Finite Group Databasebeta

← #11858280

Subgroups — #11858280

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63791C211yesmaximal, characteristic
2C2×D32×C8C211yesmaximal, characteristic
3#10593992C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
5C3×#4839C212yesmaximal, complemented
6#10590695C212yesmaximal, complemented
7#10590694C212yesmaximal, complemented
8#10590658C211yesmaximal, characteristic, complemented
9#10590658C211yesmaximal, characteristic, complemented
10#10590331C211yesmaximal, characteristic, complemented
11#10590324C212yesmaximal, complemented
12D3×#424—32nomaximal
13C2×C4×D32C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×#872C2212yes—
20#63921C411yescharacteristic
21#63921C411yescharacteristic
22#63883C411yescharacteristic
23#63883C411yescharacteristic
24C4×#624C2211yescharacteristic
25#63878C412yes—
26#63878C412yes—
27#63855C2212yes—
28C2×#3711C2212yes—
29C2×#3710C2211yescharacteristic
30C2×#3710C2211yescharacteristic
31C2×D3×C3⋊C8C2212yes—
32#63791—24no—
33D32×C8—24no—
34C32×C4⋊C8C2211yescharacteristic, complemented
35#63641C2211yescharacteristic, complemented
36#63641C2211yescharacteristic, complemented
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
38C3×Dic3⋊C8C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2212yescomplemented
41#63572C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43Dic3⋊(C3⋊C8)C2212yescomplemented
44C2×D3×M16—32no—
45C22×D3×C8—32no—
46D3×#117—32no—
47C3×#424—32no—
48#5119—32no—
49#5102—32no—
50#4999—32no—
51#4839—32no—
52#4839—32no—
53#4839—32no—
54#4839D312yescomplemented
55D3×C4⋊C8—32no—
56D3×C4⋊C8—32no—
57D3×C4⋊C8—32no—
58D3×C4⋊C8—32no—
59D3×C4⋊C8—61no—
60C22×D32C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C411yescharacteristic
62C2×C4×C3⋊D3C2×C411yescharacteristic
63C2×C4×C3⋊D3C2311yescharacteristic
64C2×C3×C4×D3C2312yes—
65C2×#624C2×C411yescharacteristic
66C2×#624C2×C411yescharacteristic
67C2×#624C2×C411yescharacteristic
68C2×D3×Dic3C2×C412yes—
69C4×D32D414yes—
70C4×D32Q814yes—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C32×C42C2311yescharacteristic
74C4×C3⋊Dic3C2×C411yescharacteristic
75C4×C3⋊Dic3C2×C411yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C8×C3⋊D3—22no—
80C8×C3⋊D3—22no—
81C3×(C2×D3)⋊C4C2×C412yes—
82C3×(C2×D3)⋊C4C2×C412yes—
83C3×Dic3⋊C4C2×C412yes—
84C3×Dic3⋊C4C2×C412yes—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88C3×ΓL(1,𝔽25)—24no—
89C3×D3×C8—24no—
90Dic3⋊Dic3C2×C412yes—
91Dic3⋊Dic3C2×C412yes—
92(C2×D3)⋊Dic3C2×C412yes—
93(C2×D3)⋊Dic3C2×C412yes—
94Dic32C2×C412yes—
95#3711—24no—
96#3710—22no—
97#3710—22no—
98D3×C3⋊C8—24no—
99C2×#424—91noSylow
100C22×C4×D3—32no—
101C2×C3×M16—32no—
102C22×C3×C8—32no—
103C3×#117—32no—
104#926—32no—
105C2×#208—32no—
106C22×C3⋊C8—32no—
107D3×M16—68no—
108C2×ΓL(1,𝔽25)—32no—
109C2×ΓL(1,𝔽25)C2×D312yes—
110C2×D3×C8—32no—
111C2×D3×C8—32no—
112C2×D3×C8—32no—
113C2×D3×C8—32no—
114C2×D3×C8—32no—
115C2×D3×C8—61no—
116C2×D3×C8—61no—
117C2×D3×C8—68no—
118C2×D3×C8C2×D312yes—
119#892—32no—
120#892—32no—
121D3×C4⋊C4—32no—
122D3×C4⋊C4—32no—
123D3×C22⋊C4—32no—
124D3×C22⋊C4—32no—
125#877—32no—
126#877—32no—
127#872—32no—
128#872C2×D312yes—
129C42×D3—32no—
130C42×D3—32no—
131C42×D3—61no—
132C3×C4⋊C8—21no—
133C3×C4⋊C8—32no—
134C3×C4⋊C8—32no—
135C3×C4⋊C8—32no—
136C3×C4⋊C8C2×D312yescomplemented
137Dic3⋊C8—32no—
138Dic3⋊C8—32no—
139Dic3⋊C8—32no—
140Dic3⋊C8—32no—
141Dic3⋊C8—32no—
142Dic3⋊C8—32no—
143Dic3⋊C8—61no—
144Dic3⋊C8—61no—
145Dic3⋊C8C2×D312yescomplemented
146Dic3⋊C8C2×D312yescomplemented
147C4⋊(C3⋊C8)—32no—
148C4⋊(C3⋊C8)—32no—
149C4⋊(C3⋊C8)—32no—
150C4⋊(C3⋊C8)—61no—
151C4⋊(C3⋊C8)C2×D312yescomplemented
152C22×C3⋊D3C22×C411yescharacteristic
153C22×C3×D3C22×C412yes—
154C2×D32—22no—
