Finite Group Databasebeta

← #11866214

Subgroups — #11866214

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#5001C211yesmaximal, characteristic, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10590551C214yesmaximal, complemented
9#10590540C214yesmaximal, complemented
10#78944—31nomaximal
11#78862—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17#64102C2214yescomplemented
18C22⋊C4×C3⋊D3—22no—
19C4×C4⋊(C3⋊D3)—22no—
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63976—22no—
23#63914C2212yescomplemented
24#63908—22no—
25#63863C2212yescomplemented
26C2×#3717C2212yescomplemented
27#63825—24no—
28C2×#3714—24no—
29C2×#3714C2214yes—
30C2×#3714C2212yescomplemented
31C3×#810C2212yescomplemented
32C3×#809C2214yescomplemented
33C3×#809C2212yescomplemented
34#63572C2214yescomplemented
35#5830—31no—
36C2×#949—31no—
37#5805—31no—
38C22×#213—31no—
39C2×#908—31no—
40C22×D24—31no—
41#5521—31no—
42#5521—31no—
43#5521—61no—
44C3×#418—31no—
45C3×#416—31no—
46#5119—31no—
47#5102—31no—
48#5002D311yescharacteristic, complemented
49#5001D311yescharacteristic, complemented
50#4819—34no—
51#4787—34no—
52#4786—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)D414yescomplemented
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—24no—
62C2×C3×#67—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72C2×#625—24no—
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75C32×C42—21no—
76#3757D412yes—
77#3752—24no—
78C4⋊(C3⋊Dic3)D412yes—
79C4×C3⋊Dic3C2312yes—
80C3×#208—22no—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84(C2×D3)⋊Dic3—24no—
85#3717—24no—
86#3714—28no—
87#3714—24no—
88#3041—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C2×C3×M16—31no—
97C22×C3×C8—31no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C2×D311yescharacteristic
101#953—62no—
102#949—64no—
103#947—32no—
104C2×#215—32no—
105#940—32no—
106#940—32no—
107#938—62no—
108#937—62no—
109#936—32no—
110C2×#213—34no—
111C2×#213—32no—
112C2×#213—64no—
113#930—62no—
114#926—31no—
115#926—31no—
116#926—61no—
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119#908—64no—
120C2×D24—34no—
121C2×D24—32no—
122C2×D24—64no—
123C2×#204—32no—
124#893—34no—
125#893—34no—
126#893—64no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129D3×C22⋊C4—64no—
130C4×D12—62no—
131C4×D12—62no—
132C4×D12—64no—
133C3×#103—32no—
134C3×#102—32no—
135C3×#102—34no—
136Dic3⋊C8—34no—
137Dic3⋊C8—34no—
138#810C2×D312yescomplemented
139#809C2×D314yescomplemented
140#809C2×D312yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3—82no—
145C22×C3×D3—22no—
146C22×C3×D3—21no—
147C22×C3×D3—42no—
148C22×C3×D3—82no—
149C2×C32×C4—22no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3C2×D414yes—
155C4⋊(C3⋊D3)—24no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)C2×D414yes—
158C4×C3⋊D3—84no—
159C3×#67—42no—
160C2×C3×Dic3—21no—
161C3×D12—22no—
162C3×D12—21no—
163C3×D12—22no—
164C3×D12—21no—
165C3×D12—42no—
166C3×C4×D3—42no—
167C3×Dic6—21no—
168C3×Dic6—21no—
169#625—84no—
170C3×C3⋊C8—22no—
171C3×C3⋊C8—22no—
172C2×AGL(1,ℤ/8)—91no—
173C22×D8—91no—
174#535—91no—
175#518—91no—
176#463—94no—
177#459—94no—
178#424—91no—
179#418—31no—
180#416—31no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—62no—
184C23×D3—61no—
185C23×D3—61no—
186C3×#41—62no—
187C3×#41—62no—
188C2×C3×Q8—31no—
189C2×C3×D4—32no—
190C2×C3×D4—31no—
