Finite Group Databasebeta

← #11866276

Subgroups — #11866276

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#10595997C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic
4C22×#3716C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590366C214yesmaximal, complemented
9#10590365C214yesmaximal, complemented
10#82544—31nomaximal
11#79087—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64106—22no—
17#64095—22no—
18#64084C2212yescomplemented
19#64078C2212yescomplemented
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C3×#893—22no—
24C3×D3×C22⋊C4—22no—
25C3×C4×D12C2214yes—
26#63830—24no—
27C2×#3716—24no—
28C2×#3716C2212yes—
29C2×#3716C2214yes—
30C2×#3714C2212yes—
31C3×C4⋊(C3⋊C8)C2214yescomplemented
32#63567C2212yescomplemented
33#63567C2214yescomplemented
34#63564C2212yescomplemented
35C3×#518—31no—
36C22×#214—31no—
37C2×#932—31no—
38C2×#908—31no—
39C22×#204—31no—
40#5526—31no—
41#5526—31no—
42#5526—61no—
43#5521D311yescharacteristic, complemented
44C3×#424—31no—
45#5120—31no—
46#5113—31no—
47#5019—34no—
48#5016—34no—
49#5004—31no—
50#5002—31no—
51#4999D311yescharacteristic, complemented
52#4844—34no—
53#4841—34no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57C22×C3⋊Dic3—21no—
58#3828—22no—
59#3828—22no—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634—22no—
63C2×#634—22no—
64C2×#634—21no—
65C2×#634C2311yescharacteristic
66C2×#634C2312yes—
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—24no—
72C32×C4⋊C4D412yes—
73C32×C22⋊C4D412yes—
74C32×C42C2312yes—
75#3752—24no—
76C4⋊(C3⋊Dic3)—24no—
77C3×#217—21no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×#208—22no—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84C2×C3×C3⋊C8C2312yes—
85#3716—28no—
86#3716—24no—
87#3714—24no—
88#3042—91noSylow
89C22×C3×D4—31no—
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C2×C3×M16—31no—
98C22×C3×C8—31no—
99C3×C4×D4—34no—
100C3×C4×D4—62no—
101C3×#117—21no—
102C3×#117—31no—
103C3×#117C2×D311yescharacteristic
104C3×#117C2×D311yescharacteristic
105C2×C3×C22⋊C4—62no—
106C2×#214—34no—
107C2×#214—32no—
108C2×#214—64no—
109#932—64no—
110C2×#213—32no—
111#926C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114#908—64no—
115C2×D24—32no—
116C2×#204—34no—
117C2×#204—32no—
118C2×#204—64no—
119#897—64no—
120#897—62no—
121#897—62no—
122#893—22no—
123#886—64no—
124#886—62no—
125#886—62no—
126D3×C22⋊C4—22no—
127#875—32no—
128#875—32no—
129#875—62no—
130C4×D12C2×D314yes—
131#869—32no—
132#869—32no—
133#869—62no—
134C3×C4⋊C8—34no—
135#821—32no—
136#816—34no—
137#816—32no—
138#810—32no—
139#810—34no—
140#809—32no—
141C4⋊(C3⋊C8)C2×D314yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—21no—
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—82no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D414yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152#638—42no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
156C4⋊(C3⋊D3)—21no—
157C4⋊(C3⋊D3)—21no—
158C4×C3⋊D3—42no—
159#634—22no—
160#634—21no—
161#634—22no—
162#634—21no—
163#634—42no—
164C2×C3×Dic3—22no—
165C3×D12—24no—
166C3×D12—22no—
167C3×D12C2×D414yes—
168C3×C4×D3—84no—
169C3×C3⋊C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—91no—
172C22×SD16—91no—
173#536—91no—
174#518—31no—
175#463—94no—
176#461—94no—
177#424—31no—
178#419—91no—
179#416—91no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C22×C3×C4—21no—
187C22×C3×C4—64no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—62no—
191C2×#67—61no—
192C2×#67—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196#235—62no—
197#235—62no—
198#235—62no—
199#235—62no—
200#235—122no—
201#235—122no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×D12D1214yes—
208C2×D12C22×D312yes—
209C2×C4×D3—24no—
210C2×C4×D3—62no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×Dic6—31no—
214C2×Dic6—32no—
215C2×Dic6—31no—
216C2×Dic6—32no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—122no—
227C2×Dic6—122no—
228C3×M16—62no—
229C2×C3×C8—32no—
230C2×C3×C8—32no—
231C2×C3×C8—62no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4D1212yes—
235C3×C4⋊C4#6712yes—
236C3×C22⋊C4—22no—
237C3×C22⋊C4—61no—
238C3×C22⋊C4—64no—
239C3×C22⋊C4D1212yes—
240C3×C22⋊C4#6712yes—
241C3×C42—22no—
242C3×C42—61no—
243C3×C42C22×D312yes—
244C3×C42C22×D312yes—
245#217—21no—
246#214—64no—
247#214—68no—
248#213—64no—
249(C2×D3)⋊C4—24no—
250(C2×D3)⋊C4—68no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—68no—
254C4⋊Dic3—64no—
255C4⋊Dic3—64no—
256C4⋊Dic3C22×D312yes—
257C4×Dic3—21no—
258#208—22no—
259C2×C3⋊C8—22no—
260C2×C3⋊C8C22×D312yes—
261C2×C3⋊C8C22×D312yes—
262D24—64no—
263#204—68no—
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—24no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—42no—
278C3⋊Dic3—41no—
279C3×Dic3—42no—
