Finite Group Databasebeta

← #11786689

Subgroups — #11786689

Order 1152.

663 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2#10592694C211yesmaximal, characteristic, complemented
3#10591349C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591088C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9#68771—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#892—21no—
18C3×D3×C4⋊C4—21no—
19C3×#67⋊C4—22no—
20C3×C4×D12—21no—
21C3×C4×Dic6—21no—
22C2×Dic3⋊Dic3—22no—
23#63635—21no—
24#63634—21no—
25#63569C414yescomplemented
26#63566—21no—
27#63563—21no—
28C3×#520—31no—
29#5523D311yescharacteristic
30C2×#837—31no—
31#5232—31no—
32#5133—31no—
33#4995—31no—
34#4995—31no—
35#4995—61no—
36#4975—31no—
37#4935—31no—
38C2×#805—31no—
39C3×#339—31no—
40#4554—31no—
41#4532D311yescharacteristic, complemented
42#4530—31no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62#3748—21no—
63#3748C2×C412yescomplemented
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×Dic3⋊C4—22no—
69C3×C4×Dic3—22no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75Dic3⋊Dic3—44no—
76#1859—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×C4×Q8—61no—
81C3×C4×D4—61no—
82C3×C4×D4—62no—
83C3×#117—21no—
84C3×#117—61no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C42—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—62no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—62no—
96C2×C4×Dic3C2×D311yescharacteristic
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101#892—21no—
102D3×C4⋊C4—21no—
103#67⋊C4—22no—
104C4×D12—21no—
105C4×Dic6—21no—
106#837—34no—
107#835—61no—
108#832—61no—
109#821—61no—
110#816—61no—
111#808—62no—
112#808—61no—
113#808—61no—
114#807—62no—
115#807—61no—
116#807—61no—
117#805—34no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—42no—
130C3×#67—22no—
131C3×#67—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C3×D12—21no—
139C3×D12C4⋊C412yescomplemented
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×C4×D3—82no—
143C3×Dic6—21no—
144C3×Dic6C4⋊C412yescomplemented
145C3⋊(C3⋊C8)—22no—
146C3×C3⋊C8—41no—
147#520—31no—
148#428—91no—
149C2×#104—91no—
150#417—91no—
151#384—91no—
152#343—91no—
153#339—31no—
154C3×#41—32no—
155C3×#41—32no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
162C22×C3×C4—32no—
163C22×C3×C4—62no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—121no—
173C22×Dic3#6712yes—
174#235—21no—
175#235—21no—
176#235Dic612yes—
177#235C4×D312yes—
178C2×D12#6711yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—22no—
181C2×Dic6#6711yescharacteristic
182C3×M16—61no—
183C3×M16—61no—
184C2×C3×C8—61no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—62no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4D1211yescharacteristic
191C3×C4⋊C4D1211yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—62no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—32no—
201C3×C42—41no—
202C3×C42—62no—
203C3×C42—61no—
204(C2×D3)⋊C4—22no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4⋊Dic3—124no—
214Dic3⋊C4—22no—
215Dic3⋊C4—124no—
216C4×Dic3—22no—
217C4×Dic3—21no—
218C4×Dic3C4×D312yescomplemented
219#208—21no—
220#208—21no—
221#208—32no—
222#208—32no—
223#208—62no—
224#208—62no—
225#208—61no—
226#208—61no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12011yescharacteristic
235C22×C32C22⋊Q811yescharacteristic
236C2×C3×D3—22no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4—41no—
240C32×C4—41no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—81no—
246C3×Dic3—24no—
247C3×Dic3—22no—
248C3×Dic3—42no—
249C2×#41—31no—
250C2×M16—31no—
251C2×M16—91no—
252C4×Q8—61no—
253C4×D4—61no—
254C4×D4—62no—
255#117—61no—
256#117D3211yescharacteristic
257C2×C4⋊C4—31no—
258C2×C4⋊C4—61no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—182no—
261C2×C42—31no—
262#107—181no—
263#106—181no—
264#104—94no—
265#103—181no—
266#102—181no—
267C23×C3—21no—
268C23×C3—61no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—21no—
272C3×Q8—32no—
273C3×Q8—61no—
274C3×D4—32no—
275C3×D4—62no—
276C3×D4—62no—
277C3×D4—61no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—122no—
298C2×C3×C4—242no—
