
157#832—32no—
158#830—34no—
159(C2×D3)⋊C8—34no—
160#816—34no—
161#810—32no—
162#810—34no—
163#809—32no—
164C23×C32—22no—
165C23×C32—42no—
166C23×C32—82no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C22×C3×D3C2×D412yes—
170C32×D4—22no—
171C32×D4—22no—
172C32×D4—42no—
173C2×C32×C4C2×D412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3—22no—
179#634—24no—
180#634—22no—
181#634C2×D414yes—
182C3×#67—24no—
183C3×#67—24no—
184C3×#67—84no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D412yes—
188C3×D12—22no—
189C3×D12—21no—
190C3×D12C2×D412yes—
191C3×C4×D3—24no—
192C3×C4×D3—22no—
193C3×C4×D3—22no—
194C3×Dic6—22no—
195C3×Dic6—21no—
196C3×Dic6C2×D412yes—
197#627—28no—
198#625—28no—
199D3×Dic3—28no—
200D3×Dic3—28no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—91no—
204C2×AGL(1,ℤ/8)—31no—
205C22×SD16—91no—
206#535—31no—
207#449—94no—
208#448—94no—
209#419—91no—
210#416—91no—
211#408—91no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—41no—
215C3×#41—34no—
216C3×#41—62no—
217C3×#41—62no—
218C3×#41—62no—
219C2×C3×Q8—31no—
220C2×C3×Q8—31no—
221C2×C3×D4—24no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—32no—
230C2×C3×D4—31no—
231C2×C3×D4—31no—
232C2×C3×D4—42no—
233C2×C3×D4—41no—
234C2×C3×D4—61no—
235C2×C3×D4—64no—
236C2×C3×D4C22×D312yes—
237C2×C3×D4C22×D312yes—
238C22×C3×C4—21no—
239C22×C3×C4—32no—
240C22×C3×C4—61no—
241C22×C3×C4C22×D311yescharacteristic
242C22×C3×C4C22×D311yescharacteristic
243C2×#67—21no—
244C2×#67—24no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67#6712yes—
248C22×Dic3—62no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251C22×Dic3—62no—
252C22×Dic3—121no—
253D3×Q8—64no—
254D3×Q8—64no—
255D3×Q8—68no—
256#237—64no—
257#237—64no—
258#237—68no—
259#237—616no—
260#237—616no—
261#235—22no—
262#235—22no—
263#235—22no—
264#235—64no—
265#235—68no—
266#235—64no—
267#235#6714yescomplemented
268C2×D12#6711yescharacteristic
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—21no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3C22×D312yes—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—32no—
277C2×Dic6—32no—
278C2×Dic6—64no—
279C2×Dic6—62no—
280C2×Dic6—64no—
281C2×Dic6—68no—
282C2×Dic6—62no—
283C2×Dic6—61no—
284C2×Dic6—62no—
285C2×Dic6—61no—
286C2×Dic6—62no—
287C2×Dic6—62no—
288C2×Dic6—64no—
289C2×Dic6—121no—
290C2×Dic6—122no—
291C2×Dic6#6711yescharacteristic
292C2×Dic6C22×D311yescharacteristic
293C3×SD16—64no—
294C3×D8—64no—
295C3×M16—62no—
296C2×C3×C8—32no—
297C3×C4⋊C4—32no—
298C3×C22⋊C4—64no—
299C3×C22⋊C4—61no—
300C3×C42—61no—
301#217—21no—
302#217—24no—
303#214—24no—
304#214—68no—
305#214—68no—
306#214—616no—
307#213—24no—
308C4⋊Dic3C22×D312yes—
309C4×Dic3—21no—
310#208—22no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—64no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318C22×C32—22no—
319C22×C32—42no—
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—
328C32×C4#12012yes—
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3—24no—
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—42no—
3352−1+4—184no—
3362−1+4—184no—
337C2×#41—31no—
338C2×#41—31no—
339C2×#41—92no—
340C2×#41—181no—
341C2×#41—182no—
342C22×Q8—92no—
343C22×Q8—91no—
344C22×Q8—181no—
345C22×D4D3211yescharacteristic
346AGL(1,ℤ/8)—64no—
347C2×SD16—32no—
348C2×SD16—94no—
349C2×SD16—184no—
350C2×D8—32no—
351C2×M16—31no—
352C22×C8—91no—
353#127—61no—
354#124—61no—
355#121—34no—
356#120—62no—
357#117—31no—
358#103—94no—
359#103—92no—
360#102—92no—
361C22⋊C8—94no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—32no—
366C23×C3—42no—
367C23×C3—44no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—61no—
371C23×C3—82no—
372C23×C3—82no—
373C23×C3—84no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—21no—
377C22×D3C2×#6712yes—
378C3×Q8—32no—
379C3×Q8—62no—
380C3×Q8—61no—
381C3×D4—24no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—32no—
387C3×D4—42no—
388C3×D4—44no—
389C3×D4—42no—
390C3×D4—42no—
391C3×D4—64no—
392C3×D4—64no—
393C3×D4—62no—
394C3×D4—61no—
395C3×D4—244no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—32no—
401C2×C3×C4—61no—
402C2×C3×C4—64no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D412yes—
408C2×C3×C4D3×D412yes—
409C2×C3×C4D3×D412yes—
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—24no—
415#67—24no—
416#67—68no—
