Finite Group Databasebeta

← #11787877

Subgroups — #11787877

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic, complemented
4#10591085C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71650—31nomaximal
9#70323—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#625—22no—
13C32×#117C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#893—22no—
19C3×D3×C22⋊C4—22no—
20C3×C4×D12—22no—
21#63914—22no—
22#63914C414yescomplemented
23C3×#809—22no—
24#63562—22no—
25#63558—22no—
26C3×#518—31no—
27C2×#940—31no—
28C2×#940—31no—
29#5521D311yescharacteristic, complemented
30C3×#418—31no—
31C2×#833—31no—
32#5215—31no—
33C2×#823—31no—
34#5001—31no—
35#5001D311yescharacteristic, complemented
36#4555—31no—
37#4532—31no—
38#4532—31no—
39#4532—31no—
40#4532—61no—
41C23×C3×D3—21no—
42C23×C3×D3D412yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12C2×C412yes—
55C2×C3×D12C2×C412yescomplemented
56C2×C3×D12D412yes—
57C2×C3×C4×D3—24no—
58C2×#625—28no—
59C2×#625—48no—
60C32×C4⋊C4D412yescomplemented
61C32×C22⋊C4—21no—
62C32×C42—21no—
63C4×C3⋊Dic3—21no—
64C4×C3⋊Dic3C2×C412yescomplemented
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#217—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3D412yescomplemented
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75#1887—91noSylow
76C22×C3×D4—31no—
77C22×C3×D4—31no—
78C22×#67—62no—
79C22×#67—62no—
80C22×D12C2×D311yescharacteristic
81C22×D12C2×D311yescharacteristic
82C2×C3×M16—31no—
83C3×C4×D4—62no—
84C3×C4×D4—62no—
85C3×#117—21no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89C2×C3×C22⋊C4—62no—
90#940—34no—
91#940—34no—
92#940—62no—
93#940—62no—
94#926C2×D311yescharacteristic
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—61no—
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102#893—22no—
103D3×C22⋊C4—22no—
104C4×D12—22no—
105C3×#102—62no—
106#833—62no—
107#832—62no—
108#823—62no—
109#809—22no—
110#809—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—44no—
116C22×C3×D3—44no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3C22⋊C414yes—
120C2×C32×C4—22no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—24no—
128C2×C3⋊Dic3—22no—
129C2×C3×Dic3—22no—
130C3×D12—22no—
131C3×D12—22no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C3×C4×D3—84no—
139#625—416no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142C2×#127—91no—
143#518—31no—
144#418—31no—
145#418—91no—
146C2×#100—91no—
147#339—91no—
148#339—91no—
149C24×C3—32no—
150C24×C3—61no—
151C23×D3—21no—
152C23×D3#6712yes—
153C2×C3×D4—32no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—64no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—68no—
170C2×#67—68no—
171C2×#67—128no—
172C2×#67—128no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12C4×D312yes—
186C2×D12C4×D312yescomplemented
187C2×D12D1212yes—
188C2×C4×D3—24no—
189C3×M16—61no—
190C3×M16—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4#6712yescomplemented
195C3×C4⋊C4#6712yescomplemented
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—41no—
199C3×C22⋊C4—64no—
200C3×C22⋊C4—61no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—41no—
204C3×C42—61no—
205#217—21no—
206(C2×D3)⋊C4—24no—
207C4⋊Dic3#6712yescomplemented
208C4×Dic3—21no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—62no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—121no—
215#208—21no—
216#208—21no—
217#208—62no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12311yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—44no—
233C2×C3×D3—44no—
234C2×C3×D3—44no—
235C2×C3×D3—42no—
236C2×C3×D3—82no—
237C2×C3×D3—82no—
238C2×C3×D3—82no—
239C32×C4—42no—
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C3⋊Dic3—24no—
245C3×Dic3—42no—
246C22×D4—31no—
247C22×D4—31no—
248C22×D4—182no—
249C2×M16—31no—
250C2×M16—91no—
251#127—94no—
252#127—182no—
253C4×D4—62no—
254C4×D4—62no—
255#117—31no—
256#117D3211yescharacteristic
257C2×C22⋊C4—62no—
258C2×C42—91no—
259#102—62no—
260#102—182no—
261#100—182no—
262C23×C3—21no—
263C23×C3—34no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3—124no—
268C23×C3—124no—
269C23×C3—121no—
270C23×C3—121no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C22×D3—22no—
274C22×D3—22no—
275C22×D3—22no—
276C22×D3—44no—
277C22×D3—44no—
278C22×D3—41no—
279C22×D3—41no—
280C22×D3(C2×D3)⋊C414yes—
