Finite Group Databasebeta

← #11872748

Subgroups — #11872748

Order 1152.

956 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596006C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591162C212yesmaximal, complemented
5#10591136C212yesmaximal, complemented
6#10590349C212yesmaximal, complemented
7#10590346C212yesmaximal, complemented
8C4×#3714C212yesmaximal, complemented
9#10590271C212yesmaximal, complemented
10#82542—31nomaximal
11#79386—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64139C2212yes—
15#64103—22no—
16#64093—22no—
17#64083C2211yescharacteristic, complemented
18C4×C4⋊(C3⋊D3)C2212yescomplemented
19#64079C2211yescharacteristic, complemented
20C3×#926C2211yescharacteristic
21C3×#893—22no—
22C3×D3×C22⋊C4—22no—
23C3×C4×D12C2212yes—
24C3×C4×D12C2212yes—
25C2×#3714C2212yes—
26C2×#3714C2212yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29C3×#803C2211yescharacteristic, complemented
30C3×C4×C3⋊C8C2211yescharacteristic, complemented
31#63575C2212yescomplemented
32#63573C2212yescomplemented
33#63564C2212yescomplemented
34#63564C2212yescomplemented
35#63563C2212yes—
36#63563C2212yes—
37C3×#518—31no—
38#5535—31no—
39#5535—31no—
40#5535—61no—
41#5521D311yescharacteristic, complemented
42C3×#433—31no—
43#5217—32no—
44#5015—32no—
45#5014—32no—
46C4×#213—32no—
47#5009—32no—
48#5003—32no—
49#5000D311yescharacteristic, complemented
50#4847—32no—
51#4843—32no—
52#4737—32no—
53#4732—32no—
54#4711—32no—
55C4×D24—32no—
56C23×C3×D3—21no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C3×D12—21no—
63C2×C3×D12—24no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C32×C4⋊C4D412yes—
68C32×C22⋊C4D412yes—
69C32×C42C2311yescharacteristic
70C32×C42C2311yescharacteristic
71#3752—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—22no—
75C3×#217—21no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3—21no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3714—24no—
83#3714—24no—
84#3122—91noSylow
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C3×C4×D4—32no—
88C3×C4×D4—32no—
89C3×C4×D4—62no—
90C3×#117—21no—
91C3×#117—31no—
92C3×#117C2×D311yescharacteristic
93C3×#117C2×D311yescharacteristic
94C2×C3×C22⋊C4—62no—
95C2×#213—32no—
96C2×#213—32no—
97#930—32no—
98#930—32no—
99#930—62no—
100#926C2×D311yescharacteristic
101C2×D24—32no—
102C2×D24—32no—
103#894—64no—
104#894—62no—
105#894—62no—
106#893—22no—
107#884—64no—
108#884—62no—
109#884—62no—
110D3×C22⋊C4—22no—
111#874—31no—
112#874—31no—
113#874—61no—
114C4×D12—32no—
115C4×D12—32no—
116C4×D12—62no—
117C4×D12C2×D312yes—
118C4×D12C2×D312yes—
119#870—31no—
120#870—31no—
121#870—61no—
122C3×C4⋊C8—32no—
123C3×C22⋊C8—32no—
124C3×#97—31no—
125C3×C4×C8—31no—
126#832—32no—
127#832—32no—
128#830C2×D312yes—
129#821—32no—
130#821—32no—
131#821—32no—
132#821—32no—
133#818—32no—
134#817—32no—
135#809—32no—
136#809—32no—
137#808—32no—
138#807—32no—
139C4⋊(C3⋊C8)C2×D312yescomplemented
140#803C2×D311yescharacteristic, complemented
141C4×C3⋊C8C2×D311yescharacteristic, complemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—82no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2411yescharacteristic
152#638—82no—
153C2×C3⋊Dic3—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—82no—
157C4×C3⋊D3—82no—
158C2×C3×Dic3—22no—
