Finite Group Databasebeta

← #11866137

Subgroups — #11866137

Order 1152.

1095 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic, complemented
3C2×#63864C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic
5#10592830C211yesmaximal, characteristic, complemented
6C3×#5118C211yesmaximal, characteristic, complemented
7#10591100C211yesmaximal, characteristic, complemented
8#10590801C214yesmaximal, complemented
9#10590754C214yesmaximal, complemented
10#83968—31nomaximal
11#79058—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#909—24no—
20C2×C3×Dic12C2212yescomplemented
21C2×C3×#204C2212yescomplemented
22Dic3×#67—22no—
23C2×#3722—22no—
24Dic3×D12C2212yescomplemented
25C4×D3×Dic3—21no—
26#63864—21no—
27#63864—21no—
28#63864C2214yes—
29#63855—21no—
30Dic3×Dic6C2212yescomplemented
31C2×#3717C2212yes—
32#63825—24no—
33C2×#3714C2212yes—
34#63648C2214yes—
35C3×Dic3⋊C8C2214yescomplemented
36#63566C2214yescomplemented
37C2×C3×#137—31no—
38Dic3×#41—31no—
39C2×#949—31no—
40C2×#947—31no—
41C2×#909D311yescharacteristic, complemented
42C2×#908—31no—
43C2×#875—31no—
44C4×#235—31no—
45C3×#423—31no—
46#5225—31no—
47#5185—34no—
48#5165—34no—
49#5131—31no—
50#5131—31no—
51#5131—61no—
52#5120—31no—
53#5118D311yescharacteristic, complemented
54#4845—34no—
55#4844—34no—
56C23×C3⋊D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C3×#67—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3D412yes—
65C3×#235—22no—
66C3×#235D414yes—
67C2×C3×D12C2311yescharacteristic
68C2×C3×C4×D3—21no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2312yes—
73C2×C3×Dic6C2311yescharacteristic
74C2×D3×Dic3—22no—
75C32×M16—22no—
76C2×C32×C8C2312yes—
77#3757—21no—
78C4⋊(C3⋊Dic3)C2312yes—
79C4×C3⋊Dic3—21no—
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3C2312yes—
83C3×#208—22no—
84C2×C3×C3⋊C8C2312yes—
85C3×Dic12—24no—
86C3×#204—24no—
87Dic3⋊Dic3—22no—
88#3722—24no—
89#3722—24no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92#3717—24no—
93#3714—24no—
94#3040—91noSylow
95C2×C3×#41—31no—
96C22×C3×Q8—31no—
97C2×#235C2×D311yescharacteristic
98C22×D12—31no—
99C22×D12—31no—
100C22×D12—61no—
101C22×Dic6C2×D311yescharacteristic
102C3×#137—64no—
103C2×C3×Q16—32no—
104C2×C3×SD16—32no—
105C2×C3×M16—21no—
106C2×C3×M16—31no—
107C2×C3×M16C2×D311yescharacteristic
108C2×C3×M16C2×D311yescharacteristic
109C2×C3×C42—31no—
110#949—64no—
111#947—34no—
112#947—61no—
113#947—61no—
114Q8×Dic3—32no—
115C2×#215—32no—
116D4×Dic3—32no—
117D4×Dic3—62no—
118C2×#213—32no—
119C4×#67—62no—
120C2×(C2×D3)⋊C4—62no—
121C2×(C2×D3)⋊C4—62no—
122#926—31no—
123#926—31no—
124#926—61no—
125#926—61no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3C2×D311yescharacteristic
128C2×#208C2×D311yescharacteristic
129#909—24no—
130#908—64no—
131C2×Dic12C2×D312yescomplemented
132C2×D24—32no—
133C2×#204—32no—
134C2×#204C2×D312yescomplemented
135#875—34no—
136#875—61no—
137#875—61no—
138C4×D12—32no—
139#872—61no—
140C42×D3—61no—
141C4×Dic6—32no—
142C3×C4⋊C8—34no—
143#835—34no—
144#821—34no—
145#821—34no—
146#821—64no—
147#816—34no—
148Dic3⋊C8C2×D314yescomplemented
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3—44no—
153C22×C3×D3—21no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4#4112yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C4⋊(C3⋊D3)—22no—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—42no—
162C3×#67—24no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—42no—
166C2×C3×Dic3—42no—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×D12—21no—
170C3×D12C2×D412yes—
171C3×C4×D3—24no—
