Finite Group Databasebeta

← #11858468

Subgroups — #11858468

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63791C211yesmaximal, characteristic
2#10594602C211yesmaximal, characteristic
3D32×C4⋊C4C211yesmaximal, characteristic
4C3⋊D3×#106C211yesmaximal, characteristic, complemented
5C3×#4861C212yesmaximal, complemented
6#10590687C211yesmaximal, characteristic, complemented
7#10590683C212yesmaximal, complemented
8#10590580C212yesmaximal, complemented
9#10590575C211yesmaximal, characteristic, complemented
10#10590573C211yesmaximal, characteristic, complemented
11#10590437C212yesmaximal, complemented
12D3×#428—32nomaximal
13C2×C4×D32—21no—
14C2×C4×D32C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2212yes—
19C3×#892C2212yes—
20C3×D3×C4⋊C4C2212yes—
21#63921—21no—
22#63900C2211yescharacteristic
23#63900C2211yescharacteristic
24D3×C4⋊Dic3C2212yes—
25#63883—21no—
26C4×#624—21no—
27#63877—22no—
28D3×Dic3⋊C4—22no—
29#63841C2212yes—
30C2×#3711C2212yes—
31C2×#3710C2211yescharacteristic
32#63791C418yescomplemented
33C32×#106C2211yescharacteristic, complemented
34#63644C2211yescharacteristic, complemented
35#63635C2211yescharacteristic, complemented
36#63635C2211yescharacteristic, complemented
37C3×#818C2212yescomplemented
38C3×#808C2212yescomplemented
39C3×#807C2212yescomplemented
40#63576C2212yescomplemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43C2×D3×M16—32no—
44D3×#117—32no—
45C2×D3×C4⋊C4—32no—
46C3×#428—32no—
47#5121—32no—
48#4995—32no—
49#4964—32no—
50#4881—32no—
51#4881—32no—
52D3×#107—32no—
53D3×#107—32no—
54#4861—32no—
55#4861D312yescomplemented
56D3×#106—32no—
57D3×#106—32no—
58D3×#106—61no—
59C22×D32D411yescharacteristic
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3C2312yes—
65C2×#624—21no—
66C2×#624—21no—
67C2×#624D411yescharacteristic
68C2×D3×Dic3—22no—
69C2×D3×Dic3D412yes—
70C4×D32—44no—
71C4×D32C2×C414yes—
72C4×D32Q814yes—
73C2×C32×C8C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78#3750—21no—
79#3750—21no—
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C8×C3⋊D3C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—22no—
86C3×C4×Dic3—22no—
87C2×C3×C3⋊C8C2312yes—
88C3×ΓL(1,𝔽25)C2×C418yescomplemented
89#3724—21no—
90#3724—21no—
91Dic3⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93Dic32—22no—
94#3711C2×C418yescomplemented
95#3710C2×C414yescomplemented
96C2×#428—91noSylow
97C22×C4×D3—32no—
98C22×C4×D3—62no—
99C2×C3×M16—32no—
100C3×#117—32no—
101C2×C3×C4⋊C4—32no—
102#926—32no—
103C2×C4⋊Dic3—32no—
104C2×Dic3⋊C4—62no—
105C2×#208—32no—
106D3×M16—316no—
107C2×ΓL(1,𝔽25)—32no—
108C2×ΓL(1,𝔽25)C2×D312yes—
109C2×D3×C8—32no—
110C2×D3×C8—32no—
111C2×D3×C8—61no—
112#892—32no—
113#892C2×D312yes—
114D3×C4⋊C4—32no—
115D3×C4⋊C4—32no—
116D3×C4⋊C4—32no—
117D3×C4⋊C4—32no—
118D3×C4⋊C4—32no—
119D3×C4⋊C4—61no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—62no—
122D3×C4⋊C4—62no—
123D3×C4⋊C4C2×D312yes—
124D3×C22⋊C4—62no—
125#877—62no—
126#872—62no—
127C42×D3—62no—
128C3×#107—32no—
129C3×#107—32no—
130C3×#106—21no—
131C3×#106—32no—
132C3×#106C2×D312yescomplemented
133#818—32no—
134#818C2×D312yescomplemented
135#817—32no—
136#817—32no—
137#817—61no—
138#808—32no—
139#808—32no—
140#808—32no—
141#808—61no—
142#808—61no—
143#808C2×D312yescomplemented
144#807—32no—
145#807—32no—
146#807—32no—
147#807C2×D312yescomplemented
148C22×C3⋊D3C2×D411yescharacteristic
149C22×C3×D3C2×D412yes—
150C2×D32—22no—
151C2×D32—22no—
152C2×D32C4⋊C414yes—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4C2411yescharacteristic
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3C2×D411yescharacteristic
159C4×C3⋊D3—42no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3C22×C412yes—
