Finite Group Databasebeta

← #11787781

Subgroups — #11787781

Order 1152.

719 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595032C211yesmaximal, characteristic
3C3×#5139C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#72021—31nomaximal
9#70417—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63980—22no—
21#63914C411yescharacteristic, complemented
22C4×#625—22no—
23#63873C411yescharacteristic, complemented
24#63863C411yescharacteristic, complemented
25#63863C411yescharacteristic, complemented
26C3×#825—22no—
27#63580—22no—
28#63568—22no—
29C3×#568—31no—
30#5832—31no—
31#5832—31no—
32#5745D311yescharacteristic, complemented
33C3×#421—31no—
34#5240—31no—
35#5236—31no—
36#5139—31no—
37#5139D311yescharacteristic, complemented
38#5006—31no—
39#4555—31no—
40#4555—31no—
41#4555—31no—
42#4555—61no—
43#4532—31no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—21no—
47C2×C3×#67D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×D12C2×C411yescharacteristic
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3D412yes—
60C2×C3×Dic6C2×C411yescharacteristic
61C2×C3×Dic6C2×C411yescharacteristic
62C2×#625—22no—
63C32×M16—21no—
64C32×M16D412yescomplemented
65C2×C32×C8—21no—
66#3757—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3C2×C411yescharacteristic
71C4×C3⋊Dic3C2×C411yescharacteristic
72C3×#217—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×#208—21no—
76C3×#208D412yescomplemented
77C2×C3×C3⋊C8—21no—
78C3×ΓL(1,𝔽25)—24no—
79C3×D3×C8—24no—
80#3724—22no—
81(C2×D3)⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83#1884—91noSylow
84C2×C3×#41—31no—
85C2×C3×#41—31no—
86C2×#235C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C3×#131—62no—
89C3×#131—62no—
90C2×C3×M16—21no—
91C2×C3×M16—31no—
92C2×C3×M16—62no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95C3×#117—31no—
96#947—31no—
97#947—31no—
98#944—31no—
99#944—31no—
100#940—31no—
101#940—31no—
102#939—62no—
103#939—62no—
104#936—31no—
105#936—31no—
106C4×#67—62no—
107C4×#67—62no—
108#926—31no—
109#926—31no—
110#926—61no—
111#926C2×D311yescharacteristic
112C2×C4×Dic3—31no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—61no—
115C2×#208C2×D311yescharacteristic
116#907—22no—
117D3×M16—22no—
118#901—22no—
119C3×#104—62no—
120#837—62no—
121#834—62no—
122#825—22no—
123#825—62no—
124#806—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C22×C3×D3C22⋊C412yes—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—41no—
138C3×#67—22no—
139C3×#67—22no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3C22⋊C412yes—
145C3×D12—21no—
146C3×D12—21no—
147C3×D12—21no—
148C3×D12—21no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×Dic6—21no—
154C3×Dic6—21no—
155C3×Dic6—21no—
156C3×Dic6—21no—
157#625—44no—
158C32×C8—22no—
159C3×C3⋊C8—22no—
160#568—31no—
161#532—91no—
162#421—31no—
163#421—91no—
164#410—91no—
165#339—91no—
166#339—91no—
167C3×#41—61no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C2×C3×Q8—31no—
176C2×C3×Q8—31no—
177C2×C3×D4—32no—
178C2×C3×D4—31no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—21no—
187C2×#67—62no—
188C2×#67—62no—
189C2×#67D1212yes—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200#235—21no—
201C2×D12C4×D311yescharacteristic
202C2×D12C4×D311yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3#6712yes—
205C2×Dic6C4×D311yescharacteristic
206C2×Dic6C4×D311yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—22no—
210C3×M16—32no—
211C3×M16—41no—
212C3×M16—64no—
213C3×M16—61no—
214C3×M16#6712yescomplemented
215C3×M16#6712yescomplemented
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—41no—
219C2×C3×C8—64no—
220C2×C3×C8—61no—
221C3×C4⋊C4—61no—
222C3×C22⋊C4—61no—
223C3×C42—61no—
224#217—21no—
225#217—62no—
226#217—62no—
227#217—61no—
228#217—61no—
229#217—121no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232C4⋊Dic3—21no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238C4×Dic3—21no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—31no—
242C4×Dic3—31no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—61no—
249C4×Dic3—121no—
250C4×Dic3—121no—
251#208—21no—
252#208#6712yescomplemented
253C2×C3⋊C8—21no—
254ΓL(1,𝔽25)—24no—
255D3×C8—24no—
256C22×C32—41no—
257C22×C32C2×C22⋊C411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12111yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C32×C4C4×D411yescharacteristic
265C32×C4C4×D411yescharacteristic
266C32×C4#12011yescharacteristic
267C32×C4#12311yescharacteristic
268C3⋊Dic3—22no—
269C3⋊Dic3—41no—
270C3⋊Dic3—81no—
271C3×Dic3—22no—
272C3×Dic3—41no—
273C3×Dic3—81no—
274C2×#41—31no—
275C2×#41—31no—
276#131—62no—
277#131—62no—
278C2×M16—31no—
279C2×M16—62no—
280C2×M16D3211yescharacteristic
281C4⋊Q8—91no—
282#127—91no—
283#124—91no—
284#124—91no—
285#121—182no—
286C4×D4—182no—
