Finite Group Databasebeta

← #11856263

Subgroups — #11856263

Order 1152.

3306 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64103C212yesmaximal, complemented
3C2×#64091C211yesmaximal, characteristic
4C32×#385C211yesmaximal, characteristic, complemented
5#10592912C211yesmaximal, characteristic, complemented
6#10592688C212yesmaximal, complemented
7#10592657C211yesmaximal, characteristic, complemented
8#10592654C211yesmaximal, characteristic, complemented
9#10592645C211yesmaximal, characteristic, complemented
10#10592364C212yesmaximal, complemented
11#10592363C212yesmaximal, complemented
12#74656—34nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—28no—
20C22×C4×C3⋊D3—24no—
21C22×C4×C3⋊D3C2212yes—
22C22×C4×C3⋊D3C2212yes—
23C2×C32×C4⋊C4C2212yescomplemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2212yes—
29C2×#3752C2212yes—
30C2×#3752C2211yescharacteristic
31C2×#3752C2212yescomplemented
32C2×#3752C2212yescomplemented
33C2×#3750C2212yescomplemented
34#64103—28no—
35#64091—24no—
36C32×#95C2212yescomplemented
37#63658C2212yescomplemented
38#63658C2212yescomplemented
39#63658C2212yescomplemented
40C23×C4×D3—34no—
41C2×#894—38no—
42C2×#882—34no—
43C3×#385D314yescomplemented
44#5213—34no—
45#4989—38no—
46#4958—34no—
47#4955—34no—
48#4946—34no—
49#4665—38no—
50#4664—38no—
51C24×C32C2311yescharacteristic
52C23×C3⋊D3—22no—
53C23×C3⋊D3—22no—
54C23×C3⋊D3—24no—
55C23×C3⋊D3—24no—
56C23×C3⋊D3D414yes—
57C23×C3⋊D3C2311yescharacteristic
58C23×C3⋊D3C2311yescharacteristic
59C23×C3⋊D3C2311yescharacteristic
60C22×C32×C4—22no—
61C22×C32×C4—24no—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2312yes—
66C2×#638—22no—
67C2×#638—22no—
68C2×#638—22no—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2312yes—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)—24no—
78C2×C4×C3⋊D3—232no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3—24no—
81C2×C4×C3⋊D3—24no—
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3—24no—
84C2×C4×C3⋊D3D418yescomplemented
85C32×C4⋊C4—24no—
86C32×C22⋊C4—22no—
87C32×C22⋊C4—22no—
88#3757—22no—
89#3752—22no—
90#3752—22no—
91#3752—24no—
92#3752—24no—
93#3752—24no—
94#3752—24no—
95#3750—24no—
96#2849—91noSylow
97C24×D3—34no—
98C23×C3×C4C2×D314yes—
99C22×#67—34no—
100C23×Dic3—34no—
101C22×D12—34no—
102C22×D12—34no—
103C22×C4×D3—38no—
104C22×C4×D3—38no—
105C22×C4×D3—632no—
106C22×C4×D3—616no—
107C2×C3×C4⋊C4C2×D318yescomplemented
108C2×C3×C22⋊C4C2×D314yes—
109C2×C3×C22⋊C4C2×D314yes—
110C2×#217—34no—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—38no—
113C2×(C2×D3)⋊C4—38no—
114C2×(C2×D3)⋊C4—38no—
115C2×(C2×D3)⋊C4—38no—
116C2×(C2×D3)⋊C4—34no—
117C2×Dic3⋊C4—38no—
118#894—632no—
119#882—616no—
120C3×#95C2×D318yescomplemented
121C3⋊#95—38no—
122C3⋊#95—38no—
123C3⋊#95—38no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32C2×D412yes—
127C23×C32#4112yes—
128C23×C32#4112yes—
129C23×C32C2411yescharacteristic
130C22×C3⋊D3—216no—
131C22×C3⋊D3—216no—
132C22×C3⋊D3—28no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—28no—
140C22×C3⋊D3—28no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3C2×D414yes—
147C22×C3⋊D3C2×D412yes—
148C22×C3⋊D3C2×D412yes—
149C22×C3⋊D3#4114yes—
150C2×C32×C4—28no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D414yes—
161#638—44no—
162C2×C3⋊Dic3—28no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3C2×D414yes—
172C4⋊(C3⋊D3)—44no—
173C4⋊(C3⋊D3)—44no—
174C4×C3⋊D3—216no—
175C4×C3⋊D3—216no—
176C24×C4—91no—
177C2×#123—92no—
178C2×#120—91no—
179#386—91no—
180#386—91no—
181#386—92no—
182#385—92no—
183#385—91no—
184#385C3⋊D311yescharacteristic, complemented
185#381—92no—
186#379—91no—
187C24×C3C22×D314yes—
188C23×D3—34no—
189C23×D3—34no—
