Finite Group Databasebeta

← #11872749

Subgroups — #11872749

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2C3×#5535C211yesmaximal, characteristic, complemented
3C3×#5000C211yesmaximal, characteristic, complemented
4#10591168C212yesmaximal, complemented
5#10591093C212yesmaximal, complemented
6#10590355C212yesmaximal, complemented
7#10590346C212yesmaximal, complemented
8C4×#3714C212yesmaximal, complemented
9#10590308C212yesmaximal, complemented
10#83435—31nomaximal
11#79386—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C32×#117C2211yescharacteristic
14#64135C2211yescharacteristic
15#64102—22no—
16C22⋊C4×C3⋊D3—22no—
17C4×C4⋊(C3⋊D3)C2212yes—
18C4×C4⋊(C3⋊D3)C2212yes—
19C3×#930C2212yes—
20C3×#894—22no—
21C3×#884—22no—
22C3×#874C2211yescharacteristic, complemented
23C3×C4×D12C2212yescomplemented
24C3×#870C2211yescharacteristic, complemented
25C2×#3714C2212yes—
26C2×#3714C2212yes—
27C3×#830C2212yes—
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29C3×#803C2211yescharacteristic, complemented
30C3×C4×C3⋊C8C2211yescharacteristic, complemented
31#63575C2212yescomplemented
32#63573C2212yescomplemented
33#63564C2212yes—
34#63564C2212yes—
35#63563C2212yescomplemented
36#63563C2212yescomplemented
37C3×#540—31no—
38#5535D311yescharacteristic, complemented
39#5521—31no—
40#5521—31no—
41#5521—61no—
42C3×#433—31no—
43#5072—32no—
44#5066—32no—
45#5036—32no—
46#5035—32no—
47#5014—32no—
48C4×#213—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×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—24no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C3×#67—22no—
64C2×C3×D12—22no—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C32×C4⋊C4D412yes—
68C32×C22⋊C4D412yes—
69C32×C42C2311yescharacteristic
70C32×C42C2311yescharacteristic
71#3757—21no—
72#3752—22no—
73#3752—22no—
74C4⋊(C3⋊Dic3)C2312yes—
75C4×C3⋊Dic3—21no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3714—24no—
83#3714—24no—
84#3122—91noSylow
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C3×#127—31no—
89C3×#125—31no—
90C3×#123—62no—
91C3×#121—32no—
92C3×#121—62no—
93C3×C4×D4—32no—
94C3×#117—21no—
95C3×#117C2×D311yescharacteristic
96C3×#117C2×D311yescharacteristic
97C2×#213—32no—
98C2×#213—32no—
99#930C2×D312yes—
100#926—31no—
101#926—31no—
102#926—61no—
103C2×D24—32no—
104C2×D24—32no—
105#894—22no—
106#893—64no—
107#893—62no—
108#893—62no—
109#884—22no—
110D3×C22⋊C4—64no—
111D3×C22⋊C4—62no—
112D3×C22⋊C4—62no—
113#874C2×D311yescharacteristic, complemented
114C4×D12—32no—
115C4×D12—32no—
116C4×D12—32no—
117C4×D12—32no—
118C4×D12—62no—
119C4×D12—62no—
120C4×D12C2×D312yescomplemented
121#870C2×D311yescharacteristic, complemented
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—24no—
145C22×C3⋊D3—82no—
146C22×C3×D3—22no—
147C2×C32×C4—22no—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C4⋊(C3⋊D3)—24no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)#4114yes—
156C4×C3⋊D3—82no—
157C4×C3⋊D3—82no—
158C3×#67—82no—
159C2×C3×Dic3—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—82no—
163C3×C4×D3—82no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166#540—31no—
167#518—91no—
168#482—92no—
169#478—92no—
170#459—92no—
171#447—92no—
172#442—92no—
173C4×D8—92no—
174#433—31no—
175C23×D3—62no—
176C23×D3—61no—
177C23×D3—61no—
178C2×C3×D4—32no—
179C2×C3×D4—62no—
180C2×C3×D4—62no—
181C22×C3×C4—21no—
182C22×C3×C4—62no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—22no—
186C2×D12—22no—
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—64no—
191C2×D12—64no—
192C2×D12—62no—
193C2×D12—68no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12C22×D312yes—
197C2×C4×D3—22no—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C3×C8—32no—
205C2×C3×C8—32no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—62no—
209C3×C4⋊C4D1212yes—
210C3×C4⋊C4#6712yes—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4D1212yes—
215C3×C22⋊C4#6712yes—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42C22×D311yescharacteristic
219C3×C42C22×D311yescharacteristic
220C3×C42C22×D311yescharacteristic
221C3×C42C22×D311yescharacteristic
222#217—62no—
223#217—61no—
224#217—61no—
225#213—64no—
226#213—64no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234(C2×D3)⋊C4—62no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—22no—
240C4×Dic3—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C2×C3⋊C8C22×D312yes—
244C2×C3⋊C8C22×D312yes—
245D24—64no—
246D24—64no—
247C22×C32—21no—
248C22×C32—22no—
249C22×C32C22×D411yescharacteristic
250C2×C3⋊D3—24no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—84no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C32×C4—21no—
258C32×C4—22no—
259C32×C4—22no—
260C32×C4C2×#4112yes—
261C3⋊Dic3—42no—
262C3×Dic3—42no—
263C22×D4—91no—
264C2×D8—92no—
265C2×D8—92no—
266#127—31no—
267#125—31no—