162C4×C3⋊D3C2×Q812yes—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C2×D412yes—
166C3×C4×D3—44no—
167C3×C4×D3C22×C414yes—
168C3×C4×D3C2×Q814yes—
169#624—42no—
170#624—42no—
171#624C4⋊C414yes—
172D3×Dic3—44no—
173D3×Dic3C4⋊C418yes—
174C32×C8C22×C412yescomplemented
175C3⋊(C3⋊C8)C22×C412yescomplemented
176C3×C3⋊C8C22×C414yescomplemented
177C22×M16—91no—
178C2×#117—91no—
179C22×C4⋊C4—91no—
180#428—32no—
181#428—92no—
182#428—92no—
183#428—92no—
184C2×#107—91no—
185C2×#107—91no—
186C2×#106—91no—
187C2×#106—91no—
188C23×D3—32no—
189C22×C3×C4—32no—
190C22×C3×C4—62no—
191C22×Dic3—32no—
192C22×Dic3—62no—
193C2×C4×D3—22no—
194C2×C4×D3—32no—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—38no—
198C2×C4×D3—38no—
199C2×C4×D3—61no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—121no—
206C2×C4×D3—121no—
207C2×C4×D3—128no—
208C2×C4×D3C22×D312yes—
209C3×M16—38no—
210C2×C3×C8—21no—
211C2×C3×C8—32no—
212C2×C3×C8C22×D312yes—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—32no—
217C3×C4⋊C4—62no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C22×D312yes—
220C3×C22⋊C4—62no—
221C3×C42—62no—
222#217—62no—
223(C2×D3)⋊C4—22no—
224(C2×D3)⋊C4—62no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—62no—
230C4⋊Dic3C22×D312yes—
231C4⋊Dic3C22×D312yes—
232Dic3⋊C4—22no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—62no—
237Dic3⋊C4—62no—
238Dic3⋊C4—121no—
239Dic3⋊C4—121no—
240C4×Dic3—22no—
241C4×Dic3—62no—
242C4×Dic3—62no—
243#208—38no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C22×D312yes—
247ΓL(1,𝔽25)—38no—
248ΓL(1,𝔽25)C4×D318yescomplemented
249D3×C8—38no—
250D3×C8—38no—
251D3×C8—64no—
252C22×C32C22×D411yescharacteristic
253C2×C3⋊D3C2×C4⋊C412yes—
254C2×C3⋊D3AGL(1,ℤ/8)12yes—
255C2×C3⋊D3#13712yes—
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3C2×C4⋊C414yes—
259D32—28no—
260C32×C4—41no—
261C32×C4—41no—
262C32×C4C23×C411yescharacteristic
263C32×C4C22×Q811yescharacteristic
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3⋊Dic3C2×C4⋊C412yes—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C2×C4⋊C414yes—
270C23×C4—91no—
271C23×C4—181no—
272C2×M16—32no—
273C2×M16—92no—
274C2×M16—98no—
275C22×C8—91no—
276C22×C8—91no—
277#117—32no—
278#117—92no—
279#117—182no—
280C2×C4⋊C4—32no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—92no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—182no—
288C2×C22⋊C4—181no—
289C2×C42—181no—
290#107—32no—
291#107—32no—
292#107—92no—
293#107—92no—
294#106—32no—
295#106—92no—
296#106—91no—
297#106—91no—
298#106—91no—
299#106D3211yescharacteristic, complemented
300C23×C3—32no—
301C22×D3—32no—
302C22×D3—38no—
303C22×D3—61no—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3D3×D412yes—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—32no—
311C2×C3×C4—34no—
312C2×C3×C4—34no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—124no—
318C2×C3×C4C23×D312yes—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—32no—
322C2×Dic3—38no—
323C2×Dic3—61no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—124no—
329C2×Dic3D3×D412yes—
330C4×D3—38no—
331C4×D3—34no—
332C4×D3—34no—
333C4×D3—38no—
334C4×D3—44no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—124no—
338C4×D3—124no—
339C4×D3—124no—
340C4×D3—124no—
341C4×D3—124no—
342C4×D3—242no—
343C4×D3—242no—
344C4×D3C2×C4×D314yes—
345C4×D3D3×Q814yes—
346C3×C8—22no—
347C3×C8—34no—
348C3×C8C2×C4×D314yescomplemented
349C3⋊C8—34no—
350C3⋊C8—62no—
351C3⋊C8C2×C4×D314yescomplemented
352C2×C32C22×C4⋊C411yescharacteristic
353C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
354C2×C32C2×#13711yescharacteristic
355C3⋊D3#42814yescomplemented
356C3×D3—24no—
357C24—91no—
358C22×C4—32no—
359C22×C4—62no—