155C2×D32—22no—
156C2×D32C4⋊C414yes—
157C2×C32×C4C22×C411yescharacteristic
158C2×C32×C4C22×C411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3C22×C411yescharacteristic
161C2×C3⋊Dic3C22×C411yescharacteristic
162C2×C3⋊Dic3C22×C411yescharacteristic
163C4×C3⋊D3—22no—
164C4×C3⋊D3—22no—
165C4×C3⋊D3C2×D412yes—
166C4×C3⋊D3C2×Q812yes—
167C2×C3×Dic3C22×C412yes—
168C2×C3×Dic3C22×C412yes—
169C2×C3×Dic3C22×C412yes—
170C3×C4×D3C2×D414yes—
171C3×C4×D3C2×Q814yes—
172#624—22no—
173#624—22no—
174#624C4⋊C414yes—
175D3×Dic3C4⋊C418yes—
176C32×C8—21no—
177C32×C8—21no—
178C3⋊(C3⋊C8)—21no—
179C3⋊(C3⋊C8)—21no—
180C3×C3⋊C8—22no—
181C3×C3⋊C8—22no—
182C22×M16—91no—
183C23×C8—91no—
184C2×#117—91no—
185#424—32no—
186#424—92no—
187#424—92no—
188#424—92no—
189C2×C4⋊C8—91no—
190C2×C4⋊C8—91no—
191C2×C4⋊C8—91no—
192C2×C4⋊C8—91no—
193C23×D3—32no—
194C22×C3×C4—32no—
195C22×Dic3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—38no—
200C2×C4×D3—38no—
201C2×C4×D3—32no—
202C2×C4×D3—32no—
203C2×C4×D3—32no—
204C2×C4×D3—32no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3C22×D312yes—
209C3×M16—64no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C2×C3×C8—64no—
215C2×C3×C8C22×D312yes—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—32no—
219C3×C22⋊C4—32no—
220C3×C22⋊C4—32no—
221C3×C42—21no—
222C3×C42—32no—
223C3×C42C22×D312yes—
224#217—32no—
225#217—32no—
226(C2×D3)⋊C4—32no—
227(C2×D3)⋊C4—32no—
228(C2×D3)⋊C4C4×D312yes—
229(C2×D3)⋊C4C4×D312yes—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232Dic3⋊C4—32no—
233Dic3⋊C4—32no—
234Dic3⋊C4C4×D312yes—
235Dic3⋊C4C4×D312yes—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C4×Dic3C22×D312yes—
245#208—64no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8C22×D312yes—
252C2×C3⋊C8C22×D312yes—
253ΓL(1,𝔽25)—24no—
254ΓL(1,𝔽25)—64no—
255D3×C8—24no—
256D3×C8—64no—
257D3×C8—64no—
258D3×C8—64no—
259D3×C8—64no—
260D3×C8—64no—
261D3×C8—122no—
262D3×C8—122no—
263C22×C32C23×C411yescharacteristic
264C2×C3⋊D3C2×C4⋊C412yes—
265C2×C3⋊D3#13112yes—
266C2×C3⋊D3#13112yes—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3C2×C4⋊C414yes—
270D32—28no—
271C32×C4—21no—
272C32×C4—21no—
273C32×C4C22×D411yescharacteristic
274C32×C4C22×Q811yescharacteristic
275C3⋊Dic3—21no—
276C3⋊Dic3—21no—
277C3⋊Dic3C2×C4⋊C412yes—
278C3×Dic3—22no—
279C3×Dic3—22no—
280C3×Dic3C2×C4⋊C414yes—
281C23×C4—91no—
282C2×M16—32no—
283C2×M16—92no—
284C2×M16—184no—
285C22×C8—32no—
286C22×C8—91no—
287C22×C8—91no—
288C22×C8—92no—
289C22×C8—91no—
290C22×C8—91no—
291C22×C8—184no—
292#117—32no—
293#117—92no—
294#117—92no—
295#117—92no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—91no—
300C2×C42—91no—
301C2×C42—91no—
302C4⋊C8—32no—
303C4⋊C8—32no—
304C4⋊C8—32no—
305C4⋊C8—92no—
306C4⋊C8—92no—
307C4⋊C8—92no—
308C4⋊C8—91no—
309C4⋊C8—91no—
310C4⋊C8—91no—
311C4⋊C8D3211yescharacteristic, complemented
312C23×C3—32no—
313C22×D3—32no—
314C22×D3—38no—
315C22×D3—61no—
316C22×D3—64no—
317C22×D3—64no—
318C22×D3C2×C4×D312yes—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—32no—
323C2×C3×C4—34no—
324C2×C3×C4—34no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4C2×C4×D312yes—
329C2×C3×C4C23×D312yes—
330C2×Dic3—32no—
331C2×Dic3—38no—
332C2×Dic3—32no—
333C2×Dic3—32no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3C2×C4×D312yes—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340C4×D3—38no—
341C4×D3—34no—
342C4×D3—34no—
343C4×D3—38no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—64no—
349C4×D3—64no—
350C4×D3—64no—
351C4×D3—122no—
352C4×D3D3×D414yes—
353C4×D3D3×Q814yes—
354C3×C8—22no—
355C3×C8—22no—
356C3×C8—41no—
357C3×C8—41no—
358C3×C8—62no—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—22no—
362C3⋊C8—62no—
363C3⋊C8—62no—
