Finite Group Databasebeta

← #11860694

Subgroups — #11860694

Order 1152.

1151 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4#10592700C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590589C214yesmaximal, complemented
9#10590456C214yesmaximal, complemented
10#82538—31nomaximal
11#79167—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#893C2214yescomplemented
20C3×D3×C22⋊C4—22no—
21C3×C4×D12—22no—
22#63974—22no—
23#63894—22no—
24#63894C2214yescomplemented
25C2×#3714C418yescomplemented
26C2×#3714C2212yes—
27C2×#3714C2212yes—
28#63636C2214yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63562C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35C22×#213—31no—
36C22×D24—31no—
37#5521—31no—
38#5521—31no—
39#5521D311yescharacteristic, complemented
40C3×#427—31no—
41#5215—31no—
42#5101—31no—
43#5014—34no—
44C4×#213—34no—
45#5001—31no—
46#5001—31no—
47#5001—31no—
48#5001—61no—
49#4998D311yescharacteristic, complemented
50#4997—31no—
51#4872—34no—
52#4869—34no—
53C23×C3⋊D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yescomplemented
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yescomplemented
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×#624—24no—
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—21no—
68C32×C42—21no—
69#3748—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×#217—21no—
72C3×#217D412yes—
73C3×(C2×D3)⋊C4—24no—
74C3×C4⋊Dic3D412yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3—21no—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8C2×C414yescomplemented
79C2×C3×C3⋊C8C2311yescharacteristic
80C2×C3×C3⋊C8C2311yescharacteristic
81#3722—24no—
82#3714C2×C418yescomplemented
83#3714C2×C418yescomplemented
84#2948—91noSylow
85C22×C3×D4—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12C2×D311yescharacteristic
90C22×C3×C8—31no—
91C3×C4×D4—34no—
92C3×C4×D4—62no—
93C3×#117—21no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C22⋊C4—62no—
99C2×#213—38no—
100C2×#213—32no—
101C2×#213—32no—
102#926C2×D311yescharacteristic
103#926C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C2×D24—38no—
109C2×D24—32no—
110C2×D24—32no—
111#893—34no—
112#893—62no—
113#893C2×D314yescomplemented
114D3×C22⋊C4—22no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117C4×D12—22no—
118C4×D12—34no—
119C4×D12—62no—
120C3×#107—32no—
121C3×#106—32no—
122#832—34no—
123#815—32no—
124C8×Dic3—32no—
125#809—34no—
126#809—34no—
127#809—34no—
128#809—64no—
129#808C2×D312yescomplemented
130#807C2×D312yescomplemented
131#803—32no—
132C4×C3⋊C8—32no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—24no—
136C22×C3⋊D3—82no—
137C22×C3×D3—22no—
138C22×C3×D3—24no—
139C22×C3×D3—82no—
140C2×C32×C4—22no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3C2×D414yes—
150C3×D12—24no—
151C3×D12—22no—
152C3×D12C22×C414yes—
153C3×C4×D3—84no—
154#624—84no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×D8—91no—
159#518—31no—
160#518—91no—
161#442—94no—
162C4×D8—94no—
163#427—31no—
164#418—91no—
165#418—91no—
166#405—91no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—64no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×D12—22no—
181C2×D12—21no—
182C2×D12—34no—
183C2×D12—34no—
184C2×D12—32no—
185C2×D12—32no—
186C2×D12—62no—
187C2×D12—64no—
188C2×D12—62no—
189C2×D12—61no—
190C2×D12—62no—
191C2×D12—61no—
192C2×D12—122no—
193C2×D12—121no—
194C2×D12C4×D314yescomplemented
195C2×D12C22×D312yes—
196C2×C4×D3—24no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C2×C3×C8—34no—
200C2×C3×C8—31no—
201C2×C3×C8—31no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4C22×D312yes—
206C3×C4⋊C4C22×D312yes—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—32no—
210C3×C22⋊C4—41no—
211C3×C22⋊C4—64no—
212C3×C22⋊C4—61no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—32no—
216C3×C42—41no—
217C3×C42—61no—
218#217—21no—
219#217#6712yes—
220#213—38no—
221#213—38no—
222(C2×D3)⋊C4—24no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225C4⋊Dic3#6712yes—
226C4⋊Dic3C22×D312yes—
227C4×Dic3—21no—
228C4×Dic3C22×D312yes—
229#208—62no—
230#208—62no—
231#208—122no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8C4×D314yescomplemented
236C2×C3⋊C8C22×D311yescharacteristic
237C2×C3⋊C8C22×D311yescharacteristic
238D24—38no—
239D24—38no—
240C22×C32—22no—
241C22×C32C4×D412yes—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3—24no—
244C2×C3⋊D3—44no—
245C2×C3⋊D3—84no—
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—84no—
249C32×C4—42no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3×Dic3—24no—
254C3×Dic3—42no—
255C22×D4—31no—
256C22×D4—91no—
257C2×D8—98no—
258C2×D8—92no—
259C2×D8—92no—
260C2×M16—91no—
261C22×C8—31no—
262C4×D4—34no—
263C4×D4—62no—
264C4×D4—94no—
265C4×D4—182no—
