Finite Group Databasebeta

← #11856285

Subgroups — #11856285

Order 1152.

2535 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×#63975C212yesmaximal, complemented
4C3×#5220C212yesmaximal, complemented
5#10591722C212yesmaximal, complemented
6#10591718C212yesmaximal, complemented
7#10591714C211yesmaximal, characteristic, complemented
8#10591375C212yesmaximal, complemented
9#10591371C212yesmaximal, complemented
10#74936—32nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C22×C32×D4C2211yescharacteristic
13C22×#638C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×#624—28no—
17C22×#624—24no—
18C22×#624C2212yes—
19C22×#624C2212yes—
20C2×#3757C2211yescharacteristic
21#64146—24no—
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2214yescomplemented
26#63975—28no—
27C2×Dic3⋊Dic3C2214yescomplemented
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C3×C3⋊#95C2214yescomplemented
31#63579C2214yescomplemented
32C23×C4×D3—32no—
33C2×#937—32no—
34C2×#937—61no—
35C2×#883—34no—
36C3×#386—32no—
37#5220D312yescomplemented
38#5210—32no—
39#4956—34no—
40#4955—32no—
41#4950—32no—
42#4668—34no—
43#4664—34no—
44C24×C32C2311yescharacteristic
45C24×C32C2311yescharacteristic
46C23×C3⋊D3—24no—
47C23×C3⋊D3—24no—
48C23×C3⋊D3—24no—
49C23×C3⋊D3D414yes—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3⋊D3C2311yescharacteristic
52C2×C32×D4—22no—
53C2×C32×D4—24no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—22no—
56C2×#638—22no—
57C2×#638—24no—
58C2×#638—24no—
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3×Dic3—24no—
62C22×C3×Dic3—28no—
63C22×C3×Dic3C2314yes—
64C22×C3×Dic3C2314yes—
65C2×#624—232no—
66C2×#624—24no—
67C2×#624—24no—
68C2×#624—24no—
69C2×#624—28no—
70C2×#624D418yescomplemented
71#3757—22no—
72#3752—22no—
73#3752—22no—
74C3×#217—24no—
75C3×#217—28no—
76Dic3⋊Dic3—28no—
77#3722—24no—
78#3722—24no—
79#2849—91noSylow
80C24×D3—32no—
81C24×D3—61no—
82C22×C3×D4—21no—
83C22×C3×D4C2×D312yes—
84C23×C3×C4—32no—
85C22×#67—32no—
86C22×#67—32no—
87C22×#67—61no—
88C22×#67—61no—
89C23×Dic3C2×D312yes—
90C22×C4×D3—34no—
91C22×C4×D3—34no—
92C22×C4×D3—616no—
93C22×C4×D3—68no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—34no—
96C2×#217—32no—
97C2×#217—61no—
98C2×#217C2×D312yes—
99C2×#217C2×D314yescomplemented
100#937—68no—
101#937—68no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—34no—
105C2×(C2×D3)⋊C4—34no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×C4⋊Dic3—34no—
109C2×Dic3⋊C4—34no—
110#883—616no—
111C3×#95—34no—
112C3⋊#95—34no—
113C3⋊#95—34no—
114C3⋊#95C2×D314yescomplemented
115C23×C32—21no—
116C23×C32—22no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32C2×D412yes—
122C23×C32#4114yes—
123C23×C32C2411yescharacteristic
124C22×C3⋊D3—232no—
125C22×C3⋊D3—28no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—28no—
131C22×C3⋊D3—28no—
132C22×C3⋊D3C2×D414yes—
133C22×C3⋊D3C2×D412yes—
134C22×C3⋊D3C2×D412yes—
135C22×C3⋊D3#4114yes—
136C32×D4—44no—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139#638—44no—
140#638—44no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3×Dic3—216no—
146C2×C3×Dic3—24no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3C2×D418yes—
152#624—216no—
153#624—216no—
154C24×C4—91no—
155C2×#123—92no—
156C2×#120—91no—
157#386—32no—
158#386—92no—
159#385—92no—
160#385—92no—
161#381—92no—
162#379—91no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3C22×D312yes—
166C24×C3C22×D312yes—
167C23×D3—32no—
168C23×D3—32no—
169C23×D3—38no—
170C23×D3—61no—
171C23×D3—61no—
172C23×D3—64no—
173C23×D3—68no—
174C23×D3—68no—
