Finite Group Databasebeta

← #11860088

Subgroups — #11860088

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#624C211yesmaximal, characteristic, complemented
2C2×#63940C211yesmaximal, characteristic
3#10594605C211yesmaximal, characteristic
4C3⋊D3×#103C211yesmaximal, characteristic, complemented
5C3×#4817C212yesmaximal, complemented
6#10591566C212yesmaximal, complemented
7#10590940C211yesmaximal, characteristic
8#10590747C212yesmaximal, complemented
9#10590668C211yesmaximal, characteristic, complemented
10#10590590C212yesmaximal, complemented
11#10590573C211yesmaximal, characteristic, complemented
12D3×#440—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×#3802C2211yescharacteristic
15C2×C4×D32—21no—
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×Q8×Dic3C2212yescomplemented
19C2×C3×#215C2212yes—
20C3×#893C2212yes—
21#63940C418yescomplemented
22#63921—21no—
23#63900—21no—
24#63900C2211yescharacteristic
25Dic3×D12C2212yes—
26C4×#624—21no—
27C4×#624C2211yescharacteristic
28#63879—22no—
29#63844—22no—
30#63844C2212yescomplemented
31C2×#3716C2212yes—
32C2×#3710C2211yescharacteristic
33C32×#103C2211yescharacteristic, complemented
34#63662C2211yescharacteristic, complemented
35#63643C2211yescharacteristic, complemented
36#63637C2211yescharacteristic, complemented
37C3×#821C2212yes—
38C3×#815C2212yescomplemented
39C3×#807C2212yescomplemented
40#63575C2212yescomplemented
41#63562C2212yes—
42#63554C2212yescomplemented
43C2×D3×SD16—32no—
44C4×D3×Q8—32no—
45C4×D3×D4—32no—
46C3×#440—32no—
47#5164—32no—
48#5026—32no—
49#5018—32no—
50#4889—32no—
51D3×#107—32no—
52#4817D312yescomplemented
53D3×#103—32no—
54D3×#103—61no—
55D3×#102—32no—
56#4757—32no—
57#4710—32no—
58D3×#97—32no—
59C22×D32—21no—
60C2×C32×Q8C2311yescharacteristic
61Q8×C3⋊D3—22no—
62Q8×C3⋊D3C2×C414yescomplemented
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—22no—
70C2×#625—21no—
71C2×#624—21no—
72C2×#624D411yescharacteristic
73C2×#624D411yescharacteristic
74C2×D3×Dic3—22no—
75#3802—22no—
76#3802C2×C414yes—
77C4×D32—44no—
78C2×C32×C8C2311yescharacteristic
79C32×C4⋊C4C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C8×C3⋊D3—22no—
84C3×#215C2×C418yescomplemented
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3C2312yes—
88C3×C4×Dic3—22no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3724—21no—
92#3724—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95Dic32D412yes—
96#3716C2×C418yescomplemented
97#3710C2×C414yescomplemented
98C2×#440—91noSylow
99C2×D3×Q8—32no—
100C2×D3×Q8—61no—
101C2×D3×D4—32no—
102C22×C4×D3—62no—
103C2×C3×SD16—32no—
104C3×C4×Q8—32no—
105C3×C4×D4—32no—
106Q8×Dic3C2×D312yescomplemented
107C2×#215C2×D312yes—
108D4×Dic3—32no—
109C2×#214—32no—
110C4×#67—62no—
111D3×SD16—316no—
112C2×#204—32no—
113C2×D3×C8—32no—
114C2×D3×C8—32no—
115C2×D3×C8—61no—
116#893C2×D312yes—
117D3×C4⋊C4—32no—
118D3×C4⋊C4—32no—
119D3×C4⋊C4—61no—
120D3×C4⋊C4—62no—
121#887—32no—
122#887—62no—
123#67⋊C4—62no—
124D3×C22⋊C4—62no—
125C4×D12—32no—
126C42×D3—32no—
127C42×D3—62no—
128C4×Dic6—32no—
129C4×Dic6—62no—
130C3×#107—32no—
131C3×#103—21no—
132C3×#103C2×D312yescomplemented
133C3×#102—32no—
134C3×#97—32no—
135#835—32no—
136#835—61no—
137#832—32no—
138#821C2×D312yes—
139#818—32no—
140#816—32no—
141#816—61no—
142#815—32no—
143#815C2×D312yescomplemented
144#810—32no—
145#810—61no—
146#809—32no—
147#807—32no—
148#807C2×D312yescomplemented
149#803—32no—
150C22×C3⋊D3C2×D411yescharacteristic
151C22×C3×D3—22no—
152C2×D32—24no—
153C2×D32—42no—
154C2×D32—42no—
155C32×Q8—21no—
156C32×Q8C22×C412yescomplemented
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3C2×D411yescharacteristic
163C4×C3⋊D3—24no—