159C3×D12—24no—
160C3×D12—22no—
161C3×D12#4114yes—
162C3×C4×D3—82no—
163C3×C4×D3—82no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166#540—91no—
167#518—31no—
168#482—92no—
169#478—92no—
170#459—92no—
171#447—92no—
172#442—92no—
173C4×D8—92no—
174#433—31no—
175C24×C3—61no—
176C23×D3—21no—
177C2×C3×D4—32no—
178C2×C3×D4—64no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—64no—
186C2×#67—62no—
187C2×#67—62no—
188C2×D12—21no—
189C2×D12—24no—
190C2×D12—32no—
191C2×D12—32no—
192C2×D12—62no—
193C2×D12—64no—
194C2×D12—62no—
195C2×D12—62no—
196C2×D12C22×D312yes—
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3—64no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C3×C8—32no—
203C2×C3×C8—32no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4D1212yes—
207C3×C4⋊C4#6712yes—
208C3×C22⋊C4—22no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—62no—
211C3×C22⋊C4—62no—
212C3×C22⋊C4D1212yes—
213C3×C22⋊C4#6712yes—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—61no—
217C3×C42C22×D311yescharacteristic
218C3×C42C22×D311yescharacteristic
219C3×C42C22×D311yescharacteristic
220C3×C42C22×D311yescharacteristic
221#217—21no—
222#213—64no—
223#213—64no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—22no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—64no—
237Dic3⋊C4—62no—
238Dic3⋊C4—62no—
239C4×Dic3—21no—
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D312yes—
242D24—64no—
243D24—64no—
244C22×C32—21no—
245C22×C32—22no—
246C22×C32C22×D411yescharacteristic
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—84no—
254C32×C4—21no—
255C32×C4—22no—
256C32×C4—22no—
257C32×C4C2×#4112yes—
258C3⋊Dic3—42no—
259C3×Dic3—42no—
260C22×D4—31no—
261C2×D8—92no—
262C2×D8—92no—
263#127—91no—
264#125—91no—
265#123—182no—
266#121—92no—
267#121—182no—
268C4×D4—32no—
269C4×D4—32no—
270C4×D4—62no—
271C4×D4—92no—
272#117—31no—
273#117D3211yescharacteristic
274C2×C22⋊C4—62no—
275#107—92no—
276#106—92no—
277C4⋊C8—32no—
278#102—92no—
279#102—92no—
280#102—92no—
281#102—92no—
282C22⋊C8—32no—
283#97—31no—
284C4×C8—31no—
285C23×C3—21no—
286C23×C3—64no—
287C23×C3—62no—
288C23×C3—242no—
289C23×C3C2×D1211yescharacteristic
290C23×C3C2×#6711yescharacteristic
291C22×D3—22no—
292C22×D3—24no—
293C22×D3—64no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—82no—
297C3×D4—34no—
298C3×D4—64no—
299C3×D4—62no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—42no—
307C2×C3×C4—62no—
308C2×C3×C4—242no—
309C2×C3×C4—242no—
310C2×C3×C4C2×D1212yes—
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4C2×D1212yes—
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6712yes—
316C2×C3×C4C23×D311yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318#67—242no—
319#67—242no—
320#67—244no—
321C2×Dic3—22no—
322C2×Dic3—64no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325D12—24no—
326D12—22no—
327D12—62no—
328D12—62no—
329D12—62no—
330D12—62no—
331D12—122no—
332D12—122no—
333D12—242no—
334D12—242no—
335D12—244no—
336D12#23514yes—
337C4×D3—82no—
338C4×D3—82no—
339C4×D3—242no—
340C4×D3—242no—
341C4×D3—244no—
342C3×C8—62no—
343C3×C8—62no—
344C3⋊C8—22no—
345C3⋊C8—22no—
346C2×C32—41no—
347C2×C32#52511yescharacteristic
348C2×C32#57612yes—
349C3⋊D3—82no—
350C3×D3—44no—
351C24—61no—
