Finite Group Databasebeta

← #11866273

Subgroups — #11866273

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596287C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3#10594982C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591570C214yesmaximal, complemented
7#10591569C214yesmaximal, complemented
8#10591119C211yesmaximal, characteristic, complemented
9#10591105C211yesmaximal, characteristic, complemented
10#83848—31nomaximal
11#78976—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64156C2212yescomplemented
16#64155—22no—
17#64153C2212yescomplemented
18#64138—22no—
19#64135C2211yescharacteristic
20C2×C3×#215—24no—
21C2×C3×#215C2214yes—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25D3×#217—22no—
26#63898C2214yes—
27Dic3×D12—22no—
28#63830—24no—
29C2×#3716C2212yes—
30C2×#3714C2212yes—
31C3×#835C2214yescomplemented
32#63572C2214yescomplemented
33#63567C2212yescomplemented
34#63564C2212yescomplemented
35C22×C3×SD16—31no—
36#5816—31no—
37#5816—31no—
38#5816—61no—
39C22×#215D311yescharacteristic, complemented
40#5798—31no—
41C2×#932—31no—
42C2×#908—31no—
43#5521—31no—
44C3×#419—31no—
45#5225D311yescharacteristic, complemented
46#5165—34no—
47#5162—34no—
48#5119—31no—
49#5113—31no—
50#5102—31no—
51#5002—31no—
52#4819—34no—
53#4818—34no—
54C23×C3×D3—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—22no—
57C2×C32×Q8—22no—
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62#3828—22no—
63#3828—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2311yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×D3×Dic3—24no—
72#3757D412yes—
73#3752—24no—
74C4⋊(C3⋊Dic3)D412yes—
75#3750—24no—
76C4×C3⋊Dic3C2312yes—
77C3×#217—21no—
78C3×#215—28no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—24no—
86#3716—24no—
87#3714—24no—
88#3042—91noSylow
89C22×C3×Q8—21no—
90C22×C3×Q8C2×D311yescharacteristic
91C22×C3×Q8C2×D311yescharacteristic
92C22×C3×D4—31no—
93C2×#235—31no—
94C2×#235—31no—
95C2×#235—61no—
96C22×D12C2×D311yescharacteristic
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C2×C3×M16—31no—
100C22×C3×C8—31no—
101C3×#117—31no—
102C2×#217—62no—
103#947—32no—
104#947—32no—
105#947—62no—
106#946—62no—
107#946—62no—
108#946—64no—
109#944—32no—
110#944—32no—
111#944—62no—
112C2×#215—24no—
113C2×#215C2×D314yes—
114D4×Dic3—34no—
115D4×Dic3—62no—
116C2×#214—32no—
117#932—64no—
118C2×#213—32no—
119#929—62no—
120#929—62no—
121#929—64no—
122#926—31no—
123#926—31no—
124#926—61no—
125#926C2×D311yescharacteristic
126C2×#208C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128#908—64no—
129C2×D24—32no—
130C2×#204—32no—
131#893—34no—
132D3×C22⋊C4—62no—
133C4×D12—62no—
134C3×#103—34no—
135#835C2×D314yescomplemented
136#821—32no—
137#816—32no—
138Dic3⋊C8—34no—
139Dic3⋊C8—34no—
140#810—32no—
141#809—32no—
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—21no—
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—82no—
147C32×Q8—22no—
148C32×Q8—22no—
149C32×Q8—42no—
150C2×C32×C4—22no—
151C2×C32×C4—42no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D412yes—
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156#638—42no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3C2×D414yes—
159C4⋊(C3⋊D3)—21no—
160C4⋊(C3⋊D3)—21no—
161C4×C3⋊D3—42no—
162#634—21no—
163#634—21no—
164C2×C3×Dic3—22no—
165C3×D12—24no—
166C3×D12—22no—
167C3×D12C2×D414yes—
168D3×Dic3—84no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—91no—
172C22×SD16—31no—
173#536—91no—
174#518—91no—
175#463—94no—
176#461—94no—
177#424—91no—
178#419—31no—
179#416—91no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—22no—
190C2×C3×Q8—42no—
191C2×C3×Q8—42no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—34no—
195C2×C3×D4—32no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—62no—
205C2×#67—61no—
206C2×#67—61no—
207C22×Dic3—64no—
208#235—62no—
209#235—62no—
210#235—62no—
211#235—62no—
212#235—122no—
213#235—122no—
214C2×D12—21no—
215C2×D12—22no—
216C2×D12—31no—
217C2×D12—31no—
218C2×D12—61no—
219C2×D12#6714yes—
220C2×D12C22×D312yes—
221C2×C4×D3—62no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—64no—
225C2×Dic6—31no—
226C2×Dic6—31no—
227C2×Dic6—61no—
228C3×SD16—68no—
229C3×M16—62no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C3×C4⋊C4—32no—
234C3×C22⋊C4—61no—
235C3×C42—61no—
236#217—21no—
237#217—32no—
238#217—32no—
239#217—62no—
240#217—64no—
241#215—28no—
242#214—64no—
243#213—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—68no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3C22×D312yes—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254Dic3⋊C4—68no—
255C4×Dic3—21no—
256C4×Dic3—32no—
257C4×Dic3—32no—
258C4×Dic3—62no—
259#208—22no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8C22×D312yes—
262C2×C3⋊C8C22×D312yes—
263D24—64no—
264#204—64no—
265C22×C32—22no—
266C22×C32#12112yes—
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—41no—
269C2×C3⋊D3—42no—
270C2×C3×D3—24no—
271C2×C3×D3—44no—
