Finite Group Databasebeta

← #11788755

Subgroups — #11788755

Order 1152.

735 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595040C211yesmaximal, characteristic
3C3×#5131C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6#10589423C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#72025—31nomaximal
9#70330—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14#64135C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63976—22no—
21#63914C412yescomplemented
22#63908—22no—
23#63863C412yescomplemented
24C3×#821—22no—
25#63580—22no—
26#63563—22no—
27C3×#568—31no—
28#5830—31no—
29#5805—31no—
30#5745D311yescharacteristic, complemented
31C3×#418—31no—
32#5240—31no—
33#5215—31no—
34#5131—31no—
35#5131D311yescharacteristic, complemented
36#5006—31no—
37#4557—31no—
38#4557—31no—
39#4557—31no—
40#4557—61no—
41#4531—31no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67D412yes—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12C2×C412yes—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3D412yes—
57C2×C3×Dic6C2×C411yescharacteristic
58C2×#625—24no—
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8D412yescomplemented
62#3757—21no—
63#3757—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3C2×C412yes—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8D412yescomplemented
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76(C2×D3)⋊Dic3—24no—
77#1910—91noSylow
78C2×C3×#41—31no—
79C22×C3×D4—31no—
80C2×#235C2×D311yescharacteristic
81C22×D12C2×D311yescharacteristic
82C3×#131—62no—
83C3×#131—62no—
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16—62no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C3×#117—31no—
90#953—62no—
91#947—32no—
92#940—32no—
93#940—32no—
94#938—62no—
95#937—62no—
96#936—32no—
97#930—62no—
98#926—31no—
99#926—31no—
100#926—31no—
101#926—31no—
102#926—61no—
103#926—61no—
104#926C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106#907—22no—
107D3×M16—22no—
108#901—22no—
109C3×#102—62no—
110#834—62no—
111#832—62no—
112#821—22no—
113#821—62no—
114#806—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—82no—
120C22×C3×D3C22⋊C412yes—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3C22⋊C412yes—
133C3×D12—21no—
134C3×D12—21no—
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—41no—
138C3×D12—41no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×Dic6—21no—
142C3×Dic6—21no—
143#625—84no—
144C32×C8—22no—
145C3×C3⋊C8—22no—
146#568—31no—
147#535—91no—
148#418—31no—
149#418—91no—
150#410—91no—
151H(3,ℤ/4)—91no—
152H(3,ℤ/4)—91no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C2×C3×D4—32no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—32no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—64no—
173C2×#67—64no—
174C2×#67D1212yes—
175#235—21no—
176#235—21no—
177#235—21no—
178#235—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C4×D312yes—
185C2×D12C4×D311yescharacteristic
186C2×C4×D3#6712yes—
187C2×Dic6C4×D311yescharacteristic
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—41no—
193C3×M16—41no—
194C3×M16—64no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—22no—
198C2×C3×C8—32no—
199C2×C3×C8—64no—
200C2×C3×C8#6712yescomplemented
201C2×C3×C8#6712yescomplemented
202C3×C4⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C42—61no—
205#217—21no—
206#217—61no—
207#217—61no—
208#217—64no—
209#217—61no—
210#217—61no—
211#217—121no—
212#217—121no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3—121no—
221C4×Dic3—21no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—62no—
225C4×Dic3—62no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228#208—21no—
229#208—21no—
230C2×C3⋊C8#6712yescomplemented
231ΓL(1,𝔽25)—24no—
232D3×C8—24no—
233C22×C32—41no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32#12111yescharacteristic
236C22×C32#12111yescharacteristic
237C2×C3×D3—22no—
238C2×C3×D3—42no—
239C2×C3×D3—44no—
240C2×C3×D3—42no—
241C2×C3×D3—82no—
242C2×C3×D3—82no—
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4#12011yescharacteristic
246C32×C4#12311yescharacteristic
247C3⋊Dic3—42no—
248C3⋊Dic3—81no—
249C3×Dic3—22no—
250C3×Dic3—81no—
251C2×#41—31no—
252C22×D4—31no—
253#131—62no—
254#131—62no—
255C2×M16—31no—
256C2×M16—62no—
257C2×M16D3211yescharacteristic
258#127—92no—
259#124—92no—
260#121—182no—
261#120—182no—
262#117—31no—
263#117—91no—
264#117—91no—
265#102—62no—
266#102—182no—
267#99—182no—
268C23×C3—21no—
269C23×C3—32no—
270C23×C3—62no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3—242no—
