Finite Group Databasebeta

← #11866807

Subgroups — #11866807

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595429C211yesmaximal, characteristic
2C2×#63944C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic
4#10594631C211yesmaximal, characteristic
5C3⋊D3×#103C211yesmaximal, characteristic, complemented
6C3×#4813C212yesmaximal, complemented
7#10591635C212yesmaximal, complemented
8#10590848C212yesmaximal, complemented
9#10590672C211yesmaximal, characteristic, complemented
10#10590579C212yesmaximal, complemented
11#10590573C211yesmaximal, characteristic, complemented
12D3×#467—32nomaximal
13C2×Q8×C3⋊D3C2211yescharacteristic
14C2×C4×D32C2211yescharacteristic
15C2×#3797C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#946C2212yes—
19C2×C3×#216C2212yescomplemented
20C2×C3×D3×C8C2212yes—
21C3×#897C2212yes—
22#63944—24no—
23#63921—21no—
24#63921—21no—
25#63900—21no—
26#63900C2211yescharacteristic
27#63899—22no—
28#63896—22no—
29#63883—21no—
30#63857C2212yes—
31#63856C2212yes—
32C2×#3719C2212yescomplemented
33C2×#3710C2211yescharacteristic
34C2×D3×C3⋊C8C2212yes—
35D32×C8—24no—
36C32×#103C2211yescharacteristic, complemented
37#63662C2211yescharacteristic, complemented
38#63643C2211yescharacteristic, complemented
39#63637C2211yescharacteristic, complemented
40C3×#816C2212yescomplemented
41C3×#807C2212yescomplemented
42#63575C2212yescomplemented
43#63565C2212yescomplemented
44C2×D3×Q16—32no—
45C22×D3×C8—32no—
46D3×C22⋊Q8—32no—
47D3×C22⋊Q8—32no—
48C3×#467—32no—
49#5188—32no—
50#5116—32no—
51#5051—32no—
52#5051—32no—
53#4887—32no—
54D3×#107—32no—
55#4813—32no—
56#4813D312yescomplemented
57D3×#103—32no—
58D3×#103—32no—
59D3×#103—61no—
60C22×D32D411yescharacteristic
61C2×C32×Q8C2311yescharacteristic
62Q8×C3⋊D3—22no—
63Q8×C3⋊D3—22no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×#634—21no—
68C2×#634C2311yescharacteristic
69C2×C3×C4×D3C2312yes—
70C2×C3×Dic6C2312yes—
71C2×#627—21no—
72C2×#624—21no—
73C2×#624—21no—
74C2×#624D411yescharacteristic
75C2×D3×Dic3D412yes—
76C4×D32—22no—
77C4×D32—22no—
78#3797—22no—
79#3797—22no—
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C8×C3⋊D3—22no—
86C3×#216—24no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C2×C3×C3⋊C8C2312yes—
93C3×D3×C8—24no—
94#3724—21no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99#3719—24no—
100#3710D414yes—
101D3×C3⋊C8—24no—
102C2×#467—91noSylow
103C2×D3×Q8—32no—
104C2×D3×Q8—32no—
105C2×D3×Q8—61no—
106C22×C4×D3—32no—
107C2×C3×Q16—32no—
108C22×C3×C8—32no—
109C3×C22⋊Q8—32no—
110C3×C22⋊Q8—32no—
111#946—32no—
112#946C2×D312yes—
113C2×#216—32no—
114C2×#216C2×D312yescomplemented
115#924—32no—
116#924—32no—
117C22×C3⋊C8—32no—
118D3×Q16—68no—
119C2×Dic12—32no—
120C2×D3×C8—32no—
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123C2×D3×C8—61no—
124C2×D3×C8—68no—
125C2×D3×C8C2×D312yes—
126#897—32no—
127#897C2×D312yes—
128#896—62no—
129#896—62no—
130D3×C4⋊C4—32no—
131D3×C4⋊C4—32no—
132D3×C4⋊C4—61no—
133D3×C4⋊C4—62no—
134D3×C4⋊C4—62no—
135D3×C22⋊C4—62no—
136D3×C22⋊C4—62no—
137#878—62no—
138#878—62no—
139C3×#107—32no—
140C3×#103—21no—
141C3×#103—32no—
142C3×#103C2×D312yescomplemented
143#835—32no—
144#835—32no—
145#835—61no—
146#818—32no—
147#816—32no—
148#816—61no—
149#816C2×D312yescomplemented
150#810—32no—
151#810—32no—
152#810—61no—
153#807—32no—
154#807C2×D312yescomplemented
155C22×C3⋊D3C2×D411yescharacteristic
156C22×C3×D3C2×D412yes—
157C2×D32—22no—
158C2×D32—22no—
159C2×D32Q1614yescomplemented
160C32×Q8—21no—
161C32×Q8—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3C2×D411yescharacteristic
168C4×C3⋊D3—42no—
