Finite Group Databasebeta

← #11869556

Subgroups — #11869556

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595282C211yesmaximal, characteristic
2D32×C4⋊C4C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4777C212yesmaximal, complemented
5#10591416C211yesmaximal, characteristic, complemented
6#10591415C212yesmaximal, complemented
7#10590935C211yesmaximal, characteristic, complemented
8#10590685C211yesmaximal, characteristic, complemented
9#10590677C212yesmaximal, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590423C212yesmaximal, complemented
12D3×#481—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×#3811—21no—
15C2×C4×D32—21no—
16C2×C4×D32C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C4⋊C4×C3⋊D3C2211yescharacteristic
19C3×#938C2212yes—
20C3×D3×C4⋊C4C2212yescomplemented
21#63974—21no—
22#63971—22no—
23#63909C2212yes—
24#63900C2211yescharacteristic
25#63900C2211yescharacteristic
26D3×C4⋊Dic3C2212yescomplemented
27#63883—21no—
28D3×Dic3⋊C4—22no—
29C2×#3710C2211yescharacteristic
30C32×#102C2211yescharacteristic, complemented
31#63659C2211yescharacteristic, complemented
32#63648C2211yescharacteristic, complemented
33#63636C2211yescharacteristic, complemented
34C3×#832C2212yescomplemented
35C3×(C2×D3)⋊C8C2212yescomplemented
36C3×#817C2212yescomplemented
37C3×#808C2212yescomplemented
38#63574C2212yescomplemented
39#63573C2212yescomplemented
40#63564C2212yescomplemented
41(C2×D3)⋊(C3⋊C8)C2212yescomplemented
42D3×#121—32no—
43C2×D3×C4⋊C4—32no—
44C3×#481—32no—
45#5034—32no—
46#4968—32no—
47#4863—32no—
48#4863—32no—
49D3×#106—32no—
50D3×#106—32no—
51#4777—32no—
52#4777D312yescomplemented
53D3×#102—32no—
54D3×#102—32no—
55D3×#102—61no—
56#4735—32no—
57D3×C22⋊C8—32no—
58C23×C3⋊D3—21no—
59C22×D32D411yescharacteristic
60C2×C32×D4C2311yescharacteristic
61C2×#638—21no—
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×#67—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2312yes—
70#3811—44no—
71C2×#626—22no—
72C2×#624—21no—
73C2×#624—21no—
74C2×#624D411yescharacteristic
75C2×D3×Dic3—22no—
76C2×D3×Dic3D412yes—
77C4×D32—22no—
78C4×D32—22no—
79C4×D32—44no—
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C8×C3⋊D3—22no—
86C3×#217—22no—
87C3×C4⋊Dic3C2312yes—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—22no—
90C2×C3×C3⋊C8C2312yes—
91#3724—21no—
92#3724—21no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95#3710—22no—
96C2×#481—91noSylow
97C2×D3×D4—32no—
98C2×D3×D4—61no—
99C2×D3×D4—62no—
100C22×C4×D3—32no—
101C22×C4×D3—62no—
102C3×#121—32no—
103C2×C3×C4⋊C4—32no—
104#939—62no—
105#938C2×D312yes—
106#930—32no—
107C2×C4⋊Dic3—32no—
108C2×Dic3⋊C4—62no—
109C2×D3×C8—32no—
110C2×D3×C8—32no—
111C2×D3×C8—61no—
112#895—32no—
113D3×C4⋊C4—32no—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—32no—
116D3×C4⋊C4—32no—
117D3×C4⋊C4—61no—
118D3×C4⋊C4—62no—
119D3×C4⋊C4—62no—
120D3×C4⋊C4C2×D312yescomplemented
121#884—62no—
122D3×C22⋊C4—62no—
123C3×#106—32no—
124C3×#106—32no—
125C3×#102—21no—
126C3×#102—32no—
127C3×#102C2×D312yescomplemented
128C3×C22⋊C8—32no—
129#832—32no—
130#832—61no—
131#832C2×D312yescomplemented
132#830—32no—
133#821—32no—
134#821—32no—
135#821—61no—
136(C2×D3)⋊C8—32no—
137(C2×D3)⋊C8C2×D312yescomplemented
138#817—32no—
139#817C2×D312yescomplemented
140#809—32no—
141#809—32no—
142#809—61no—
143#808—32no—
144#808—32no—
145#808—32no—
146#808C2×D312yescomplemented
147C23×C32—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3C2×D411yescharacteristic
153C22×C3×D3C2×D412yes—
154C2×D32—22no—
155C2×D32—22no—
156C2×D32SD1614yes—
157C32×D4—21no—
158C32×D4—21no—
159C2×C32×C4—21no—
160C2×C32×C4C2411yescharacteristic
161#638—42no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3C2×D411yescharacteristic
164C4⋊(C3⋊D3)—21no—
165C4⋊(C3⋊D3)—21no—
166C4×C3⋊D3—42no—
167C4×C3⋊D3#4112yes—
168C4×C3⋊D3#4112yes—
169C3×#67—44no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D412yes—
