Finite Group Databasebeta

← #11788857

Subgroups — #11788857

Order 1152.

933 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596275C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic, complemented
3C2×C3×#834C211yesmaximal, characteristic, complemented
4C2×#63581C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71656—31nomaximal
7#70024—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#638C2211yescharacteristic
10#64162—21no—
11C2×#3757C2211yescharacteristic
12#64148—22no—
13#64146C412yescomplemented
14#64144C412yescomplemented
15#64138—21no—
16C2×C3×#217—21no—
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C3×D4×Dic3—24no—
20C3×#926—21no—
21C3×#834—22no—
22#63581—24no—
23C3×#518—31no—
24#5804—31no—
25#5804—31no—
26#5804—61no—
27#5798D311yescharacteristic, complemented
28C2×C3×#99—31no—
29C2×#834D311yescharacteristic, complemented
30C2×#806—32no—
31C2×#806—32no—
32#4527—32no—
33#4526—32no—
34C24×C32D411yescharacteristic
35C24×C32C2311yescharacteristic
36C23×C3⋊D3C2×C411yescharacteristic, complemented
37C2×C32×D4—22no—
38C2×C32×D4—22no—
39C2×C32×D4C2×C412yes—
40C2×C32×D4D412yes—
41C22×C32×C4D411yescharacteristic
42C2×#638—21no—
43C2×#638—21no—
44C2×#638—22no—
45C2×#638—22no—
46C2×#638—22no—
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3C2×C411yescharacteristic, complemented
49C22×C3×Dic3—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—22no—
52#3757—22no—
53#3757—21no—
54#3757C2×C412yescomplemented
55#3752—22no—
56#3750—22no—
57C3×#217—22no—
58C3×#217—22no—
59C3×#217—22no—
60C3×#217—22no—
61C3×#217D414yescomplemented
62C3×C4⋊Dic3—22no—
63C3×C4×Dic3—22no—
64#1913—91noSylow
65C22×C3×D4—21no—
66C22×C3×D4C2×D311yescharacteristic
67C22×C3×D4C2×D311yescharacteristic
68C22×#67—31no—
69C22×#67—31no—
70C22×#67—61no—
71C3×C4×D4—64no—
72C3×#117—61no—
73C2×C3×C22⋊C4—32no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4—61no—
76#953—62no—
77#953—61no—
78#953—61no—
79C2×#217—21no—
80C2×#217—31no—
81C2×#217—31no—
82C2×#217—61no—
83C2×#217C2×D312yes—
84C2×#217C2×D312yes—
85#939—64no—
86#939—62no—
87#939—62no—
88#937—32no—
89#937—32no—
90#937—62no—
91#935—32no—
92#935—32no—
93#935—62no—
94D4×Dic3—24no—
95#929—62no—
96#929—61no—
97#929—61no—
98#926—21no—
99C3×#99—62no—
100#834—22no—
101#806—64no—
102#806—64no—
103C23×C32—21no—
104C23×C32—21no—
105C23×C32—81no—
106C23×C32—81no—
107C23×C32C22⋊C412yes—
108C23×C32C22×C411yescharacteristic
109C23×C32C2×D411yescharacteristic
110C23×C32C2×D411yescharacteristic
111C23×C32C2×D412yes—
112C23×C32#4112yes—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—81no—
116C32×D4—24no—
117C32×D4—24no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22⋊C412yes—
121#638—41no—
122#638—42no—
123#638—41no—
124#638—82no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—81no—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—82no—
132C2×C3×Dic3—82no—
133C2×C3×Dic3—82no—
134#534—91no—
135#518—31no—
136C2×#99—31no—
137C2×#99—92no—
138#342—92no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3D1211yescharacteristic
142C24×C3#6711yescharacteristic
143C24×C3C22×D311yescharacteristic
144C24×C3C22×D311yescharacteristic
145C23×D3—31no—
146C23×D3—31no—
147C23×D3—61no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—42no—
155C2×C3×D4—42no—
156C2×C3×D4C4×D312yes—
157C2×C3×D4C4×D312yes—
158C2×C3×D4D1212yes—
159C2×C3×D4#6712yes—
160C22×C3×C4—21no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4—62no—
