Finite Group Databasebeta

← #11866280

Subgroups — #11866280

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic, complemented
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×C3×#932C211yesmaximal, characteristic
4#10594855C211yesmaximal, characteristic, complemented
5#10591497C214yesmaximal, complemented
6#10591476C214yesmaximal, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#83935—31nomaximal
11#83848—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3757—22no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yes—
18#64135C2211yescharacteristic
19#64135C2211yescharacteristic
20C2×C3×#214—24no—
21C2×C3×#214C2212yes—
22C2×C3×#214C2214yes—
23C3×#932—24no—
24C2×C3×#213C2212yes—
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63961—22no—
28#63873C2212yescomplemented
29#63863C2212yescomplemented
30#63856—22no—
31#63572C2214yescomplemented
32#63566C2212yescomplemented
33#63566C2214yescomplemented
34#63563C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×SD16—31no—
37#5825—31no—
38#5816—31no—
39#5798—31no—
40#5798—31no—
41#5798—61no—
42C22×#214D311yescharacteristic, complemented
43C2×#932D311yescharacteristic
44#5233—31no—
45#5225—31no—
46#5165—34no—
47#5162—34no—
48#5162—34no—
49#5153—34no—
50#5120—31no—
51#5119—31no—
52#5113—31no—
53#5102—31no—
54C24×C32—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4D414yes—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—24no—
61C2×C3×#67—21no—
62C22×C3×Dic3—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12C2311yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72#3757—21no—
73#3757—24no—
74#3757D412yes—
75C4⋊(C3⋊Dic3)D412yes—
76C4⋊(C3⋊Dic3)C2312yes—
77C4×C3⋊Dic3—21no—
78C4×C3⋊Dic3C2312yes—
79C3×#214—24no—
80C3×#214—28no—
81C3×#213—24no—
82C3×#208—22no—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8C2312yes—
85C2×C3×C3⋊C8C2312yes—
86#3724—24no—
87(C2×D3)⋊Dic3—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—21no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C2×#235C2×D311yescharacteristic
95C22×Dic6C2×D311yescharacteristic
96C3×AGL(1,ℤ/8)—64no—
97C2×C3×SD16—34no—
98C2×C3×SD16—32no—
99C2×C3×SD16—64no—
100C2×C3×D8—32no—
101C2×C3×M16—31no—
102C22×C3×C8—31no—
103C2×#217—62no—
104C2×#217—62no—
105C2×#217—64no—
106#947—32no—
107#946—62no—
108#944—32no—
109#944—32no—
110#936—32no—
111#935—62no—
112D4×Dic3—34no—
113D4×Dic3—34no—
114D4×Dic3—64no—
115D4×Dic3—62no—
116D4×Dic3—62no—
117D4×Dic3—64no—
118C2×#214—24no—
119C2×#214C2×D314yes—
120C2×#214C2×D312yes—
121#932—24no—
122C2×#213C2×D312yes—
123#929—62no—
124#926—31no—
125#926—31no—
126#926—31no—
127#926—31no—
128#926—61no—
129#926—61no—
130#924—62no—
131C2×#208C2×D311yescharacteristic
132C22×C3⋊C8C2×D311yescharacteristic
133#835—32no—
134#835—34no—
135#832—32no—
136#821—32no—
137#816—34no—
138#816—32no—
139Dic3⋊C8—34no—
140Dic3⋊C8—34no—
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—82no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C32×D4—24no—
147C32×D4—22no—
148C32×D4C2×D414yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—84no—
155C2×C3⋊Dic3C2×D414yes—
156C3×#67—42no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—42no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—42no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—22no—
