Finite Group Databasebeta

← #11866211

Subgroups — #11866211

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3745C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5113C211yesmaximal, characteristic, complemented
6C3×#5102C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic, complemented
8#10590770C214yesmaximal, complemented
9#10590765C214yesmaximal, complemented
10#79086—31nomaximal
11#78862—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3745—24no—
17C2×#3745C2214yes—
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63981—22no—
22#63974—22no—
23#63911C2212yescomplemented
24#63909—22no—
25#63894—22no—
26#63894C2214yescomplemented
27#63864C2212yescomplemented
28C2×#3717C2212yescomplemented
29#63825—24no—
30C2×#3714C2212yescomplemented
31C3×#821C2212yescomplemented
32C3×#816C2212yescomplemented
33C3×Dic3⋊C8C2214yescomplemented
34#63564C2214yescomplemented
35#5830—31no—
36C2×#949—31no—
37C2×#908—31no—
38C22×D24—31no—
39C22×D24—31no—
40C22×D24—61no—
41#5525—31no—
42#5521—31no—
43#5521—31no—
44C3×#424—31no—
45C3×#416—31no—
46#5131—31no—
47#5113D311yescharacteristic, complemented
48#5102D311yescharacteristic, complemented
49#5001—31no—
50#4844—34no—
51#4843—34no—
52#4819—34no—
53#4786—34no—
54C23×C3⋊D3—21no—
55C23×C3⋊D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)D414yescomplemented
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C3×#67—21no—
66C3×#235—22no—
67C3×#235—22no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#626—24no—
72C2×#624—24no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75#3745—28no—
76C3×#217—21no—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×C4×Dic3C2312yes—
82C3×#208—22no—
83C2×C3×C3⋊C8C2312yes—
84#3722—24no—
85#3722—24no—
86#3717—24no—
87#3714—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C2×#235C2×D311yescharacteristic
91C22×D12—31no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×D12—61no—
97C2×C3×M16—31no—
98C22×C3×C8—21no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C3×#117—31no—
102C3×#117—31no—
103#949—64no—
104#947—32no—
105C2×#215—32no—
106#940—32no—
107#937—62no—
108C2×#213—32no—
109#930—62no—
110#926C2×D311yescharacteristic
111#926C2×D311yescharacteristic
112C2×#208C2×D311yescharacteristic
113#908—64no—
114C2×D24—32no—
115C2×D24—34no—
116C2×D24—34no—
117C2×D24—64no—
118C2×D24—64no—
119C2×D24—64no—
120C2×D24—68no—
121C2×#204—32no—
122#895—62no—
123#893—34no—
124#893—62no—
125#882—62no—
126D3×C22⋊C4—62no—
127D3×C22⋊C4—62no—
128#875—32no—
129#874—32no—
130C4×D12—34no—
131C4×D12—62no—
132C3×C4⋊C8—34no—
133C3×#103—32no—
134C3×#102—32no—
135#821—34no—
136#821C2×D312yescomplemented
137#816C2×D312yescomplemented
138Dic3⋊C8C2×D314yescomplemented
139#809—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—82no—
146C22×C3⋊D3—82no—
147C22×C3×D3—21no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)—24no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—42no—
157C4⋊(C3⋊D3)C2×D414yes—
158C3×#67—42no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3C2×D414yes—
162C3×D12—21no—
163C3×D12—21no—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167#626—84no—
168#624—84no—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C2×AGL(1,ℤ/8)—91no—
172C22×D8—91no—
173#535—91no—
174#518—91no—
175#463—94no—
176#459—94no—
177#424—31no—
178#418—91no—
179#416—31no—
180C23×D3—61no—
181C23×D3—61no—
182C23×D3—61no—
183C23×D3—61no—
184C23×D3—121no—
185C23×D3—121no—