173C3×C4×D3—22no—
174C3×C4×D3—22no—
175C3×C4×D3—44no—
176#626—44no—
177#624—22no—
178#624—42no—
179#624—42no—
180D3×Dic3—24no—
181D3×Dic3—44no—
182C32×C8—21no—
183C3⋊(C3⋊C8)—21no—
184C3×C3⋊C8—22no—
185C2×#121—91no—
186C22×C4⋊C4—91no—
187#481—32no—
188#481—92no—
189#481—92no—
190#481—92no—
191C2×#106—91no—
192C2×#106—91no—
193C2×#102—91no—
194C2×#102—91no—
195C2×C22⋊C8—91no—
196C23×D3—32no—
197C23×D3—62no—
198C23×D3—121no—
199C2×C3×D4—21no—
200C2×C3×D4—62no—
201C2×C3×D4C22×D312yes—
202C22×C3×C4—32no—
203C22×C3×C4—62no—
204C2×#67—22no—
205C2×#67—62no—
206C2×#67—62no—
207C2×#67—121no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210D3×D4—64no—
211D3×D4—64no—
212D3×D4—64no—
213D3×D4—122no—
214D3×D4—128no—
215C2×D12—32no—
216C2×D12—61no—
217C2×D12—62no—
218C2×C4×D3—22no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—61no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—121no—
230C2×C4×D3—128no—
231C2×C4×D3C22×D312yes—
232C2×C3×C8—21no—
233C2×C3×C8—32no—
234C2×C3×C8C22×D312yes—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4C22×D312yes—
240C3×C22⋊C4—62no—
241#217—22no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244C4⋊Dic3—32no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3C22×D312yes—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—121no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8C22×D312yes—
258D3×C8—64no—
259D3×C8—64no—
260D3×C8—122no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—41no—
266C2×C3⋊D3—41no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—84no—
269C2×C3⋊D3#12312yes—
270C2×C3⋊D3C2×SD1612yes—
271C2×C3⋊D3AGL(1,ℤ/8)12yes—
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3C2×SD1614yes—
275D32—28no—
276C32×C4—41no—
277C32×C4C2×#4111yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—41no—
280C3⋊Dic3#12312yes—
281C3×Dic3—22no—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C22×D4—91no—
285C22×D4—181no—
286C23×C4—91no—
287C23×C4—181no—
288C22×C8—91no—
289C22×C8—91no—
290#121—32no—
291#121—92no—
292#121—182no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—92no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—181no—
299C2×C4⋊C4—182no—
300C2×C22⋊C4—181no—
301#106—32no—
302#106—32no—
303#106—92no—
304#106—92no—
305#102—32no—
306#102—92no—
307#102—91no—
308#102—91no—
309#102—91no—
310#102D3211yescharacteristic, complemented
311C22⋊C8—32no—
312C22⋊C8—92no—
313C23×C3—22no—
314C23×C3—32no—
315C23×C3—41no—
316C22×D3—32no—
317C22×D3—38no—
318C22×D3—61no—
319C22×D3—64no—
320C22×D3—64no—
321C22×D3—62no—
322C22×D3—121no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—124no—
326C22×D3—124no—
327C22×D3—242no—
328C22×D3—242no—
329C22×D3D3×D412yes—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—41no—
334C3×D4—124no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—41no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—124no—
344C2×C3×C4C23×D312yes—
345#67—44no—
346#67—124no—
347#67—124no—
348#67—124no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—32no—
352C2×Dic3—61no—
353C2×Dic3—64no—
354C2×Dic3—62no—
355C2×Dic3—121no—
356C2×Dic3—124no—
357C2×Dic3D3×D412yes—
358D12—62no—
359D12—62no—
360D12—62no—
361D12—121no—
362D12—124no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—34no—
366C4×D3—34no—
367C4×D3—44no—
368C4×D3—62no—
369C4×D3—62no—
370C4×D3—64no—
371C4×D3—64no—
372C4×D3—124no—
373C4×D3—124no—
374C4×D3—124no—
375C4×D3—124no—
376C4×D3—242no—
377C3×C8—22no—
378C3×C8—41no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—62no—
382C3⋊C8—121no—
383C2×C32—81no—
384C2×C32C2×#12311yescharacteristic
385C2×C32C22×SD1611yescharacteristic
386C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
387C3⋊D3—81no—
388C3⋊D3#48114yescomplemented
389C3×D3—24no—
390C24—91no—
391C24—181no—
392C2×D4—62no—
393C2×D4—91no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4—181no—
398C2×D4—364no—