164C4×C3⋊D3—42no—
165C4×C3⋊D3C22×C412yes—
166C4×C3⋊D3#4112yes—
167#634—21no—
168#634—24no—
169#634C22×C412yescomplemented
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D412yes—
172C2×C3×Dic3C2×D412yes—
173C3×D12—22no—
174C3×D12C22×C414yes—
175C3×C4×D3—44no—
176#625—24no—
177#624—22no—
178#624—22no—
179#624—42no—
180D3×Dic3—44no—
181C32×C8—21no—
182C3⋊(C3⋊C8)—21no—
183C3×C3⋊C8C22×C414yescomplemented
184C22×SD16—91no—
185C2×C4×Q8—91no—
186C2×C4×D4—91no—
187#440—32no—
188#440—92no—
189#440—92no—
190#440—92no—
191C2×#107—91no—
192C2×#103—91no—
193C2×#102—91no—
194C2×#97—91no—
195C23×D3—62no—
196C2×C3×Q8—21no—
197C2×C3×Q8C22×D312yes—
198C2×C3×D4—32no—
199C22×C3×C4—62no—
200C2×#67—62no—
201C22×Dic3—62no—
202D3×Q8—38no—
203D3×Q8—64no—
204D3×Q8—64no—
205D3×Q8—122no—
206D3×D4—38no—
207D3×D4—64no—
208C2×D12C22×D312yes—
209C2×C4×D3—22no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—121no—
219C2×C4×D3—121no—
220C2×C4×D3—128no—
221C2×Dic6—32no—
222C2×Dic6—61no—
223C2×Dic6—62no—
224C2×Dic6—121no—
225C3×SD16—38no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4C22×D312yes—
233C3×C22⋊C4—62no—
234C3×C42—32no—
235C3×C42—62no—
236#217—62no—
237#215C4×D318yescomplemented
238#214—38no—
239(C2×D3)⋊C4—22no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—22no—
242C4⋊Dic3—32no—
243C4⋊Dic3—61no—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—62no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—121no—
250C4×Dic3—22no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3C22×D312yes—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8C22×D312yes—
259#204—38no—
260D3×C8—38no—
261D3×C8—64no—
262D3×C8—122no—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3C4×D412yes—
265C2×C3⋊D3AGL(1,ℤ/8)12yes—
266C2×C3⋊D3#13712yes—
267C2×C3×D3—24no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270D32—48no—
271C32×C4—22no—
272C32×C4—41no—
273C32×C4C23×C411yescharacteristic
274C32×C4C2×#4111yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—41no—
277C3⋊Dic3C4×D412yes—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3—42no—
281C22×Q8—91no—
282C22×D4—91no—
283C23×C4—181no—
284C2×SD16—32no—
285C2×SD16—92no—
286C2×SD16—98no—
287C22×C8—91no—
288C22×C8—91no—
289C4×Q8—32no—
290C4×Q8—92no—
291C4×Q8—182no—
292C4×D4—32no—
293C4×D4—92no—
294C4×D4—182no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—181no—
298C2×C22⋊C4—181no—
299C2×C42—91no—
300C2×C42—181no—
301#107—32no—
302#107—92no—
303#103—91no—
304#103—91no—
305#103—91no—
306#103D3211yescharacteristic, complemented
307#102—32no—
308#102—92no—
309#97—32no—
310#97—92no—
311C23×C3—62no—
312C22×D3—22no—
313C22×D3—32no—
314C22×D3—61no—
315C22×D3—68no—
316C22×D3—124no—
317C22×D3—124no—
318C3×Q8—22no—
319C3×Q8—22no—
320C3×Q8—41no—
321C3×Q8C2×C4×D314yescomplemented
322C3×D4—34no—
323C3×D4—62no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—62no—
332C2×C3×C4—124no—
333C2×C3×C4C23×D312yes—
334#67—68no—
335C2×Dic3—22no—
336C2×Dic3—32no—
337C2×Dic3—61no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—124no—
343C2×Dic3D3×D412yes—
344C2×Dic3D3×D412yes—
345D12—22no—
346D12C2×C4×D314yes—
347C4×D3—34no—
348C4×D3—34no—
349C4×D3—44no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—64no—
353C4×D3—64no—
354C4×D3—68no—
355C4×D3—124no—
356C4×D3—124no—
357C4×D3—124no—
358C4×D3—124no—
359C4×D3—242no—
360Dic6—34no—
361Dic6—62no—
362Dic6—68no—
363Dic6—62no—
364Dic6—124no—
365Dic6—121no—
366C3×C8—22no—
367C3×C8—34no—
368C3×C8—41no—
369C3⋊C8—62no—
370C3⋊C8—121no—
371C3⋊C8C2×C4×D314yescomplemented
372C2×C32C2×C4×D411yescharacteristic
373C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
374C2×C32C2×#13711yescharacteristic
