Finite Group Databasebeta

← #11866368

Subgroups — #11866368

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic
3#10594818C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5#10592830C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590801C214yesmaximal, complemented
9#10590799C214yesmaximal, complemented
10#83969—31nomaximal
11#79099—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#909—24no—
20C2×C3×Dic12C2212yescomplemented
21C2×C3×#204C2212yescomplemented
22#63981—22no—
23#63955—22no—
24#63911C2212yes—
25#63909—22no—
26#63864C2212yes—
27#63843—22no—
28Dic3×Dic6C2214yescomplemented
29C2×#3717—24no—
30C2×#3717C2214yes—
31#63648C2214yes—
32C3×Dic3⋊C8C2214yescomplemented
33#63566C2212yescomplemented
34#63563C2212yescomplemented
35C2×C3×#137—31no—
36#5830—31no—
37#5812—31no—
38C22×#215—31no—
39C2×#909D311yescharacteristic, complemented
40C22×#204—31no—
41#5525—31no—
42#5516—31no—
43C3×#424—31no—
44#5233—31no—
45#5185—34no—
46#5163—34no—
47#5131—31no—
48#5131—31no—
49#5131—61no—
50#5119D311yescharacteristic, complemented
51#5113—31no—
52#4848—34no—
53#4845—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C3×#67—21no—
61C22×C3×Dic3—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12C2311yescharacteristic
65C2×C3×C4×D3—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6D414yescomplemented
69C2×C3×Dic6C2311yescharacteristic
70C2×C3×Dic6C2312yes—
71C2×#626—24no—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74#3757—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C4×C3⋊Dic3—21no—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82C3×Dic12—24no—
83C3×#204—24no—
84Dic3⋊Dic3—24no—
85#3722—24no—
86Dic32—24no—
87#3717—28no—
88#3043—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×Dic6C2×D311yescharacteristic
96C3×#137—64no—
97C2×C3×Q16—32no—
98C2×C3×SD16—32no—
99C2×C3×M16—21no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102C22×C3×C8—31no—
103C3×#117—31no—
104#947—32no—
105Q8×Dic3—34no—
106Q8×Dic3—62no—
107C2×#215—34no—
108C2×#215—64no—
109#940—32no—
110#937—62no—
111#930—62no—
112#926—31no—
113#926—31no—
114#926—61no—
115#926—62no—
116#926C2×D311yescharacteristic
117C22×C3⋊C8C2×D311yescharacteristic
118#909—24no—
119C2×Dic12C2×D312yescomplemented
120C2×#204—34no—
121C2×#204—64no—
122C2×#204C2×D312yescomplemented
123#895—62no—
124#887—62no—
125#882—62no—
126#877—62no—
127#875—32no—
128#874—32no—
129C4×Dic6—34no—
130C3×C4⋊C8—34no—
131#835—32no—
132#832—32no—
133#821—32no—
134#821—34no—
135#821—34no—
136#821—64no—
137#816—32no—
138Dic3⋊C8C2×D314yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—82no—
143C22×C3×D3—21no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—42no—
152C3×#67—42no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—21no—
158C3×D12—21no—
159C3×C4×D3—42no—
160C3×Dic6—24no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—21no—
164C3×Dic6C2×D414yes—
165#626—84no—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C2×#137—31no—
169C22×SD16—91no—
170#535—91no—
171#519—91no—
172#464—94no—
173#460—94no—
174#424—31no—
175#418—91no—
176#416—91no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C3×#41—62no—
181C3×#41—62no—
182C2×C3×Q8—34no—
183C2×C3×Q8—32no—
184C2×C3×Q8—31no—
185C2×C3×Q8—61no—
186C2×C3×Q8—62no—
187C2×C3×D4—31no—
188C2×C3×D4—61no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C2×#67—64no—
196C22×Dic3—21no—
197#235—22no—
198#235—22no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—62no—
202C2×D12—64no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—64no—
210C2×D12—121no—
211C2×D12—122no—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×Dic6—21no—
215C2×Dic6—22no—
216C2×Dic6#6714yescomplemented
217C2×Dic6C22×D311yescharacteristic
218C2×Dic6C22×D312yes—
219C3×Q16—64no—
220C3×SD16—64no—
221C3×M16—22no—
222C3×M16—22no—
223C3×M16—42no—
224C2×C3×C8—22no—
225C2×C3×C8—32no—
226C2×C3×C8—62no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—32no—
230C3×C22⋊C4—32no—
231C3×C42—32no—
232#217—61no—
233#217—61no—
234#217—121no—
235#217D1212yes—
236#215—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239C4⋊Dic3—32no—
240C4⋊Dic3—32no—
241C4⋊Dic3—62no—
242C4⋊Dic3—64no—
243C4⋊Dic3D1212yes—
244Dic3⋊C4—64no—
245C4×Dic3—64no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—64no—
249C4×Dic3—121no—
250C4×Dic3C22×D312yes—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253Dic12—24no—
254#204—24no—
255#204—68no—
256C22×C32—22no—
257C22×C32#12112yes—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—44no—
261C2×C3⋊D3—84no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—24no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—31no—
273C22×D4—91no—
274#137—64no—
275C2×Q16—32no—
276C2×SD16—32no—
277C2×SD16—94no—
278C2×SD16—184no—
279C2×M16D3211yescharacteristic
280C22×C8—31no—
281#127—92no—
282#124—92no—
