Finite Group Databasebeta

← #11866206

Subgroups — #11866206

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C3×#5798C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4#10595042C211yesmaximal, characteristic, complemented
5#10591481C214yesmaximal, complemented
6#10591468C214yesmaximal, complemented
7#10591116C211yesmaximal, characteristic, complemented
8#10591105C211yesmaximal, characteristic, complemented
9#10591085C211yesmaximal, characteristic, complemented
10#83826—31nomaximal
11#82540—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×#3754C2212yescomplemented
16#64141—24no—
17C2×#3753C2212yescomplemented
18C2×#3748C2211yescharacteristic
19C2×C3×#217—22no—
20C3×D4×Dic3—22no—
21C3×D4×Dic3C2214yescomplemented
22C2×C3×#213—24no—
23C2×C3×#213C2214yes—
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27#63977—22no—
28#63916—22no—
29#63911C2212yescomplemented
30#63860C2212yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63567C2212yescomplemented
33#63564C2212yescomplemented
34#63562C2214yescomplemented
35C22×C3×D8—31no—
36C3×#518—31no—
37#5805—31no—
38#5798D311yescharacteristic, complemented
39C2×#932—31no—
40C2×#932—31no—
41C2×#932—61no—
42C22×#213D311yescharacteristic, complemented
43#5525—31no—
44#5215—31no—
45#5153—34no—
46#5150—34no—
47#5113—31no—
48#5102—31no—
49#5016—34no—
50#5015—34no—
51#5002—31no—
52#5001—31no—
53#4999—31no—
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—22no—
58C2×C32×D4D414yescomplemented
59C2×C32×D4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×#638—21no—
62#3828—22no—
63#3828—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2311yescharacteristic
67C22×C3×Dic3—24no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×#626—24no—
73#3754—24no—
74#3753—24no—
75#3748—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#217—21no—
78C3×#217—24no—
79C3×#217D412yes—
80C3×#213—28no—
81C3×C4⋊Dic3D412yes—
82C3×C4⋊Dic3C2312yes—
83C3×C4×Dic3—21no—
84C3×C4×Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8C2312yes—
87(C2×D3)⋊Dic3—24no—
88#3041—91noSylow
89C22×C3×D4—21no—
90C22×C3×D4—31no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C2×#235—31no—
94C2×#235—31no—
95C2×#235—61no—
96C22×D12C2×D311yescharacteristic
97C2×C3×D8—34no—
98C2×C3×D8—64no—
99C22×C3×C8—31no—
100C3×C4×D4—34no—
101C3×C4×D4—62no—
102C3×#117—31no—
103C3×#117—31no—
104C2×C3×C22⋊C4—62no—
105#953—62no—
106C2×#217—22no—
107#940—32no—
108#938—62no—
109#936—32no—
110D4×Dic3—22no—
111D4×Dic3C2×D314yescomplemented
112C2×#214—32no—
113C2×#214—32no—
114C2×#214—62no—
115#932—68no—
116#932—64no—
117#932—64no—
118C2×#213—24no—
119C2×#213—32no—
120C2×#213—32no—
121C2×#213—62no—
122C2×#213C2×D314yes—
123#926C2×D311yescharacteristic
124#926C2×D311yescharacteristic
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129#895—62no—
130#882—62no—
131#875—32no—
132#874—32no—
133#832—34no—
134#821—32no—
135#816—32no—
136Dic3⋊C8—34no—
137#810—32no—
138#809—34no—
139#809—32no—
140C4⋊(C3⋊C8)—34no—
141C23×C32—22no—
142C23×C32—24no—
143C23×C32—82no—
144C23×C32C2×D411yescharacteristic
145C22×C3⋊D3—21no—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—82no—
149C32×D4—24no—
150C32×D4—22no—
151C32×D4C2×D414yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4#4112yes—
155C2×C32×C4C2411yescharacteristic
156#638—42no—
157C2×C3⋊Dic3—21no—
158C4⋊(C3⋊D3)—21no—
159C4⋊(C3⋊D3)—21no—
160C4×C3⋊D3—42no—
161#634—21no—
162#634—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—84no—
165C2×C3×Dic3C2×D414yes—
166C3×D12—22no—
167C3×D12—22no—
168C3×D12—42no—
169#626—84no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—22no—
172C2×AGL(1,ℤ/8)—91no—
173C22×D8—31no—
174#535—91no—
175#518—31no—
176#463—94no—
177#459—94no—