364C3⋊C8—121no—
365C3⋊C8—121no—
366C2×C32C22×C4⋊C411yescharacteristic
367C2×C32C2×#13111yescharacteristic
368C2×C32C2×#13111yescharacteristic
369C3⋊D3#42414yescomplemented
370C3×D3—24no—
371C24—91no—
372C22×C4—32no—
373C22×C4—91no—
374C22×C4—94no—
375C22×C4—94no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—92no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382M16—64no—
383M16—184no—
384C2×C8—32no—
385C2×C8—32no—
386C2×C8—64no—
387C2×C8—91no—
388C2×C8—91no—
389C2×C8—182no—
390C2×C8—182no—
391C2×C8—182no—
392C2×C8—182no—
393C2×C8—184no—
394C2×C8C2×D3211yescharacteristic
395C2×C8C2×D3211yescharacteristic
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4—92no—
399C4⋊C4—92no—
400C22⋊C4—32no—
401C22⋊C4—32no—
402C22⋊C4—92no—
403C22⋊C4—92no—
404C42—32no—
405C42—92no—
406C42—91no—
407C42—91no—
408C42—91no—
409C42C2×D3211yescharacteristic
410C22×C3—21no—
411C22×C3—34no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3C22×C4×D312yes—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—34no—
418C2×D3—34no—
419C2×D3—34no—
420C2×D3—62no—
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—616no—
424C2×D3D3×C4⋊C414yes—
425C3×C4—22no—
426C3×C4—22no—
427C3×C4—22no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—34no—
431C3×C4—41no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4C2×D3×D412yes—
435C3×C4C2×D3×Q812yes—
436Dic3—22no—
437Dic3—22no—
438Dic3—34no—
439Dic3—62no—
440Dic3—62no—
441Dic3—62no—
442Dic3—62no—
443Dic3—121no—
444Dic3D3×C4⋊C414yes—
445C32C2×#42411yescharacteristic, complemented, Sylow
446C23—32no—
447C23—94no—
448C23—91no—
449C23—182no—
450C23—182no—
451C2×C4—32no—
452C2×C4—34no—
453C2×C4—34no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—94no—
457C2×C4—98no—
458C2×C4—91no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—91no—
462C2×C4—91no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—182no—
467C2×C4C4×D3211yescharacteristic
468C2×C4C4×D3211yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—21no—
471C8—21no—
472C8—62no—
473C8—62no—
474C8—181no—
475C8—181no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—64no—
480C2×C3C2×D3×C4⋊C412yes—
481C2×C3D3×#13112yes—
482C2×C3D3×#13112yes—
483D3—24no—
484D3—38no—
485D3—64no—
486C22—34no—
487C22—62no—
488C22—62no—
489C22—92no—
490C22—92no—
491C22—92no—
492C22—188no—
493C22C2×C4×D3211yescharacteristic
494C4—21no—
495C4—21no—
496C4—34no—
497C4—62no—
498C4—62no—
499C4—92no—
500C4—181no—
501C4—181no—
502C4D32×D411yescharacteristic
503C4D32×Q811yescharacteristic
504C3—21no—
505C3D3×#42412yescomplemented
506C2—64no—
507C2—94no—
508C2D32×C4⋊C411yescharacteristic
509C2#1059466911yescharacteristic
510C2#1059470711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC22×D32C2×C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C2×#424
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3⋊D3×C4⋊C8C2semidirect
5. C3×#4839C2semidirect
6. #10590695C2semidirect
7. #10590694C2semidirect
8. #10590658C2semidirect
9. #10590658C2semidirect
10. #10590331C2semidirect
11. #10590324C2semidirect
34. C32×C4⋊C8C22semidirect
35. #63641C22semidirect
36. #63641C22semidirect
37. C4⋊(C3⋊(C3⋊C8))C22semidirect
38. C3×Dic3⋊C8C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63572C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
43. Dic3⋊(C3⋊C8)C22semidirect
54. #4839D3semidirect
136. C3×C4⋊C8C2×D3semidirect
145. Dic3⋊C8C2×D3semidirect
146. Dic3⋊C8C2×D3semidirect
151. C4⋊(C3⋊C8)C2×D3semidirect
311. C4⋊C8D32semidirect
369. C3⋊D3#424semidirect
445. C32C2×#424semidirect
505. C3D3×#424semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
C2×D32×C82
#105939922
C3⋊D3×C4⋊C82
C3×#48392
#105906952
#105906942
#105906582
#105903312
#105903242
D3×#4243