399C2×D4C2×D3211yescharacteristic
400C22×C4—32no—
401C22×C4—62no—
402C22×C4—91no—
403C22×C4—92no—
404C22×C4—91no—
405C22×C4—181no—
406C22×C4—182no—
407C22×C4—182no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—182no—
411C22×C4—364no—
412C2×C8—32no—
413C2×C8—91no—
414C2×C8—182no—
415C2×C8—182no—
416C2×C8C2×D3211yescharacteristic
417C4⋊C4—32no—
418C4⋊C4—32no—
419C4⋊C4—62no—
420C4⋊C4—91no—
421C4⋊C4—181no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C2×D3211yescharacteristic
426C22⋊C4—62no—
427C22⋊C4—182no—
428C22×C3—21no—
429C22×C3—34no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—62no—
435C22×C3—62no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3C2×D3×D412yes—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—34no—
442C2×D3—34no—
443C2×D3—34no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—616no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—241no—
453C2×D3—241no—
454C2×D3—248no—
455C2×D3—248no—
456C2×D3D3×SD1614yes—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—42no—
460C3×C4—62no—
461C3×C4—81no—
462C3×C4—122no—
463C3×C4—122no—
464C3×C4D3×#4112yes—
465C3×C4D3×#4112yes—
466Dic3—22no—
467Dic3—34no—
468Dic3—42no—
469Dic3—42no—
470Dic3—62no—
471Dic3—122no—
472Dic3—241no—
473C32C2×#48111yescharacteristic, complemented, Sylow
474C23—21no—
475C23—32no—
476C23—94no—
477C23—91no—
478C23—182no—
479C23—182no—
480C23—181no—
481C23—362no—
482C23—362no—
483C23—362no—
484D4—21no—
485D4—21no—
486D4—124no—
487D4—181no—
488D4—181no—
489D4—362no—
490D4—364no—
491C2×C4—21no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—91no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—124no—
501C2×C4—182no—
502C2×C4—184no—
503C2×C4—181no—
504C2×C4—362no—
505C2×C4—362no—
506C2×C4—362no—
507C2×C4—364no—
508C2×C4C22×D3211yescharacteristic
509C8—21no—
510C8—62no—
511C8—181no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—64no—
516C2×C3—82no—
517C2×C3—82no—
518C2×C3D3×#12312yes—
519C2×C3C2×D3×SD1612yes—
520C2×C3D3×AGL(1,ℤ/8)12yes—
521D3—24no—
522D3—38no—
523D3—64no—
524D3—242no—
525D3—242no—
526C22—34no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—62no—
531C22—62no—
532C22—92no—
533C22—92no—
534C22—92no—
535C22—188no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22—724no—
540C22D32×D411yescharacteristic
541C4—41no—
542C4—62no—
543C4—92no—
544C4—122no—
545C4—122no—
546C4—361no—
547C4#6430611yescharacteristic
548C4#6431211yescharacteristic
549C3—21no—
550C3D3×#48112yescomplemented
551C2—64no—
552C2—81no—
553C2—94no—
554C2—721no—
555C2#1059426011yescharacteristic
556C2#1059472611yescharacteristic
557C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595282C2
hypercenter#102D32
hypocenterC32C2×#481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D32×C4⋊C4C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4777C2semidirect
5. #10591416C2semidirect
6. #10591415C2semidirect
7. #10590935C2semidirect
8. #10590685C2semidirect
9. #10590677C2semidirect
10. #10590575C2semidirect
11. #10590423C2semidirect
20. C3×D3×C4⋊C4C22semidirect
26. D3×C4⋊Dic3C22semidirect
30. C32×#102C22semidirect
31. #63659C22semidirect
32. #63648C22semidirect
33. #63636C22semidirect
34. C3×#832C22semidirect
35. C3×(C2×D3)⋊C8C22semidirect
36. C3×#817C22semidirect
37. C3×#808C22semidirect
38. #63574C22semidirect
39. #63573C22semidirect
40. #63564C22semidirect
41. (C2×D3)⋊(C3⋊C8)C22semidirect
52. #4777D3semidirect
120. D3×C4⋊C4C2×D3semidirect
127. C3×#102C2×D3semidirect
131. #832C2×D3semidirect
137. (C2×D3)⋊C8C2×D3semidirect
139. #817C2×D3semidirect
146. #808C2×D3semidirect
310. #102D32semidirect
388. C3⋊D3#481semidirect
473. C32C2×#481semidirect
550. C3D3×#481semidirect

Maximal subgroups

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

subgroupindex
#105952822
D32×C4⋊C42
C3⋊D3×#1022
C3×#47772
#105914162
#105914152
#105909352
#105906852
#105906772
#105905752
#105904232
D3×#4813