272C2×C3×D3—84no—
273C32×C4—42no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—24no—
278C3⋊Dic3—41no—
279C3×Dic3—42no—
280C2×#41—91no—
281C22×Q8D3211yescharacteristic
282C22×D4—31no—
283AGL(1,ℤ/8)—184no—
284C2×SD16—34no—
285C2×SD16—64no—
286C2×SD16—92no—
287C2×D8—92no—
288C2×M16—31no—
289C22×C8—31no—
290C4⋊Q8—92no—
291#124—92no—
292#123—182no—
293C22⋊Q8—182no—
294C4×D4—94no—
295C4×D4—182no—
296#117—31no—
297#117—91no—
298C2×C22⋊C4—182no—
299C4⋊C8—94no—
300#103—34no—
301#103—92no—
302#102—92no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—64no—
306C23×C3—242no—
307C23×C3D3×D411yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—22no—
310C22×D3—24no—
311C22×D3—62no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—82no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—44no—
322C3×Q8—42no—
323C3×Q8—42no—
324C3×D4—34no—
325C3×D4—64no—
326C3×D4—62no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—44no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D412yes—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4#23712yes—
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346#67—124no—
347#67—122no—
348#67—122no—
349C2×Dic3—22no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—64no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—244no—
357D12—24no—
358D12—22no—
359D12—61no—
360D12—61no—
361D12—61no—
362D12—61no—
363D12—121no—
364D12—121no—
365D12C2×#6714yes—
366C4×D3—124no—
367C4×D3—122no—
368C4×D3—122no—
369C4×D3—244no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—121no—
375Dic6—121no—
376C3×C8—62no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—22no—
380C2×C32—22no—
381C2×C32C2×#12111yescharacteristic
382C2×C32#57712yes—
383C3⋊D3—81no—
384C3×D3—44no—
385C24—61no—
386#41—182no—
387#41—182no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—91no—
392C2×Q8C2×D3212yes—
393C2×D4—32no—
394C2×D4—34no—
395C2×D4—62no—
396C2×D4—61no—
397C2×D4—91no—
398C2×D4—181no—
399C22×C4—21no—
400C22×C4—184no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403SD16—68no—
404SD16—184no—
405D8—184no—
406M16—62no—
407C2×C8—32no—
408C2×C8—32no—
409C2×C8—62no—
410C4⋊C4—32no—
411C4⋊C4—92no—
412C4⋊C4—184no—
413C22⋊C4—61no—
414C22⋊C4—92no—
415C22⋊C4—184no—
416C22⋊C4—184no—
417C42—61no—
418C42—92no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—42no—
424C22×C3—64no—
425C22×C3—124no—
426C22×C3—244no—
427C22×C3#88412yes—
428C22×C3#93912yes—
429C22×C3C2×D3×D411yescharacteristic
430C22×C3C2×D3×D411yescharacteristic
431C2×D3—24no—
432C2×D3—44no—
433C2×D3—84no—
434C2×D3—122no—
435C2×D3—124no—
436C2×D3—121no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—121no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—122no—
447C3×C4#88412yes—
448C3×C4#93912yes—
449C3×C4C2×#23511yescharacteristic
450C3×C4C2×D3×D411yescharacteristic
451C3×C4C2×#23711yescharacteristic
452C3×C4C22×#6711yescharacteristic
453Dic3—42no—
454Dic3—64no—
455Dic3—64no—
456Dic3—124no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—62no—
462C23—64no—
463C23—181no—
464C23—242no—
465C23#381111yescharacteristic
466Q8—22no—
467Q8—22no—
468Q8—42no—
469Q8—181no—
470Q8—181no—
471D4—34no—
472D4—62no—
473D4—64no—
474D4—181no—
475D4—181no—
476D4—362no—
477C2×C4—22no—
478C2×C4—42no—
479C2×C4—62no—
480C2×C4—94no—
481C2×C4—181no—
482C2×C4—362no—
483C2×C4—724no—
484C2×C4#380412yes—
485C2×C4D3×#6712yes—
486C2×C4#381111yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—62no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—22no—
494C2×C3—42no—
495C2×C3—124no—
496C2×C3C2×#88411yescharacteristic
497C2×C3#576212yes—
498C2×C3#577812yes—
499C2×C3C2×#93911yescharacteristic
500D3—44no—
501D3—242no—
502D3—241no—
503D3—241no—
504C22—22no—
505C22—64no—
506C22—124no—
507C22—244no—
508C22—361no—
509C22—362no—
510C22#6397112yes—
511C22C2×#381111yescharacteristic
512C4—42no—
513C4—122no—
514C4—184no—
515C4—361no—
516C4#6397112yes—
517C4C2×#380411yescharacteristic
518C4C2×D3×#6711yescharacteristic
519C3—21no—
520C3#7897611yescharacteristic, complemented
521C3#8384811yescharacteristic, complemented
522C2—22no—
523C2—124no—
524C2—721no—
525C2#1059532412yes—
526C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
hypercenterC22×Q8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596287C2semidirect
2. C22×C3×#215C2semidirect
3. #10594982C2semidirect
5. C3×#5225C2semidirect
6. #10591570C2semidirect
7. #10591569C2semidirect
8. #10591119C2semidirect
9. #10591105C2semidirect
15. #64156C22semidirect
17. #64153C22semidirect
31. C3×#835C22semidirect
32. #63572C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
39. C22×#215D3semidirect
45. #5225D3semidirect
135. #835C2×D3semidirect
460. C32#3042semidirect
520. C3#78976semidirect
521. C3#83848semidirect

Maximal subgroups

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

subgroupindex
#105962872
C22×C3×#2152
#105949822
C2×#638302
C3×#52252
#105915702
#105915692
#105911192
#105911052
#838483
#789763