169C4×C3⋊D3—42no—
170C4×C3⋊D3C2×D412yes—
171C4×C3⋊D3#4112yes—
172#634—21no—
173#634—21no—
174#634—42no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182#627—42no—
183#624—22no—
184#624—42no—
185#624—42no—
186D3×Dic3—24no—
187C32×C8—21no—
188C3⋊(C3⋊C8)—21no—
189C3×C3⋊C8C2×D414yes—
190C22×Q16—91no—
191C23×C8—91no—
192C2×C22⋊Q8—91no—
193C2×C22⋊Q8—91no—
194#467—32no—
195#467—92no—
196#467—92no—
197#467—92no—
198C2×#107—91no—
199C2×#103—91no—
200C2×#103—91no—
201C23×D3—32no—
202C2×C3×Q8—21no—
203C2×C3×Q8—32no—
204C2×C3×Q8C22×D312yes—
205C22×C3×C4—32no—
206C22×Dic3—32no—
207D3×Q8—64no—
208D3×Q8—64no—
209D3×Q8—64no—
210D3×Q8—64no—
211D3×Q8—64no—
212D3×Q8—122no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—61no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—121no—
224C2×C4×D3—121no—
225C2×C4×D3C22×D312yes—
226C2×Dic6—32no—
227C2×Dic6—61no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C2×Dic6—121no—
231C2×Dic6C22×D312yes—
232C3×Q16—64no—
233C2×C3×C8—21no—
234C2×C3×C8—32no—
235C2×C3×C8—64no—
236C2×C3×C8C22×D312yes—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4C22×D312yes—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244#217—62no—
245#217—62no—
246#216—24no—
247#216—64no—
248(C2×D3)⋊C4—22no—
249(C2×D3)⋊C4—22no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—22no—
253C4⋊Dic3—32no—
254C4⋊Dic3—61no—
255C4⋊Dic3—62no—
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—22no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—121no—
264C2×C3⋊C8—32no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8C22×D312yes—
268Dic12—64no—
269D3×C8—24no—
270D3×C8—38no—
271D3×C8—64no—
272D3×C8—64no—
273D3×C8—122no—
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3#12112yes—
276C2×C3⋊D3C2×Q1612yes—
277C2×C3⋊D3#13512yes—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3C2×Q1614yescomplemented
281D32—28no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4C22×D411yescharacteristic
285C32×C4C2×#4111yescharacteristic
286C3⋊Dic3—41no—
287C3⋊Dic3—41no—
288C3⋊Dic3#12112yes—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—42no—
292C22×Q8—91no—
293C22×Q8—91no—
294C23×C4—91no—
295C2×Q16—32no—
296C2×Q16—92no—
297C2×Q16—184no—
298C22×C8—32no—
299C22×C8—91no—
300C22×C8—92no—
301C22×C8—91no—
302C22×C8—184no—
303C22⋊Q8—32no—
304C22⋊Q8—32no—
305C22⋊Q8—92no—
306C22⋊Q8—92no—
307C22⋊Q8—182no—
308C22⋊Q8—182no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—181no—
312C2×C4⋊C4—181no—
313C2×C22⋊C4—181no—
314C2×C22⋊C4—181no—
315#107—32no—
316#107—92no—
317#103—32no—
318#103—92no—
319#103—91no—
320#103—91no—
321#103—91no—
322#103D3211yescharacteristic, complemented
323C23×C3—32no—
324C22×D3—32no—
325C22×D3—38no—
326C22×D3—61no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3D3×D412yes—
330C3×Q8—22no—
331C3×Q8—22no—
332C3×Q8—22no—
333C3×Q8—41no—
334C3×Q8—62no—
335C3×Q8—62no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4C23×D312yes—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—61no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3D3×D412yes—
357C4×D3—22no—
358C4×D3—22no—
359C4×D3—34no—
360C4×D3—34no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—64no—
364C4×D3—64no—
365C4×D3—124no—
366C4×D3—124no—
367C4×D3—124no—
368C4×D3—124no—
369C4×D3—124no—
370C4×D3—242no—
371Dic6—22no—
372Dic6—22no—
373Dic6—62no—
374Dic6—62no—
375Dic6—62no—
376Dic6—121no—
377Dic6—124no—
378Dic6—124no—
379Dic6—124no—
380C3×C8—22no—
381C3×C8—34no—
382C3×C8—41no—
383C3⋊C8—62no—
384C3⋊C8—121no—
385C3⋊C8D3×D414yes—
386C2×C32C2×#12111yescharacteristic
387C2×C32C22×Q1611yescharacteristic