274C23×C3C2×D1211yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—22no—
277C22×D3—41no—
278C22×D3—41no—
279C22×D3—82no—
280C22×D3(C2×D3)⋊C412yes—
281C3×Q8—61no—
282C3×Q8—61no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—61no—
286C3×D4—61no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—121no—
290C3×D4—121no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—32no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—121no—
301C2×C3×C4C2×C4×D311yescharacteristic
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313#67—22no—
314#67—22no—
315#67—244no—
316#67—244no—
317C2×Dic3—41no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3(C2×D3)⋊C412yes—
325D12—22no—
326D12—21no—
327D12—21no—
328D12—22no—
329D12—41no—
330D12—41no—
331C4×D3—22no—
332C4×D3—22no—
333Dic6—21no—
334Dic6—21no—
335C3×C8—22no—
336C3×C8—22no—
337C3×C8—42no—
338C3×C8—62no—
339C3⋊C8—22no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32#38611yescharacteristic
344C3×D3—42no—
345C3×D3—82no—
346C24—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C2×D4—32no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C2×D4—184no—
361C22×C4—32no—
362C22×C4C2×D3211yescharacteristic
363M16—21no—
364M16—21no—
365M16—64no—
366M16—61no—
367M16—61no—
368C2×C8—32no—
369C2×C8—64no—
370C2×C8#62512yescomplemented
371C4⋊C4—61no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C22⋊C4—61no—
375C22⋊C4—184no—
376C22⋊C4—181no—
377C22⋊C4—181no—
378C42—61no—
379C42—92no—
380C42—181no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—62no—
387C22×C3—81no—
388C22×C3—122no—
389C22×C3—124no—
390C22×C3—122no—
391C22×C3—242no—
392C22×C3—242no—
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3#88411yescharacteristic
395C22×C3C2×(C2×D3)⋊C411yescharacteristic
396C22×C3#93011yescharacteristic
397C22×C3#93011yescharacteristic
398C22×C3#93811yescharacteristic
399C2×D3—22no—
400C2×D3—42no—
401C2×D3—44no—
402C2×D3—42no—
403C2×D3—82no—
404C2×D3—82no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—62no—
410C3×C4—241no—
411C3×C4#67⋊C411yescharacteristic
412C3×C4#88311yescharacteristic
413C3×C4C4×#6711yescharacteristic
414C3×C4C4×#6711yescharacteristic
415C3×C4C4×#6711yescharacteristic
416C3×C4#92911yescharacteristic
417C3×C4#93711yescharacteristic
418C3×C4#95311yescharacteristic
419Dic3—22no—
420Dic3—81no—
421Dic3—122no—
422Dic3—122no—
423Dic3—242no—
424Dic3—241no—
425Dic3—241no—
426Dic3—242no—
427C32#191011yescharacteristic, complemented, Sylow
428C23—32no—
429C23—62no—
430C23—121no—
431C23—121no—
432C23—242no—
433C23D3×D1211yescharacteristic
434Q8—61no—
435Q8—61no—
436D4—62no—
437D4—62no—
438D4—61no—
439D4—62no—
440D4—61no—
441D4—62no—
442D4—121no—
443D4—121no—
444D4—724no—
445C2×C4—32no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—182no—
450C2×C4—361no—
451C2×C4#379511yescharacteristic
452C2×C4#379811yescharacteristic
453C2×C4C4×D3211yescharacteristic
454C2×C4C2×#62511yescharacteristic
455C2×C4D3×#6711yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C8—22no—
458C8—62no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—122no—
470C2×C3—242no—
471C2×C3#495611yescharacteristic
472C2×C3#521311yescharacteristic
473D3—42no—
474D3—82no—
475C22—41no—
476C22—62no—
477C22—122no—
478C22—124no—
479C22—122no—
480C22—242no—
481C22—242no—
482C22#6390611yescharacteristic
483C22#6390811yescharacteristic
484C22D3×(C2×D3)⋊C411yescharacteristic
485C4—62no—
486C4—241no—
487C4—362no—
488C4—721no—
489C4#6387911yescharacteristic
490C4C4×#62511yescharacteristic
491C4#6390511yescharacteristic
492C4#6397611yescharacteristic
493C3—21no—
494C3#7033011yescharacteristic, complemented
495C3#7202511yescharacteristic, complemented
496C2—21no—
497C2—21no—
498C2—21no—
499C2—122no—
500C2—242no—
501C2#1059138111yescharacteristic
subgroupG/H
centerC2#10591381
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595040C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1910
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. C3×#5131C2semidirect
4. #10591231C2semidirect
5. #10591086C2semidirect
6. #10589423C2semidirect
7. #10589158C2semidirect
21. #63914C4semidirect
23. #63863C4semidirect
30. #5745D3semidirect
35. #5131D3semidirect
61. C2×C32×C8D4semidirect
73. C2×C3×C3⋊C8D4semidirect
200. C2×C3×C8#67semidirect
201. C2×C3×C8#67semidirect
230. C2×C3⋊C8#67semidirect
370. C2×C8#625semidirect
427. C32#1910semidirect
494. C3#70330semidirect
495. C3#72025semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950402
C3×#51312
#105912312
#105910862
#105894232
#105891582
#720253
#703303