Finite Group Databasebeta

← #11801907

Subgroups — #11801907

Order 1152.

1965 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×#63841C211yesmaximal, characteristic, complemented
4#10592928C211yesmaximal, characteristic, complemented
5C3×#5229C211yesmaximal, characteristic, complemented
6#10591376C214yesmaximal, complemented
7#10591323C211yesmaximal, characteristic, complemented
8#10591318C211yesmaximal, characteristic, complemented
9#10591237C214yesmaximal, complemented
10#84086—31nomaximal
11#76478—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×C3×#239—24no—
14C2×C3×#239—24no—
15C2×C3×#239C418yescomplemented
16C22×C3×D12C2212yes—
17C22×C3×D12C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×D3×Dic3C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C4×D3×Dic3—24no—
31#63841—24no—
32#63658C2214yes—
33C3×C3⋊#95C2214yes—
34C22×C3×#41—31no—
35C22×#239D311yescharacteristic
36C2×#926—31no—
37C22×C4×Dic3—31no—
38C2×#892—31no—
39C2×C42×D3—31no—
40C3×#391—31no—
41#5229—31no—
42#5229—31no—
43#5229—61no—
44#5229D311yescharacteristic, complemented
45#5221—31no—
46#5221—31no—
47#5220—34no—
48C4×#217—34no—
49#4988—31no—
50#4939—31no—
51#4666—34no—
52#4665—34no—
53C23×C3×D3C2312yes—
54C23×C3×D3C2311yescharacteristic
55C2×C32×Q8—22no—
56C2×C32×Q8—22no—
57C2×C32×Q8C2×C414yescomplemented
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C3×#239—232no—
66C2×C3×D12—24no—
67C2×C3×D12—24no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12C2×C418yes—
71C2×C3×D12C2×C414yescomplemented
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3—24no—
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3C2×C418yescomplemented
76C2×C3×C4×D3D414yes—
77C2×C3×C4×D3D414yes—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C4⋊(C3⋊Dic3)—22no—
82C4×C3⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4×Dic3—22no—
85(C2×D3)⋊Dic3—24no—
86(C2×D3)⋊Dic3—28no—
87(C2×D3)⋊Dic3—28no—
88Dic32—24no—
89Dic32—24no—
90#2297—91noSylow
91C2×C3×#41—38no—
92C2×C3×#41—64no—
93C2×C3×#41—64no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×D4—32no—
98C22×C3×D4—31no—
99C23×C3×C4—31no—
100C23×C3×C4—32no—
101C23×Dic3—32no—
102C2×#239—24no—
103C2×#239—24no—
104C2×#239Dic318yescomplemented
105C22×D12C2×D312yes—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—32no—
108C22×C4×D3C2×D312yes—
109C22×C4×D3C2×D311yescharacteristic
110C2×C3×C4⋊C4—31no—
111C2×C3×C42—31no—
112C2×#217—34no—
113C2×#217—34no—
114C2×#217—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—34no—
117C2×(C2×D3)⋊C4—34no—
118#926—64no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3—64no—
131C2×C4×Dic3C2×D311yescharacteristic
132#892—64no—
133C42×D3—64no—
134C3×#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95—64no—
138C3⋊#95C2×D314yes—
139C23×C32C2411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—24no—
145C22×C3×D3—24no—
146C22×C3×D3C22×C414yes—
147C22×C3×D3C22×C412yes—
148C22×C3×D3C2×D412yes—
149C22×C3×D3C2×D412yes—
150C32×Q8—28no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C414yes—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3#4114yescomplemented
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—24no—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3#4114yescomplemented
170C3×D12—216no—
171C3×D12—28no—
172C3×C4×D3—216no—
173C3×C4×D3C22⋊C4116yescomplemented
174D3×Dic3—216no—
175C22×#41—31no—
176C2×#117—91no—
177C22×C42—91no—
178#391—31no—
179#391—91no—
180#390—91no—
181#390—91no—
182#386—94no—
183C4×C22⋊C4—94no—
184C24×C3—31no—
185C24×C3—32no—
186C23×D3C22×D312yes—
187C23×D3C22×D311yescharacteristic
188C3×#41—632no—
189C2×C3×Q8—22no—
190C2×C3×Q8—22no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—24no—
194C2×C3×Q8—42no—
195C2×C3×Q8—42no—
196C2×C3×Q8C4×D314yescomplemented
197C2×C3×Q8C2×Dic314yescomplemented
198C2×C3×D4—38no—
199C2×C3×D4—34no—
200C2×C3×D4—64no—