191C2×C3×D4—61no—
192C2×C3×D4—62no—
193C2×C3×D4—62no—
194C2×C3×D4—61no—
195C22×C3×C4—21no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—21no—
200C2×#67—64no—
201C2×#67—64no—
202#235—22no—
203#235—22no—
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—21no—
207C2×D12—34no—
208C2×D12—34no—
209C2×D12—32no—
210C2×D12—32no—
211C2×D12—62no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—64no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12C22×D311yescharacteristic
220C2×D12C22×D312yes—
221C2×C4×D3—21no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—68no—
225C2×Dic6C22×D311yescharacteristic
226C3×M16—62no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—62no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C42—22no—
237C3×C42—21no—
238C3×C42—21no—
239#217—32no—
240#217—32no—
241#217—62no—
242#217—64no—
243#215—64no—
244#213—68no—
245#213—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—68no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—62no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256#208—22no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260D24—68no—
261D24—64no—
262#204—64no—
263C22×C32—22no—
264C22×C32#12112yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—24no—
267C2×C3⋊D3—44no—
268C2×C3⋊D3—84no—
269C2×C3×D3—41no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—44no—
273C2×C3×D3—84no—
274C32×C4—42no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—24no—
279C3×Dic3—41no—
280C2×#41—31no—
281C22×D4—31no—
282C22×D4—91no—
283AGL(1,ℤ/8)—184no—
284C2×SD16—92no—
285C2×D8—94no—
286C2×D8—92no—
287C2×D8—184no—
288C2×M16—31no—
289C22×C8—31no—
290#127—92no—
291#124—92no—
292#121—182no—
293#120—182no—
294C4×D4—94no—
295C4×D4—182no—
296#117—91no—
297#117D3211yescharacteristic
298C2×C22⋊C4—182no—
299C4⋊C8—94no—
300#103—32no—
301#102—32no—
302#102—34no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—61no—
306C23×C3—122no—
307C23×C3—242no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—22no—
311C22×D3—21no—
312C22×D3—42no—
313C22×D3—64no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—68no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—82no—
320C22×D3—242no—
321C22×D3—242no—
322C22×D3—244no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×D4—62no—
326C3×D4—61no—
327C3×D4—62no—
328C3×D4—61no—
329C3×D4—122no—
330C3×D4—122no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—61no—
339C2×C3×C4—122no—
340C2×C3×C4#23512yes—
341C2×C3×C4#23512yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4D3×D412yes—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—42no—
349#67—244no—
350#67—244no—
351C2×Dic3—21no—
352C2×Dic3—34no—
353C2×Dic3—34no—
354C2×Dic3—64no—
355D12—22no—
356D12—21no—
357D12—22no—
358D12—21no—
359D12—34no—
360D12—34no—
361D12—42no—
362D12—64no—
363D12—64no—
364D12—68no—
365D12—64no—
366D12—64no—
367D12—62no—
368D12—62no—
369C4×D3—42no—
370C4×D3—244no—
371C4×D3—244no—
372C4×D3—248no—
373Dic6—21no—
374Dic6—21no—
375C3×C8—62no—
376C3×C8—62no—
377C3⋊C8—22no—
378C3⋊C8—22no—
379C2×C32—22no—
380C2×C32C2×#12111yescharacteristic
381C2×C32#57612yes—
382C3⋊D3—44no—
383C3×D3—81no—
384C3×D3—82no—
385C24—61no—
386C24—181no—
387#41—62no—
388#41—62no—
389C2×Q8—31no—
390C2×D4—32no—
391C2×D4—31no—
392C2×D4—61no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4—92no—
397C2×D4—94no—
398C2×D4—184no—