417#67—68no—
418#67—84no—
419C2×Dic3—21no—
420C2×Dic3—22no—
421C2×Dic3—68no—
422C2×Dic3—68no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—122no—
428C2×Dic3—124no—
429C2×Dic3C2×#6712yes—
430D12—22no—
431D12—21no—
432D12C2×#6712yes—
433C4×D3—24no—
434C4×D3—22no—
435C4×D3—22no—
436C4×D3—68no—
437C4×D3—68no—
438Dic6—22no—
439Dic6—21no—
440Dic6—34no—
441Dic6—34no—
442Dic6—64no—
443Dic6—68no—
444Dic6—68no—
445Dic6—64no—
446Dic6—64no—
447Dic6—62no—
448Dic6—62no—
449Dic6—122no—
450Dic6—124no—
451Dic6C2×#6712yes—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—64no—
455C3⋊C8—62no—
456C3⋊C8—62no—
457C2×C32—22no—
458C2×C32—82no—
459C2×C32C2×#12011yescharacteristic
460C2×C32#57712yes—
461C3×D3—42no—
462C3×D3—42no—
463C24—21no—
464#41—34no—
465#41—62no—
466#41—62no—
467#41—62no—
468#41—184no—
469#41—184no—
470#41—188no—
471#41—1816no—
472C2×Q8—31no—
473C2×Q8—31no—
474C2×Q8—92no—
475C2×Q8—94no—
476C2×Q8—182no—
477C2×Q8—184no—
478C2×Q8—184no—
479C2×Q8—188no—
480C2×Q8—181no—
481C2×Q8—182no—
482C2×D4—22no—
483C2×D4—21no—
484C2×D4—22no—
485C2×D4—32no—
486C2×D4—31no—
487C2×D4—31no—
488C2×D4—61no—
489C2×D4—64no—
490C2×D4—182no—
491C2×D4C2×D3212yes—
492C22×C4—32no—
493C22×C4—61no—
494C22×C4—182no—
495C22×C4—182no—
496C22×C4—181no—
497C22×C4C2×D3211yescharacteristic
498SD16—64no—
499SD16—188no—
500D8—64no—
501M16—62no—
502C2×C8—32no—
503C2×C8—92no—
504C2×C8—182no—
505C4⋊C4—32no—
506C22⋊C4—64no—
507C22⋊C4—61no—
508C42—61no—
509C22×C3—24no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—44no—
519C22×C3—64no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—84no—
523C22×C3—88no—
524C22×C3—84no—
525C22×C3—84no—
526C22×C3—122no—
527C22×C3#93712yes—
528C22×C3#93712yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—24no—
534C2×D3—42no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—22no—
538C3×C4—62no—
539C3×C4—62no—
540C3×C4—122no—
541C3×C4#93712yes—
542C3×C4#93712yes—
543C3×C4C2×D3×D411yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—22no—
548Dic3—22no—
549Dic3—42no—
550Dic3—64no—
551Dic3—64no—
552Dic3—124no—
553C32#301011yescharacteristic, complemented, Sylow
554C23—22no—
555C23—32no—
556C23—42no—
557C23—61no—
558C23—82no—
559C23D3×#6711yescharacteristic
560Q8—32no—
561Q8—61no—
562Q8—62no—
563Q8—94no—
564Q8—188no—
565Q8—182no—
566Q8—184no—
567D4—22no—
568D4—22no—
569D4—32no—
570D4—42no—
571D4—64no—
572D4—64no—
573D4—61no—
574D4—62no—
575D4—188no—
576D4—244no—
577C2×C4—32no—
578C2×C4—61no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—64no—
582C2×C4—62no—
583C2×C4—188no—
584C2×C4—188no—
585C2×C4—182no—
586C2×C4—184no—
587C2×C4D3×#6712yes—
588C2×C4D3×#6711yescharacteristic
589C2×C4#381112yes—
590C2×C4C22×D3211yescharacteristic
591C8—62no—
592C8—182no—
593C2×C3—24no—
594C2×C3—22no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—84no—
599C2×C3—82no—
600C2×C3—82no—
601C2×C3—122no—
602C2×C3—122no—
603C2×C3#577512yes—
604C2×C3C2×#93711yescharacteristic
605C2×C3C2×#93711yescharacteristic
606C2×C3#583612yes—
607D3—42no—
608D3—42no—
609C22—22no—
610C22—44no—
611C22—42no—
612C22—64no—
613C22—62no—
614C22—62no—
615C22—84no—
616C22—122no—
617C22#6398312yes—
618C22C2×D3×#6711yescharacteristic
619C4—62no—
620C4—62no—
621C4—122no—
622C4—184no—
623C4#6398312yes—
624C4C2×D3×#6711yescharacteristic
625C4C2×#381111yescharacteristic
626C3—21no—
627C3#8339011yescharacteristic, complemented
628C3#8394811yescharacteristic, complemented
629C2—22no—
630C2—82no—
631C2—122no—
632C2—122no—
633C2#1059510612yes—
634C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3010
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
1. C2×#64298C2semidirect
2. C22×#3754C2semidirect
3. C3×#5805C2semidirect
4. C2×C3×#932C2semidirect
5. #10591519C2semidirect
6. #10591517C2semidirect
7. #10591107C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
20. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
35. #63567C22semidirect
36. #63565C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #5805D3semidirect
47. C2×#932D3semidirect
67. C2×#634D4semidirect
75. C3×#235D4semidirect
267. #235#67semidirect
553. C32#3010semidirect
627. C3#83390semidirect
628. C3#83948semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C22×#37542
C3×#58052
C2×C3×#9322
#105915192
#105915172
#105911072
#105910832
#105910712
#839483
#833903