Finite Group Databasebeta

← #11869467

Subgroups — #11869467

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594612C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic, complemented
3C3⋊D3×#107C211yesmaximal, characteristic, complemented
4C3×#4885C212yesmaximal, complemented
5#10590940C211yesmaximal, characteristic, complemented
6#10590935C211yesmaximal, characteristic, complemented
7#10590834C212yesmaximal, complemented
8#10590593C211yesmaximal, characteristic, complemented
9#10590575C211yesmaximal, characteristic, complemented
10#10590502C212yesmaximal, complemented
11#10590449C212yesmaximal, complemented
12D3×#482—32nomaximal
13C2×#3802—21no—
14C2×#3802C2211yescharacteristic
15C2×C4×D32C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#895C2212yes—
20C3×#892C2212yescomplemented
21#63921—21no—
22#63921—21no—
23#63908C2212yes—
24#63900C2211yescharacteristic
25#63885—22no—
26C4×#624—21no—
27#63877—22no—
28#63841C2212yescomplemented
29C2×#3710C2211yescharacteristic
30C32×#107C2211yescharacteristic, complemented
31#63645C2211yescharacteristic, complemented
32#63634C2211yescharacteristic, complemented
33#63634C2211yescharacteristic, complemented
34C3×#821C2212yescomplemented
35C3×(C2×D3)⋊C8C2212yescomplemented
36C3×#809C2212yescomplemented
37C3×#808C2212yescomplemented
38#63573C2212yescomplemented
39#63563C2212yescomplemented
40#63562C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42D3×#121—32no—
43D3×#117—32no—
44C3×#482—32no—
45#5035—32no—
46#5003—32no—
47#4885D312yescomplemented
48D3×#107—32no—
49D3×#107—61no—
50#4866—32no—
51D3×#106—32no—
52#4784—32no—
53#4779—32no—
54D3×#102—32no—
55D3×#102—32no—
56#4737—32no—
57D3×C22⋊C8—32no—
58C22×D32—21no—
59C22×D32D411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3C2312yes—
66C2×#625—22no—
67C2×#625—21no—
68C2×#624—21no—
69C2×#624D411yescharacteristic
70C2×D3×Dic3D412yes—
71#3802—22no—
72#3802—22no—
73#3802—44no—
74C4×D32—22no—
75C4×D32—22no—
76C2×C32×C8C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—21no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C8×C3⋊D3—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—22no—
87C3×C4⋊Dic3C2312yes—
88C3×C4×Dic3—22no—
89C2×C3×C3⋊C8C2312yes—
90#3724—21no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3710—22no—
95C2×#482—91noSylow
96C2×D3×D4—32no—
97C2×D3×D4—62no—
98C22×C4×D3—32no—
99C3×#121—32no—
100C3×#117—32no—
101#939—62no—
102#938—32no—
103#930—32no—
104#926—32no—
105C2×D3×C8—32no—
106C2×D3×C8—32no—
107C2×D3×C8—61no—
108#895C2×D312yes—
109#892—32no—
110#892C2×D312yescomplemented
111D3×C4⋊C4—32no—
112D3×C4⋊C4—32no—
113D3×C4⋊C4—32no—
114D3×C4⋊C4—61no—
115D3×C4⋊C4—61no—
116#884—62no—
117D3×C22⋊C4—62no—
118D3×C22⋊C4—62no—
119#877—62no—
120#872—62no—
121C42×D3—62no—
122C3×#107—21no—
123C3×#107C2×D312yescomplemented
124C3×#106—32no—
125C3×#102—32no—
126C3×#102—32no—
127C3×C22⋊C8—32no—
128#832—32no—
129#832—32no—
130#830—32no—
131#821—32no—
132#821C2×D312yescomplemented
133(C2×D3)⋊C8—32no—
134(C2×D3)⋊C8C2×D312yescomplemented
135#818—32no—
136#818—61no—
137#817—32no—
138#809—32no—
139#809C2×D312yescomplemented
140#808—32no—
141#808C2×D312yescomplemented
142#807—32no—
143#807—32no—
144#807—61no—
145#807—61no—
146C22×C3⋊D3C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3C2×D412yes—
149C2×D32—22no—
150C2×D32—22no—
151C2×D32—22no—
152C2×D32—42no—
153C2×D32—42no—
154C2×D32—42no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3C2×D411yescharacteristic
161C4×C3⋊D3—42no—
162C4×C3⋊D3—42no—
163C4×C3⋊D3#4112yes—