299C2×C3×C4C2×Dic611yescharacteristic
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23711yescharacteristic
308C2×C3×C4D3×Q811yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311#67—22no—
312#67—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—21no—
317C2×Dic3—22no—
318C2×Dic3—42no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—242no—
325D12—21no—
326D12Dic3⋊C412yescomplemented
327C4×D3—22no—
328C4×D3—22no—
329C4×D3—82no—
330Dic6—21no—
331Dic6Dic3⋊C412yescomplemented
332C3×C8—121no—
333C3⋊C8—41no—
334C3⋊C8—64no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32—21no—
338C2×C32—21no—
339C2×C32#38511yescharacteristic
340C2×C32#45311yescharacteristic
341C2×C32#45611yescharacteristic
342C3×D3—42no—
343#41—32no—
344#41—32no—
345#41—61no—
346#41—61no—
347C2×Q8—31no—
348C2×D4—31no—
349C2×D4—61no—
350C22×C4—32no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—181no—
355C22×C4C2×D3211yescharacteristic
356M16—61no—
357M16—61no—
358M16—92no—
359M16—181no—
360C2×C8—61no—
361C2×C8—181no—
362C4⋊C4—62no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C4⋊C4—364no—
368C4⋊C4#62611yescharacteristic
369C4⋊C4#62611yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—62no—
372C42—21no—
373C42—32no—
374C42—62no—
375C42—61no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—62no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3#67⋊C411yescharacteristic
389C22×C3#88211yescharacteristic
390C22×C3#89611yescharacteristic
391C22×C3#92411yescharacteristic
392C22×C3C4×#6711yescharacteristic
393C22×C3#95311yescharacteristic
394C2×D3—22no—
395C2×D3—41no—
396C2×D3—41no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—64no—
406C3×C4—62no—
407C3×C4—81no—
408C3×C4—81no—
409C3×C4—122no—
410C3×C4C4×D1211yescharacteristic
411C3×C4#88311yescharacteristic
412C3×C4D3×C4⋊C411yescharacteristic
413C3×C4#89711yescharacteristic
414C3×C4C2×Dic3⋊C411yescharacteristic
415C3×C4#92411yescharacteristic
416C3×C4C4×#6711yescharacteristic
417C3×C4#92911yescharacteristic
418Dic3—24no—
419Dic3—22no—
420Dic3—42no—
421Dic3—242no—
422Dic3—241no—
423Dic3—241no—
424C32#185911yescharacteristic, complemented, Sylow
425C23—61no—
426C23D3×#6711yescharacteristic
427Q8—32no—
428Q8—61no—
429D4—32no—
430D4—62no—
431D4—62no—
432D4—61no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—61no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—122no—
443C2×C4—242no—
444C2×C4—362no—
445C2×C4—361no—
446C2×C4D3×Dic611yescharacteristic
447C2×C4#379511yescharacteristic
448C2×C4#379811yescharacteristic
449C2×C4C4×D3211yescharacteristic
450C2×C4C2×#62611yescharacteristic
451C2×C4D3×#6711yescharacteristic
452C8—121no—
453C8—182no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—41no—
462C2×C3—41no—
463C2×C3—122no—
464C2×C3#466811yescharacteristic
465C2×C3#482211yescharacteristic
466C2×C3#482611yescharacteristic
467C2×C3#521011yescharacteristic
468C2×C3#524111yescharacteristic
469C2×C3#524611yescharacteristic
470D3—42no—
471C22—21no—
472C22—21no—
473C22—62no—
474C22—121no—
475C22—121no—
476C22#6385111yescharacteristic
477C22#6387911yescharacteristic
478C22#6397711yescharacteristic
479C4—41no—
480C4—41no—
481C4—64no—
482C4—62no—
483C4—122no—
484C4—721no—
485C4#6385711yescharacteristic
486C4D3×Dic3⋊C411yescharacteristic
487C4C4×#62611yescharacteristic
488C4#6390511yescharacteristic
489C3—21no—
490C3#6877111yescharacteristic, complemented
491C3#7166411yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—122no—
495C2#1059127811yescharacteristic
496C2#1059166611yescharacteristic
497C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592694C2semidirect
3. #10591349C2semidirect
6. C3×#4532C2semidirect
7. #10589167C2semidirect
25. #63569C4semidirect
41. #4532D3semidirect
63. #3748C2×C4semidirect
71. C3×C4×Dic3C2×C4semidirect
139. C3×D12C4⋊C4semidirect
144. C3×Dic6C4⋊C4semidirect
218. C4×Dic3C4×D3semidirect
326. D12Dic3⋊C4semidirect
331. Dic6Dic3⋊C4semidirect
424. C32#1859semidirect
490. C3#68771semidirect
491. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
#105926942
#105913492
C2×#635692
#105910882
C3×#45322
#105891672
#716643
#687713