186C3×#41—62no—
187C3×#41—62no—
188C2×C3×Q8—31no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—21no—
196C2×#67—64no—
197#235—22no—
198#235—22no—
199C2×D12—34no—
200C2×D12—34no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—32no—
205C2×D12—64no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—62no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—64no—
220C2×D12—122no—
221C2×D12—122no—
222C2×D12—121no—
223C2×D12—121no—
224C2×D12C22×D311yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×Dic6C22×D311yescharacteristic
229C3×M16—62no—
230C2×C3×C8—24no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—32no—
235C2×C3×C8C22×D312yes—
236C2×C3×C8C22×D312yes—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—32no—
239C3×C22⋊C4—32no—
240C3×C22⋊C4—61no—
241C3×C42—32no—
242C3×C42—61no—
243#217—21no—
244#217D1212yes—
245#215—64no—
246#213—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3D1212yes—
252C4⋊Dic3C22×D312yes—
253C4×Dic3—21no—
254C4×Dic3C22×D312yes—
255#208—22no—
256C2×C3⋊C8C22×D312yes—
257D24—68no—
258D24—68no—
259D24—616no—
260D24—64no—
261#204—64no—
262C22×C32—22no—
263C22×C32#12112yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—24no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—44no—
268C2×C3⋊D3—44no—
269C2×C3⋊D3—84no—
270C2×C3⋊D3—84no—
271C2×C3×D3—41no—
272C2×C3×D3—42no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—24no—
277C3×Dic3—41no—
278C3×Dic3—42no—
279C2×#41—31no—
280C22×D4—91no—
281C22×D4—91no—
282AGL(1,ℤ/8)—184no—
283C2×SD16—92no—
284C2×D8—92no—
285C2×D8—94no—
286C2×D8—184no—
287C2×M16—31no—
288C22×C8D3211yescharacteristic
289#127—92no—
290#124—92no—
291#121—182no—
292#120—182no—
293C4×D4—94no—
294C4×D4—182no—
295#117—31no—
296#117—31no—
297C2×C22⋊C4—182no—
298C4⋊C8—34no—
299#103—32no—
300#102—32no—
301#102—94no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3C2×D1211yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—21no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—122no—
314C22×D3—124no—
315C22×D3—122no—
316C22×D3—124no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—242no—
320C22×D3—242no—
321C22×D3—242no—
322C22×D3—242no—
323C22×D3—244no—
324C22×D3—244no—
325C3×Q8—61no—
326C3×Q8—61no—
327C3×D4—61no—
328C3×D4—61no—
329C3×D4—122no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—34no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—122no—
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4#23512yes—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D412yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4#23912yes—
344C2×C3×C4C23×D311yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346#67—42no—
347#67—244no—
348C2×Dic3—22no—
349C2×Dic3—21no—
350C2×Dic3C2×D1214yes—
351D12—21no—
352D12—21no—
353D12—34no—
354D12—34no—
355D12—64no—
356D12—64no—
357D12—64no—
358D12—64no—
359D12—62no—
360D12—62no—
361D12—62no—
362D12—62no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—122no—
367D12—124no—
368D12—124no—
369D12—122no—
370D12—122no—
371D12—244no—
372C4×D3—42no—
373C4×D3—244no—
374C4×D3—244no—
375Dic6—21no—
376Dic6—21no—
377C3×C8—24no—
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—62no—
381C3⋊C8—22no—
382C2×C32—22no—
383C2×C32C2×#12111yescharacteristic
384C2×C32#57612yes—
385C3⋊D3—44no—
386C3⋊D3—82no—
387C3×D3—81no—
388C24—181no—
389C24—181no—
390#41—62no—
391#41—62no—
392C2×Q8—31no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4—92no—