281C3×D4—62no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C3×D4—62no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—42no—
298C2×C3×C4—62no—
299C2×C3×C4—244no—
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312#67—1216no—
313#67—1216no—
314C2×Dic3—22no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3—124no—
321D12—22no—
322D12—22no—
323D12—22no—
324D12—22no—
325D12—22no—
326D12—22no—
327D12—41no—
328D12—41no—
329C4×D3—84no—
330C3×C8—121no—
331C3⋊C8—41no—
332C3⋊C8—122no—
333C3⋊C8—121no—
334C3⋊C8—121no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32#38611yescharacteristic
338C2×C32#45312yes—
339C3×D3—44no—
340C3×D3—82no—
341C24—32no—
342C24—61no—
343C2×D4—32no—
344C2×D4—32no—
345C2×D4—32no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—188no—
356C2×D4—368no—
357C22×C4—64no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360M16—61no—
361M16—61no—
362M16—181no—
363M16—181no—
364C2×C8—61no—
365C2×C8—181no—
366C4⋊C4—32no—
367C4⋊C4#62512yescomplemented
368C22⋊C4—21no—
369C22⋊C4—64no—
370C22⋊C4—61no—
371C42—21no—
372C42—61no—
373C42—92no—
374C42—181no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—42no—
381C22×C3—64no—
382C22×C3—124no—
383C22×C3—124no—
384C22×C3—124no—
385C22×C3—122no—
386C22×C3—242no—
387C22×C3—242no—
388C22×C3—242no—
389C22×C3D3×C22⋊C411yescharacteristic
390C22×C3#88311yescharacteristic
391C22×C3C2×(C2×D3)⋊C411yescharacteristic
392C22×C3#92911yescharacteristic
393C22×C3#93711yescharacteristic
394C22×C3#95311yescharacteristic
395C2×D3—24no—
396C2×D3—44no—
397C2×D3—44no—
398C2×D3—44no—
399C2×D3—42no—
400C2×D3—82no—
401C2×D3—82no—
402C2×D3—82no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—82no—
410C3×C4—122no—
411C3×C4#67⋊C411yescharacteristic
412C3×C4#88411yescharacteristic
413C3×C4C4×#6711yescharacteristic
414C3×C4C4×#6711yescharacteristic
415C3×C4C4×#6711yescharacteristic
416C3×C4#93011yescharacteristic
417C3×C4#93011yescharacteristic
418C3×C4#93811yescharacteristic
419Dic3—42no—
420Dic3—64no—
421Dic3—64no—
422Dic3—124no—
423C32#188711yescharacteristic, complemented, Sylow
424C23—34no—
425C23—62no—
426C23—62no—
427C23—62no—
428C23—124no—
429C23—124no—
430C23—121no—
431C23—121no—
432C23D3×#6711yescharacteristic
433D4—62no—
434D4—62no—
435D4—62no—
436D4—62no—
437D4—62no—
438D4—62no—
439D4—121no—
440D4—121no—
441D4—3616no—
442C2×C4—22no—
443C2×C4—62no—
444C2×C4—184no—
445C2×C4—182no—
446C2×C4—244no—
447C2×C4#379511yescharacteristic
448C2×C4#379811yescharacteristic
449C2×C4C4×D3211yescharacteristic
450C2×C4D3×D1211yescharacteristic
451C2×C4C2×#62511yescharacteristic
452C2×C4D3×#6711yescharacteristic
453C8—121no—
454C8—361no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—22no—
461C2×C3—41no—
462C2×C3—41no—
463C2×C3—124no—
464C2×C3—242no—
465C2×C3#495611yescharacteristic
466C2×C3#519812yes—
467C2×C3#521311yescharacteristic
468C2×C3#524112yes—
469D3—44no—
470D3—82no—
471C22—22no—
472C22—64no—
473C22—124no—
474C22—124no—
475C22—124no—
476C22—122no—
477C22—242no—
478C22—242no—
479C22—242no—
480C22#6390511yescharacteristic
481C22D3×(C2×D3)⋊C411yescharacteristic
482C22#6397611yescharacteristic
483C4—42no—
484C4—122no—
485C4—184no—
486C4#6387911yescharacteristic
487C4C4×#62511yescharacteristic
488C4#6390611yescharacteristic
489C4#6390811yescharacteristic
490C3—21no—
491C3#7032311yescharacteristic, complemented
492C3#7165011yescharacteristic, complemented
493C2—21no—
494C2—21no—
495C2—124no—
496C2—242no—
497C2#1059138111yescharacteristic
498C2#1059166512yes—
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×#63914C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1887
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
3. C3×#5001C2semidirect
4. #10591085C2semidirect
5. C2×#63558C2semidirect
6. #10589398C2semidirect
7. #10589160C2semidirect
22. #63914C4semidirect
29. #5521D3semidirect
35. #5001D3semidirect
55. C2×C3×D12C2×C4semidirect
60. C32×C4⋊C4D4semidirect
64. C4×C3⋊Dic3C2×C4semidirect
70. C3×C4⋊Dic3D4semidirect
186. C2×D12C4×D3semidirect
194. C3×C4⋊C4#67semidirect
195. C3×C4⋊C4#67semidirect
207. C4⋊Dic3#67semidirect
367. C4⋊C4#625semidirect
423. C32#1887semidirect
491. C3#70323semidirect
492. C3#71650semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C2×#639142
C3×#50012
#105910852
C2×#635582
#105893982
#105891602
#716503
#703233