Finite Group Databasebeta

← #11859908

Subgroups — #11859908

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63796C211yesmaximal, characteristic
2#10594605C211yesmaximal, characteristic
3#10594363C211yesmaximal, characteristic, complemented
4C3⋊D3×#106C211yesmaximal, characteristic, complemented
5C3×#4852C212yesmaximal, complemented
6Dic3×#204C212yesmaximal, complemented
7C8×#624C211yesmaximal, characteristic, complemented
8#10590601C211yesmaximal, characteristic, complemented
9#10590593C211yesmaximal, characteristic
10#10590475C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12C4×D3×SD16—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C4×D32—21no—
15C2×#3797C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C2×C3×#204C2212yes—
20C3×#893C2212yes—
21C3×#887C2212yescomplemented
22#63921—21no—
23Dic3×D12C2212yes—
24#63883—21no—
25C4×#624—21no—
26C4×#624C2211yescharacteristic
27#63879—22no—
28Dic3×Dic6C2212yescomplemented
29#63837—22no—
30C2×#3715C2212yes—
31C2×#3710C2211yescharacteristic
32#63796C418yescomplemented
33C32×#106C2211yescharacteristic, complemented
34#63644C2211yescharacteristic, complemented
35#63635C2211yescharacteristic, complemented
36#63635C2211yescharacteristic, complemented
37C3×C8×Dic3C2212yescomplemented
38C3×#810C2212yescomplemented
39C3×#809C2212yes—
40#63566C2212yescomplemented
41#63563C2212yes—
42Dic3×C3⋊C8C2212yescomplemented
43C2×D3×SD16—32no—
44C4×D3×Q8—32no—
45C4×D3×D4—32no—
46C3×C4×SD16—32no—
47Dic3×SD16—32no—
48C4×#215—32no—
49C4×#214—32no—
50D3×#106—32no—
51D3×#106—61no—
52#4852D312yescomplemented
53D3×#103—32no—
54#4788—32no—
55D3×#102—32no—
56#4758—32no—
57C4×#204—32no—
58C4×D3×C8—32no—
59C22×D32—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6C2312yes—
66C2×#627—21no—
67C2×#625—21no—
68C2×#624—21no—
69C2×#624D411yescharacteristic
70C2×#624D411yescharacteristic
71C2×D3×Dic3—22no—
72#3802—22no—
73#3802C2×C414yes—
74C4×D32—44no—
75#3797—22no—
76#3797C2×C414yescomplemented
77C2×C32×C8C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83#3750—21no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C8×C3⋊D3C2×C414yescomplemented
86C3×(C2×D3)⋊C4—22no—
87C3×Dic3⋊C4—22no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91C3×#204C2×C418yescomplemented
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95Dic32D412yes—
96#3715C2×C418yescomplemented
97#3710—22no—
98C2×C4×SD16—91noSylow
99C2×D3×Q8—32no—
100C2×D3×D4—32no—
101C22×C4×D3—62no—
102C2×C3×SD16—32no—
103C3×C4×Q8—32no—
104C3×C4×D4—32no—
105Q8×Dic3—32no—
106C2×#215—32no—
107D4×Dic3—32no—
108C2×#214—32no—
109C4×#67—62no—
110D3×SD16—316no—
111C2×#204C2×D312yes—
112C2×D3×C8—32no—
113C2×D3×C8—32no—
114C2×D3×C8—61no—
115#893C2×D312yes—
116D3×C4⋊C4—32no—
117D3×C4⋊C4—32no—
118D3×C4⋊C4—61no—
119D3×C4⋊C4—61no—
120D3×C4⋊C4—62no—
121#887—62no—
122#887C2×D312yescomplemented
123#67⋊C4—62no—
124D3×C22⋊C4—62no—
125C4×D12—32no—
126C42×D3—32no—
127C42×D3—62no—
128C4×Dic6—32no—
129C4×Dic6—62no—
130C3×#106—21no—
131C3×#106C2×D312yescomplemented
132C3×#103—32no—
133C3×#102—32no—
134C3×C4×C8—32no—
135#835—32no—
136#832—32no—
137#821—32no—
138#817—32no—
139#817—61no—
140#816—32no—
141C8×Dic3—32no—
142C8×Dic3C2×D312yescomplemented
143#810C2×D312yescomplemented
144#809C2×D312yes—
145#808—32no—
146#808—32no—
147#808—61no—
148#808—61no—
149C4×C3⋊C8—32no—
150C22×C3⋊D3C2×D411yescharacteristic
151C22×C3×D3—22no—
152C2×D32—24no—
153C2×D32—42no—
154C2×D32—42no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3C22×C412yes—
164C4×C3⋊D3#4112yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C2×C3×Dic3C2×D412yes—
168C3×D12—22no—