360C22×C4—91no—
361C22×C4—94no—
362C22×C4—94no—
363C22×C4—92no—
364C22×C4—91no—
365C22×C4—181no—
366C22×C4—181no—
367C22×C4—181no—
368C22×C4—181no—
369C22×C4—182no—
370C22×C4—364no—
371M16—38no—
372M16—98no—
373C2×C8—32no—
374C2×C8—94no—
375C2×C8—91no—
376C2×C8—94no—
377C2×C8C2×D3211yescharacteristic
378C4⋊C4—32no—
379C4⋊C4—32no—
380C4⋊C4—62no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—182no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4C2×D3211yescharacteristic
389C4⋊C4C2×D3211yescharacteristic
390C22⋊C4—62no—
391C22⋊C4—182no—
392C42—62no—
393C42—182no—
394C22×C3—21no—
395C22×C3—34no—
396C22×C3—62no—
397C22×C3—62no—
398C22×C3C2×D3×D412yes—
399C2×D3—22no—
400C2×D3—22no—
401C2×D3—34no—
402C2×D3—34no—
403C2×D3—34no—
404C2×D3—62no—
405C2×D3—62no—
406C2×D3—62no—
407C2×D3—616no—
408C2×D3D3×C4⋊C414yes—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—34no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—81no—
415C3×C4—81no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4C22×C4×D312yes—
419C3×C4C2×D3×Q812yes—
420Dic3—34no—
421Dic3—42no—
422Dic3—42no—
423Dic3—62no—
424Dic3—122no—
425Dic3—122no—
426Dic3—241no—
427Dic3—241no—
428Dic3D3×C4⋊C414yes—
429C32C2×#42811yescharacteristic, complemented, Sylow
430C23—32no—
431C23—94no—
432C23—91no—
433C23—182no—
434C23—182no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—32no—
438C2×C4—34no—
439C2×C4—34no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—94no—
443C2×C4—98no—
444C2×C4—91no—
445C2×C4—92no—
446C2×C4—92no—
447C2×C4—124no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—362no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4—364no—
455C2×C4C22×D3211yescharacteristic
456C8—34no—
457C8—92no—
458C8C4×D3212yescomplemented
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—64no—
463C2×C3C2×D3×C4⋊C412yes—
464C2×C3D3×AGL(1,ℤ/8)12yes—
465C2×C3D3×#13712yes—
466D3—24no—
467D3—38no—
468D3—64no—
469C22—34no—
470C22—62no—
471C22—62no—
472C22—92no—
473C22—92no—
474C22—92no—
475C22—188no—
476C22D32×D411yescharacteristic
477C4—34no—
478C4—41no—
479C4—41no—
480C4—92no—
481C4—122no—
482C4—122no—
483C4—361no—
484C4—361no—
485C4C2×C4×D3211yescharacteristic
486C4D32×Q811yescharacteristic
487C3—21no—
488C3D3×#42812yescomplemented
489C2—64no—
490C2—94no—
491C2D32×C4⋊C411yescharacteristic
492C2#1059474011yescharacteristic
493C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#428
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3⋊D3×#106C2semidirect
5. C3×#4861C2semidirect
6. #10590687C2semidirect
7. #10590683C2semidirect
8. #10590580C2semidirect
9. #10590575C2semidirect
10. #10590573C2semidirect
11. #10590437C2semidirect
32. #63791C4semidirect
33. C32×#106C22semidirect
34. #63644C22semidirect
35. #63635C22semidirect
36. #63635C22semidirect
37. C3×#818C22semidirect
38. C3×#808C22semidirect
39. C3×#807C22semidirect
40. #63576C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
55. #4861D3semidirect
81. C8×C3⋊D3C2×C4semidirect
88. C3×ΓL(1,𝔽25)C2×C4semidirect
94. #3711C2×C4semidirect
95. #3710C2×C4semidirect
132. C3×#106C2×D3semidirect
134. #818C2×D3semidirect
143. #808C2×D3semidirect
147. #807C2×D3semidirect
174. C32×C8C22×C4semidirect
175. C3⋊(C3⋊C8)C22×C4semidirect
176. C3×C3⋊C8C22×C4semidirect
248. ΓL(1,𝔽25)C4×D3semidirect
299. #106D32semidirect
348. C3×C8C2×C4×D3semidirect
351. C3⋊C8C2×C4×D3semidirect
355. C3⋊D3#428semidirect
429. C32C2×#428semidirect
458. C8C4×D32semidirect
488. C3D3×#428semidirect

Maximal subgroups

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

subgroupindex
C2×#637912
#105946022
D32×C4⋊C42
C3⋊D3×#1062
C3×#48612
#105906872
#105906832
#105905802
#105905752
#105905732
#105904372
D3×#4283