Finite Group Databasebeta

← #11866293

Subgroups — #11866293

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2#10594982C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5#10592819C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590755C214yesmaximal, complemented
9#10590752C214yesmaximal, complemented
10#83935—31nomaximal
11#79087—31nomaximal
12C22×#634C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64135C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#908—24no—
20C2×C3×D24C2212yes—
21C2×C3×#204C2212yes—
22D3×#217—22no—
23#63962—22no—
24#63898—22no—
25Dic3×D12C2214yes—
26#63866C2212yescomplemented
27#63860C2212yescomplemented
28#63857—22no—
29C2×#3716—24no—
30C2×#3716C2214yes—
31#63643C2214yescomplemented
32C3×Dic3⋊C8C2214yescomplemented
33#63566C2212yescomplemented
34#63563C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36#5825—31no—
37#5798—31no—
38C22×#214—31no—
39C2×#908D311yescharacteristic
40C22×#204—31no—
41#5526—31no—
42#5521—31no—
43C3×#424—31no—
44#5233—31no—
45#5162—34no—
46#5153—34no—
47#5120—31no—
48#5120—31no—
49#5120—61no—
50#5119D311yescharacteristic, complemented
51#5113—31no—
52#4844—34no—
53#4841—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C2×C3×#67—21no—
62C3×#235—22no—
63C3×#235—22no—
64C2×C3×D12—21no—
65C2×C3×D12—22no—
66C2×C3×D12D414yes—
67C2×C3×D12C2311yescharacteristic
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×D3×Dic3—24no—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74#3757—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C4×C3⋊Dic3—21no—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82C3×D24—24no—
83C3×#204—24no—
84Dic3⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86(C2×D3)⋊Dic3—24no—
87#3716—28no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12C2×D311yescharacteristic
93C22×Dic6—31no—
94C22×Dic6—31no—
95C22×Dic6—61no—
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—32no—
98C2×C3×D8—32no—
99C2×C3×M16—21no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C2×D311yescharacteristic
102C22×C3×C8—31no—
103C3×#117—31no—
104C2×#217—62no—
105#944—32no—
106#936—32no—
107#935—62no—
108D4×Dic3—34no—
109D4×Dic3—62no—
110C2×#214—34no—
111C2×#214—64no—
112#926—31no—
113#926—31no—
114#926—61no—
115#926C2×D311yescharacteristic
116#924—62no—
117C22×C3⋊C8C2×D311yescharacteristic
118#908—24no—
119C2×D24C2×D312yes—
120C2×#204—34no—
121C2×#204—64no—
122C2×#204C2×D312yes—
123#897—62no—
124#893—62no—
125#886—62no—
126D3×C22⋊C4—62no—
127#875—32no—
128C4×D12—34no—
129#869—32no—
130C3×C4⋊C8—34no—
131#835—32no—
132#832—32no—
133#821—32no—
134#816—32no—
135#816—34no—
136#816—34no—
137#816—64no—
138Dic3⋊C8C2×D314yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151#634—22no—
152#634—22no—
153#634—42no—
154C3×#67—42no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3C2×D414yes—
157C3×D12—24no—
158C3×D12—21no—
159C3×D12—22no—
160C3×D12—21no—
161C3×D12C2×D414yes—
162C3×C4×D3—42no—
163C3×Dic6—21no—
164C3×Dic6—21no—
165D3×Dic3—84no—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C2×AGL(1,ℤ/8)—31no—
169C22×SD16—91no—
170#536—91no—
171#518—91no—
172#463—94no—
173#461—94no—
174#424—31no—
175#419—91no—
176#416—91no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—31no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—31no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C2×#67—21no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—64no—
196C22×Dic3—121no—
197#235—22no—
198#235—22no—
199C2×D12—21no—
200C2×D12—22no—
201C2×D12#6714yes—
202C2×D12C22×D311yescharacteristic
203C2×D12C22×D312yes—
204C2×C4×D3—21no—
205C2×C4×D3—64no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—62no—
209C2×Dic6—64no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—121no—
217C2×Dic6—122no—
218C2×Dic6C22×D311yescharacteristic
219C3×SD16—64no—
220C3×D8—64no—
221C3×M16—22no—
222C3×M16—22no—
223C3×M16—42no—
224C2×C3×C8—22no—
225C2×C3×C8—32no—
226C2×C3×C8—62no—
227C2×C3×C8C22×D312yes—
228C2×C3×C8C22×D312yes—
229C3×C4⋊C4—32no—
230C3×C22⋊C4—32no—
231C3×C42—32no—
232#217—61no—
233#217—61no—
234#217—64no—
235#217—64no—
236#217—121no—
237#217D1212yes—
238#214—68no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—64no—
245C4⋊Dic3D1212yes—
246Dic3⋊C4—64no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—121no—
250C4×Dic3C22×D312yes—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253D24—24no—
254#204—24no—
255#204—68no—
256C22×C32—22no—
257C22×C32#12112yes—
258C22×C32C22×D411yescharacteristic
259C2×C3×D3—24no—
260C2×C3×D3—44no—
261C2×C3×D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3—84no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3⋊Dic3—42no—
269C3×Dic3—24no—
270C3×Dic3—41no—
