Finite Group Databasebeta

← #11872750

Subgroups — #11872750

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5535C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3#10592699C211yesmaximal, characteristic, complemented
4#10591160C212yesmaximal, complemented
5#10591090C212yesmaximal, complemented
6#10590347C212yesmaximal, complemented
7#10590344C212yesmaximal, complemented
8C4×#3713C212yesmaximal, complemented
9#10590270C212yesmaximal, complemented
10#83435—31nomaximal
11#82542—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#930C2212yes—
15C3×#926C2211yescharacteristic
16C3×#894—22no—
17C3×#893—22no—
18C3×#884—22no—
19C3×D3×C22⋊C4—22no—
20C3×#874C2211yescharacteristic, complemented
21C3×C4×D12C2212yes—
22C3×C4×D12C2212yes—
23C3×C4×D12C2212yescomplemented
24C3×#870C2211yescharacteristic, complemented
25C2×#3713C2212yes—
26C2×#3713C2212yes—
27#63657C2212yes—
28C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
29#63630C2211yescharacteristic, complemented
30C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
31#63576C2212yescomplemented
32#63574C2212yescomplemented
33#63562C2212yes—
34#63562C2212yes—
35#63562C2212yescomplemented
36#63562C2212yescomplemented
37C3×#540—31no—
38C3×#518—31no—
39#5535D311yescharacteristic, complemented
40#5521D311yescharacteristic, complemented
41#5217—32no—
42#5072—32no—
43#5066—32no—
44#5036—32no—
45#5035—32no—
46#5015—32no—
47#5014—32no—
48#5014—32no—
49C4×#213—32no—
50C4×#213—32no—
51#5009—32no—
52#5003—32no—
53#5000—31no—
54#5000—31no—
55#5000—61no—
56C23×C3×D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C3×#67—22no—
59C2×C3×D12—21no—
60C2×C3×D12—24no—
61C2×C3×D12—22no—
62C2×C3×D12C2312yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C32×C4⋊C4D412yes—
68C32×C22⋊C4D412yes—
69C32×C42C2311yescharacteristic
70C32×C42C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×#217—21no—
74C3×(C2×D3)⋊C4—22no—
75C3×(C2×D3)⋊C4—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—21no—
82#3713—24no—
83#3713—24no—
84#3122—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C3×#127—31no—
88C3×#125—31no—
89C3×#123—62no—
90C3×#121—32no—
91C3×#121—62no—
92C3×C4×D4—32no—
93C3×C4×D4—32no—
94C3×C4×D4—32no—
95C3×C4×D4—62no—
96C3×#117—21no—
97C3×#117—31no—
98C3×#117C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C2×C3×C22⋊C4—62no—
101C2×#213—32no—
102C2×#213—32no—
103C2×#213—32no—
104C2×#213—32no—
105#930C2×D312yes—
106#926C2×D311yescharacteristic
107#894—22no—
108#893—22no—
109#884—22no—
110D3×C22⋊C4—22no—
111#874C2×D311yescharacteristic, complemented
112C4×D12C2×D312yes—
113C4×D12C2×D312yes—
114C4×D12C2×D312yescomplemented
115#870C2×D311yescharacteristic, complemented
116#832—32no—
117#832—32no—
118#832—32no—
119#832—32no—
120#830—32no—
121#830—32no—
122#830—62no—
123#809—32no—
124#809—32no—
125#809—32no—
126#809—32no—
127#808—32no—
128#808—32no—
129#807—32no—
130#807—32no—
131C4⋊(C3⋊C8)—32no—
132C4⋊(C3⋊C8)—32no—
133C4⋊(C3⋊C8)—62no—
134#803—31no—
135#803—31no—
136#803—61no—
137C4×C3⋊C8—31no—
138C4×C3⋊C8—31no—
139C4×C3⋊C8—61no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—24no—
143C22×C3×D3—22no—
144C22×C3×D3—82no—
145C2×C32×C4—22no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2411yescharacteristic