268#123—62no—
269#121—32no—
270#121—62no—
271C4×D4—32no—
272C4×D4—92no—
273C4×D4—92no—
274C4×D4—182no—
275#117—91no—
276#117D3211yescharacteristic
277C2×C22⋊C4—182no—
278#107—92no—
279#106—92no—
280C4⋊C8—32no—
281#102—92no—
282#102—92no—
283#102—92no—
284#102—92no—
285C22⋊C8—32no—
286#97—31no—
287C4×C8—31no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3C2×D1211yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—22no—
293C22×D3—64no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—68no—
297C22×D3—64no—
298C22×D3—64no—
299C22×D3—242no—
300C22×D3—242no—
301C22×D3—244no—
302C3×D4—62no—
303C3×D4—62no—
304C3×D4—242no—
305C3×D4—242no—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—62no—
314C2×C3×C4—242no—
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4C2×D1212yes—
317C2×C3×C4C2×D1212yes—
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6712yes—
320C2×C3×C4C2×#6712yes—
321C2×C3×C4C23×D311yescharacteristic
322C2×C3×C4C23×D311yescharacteristic
323#67—82no—
324C2×Dic3—22no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328D12—22no—
329D12—22no—
330D12—34no—
331D12—34no—
332D12—64no—
333D12—68no—
334D12—64no—
335D12—64no—
336D12—64no—
337D12—62no—
338D12—62no—
339D12—82no—
340C4×D3—82no—
341C4×D3—242no—
342C4×D3—242no—
343C4×D3—242no—
344C4×D3—242no—
345C4×D3—244no—
346C4×D3—244no—
347C3×C8—62no—
348C3×C8—62no—
349C3⋊C8—22no—
350C3⋊C8—22no—
351C2×C32—41no—
352C2×C32#52511yescharacteristic
353C2×C32#57612yes—
354C3⋊D3—44no—
355C3×D3—82no—
356C24—181no—
357C2×D4—32no—
358C2×D4—62no—
359C2×D4—62no—
360C2×D4—92no—
361C2×D4—184no—
362C2×D4—181no—
363C22×C4—62no—
364C22×C4—182no—
365C22×C4—182no—
366C22×C4C2×D3211yescharacteristic
367D8—184no—
368D8—184no—
369C2×C8—32no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4—62no—
373C4⋊C4—92no—
374C4⋊C4#62612yes—
375C22⋊C4—62no—
376C22⋊C4—62no—
377C22⋊C4—181no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C22⋊C4#62612yes—
381C42—181no—
382C42C2×D3211yescharacteristic
383C42C2×D3211yescharacteristic
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—42no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3—122no—
394C22×C3C22×D1211yescharacteristic
395C22×C3C22×#6711yescharacteristic
396C2×D3—42no—
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—68no—
400C2×D3—64no—
401C2×D3—64no—
402C2×D3—124no—
403C2×D3—124no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—248no—
409C2×D3—244no—
410C2×D3—244no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—42no—
420C3×C4—42no—
421C3×C4—122no—
422C3×C4D3×#4112yes—
423C3×C4D3×#4112yes—
424Dic3—42no—
425Dic3—124no—
426Dic3—122no—
427Dic3—122no—
428C32#312211yescharacteristic, complemented, Sylow
429C23—62no—
430C23—184no—
431C23—182no—
432C23—722no—
433C23C2×#62611yescharacteristic
434D4—62no—
435D4—62no—
436D4—94no—
437D4—184no—
438D4—182no—
439D4—242no—
440D4—242no—
441C2×C4—22no—
442C2×C4—62no—
443C2×C4—182no—
444C2×C4—242no—
445C2×C4—722no—
446C2×C4—722no—
447C2×C4C2×#62611yescharacteristic
448C2×C4C2×#62612yes—
449C2×C4C2×#62612yes—
450C2×C4C22×D3211yescharacteristic
451C8—62no—
452C8—62no—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—42no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—242no—
459C2×C3#552411yescharacteristic
460C2×C3#575212yes—
461C2×C3#582811yescharacteristic
462C2×C3#583512yes—
463D3—82no—
464D3—128no—
465D3—124no—
466D3—124no—
467C22—22no—
468C22—21no—
469C22—122no—
470C22—122no—
471C22—122no—
472C22—184no—
473C22—362no—
474C22—362no—
475C22—724no—
476C22C22×#62611yescharacteristic
477C4—22no—
478C4—22no—
479C4—21no—
480C4—122no—
481C4—362no—
482C4#6430612yes—
483C3—21no—
484C3#7938611yescharacteristic, complemented
485C3#8343511yescharacteristic, complemented
486C2—41no—
487C2—242no—
488C2—364no—
489C2#1059503411yescharacteristic
490C2#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. #10595992C2semidirect
2. C3×#5535C2semidirect
3. C3×#5000C2semidirect
4. #10591168C2semidirect
5. #10591093C2semidirect
6. #10590355C2semidirect
7. #10590346C2semidirect
8. C4×#3714C2semidirect
9. #10590308C2semidirect
22. C3×#874C22semidirect
23. C3×C4×D12C22semidirect
24. C3×#870C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. C3×#803C22semidirect
30. C3×C4×C3⋊C8C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
35. #63563C22semidirect
36. #63563C22semidirect
38. #5535D3semidirect
49. #5000D3semidirect
113. #874C2×D3semidirect
120. C4×D12C2×D3semidirect
121. #870C2×D3semidirect
139. C4⋊(C3⋊C8)C2×D3semidirect
140. #803C2×D3semidirect
141. C4×C3⋊C8C2×D3semidirect
428. C32#3122semidirect
484. C3#79386semidirect
485. C3#83435semidirect

Maximal subgroups

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

subgroupindex
#105959922
C3×#55352
C3×#50002
#105911682
#105910932
#105903552
#105903462
C4×#37142
#105903082
#834353
#793863