Finite Group Databasebeta

← #11860700

Subgroups — #11860700

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591096C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic, complemented
8#10590346C214yesmaximal, complemented
9C4×#3714C214yesmaximal, complemented
10#82538—31nomaximal
11#78561—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16#64102—22no—
17C22⋊C4×C3⋊D3—22no—
18C4×C4⋊(C3⋊D3)C2214yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—22no—
23C3×D3×C22⋊C4—22no—
24C3×C4×D12C2214yescomplemented
25C2×#3714C418yescomplemented
26C2×#3714C2212yes—
27C2×#3714C2212yes—
28C3×#803C2212yescomplemented
29C3×C4×C3⋊C8C2212yescomplemented
30#63575C2212yescomplemented
31#63573C2212yescomplemented
32#63564C2214yescomplemented
33#63563C2214yescomplemented
34C3×#518—31no—
35C22×#213—31no—
36C22×D24—31no—
37#5521—31no—
38#5521—31no—
39#5521—61no—
40#5521D311yescharacteristic, complemented
41C3×#405—31no—
42#5215—31no—
43#5131—31no—
44#5131—31no—
45#5106—31no—
46#5014—34no—
47C4×#213—34no—
48#5001—31no—
49#4998—31no—
50#4997D311yescharacteristic, complemented
51#4711—34no—
52C4×D24—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×C4×C3⋊D3—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—24no—
66C32×C4⋊C4D412yes—
67C32×C22⋊C4D412yes—
68C32×C42C2312yes—
69#3757—21no—
70#3752—24no—
71C4⋊(C3⋊Dic3)C2312yes—
72C4×C3⋊Dic3—21no—
73C3×#217—21no—
74C3×(C2×D3)⋊C4—24no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3—21no—
77C3×#208—22no—
78C2×C3×C3⋊C8C2×C414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
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
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×C4×D4—34no—
93C3×C4×D4—62no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C2×D311yescharacteristic
98C2×C3×C22⋊C4—62no—
99C2×#213—38no—
100C2×#213—32no—
101C2×#213—32no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×D24—38no—
109C2×D24—32no—
110C2×D24—32no—
111#893—22no—
112#893—64no—
113#893—62no—
114#893—62no—
115D3×C22⋊C4—22no—
116D3×C22⋊C4—64no—
117D3×C22⋊C4—62no—
118D3×C22⋊C4—62no—
119C4×D12—34no—
120C4×D12—34no—
121C4×D12—64no—
122C4×D12C2×D314yescomplemented
123C3×#97—32no—
124C3×C4×C8—32no—
125#832—34no—
126#821—34no—
127#821—34no—
128#818—32no—
129#817—32no—
130#809—34no—
131#808—32no—
132#807—32no—
133#803C2×D312yescomplemented
134C4×C3⋊C8C2×D312yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3—82no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D414yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)C22×C414yes—
151C4×C3⋊D3—84no—
152C2×C3×Dic3—22no—
153C3×D12—24no—
154C3×D12—22no—
155C3×D12C22×C414yes—
156C3×C4×D3—84no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8C22×C412yes—
159C3×C3⋊C8C22×C412yes—
160C22×D8—91no—
161#518—31no—
162#518—91no—
163#442—94no—
164C4×D8—94no—
165#427—91no—
166#418—91no—
167#418—91no—
168#405—31no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3—62no—
172C23×D3—61no—
173C23×D3—61no—
174C2×C3×D4—34no—
175C2×C3×D4—32no—
176C2×C3×D4—61no—
177C2×C3×D4—62no—
178C22×C3×C4—21no—
179C22×C3×C4—64no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×D12—22no—
183C2×D12—21no—
184C2×D12—34no—
185C2×D12—34no—