175C23×D3—64no—
176C23×D3—64no—
177C23×D3—124no—
178C23×D3—124no—
179C23×D3—124no—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4—24no—
183C2×C3×D4—24no—
184C2×C3×D4—44no—
185C22×C3×C4—21no—
186C22×C3×C4—34no—
187C22×C3×C4—34no—
188C22×C3×C4—68no—
189C22×C3×C4—64no—
190C22×C3×C4C22×D312yes—
191C2×#67—68no—
192C2×#67—64no—
193C2×#67—64no—
194C2×#67—68no—
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—124no—
198C2×#67—124no—
199C22×Dic3—24no—
200C22×Dic3—28no—
201C22×Dic3—32no—
202C22×Dic3—32no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3C22×D314yes—
206C22×Dic3C22×D314yes—
207C2×C4×D3—316no—
208C2×C4×D3—68no—
209C2×C4×D3—68no—
210C2×C4×D3—68no—
211C2×C4×D3—68no—
212C2×C4×D3—664no—
213C2×C4×D3—68no—
214C3×C22⋊C4—68no—
215C3×C22⋊C4—64no—
216#217—24no—
217#217—28no—
218#217—64no—
219#217—64no—
220(C2×D3)⋊C4—68no—
221(C2×D3)⋊C4—68no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—68no—
227Dic3⋊C4—68no—
228C22×C32—22no—
229C22×C32—22no—
230C22×C32—28no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—44no—
235C22×C32#12314yescomplemented
236C22×C32C22×D411yescharacteristic
237C22×C32C22×D412yes—
238C22×C32C2×#4112yes—
239C22×C32C2×#4112yes—
240C2×C3⋊D3—232no—
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3—28no—
246C2×C3⋊D3—28no—
247C2×C3⋊D3#12014yes—
248C2×C3⋊D3#12314yescomplemented
249C32×C4—41no—
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C3×Dic3—28no—
253C3×Dic3—44no—
254C25—91no—
255C22×D4—91no—
256C22×D4—91no—
257C22×D4D3211yescharacteristic
258C23×C4—32no—
259C23×C4—92no—
260C23×C4—92no—
261C23×C4—188no—
262C23×C4—184no—
263#123—188no—
264#120—184no—
265C2×C4⋊C4—94no—
266C2×C22⋊C4—34no—
267C2×C22⋊C4—32no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—91no—
271C2×C22⋊C4—91no—
272C2×C22⋊C4—91no—
273#95—34no—
274#95—94no—
275C23×C3—24no—
276C23×C3—24no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—24no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—24no—
283C23×C3—21no—
284C23×C3—24no—
285C23×C3—22no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—42no—
291C23×C3#23514yes—
292C23×C3D3×D414yes—
293C23×C3#23714yes—
294C23×C3C23×D312yes—
295C22×D3—38no—
296C22×D3—34no—
297C22×D3—34no—
298C22×D3—38no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—64no—
302C22×D3—64no—
303C22×D3—616no—
304C22×D3—616no—
305C22×D3—632no—
306C22×D3—632no—
307C22×D3—616no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—64no—
314C22×D3—128no—
315C22×D3—128no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—128no—
321C22×D3—1232no—
322C3×D4—48no—
323C3×D4—48no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—38no—
329C2×C3×C4—42no—
330C2×C3×C4—616no—
331C2×C3×C4—64no—
332C2×C3×C4—64no—
333C2×C3×C4—64no—
334C2×C3×C4—64no—
335C2×C3×C4—64no—
336#67—128no—
337#67—128no—
338#67—128no—
339#67—128no—
340C2×Dic3—216no—
341C2×Dic3—24no—
342C2×Dic3—24no—
343C2×Dic3—24no—
344C2×Dic3—24no—
345C2×Dic3—24no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—64no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—64no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3D3×D418yes—
355C4×D3—632no—
356C4×D3—632no—
357C2×C32—24no—
358C2×C32—81no—
359C2×C32C2×#12011yescharacteristic
360C2×C32C2×#12311yescharacteristic
361C2×C32C2×#12311yescharacteristic
362C2×C32#52514yes—
363C3⋊D3—24no—
364C3⋊D3—24no—
365C24—91no—
366C24—91no—
367C24—94no—
368C24—184no—
369C24—184no—
370C24—184no—
371C24C2×D3211yescharacteristic
372C24C2×D3211yescharacteristic
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—182no—