283#121—182no—
284#120—182no—
285C4×Q8—94no—
286C4×Q8—182no—
287#117—31no—
288#117—91no—
289#117—182no—
290C4⋊C8—34no—
291#103—92no—
292#102—92no—
293#102—94no—
294C23×C3—21no—
295C23×C3—61no—
296C23×C3C2×D1211yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—21no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—122no—
302C22×D3—124no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—242no—
306C22×D3—242no—
307C22×D3—244no—
308C3×Q8—34no—
309C3×Q8—64no—
310C3×Q8—62no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—61no—
314C3×D4—61no—
315C3×D4—122no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—64no—
322C2×C3×C4—62no—
323C2×C3×C4—61no—
324C2×C3×C4—122no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D412yes—
328C2×C3×C4#23712yes—
329C2×C3×C4#23912yes—
330C2×C3×C4C2×#6712yes—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—42no—
334#67—244no—
335C2×Dic3—24no—
336C2×Dic3—22no—
337C2×Dic3—21no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341C2×Dic3C2×D1214yes—
342D12—21no—
343D12—21no—
344D12—64no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—122no—
350D12—124no—
351D12—122no—
352D12—122no—
353D12—244no—
354C4×D3—42no—
355Dic6—24no—
356Dic6—22no—
357Dic6—21no—
358Dic6—21no—
359Dic6C2×#6714yes—
360C3×C8—22no—
361C3×C8—22no—
362C3×C8—42no—
363C3×C8—62no—
364C3⋊C8—22no—
365C2×C32—22no—
366C2×C32C2×#12111yescharacteristic
367C2×C32#57712yes—
368C3⋊D3—82no—
369C3×D3—81no—
370C24—181no—
371#41—62no—
372#41—62no—
373C2×Q8—32no—
374C2×Q8—31no—
375C2×Q8—34no—
376C2×Q8—62no—
377C2×Q8—61no—
378C2×D4—31no—
379C2×D4—61no—
380C2×D4—92no—
381C2×D4—184no—
382C2×D4—182no—
383C2×D4—181no—
384C2×D4—182no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4C2×D3211yescharacteristic
388Q16—64no—
389SD16—64no—
390SD16—188no—
391M16—22no—
392C2×C8—32no—
393C2×C8—62no—
394C2×C8C2×D3212yes—
395C4⋊C4—32no—
396C4⋊C4—92no—
397C4⋊C4—184no—
398C22⋊C4—32no—
399C22⋊C4—184no—
400C22⋊C4—181no—
401C42—32no—
402C42—184no—
403C42—181no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—42no—
409C22×C3—122no—
410C22×C3—121no—
411C22×C3#89512yes—
412C22×C3#93912yes—
413C22×C3C22×D1211yescharacteristic
414C22×C3C2×D3×D411yescharacteristic
415C2×D3—42no—
416C2×D3—41no—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—122no—
420C2×D3—124no—
421C2×D3—122no—
422C2×D3—244no—
423C2×D3—244no—
424C2×D3—244no—
425C2×D3—248no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—64no—
430C3×C4—64no—
431C3×C4—121no—
432C3×C4#89512yes—
433C3×C4#93912yes—
434C3×C4C2×D3×D411yescharacteristic
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23911yescharacteristic
437C3×C4C22×#6711yescharacteristic
438Dic3—24no—
439Dic3—24no—
440Dic3—41no—
441Dic3—122no—
442Dic3—122no—
443Dic3—242no—
444C32#304311yescharacteristic, complemented, Sylow
445C23—61no—
446C23—182no—
447C23—362no—
448C23—722no—
449C23D3×D1211yescharacteristic
450Q8—34no—
451Q8—62no—
452Q8—64no—
453Q8—61no—
454Q8—61no—
455D4—61no—
456D4—61no—
457D4—122no—
458D4—182no—
459D4—182no—
460D4—362no—
461D4—724no—
462C2×C4—34no—
463C2×C4—62no—
464C2×C4—64no—
465C2×C4—61no—
466C2×C4—122no—
467C2×C4—182no—
468C2×C4#379612yes—
469C2×C4D3×D1211yescharacteristic
470C2×C4D3×#6712yes—
471C2×C4C22×D3211yescharacteristic
472C8—22no—
473C8—62no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—42no—
479C2×C3—241no—
480C2×C3C2×#89511yescharacteristic
481C2×C3#575112yes—
482C2×C3#577812yes—
483C2×C3C2×#93911yescharacteristic
484D3—81no—
485D3—244no—
486D3—242no—
487D3—242no—
488C22—22no—
489C22—121no—
490C22—122no—
491C22—362no—
492C22—364no—
493C22—724no—
494C22#6388612yes—
495C22C2×D3×D1211yescharacteristic
496C4—64no—
497C4—64no—
498C4—121no—
499C4—362no—
500C4#6388612yes—
501C4C2×#379611yescharacteristic
502C4C2×D3×#6711yescharacteristic
503C3—21no—
504C3#7909911yescharacteristic, complemented
505C3#8396911yescharacteristic, complemented
506C2—22no—
507C2—241no—
508C2—722no—
509C2#1059471512yes—
510C2C2×#6388611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595045C2
hypercenterC2×M16D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#909C2semidirect
3. #10594818C2semidirect
4. C22×#3717C2semidirect
5. #10592830C2semidirect
6. C3×#5119C2semidirect
7. #10591084C2semidirect
8. #10590801C2semidirect
9. #10590799C2semidirect
20. C2×C3×Dic12C22semidirect
21. C2×C3×#204C22semidirect
28. Dic3×Dic6C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
39. C2×#909D3semidirect
50. #5119D3semidirect
68. C2×C3×Dic6D4semidirect
119. C2×Dic12C2×D3semidirect
122. C2×#204C2×D3semidirect
138. Dic3⋊C8C2×D3semidirect
216. C2×Dic6#67semidirect
444. C32#3043semidirect
504. C3#79099semidirect
505. C3#83969semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105950452
#105948182
C22×#37172
#105928302
C3×#51192
#105910842
#105908012
#105907992
#839693
#790993