190C23×D3—316no—
191C23×D3—34no—
192C23×D3—616no—
193C23×D3—616no—
194C23×D3—68no—
195C23×D3—68no—
196C22×C3×C4—28no—
197C22×C3×C4—216no—
198C22×C3×C4C22×D314yes—
199C22×C3×C4C22×D318yes—
200C22×C3×C4C22×D314yes—
201C22×C3×C4C22×D318yes—
202C2×#67—68no—
203C2×#67—68no—
204C2×#67—68no—
205C22×Dic3—38no—
206C22×Dic3—34no—
207C22×Dic3—38no—
208C22×Dic3—616no—
209C22×Dic3—68no—
210C2×D12—68no—
211C2×D12—68no—
212C2×D12—616no—
213C2×D12—616no—
214C2×C4×D3—332no—
215C2×C4×D3—616no—
216C2×C4×D3—616no—
217C2×C4×D3—616no—
218C2×C4×D3—616no—
219C2×C4×D3—6128no—
220C2×C4×D3—616no—
221C3×C4⋊C4—216no—
222C3×C22⋊C4—28no—
223C3×C22⋊C4—28no—
224#217—68no—
225(C2×D3)⋊C4—616no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—68no—
228(C2×D3)⋊C4—616no—
229(C2×D3)⋊C4—616no—
230(C2×D3)⋊C4—616no—
231Dic3⋊C4—616no—
232C22×C32—22no—
233C22×C32—22no—
234C22×C32—24no—
235C22×C32—24no—
236C22×C32#12314yescomplemented
237C22×C32C22×D411yescharacteristic
238C22×C32C22×D412yes—
239C22×C32C2×#4111yescharacteristic
240C22×C32C2×#4111yescharacteristic
241C22×C32C2×#4112yes—
242C2×C3⋊D3—232no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3—22no—
246C2×C3⋊D3—22no—
247C2×C3⋊D3—24no—
248C2×C3⋊D3—24no—
249C2×C3⋊D3—24no—
250C2×C3⋊D3—24no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3#12014yes—
257C2×C3⋊D3#12314yescomplemented
258C32×C4—24no—
259C32×C4—41no—
260C32×C4—41no—
261C32×C4—42no—
262C3⋊Dic3—24no—
263C3⋊Dic3—41no—
264C3⋊Dic3—42no—
265C25—91no—
266C22×D4—91no—
267C22×D4—91no—
268C22×D4—91no—
269C23×C4—92no—
270C23×C4—91no—
271C23×C4—92no—
272C23×C4—188no—
273C23×C4—184no—
274C23×C4C2×C3⋊D311yescharacteristic
275#123—188no—
276#120—184no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4C2×C3⋊D312yescomplemented
279C2×C22⋊C4—91no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—91no—
282C2×C22⋊C4—92no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—92no—
286C2×C22⋊C4C2×C3⋊D311yescharacteristic
287C2×C22⋊C4C2×C3⋊D311yescharacteristic
288#95—92no—
289#95—92no—
290#95—92no—
291#95C2×C3⋊D312yescomplemented
292C23×C3—28no—
293C23×C3—28no—
294C23×C3#23518yes—
295C23×C3D3×D418yes—
296C23×C3#23918yes—
297C23×C3C23×D314yes—
298C22×D3—316no—
299C22×D3—38no—
300C22×D3—38no—
301C22×D3—316no—
302C22×D3—632no—
303C22×D3—632no—
304C22×D3—664no—
305C22×D3—664no—
306C22×D3—632no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—68no—
310C22×D3—64no—
311C22×D3—64no—
312C22×D3—68no—
313C22×D3—64no—
314C22×D3—68no—
315C22×D3—64no—
316C22×D3—64no—
317C22×D3—68no—
318C2×C3×C4—232no—
319C2×C3×C4—28no—
320C2×C3×C4—28no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—28no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—28no—
327C2×C3×C4—28no—
328C2×C3×C4D3×D4116yes—
329#67—1216no—
330C2×Dic3—316no—
331C2×Dic3—632no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3—64no—
335C2×Dic3—68no—
336C2×Dic3—64no—
337C2×Dic3—68no—
338C2×Dic3—64no—
339C2×Dic3—68no—
340D12—1216no—
341D12—1216no—
342C4×D3—664no—
343C4×D3—664no—
344C2×C32—24no—
345C2×C32C2×#12011yescharacteristic
346C2×C32C2×#12311yescharacteristic
347C2×C32C2×#12311yescharacteristic
348C2×C32#52512yes—
349C2×C32#52512yes—
350C3⋊D3—24no—
351C3⋊D3—24no—
352C3⋊D3—81no—
353C24—91no—
354C24—91no—
355C24—94no—
356C24—91no—
357C24—184no—
358C24—184no—
359C24—182no—
360C24—182no—
361C24C22×C3⋊D311yescharacteristic
362C2×D4—182no—
363C2×D4—182no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4—182no—
367C2×D4—182no—
368C2×D4—182no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—92no—
372C22×C4—98no—
373C22×C4—91no—
374C22×C4—92no—
375C22×C4—184no—
376C22×C4—184no—
377C22×C4—184no—
378C22×C4—184no—
379C22×C4—1832no—
380C22×C4—184no—
381C22×C4—182no—
382C22×C4—184no—