169C3×D12C22×C414yes—
170C3×C4×D3—44no—
171C3×Dic6—22no—
172C3×Dic6C22×C414yescomplemented
173#627—24no—
174#625—24no—
175#624—24no—
176#624—22no—
177#624SD1614yescomplemented
178D3×Dic3—44no—
179C32×C8C22×C412yescomplemented
180C3⋊(C3⋊C8)C22×C412yescomplemented
181C3×C3⋊C8—22no—
182C22×SD16—91no—
183C2×C4×Q8—91no—
184C2×C4×D4—91no—
185C4×SD16—32no—
186C4×SD16—92no—
187C4×SD16—92no—
188C4×SD16—92no—
189C2×#106—91no—
190C2×#103—91no—
191C2×#102—91no—
192C2×C4×C8—91no—
193C23×D3—62no—
194C2×C3×Q8—32no—
195C2×C3×D4—32no—
196C22×C3×C4—62no—
197C2×#67—62no—
198C22×Dic3—62no—
199D3×Q8—38no—
200D3×Q8—64no—
201D3×D4—38no—
202D3×D4—64no—
203C2×D12C22×D312yes—
204C2×C4×D3—22no—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—61no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—121no—
214C2×C4×D3—121no—
215C2×C4×D3—128no—
216C2×Dic6—62no—
217C2×Dic6C22×D312yes—
218C3×SD16—38no—
219C2×C3×C8—21no—
220C2×C3×C8—32no—
221C2×C3×C8C22×D312yes—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—62no—
225C3×C4⋊C4C22×D312yes—
226C3×C4⋊C4C22×D312yes—
227C3×C22⋊C4—62no—
228C3×C42—32no—
229C3×C42—62no—
230#217—62no—
231#215—38no—
232#214—38no—
233(C2×D3)⋊C4—22no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3—62no—
240Dic3⋊C4—22no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—121no—
245Dic3⋊C4—121no—
246C4×Dic3—22no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3C22×D312yes—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8C22×D312yes—
255#204C4×D318yescomplemented
256D3×C8—38no—
257D3×C8—64no—
258D3×C8—64no—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3C4×D412yes—
261C2×C3⋊D3C2×SD1612yes—
262C2×C3⋊D3#13512yes—
263C2×C3×D3—24no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266D32—48no—
267C32×C4—41no—
268C32×C4—41no—
269C32×C4C23×C411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3⋊Dic3—41no—
272C3⋊Dic3—41no—
273C3⋊Dic3C4×D412yes—
274C3×Dic3—24no—
275C3×Dic3—22no—
276C3×Dic3C2×SD1614yescomplemented
277C22×Q8—91no—
278C22×D4—91no—
279C23×C4—181no—
280C2×SD16—32no—
281C2×SD16—98no—
282C2×SD16—92no—
283C22×C8—91no—
284C22×C8—91no—
285C4×Q8—32no—
286C4×Q8—92no—
287C4×Q8—182no—
288C4×D4—32no—
289C4×D4—92no—
290C4×D4—182no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C42—91no—
296C2×C42—181no—
297#106—91no—
298#106—91no—
299#106—91no—
300#106D3211yescharacteristic, complemented
301#103—32no—
302#103—92no—
303#102—32no—
304#102—92no—
305C4×C8—32no—
306C4×C8—92no—
307C23×C3—62no—
308C22×D3—22no—
309C22×D3—32no—
310C22×D3—61no—
311C22×D3—68no—
312C22×D3—124no—
313C22×D3—124no—
314C3×Q8—34no—
315C3×Q8—62no—
316C3×D4—34no—
317C3×D4—62no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—62no—
326C2×C3×C4—124no—
327C2×C3×C4C23×D312yes—
328#67—68no—
329C2×Dic3—22no—
330C2×Dic3—32no—
331C2×Dic3—61no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—124no—
337C2×Dic3D3×D412yes—
338C2×Dic3D3×D412yes—
339D12—22no—
340D12C2×C4×D314yes—
341C4×D3—34no—
342C4×D3—34no—
343C4×D3—38no—
344C4×D3—44no—
345C4×D3—62no—
346C4×D3—62no—
347C4×D3—64no—
348C4×D3—68no—
349C4×D3—124no—
350C4×D3—124no—
351C4×D3—124no—
352C4×D3—242no—
353C4×D3—242no—
354Dic6—22no—
355Dic6—68no—
356Dic6C2×C4×D314yescomplemented
357C3×C8—22no—
358C3×C8—62no—
359C3×C8C2×C4×D314yescomplemented
360C3⋊C8—22no—
361C3⋊C8—34no—
362C3⋊C8—62no—
363C2×C32C2×C4×D411yescharacteristic
364C2×C32C22×SD1611yescharacteristic
365C2×C32C2×#13511yescharacteristic
366C3⋊D3C4×SD1614yescomplemented
367C3×D3—44no—
368C24—181no—
369C2×Q8—32no—
370C2×Q8—94no—
371C2×Q8—181no—
372C2×Q8—182no—
373C2×D4—32no—
374C2×D4—94no—
375C2×D4—182no—
376C2×D4—181no—
