Finite Group Databasebeta

← #11866204

Subgroups — #11866204

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C3×#5798C211yesmaximal, characteristic, complemented
3C2×C3×#932C211yesmaximal, characteristic, complemented
4#10595045C211yesmaximal, characteristic, complemented
5#10591481C214yesmaximal, complemented
6#10591471C214yesmaximal, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10591096C211yesmaximal, characteristic, complemented
9#10591083C211yesmaximal, characteristic, complemented
10#83934—31nomaximal
11#82540—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×#3753—24no—
16C2×#3753C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yescomplemented
21C2×C3×#214C2212yescomplemented
22C3×#932—24no—
23C2×C3×#213C2212yescomplemented
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63981—22no—
28#63911C2212yescomplemented
29#63909—22no—
30#63864C2212yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63565C2212yescomplemented
33#63564C2214yescomplemented
34#63562C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C3×#518—31no—
37#5830—31no—
38#5798D311yescharacteristic, complemented
39C2×#932D311yescharacteristic, complemented
40C22×#213—31no—
41C22×#213—31no—
42C22×#213—61no—
43#5525—31no—
44#5233—31no—
45#5165—34no—
46#5150—34no—
47#5131—31no—
48#5119—31no—
49#5016—34no—
50#5015—34no—
51#5002—31no—
52#5001—31no—
53#4999—31no—
54C24×C32—21no—
55C23×C3⋊D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4D414yescomplemented
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C3×#67—21no—
66C22×C3×Dic3—24no—
67C3×#235—22no—
68C3×#235—22no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#626—24no—
73#3753—28no—
74C2×C3⋊(C3⋊C8)—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—21no—
77C3×#217—24no—
78C3×#217D412yes—
79C3×#214—24no—
80C3×#213—24no—
81C3×C4⋊Dic3D412yes—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×C4×Dic3C2312yes—
85C3×#208—22no—
86C2×C3×C3⋊C8C2312yes—
87#3722—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C2×#235C2×D311yescharacteristic
94C22×D12—31no—
95C22×D12—31no—
96C22×D12—61no—
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—32no—
99C2×C3×D8—32no—
100C2×C3×M16—31no—
101C3×C4×D4—34no—
102C3×C4×D4—62no—
103C3×#117—31no—
104C3×#117—31no—
105C2×C3×C22⋊C4—62no—
106C2×#217—22no—
107#947—32no—
108#940—32no—
109#937—62no—
110D4×Dic3—22no—
111D4×Dic3C2×D314yescomplemented
112C2×#214C2×D312yescomplemented
113#932—24no—
114C2×#213—34no—
115C2×#213—34no—
116C2×#213—64no—
117C2×#213—68no—
118C2×#213—64no—
119C2×#213—64no—
120C2×#213C2×D312yescomplemented
121#930—62no—
122#926C2×D311yescharacteristic
123#926C2×D311yescharacteristic
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8—31no—
126C22×C3⋊C8—31no—
127C22×C3⋊C8—61no—
128#895—62no—
129#882—62no—
130#875—32no—
131#874—32no—
132#835—32no—
133#832—32no—
134#821—34no—
135Dic3⋊C8—34no—
136#810—32no—
137#809—32no—
138#809—34no—
139C4⋊(C3⋊C8)—34no—
140C23×C32—22no—
141C23×C32—24no—
142C23×C32—82no—
143C23×C32C2×D411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—82no—
147C22×C3×D3—21no—
148C32×D4—24no—
149C32×D4—22no—
150C32×D4C2×D414yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—42no—
158C3×#67—42no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—84no—
162C2×C3×Dic3C2×D414yes—
163C3×D12—21no—
164C3×D12—21no—
165C3×C4×D3—42no—
166C3×Dic6—21no—
167C3×Dic6—21no—
168#626—84no—
169C3⋊(C3⋊C8)—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—31no—
172C22×D8—91no—
173#535—91no—
174#518—31no—
175#463—94no—
176#459—94no—
177#424—91no—
178#418—91no—