178#424—91no—
179#418—91no—
180#416—91no—
181C24×C3—21no—
182C24×C3—21no—
183C24×C3—41no—
184C24×C3—61no—
185C23×D3—21no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—24no—
191C2×C3×D4—22no—
192C2×C3×D4—32no—
193C2×C3×D4—42no—
194C2×C3×D4—41no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C2×C3×D4D1214yescomplemented
199C2×C3×D4#6714yescomplemented
200C2×C3×D4C22×D312yes—
201C2×C3×D4C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—64no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C2×#67—61no—
207C2×#67—61no—
208C2×#67—64no—
209C2×#67—121no—
210C22×Dic3—24no—
211#235—64no—
212#235—62no—
213#235—62no—
214#235—62no—
215#235—62no—
216#235—122no—
217C2×D12—22no—
218C2×D12—22no—
219C2×D12—21no—
220C2×D12—31no—
221C2×D12—31no—
222C2×D12—61no—
223C2×D12—64no—
224C2×D12C22×D312yes—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—121no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—61no—
231C3×D8—68no—
232C2×C3×C8—32no—
233C2×C3×C8—62no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C22⋊C4—32no—
237C3×C22⋊C4—64no—
238C3×C22⋊C4—61no—
239C3×C42—32no—
240C3×C42—61no—
241#217—21no—
242#217—24no—
243#217—64no—
244#217#6712yes—
245#214—68no—
246#214—64no—
247#214—64no—
248#213—28no—
249#213—68no—
250#213—64no—
251#213—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3#6712yes—
254C4⋊Dic3C22×D312yes—
255C4×Dic3—21no—
256C4×Dic3C22×D312yes—
257#208—64no—
258#208—62no—
259#208—62no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8—32no—
262C2×C3⋊C8—32no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8C22×D312yes—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32—44no—
268C22×C32—84no—
269C22×C32#12112yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—41no—
272C2×C3⋊D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—44no—
275C2×C3×D3—84no—
276C32×C4#12112yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—41no—
280C3×Dic3—24no—
281C3×Dic3—42no—
282C2×#41—91no—
283C22×D4—31no—
284C22×D4D3211yescharacteristic
285AGL(1,ℤ/8)—184no—
286C2×SD16—92no—
287C2×D8—34no—
288C2×D8—64no—
289C2×D8—92no—
290C2×M16—91no—
291C22×C8—31no—
292#127—92no—
293#124—92no—
294#121—182no—
295#120—182no—
296C4×D4—34no—
297C4×D4—62no—
298#117—31no—
299#117—31no—
300C2×C22⋊C4—62no—
301C4⋊C8—94no—
302#103—92no—
303#102—92no—
304#102—94no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—24no—
308C23×C3—24no—
309C23×C3—21no—
310C23×C3—42no—
311C23×C3—44no—
312C23×C3—62no—
313C23×C3—82no—
314C23×C3—82no—
315C23×C3—84no—
316C23×C3—122no—
317C23×C3—242no—
318C23×C3D3×D411yescharacteristic
319C23×C3C2×#6711yescharacteristic
320C22×D3—22no—
321C22×D3—42no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—82no—
325C22×D3—121no—
326C3×D4—24no—
327C3×D4—24no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—24no—
331C3×D4—42no—
332C3×D4—44no—
333C3×D4—62no—
334C3×D4—62no—
335C3×D4—122no—
336C3×D4C2×D1214yes—
337C3×D4C2×#6714yes—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—34no—
343C2×C3×C4—62no—
344C2×C3×C4—244no—
345C2×C3×C4C2×D1212yes—
346C2×C3×C4#23512yes—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23712yes—
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—124no—
354#67—122no—
355#67—122no—
356#67—244no—
357C2×Dic3—22no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—84no—
361C2×Dic3—121no—
362C2×Dic3C2×#6714yes—
363D12—22no—
364D12—22no—
365D12—42no—
366D12—62no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—121no—
372D12—244no—
373C4×D3—124no—
374C4×D3—122no—
375C4×D3—122no—
376Dic6—62no—
377Dic6—61no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—121no—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—64no—
385C3⋊C8—62no—
386C3⋊C8—62no—
