Finite Group Databasebeta

← #11783787

Subgroups — #11783787

Order 1152.

791 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#823C211yesmaximal, characteristic
4C2×#63558C211yesmaximal, characteristic
5#10591060C211yesmaximal, characteristic, complemented
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8Dic3×#100—31nomaximal
9#68972—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3C412yes—
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×(C2×D3)⋊Dic3C412yes—
19#63898—21no—
20#63898—21no—
21#63898—21no—
22#63898—21no—
23#63642—21no—
24C8×C3⋊Dic3—21no—
25C3×#823C414yescomplemented
26#63558C414yescomplemented
27#63555—21no—
28#63553—21no—
29C2×D4×Dic3—31no—
30C2×#893—31no—
31C2×C3×#100—31no—
32C2×#833—31no—
33C2×#823—31no—
34C2×#823D311yescharacteristic
35Dic3×M16—31no—
36Dic3×M16—31no—
37Dic3×M16—31no—
38Dic3×M16—31no—
39Dic3×M16—61no—
40C3×#343—31no—
41#4554—31no—
42#4554D311yescharacteristic, complemented
43#4530—31no—
44C23×C3×D3C2×C412yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C412yes—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12C2×C412yes—
54C2×C3×D12C2×C412yes—
55C2×D3×Dic3—22no—
56C2×D3×Dic3—22no—
57C2×D3×Dic3—44no—
58C32×M16—21no—
59C32×M16C2×C412yescomplemented
60C2×C32×C8—21no—
61C4×C3⋊Dic3D411yescharacteristic
62C4×C3⋊Dic3D411yescharacteristic
63C4×C3⋊Dic3D411yescharacteristic
64C4×C3⋊Dic3D411yescharacteristic
65#3748—21no—
66#3748C2×C412yescomplemented
67C2×C3⋊(C3⋊C8)—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—22no—
77(C2×D3)⋊Dic3—22no—
78C4×#100—91noSylow
79C22×C3×D4—31no—
80C23×Dic3—32no—
81C22×D12C2×D311yescharacteristic
82C22×C4×D3—32no—
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×#217—32no—
90D4×Dic3—61no—
91D4×Dic3—61no—
92D4×Dic3—61no—
93D4×Dic3—61no—
94C2×(C2×D3)⋊C4—32no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4×Dic3—31no—
97C2×C4×Dic3—31no—
98C2×C4×Dic3—61no—
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104#893—61no—
105#893—61no—
106#893—61no—
107#893—61no—
108C3×#100—34no—
109#833—34no—
110#823—34no—
111#823Dic314yescomplemented
112#815—61no—
113#815—61no—
114#815—61no—
115#815—61no—
116#815—62no—
117C8×Dic3—61no—
118C8×Dic3—61no—
119C8×Dic3—61no—
120C8×Dic3—61no—
121C8×Dic3—62no—
122C23×C32C22×C411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C22×C3×D3C4214yes—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3C22⋊C411yescharacteristic
137C2×C3⋊Dic3C22⋊C411yescharacteristic
138C2×C3⋊Dic3C22⋊C411yescharacteristic
139C2×C3⋊Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—22no—
146D3×Dic3—44no—
147D3×Dic3—44no—
148C32×C8—22no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×C4×D4—91no—
153C2×#100—31no—
154C2×#100—91no—
155C4×M16—91no—
156C4×M16—91no—
157#343—31no—
158#343—91no—
159C24×C3—32no—
160C23×D3C4×D312yes—
161C2×C3×D4—32no—
162C2×C3×D4—32no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—32no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—62no—
178C22×Dic3—62no—
179C22×Dic3—124no—
180C22×Dic3C4×D312yes—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12C4×D312yes—
186C2×D12C2×Dic312yes—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—124no—
190C3×M16—22no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—22no—
194C3×M16—32no—