150C3×#67—82no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C3×D12—24no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—82no—
158C3×D12#4114yes—
159C3×C4×D3—82no—
160C3×C4×D3—82no—
161C3×C4×D3—82no—
162C3⋊(C3⋊C8)—22no—
163C3⋊(C3⋊C8)—22no—
164#540—31no—
165#518—31no—
166#482—92no—
167#478—92no—
168#459—92no—
169#447—92no—
170#442—92no—
171C4×D8—92no—
172#433—91no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×D4—32no—
176C2×C3×D4—32no—
177C2×C3×D4—64no—
178C2×C3×D4—62no—
179C2×C3×D4—61no—
180C2×C3×D4—62no—
181C22×C3×C4—21no—
182C22×C3×C4—62no—
183C22×C3×C4—62no—
184C22×C3×C4—62no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—22no—
188C2×D12—21no—
189C2×D12—24no—
190C2×D12—22no—
191C2×D12C22×D312yes—
192C2×D12C22×D312yes—
193C2×C4×D3—22no—
194C2×C4×D3—22no—
195C2×C4×D3—22no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4#6712yes—
201C3×C4⋊C4#6712yes—
202C3×C22⋊C4—22no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—62no—
205C3×C22⋊C4—62no—
206C3×C22⋊C4—62no—
207C3×C22⋊C4—62no—
208C3×C22⋊C4#6712yes—
209C3×C22⋊C4#6712yes—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—61no—
213C3×C42C22×D311yescharacteristic
214C3×C42C22×D311yescharacteristic
215C3×C42C22×D311yescharacteristic
216C3×C42C22×D311yescharacteristic
217#217—21no—
218#213—64no—
219#213—64no—
220#213—64no—
221#213—64no—
222(C2×D3)⋊C4—22no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—22no—
226C4⋊Dic3C22×D312yes—
227C4⋊Dic3C22×D312yes—
228Dic3⋊C4—22no—
229C4×Dic3—21no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—62no—
236C22×C32—21no—
237C22×C32—22no—
238C22×C32C22×D411yescharacteristic
239C2×C3×D3—24no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—84no—
246C32×C4—21no—
247C32×C4—22no—
248C32×C4—22no—
249C32×C4C2×#4112yes—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C22×D4—31no—
253C2×D8—92no—
254C2×D8—92no—
255#127—31no—
256#125—31no—
257#123—62no—
258#121—32no—
259#121—62no—
260C4×D4—32no—
261C4×D4—32no—
262C4×D4—32no—
263C4×D4—62no—
264#117—31no—
265#117D3211yescharacteristic
266C2×C22⋊C4—62no—
267#107—92no—
268#106—92no—
269C4⋊C8—92no—
270#102—92no—
271#102—92no—
272#102—92no—
273#102—92no—
274C22⋊C8—92no—
275#97—91no—
276C4×C8—91no—
277C23×C3—21no—
278C23×C3—64no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—242no—
282C23×C3C2×#6711yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—22no—
285C22×D3—24no—
286C22×D3—22no—
287C22×D3—82no—
288C3×D4—34no—
289C3×D4—64no—
290C3×D4—62no—
291C3×D4—62no—
292C3×D4—62no—
293C3×D4—242no—
294C3×D4—242no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—242no—
305C2×C3×C4—242no—
306C2×C3×C4—242no—
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6712yes—
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6712yes—
311C2×C3×C4C2×#6712yes—
312C2×C3×C4C2×#6712yes—
313C2×C3×C4C23×D311yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315#67—82no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318D12—24no—
319D12—22no—
320D12—22no—
321D12—22no—
322D12—82no—
323D12#23514yes—
324C4×D3—82no—
325C4×D3—82no—
326C4×D3—82no—
327C3⋊C8—62no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C3⋊C8—62no—
331C3⋊C8—122no—
332C3⋊C8—122no—
333C2×C32—41no—
334C2×C32#52511yescharacteristic
335C2×C32#57612yes—
