Finite Group Databasebeta

← #11868682

Subgroups — #11868682

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3#10592623C211yesmaximal, characteristic, complemented
4#10591139C212yesmaximal, complemented
5#10591085C212yesmaximal
6#10590270C214yesmaximal, complemented
7#10590269C212yesmaximal, complemented
8#10590266C212yesmaximal, complemented
9#83350—31nomaximal
10#82296—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14C2×#3748C2212yes—
15C2×C3×(C2×D3)⋊C4—21no—
16C3×#926C2212yes—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C3×#924—21no—
19C3×#924—21no—
20C3×C4×D12—21no—
21C3×C4×D12—21no—
22C3×C4×D12C2212yes—
23C3×C4×D12C2212yes—
24C3×#870C2212yescomplemented
25C3×#869C2211yescharacteristic, complemented
26C3×#869C2211yescharacteristic, complemented
27C3×C4×Dic6—21no—
28C3×C4×Dic6—21no—
29C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
30C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
31#63576C2214yescomplemented
32#63574C2214yescomplemented
33#63562C2214yes—
34#63562C2214yes—
35C3×#533—31no—
36C2×C3×C4×D4—31no—
37C2×C4×D12D311yescharacteristic
38#5470D311yescharacteristic, complemented
39#5215—32no—
40#5087—32no—
41#5084—32no—
42#5066—34no—
43#5009—34no—
44#5008—32no—
45#5007—32no—
46#5001—32no—
47#4995—32no—
48#4964—32no—
49#4924—31no—
50#4924—31no—
51#4924—61no—
52C23×C3×D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12Q814yescomplemented
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—44no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3748—24no—
71C2×C3⋊(C3⋊C8)C2314yes—
72C3×#217—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—22no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84#3077—91noSylow
85C22×C3×D4—31no—
86C23×C3×C4—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C3×C4⋊Q8—31no—
90C3×C4⋊Q8—31no—
91C3×#125—32no—
92C3×C22⋊Q8—61no—
93C3×C22⋊Q8—61no—
94C3×C4×Q8—61no—
95C3×C4×Q8—61no—
96C3×C4×D4—32no—
97C3×C4×D4—32no—
98C3×C4×D4—61no—
99C3×C4×D4—61no—
100C3×#117—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—61no—
103C2×C3×C42—21no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×(C2×D3)⋊C4—21no—
107#926C2×D312yes—
108C2×C4⋊Dic3C2×D311yescharacteristic
109#924—21no—
110#924—21no—
111C2×#208—32no—
112C2×#208—32no—
113C2×#208—62no—
114C4×D12—21no—
115C4×D12—21no—
116C4×D12C2×D312yes—
117C4×D12C2×D312yes—
118#870C2×D312yescomplemented
119#869C2×D311yescharacteristic, complemented
120#869C2×D311yescharacteristic, complemented
121C4×Dic6—21no—
122C4×Dic6—21no—
123#832—34no—
124#832—34no—
125#809—34no—
126#809—34no—
127#808—34no—
128#808—34no—
129#807—34no—
130#807—34no—
131C4⋊(C3⋊C8)—32no—
132C4⋊(C3⋊C8)—32no—
133C4⋊(C3⋊C8)—32no—
134C4⋊(C3⋊C8)—32no—
135C4⋊(C3⋊C8)—62no—
136C4⋊(C3⋊C8)—62no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—24no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C2×C32×C4—22no—
143C2×C32×C4—41no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×Q812yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12C2×Q814yes—
159C3×C4×D3—44no—
160C3×C4×D3—44no—
161C3×Dic6—42no—
162C3×Dic6—42no—
163C3⋊(C3⋊C8)—24no—
164#533—31no—
165C2×C4×D4—31no—
166#478—94no—
167#476—92no—
168#474—92no—
169#428—92no—
170#423—91no—
171#418—92no—
172C24×C3—61no—
173C23×D3—21no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×D4—34no—
177C2×C3×D4—32no—
178C2×C3×D4—62no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—61no—
184C22×C3×C4—62no—
185C22×C3×C4—62no—
186C22×C3×C4—124no—
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C2×D12—22no—
195C2×D12—21no—
196C2×D12Dic614yescomplemented
197C2×D12C22×D312yes—
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3—44no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—62no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—62no—
219C3×C42#6711yescharacteristic
220C3×C42#6711yescharacteristic
221C3×C42#6711yescharacteristic
222C3×C42#6711yescharacteristic
223C3×C42C22×D311yescharacteristic
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226C3×C42C22×D311yescharacteristic
227#217—22no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—22no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3C22×D312yes—
234C4⋊Dic3C22×D312yes—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—22no—
237Dic3⋊C4—22no—
238C4×Dic3—22no—
239#208—64no—
240#208—64no—
241#208—124no—
242C2×C3⋊C8—34no—
243C2×C3⋊C8—34no—
244C2×C3⋊C8—64no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32C22⋊Q812yes—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—24no—
250C2×C3×D3—48no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C32×C4—21no—
254C32×C4—21no—
255C32×C4—21no—
256C32×C4C22⋊Q812yes—
257C32×C4AGL(1,ℤ/8)12yes—
258C32×C4C22×Q811yescharacteristic
259C32×C4C2×#4111yescharacteristic
260C3×Dic3—42no—
261C3×Dic3—42no—
