Finite Group Databasebeta

← #11787881

Subgroups — #11787881

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic, complemented
3#10592914C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71763—31nomaximal
9#70323—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C22×C3×D12C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#940—22no—
16C3×#940C414yescomplemented
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20D3×#217—22no—
21#63898—22no—
22Dic3×D12—22no—
23#63659—22no—
24C3×#832—22no—
25#63558—22no—
26C2×C3×#127—31no—
27C2×#940D311yescharacteristic
28#5798—31no—
29#5521—31no—
30C3×#418—31no—
31C2×#833—31no—
32#5215—31no—
33#5215—31no—
34#5215—61no—
35#5215D311yescharacteristic, complemented
36C2×#823—31no—
37#4555—31no—
38#4532—31no—
39#4523—31no—
40#4523—31no—
41C24×C32—21no—
42C23×C3×D3D412yes—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yescomplemented
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—28no—
51C2×C3×#67—48no—
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yes—
58C2×C3×D12D412yes—
59C2×D3×Dic3—24no—
60#3757—21no—
61C4⋊(C3⋊Dic3)D412yescomplemented
62C4×C3⋊Dic3—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×C4⋊Dic3D412yescomplemented
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3C2×C412yescomplemented
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8—21no—
74(C2×D3)⋊Dic3—24no—
75#1887—91noSylow
76C22×C3×D4—21no—
77C22×C3×D4—31no—
78C22×C3×D4—62no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C2×D311yescharacteristic
81C22×#67—22no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C3×#127—34no—
85C3×#127—62no—
86C3×#117—31no—
87C2×C3×C42—31no—
88C2×#217—62no—
89#940—22no—
90#940Dic314yescomplemented
91D4×Dic3—62no—
92D4×Dic3—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×C4×Dic3C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102#893—62no—
103D3×C22⋊C4—62no—
104C4×D12—62no—
105C3×#102—62no—
106#833—62no—
107#832—22no—
108#832—62no—
109#832—62no—
110#832—64no—
111#823—62no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32—41no—
115C23×C32—44no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—44no—
120C22×C3×D3C22⋊C414yes—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—22no—
132C3×#67—416no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—22no—
139C3×D12—22no—
140D3×Dic3—84no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143C2×#127—31no—
144#518—91no—
145#418—31no—
146#418—91no—
147C2×#100—91no—
148#339—91no—
149#339—91no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—32no—
153C24×C3—41no—
154C23×D3#6712yes—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—22no—
168C2×C3×D4—32no—
169C2×C3×D4—32no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—68no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—128no—
179C2×C3×D4C4×D312yescomplemented
180C2×C3×D4C2×Dic312yescomplemented
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—28no—
186C2×#67—48no—
187C22×Dic3—21no—
188C22×Dic3—64no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12C2×Dic312yes—
194C2×D12#6712yes—
195C2×C4×D3—64no—
196C3×M16—61no—
197C3×M16—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—32no—
200C3×C22⋊C4—61no—
201C3×C42—32no—
202C3×C42—61no—
203C3×C42—61no—
204#217—21no—
205#217—64no—
206#217—61no—
207#217—61no—
208#217—121no—
209(C2×D3)⋊C4—64no—
210C4⋊Dic3—32no—
211C4⋊Dic3—32no—
212C4⋊Dic3—62no—
213C4⋊Dic3#6712yescomplemented
214C4×Dic3—21no—
215C4×Dic3—21no—
216C4×Dic3—61no—
217C4×Dic3—61no—
218C4×Dic3—121no—
219C4×Dic3C2×Dic312yescomplemented
220#208—21no—
221#208—21no—
222#208—61no—
223#208—61no—
224#208—61no—
225#208—61no—
226#208—121no—
227#208—121no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C22×C32—22no—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32—82no—
236C22×C32—82no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32#12311yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—44no—
243C2×C3×D3—82no—
244C32×C4C4×D411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4#12111yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×D4—31no—
252C22×D4—62no—
253C22×D4D3211yescharacteristic
254C2×M16—31no—
255C2×M16—91no—
256#127—34no—
257#127—62no—
258C4×D4—182no—
259C4×D4—182no—
260#117—31no—
261#117—91no—
262C2×C22⋊C4—182no—
263C2×C42—31no—
264#102—62no—
265#102—182no—
266#100—182no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—34no—
271C23×C3—42no—
272C23×C3—44no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—44no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—84no—
283C23×C3—124no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—44no—