201C2×C3×D4—64no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—34no—
209C22×C3×C4—34no—
210C22×C3×C4—32no—
211C22×C3×C4—38no—
212C22×C3×C4—32no—
213C22×C3×C4—64no—
214C22×C3×C4—64no—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226C22×Dic3—64no—
227C22×Dic3—64no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231#239—232no—
232C2×D12—24no—
233C2×D12—24no—
234C2×D12—22no—
235C2×D12—22no—
236C2×D12C2×Dic318yes—
237C2×D12C2×Dic314yescomplemented
238C2×C4×D3—24no—
239C2×C4×D3—24no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3C2×Dic314yes—
244C2×C4×D3C2×Dic318yescomplemented
245C2×C4×D3#6714yes—
246C2×C4×D3#6714yes—
247C3×C4⋊C4—62no—
248C3×C42—62no—
249#217—68no—
250#217—64no—
251#217—68no—
252(C2×D3)⋊C4—68no—
253(C2×D3)⋊C4—68no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—22no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—122no—
259C4×Dic3—22no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—122no—
267C22×C32C23×C411yescharacteristic
268C22×C32C22×D411yescharacteristic
269C22×C32C22×D411yescharacteristic
270C22×C32C2×#4112yes—
271C22×C32C2×#4112yes—
272C2×C3×D3—24no—
273C2×C3×D3—24no—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—24no—
277C2×C3×D3—28no—
278C2×C3×D3—44no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3C2×C22⋊C414yes—
282C32×C4—24no—
283C32×C4C2×C22⋊C414yes—
284C3⋊Dic3—24no—
285C3⋊Dic3—42no—
286C3×Dic3—24no—
287C3×Dic3—42no—
288C3×Dic3C2×C22⋊C414yes—
289C2×#41—38no—
290C2×#41—64no—
291C2×#41—64no—
292C22×Q8D3211yescharacteristic
293C22×D4—32no—
294C22×D4—31no—
295C23×C4—31no—
296C23×C4—32no—
297C23×C4—92no—
298#117—184no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—91no—
301C2×C22⋊C4—92no—
302C2×C22⋊C4—94no—
303C2×C22⋊C4—94no—
304C2×C42—31no—
305C2×C42—92no—
306C2×C42—92no—
307C2×C42—91no—
308C2×C42—184no—
309#95—34no—
310#95—94no—
311C23×C3—21no—
312C23×C3—32no—
313C23×C3—32no—
314C23×C3—32no—
315C23×C3—34no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—62no—
319C23×C3—62no—
320C23×C3—64no—
321C23×C3—64no—
322C23×C3C23×D311yescharacteristic
323C23×C3C23×D311yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—24no—
327C22×D3—24no—
328C22×D3—22no—
329C22×D3—22no—
330C22×D3C22×Dic314yes—
331C22×D3C22×Dic312yes—
332C22×D3C2×#6712yes—
333C22×D3C2×#6712yes—
334C3×Q8—28no—
335C3×Q8—28no—
336C3×Q8—48no—
337C3×D4—616no—
338C3×D4—68no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—24no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—316no—
351C2×C3×C4—34no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—616no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—64no—
358C2×C3×C4—62no—
359C2×C3×C4C2×C4×D314yes—
360C2×C3×C4C2×C4×D312yes—
361C2×C3×C4D3×D412yes—
362C2×C3×C4D3×D412yes—
363C2×C3×C4C22×Dic314yes—
364C2×C3×C4C22×Dic312yes—
365C2×C3×C4C2×#6712yes—
366C2×C3×C4C2×#6712yes—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—24no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
374C2×Dic3—616no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—122no—
386C2×Dic3—124no—
387C2×Dic3#23914yescomplemented
388C2×Dic3C22×Dic312yes—
389C2×Dic3C2×#6712yes—
390C2×Dic3C2×#6712yes—
391D12—216no—
392D12—28no—
393C4×D3—216no—
394C4×D3—616no—
395C4×D3#217116yescomplemented
396C2×C32C22×C22⋊C411yescharacteristic
397C2×C32C4×#4112yes—
398C2×C32#52512yes—
399C2×C32#53211yescharacteristic
400C2×C32#53211yescharacteristic
401C3×D3—24no—
402C3×D3—44no—
403C24—31no—
404C24—32no—
405#41—632no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8D3×Dic314yescomplemented
409C2×D4—38no—
410C2×D4—34no—
411C2×D4—64no—
412C2×D4—64no—
413C2×D4—62no—
414C2×D4—62no—
415C22×C4—31no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—34no—
419C22×C4—32no—
420C22×C4—38no—
421C22×C4—32no—
422C22×C4—64no—
423C22×C4—64no—
424C22×C4—92no—
425C22×C4—92no—
426C22×C4—184no—
427C22×C4—184no—