376C2×D4—182no—
377C2×D4—184no—
378C2×D4—184no—
379C22×C4—34no—
380C22×C4—34no—
381C22×C4—68no—
382C22×C4—64no—
383C22×C4—98no—
384C22×C4—91no—
385C22×C4—91no—
386C22×C4—188no—
387C22×C4—184no—
388C22×C4—184no—
389C22×C4—184no—
390C22×C4—1832no—
391C22×C4C2×D3211yescharacteristic
392C4⋊C4—188no—
393C22⋊C4—68no—
394C22⋊C4—64no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C22⋊C4—184no—
398C22⋊C4—184no—
399C22⋊C4—182no—
400C22×C3—24no—
401C22×C3—28no—
402C22×C3—24no—
403C22×C3—28no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—24no—
409C22×C3—48no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—44no—
418C22×C3—42no—
419C22×C3—44no—
420C22×C3—84no—
421C22×C3#88318yescomplemented
422C22×C3C2×#23512yes—
423C22×C3C2×D3×D414yes—
424C22×C3C2×D3×D412yes—
425C22×C3C2×#23712yes—
426C22×C3D3×#4114yes—
427C2×D3—38no—
428C2×D3—38no—
429C2×D3—64no—
430C2×D3—64no—
431C2×D3—664no—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—68no—
436C2×D3—68no—
437C2×D3—64no—
438C2×D3—68no—
439C2×D3—68no—
440C2×D3—128no—
441C2×D3—128no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—1232no—
447C3×C4—42no—
448C3×C4—42no—
449C3×C4—68no—
450C3×C4—124no—
451Dic3—28no—
452Dic3—44no—
453Dic3—122no—
454Dic3—122no—
455Dic3—122no—
456Dic3—122no—
457C32#284911yescharacteristic, complemented, Sylow
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—21no—
464C23—94no—
465C23—94no—
466C23—92no—
467C23—92no—
468C23—188no—
469C23—188no—
470C23—1832no—
471C23—182no—
472C23—182no—
473C23—182no—
474C23—182no—
475C23—188no—
476C23#380414yes—
477C23#381112yes—
478C23C22×D3211yescharacteristic
479D4—44no—
480D4—364no—
481D4—364no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—38no—
485C2×C4—616no—
486C2×C4—64no—
487C2×C4—64no—
488C2×C4—64no—
489C2×C4—64no—
490C2×C4—64no—
491C2×C4—1816no—
492C2×C4—1816no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C3—28no—
498C2×C3—24no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—44no—
503C2×C3—82no—
504C2×C3—82no—
505C2×C3C2×#88312yes—
506C2×C3#554714yes—
507C2×C3D3×#12012yes—
508C2×C3#560614yes—
509C2×C3D3×#12312yes—
510D3—68no—
511D3—68no—
512D3—124no—
513D3—124no—
514C22—28no—
515C22—22no—
516C22—22no—
517C22—44no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—94no—
522C22—94no—
523C22—1832no—
524C22—188no—
525C22—188no—
526C22—182no—
527C22—182no—
528C22—182no—
529C22—182no—
530C22#6397514yescomplemented
531C22D32×D412yes—
532C22#6431212yes—
533C22C2×#380412yes—
534C22C2×#381111yescharacteristic
535C4—41no—
536C4—68no—
537C4—124no—
538C4—361no—
539C4—361no—
540C3—21no—
541C3#7493612yescomplemented
542C2—24no—
543C2—81no—
544C2—184no—
545C2—184no—
546C2#1059513814yes—
547C2#1059516911yescharacteristic
548C2#1059527811yescharacteristic
549C2C2×#6397511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
3. C2×#63975C2semidirect
4. C3×#5220C2semidirect
5. #10591722C2semidirect
6. #10591718C2semidirect
7. #10591714C2semidirect
8. #10591375C2semidirect
9. #10591371C2semidirect
25. C2×C3×#217C22semidirect
27. C2×Dic3⋊Dic3C22semidirect
30. C3×C3⋊#95C22semidirect
31. #63579C22semidirect
37. #5220D3semidirect
70. C2×#624D4semidirect
99. C2×#217C2×D3semidirect
114. C3⋊#95C2×D3semidirect
235. C22×C32#123semidirect
248. C2×C3⋊D3#123semidirect
421. C22×C3#883semidirect
457. C32#2849semidirect
530. C22#63975semidirect
541. C3#74936semidirect

Maximal subgroups

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

subgroupindex
C23×#6242
C2×#641462
C2×#639752
C3×#52202
#105917222
#105917182
#105917142
#105913752
#105913712
#749363