271C2×#41—31no—
272C22×Q8—91no—
273C22×D4—31no—
274AGL(1,ℤ/8)—64no—
275C2×SD16—32no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×D8—32no—
279C2×M16D3211yescharacteristic
280C22×C8—31no—
281C4⋊Q8—92no—
282#124—92no—
283#123—182no—
284C22⋊Q8—182no—
285C4×D4—94no—
286C4×D4—182no—
287#117—31no—
288#117—91no—
289C2×C22⋊C4—182no—
290C4⋊C8—34no—
291#103—92no—
292#103—94no—
293#102—92no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—64no—
297C23×C3—61no—
298C23×C3—242no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—22no—
302C22×D3—24no—
303C22×D3—21no—
304C22×D3—82no—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—61no—
310C3×D4—62no—
311C3×D4—61no—
312C3×D4—122no—
313C2×C3×C4—21no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—34no—
318C2×C3×C4—61no—
319C2×C3×C4—122no—
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D412yes—
323C2×C3×C4#23712yes—
324C2×C3×C4#23912yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328#67—42no—
329C2×Dic3—21no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—124no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—244no—
340C2×Dic3C2×D1214yes—
341D12—24no—
342D12—22no—
343D12—21no—
344D12—21no—
345D12C2×#6714yes—
346C4×D3—42no—
347C4×D3—244no—
348Dic6—21no—
349Dic6—21no—
350Dic6—64no—
351Dic6—62no—
352Dic6—62no—
353Dic6—62no—
354Dic6—62no—
355Dic6—122no—
356Dic6—124no—
357Dic6—122no—
358Dic6—122no—
359C3×C8—22no—
360C3×C8—22no—
361C3×C8—42no—
362C3×C8—62no—
363C3⋊C8—22no—
364C2×C32—22no—
365C2×C32C2×#12111yescharacteristic
366C2×C32#57712yes—
367C3×D3—44no—
368C3×D3—81no—
369C24—61no—
370#41—62no—
371#41—62no—
372C2×Q8—31no—
373C2×Q8—92no—
374C2×Q8—181no—
375C2×Q8—182no—
376C2×Q8—182no—
377C2×D4—32no—
378C2×D4—31no—
379C2×D4—34no—
380C2×D4—61no—
381C2×D4—62no—
382C2×D4—61no—
383C22×C4—61no—
384C22×C4—184no—
385C22×C4—181no—
386C22×C4C2×D3211yescharacteristic
387SD16—64no—
388SD16—188no—
389D8—64no—
390M16—22no—
391C2×C8—32no—
392C2×C8—62no—
393C2×C8C2×D3212yes—
394C4⋊C4—32no—
395C4⋊C4—92no—
396C4⋊C4—184no—
397C22⋊C4—32no—
398C22⋊C4—184no—
399C22⋊C4—184no—
400C22⋊C4—181no—
401C42—32no—
402C42—181no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3—64no—
409C22×C3—124no—
410C22×C3—122no—
411C22×C3—121no—
412C22×C3—244no—
413C22×C3#89512yes—
414C22×C3#93912yes—
415C22×C3C22×D1211yescharacteristic
416C22×C3C2×D3×D411yescharacteristic
417C2×D3—24no—
418C2×D3—44no—
419C2×D3—42no—
420C2×D3—41no—
421C2×D3—84no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—64no—
426C3×C4—121no—
427C3×C4#89512yes—
428C3×C4#93912yes—
429C3×C4C2×D3×D411yescharacteristic
430C3×C4C2×#23711yescharacteristic
431C3×C4C2×#23911yescharacteristic
432C3×C4C22×#6711yescharacteristic
433Dic3—24no—
434Dic3—41no—
435Dic3—124no—
436Dic3—122no—
437Dic3—122no—
438Dic3—122no—
439Dic3—122no—
440Dic3—242no—
441C32#304211yescharacteristic, complemented, Sylow
442C23—62no—
443C23—64no—
444C23—61no—
445C23—242no—
446C23D3×D1211yescharacteristic
447Q8—61no—
448Q8—61no—
449Q8—182no—
450Q8—182no—
451Q8—362no—
452D4—34no—
453D4—62no—
454D4—61no—
455D4—61no—
456D4—64no—
457D4—122no—
458C2×C4—34no—
459C2×C4—61no—
460C2×C4—122no—
461C2×C4—182no—
462C2×C4—182no—
463C2×C4—362no—
464C2×C4—724no—
465C2×C4#379612yes—
466C2×C4D3×D1211yescharacteristic
467C2×C4D3×#6712yes—
468C2×C4C22×D3211yescharacteristic
469C8—22no—
470C8—62no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3—241no—
478C2×C3C2×#89511yescharacteristic
479C2×C3#575112yes—
480C2×C3#577512yes—
481C2×C3C2×#93911yescharacteristic
482D3—44no—
483D3—81no—
484C22—22no—
485C22—64no—
486C22—124no—
487C22—121no—
488C22—122no—
489C22—244no—
490C22#6388612yes—
491C22C2×D3×D1211yescharacteristic
492C4—64no—
493C4—121no—
494C4—362no—
495C4—362no—
496C4#6388612yes—
497C4C2×#379611yescharacteristic
498C4C2×D3×#6711yescharacteristic
499C3—21no—
500C3#7908711yescharacteristic, complemented
501C3#8393511yescharacteristic, complemented
502C2—22no—
503C2—124no—
504C2—241no—
505C2#1059471312yes—
506C2C2×#6388611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×C3×#908C2
hypercenterC2×M16D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594982C2semidirect
3. #10594856C2semidirect
4. C22×#3716C2semidirect
5. #10592819C2semidirect
6. C3×#5119C2semidirect
7. #10591084C2semidirect
8. #10590755C2semidirect
9. #10590752C2semidirect
26. #63866C22semidirect
27. #63860C22semidirect
31. #63643C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
50. #5119D3semidirect
138. Dic3⋊C8C2×D3semidirect
441. C32#3042semidirect
500. C3#79087semidirect
501. C3#83935semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105949822
#105948562
C22×#37162
#105928192
C3×#51192
#105910842
#105907552
#105907522
#839353
#790873