172C3×Dic6—21no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—42no—
176C3×Dic6C2×D412yes—
177D3×Dic3—44no—
178C32×C8—22no—
179C3×C3⋊C8—22no—
180C2×#137—31no—
181C2×AGL(1,ℤ/8)—91no—
182C2×#124—91no—
183C4×#41—91no—
184#464—94no—
185#463—94no—
186#423—31no—
187#419—91no—
188#418—91no—
189C23×D3—61no—
190C23×D3—61no—
191C23×D3—121no—
192C3×#41—34no—
193C3×#41—62no—
194C2×C3×Q8—31no—
195C2×C3×Q8—32no—
196C2×C3×Q8—61no—
197C2×C3×Q8—62no—
198C2×C3×Q8—62no—
199C2×C3×D4—31no—
200C2×C3×D4—61no—
201C22×C3×C4—21no—
202C22×C3×C4—32no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C22×Dic3—21no—
209C22×Dic3—62no—
210C22×Dic3D1212yes—
211#235—22no—
212#235#6714yes—
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—121no—
224C2×D12—122no—
225C2×D12C22×D311yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—62no—
228C2×Dic6—22no—
229C2×Dic6—22no—
230C2×Dic6—21no—
231C2×Dic6C22×D312yes—
232C2×Dic6C22×D311yescharacteristic
233C3×Q16—64no—
234C3×SD16—64no—
235C3×M16—22no—
236C3×M16—22no—
237C3×M16—42no—
238C3×M16—62no—
239C2×C3×C8—22no—
240C2×C3×C8—32no—
241C2×C3×C8C22×D312yes—
242C2×C3×C8C22×D312yes—
243C3×C42—31no—
244C3×C42—31no—
245C3×C42—32no—
246#217—61no—
247#217—61no—
248#217—62no—
249#217—121no—
250#215—64no—
251#213—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257C4⋊Dic3—32no—
258C4⋊Dic3—32no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261Dic3⋊C4—62no—
262C4×Dic3—62no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C4×Dic3—62no—
266C4×Dic3—121no—
267C4×Dic3D1211yescharacteristic
268C4×Dic3D1211yescharacteristic
269C4×Dic3C22×D312yes—
270#208—22no—
271C2×C3⋊C8C22×D312yes—
272Dic12—24no—
273D24—64no—
274#204—24no—
275#204—64no—
276C22×C32—22no—
277C22×C32#12112yes—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—42no—
280C2×C3⋊D3—44no—
281C2×C3⋊D3—84no—
282C2×C3×D3—22no—
283C2×C3×D3—42no—
284C32×C4#12112yes—
285C32×C4C22×D411yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C2×#41—31no—
293C22×Q8—31no—
294C22×D4—91no—
295#137—64no—
296AGL(1,ℤ/8)—184no—
297C2×Q16—32no—
298C2×SD16—32no—
299C2×SD16—92no—
300C2×D8—92no—
301C2×M16—31no—
302C2×M16D3211yescharacteristic
303#124—94no—
304#124—181no—
305#124—181no—
306C4×Q8—92no—
307C4×D4—92no—
308C4×D4—182no—
309#117—91no—
310#117—181no—
311C2×C22⋊C4—182no—
312C2×C42—31no—
313C2×C42—181no—
314C4⋊C8—34no—
315#103—94no—
316#102—94no—
317C23×C3—21no—
318C23×C3—61no—
319C23×C3C2×D1211yescharacteristic
320C23×C3D3×D411yescharacteristic
321C22×D3—21no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—122no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—124no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—244no—
331C3×Q8—32no—
332C3×Q8—61no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×Q8—122no—
336C3×D4—32no—
337C3×D4—64no—
338C3×D4—61no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—61no—
346C2×C3×C4—64no—
347C2×C3×C4—62no—
348C2×C3×C4—122no—
349C2×C3×C4—122no—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4#23912yes—
355C2×C3×C4C2×#6712yes—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—24no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—42no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—124no—
367C2×Dic3C2×D1212yes—
368C2×Dic3C2×D1212yes—
369D12—21no—
370D12—64no—
371D12—62no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—122no—
376D12—124no—
377D12—122no—
378D12—122no—
379D12C2×#6712yes—
380C4×D3—24no—
381C4×D3—124no—
382Dic6—21no—
383Dic6—22no—
384Dic6—22no—
385Dic6—42no—
386Dic6C2×#6712yes—
387C3×C8—22no—
388C3×C8—22no—
389C3×C8—42no—
390C3×C8—62no—
391C3⋊C8—22no—
392C2×C32—22no—