399C2×D4—182no—
400C2×D4—181no—
401C22×C4—61no—
402C22×C4—184no—
403C22×C4C2×D3211yescharacteristic
404SD16—184no—
405D8—188no—
406D8—184no—
407M16—62no—
408C2×C8—32no—
409C2×C8—32no—
410C2×C8—62no—
411C4⋊C4—92no—
412C4⋊C4C2×D3212yes—
413C22⋊C4—21no—
414C22⋊C4—92no—
415C22⋊C4—184no—
416C22⋊C4—184no—
417C42—21no—
418C42—92no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—42no—
424C22×C3—121no—
425C22×C3—122no—
426C22×C3—124no—
427C22×C3—122no—
428C22×C3—244no—
429C22×C3#88412yes—
430C22×C3#88412yes—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C2×D3×D411yescharacteristic
433C2×D3—41no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—44no—
437C2×D3—68no—
438C2×D3—64no—
439C2×D3—64no—
440C2×D3—84no—
441C2×D3—128no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—244no—
445C2×D3—244no—
446C2×D3—248no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—44no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—121no—
454C3×C4#88412yes—
455C3×C4#88412yes—
456C3×C4C2×#23511yescharacteristic
457C3×C4C2×#23511yescharacteristic
458C3×C4C2×D3×D411yescharacteristic
459C3×C4C2×D3×D411yescharacteristic
460Dic3—41no—
461Dic3—64no—
462Dic3—64no—
463Dic3—124no—
464C32#304111yescharacteristic, complemented, Sylow
465C23—62no—
466C23—61no—
467C23—122no—
468C23—182no—
469C23—184no—
470C23—242no—
471C23—722no—
472C23#381111yescharacteristic
473Q8—61no—
474Q8—61no—
475D4—62no—
476D4—61no—
477D4—62no—
478D4—61no—
479D4—94no—
480D4—122no—
481D4—122no—
482D4—182no—
483D4—184no—
484D4—724no—
485C2×C4—22no—
486C2×C4—61no—
487C2×C4—94no—
488C2×C4—122no—
489C2×C4—724no—
490C2×C4#379812yes—
491C2×C4#380212yes—
492C2×C4#381111yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—62no—
495C8—62no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—42no—
501C2×C3—242no—
502C2×C3—241no—
503C2×C3C2×#88411yescharacteristic
504C2×C3C2×#88411yescharacteristic
505C2×C3#576912yes—
506C2×C3#577412yes—
507D3—81no—
508D3—82no—
509D3—128no—
510D3—124no—
511D3—124no—
512C22—22no—
513C22—122no—
514C22—124no—
515C22—121no—
516C22—122no—
517C22—184no—
518C22—244no—
519C22—364no—
520C22—724no—
521C22#6391212yes—
522C22C2×#381111yescharacteristic
523C4—42no—
524C4—121no—
525C4—184no—
526C4#6391212yes—
527C4C2×#379811yescharacteristic
528C4C2×#380211yescharacteristic
529C3—21no—
530C3#7886211yescharacteristic, complemented
531C3#7894411yescharacteristic, complemented
532C2—22no—
533C2—242no—
534C2—241no—
535C2—364no—
536C2C2×#6391211yescharacteristic
537C2#1059546112yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
2. #10595040C2semidirect
3. C2×#63825C2semidirect
4. C22×#3714C2semidirect
5. C3×#5002C2semidirect
6. C3×#5001C2semidirect
7. #10591119C2semidirect
8. #10590551C2semidirect
9. #10590540C2semidirect
17. #64102C22semidirect
23. #63914C22semidirect
25. #63863C22semidirect
26. C2×#3717C22semidirect
30. C2×#3714C22semidirect
31. C3×#810C22semidirect
32. C3×#809C22semidirect
33. C3×#809C22semidirect
34. #63572C22semidirect
48. #5002D3semidirect
49. #5001D3semidirect
59. C2×C4⋊(C3⋊D3)D4semidirect
138. #810C2×D3semidirect
139. #809C2×D3semidirect
140. #809C2×D3semidirect
464. C32#3041semidirect
530. C3#78862semidirect
531. C3#78944semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105950402
C2×#638252
C22×#37142
C3×#50022
C3×#50012
#105911192
#105905512
#105905402
#789443
#788623