287#117—31no—
288#117—91no—
289C2×C42—91no—
290#104—62no—
291#104—182no—
292#99—182no—
293C23×C3—21no—
294C23×C3—32no—
295C23×C3—61no—
296C23×C3C2×D1211yescharacteristic
297C23×C3D3×D411yescharacteristic
298C22×D3—21no—
299C22×D3(C2×D3)⋊C412yes—
300C3×Q8—61no—
301C3×Q8—61no—
302C3×Q8—61no—
303C3×Q8—61no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—61no—
307C3×D4—61no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—121no—
311C3×D4—121no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—32no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—61no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—22no—
338#67—22no—
339#67—41no—
340#67—41no—
341#67—124no—
342#67—124no—
343C2×Dic3—21no—
344C2×Dic3—41no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—124no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3(C2×D3)⋊C412yes—
358D12—21no—
359D12—21no—
360D12—21no—
361D12—21no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—41no—
365C4×D3—41no—
366Dic6—21no—
367Dic6—21no—
368Dic6—21no—
369Dic6—21no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—42no—
373C3×C8—62no—
374C3⋊C8—22no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32#38611yescharacteristic
379C3×D3—42no—
380C3×D3—81no—
381#41—61no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—61no—
386#41—61no—
387#41—61no—
388#41—61no—
389C2×Q8—31no—
390C2×Q8—31no—
391C2×D4—32no—
392C2×D4—31no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4—182no—
396C22×C4—32no—
397C22×C4—61no—
398C22×C4—181no—
399C22×C4C2×D3211yescharacteristic
400M16—21no—
401M16—32no—
402M16—64no—
403M16—61no—
404M16#62512yescomplemented
405C2×C8—21no—
406C2×C8—64no—
407C2×C8—61no—
408C4⋊C4—61no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C22⋊C4—61no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C22⋊C4—181no—
415C42—61no—
416C42—91no—
417C42—91no—
418C42—181no—
419C42—181no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—42no—
426C22×C3—62no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3D3×C22⋊C411yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3C2×(C2×D3)⋊C411yescharacteristic
433C22×C3#93011yescharacteristic
434C22×C3#93011yescharacteristic
435C22×C3#93811yescharacteristic
436C2×D3—22no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—62no—
445C3×C4—121no—
446C3×C4—241no—
447C3×C4#67⋊C411yescharacteristic
448C3×C4#88311yescharacteristic
449C3×C4C4×#6711yescharacteristic
450C3×C4C4×#6711yescharacteristic
451C3×C4C4×#6711yescharacteristic
452C3×C4#92911yescharacteristic
453C3×C4#93711yescharacteristic
454C3×C4#95311yescharacteristic
455Dic3—22no—
456Dic3—41no—
457Dic3—62no—
458Dic3—62no—
459Dic3—81no—
460Dic3—122no—
461Dic3—121no—
462Dic3—121no—
463Dic3—122no—
464Dic3—242no—
465Dic3—241no—
466Dic3—241no—
467C32#188411yescharacteristic, complemented, Sylow
468C23—32no—
469C23—61no—
470C23D3×D1211yescharacteristic
471Q8—61no—
472Q8—61no—
473Q8—61no—
474Q8—61no—
475D4—62no—
476D4—62no—
477D4—61no—
478D4—61no—
479D4—61no—
480D4—61no—
481D4—121no—
482D4—121no—
483D4—364no—
484C2×C4—32no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—61no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—362no—
494C2×C4—361no—
495C2×C4#379511yescharacteristic
496C2×C4#379811yescharacteristic
497C2×C4C4×D3211yescharacteristic
498C2×C4C2×#62511yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C8—22no—
502C8—62no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—122no—
514C2×C3—241no—
515C2×C3#495611yescharacteristic
516C2×C3#521311yescharacteristic
517D3—42no—
518D3—81no—
519C22—41no—
520C22—62no—
521C22—122no—
522C22—122no—
523C22—121no—
524C22#6390611yescharacteristic
525C22#6390811yescharacteristic
526C22D3×(C2×D3)⋊C411yescharacteristic
527C4—62no—
528C4—121no—
529C4—182no—
530C4—241no—
531C4—361no—
532C4—721no—
533C4#6387911yescharacteristic
534C4C4×#62511yescharacteristic
535C4#6390511yescharacteristic
536C4#6397611yescharacteristic
537C3—21no—
538C3#7041711yescharacteristic, complemented
539C3#7202111yescharacteristic, complemented
540C2—21no—
541C2—21no—
542C2—21no—
543C2—122no—
544C2—241no—
545C2#1059138111yescharacteristic
subgroupG/H
centerC4#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. C3×#5139C2semidirect
4. #10591231C2semidirect
5. #10591110C2semidirect
6. #10589421C2semidirect
7. #10589160C2semidirect
21. #63914C4semidirect
23. #63873C4semidirect
24. #63863C4semidirect
25. #63863C4semidirect
32. #5745D3semidirect
37. #5139D3semidirect
64. C32×M16D4semidirect
76. C3×#208D4semidirect
214. C3×M16#67semidirect
215. C3×M16#67semidirect
252. #208#67semidirect
404. M16#625semidirect
467. C32#1884semidirect
538. C3#70417semidirect
539. C3#72021semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950322
C3×#51392
#105912312
#105911102
#105894212
#105891602
#720213
#704173