352C2×D4—32no—
353C2×D4—64no—
354C2×D4—61no—
355C2×D4—92no—
356C2×D4—182no—
357C2×D4—182no—
358C22×C4—62no—
359C22×C4—62no—
360C22×C4—182no—
361C22×C4C2×D3211yescharacteristic
362D8—184no—
363D8—184no—
364C2×C8—32no—
365C2×C8—32no—
366C4⋊C4—32no—
367C4⋊C4—92no—
368C4⋊C4—182no—
369C4⋊C4#62612yes—
370C22⋊C4—61no—
371C22⋊C4—62no—
372C22⋊C4—62no—
373C22⋊C4—182no—
374C22⋊C4—182no—
375C22⋊C4#62612yes—
376C42—61no—
377C42C2×D3211yescharacteristic
378C42C2×D3211yescharacteristic
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—21no—
384C22×C3—42no—
385C22×C3—41no—
386C22×C3—64no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—244no—
390C22×C3C22×D1211yescharacteristic
391C22×C3C22×#6711yescharacteristic
392C2×D3—24no—
393C2×D3—42no—
394C2×D3—42no—
395C2×D3—84no—
396C2×D3—124no—
397C2×D3—124no—
398C2×D3—124no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—122no—
403C2×D3—122no—
404C2×D3—122no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—22no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—41no—
415C3×C4—122no—
416C3×C4C2×#23512yes—
417C3×C4D3×#4112yes—
418Dic3—42no—
419Dic3—124no—
420Dic3—122no—
421Dic3—122no—
422C32#312211yescharacteristic, complemented, Sylow
423C23—64no—
424C23—62no—
425C23—182no—
426C23—242no—
427C23C2×#62611yescharacteristic
428D4—34no—
429D4—64no—
430D4—62no—
431D4—182no—
432D4—182no—
433D4—722no—
434D4—722no—
435C2×C4—22no—
436C2×C4—62no—
437C2×C4—182no—
438C2×C4—242no—
439C2×C4—242no—
440C2×C4—722no—
441C2×C4C2×#62611yescharacteristic
442C2×C4C2×#62612yes—
443C2×C4C2×#62612yes—
444C2×C4C22×D3211yescharacteristic
445C8—62no—
446C8—62no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—81no—
452C2×C3—124no—
453C2×C3#552411yescharacteristic
454C2×C3#575212yes—
455C2×C3#579111yescharacteristic
456C2×C3#583512yes—
457D3—44no—
458D3—244no—
459D3—242no—
460D3—242no—
461C22—22no—
462C22—21no—
463C22—64no—
464C22—122no—
465C22—122no—
466C22—244no—
467C22—362no—
468C22—362no—
469C22—362no—
470C22C22×#62611yescharacteristic
471C4—22no—
472C4—22no—
473C4—21no—
474C4—122no—
475C4—362no—
476C4D3×#23512yes—
477C3—21no—
478C3#7938611yescharacteristic, complemented
479C3#8254211yescharacteristic, complemented
480C2—41no—
481C2—124no—
482C2—722no—
483C2#1059502311yescharacteristic
484C2#1059544912yes—
subgroupG/H
centerC22C22×#626
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. #10596006C2semidirect
2. C3×#5521C2semidirect
3. C3×#5000C2semidirect
4. #10591162C2semidirect
5. #10591136C2semidirect
6. #10590349C2semidirect
7. #10590346C2semidirect
8. C4×#3714C2semidirect
9. #10590271C2semidirect
17. #64083C22semidirect
18. C4×C4⋊(C3⋊D3)C22semidirect
19. #64079C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×#803C22semidirect
30. C3×C4×C3⋊C8C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
33. #63564C22semidirect
34. #63564C22semidirect
41. #5521D3semidirect
49. #5000D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. #803C2×D3semidirect
141. C4×C3⋊C8C2×D3semidirect
422. C32#3122semidirect
478. C3#79386semidirect
479. C3#82542semidirect

Maximal subgroups

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

subgroupindex
#105960062
C3×#55212
C3×#50002
#105911622
#105911362
#105903492
#105903462
C4×#37142
#105902712
#825423
#793863