195C3×M16—32no—
196C3×M16—61no—
197C3×M16—61no—
198C3×M16C4×D312yescomplemented
199C3×M16C2×Dic312yescomplemented
200C2×C3×C8—22no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207#217—62no—
208#217—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4×Dic3—31no—
214C4×Dic3—31no—
215C4×Dic3—31no—
216C4×Dic3—31no—
217C4×Dic3—31no—
218C4×Dic3—31no—
219C4×Dic3—31no—
220C4×Dic3—31no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225#208—21no—
226#208—21no—
227#208—32no—
228#208—32no—
229#208—62no—
230#208—62no—
231#208—61no—
232#208—61no—
233#208C4×D312yescomplemented
234#208C2×Dic312yescomplemented
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32C2×C4211yescharacteristic
243C22×C32C2×C22⋊C411yescharacteristic
244C22×C32#11711yescharacteristic
245C2×C3×D3—24no—
246C2×C3×D3—44no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—44no—
250C32×C4C4×D411yescharacteristic
251C32×C4C4×D411yescharacteristic
252C32×C4C4×D411yescharacteristic
253C32×C4C4×D411yescharacteristic
254C3⋊Dic3—21no—
255C3⋊Dic3—21no—
256C3⋊Dic3—21no—
257C3⋊Dic3#10012yescomplemented
258C3×Dic3—42no—
259C22×D4—31no—
260C23×C4—92no—
261C2×M16—31no—
262C2×M16—31no—
263C2×M16—91no—
264C2×M16D3211yescharacteristic
265C4×D4—181no—
266C4×D4—181no—
267C4×D4—181no—
268C4×D4—181no—
269C2×C4⋊C4—31no—
270C2×C22⋊C4—92no—
271C2×C42—91no—
272#100—34no—
273#100—94no—
274#97—181no—
275#97—181no—
276C4×C8—181no—
277C4×C8—181no—
278C23×C3—21no—
279C23×C3—34no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—122no—
283C23×C3—122no—
284C23×C3C2×C4×D311yescharacteristic
285C23×C3C2×C4×D311yescharacteristic
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—42no—
289C22×D3—42no—
290C22×D3C4×Dic314yes—
291C3×D4—62no—
292C3×D4—62no—
293C3×D4—62no—
294C3×D4—62no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—62no—
302C2×C3×C4—122no—
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23911yescharacteristic
314C2×C3×C4C22×Dic311yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—31no—
317C2×Dic3—31no—
318C2×Dic3—31no—
319C2×Dic3—31no—
320C2×Dic3—31no—
321C2×Dic3—31no—
322C2×Dic3—31no—
323C2×Dic3—31no—
324C2×Dic3—42no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—122no—
332C2×Dic3—124no—
333C2×Dic3—124no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—122no—
337D12—22no—
338D12—22no—
339D12—22no—
340D12—22no—
341C4×D3—124no—
342C4×D3—124no—
343C3×C8—24no—
344C3×C8—22no—
345C3×C8—22no—
346C3×C8—62no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—22no—
350C3⋊C8—64no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32C4×C22⋊C411yescharacteristic
356C2×C32C2×#10011yescharacteristic
357C2×C32#41311yescharacteristic
358C3×D3—44no—
359C24—32no—
360C2×D4—32no—
361C2×D4—32no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C22×C4—32no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—182no—
370C22×C4—182no—
371C22×C4—364no—
372C22×C4C2×D3211yescharacteristic
373M16—21no—
374M16—32no—
375M16—32no—
376M16—61no—
377M16—61no—
378M16—92no—
379M16—181no—
380M16D3×Dic312yescomplemented
381C2×C8—21no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—181no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C22⋊C4—182no—
388C22⋊C4—182no—
389C42—91no—
390C42—91no—
391C42—91no—