179#416—91no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—41no—
183C23×D3—61no—
184C23×D3—61no—
185C23×D3—121no—
186C3×#41—62no—
187C3×#41—62no—
188C2×C3×Q8—31no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—24no—
194C2×C3×D4—22no—
195C2×C3×D4—31no—
196C2×C3×D4—42no—
197C2×C3×D4—41no—
198C2×C3×D4—61no—
199C2×C3×D4D1214yescomplemented
200C2×C3×D4#6714yescomplemented
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—21no—
204C22×C3×C4—64no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—21no—
209C2×#67—64no—
210C22×Dic3—24no—
211#235—22no—
212#235—22no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—62no—
216C2×D12—64no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—64no—
224C2×D12—122no—
225C2×D12—121no—
226C2×D12C22×D311yescharacteristic
227C2×C4×D3—21no—
228C2×Dic6C22×D311yescharacteristic
229C3×SD16—64no—
230C3×D8—64no—
231C3×M16—62no—
232C2×C3×C8—32no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C22⋊C4—32no—
236C3×C22⋊C4—64no—
237C3×C22⋊C4—61no—
238C3×C42—32no—
239C3×C42—61no—
240#217—21no—
241#217—24no—
242#217#6712yes—
243#214—24no—
244#213—24no—
245#213—616no—
246#213—68no—
247#213—68no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250C4⋊Dic3#6712yes—
251C4⋊Dic3C22×D312yes—
252C4×Dic3—21no—
253C4×Dic3C22×D312yes—
254#208—22no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—64no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8C22×D312yes—
262C22×C32—22no—
263C22×C32—24no—
264C22×C32—44no—
265C22×C32—84no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—42no—
269C2×C3⋊D3—44no—
270C2×C3⋊D3—84no—
271C2×C3×D3—41no—
272C2×C3×D3—42no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C2×#41—31no—
280C22×D4—91no—
281C22×D4D3211yescharacteristic
282AGL(1,ℤ/8)—64no—
283C2×SD16—32no—
284C2×D8—32no—
285C2×D8—94no—
286C2×D8—184no—
287C2×M16—31no—
288C22×C8—91no—
289#127—92no—
290#124—92no—
291#121—182no—
292#120—182no—
293C4×D4—34no—
294C4×D4—62no—
295#117—31no—
296#117—31no—
297C2×C22⋊C4—62no—
298C4⋊C8—94no—
299#103—92no—
300#102—94no—
301#102—92no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—21no—
307C23×C3—42no—
308C23×C3—44no—
309C23×C3—61no—
310C23×C3—82no—
311C23×C3—82no—
312C23×C3—84no—
313C23×C3D3×D411yescharacteristic
314C23×C3C2×#6711yescharacteristic
315C22×D3—21no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C22×D3—124no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—242no—
323C22×D3—242no—
324C22×D3—244no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—24no—
328C3×D4—24no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—24no—
332C3×D4—42no—
333C3×D4—44no—
334C3×D4—61no—
335C3×D4—61no—
336C3×D4—122no—
337C3×D4C2×D1214yes—
338C3×D4C2×#6714yes—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—34no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—122no—
347C2×C3×C4—244no—
348C2×C3×C4C2×D1212yes—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23712yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—42no—
357#67—244no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—84no—
361C2×Dic3C2×#6714yes—
362D12—21no—
363D12—21no—
364D12—64no—
365D12—62no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—122no—
370D12—124no—
371D12—122no—
372D12—122no—
373D12—244no—
374C4×D3—42no—
375Dic6—21no—
376Dic6—21no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—64no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32—22no—
383C2×C32—44no—
384C2×C32C2×#12111yescharacteristic
385C2×C32#57612yes—
386C3⋊D3—82no—
387C3×D3—81no—
388C24—21no—
389C24—181no—
390#41—62no—
391#41—62no—