428C22×C4—184no—
429C22×C4C2×D3212yes—
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—62no—
432C4⋊C4—182no—
433C22⋊C4—188no—
434C22⋊C4—188no—
435C22⋊C4—184no—
436C42—62no—
437C42—184no—
438C42—184no—
439C42—182no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—34no—
446C22×C3—62no—
447C22×C3—62no—
448C22×C3—64no—
449C22×C3—64no—
450C22×C3—64no—
451C22×C3—68no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—124no—
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C2×#23912yes—
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C22×C3D3×#4112yes—
462C22×C3C23×Dic311yescharacteristic
463C22×C3C22×#6711yescharacteristic
464C22×C3C22×#6711yescharacteristic
465C2×D3—24no—
466C2×D3—24no—
467C2×D3—22no—
468C2×D3—22no—
469C2×D3—28no—
470C2×D3—24no—
471C2×D3—44no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3C2×#21714yes—
475C3×C4—24no—
476C3×C4—24no—
477C3×C4—24no—
478C3×C4—34no—
479C3×C4—44no—
480C3×C4—64no—
481C3×C4—122no—
482C3×C4D3×C22⋊C414yes—
483C3×C4C2×#21714yes—
484Dic3—24no—
485Dic3—42no—
486Dic3—64no—
487Dic3—64no—
488Dic3—124no—
489Dic3—122no—
490Dic3—122no—
491Dic3—242no—
492Dic3C2×#21714yes—
493C32#229711yescharacteristic, complemented, Sylow
494C23—32no—
495C23—32no—
496C23—32no—
497C23—34no—
498C23—62no—
499C23—62no—
500C23—64no—
501C23—64no—
502C23—62no—
503C23—62no—
504C23C22×D3211yescharacteristic
505Q8—28no—
506D4—616no—
507D4—68no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—32no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—316no—
514C2×C4—34no—
515C2×C4—616no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—64no—
519C2×C4—62no—
520C2×C4—94no—
521C2×C4—1816no—
522C2×C4—182no—
523C2×C4—182no—
524C2×C4—184no—
525C2×C4—182no—
526C2×C4C2×D3×Dic314yes—
527C2×C4C2×D3×Dic312yes—
528C2×C4D3×#6712yes—
529C2×C4D3×#6712yes—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—64no—
536C2×C3—124no—
537C2×C3C2×D3×C22⋊C411yescharacteristic
538C2×C3C4×#23912yes—
539C2×C3#562712yes—
540C2×C3#566811yescharacteristic
541C2×C3#572511yescharacteristic
542C2×C3Dic3×#4112yes—
543C2×C3#582812yes—
544C2×C3#583211yescharacteristic
545C2×C3#583211yescharacteristic
546C2×C3C22×#21711yescharacteristic
547D3—24no—
548D3—44no—
549C22—34no—
550C22—62no—
551C22—62no—
552C22—64no—
553C22—64no—
554C22—68no—
555C22—64no—
556C22—122no—
557C22—122no—
558C22—124no—
559C22D3×#23912yes—
560C22#6431912yes—
561C22C22×D3×Dic311yescharacteristic
562C22C2×D3×#6711yescharacteristic
563C22C2×D3×#6711yescharacteristic
564C4—24no—
565C4—34no—
566C4—64no—
567C4—122no—
568C4—184no—
569C4—362no—
570C4D3×#21714yes—
571C3—21no—
572C3#7647811yescharacteristic, complemented
573C3#8408611yescharacteristic, complemented
574C2—64no—
575C2—124no—
576C2#1059535911yescharacteristic
577C2#1059536011yescharacteristic
578C2Dic3×#23912yes—
579C2#1059542412yes—
580C2C2×D3×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#239C2
hypercenterC22×Q8D32
hypocenterC32#2297
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Dic3C2semidirect
3. C2×#63841C2semidirect
4. #10592928C2semidirect
5. C3×#5229C2semidirect
6. #10591376C2semidirect
7. #10591323C2semidirect
8. #10591318C2semidirect
9. #10591237C2semidirect
15. C2×C3×#239C4semidirect
44. #5229D3semidirect
57. C2×C32×Q8C2×C4semidirect
71. C2×C3×D12C2×C4semidirect
75. C2×C3×C4×D3C2×C4semidirect
104. C2×#239Dic3semidirect
161. C2×C3⋊Dic3#41semidirect
169. C2×C3×Dic3#41semidirect
173. C3×C4×D3C22⋊C4semidirect
196. C2×C3×Q8C4×D3semidirect
197. C2×C3×Q8C2×Dic3semidirect
237. C2×D12C2×Dic3semidirect
244. C2×C4×D3C2×Dic3semidirect
387. C2×Dic3#239semidirect
395. C4×D3#217semidirect
408. C2×Q8D3×Dic3semidirect
493. C32#2297semidirect
572. C3#76478semidirect
573. C3#84086semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×C4×D3×Dic32
C2×#638412
#105929282
C3×#52292
#105913762
#105913232
#105913182
#105912372
#840863
#764783