166C3×Dic6—21no—
167C3×Dic6—42no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—31no—
171C22×SD16—31no—
172#536—91no—
173#518—91no—
174#463—94no—
175#461—94no—
176#424—91no—
177#419—91no—
178#416—91no—
179C24×C3—22no—
180C24×C3—21no—
181C24×C3—21no—
182C3×#41—62no—
183C3×#41—62no—
184C2×C3×Q8—31no—
185C2×C3×Q8—32no—
186C2×C3×Q8—61no—
187C2×C3×Q8—62no—
188C2×C3×Q8—62no—
189C2×C3×D4—22no—
190C2×C3×D4—24no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—24no—
196C2×C3×D4—22no—
197C2×C3×D4—31no—
198C2×C3×D4—61no—
199C2×C3×D4#6714yes—
200C2×C3×D4#6714yes—
201C2×C3×D4C22×D312yes—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—21no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—21no—
209C22×Dic3—21no—
210C22×Dic3—64no—
211C22×Dic3—64no—
212C22×Dic3—68no—
213#235—22no—
214#235—22no—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D312yes—
221C2×Dic6C22×D311yescharacteristic
222C3×SD16—68no—
223C3×SD16—64no—
224C3×D8—64no—
225C3×M16—62no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—62no—
229#217—32no—
230#217—32no—
231#217—62no—
232#217—64no—
233#217—64no—
234#217—64no—
235#217—62no—
236#217—68no—
237#217—61no—
238#217—61no—
239#214—24no—
240#214—28no—
241#213—24no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3—32no—
244C4⋊Dic3—32no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257#208—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261C22×C32—24no—
262C22×C32—22no—
263C22×C32—44no—
264C22×C32—84no—
265C22×C32#12112yes—
266C22×C32C22×D411yescharacteristic
267C2×C3×D3—41no—
268C2×C3×D3—42no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—24no—
273C3⋊Dic3—42no—
274C3×Dic3—42no—
275C3×Dic3—41no—
276C2×#41—31no—
277C22×Q8—31no—
278C22×D4D3211yescharacteristic
279AGL(1,ℤ/8)—64no—
280C2×SD16—34no—
281C2×SD16—32no—
282C2×SD16—64no—
283C2×D8—32no—
284C2×M16—31no—
285C22×C8—31no—
286C4⋊Q8—92no—
287#124—92no—
288#123—182no—
289C22⋊Q8—182no—
290C4×D4—94no—
291C4×D4—182no—
292#117—91no—
293#117—91no—
294C2×C22⋊C4—182no—
295C4⋊C8—94no—
296#103—92no—
297#103—94no—
298#102—92no—
299C23×C3—24no—
300C23×C3—28no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—21no—
306C23×C3—61no—
307C23×C3—82no—
308C23×C3—82no—
309C23×C3—84no—
310C23×C3D3×D411yescharacteristic
311C23×C3D3×D411yescharacteristic
312C22×D3—21no—
313C3×Q8—62no—
314C3×Q8—61no—
315C3×Q8—62no—
316C3×Q8—61no—
317C3×Q8—122no—
318C3×D4—24no—
319C3×D4—28no—
320C3×D4—24no—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—24no—
325C3×D4—61no—
326C3×D4—61no—
327C3×D4—122no—
328C3×D4C2×#6714yes—
329C3×D4C2×#6714yes—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—122no—
337C2×C3×C4—122no—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23712yes—
341C2×C3×C4#23712yes—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346#67—42no—
347C2×Dic3—21no—
348C2×Dic3—22no—
349C2×Dic3—34no—
350C2×Dic3—34no—
351C2×Dic3—42no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—244no—
357C2×Dic3—244no—
358C2×Dic3—248no—
359D12—21no—
360D12—21no—
361C4×D3—42no—
362Dic6—22no—
363Dic6—21no—
364Dic6—22no—
365Dic6—21no—
366Dic6—42no—
367C3×C8—62no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—22no—
371C2×C32—22no—
372C2×C32—44no—
373C2×C32C2×#12111yescharacteristic