164C22×C3×C4D1211yescharacteristic
165C22×C3×C4#6711yescharacteristic
166C2×#67—62no—
167C2×#67—62no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—62no—
171C2×#67—62no—
172C2×#67—62no—
173C2×#67—62no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—64no—
177C2×#67—62no—
178C2×#67—62no—
179C2×#67—122no—
180C2×#67—122no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—61no—
187C22×Dic3—62no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C3×C4⋊C4—62no—
191C3×C22⋊C4—34no—
192C3×C22⋊C4—62no—
193C3×C22⋊C4—62no—
194C3×C22⋊C4—62no—
195C3×C22⋊C4—62no—
196C3×C42—62no—
197#217—22no—
198#217—22no—
199#217—22no—
200#217—22no—
201#217—32no—
202#217—32no—
203#217—62no—
204#217—62no—
205#217—64no—
206#217—62no—
207#217—62no—
208#217—61no—
209#217—61no—
210#217#6714yescomplemented
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—62no—
214C4⋊Dic3—22no—
215Dic3⋊C4—64no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218C4×Dic3—22no—
219C22×C32—22no—
220C22×C32—41no—
221C22×C32—41no—
222C22×C32—41no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32—42no—
226C22×C32—42no—
227C22×C32—81no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C4×D412yes—
230C22×C32#12011yescharacteristic
231C22×C32#12112yes—
232C22×C32#12311yescharacteristic
233C2×C3⋊D3—42no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—82no—
236C32×C4—22no—
237C3⋊Dic3—42no—
238C3⋊Dic3—41no—
239C3×Dic3—44no—
240C3×Dic3—82no—
241C22×D4—91no—
242C22×D4D3211yescharacteristic
243#123—92no—
244#123—181no—
245#121—182no—
246#120—92no—
247#120—181no—
248C4×D4—64no—
249#117—61no—
250C2×C22⋊C4—32no—
251C2×C22⋊C4—32no—
252C2×C22⋊C4—61no—
253C2×C22⋊C4—91no—
254#99—62no—
255#99—184no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—22no—
266C23×C3—41no—
267C23×C3—41no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3—81no—
271C23×C3—81no—
272C23×C3—82no—
273C23×C3—82no—
274C23×C3(C2×D3)⋊C412yes—
275C23×C3(C2×D3)⋊C412yes—
276C23×C3C2×C4×D311yescharacteristic
277C23×C3C2×C4×D311yescharacteristic
278C23×C3C2×D1211yescharacteristic
279C23×C3C2×D1211yescharacteristic
280C23×C3#23512yes—
281C23×C3D3×D412yes—
282C23×C3#23712yes—
283C23×C3C2×#6711yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C23×C3C2×#6712yes—
286C22×D3—62no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—122no—
292C22×D3—242no—
293C22×D3—241no—
294C22×D3—241no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—24no—
299C3×D4—44no—
300C3×D4—44no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—64no—
309C2×C3×C4—122no—
310C2×C3×C4—242no—
311C2×C3×C4—242no—
312C2×C3×C4—242no—
313C2×C3×C4(C2×D3)⋊C412yes—
314C2×C3×C4(C2×D3)⋊C412yes—
315#67—122no—
316#67—122no—
317#67—124no—
318#67—121no—
319#67—121no—
320#67—121no—
321#67—122no—
322#67—122no—
323#67—121no—
324#67—242no—
325#67—242no—
326#67—244no—
327C2×Dic3—24no—
328C2×Dic3—42no—
329C2×Dic3—62no—
330C2×Dic3—64no—
331C2×Dic3—62no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—82no—
338C2×Dic3—82no—
339C2×Dic3—82no—
340C2×Dic3—122no—
341C2×Dic3—241no—
342C2×Dic3—241no—
343C2×Dic3—242no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—22no—
347C2×C32—22no—
348C2×C32—21no—
349C2×C32—42no—
350C2×C32#38611yescharacteristic
351C3⋊D3—81no—
352C24—91no—
353C24#62611yescharacteristic
354C24C2×D3211yescharacteristic
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—182no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—182no—
361C2×D4—182no—