280C2×#41—91no—
281C22×Q8—91no—
282C22×D4—31no—
283AGL(1,ℤ/8)—184no—
284C2×SD16—94no—
285C2×SD16—92no—
286C2×SD16—184no—
287C2×D8—92no—
288C2×M16—31no—
289C22×C8—31no—
290C4⋊Q8—92no—
291#124—92no—
292#123—182no—
293C22⋊Q8—182no—
294C4×D4—34no—
295C4×D4—62no—
296#117—31no—
297#117D3211yescharacteristic
298C2×C22⋊C4—62no—
299C4⋊C8—34no—
300#103—92no—
301#103—94no—
302#102—92no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—64no—
306C23×C3—242no—
307C23×C3C2×D1211yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—22no—
310C22×D3—24no—
311C22×D3—62no—
312C22×D3—61no—
313C22×D3—61no—
314C22×D3—82no—
315C3×D4—34no—
316C3×D4—64no—
317C3×D4—62no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—24no—
323C2×C3×C4—62no—
324C2×C3×C4—244no—
325C2×C3×C4C2×D1212yes—
326C2×C3×C4C2×D1214yes—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4#23912yes—
331C2×C3×C4C2×#6714yes—
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—124no—
336#67—122no—
337#67—122no—
338C2×Dic3—22no—
339C2×Dic3—62no—
340C2×Dic3—64no—
341C2×Dic3—61no—
342C2×Dic3—62no—
343C2×Dic3—61no—
344C2×Dic3—62no—
345C2×Dic3—124no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348D12—24no—
349D12—22no—
350D12—61no—
351D12—61no—
352D12—61no—
353D12—61no—
354D12—121no—
355D12—121no—
356D12C2×D1214yes—
357C4×D3—84no—
358C4×D3—124no—
359C4×D3—122no—
360C4×D3—122no—
361Dic6—62no—
362Dic6—61no—
363Dic6—62no—
364Dic6—61no—
365Dic6—62no—
366Dic6—61no—
367Dic6—62no—
368Dic6—61no—
369Dic6—122no—
370Dic6—122no—
371Dic6—121no—
372Dic6—121no—
373Dic6—124no—
374Dic6—122no—
375Dic6—122no—
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—92no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×Q8—182no—
392C2×Q8—182no—
393C2×D4—32no—
394C2×D4—34no—
395C2×D4—62no—
396C2×D4—61no—
397C2×D4—91no—
398C2×D4—181no—
399C22×C4—64no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403SD16—188no—
404SD16—184no—
405D8—184no—
406M16—62no—
407C2×C8—32no—
408C2×C8—32no—
409C2×C8—62no—
410C4⋊C4—32no—
411C4⋊C4—184no—
412C4⋊C4#62612yes—
413C22⋊C4—61no—
414C22⋊C4—64no—
415C22⋊C4—184no—
416C22⋊C4#62612yes—
417C42—61no—
418C42C2×D3212yes—
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#89512yes—
428C22×C3#93012yes—
429C22×C3C22×D1211yescharacteristic
430C22×C3C22×#6711yescharacteristic
431C2×D3—24no—
432C2×D3—44no—
433C2×D3—84no—
434C2×D3—122no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—122no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—44no—
446C3×C4—122no—
447C3×C4#89512yes—
448C3×C4#93012yes—
449C3×C4C22×D1211yescharacteristic
450C3×C4C2×#23511yescharacteristic
451C3×C4C2×D3×D411yescharacteristic
452C3×C4C2×#23911yescharacteristic
453Dic3—42no—
454Dic3—124no—
455Dic3—122no—
456Dic3—122no—
457Dic3—121no—
458Dic3—122no—
459Dic3—121no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—62no—
462C23—64no—
463C23—181no—
464C23—242no—
465C23C2×#62611yescharacteristic
466Q8—182no—
467Q8—181no—
468Q8—182no—
469Q8—181no—
470Q8—362no—
471D4—34no—
472D4—62no—
473D4—64no—
474D4—181no—
475D4—181no—
476D4—362no—
477C2×C4—62no—
478C2×C4—182no—
479C2×C4—181no—
480C2×C4—244no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4#379912yes—
484C2×C4D3×D1212yes—
485C2×C4C2×#62614yes—
486C2×C4C2×#62611yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—62no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—124no—
496C2×C3C2×#89511yescharacteristic
497C2×C3#575112yes—
498C2×C3C2×#93011yescharacteristic
499C2×C3#583612yes—
500D3—44no—
501D3—242no—
502D3—241no—
503D3—241no—
504C22—22no—
505C22—64no—
506C22—124no—
507C22—244no—
508C22—362no—
509C22—361no—
510C22#6390912yes—
511C22C22×#62611yescharacteristic
512C4—24no—
513C4—122no—
514C4—361no—
515C4—362no—
516C4#6390912yes—
517C4C2×#379911yescharacteristic
518C4C2×D3×D1211yescharacteristic
519C3—21no—
520C3#7908711yescharacteristic, complemented
521C3#8254411yescharacteristic, complemented
522C2—22no—
523C2—124no—
524C2—721no—
525C2C2×#6390911yescharacteristic
526C2#1059544712yes—
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63830C2
hypercenter#117D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595997C2semidirect
2. C3×#5521C2semidirect
4. C22×#3716C2semidirect
5. C3×#4999C2semidirect
6. #10591107C2semidirect
7. #10591105C2semidirect
8. #10590366C2semidirect
9. #10590365C2semidirect
18. #64084C22semidirect
19. #64078C22semidirect
31. C3×C4⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
43. #5521D3semidirect
51. #4999D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
460. C32#3042semidirect
520. C3#79087semidirect
521. C3#82544semidirect

Maximal subgroups

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

subgroupindex
#105959972
C3×#55212
C2×#638302
C22×#37162
C3×#49992
#105911072
#105911052
#105903662
#105903652
#825443
#790873