186C2×D12—32no—
187C2×D12—32no—
188C2×D12—62no—
189C2×D12—64no—
190C2×D12—62no—
191C2×D12—64no—
192C2×D12—61no—
193C2×D12—62no—
194C2×D12—62no—
195C2×D12—61no—
196C2×D12C4×D314yescomplemented
197C2×D12C22×D312yes—
198C2×C4×D3—24no—
199C2×C4×D3—68no—
200C2×C4×D3—64no—
201C2×C4×D3—64no—
202C3×M16—62no—
203C2×C3×C8—34no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8—32no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4D1212yes—
210C3×C4⋊C4#6712yes—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—64no—
214C3×C22⋊C4D1212yes—
215C3×C22⋊C4#6712yes—
216C3×C42—22no—
217C3×C42—61no—
218C3×C42C22×D312yes—
219C3×C42C22×D312yes—
220#217—21no—
221#217—62no—
222#217—61no—
223#217—61no—
224#213—38no—
225#213—38no—
226(C2×D3)⋊C4—24no—
227(C2×D3)⋊C4—68no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234C4×Dic3—21no—
235C4×Dic3—62no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238#208—22no—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D311yescharacteristic
242C2×C3⋊C8C22×D311yescharacteristic
243D24—38no—
244D24—38no—
245C22×C32—22no—
246C22×C32C4×D412yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—44no—
250C2×C3⋊D3—84no—
251C2×C3×D3—24no—
252C2×C3×D3—44no—
253C2×C3×D3—84no—
254C32×C4—24no—
255C32×C4C4×D412yes—
256C32×C4C23×C411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—42no—
259C3×Dic3—42no—
260C22×D4—31no—
261C22×D4—91no—
262C2×D8—98no—
263C2×D8—92no—
264C2×D8—92no—
265C2×M16—31no—
266C22×C8—31no—
267C4×D4—34no—
268C4×D4—62no—
269C4×D4—94no—
270C4×D4—182no—
271#117—31no—
272#117—91no—
273#117D3211yescharacteristic
274C2×C22⋊C4—62no—
275C2×C22⋊C4—182no—
276#107—92no—
277#106—92no—
278#102—94no—
279#102—94no—
280#97—32no—
281C4×C8—32no—
282C23×C3—21no—
283C23×C3—62no—
284C23×C3—64no—
285C23×C3—242no—
286C23×C3C2×D1211yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—22no—
289C22×D3—24no—
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—68no—
294C22×D3—64no—
295C22×D3—64no—
296C22×D3—82no—
297C22×D3—242no—
298C22×D3—242no—
299C22×D3—244no—
300C3×D4—34no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—24no—
308C2×C3×C4—62no—
309C2×C3×C4—244no—
310C2×C3×C4C2×C4×D312yes—
311C2×C3×C4C2×C4×D312yes—
312C2×C3×C4C2×D1214yes—
313C2×C3×C4C2×D1211yescharacteristic
314C2×C3×C4#23512yes—
315C2×C3×C4#23512yes—
316C2×C3×C4C2×#6714yes—
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324D12—24no—
325D12—22no—
326D12—34no—
327D12—34no—
328D12—64no—
329D12—64no—
330D12—68no—
331D12—64no—
332D12—64no—
333D12—62no—
334D12—62no—
335D12C2×C4×D314yes—
336C4×D3—84no—
337C4×D3—244no—
338C4×D3—244no—
339C4×D3—248no—
340C3×C8—32no—
341C3×C8—32no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8C2×C4×D312yes—
345C3⋊C8C2×C4×D312yes—
346C2×C32—22no—
347C2×C32C2×C4×D411yescharacteristic
348C2×C32#57612yes—
349C3⋊D3—44no—
350C3×D3—44no—
351C24—61no—
352C24—181no—
353C2×D4—32no—
354C2×D4—34no—
355C2×D4—62no—
356C2×D4—61no—
357C2×D4—92no—
358C2×D4—94no—
359C2×D4—182no—
360C2×D4—181no—
361C22×C4—64no—
362C22×C4—184no—
363C22×C4C2×D3211yescharacteristic
364D8—98no—
365D8—98no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—34no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4—92no—