362C2×D4#62412yes—
363C2×D4#62612yes—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4—62no—
367C22×C4—91no—
368C22×C4—181no—
369C22×C4#62611yescharacteristic
370C4⋊C4—62no—
371C4⋊C4—182no—
372C22⋊C4—34no—
373C22⋊C4—62no—
374C22⋊C4—62no—
375C22⋊C4—62no—
376C22⋊C4—62no—
377C22⋊C4—92no—
378C22⋊C4—182no—
379C22⋊C4—181no—
380C22⋊C4—182no—
381C42—62no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—42no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—44no—
408C22×C3—82no—
409C22×C3—82no—
410C22×C3—82no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—82no—
414C22×C3#67⋊C412yes—
415C22×C3#88211yescharacteristic
416C22×C3#88611yescharacteristic
417C22×C3C2×(C2×D3)⋊C411yescharacteristic
418C22×C3C2×(C2×D3)⋊C411yescharacteristic
419C22×C3C4×#6712yes—
420C22×C3#92911yescharacteristic
421C22×C3#93012yes—
422C22×C3#93912yes—
423C22×C3#95311yescharacteristic
424C2×D3—122no—
425C2×D3—124no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—244no—
431C2×D3—242no—
432C2×D3—242no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—42no—
436C3×C4—124no—
437C3×C4—242no—
438Dic3—44no—
439Dic3—82no—
440Dic3—122no—
441Dic3—124no—
442Dic3—122no—
443Dic3—122no—
444Dic3—121no—
445Dic3—121no—
446C32#191311yescharacteristic, complemented, Sylow
447C23—21no—
448C23—21no—
449C23—81no—
450C23—81no—
451C23—181no—
452C23—182no—
453C23—721no—
454C23#372212yes—
455C23#380412yes—
456C23C2×#62411yescharacteristic
457C23C2×#62611yescharacteristic
458C23C2×#62611yescharacteristic
459C23D3×#6712yes—
460D4—24no—
461D4—24no—
462D4—361no—
463D4—361no—
464D4—362no—
465D4—722no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—64no—
469C2×C4—122no—
470C2×C4—182no—
471C2×C4—182no—
472C2×C4—181no—
473C2×C4—242no—
474C2×C4—242no—
475C2×C4—242no—
476C2×C4—721no—
477C2×C4#372212yes—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—22no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—22no—
487C2×C3—22no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—42no—
491C2×C3—41no—
492C2×C3—41no—
493C2×C3—42no—
494C2×C3—42no—
495C2×C3—42no—
496C2×C3—82no—
497C2×C3#495811yescharacteristic
498C2×C3#521311yescharacteristic
499D3—242no—
500D3—241no—
501D3—241no—
502C22—22no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—81no—
511C22—362no—
512C22—361no—
513C22—722no—
514C22#6395212yes—
515C22C2×#372211yescharacteristic
516C22#6396611yescharacteristic
517C22#6397711yescharacteristic
518C22#6397812yes—
519C4—22no—
520C4—124no—
521C4—242no—
522C4—362no—
523C4—361no—
524C3—21no—
525C3#7002411yescharacteristic, complemented
526C3#7165611yescharacteristic, complemented
527C2—21no—
528C2—22no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—42no—
533C2—721no—
534C2#1059171111yescharacteristic
subgroupG/H
centerC2#10591711
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radical#10596275C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5798C2semidirect
3. C2×C3×#834C2semidirect
4. C2×#63581C2semidirect
5. #10589186C2semidirect
13. #64146C4semidirect
14. #64144C4semidirect
27. #5798D3semidirect
29. C2×#834D3semidirect
36. C23×C3⋊D3C2×C4semidirect
48. C22×C3⋊Dic3C2×C4semidirect
54. #3757C2×C4semidirect
61. C3×#217D4semidirect
210. #217#67semidirect
446. C32#1913semidirect
525. C3#70024semidirect
526. C3#71656semidirect

Maximal subgroups

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

subgroupindex
#105962752
C3×#57982
C2×C3×#8342
C2×#635812
#105891862
#716563
#700243