375C3⋊D3#44014yescomplemented
376C3×D3—44no—
377C24—181no—
378C2×Q8—94no—
379C2×Q8—91no—
380C2×Q8—181no—
381C2×Q8—182no—
382C2×Q8C2×D3211yescharacteristic
383C2×D4—32no—
384C2×D4—94no—
385C2×D4—182no—
386C2×D4—181no—
387C22×C4—62no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—182no—
394C22×C4—181no—
395C22×C4—364no—
396SD16—38no—
397SD16—98no—
398C2×C8—32no—
399C2×C8—94no—
400C2×C8—91no—
401C2×C8—182no—
402C2×C8C2×D3211yescharacteristic
403C4⋊C4—32no—
404C4⋊C4—62no—
405C4⋊C4—91no—
406C4⋊C4—181no—
407C4⋊C4—182no—
408C4⋊C4—181no—
409C4⋊C4C2×D3211yescharacteristic
410C22⋊C4—62no—
411C22⋊C4—182no—
412C42—32no—
413C42—62no—
414C42—92no—
415C42—182no—
416C22×C3—21no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3C2×D3×D412yes—
421C2×D3—24no—
422C2×D3—34no—
423C2×D3—34no—
424C2×D3—34no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—62no—
428C2×D3—62no—
429C2×D3—62no—
430C2×D3—1216no—
431C3×C4—24no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—62no—
437C3×C4—62no—
438C3×C4—81no—
439C3×C4—122no—
440C3×C4C22×C4×D312yes—
441C3×C4D3×#4112yes—
442Dic3—22no—
443Dic3—22no—
444Dic3—34no—
445Dic3—42no—
446Dic3—62no—
447Dic3—64no—
448Dic3—122no—
449Dic3—122no—
450Dic3—241no—
451C32C2×#44011yescharacteristic, complemented, Sylow
452C23—62no—
453C23—91no—
454C23—184no—
455C23—362no—
456C23—362no—
457Q8—21no—
458Q8—92no—
459Q8—184no—
460Q8—181no—
461Q8C4×D3212yescomplemented
462D4—34no—
463D4—62no—
464D4—184no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—62no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—124no—
474C2×C4—184no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—362no—
480C2×C4—364no—
481C2×C4—362no—
482C2×C4C22×D3211yescharacteristic
483C8—21no—
484C8—34no—
485C8—181no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—124no—
490C2×C3C4×D3×D412yes—
491C2×C3D3×AGL(1,ℤ/8)12yes—
492C2×C3D3×#13712yes—
493D3—38no—
494D3—44no—
495D3—64no—
496C22—64no—
497C22—92no—
498C22—92no—
499C22—92no—
500C22—122no—
501C22—122no—
502C22—368no—
503C22D32×D411yescharacteristic
504C4—22no—
505C4—41no—
506C4—62no—
507C4—62no—
508C4—92no—
509C4—122no—
510C4—182no—
511C4—361no—
512C4C2×C4×D3211yescharacteristic
513C4#6431211yescharacteristic
514C3—21no—
515C3D3×#44012yescomplemented
516C2—94no—
517C2—124no—
518C2#1059425511yescharacteristic
519C2#1059474011yescharacteristic
520C2#1059476011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. Q8×#624C2semidirect
4. C3⋊D3×#103C2semidirect
5. C3×#4817C2semidirect
6. #10591566C2semidirect
8. #10590747C2semidirect
9. #10590668C2semidirect
10. #10590590C2semidirect
11. #10590573C2semidirect
18. C3×Q8×Dic3C22semidirect
21. #63940C4semidirect
30. #63844C22semidirect
33. C32×#103C22semidirect
34. #63662C22semidirect
35. #63643C22semidirect
36. #63637C22semidirect
38. C3×#815C22semidirect
39. C3×#807C22semidirect
40. #63575C22semidirect
42. #63554C22semidirect
52. #4817D3semidirect
62. Q8×C3⋊D3C2×C4semidirect
84. C3×#215C2×C4semidirect
96. #3716C2×C4semidirect
97. #3710C2×C4semidirect
106. Q8×Dic3C2×D3semidirect
132. C3×#103C2×D3semidirect
143. #815C2×D3semidirect
148. #807C2×D3semidirect
156. C32×Q8C22×C4semidirect
169. #634C22×C4semidirect
183. C3×C3⋊C8C22×C4semidirect
237. #215C4×D3semidirect
306. #103D32semidirect
321. C3×Q8C2×C4×D3semidirect
371. C3⋊C8C2×C4×D3semidirect
375. C3⋊D3#440semidirect
451. C32C2×#440semidirect
461. Q8C4×D32semidirect
515. C3D3×#440semidirect

Maximal subgroups

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

subgroupindex
Q8×#6242
C2×#639402
#105946052
C3⋊D3×#1032
C3×#48172
#105915662
#105909402
#105907472
#105906682
#105905902
#105905732
D3×#4403