387C2×C32—22no—
388C2×C32—44no—
389C2×C32C2×#12111yescharacteristic
390C2×C32#57612yes—
391C3⋊D3—81no—
392C3×D3—82no—
393C24—21no—
394C24—61no—
395#41—182no—
396#41—182no—
397C2×Q8—91no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—32no—
401C2×D4—62no—
402C2×D4—62no—
403C2×D4—61no—
404C2×D4—91no—
405C2×D4—184no—
406C2×D4—181no—
407C2×D4#62614yescomplemented
408C2×D4C2×D3212yes—
409C22×C4—64no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412SD16—184no—
413D8—68no—
414D8—184no—
415M16—182no—
416C2×C8—32no—
417C2×C8—62no—
418C2×C8—92no—
419C4⋊C4—32no—
420C4⋊C4—32no—
421C22⋊C4—32no—
422C22⋊C4—64no—
423C22⋊C4—61no—
424C22⋊C4—184no—
425C42—32no—
426C42—61no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—42no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—84no—
438C22×C3—84no—
439C22×C3—84no—
440C22×C3—88no—
441C22×C3—122no—
442C22×C3—124no—
443C22×C3—244no—
444C22×C3#93012yes—
445C22×C3#93912yes—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—44no—
449C2×D3—42no—
450C2×D3—84no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—122no—
456C2×D3—242no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—64no—
461C3×C4—122no—
462C3×C4#93012yes—
463C3×C4#93912yes—
464C3×C4C22×D1211yescharacteristic
465C3×C4C2×#23511yescharacteristic
466C3×C4C2×#23711yescharacteristic
467C3×C4C22×#6711yescharacteristic
468Dic3—24no—
469Dic3—42no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473C32#304111yescharacteristic, complemented, Sylow
474C23—22no—
475C23—24no—
476C23—62no—
477C23—82no—
478C23—122no—
479C23—181no—
480C23—242no—
481C23D3×#6711yescharacteristic
482Q8—181no—
483Q8—181no—
484D4—22no—
485D4—24no—
486D4—62no—
487D4—62no—
488D4—122no—
489D4—181no—
490D4—181no—
491D4—362no—
492D4—724no—
493D4C2×#62614yes—
494C2×C4—34no—
495C2×C4—62no—
496C2×C4—181no—
497C2×C4—244no—
498C2×C4—362no—
499C2×C4#380412yes—
500C2×C4C2×#62612yes—
501C2×C4D3×#6711yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—62no—
504C8—182no—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—42no—
510C2×C3—44no—
511C2×C3—44no—
512C2×C3—84no—
513C2×C3—242no—
514C2×C3#575712yes—
515C2×C3C2×#93011yescharacteristic
516C2×C3C2×#93911yescharacteristic
517C2×C3#583512yes—
518D3—82no—
519D3—242no—
520D3—241no—
521D3—241no—
522C22—22no—
523C22—24no—
524C22—44no—
525C22—84no—
526C22—124no—
527C22—122no—
528C22—244no—
529C22—362no—
530C22—361no—
531C22#6397812yes—
532C22C2×D3×#6711yescharacteristic
533C4—64no—
534C4—122no—
535C4—361no—
536C4#6397812yes—
537C4C2×#380411yescharacteristic
538C4C22×#62611yescharacteristic
539C3—21no—
540C3#8254011yescharacteristic, complemented
541C3#8382611yescharacteristic, complemented
542C2—22no—
543C2—44no—
544C2—242no—
545C2—721no—
546C2#1059509612yes—
547C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3041
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. C2×#64141C2semidirect
2. C3×#5798C2semidirect
3. C22×C3×#213C2semidirect
4. #10595042C2semidirect
5. #10591481C2semidirect
6. #10591468C2semidirect
7. #10591116C2semidirect
8. #10591105C2semidirect
9. #10591085C2semidirect
15. C2×#3754C22semidirect
17. C2×#3753C22semidirect
21. C3×D4×Dic3C22semidirect
29. #63911C22semidirect
30. #63860C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
33. #63564C22semidirect
34. #63562C22semidirect
38. #5798D3semidirect
42. C22×#213D3semidirect
58. C2×C32×D4D4semidirect
111. D4×Dic3C2×D3semidirect
198. C2×C3×D4D12semidirect
199. C2×C3×D4#67semidirect
407. C2×D4#626semidirect
473. C32#3041semidirect
540. C3#82540semidirect
541. C3#83826semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C3×#57982
C22×C3×#2132
#105950422
#105914812
#105914682
#105911162
#105911052
#105910852
#838263
#825403