396C2×D4—92no—
397C2×D4—94no—
398C2×D4—184no—
399C2×D4—182no—
400C2×D4—182no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—182no—
404C22×C4—61no—
405C22×C4—184no—
406C22×C4C2×D3211yescharacteristic
407SD16—184no—
408D8—188no—
409D8—184no—
410M16—62no—
411C2×C8—22no—
412C2×C8—32no—
413C2×C8C2×D3212yes—
414C4⋊C4—32no—
415C4⋊C4—32no—
416C22⋊C4—32no—
417C22⋊C4—61no—
418C22⋊C4—184no—
419C22⋊C4—184no—
420C42—32no—
421C42—61no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—21no—
426C22×C3—22no—
427C22×C3—122no—
428C22×C3—121no—
429C22×C3#88412yes—
430C22×C3#89512yes—
431C22×C3C22×D1211yescharacteristic
432C22×C3C2×D3×D411yescharacteristic
433C2×D3—41no—
434C2×D3—42no—
435C2×D3—64no—
436C2×D3—64no—
437C2×D3—124no—
438C2×D3—124no—
439C2×D3—124no—
440C2×D3—124no—
441C2×D3—122no—
442C2×D3—124no—
443C2×D3—122no—
444C2×D3—124no—
445C2×D3—244no—
446C2×D3—244no—
447C2×D3—244no—
448C2×D3—244no—
449C2×D3—248no—
450C2×D3—248no—
451C2×D3—244no—
452C2×D3—244no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—64no—
457C3×C4—122no—
458C3×C4—121no—
459C3×C4#88412yes—
460C3×C4#89512yes—
461C3×C4C2×#23511yescharacteristic
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464C3×C4C2×#23911yescharacteristic
465Dic3—24no—
466Dic3—41no—
467Dic3—42no—
468C32#304111yescharacteristic, complemented, Sylow
469C23—61no—
470C23—182no—
471C23—184no—
472C23—182no—
473C23—362no—
474C23—722no—
475C23—722no—
476C23D3×D1211yescharacteristic
477Q8—61no—
478Q8—61no—
479D4—61no—
480D4—61no—
481D4—94no—
482D4—122no—
483D4—182no—
484D4—182no—
485D4—182no—
486D4—184no—
487D4—362no—
488D4—724no—
489C2×C4—34no—
490C2×C4—62no—
491C2×C4—61no—
492C2×C4—122no—
493C2×C4—724no—
494C2×C4#379912yes—
495C2×C4D3×D1211yescharacteristic
496C2×C4#381112yes—
497C2×C4C22×D3211yescharacteristic
498C8—22no—
499C8—62no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—241no—
506C2×C3C2×#88411yescharacteristic
507C2×C3C2×#89511yescharacteristic
508C2×C3#575212yes—
509C2×C3#576912yes—
510D3—81no—
511D3—124no—
512D3—124no—
513D3—244no—
514D3—244no—
515D3—242no—
516D3—242no—
517C22—22no—
518C22—122no—
519C22—121no—
520C22—184no—
521C22—364no—
522C22—364no—
523C22—362no—
524C22—724no—
525C22—724no—
526C22#6391012yes—
527C22C2×D3×D1211yescharacteristic
528C4—64no—
529C4—122no—
530C4—121no—
531C4#6391012yes—
532C4C2×#379911yescharacteristic
533C4C2×#381111yescharacteristic
534C3—21no—
535C3#7886211yescharacteristic, complemented
536C3#7908611yescharacteristic, complemented
537C2—22no—
538C2—241no—
539C2—364no—
540C2—722no—
541C2#1059468012yes—
542C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3745C2semidirect
2. #10595045C2semidirect
3. #10594996C2semidirect
4. C2×#63825C2semidirect
5. C3×#5113C2semidirect
6. C3×#5102C2semidirect
7. #10591096C2semidirect
8. #10590770C2semidirect
9. #10590765C2semidirect
23. #63911C22semidirect
26. #63894C22semidirect
27. #63864C22semidirect
28. C2×#3717C22semidirect
30. C2×#3714C22semidirect
31. C3×#821C22semidirect
32. C3×#816C22semidirect
33. C3×Dic3⋊C8C22semidirect
34. #63564C22semidirect
47. #5113D3semidirect
48. #5102D3semidirect
62. C2×C4⋊(C3⋊D3)D4semidirect
136. #821C2×D3semidirect
137. #816C2×D3semidirect
138. Dic3⋊C8C2×D3semidirect
468. C32#3041semidirect
535. C3#78862semidirect
536. C3#79086semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
#105950452
#105949962
C2×#638252
C3×#51132
C3×#51022
#105910962
#105907702
#105907652
#790863
#788623