373C4⋊C4#62612yes—
374C22⋊C4—61no—
375C22⋊C4—64no—
376C22⋊C4—181no—
377C22⋊C4—184no—
378C22⋊C4#62612yes—
379C42—61no—
380C42—181no—
381C42C2×D3212yes—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—42no—
387C22×C3—64no—
388C22×C3—124no—
389C22×C3—244no—
390C22×C3C4×D1212yes—
391C22×C3C4×#6712yes—
392C22×C3C22×D1211yescharacteristic
393C22×C3C22×#6711yescharacteristic
394C2×D3—24no—
395C2×D3—44no—
396C2×D3—68no—
397C2×D3—64no—
398C2×D3—64no—
399C2×D3—84no—
400C2×D3—128no—
401C2×D3—124no—
402C2×D3—124no—
403C2×D3—244no—
404C2×D3—244no—
405C2×D3—248no—
406C3×C4—24no—
407C3×C4—24no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—22no—
411C3×C4—44no—
412C3×C4—122no—
413C3×C4C4×D1212yes—
414C3×C4C4×#6712yes—
415C3×C4C22×C4×D311yescharacteristic
416C3×C4C22×C4×D311yescharacteristic
417C3×C4C2×#23511yescharacteristic
418C3×C4C2×#23511yescharacteristic
419Dic3—42no—
420Dic3—124no—
421Dic3—122no—
422Dic3—122no—
423C32#294811yescharacteristic, complemented, Sylow
424C23—62no—
425C23—64no—
426C23—182no—
427C23—184no—
428C23—242no—
429C23—722no—
430C23C2×#62611yescharacteristic
431D4—34no—
432D4—62no—
433D4—64no—
434D4—94no—
435D4—182no—
436D4—184no—
437C2×C4—62no—
438C2×C4—182no—
439C2×C4—244no—
440C2×C4—724no—
441C2×C4#379812yes—
442C2×C4C4×D3212yes—
443C2×C4C2×#62614yes—
444C2×C4C2×#62611yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—32no—
447C8—32no—
448C8—62no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—42no—
454C2×C3—124no—
455C2×C3C2×C4×D1211yescharacteristic
456C2×C3#575212yes—
457C2×C3C2×C4×#6711yescharacteristic
458C2×C3#583512yes—
459D3—44no—
460D3—128no—
461D3—124no—
462D3—124no—
463C22—22no—
464C22—64no—
465C22—124no—
466C22—184no—
467C22—244no—
468C22—364no—
469C22—724no—
470C22C4×#62612yes—
471C22C22×#62611yescharacteristic
472C4—24no—
473C4—122no—
474C4—362no—
475C4C4×#62612yes—
476C4C2×#379811yescharacteristic
477C4C2×C4×D3211yescharacteristic
478C3—21no—
479C3#7856111yescharacteristic, complemented
480C3#8253811yescharacteristic, complemented
481C2—22no—
482C2—124no—
483C2—364no—
484C2C2×C4×#62611yescharacteristic
485C2#1059544912yes—
subgroupG/H
centerC22C22×#626
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 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
2. C3×#5521C2semidirect
4. C3×#4997C2semidirect
5. #10591122C2semidirect
6. #10591096C2semidirect
7. #10591086C2semidirect
8. #10590346C2semidirect
9. C4×#3714C2semidirect
18. C4×C4⋊(C3⋊D3)C22semidirect
24. C3×C4×D12C22semidirect
25. C2×#3714C4semidirect
28. C3×#803C22semidirect
29. C3×C4×C3⋊C8C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
32. #63564C22semidirect
33. #63563C22semidirect
40. #5521D3semidirect
50. #4997D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
82. #3714C2×C4semidirect
83. #3714C2×C4semidirect
122. C4×D12C2×D3semidirect
133. #803C2×D3semidirect
134. C4×C3⋊C8C2×D3semidirect
196. C2×D12C4×D3semidirect
239. C2×C3⋊C8C4×D3semidirect
423. C32#2948semidirect
479. C3#78561semidirect
480. C3#82538semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55212
C22×#37142
C3×#49972
#105911222
#105910962
#105910862
#105903462
C4×#37142
#825383
#785613