289C22×D3#21714yes—
290C3×D4—24no—
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—42no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—62no—
303C3×D4—62no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—1216no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—64no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4C22×Dic311yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328#67—416no—
329C2×Dic3—24no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—244no—
336D12—22no—
337D12—22no—
338D12—22no—
339D12—22no—
340C4×D3—244no—
341C3×C8—121no—
342C3⋊C8—41no—
343C3⋊C8—122no—
344C3⋊C8—121no—
345C3⋊C8—121no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—82no—
349C2×C32#38611yescharacteristic
350C2×C32#45312yes—
351C3×D3—44no—
352C24—21no—
353C24—32no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—32no—
360C2×D4—32no—
361C2×D4—68no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C2×D4—128no—
367C2×D4D3×Dic312yescomplemented
368C22×C4—61no—
369C22×C4—184no—
370C22×C4C2×D3211yescharacteristic
371M16—61no—
372M16—61no—
373M16—181no—
374M16—181no—
375C2×C8—61no—
376C2×C8—181no—
377C4⋊C4—32no—
378C4⋊C4—92no—
379C22⋊C4—61no—
380C22⋊C4—184no—
381C22⋊C4—181no—
382C42—32no—
383C42—61no—
384C42—61no—
385C42—181no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—42no—
392C22×C3—44no—
393C22×C3—44no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—64no—
398C22×C3—84no—
399C22×C3—82no—
400C22×C3—82no—
401C22×C3—84no—
402C22×C3—84no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—124no—
406C22×C3—124no—
407C22×C3—242no—
408C22×C3D3×C22⋊C411yescharacteristic
409C22×C3#88311yescharacteristic
410C22×C3#93511yescharacteristic
411C22×C3#93711yescharacteristic
412C22×C3#93711yescharacteristic
413C22×C3C2×#21711yescharacteristic
414C2×D3—24no—
415C2×D3—44no—
416C2×D3—44no—
417C2×D3—82no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—64no—
423C3×C4—122no—
424C3×C4#67⋊C411yescharacteristic
425C3×C4#88411yescharacteristic
426C3×C4C4×#6711yescharacteristic
427C3×C4D4×Dic311yescharacteristic
428C3×C4D4×Dic311yescharacteristic
429C3×C4#93811yescharacteristic
430C3×C4#93911yescharacteristic
431C3×C4#93911yescharacteristic
432Dic3—24no—
433Dic3—42no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32#188711yescharacteristic, complemented, Sylow
438C23—22no—
439C23—34no—
440C23—44no—
441C23—41no—
442C23—41no—
443C23—62no—
444C23—62no—
445C23—124no—
446C23D3×#6711yescharacteristic
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—62no—
452D4—62no—
453D4—62no—
454D4—62no—
455D4—1216no—
456C2×C4—64no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—182no—
460C2×C4—724no—
461C2×C4C2×D3×Dic311yescharacteristic
462C2×C4#380411yescharacteristic
463C2×C4#380511yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C2×C4D3×#6711yescharacteristic
466C2×C4#381111yescharacteristic
467C8—121no—
468C8—361no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—84no—
478C2×C3—82no—
479C2×C3—82no—
480C2×C3—124no—
481C2×C3#495611yescharacteristic
482C2×C3#507712yes—
483C2×C3#519812yes—
484C2×C3#522011yescharacteristic
485D3—44no—
486C22—22no—
487C22—44no—
488C22—42no—
489C22—64no—
490C22—82no—
491C22—82no—
492C22—124no—
493C22—124no—
494C22—242no—
495C22D3×#21711yescharacteristic
496C22#6396911yescharacteristic
497C22#6398311yescharacteristic
498C4—64no—
499C4—122no—
500C4—362no—
501C4#6397011yescharacteristic
502C4#6397111yescharacteristic
503C4Dic3×#6711yescharacteristic
504C4#67⋊Dic311yescharacteristic
505C3—21no—
506C3#7032311yescharacteristic, complemented
507C3#7176311yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—82no—
511C2—124no—
512C2#1059152312yes—
513C2#1059172111yescharacteristic
subgroupG/H
centerC22#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#120
prime radicalC2×C3×#940C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1887
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
2. #10594982C2semidirect
3. #10592914C2semidirect
4. C3×#5215C2semidirect
5. C2×#63558C2semidirect
6. #10589162C2semidirect
7. #10589161C2semidirect
16. C3×#940C4semidirect
35. #5215D3semidirect
48. C2×C32×D4C2×C4semidirect
61. C4⋊(C3⋊Dic3)D4semidirect
67. C3×C4⋊Dic3D4semidirect
70. C3×C4×Dic3C2×C4semidirect
90. #940Dic3semidirect
179. C2×C3×D4C4×D3semidirect
180. C2×C3×D4C2×Dic3semidirect
213. C4⋊Dic3#67semidirect
219. C4×Dic3C2×Dic3semidirect
367. C2×D4D3×Dic3semidirect
437. C32#1887semidirect
506. C3#70323semidirect
507. C3#71763semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
#105949822
#105929142
C3×#52152
C2×#635582
#105891622
#105891612
#717633
#703233