266#117—31no—
267#117—31no—
268#117D3211yescharacteristic
269C2×C22⋊C4—62no—
270C2×C22⋊C4—182no—
271#107—32no—
272#106—32no—
273#102—94no—
274#102—94no—
275#97—92no—
276C4×C8—92no—
277C23×C3—21no—
278C23×C3—62no—
279C23×C3—64no—
280C23×C3—242no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C22×D3—22no—
284C22×D3—24no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—82no—
290C22×D3—122no—
291C22×D3—124no—
292C22×D3—242no—
293C22×D3—242no—
294C22×D3—244no—
295C3×D4—34no—
296C3×D4—64no—
297C3×D4—62no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—34no—
305C2×C3×C4—42no—
306C2×C3×C4—62no—
307C2×C3×C4—244no—
308C2×C3×C4C2×C4×D312yes—
309C2×C3×C4C2×C4×D312yes—
310C2×C3×C4#23512yes—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23912yes—
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316C2×Dic3—22no—
317C2×Dic3C2×#6714yes—
318D12—24no—
319D12—22no—
320D12—34no—
321D12—34no—
322D12—64no—
323D12—64no—
324D12—64no—
325D12—62no—
326D12—62no—
327D12—122no—
328D12—124no—
329D12C2×C4×D314yes—
330C4×D3—84no—
331C4×D3—244no—
332C4×D3—244no—
333C3×C8—32no—
334C3×C8—32no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C3⋊C8C2×C4×D312yes—
339C3⋊C8C2×C4×D312yes—
340C2×C32—22no—
341C2×C32C2×C4×D411yescharacteristic
342C2×C32#57612yes—
343C3⋊D3—44no—
344C3×D3—44no—
345C24—61no—
346C24—181no—
347C2×D4—32no—
348C2×D4—34no—
349C2×D4—62no—
350C2×D4—61no—
351C2×D4—92no—
352C2×D4—94no—
353C2×D4—182no—
354C2×D4—181no—
355C22×C4—64no—
356C22×C4—184no—
357C22×C4C2×D3211yescharacteristic
358D8—98no—
359D8—98no—
360M16—182no—
361C2×C8—31no—
362C2×C8—31no—
363C2×C8—34no—
364C2×C8—92no—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4C2×D3212yes—
368C22⋊C4—21no—
369C22⋊C4—32no—
370C22⋊C4—64no—
371C22⋊C4—61no—
372C22⋊C4—184no—
373C42—21no—
374C42—32no—
375C42—61no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—42no—
381C22×C3—64no—
382C22×C3—124no—
383C22×C3—244no—
384C22×C3#89312yes—
385C22×C3C4×#6712yes—
386C22×C3C2×D3×D411yescharacteristic
387C22×C3C22×#6711yescharacteristic
388C2×D3—24no—
389C2×D3—44no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—84no—
393C2×D3—124no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—244no—
397C2×D3—244no—
398C2×D3—244no—
399C2×D3—248no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—42no—
404C3×C4—42no—
405C3×C4—64no—
406C3×C4—82no—
407C3×C4—122no—
408C3×C4#89312yes—
409C3×C4C4×#6712yes—
410C3×C4C22×C4×D311yescharacteristic
411C3×C4C22×C4×D311yescharacteristic
412C3×C4C2×#23511yescharacteristic
413C3×C4C2×#23911yescharacteristic
414Dic3—24no—
415Dic3—42no—
416C32#294811yescharacteristic, complemented, Sylow
417C23—62no—
418C23—64no—
419C23—182no—
420C23—184no—
421C23—242no—
422C23—722no—
423C23D3×#6711yescharacteristic
424D4—34no—
425D4—62no—
426D4—64no—
427D4—94no—
428D4—182no—
429D4—184no—
430C2×C4—22no—
431C2×C4—34no—
432C2×C4—62no—
433C2×C4—244no—
434C2×C4—724no—
435C2×C4#379912yes—
436C2×C4C4×D3212yes—
437C2×C4D3×#6711yescharacteristic
438C2×C4C22×D3211yescharacteristic
439C8—32no—
440C8—32no—
441C8—182no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—42no—
447C2×C3—124no—
448C2×C3C2×#89311yescharacteristic
449C2×C3#576912yes—
450C2×C3C2×C4×#6711yescharacteristic
451C2×C3#583512yes—
452D3—44no—
453D3—124no—
454D3—124no—
455D3—244no—
456C22—22no—
457C22—64no—
458C22—124no—
459C22—184no—
460C22—244no—
461C22—364no—
462C22—724no—
463C22#6390412yes—
464C22C2×D3×#6711yescharacteristic
465C4—42no—
466C4—64no—
467C4—122no—
468C4#6390412yes—
469C4C2×#379911yescharacteristic
470C4C2×C4×D3211yescharacteristic
471C3—21no—
472C3#7916711yescharacteristic, complemented
473C3#8253811yescharacteristic, complemented
474C2—22no—
475C2—124no—
476C2—364no—
477C2C2×#6390411yescharacteristic
478C2#1059545612yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2948
LCSG ▷ 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
2. #10594996C2semidirect
4. #10592700C2semidirect
5. C3×#4998C2semidirect
6. #10591085C2semidirect
7. #10591055C2semidirect
8. #10590589C2semidirect
9. #10590456C2semidirect
19. C3×#893C22semidirect
24. #63894C22semidirect
25. C2×#3714C4semidirect
28. #63636C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
31. #63562C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
39. #5521D3semidirect
49. #4998D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
82. #3714C2×C4semidirect
83. #3714C2×C4semidirect
113. #893C2×D3semidirect
129. #808C2×D3semidirect
130. #807C2×D3semidirect
194. C2×D12C4×D3semidirect
235. C2×C3⋊C8C4×D3semidirect
416. C32#2948semidirect
472. C3#79167semidirect
473. C3#82538semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105949962
C22×#37142
#105927002
C3×#49982
#105910852
#105910552
#105905892
#105904562
#825383
#791673