164C4×C3⋊D3#4112yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D412yes—
167C3×D12—22no—
168C3×D12—22no—
169C3×D12—44no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172#625—44no—
173#625—42no—
174#624—22no—
175#624—42no—
176D3×Dic3—24no—
177C32×C8—21no—
178C3⋊(C3⋊C8)—21no—
179C3×C3⋊C8—22no—
180C2×#121—91no—
181C2×#117—91no—
182#482—32no—
183#482—92no—
184#482—92no—
185#482—92no—
186C2×#107—91no—
187C2×#106—91no—
188C2×#102—91no—
189C2×#102—91no—
190C2×C22⋊C8—91no—
191C23×D3—32no—
192C23×D3—62no—
193C2×C3×D4—32no—
194C2×C3×D4—62no—
195C22×C3×C4—32no—
196C2×#67—62no—
197C2×#67—62no—
198C2×#67—62no—
199C22×Dic3—32no—
200D3×D4—64no—
201D3×D4—64no—
202D3×D4—128no—
203C2×D12—22no—
204C2×D12C22×D312yes—
205C2×C4×D3—32no—
206C2×C4×D3—32no—
207C2×C4×D3—32no—
208C2×C4×D3—61no—
209C2×C4×D3—64no—
210C2×C4×D3—64no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—121no—
215C2×C4×D3—121no—
216C2×C4×D3C22×D312yes—
217C2×C3×C8—21no—
218C2×C3×C8—32no—
219C2×C3×C8C22×D312yes—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—62no—
228#217—62no—
229#217—62no—
230(C2×D3)⋊C4—22no—
231(C2×D3)⋊C4—22no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—121no—
243Dic3⋊C4—121no—
244C4×Dic3—22no—
245C4×Dic3—62no—
246C4×Dic3—62no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8C22×D312yes—
250D3×C8—64no—
251D3×C8—64no—
252D3×C8—64no—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3#12312yes—
255C2×C3⋊D3#13512yes—
256C2×C3⋊D3AGL(1,ℤ/8)12yes—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263D32—44no—
264D32—84no—
265C32×C4—41no—
266C32×C4—41no—
267C32×C4C2×#4111yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—41no—
270C3⋊Dic3—41no—
271C3⋊Dic3#12312yes—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C22×D4—91no—
275C22×D4—181no—
276C23×C4—91no—
277C22×C8—91no—
278C22×C8—91no—
279#121—32no—
280#121—92no—
281#121—182no—
282#117—32no—
283#117—92no—
284#117—182no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—91no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—181no—
289C2×C22⋊C4—181no—
290C2×C42—181no—
291#107—91no—
292#107—91no—
293#107—91no—
294#107D3211yescharacteristic, complemented
295#106—32no—
296#106—92no—
297#102—32no—
298#102—32no—
299#102—92no—
300#102—92no—
301C22⋊C8—32no—
302C22⋊C8—92no—
303C23×C3—32no—
304C23×C3—62no—
305C22×D3—22no—
306C22×D3—32no—
307C22×D3—61no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—124no—
312C22×D3—124no—
313C22×D3—124no—
314C22×D3D3×D412yes—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—124no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4C23×D312yes—
328#67—124no—
329#67—124no—
330#67—124no—
331C2×Dic3—22no—
332C2×Dic3—32no—
333C2×Dic3—61no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3D3×D412yes—
340D12—22no—
341D12—22no—
342D12—44no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—34no—
346C4×D3—34no—
347C4×D3—62no—
348C4×D3—62no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—124no—
352C4×D3—124no—
353C4×D3—124no—
354C4×D3—242no—
355C4×D3—242no—
356C3×C8—22no—
357C3×C8—22no—
358C3×C8—62no—
359C3⋊C8—22no—
360C3⋊C8—62no—
361C3⋊C8—62no—
362C2×C32C2×#12311yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C3⋊D3#48214yescomplemented
366C3×D3—42no—
367C3×D3—82no—
368C24—91no—
369C24—181no—
370C2×D4—32no—
371C2×D4—62no—
372C2×D4—182no—
373C2×D4—182no—
374C2×D4—181no—
375C2×D4—182no—
376C2×D4—364no—
377C22×C4—32no—
378C22×C4—91no—
379C22×C4—92no—
380C22×C4—91no—
381C22×C4—181no—