374C2×C32#57712yes—
375C3×D3—81no—
376C24—21no—
377#41—62no—
378#41—62no—
379C2×Q8—32no—
380C2×Q8—31no—
381C2×Q8—61no—
382C2×Q8—62no—
383C2×Q8—62no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—31no—
387C2×D4—61no—
388C2×D4#62514yes—
389C2×D4C2×D3212yes—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—184no—
393C22×C4C2×D3211yescharacteristic
394SD16—68no—
395SD16—64no—
396D8—64no—
397M16—62no—
398C2×C8—32no—
399C2×C8—32no—
400C2×C8—62no—
401C4⋊C4—92no—
402C4⋊C4—92no—
403C4⋊C4—184no—
404C22⋊C4—92no—
405C22⋊C4—184no—
406C22⋊C4—184no—
407C22⋊C4—181no—
408C42—92no—
409C42—181no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—28no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—42no—
418C22×C3—48no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—84no—
422C22×C3—84no—
423C22×C3—88no—
424C22×C3—122no—
425C22×C3—121no—
426C22×C3#93912yes—
427C22×C3#93912yes—
428C22×C3C2×D3×D411yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C2×D3—42no—
431C2×D3—41no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—121no—
436C3×C4—122no—
437C3×C4#93912yes—
438C3×C4#93912yes—
439C3×C4C2×#23711yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C22×#6711yescharacteristic
442C3×C4C22×#6711yescharacteristic
443Dic3—42no—
444Dic3—41no—
445Dic3—64no—
446Dic3—64no—
447Dic3—124no—
448Dic3—124no—
449Dic3—122no—
450Dic3—122no—
451C32#304211yescharacteristic, complemented, Sylow
452C23—22no—
453C23—24no—
454C23—61no—
455C23—82no—
456C23#381111yescharacteristic
457Q8—62no—
458Q8—61no—
459Q8—62no—
460Q8—61no—
461Q8—122no—
462D4—22no—
463D4—24no—
464D4—61no—
465D4—61no—
466D4—122no—
467D4C2×#62514yes—
468C2×C4—62no—
469C2×C4—61no—
470C2×C4—94no—
471C2×C4—122no—
472C2×C4—122no—
473C2×C4—182no—
474C2×C4—724no—
475C2×C4#380512yes—
476C2×C4C2×#62512yes—
477C2×C4#381111yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—62no—
480C8—62no—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—42no—
486C2×C3—48no—
487C2×C3—44no—
488C2×C3—44no—
489C2×C3—241no—
490C2×C3#576212yes—
491C2×C3#577512yes—
492C2×C3C2×#93911yescharacteristic
493C2×C3C2×#93911yescharacteristic
494D3—81no—
495C22—22no—
496C22—24no—
497C22—44no—
498C22—84no—
499C22—122no—
500C22—121no—
501C22#6398012yes—
502C22C2×#381111yescharacteristic
503C4—121no—
504C4—122no—
505C4—184no—
506C4—362no—
507C4#6398012yes—
508C4C2×#380511yescharacteristic
509C4C22×#62511yescharacteristic
510C3—21no—
511C3#8384811yescharacteristic, complemented
512C3#8393511yescharacteristic, complemented
513C2—22no—
514C2—44no—
515C2—241no—
516C2#1059511512yes—
517C2C2×#6398011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596269C2semidirect
2. C22×C3×#214C2semidirect
4. #10594855C2semidirect
5. #10591497C2semidirect
6. #10591476C2semidirect
7. #10591119C2semidirect
8. #10591100C2semidirect
9. #10591084C2semidirect
28. #63873C22semidirect
29. #63863C22semidirect
31. #63572C22semidirect
32. #63566C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
42. C22×#214D3semidirect
451. C32#3042semidirect
511. C3#83848semidirect
512. C3#83935semidirect

Maximal subgroups

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

subgroupindex
#105962692
C22×C3×#2142
C2×C3×#9322
#105948552
#105914972
#105914762
#105911192
#105911002
#105910842
#839353
#838483