393C2×C32C2×#12111yescharacteristic
394C2×C32#57512yes—
395C3⋊D3—82no—
396C3×D3—42no—
397C24—181no—
398#41—34no—
399#41—62no—
400C2×Q8—31no—
401C2×Q8—32no—
402C2×Q8—61no—
403C2×Q8—62no—
404C2×Q8—62no—
405C2×D4—31no—
406C2×D4—61no—
407C2×D4—92no—
408C2×D4—182no—
409C2×D4—181no—
410C2×D4—182no—
411C22×C4—32no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—182no—
415C22×C4C2×D3211yescharacteristic
416Q16—64no—
417SD16—64no—
418SD16—184no—
419D8—184no—
420M16—22no—
421M16—62no—
422C2×C8—32no—
423C2×C8C2×D3212yes—
424C4⋊C4—92no—
425C4⋊C4—182no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C22⋊C4—182no—
429C22⋊C4—181no—
430C42—32no—
431C42—31no—
432C42—31no—
433C42—182no—
434C42—181no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—42no—
440C22×C3—62no—
441C22×C3—122no—
442C22×C3#89512yes—
443C22×C3#93912yes—
444C22×C3C22×D1211yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—22no—
447C2×D3—42no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—122no—
451C2×D3—124no—
452C2×D3—122no—
453C2×D3—244no—
454C2×D3—244no—
455C2×D3—244no—
456C2×D3—248no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—122no—
464C3×C4#89512yes—
465C3×C4#93912yes—
466C3×C4C2×D3×D411yescharacteristic
467C3×C4C2×#23711yescharacteristic
468C3×C4C2×#23911yescharacteristic
469C3×C4C22×#6711yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—22no—
473Dic3—42no—
474Dic3—122no—
475Dic3—122no—
476Dic3—242no—
477C32#304011yescharacteristic, complemented, Sylow
478C23—61no—
479C23—182no—
480C23—364no—
481C23—362no—
482C23D3×D1211yescharacteristic
483Q8—32no—
484Q8—61no—
485Q8—62no—
486Q8—62no—
487Q8—122no—
488D4—32no—
489D4—64no—
490D4—61no—
491D4—182no—
492D4—182no—
493D4—362no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—61no—
497C2×C4—64no—
498C2×C4—62no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—182no—
502C2×C4—364no—
503C2×C4#379612yes—
504C2×C4D3×D1211yescharacteristic
505C2×C4D3×#6712yes—
506C2×C4C22×D3211yescharacteristic
507C8—22no—
508C8—62no—
509C2×C3—22no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—22no—
513C2×C3—42no—
514C2×C3—122no—
515C2×C3C2×#89511yescharacteristic
516C2×C3#574812yes—
517C2×C3#577712yes—
518C2×C3C2×#93911yescharacteristic
519D3—42no—
520D3—244no—
521D3—242no—
522D3—242no—
523C22—22no—
524C22—62no—
525C22—122no—
526C22—362no—
527C22—364no—
528C22—724no—
529C22#6388612yes—
530C22C2×D3×D1211yescharacteristic
531C4—62no—
532C4—62no—
533C4—62no—
534C4—122no—
535C4—362no—
536C4#6388612yes—
537C4C2×#379611yescharacteristic
538C4C2×D3×#6711yescharacteristic
539C3—21no—
540C3#7905811yescharacteristic, complemented
541C3#8396811yescharacteristic, complemented
542C2—22no—
543C2—122no—
544C2—722no—
545C2#1059471112yes—
546C2C2×#6388611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63825C2
hypercenterC2×M16D32
hypocenterC32#3040
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
2. Dic3×#235C2semidirect
3. C2×#63864C2semidirect
5. #10592830C2semidirect
6. C3×#5118C2semidirect
7. #10591100C2semidirect
8. #10590801C2semidirect
9. #10590754C2semidirect
20. C2×C3×Dic12C22semidirect
21. C2×C3×#204C22semidirect
24. Dic3×D12C22semidirect
30. Dic3×Dic6C22semidirect
35. C3×Dic3⋊C8C22semidirect
36. #63566C22semidirect
41. C2×#909D3semidirect
53. #5118D3semidirect
131. C2×Dic12C2×D3semidirect
134. C2×#204C2×D3semidirect
148. Dic3⋊C8C2×D3semidirect
477. C32#3040semidirect
540. C3#79058semidirect
541. C3#83968semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
Dic3×#2352
C2×#638642
C2×#638252
#105928302
C3×#51182
#105911002
#105908012
#105907542
#839683
#790583