377C22×C4—62no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—181no—
382C22×C4—181no—
383C22×C4—182no—
384C22×C4—181no—
385C22×C4—364no—
386SD16—38no—
387SD16—98no—
388C2×C8—32no—
389C2×C8—91no—
390C2×C8—94no—
391C2×C8—182no—
392C2×C8C2×D3211yescharacteristic
393C4⋊C4—62no—
394C4⋊C4—91no—
395C4⋊C4—91no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—182no—
399C4⋊C4C2×D3211yescharacteristic
400C4⋊C4C2×D3211yescharacteristic
401C22⋊C4—62no—
402C22⋊C4—182no—
403C42—32no—
404C42—62no—
405C42—92no—
406C42—182no—
407C22×C3—21no—
408C22×C3—64no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×D3×D412yes—
412C2×D3—24no—
413C2×D3—34no—
414C2×D3—34no—
415C2×D3—34no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—62no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—1216no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—34no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—62no—
428C3×C4—64no—
429C3×C4—81no—
430C3×C4—81no—
431C3×C4C22×C4×D312yes—
432C3×C4D3×#4112yes—
433Dic3—22no—
434Dic3—24no—
435Dic3—34no—
436Dic3—62no—
437Dic3—122no—
438Dic3—122no—
439Dic3—241no—
440Dic3—241no—
441Dic3D3×SD1614yescomplemented
442C32C2×C4×SD1611yescharacteristic, complemented, Sylow
443C23—62no—
444C23—91no—
445C23—184no—
446C23—362no—
447C23—362no—
448Q8—34no—
449Q8—62no—
450Q8—184no—
451D4—34no—
452D4—62no—
453D4—184no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—62no—
459C2×C4—94no—
460C2×C4—91no—
461C2×C4—92no—
462C2×C4—92no—
463C2×C4—124no—
464C2×C4—182no—
465C2×C4—184no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—364no—
469C2×C4—362no—
470C2×C4—362no—
471C2×C4C22×D3211yescharacteristic
472C8—62no—
473C8—92no—
474C8C4×D3212yescomplemented
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—124no—
479C2×C3C4×D3×D412yes—
480C2×C3C2×D3×SD1612yes—
481C2×C3D3×#13512yes—
482D3—38no—
483D3—44no—
484D3—64no—
485C22—64no—
486C22—92no—
487C22—92no—
488C22—92no—
489C22—122no—
490C22—122no—
491C22—368no—
492C22D32×D411yescharacteristic
493C4—34no—
494C4—41no—
495C4—41no—
496C4—64no—
497C4—62no—
498C4—92no—
499C4—361no—
500C4—361no—
501C4C2×C4×D3211yescharacteristic
502C4#6431911yescharacteristic
503C3—21no—
504C3C4×D3×SD1612yescomplemented
505C2—94no—
506C2—124no—
507C2#1059460511yescharacteristic
508C2D32×SD1611yescharacteristic
509C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10594363C2semidirect
4. C3⋊D3×#106C2semidirect
5. C3×#4852C2semidirect
6. Dic3×#204C2semidirect
7. C8×#624C2semidirect
8. #10590601C2semidirect
10. #10590475C2semidirect
11. #10590453C2semidirect
21. C3×#887C22semidirect
28. Dic3×Dic6C22semidirect
32. #63796C4semidirect
33. C32×#106C22semidirect
34. #63644C22semidirect
35. #63635C22semidirect
36. #63635C22semidirect
37. C3×C8×Dic3C22semidirect
38. C3×#810C22semidirect
40. #63566C22semidirect
42. Dic3×C3⋊C8C22semidirect
52. #4852D3semidirect
76. #3797C2×C4semidirect
85. C8×C3⋊D3C2×C4semidirect
91. C3×#204C2×C4semidirect
96. #3715C2×C4semidirect
122. #887C2×D3semidirect
131. C3×#106C2×D3semidirect
142. C8×Dic3C2×D3semidirect
143. #810C2×D3semidirect
172. C3×Dic6C22×C4semidirect
177. #624SD16semidirect
179. C32×C8C22×C4semidirect
180. C3⋊(C3⋊C8)C22×C4semidirect
255. #204C4×D3semidirect
276. C3×Dic3C2×SD16semidirect
300. #106D32semidirect
356. Dic6C2×C4×D3semidirect
359. C3×C8C2×C4×D3semidirect
366. C3⋊D3C4×SD16semidirect
441. Dic3D3×SD16semidirect
442. C32C2×C4×SD16semidirect
474. C8C4×D32semidirect
504. C3C4×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#637962
#105946052
#105943632
C3⋊D3×#1062
C3×#48522
Dic3×#2042
C8×#6242
#105906012
#105905932
#105904752
#105904532
C4×D3×SD163