382C22×C4—181no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—181no—
386C2×C8—32no—
387C2×C8—91no—
388C2×C8—182no—
389C2×C8—182no—
390C2×C8C2×D3211yescharacteristic
391C4⋊C4—32no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C4⋊C4C2×D3211yescharacteristic
398C4⋊C4C2×D3211yescharacteristic
399C22⋊C4—62no—
400C22⋊C4—62no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C42—62no—
404C42—182no—
405C22×C3—21no—
406C22×C3—62no—
407C22×C3—62no—
408C22×C3—62no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3C2×D3×D412yes—
413C2×D3—22no—
414C2×D3—22no—
415C2×D3—22no—
416C2×D3—34no—
417C2×D3—34no—
418C2×D3—34no—
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—62no—
423C2×D3—62no—
424C2×D3—62no—
425C2×D3—128no—
426C2×D3—248no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—62no—
432C3×C4—81no—
433C3×C4—81no—
434C3×C4—122no—
435C3×C4D3×#4112yes—
436C3×C4D3×#4112yes—
437Dic3—22no—
438Dic3—34no—
439Dic3—42no—
440Dic3—62no—
441Dic3—122no—
442Dic3—122no—
443Dic3—241no—
444Dic3—241no—
445C32C2×#48211yescharacteristic, complemented, Sylow
446C23—32no—
447C23—62no—
448C23—91no—
449C23—182no—
450C23—182no—
451C23—182no—
452C23—362no—
453C23—362no—
454C23—362no—
455D4—62no—
456D4—62no—
457D4—124no—
458D4—362no—
459D4—364no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—32no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—91no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—182no—
470C2×C4—184no—
471C2×C4—181no—
472C2×C4—181no—
473C2×C4—362no—
474C2×C4—362no—
475C2×C4—362no—
476C2×C4C22×D3211yescharacteristic
477C8—21no—
478C8—62no—
479C8—181no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—122no—
484C2×C3—242no—
485C2×C3D3×#12312yes—
486C2×C3D3×#13512yes—
487C2×C3D3×AGL(1,ℤ/8)12yes—
488D3—38no—
489D3—42no—
490D3—64no—
491D3—82no—
492C22—62no—
493C22—62no—
494C22—62no—
495C22—92no—
496C22—92no—
497C22—92no—
498C22—122no—
499C22—122no—
500C22—122no—
501C22—364no—
502C22—724no—
503C22D32×D411yescharacteristic
504C4—41no—
505C4—41no—
506C4—62no—
507C4—92no—
508C4—122no—
509C4—361no—
510C4—361no—
511C4#6430611yescharacteristic
512C4#6431911yescharacteristic
513C3—21no—
514C3D3×#48212yescomplemented
515C2—94no—
516C2—122no—
517C2—242no—
518C2#1059460811yescharacteristic
519C2#1059472611yescharacteristic
520C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10594612C2
hypercenter#107D32
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594602C2semidirect
3. C3⋊D3×#107C2semidirect
4. C3×#4885C2semidirect
5. #10590940C2semidirect
6. #10590935C2semidirect
7. #10590834C2semidirect
8. #10590593C2semidirect
9. #10590575C2semidirect
10. #10590502C2semidirect
11. #10590449C2semidirect
20. C3×#892C22semidirect
28. #63841C22semidirect
30. C32×#107C22semidirect
31. #63645C22semidirect
32. #63634C22semidirect
33. #63634C22semidirect
34. C3×#821C22semidirect
35. C3×(C2×D3)⋊C8C22semidirect
36. C3×#809C22semidirect
37. C3×#808C22semidirect
38. #63573C22semidirect
39. #63563C22semidirect
40. #63562C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
47. #4885D3semidirect
110. #892C2×D3semidirect
123. C3×#107C2×D3semidirect
132. #821C2×D3semidirect
134. (C2×D3)⋊C8C2×D3semidirect
139. #809C2×D3semidirect
141. #808C2×D3semidirect
294. #107D32semidirect
365. C3⋊D3#482semidirect
445. C32C2×#482semidirect
514. C3D3×#482semidirect

Maximal subgroups

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

subgroupindex
#105946122
#105946022
C3⋊D3×#1072
C3×#48852
#105909402
#105909352
#105908342
#105905932
#105905752
#105905022
#105904492
D3×#4823