392C2×Q8—31no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—31no—
396C2×D4—61no—
397C2×D4—92no—
398C2×D4—184no—
399C2×D4—182no—
400C2×D4—182no—
401C2×D4—181no—
402C2×D4#62614yescomplemented
403C2×D4C2×D3212yes—
404C22×C4—64no—
405C22×C4—61no—
406C22×C4C2×D3211yescharacteristic
407SD16—64no—
408D8—64no—
409D8—188no—
410M16—62no—
411C2×C8—32no—
412C2×C8—92no—
413C2×C8—182no—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C22⋊C4—32no—
417C22⋊C4—64no—
418C22⋊C4—61no—
419C22⋊C4—184no—
420C42—32no—
421C42—61no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—84no—
433C22×C3—84no—
434C22×C3—84no—
435C22×C3—88no—
436C22×C3—121no—
437C22×C3—122no—
438C22×C3#93012yes—
439C22×C3#93912yes—
440C22×C3C2×D3×D411yescharacteristic
441C22×C3C22×#6711yescharacteristic
442C2×D3—42no—
443C2×D3—41no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—124no—
449C2×D3—244no—
450C2×D3—248no—
451C2×D3—244no—
452C2×D3—244no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—64no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4#93012yes—
460C3×C4#93912yes—
461C3×C4C22×D1211yescharacteristic
462C3×C4C2×#23511yescharacteristic
463C3×C4C2×#23711yescharacteristic
464C3×C4C22×#6711yescharacteristic
465Dic3—24no—
466Dic3—41no—
467Dic3—42no—
468C32#304111yescharacteristic, complemented, Sylow
469C23—22no—
470C23—24no—
471C23—61no—
472C23—82no—
473C23—182no—
474C23—362no—
475C23—722no—
476C23D3×#6711yescharacteristic
477Q8—61no—
478Q8—61no—
479D4—22no—
480D4—24no—
481D4—61no—
482D4—61no—
483D4—122no—
484D4—182no—
485D4—182no—
486D4—362no—
487D4—724no—
488D4C2×#62614yes—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—122no—
493C2×C4—244no—
494C2×C4#380412yes—
495C2×C4C2×#62612yes—
496C2×C4D3×#6711yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—62no—
499C8—182no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—44no—
506C2×C3—44no—
507C2×C3—84no—
508C2×C3—241no—
509C2×C3#577412yes—
510C2×C3C2×#93011yescharacteristic
511C2×C3C2×#93911yescharacteristic
512C2×C3#583512yes—
513D3—81no—
514D3—244no—
515D3—242no—
516D3—242no—
517C22—22no—
518C22—24no—
519C22—44no—
520C22—84no—
521C22—122no—
522C22—121no—
523C22—364no—
524C22—362no—
525C22—724no—
526C22#6397812yes—
527C22C2×D3×#6711yescharacteristic
528C4—64no—
529C4—122no—
530C4—121no—
531C4#6397812yes—
532C4C2×#380411yescharacteristic
533C4C22×#62611yescharacteristic
534C3—21no—
535C3#8254011yescharacteristic, complemented
536C3#8393411yescharacteristic, complemented
537C2—22no—
538C2—44no—
539C2—241no—
540C2—722no—
541C2#1059509712yes—
542C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3041
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. C22×#3753C2semidirect
2. C3×#5798C2semidirect
3. C2×C3×#932C2semidirect
4. #10595045C2semidirect
5. #10591481C2semidirect
6. #10591471C2semidirect
7. #10591117C2semidirect
8. #10591096C2semidirect
9. #10591083C2semidirect
20. C3×D4×Dic3C22semidirect
21. C2×C3×#214C22semidirect
23. C2×C3×#213C22semidirect
28. #63911C22semidirect
30. #63864C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63565C22semidirect
33. #63564C22semidirect
34. #63562C22semidirect
38. #5798D3semidirect
39. C2×#932D3semidirect
58. C2×C32×D4D4semidirect
111. D4×Dic3C2×D3semidirect
112. C2×#214C2×D3semidirect
120. C2×#213C2×D3semidirect
199. C2×C3×D4D12semidirect
200. C2×C3×D4#67semidirect
402. C2×D4#626semidirect
468. C32#3041semidirect
535. C3#82540semidirect
536. C3#83934semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C3×#57982
C2×C3×#9322
#105950452
#105914812
#105914712
#105911172
#105910962
#105910832
#839343
#825403