388C2×C32C2×#13511yescharacteristic
389C3⋊D3#46714yescomplemented
390C3×D3—24no—
391C24—91no—
392C2×Q8—32no—
393C2×Q8—91no—
394C2×Q8—181no—
395C2×Q8—181no—
396C2×Q8—182no—
397C2×Q8—182no—
398C2×Q8—182no—
399C2×Q8—182no—
400C2×Q8C2×D3211yescharacteristic
401C22×C4—32no—
402C22×C4—91no—
403C22×C4—92no—
404C22×C4—91no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—181no—
410C22×C4—181no—
411Q16—64no—
412Q16—184no—
413C2×C8—32no—
414C2×C8—64no—
415C2×C8—94no—
416C2×C8—91no—
417C2×C8—182no—
418C2×C8—184no—
419C2×C8C2×D3211yescharacteristic
420C4⋊C4—32no—
421C4⋊C4—62no—
422C4⋊C4—62no—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C4⋊C4—182no—
426C4⋊C4—182no—
427C4⋊C4—181no—
428C4⋊C4C2×D3211yescharacteristic
429C22⋊C4—62no—
430C22⋊C4—62no—
431C22⋊C4—182no—
432C22⋊C4—182no—
433C22×C3—21no—
434C22×C3—34no—
435C22×C3—62no—
436C22×C3—62no—
437C22×C3C2×D3×D412yes—
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—34no—
441C2×D3—34no—
442C2×D3—34no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—616no—
447C2×D3D3×Q1614yescomplemented
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—62no—
454C3×C4—81no—
455C3×C4—122no—
456C3×C4—122no—
457C3×C4C2×D3×D412yes—
458C3×C4D3×#4112yes—
459Dic3—22no—
460Dic3—34no—
461Dic3—42no—
462Dic3—42no—
463Dic3—62no—
464Dic3—122no—
465Dic3—122no—
466Dic3—122no—
467Dic3—241no—
468C32C2×#46711yescharacteristic, complemented, Sylow
469C23—32no—
470C23—94no—
471C23—91no—
472C23—182no—
473C23—182no—
474Q8—21no—
475Q8—21no—
476Q8—62no—
477Q8—62no—
478Q8—181no—
479Q8—181no—
480Q8—362no—
481Q8—362no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—32no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—91no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—182no—
493C2×C4—184no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4—362no—
499C2×C4—362no—
500C2×C4C22×D3211yescharacteristic
501C8—21no—
502C8—34no—
503C8—181no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—64no—
508C2×C3D3×#12112yes—
509C2×C3C2×D3×Q1612yes—
510C2×C3D3×#13512yes—
511D3—24no—
512D3—38no—
513D3—64no—
514C22—34no—
515C22—62no—
516C22—62no—
517C22—92no—
518C22—92no—
519C22—92no—
520C22—188no—
521C22D32×D411yescharacteristic
522C4—41no—
523C4—41no—
524C4—62no—
525C4—92no—
526C4—122no—
527C4—122no—
528C4—361no—
529C4—361no—
530C4#6430611yescharacteristic
531C4D32×D411yescharacteristic
532C3—21no—
533C3D3×#46712yescomplemented
534C2—64no—
535C2—94no—
536C2#1059426511yescharacteristic
537C2#1059474711yescharacteristic
538C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#467
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63944C2semidirect
5. C3⋊D3×#103C2semidirect
6. C3×#4813C2semidirect
7. #10591635C2semidirect
8. #10590848C2semidirect
9. #10590672C2semidirect
10. #10590579C2semidirect
11. #10590573C2semidirect
19. C2×C3×#216C22semidirect
32. C2×#3719C22semidirect
36. C32×#103C22semidirect
37. #63662C22semidirect
38. #63643C22semidirect
39. #63637C22semidirect
40. C3×#816C22semidirect
41. C3×#807C22semidirect
42. #63575C22semidirect
43. #63565C22semidirect
56. #4813D3semidirect
114. C2×#216C2×D3semidirect
142. C3×#103C2×D3semidirect
149. #816C2×D3semidirect
154. #807C2×D3semidirect
159. C2×D32Q16semidirect
280. C2×C3×D3C2×Q16semidirect
322. #103D32semidirect
389. C3⋊D3#467semidirect
447. C2×D3D3×Q16semidirect
468. C32C2×#467semidirect
533. C3D3×#467semidirect

Maximal subgroups

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

subgroupindex
#105954292
C2×#639442
C2×D32×C82
#105946312
C3⋊D3×#1032
C3×#48132
#105916352
#105908482
#105906722
#105905792
#105905732
D3×#4673