262C3×Dic3—42no—
263C22×D4—31no—
264C23×C4—61no—
265C2×M16—92no—
266C4⋊Q8—31no—
267C4⋊Q8—31no—
268#125—32no—
269C22⋊Q8—61no—
270C22⋊Q8—61no—
271C4×Q8—61no—
272C4×Q8—61no—
273C4×D4—32no—
274C4×D4—32no—
275C4×D4—61no—
276C4×D4—61no—
277#117—32no—
278C2×C4⋊C4—31no—
279C2×C22⋊C4—61no—
280C2×C42D3211yescharacteristic
281#107—94no—
282#106—94no—
283C4⋊C8—92no—
284C4⋊C8—92no—
285#102—94no—
286#102—94no—
287C23×C3—21no—
288C23×C3—64no—
289C23×C3—62no—
290C23×C3—122no—
291C23×C3—122no—
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×#6711yescharacteristic
294C22×D3—24no—
295C22×D3—22no—
296C22×D3—42no—
297C22×D3—42no—
298C3×Q8—122no—
299C3×Q8—122no—
300C3×D4—34no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—42no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—124no—
321C2×C3×C4—122no—
322C2×C3×C4—124no—
323C2×C3×C4C2×Dic612yes—
324C2×C3×C4#23512yes—
325C2×C3×C4D3×Q812yes—
326C2×C3×C4#23912yes—
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—42no—
343D12—24no—
344D12—22no—
345D12C2×Dic614yes—
346C4×D3—44no—
347C4×D3—44no—
348Dic6—42no—
349Dic6—42no—
350C3⋊C8—64no—
351C3⋊C8—64no—
352C3⋊C8—124no—
353C2×C32—22no—
354C2×C32C2×C22⋊Q811yescharacteristic
355C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
356C2×C32#57511yescharacteristic
357C3×D3—44no—
358C24—61no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×D4—32no—
362C2×D4—34no—
363C2×D4—62no—
364C2×D4—61no—
365C22×C4—61no—
366C22×C4—62no—
367C22×C4—62no—
368C22×C4—124no—
369C22×C4#62511yescharacteristic
370C22×C4#62511yescharacteristic
371C22×C4C2×D3211yescharacteristic
372M16—184no—
373C2×C8—94no—
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—32no—
377C4⋊C4—61no—
378C4⋊C4—62no—
379C4⋊C4—62no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C22⋊C4—62no—
383C22⋊C4—62no—
384C22⋊C4—62no—
385C42—62no—
386C42#62511yescharacteristic
387C42#62511yescharacteristic
388C42C2×D3211yescharacteristic
389C42C2×D3211yescharacteristic
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—64no—
399C22×C3—128no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3#92412yes—
403C22×C3#94612yes—
404C22×C3C22×#6711yescharacteristic
405C22×C3C22×#6711yescharacteristic
406C2×D3—24no—
407C2×D3—48no—
408C2×D3—42no—
409C2×D3—42no—
410C3×C4—22no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—22no—
420C3×C4—22no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—122no—
424C3×C4—122no—
425C3×C4—122no—
426C3×C4#92412yes—
427C3×C4#93212yes—
428C3×C4#94612yes—
429C3×C4#94912yes—
430C3×C4C22×Dic611yescharacteristic
431C3×C4C2×#23511yescharacteristic
432C3×C4C2×D3×Q811yescharacteristic
433C3×C4C2×#23911yescharacteristic
434Dic3—42no—
435Dic3—42no—
436Dic3—42no—
437C32#307711yescharacteristic, complemented, Sylow
438C23—62no—
439C23—64no—
440C23—122no—
441C23—122no—
442C23C2×#62511yescharacteristic
443Q8—122no—
444Q8—122no—
445D4—34no—
446D4—62no—
447D4—64no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—124no—
454C2×C4—122no—
455C2×C4—124no—
456C2×C4D3×Dic612yes—
457C2×C4#379912yes—
458C2×C4C2×#62511yescharacteristic
459C2×C4C2×#62511yescharacteristic
460C2×C4C2×#62511yescharacteristic
461C2×C4C2×#62511yescharacteristic
462C2×C4C2×#62511yescharacteristic
463C2×C4C22×D3211yescharacteristic
464C8—184no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—42no—
471C2×C3—124no—
472C2×C3C2×#92411yescharacteristic
473C2×C3C2×#93211yescharacteristic
474C2×C3C2×#94611yescharacteristic
475C2×C3C2×#94911yescharacteristic
476C2×C3#582211yescharacteristic
477C2×C3#582211yescharacteristic
478D3—44no—
479C22—21no—
480C22—21no—
481C22—64no—
482C22—128no—
483C22—122no—
484C22—122no—
485C22#6385612yes—
486C22C22×#62511yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—122no—
491C4—122no—
492C4—122no—
493C4#6382312yes—
494C4#6385612yes—
495C4C2×D3×Dic611yescharacteristic
496C4C2×#379911yescharacteristic
497C3—21no—
498C3#8229611yescharacteristic, complemented
499C3#8335011yescharacteristic, complemented
500C2—22no—
501C2—124no—
502C2C2×#6382311yescharacteristic
503C2#1059478611yescharacteristic
504C2C2×#6385611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. #10592623C2semidirect
4. #10591139C2semidirect
6. #10590270C2semidirect
7. #10590269C2semidirect
8. #10590266C2semidirect
24. C3×#870C22semidirect
25. C3×#869C22semidirect
26. C3×#869C22semidirect
29. C4⋊(C3⋊(C3⋊C8))C22semidirect
30. C4⋊(C3⋊(C3⋊C8))C22semidirect
31. #63576C22semidirect
32. #63574C22semidirect
38. #5470D3semidirect
59. C2×C3×D12Q8semidirect
118. #870C2×D3semidirect
119. #869C2×D3semidirect
120. #869C2×D3semidirect
196. C2×D12Dic6semidirect
437. C32#3077semidirect
498. C3#82296semidirect
499. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C3×#54702
#105926232
#105911392
#105910852
#105902702
#105902692
#105902662
#833503
#822963