336C3×D3—44no—
337C3×D3—82no—
338C24—61no—
339C2×D4—32no—
340C2×D4—32no—
341C2×D4—64no—
342C2×D4—62no—
343C2×D4—61no—
344C2×D4—62no—
345C22×C4—62no—
346C22×C4—62no—
347C22×C4—62no—
348C22×C4C2×D3211yescharacteristic
349D8—184no—
350D8—184no—
351C2×C8—92no—
352C2×C8—92no—
353C4⋊C4—32no—
354C4⋊C4—32no—
355C4⋊C4—62no—
356C4⋊C4#62512yes—
357C22⋊C4—61no—
358C22⋊C4—62no—
359C22⋊C4—62no—
360C22⋊C4—62no—
361C22⋊C4—62no—
362C22⋊C4#62512yes—
363C42—61no—
364C42C2×D3211yescharacteristic
365C42C2×D3211yescharacteristic
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—41no—
372C22×C3—42no—
373C22×C3—64no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3—122no—
377C22×C3—122no—
378C22×C3—122no—
379C22×C3—244no—
380C22×C3C22×#6711yescharacteristic
381C22×C3C22×#6711yescharacteristic
382C2×D3—24no—
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—42no—
386C2×D3—42no—
387C2×D3—42no—
388C2×D3—84no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—41no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—122no—
400C3×C4—122no—
401C3×C4C2×#23512yes—
402C3×C4D3×#4112yes—
403Dic3—42no—
404Dic3—42no—
405C32#312211yescharacteristic, complemented, Sylow
406C23—64no—
407C23—62no—
408C23—62no—
409C23—242no—
410C23C2×#62511yescharacteristic
411D4—34no—
412D4—64no—
413D4—62no—
414D4—62no—
415D4—62no—
416D4—242no—
417D4—242no—
418C2×C4—22no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—242no—
422C2×C4—242no—
423C2×C4—242no—
424C2×C4C2×#62511yescharacteristic
425C2×C4C2×#62512yes—
426C2×C4C2×#62512yes—
427C2×C4C22×D3211yescharacteristic
428C8—182no—
429C8—182no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—81no—
435C2×C3—124no—
436C2×C3—242no—
437C2×C3#579111yescharacteristic
438C2×C3#582811yescharacteristic
439C2×C3#583512yes—
440C2×C3#583512yes—
441D3—44no—
442D3—82no—
443C22—22no—
444C22—21no—
445C22—64no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22—122no—
450C22—122no—
451C22—244no—
452C22C22×#62511yescharacteristic
453C4—22no—
454C4—22no—
455C4—21no—
456C4—122no—
457C4—122no—
458C4D3×#23512yes—
459C3—21no—
460C3#8254211yescharacteristic, complemented
461C3#8343511yescharacteristic, complemented
462C2—41no—
463C2—124no—
464C2—242no—
465C2#1059502211yescharacteristic
466C2#1059544412yes—
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3122
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. C3×#5535C2semidirect
2. C3×#5521C2semidirect
3. #10592699C2semidirect
4. #10591160C2semidirect
5. #10591090C2semidirect
6. #10590347C2semidirect
7. #10590344C2semidirect
8. C4×#3713C2semidirect
9. #10590270C2semidirect
20. C3×#874C22semidirect
23. C3×C4×D12C22semidirect
24. C3×#870C22semidirect
28. C4⋊(C3⋊(C3⋊C8))C22semidirect
29. #63630C22semidirect
30. C4×C3⋊(C3⋊C8)C22semidirect
31. #63576C22semidirect
32. #63574C22semidirect
35. #63562C22semidirect
36. #63562C22semidirect
39. #5535D3semidirect
40. #5521D3semidirect
111. #874C2×D3semidirect
114. C4×D12C2×D3semidirect
115. #870C2×D3semidirect
405. C32#3122semidirect
460. C3#82542semidirect
461. C3#83435semidirect

Maximal subgroups

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

subgroupindex
C3×#55352
C3×#55212
#105926992
#105911602
#105910902
#105903472
#105903442
C4×#37132
#105902702
#834353
#825423