392C42—91no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—64no—
403C22×C3—124no—
404C22×C3—124no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3C42×D311yescharacteristic
408C22×C3#87711yescharacteristic
409C22×C3D3×C22⋊C411yescharacteristic
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3#89211yescharacteristic
412C22×C3C2×C4×Dic311yescharacteristic
413C2×D3—24no—
414C2×D3—44no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—44no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—122no—
423C3×C4#67⋊C411yescharacteristic
424C3×C4#67⋊C411yescharacteristic
425C3×C4#67⋊C411yescharacteristic
426C3×C4#67⋊C411yescharacteristic
427C3×C4#89311yescharacteristic
428C3×C4#89311yescharacteristic
429C3×C4D4×Dic311yescharacteristic
430C3×C4D4×Dic311yescharacteristic
431Dic3—32no—
432Dic3—32no—
433Dic3—42no—
434Dic3—62no—
435Dic3—62no—
436Dic3—61no—
437Dic3—61no—
438Dic3—61no—
439Dic3—61no—
440Dic3—61no—
441Dic3—61no—
442Dic3—121no—
443Dic3—121no—
444C32C4×#10011yescharacteristic, complemented, Sylow
445C23—34no—
446C23—62no—
447C23—62no—
448C23—122no—
449C23—122no—
450C23C4×D3211yescharacteristic
451D4—62no—
452D4—62no—
453D4—62no—
454D4—62no—
455C2×C4—62no—
456C2×C4—91no—
457C2×C4—91no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—122no—
461C2×C4—182no—
462C2×C4—364no—
463C2×C4—364no—
464C2×C4—361no—
465C2×C4#379611yescharacteristic
466C2×C4C4×D3211yescharacteristic
467C2×C4#380211yescharacteristic
468C2×C4C2×D3×Dic311yescharacteristic
469C2×C4#380511yescharacteristic
470C2×C4#381111yescharacteristic
471C8—22no—
472C8—62no—
473C8—62no—
474C8—182no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—124no—
485C2×C3#466611yescharacteristic
486C2×C3D3×#10011yescharacteristic
487C2×C3D3×#10011yescharacteristic
488C2×C3#474511yescharacteristic
489C2×C3#475111yescharacteristic
490C2×C3Dic3×C22⋊C411yescharacteristic
491D3—44no—
492C22—21no—
493C22—21no—
494C22—64no—
495C22—124no—
496C22—124no—
497C22—122no—
498C22—122no—
499C22C4×D3×Dic311yescharacteristic
500C22#6387811yescharacteristic
501C22#6392111yescharacteristic
502C4—92no—
503C4—122no—
504C4—181no—
505C4—181no—
506C4—181no—
507C4#6388111yescharacteristic
508C4#6389811yescharacteristic
509C4#6390211yescharacteristic
510C4#67⋊Dic311yescharacteristic
511C3—21no—
512C3#6897211yescharacteristic, complemented
513C3Dic3×#10011yescharacteristic, complemented
514C2—21no—
515C2—21no—
516C2—124no—
517C2#1059100111yescharacteristic
518C2#1059101011yescharacteristic
519C2#1059136811yescharacteristic
subgroupG/H
centerC22#63921
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. M16×C3⋊Dic3C2semidirect
5. #10591060C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
25. C3×#823C4semidirect
26. #63558C4semidirect
42. #4554D3semidirect
59. C32×M16C2×C4semidirect
66. #3748C2×C4semidirect
72. C3×#208C2×C4semidirect
73. C3×#208C2×C4semidirect
111. #823Dic3semidirect
198. C3×M16C4×D3semidirect
199. C3×M16C2×Dic3semidirect
233. #208C4×D3semidirect
234. #208C2×Dic3semidirect
257. C3⋊Dic3#100semidirect
380. M16D3×Dic3semidirect
444. C32C4×#100semidirect
512. C3#68972semidirect
513. C3Dic3×#100semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
M16×C3⋊Dic32
C2×C3×#8232
C2×#635582
#105910602
C3×#45542
#105891672
Dic3×#1003
#689723