383C22×C4C22×C3⋊D311yescharacteristic
384C22×C4C22×C3⋊D312yes—
385C22×C4C22×C3⋊D311yescharacteristic
386C22×C4C22×C3⋊D312yes—
387C4⋊C4—24no—
388C4⋊C4—184no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—184no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C22⋊C4—184no—
395C22⋊C4—184no—
396C22⋊C4—182no—
397C22⋊C4—184no—
398C22×C3—28no—
399C22×C3—216no—
400C22×C3—28no—
401C22×C3—216no—
402C22×C3#894116yescomplemented
403C22×C3C2×#23514yes—
404C22×C3C2×D3×D414yes—
405C22×C3C2×D3×D418yes—
406C22×C3C2×#23914yes—
407C22×C3D3×#4118yes—
408C2×D3—316no—
409C2×D3—316no—
410C2×D3—6128no—
411C2×D3—68no—
412C2×D3—68no—
413C2×D3—68no—
414C2×D3—616no—
415C2×D3—616no—
416C2×D3—68no—
417C2×D3—616no—
418C2×D3—616no—
419C2×D3—124no—
420C2×D3—124no—
421C2×D3—128no—
422C2×D3—124no—
423C2×D3—128no—
424C3×C4—216no—
425C3×C4—44no—
426C3×C4—48no—
427C3×C4—44no—
428Dic3—616no—
429Dic3—124no—
430Dic3—128no—
431C32#284911yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—94no—
435C23—92no—
436C23—92no—
437C23—94no—
438C23—188no—
439C23—188no—
440C23—1816no—
441C23—1816no—
442C23—181no—
443C23—181no—
444C23—188no—
445C23—182no—
446C23—181no—
447C23—181no—
448C23—182no—
449C23—181no—
450C23—182no—
451C23—181no—
452C23—181no—
453C23—182no—
454C23#382812yes—
455C23D4×C3⋊D312yes—
456C23#383212yes—
457C23C23×C3⋊D311yescharacteristic
458D4—364no—
459D4—364no—
460D4—364no—
461C2×C4—28no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—94no—
472C2×C4—1816no—
473C2×C4—1816no—
474C2×C4—188no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—182no—
479C2×C4—181no—
480C2×C4—182no—
481C2×C4—181no—
482C2×C4—182no—
483C2×C4D4×C3⋊D314yes—
484C2×C3—216no—
485C2×C3C2×#89414yes—
486C2×C3#554718yes—
487C2×C3D3×#12014yes—
488C2×C3#562718yes—
489C2×C3D3×#12314yes—
490D3—616no—
491D3—616no—
492D3—244no—
493C22—24no—
494C22—22no—
495C22—24no—
496C22—22no—
497C22—94no—
498C22—94no—
499C22—1832no—
500C22—184no—
501C22—184no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22—184no—
506C22—184no—
507C22—182no—
508C22—362no—
509C22—361no—
510C22—361no—
511C22—362no—
512C22—361no—
513C22#6410314yescomplemented
514C22C2×#382811yescharacteristic
515C22C2×D4×C3⋊D312yes—
516C22C2×D4×C3⋊D311yescharacteristic
517C22C2×#383211yescharacteristic
518C22#41×C3⋊D312yes—
519C4—24no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—184no—
524C4—362no—
525C4—361no—
526C3#7465614yescomplemented
527C2—24no—
528C2—184no—
529C2—184no—
530C2—721no—
531C2C2×#6410311yescharacteristic
532C2#1059601812yes—
533C2C3⋊D3×#12011yescharacteristic
534C2#1059609812yes—
535C2C3⋊D3×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#385C2
prime radicalC2×#64091C2
hypercenter#385C3⋊D3
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
2. C2×#64103C2semidirect
4. C32×#385C2semidirect
5. #10592912C2semidirect
6. #10592688C2semidirect
7. #10592657C2semidirect
8. #10592654C2semidirect
9. #10592645C2semidirect
10. #10592364C2semidirect
11. #10592363C2semidirect
23. C2×C32×C4⋊C4C22semidirect
31. C2×#3752C22semidirect
32. C2×#3752C22semidirect
33. C2×#3750C22semidirect
36. C32×#95C22semidirect
37. #63658C22semidirect
38. #63658C22semidirect
39. #63658C22semidirect
43. C3×#385D3semidirect
84. C2×C4×C3⋊D3D4semidirect
107. C2×C3×C4⋊C4C2×D3semidirect
120. C3×#95C2×D3semidirect
184. #385C3⋊D3semidirect
236. C22×C32#123semidirect
257. C2×C3⋊D3#123semidirect
278. C2×C4⋊C4C2×C3⋊D3semidirect
291. #95C2×C3⋊D3semidirect
402. C22×C3#894semidirect
431. C32#2849semidirect
513. C22#64103semidirect
526. C3#74656semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×#641032
C2×#640912
C32×#3852
#105929122
#105926882
#105926572
#105926542
#105926452
#105923642
#105923632
#746563