Finite Group Databasebeta

← #80932

Subgroups — #80932

Order 384.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5778C211yesmaximal, characteristic, complemented
2#5774C211yesmaximal, characteristic, complemented
3#5762C211yesmaximal, characteristic, complemented
4#5752C211yesmaximal, characteristic, complemented
5C3×#471C211yesmaximal, characteristic, complemented
6#5202C211yesmaximal, characteristic, complemented
7#5198C211yesmaximal, characteristic, complemented
8#5176C211yesmaximal, characteristic, complemented
9#5145C211yesmaximal, characteristic, complemented
10#4897C211yesmaximal, characteristic, complemented
11#4894C211yesmaximal, characteristic, complemented
12#4754C211yesmaximal, characteristic, complemented
13#4753C211yesmaximal, characteristic, complemented
14#4749C211yesmaximal, characteristic, complemented
15#4747C211yesmaximal, characteristic, complemented
16#3288—31nomaximal, Sylow
17#1009C2211yescharacteristic
18#1009C2211yescharacteristic, complemented
19#1007C2211yescharacteristic, complemented
20#1004C2211yescharacteristic, complemented
21C3×#137C2211yescharacteristic, complemented
22C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×SD16C2211yescharacteristic, complemented
24C3×#131C2211yescharacteristic, complemented
25#950C2211yescharacteristic
26#947C2211yescharacteristic, complemented
27#942C2211yescharacteristic, complemented
28C2×#215C2211yescharacteristic, complemented
29#940C2211yescharacteristic, complemented
30#932C2211yescharacteristic, complemented
31C2×#213C2211yescharacteristic, complemented
32#919—21no—
33#918—21no—
34#916—21no—
35#916—21no—
36#915—21no—
37#914—21no—
38#914—21no—
39#914—21no—
40D3×SD16—21no—
41D3×SD16—21no—
42#911—21no—
43D3×D8—21no—
44#908—21no—
45#908—21no—
46#908C2211yescharacteristic
47#908C2211yescharacteristic, complemented
48#908C2211yescharacteristic, complemented
49#908C2211yescharacteristic, complemented
50#907C2211yescharacteristic, complemented
51#907C2211yescharacteristic, complemented
52#904—21no—
53#904C2211yescharacteristic
54C2×D24—21no—
55C2×D24C2211yescharacteristic, complemented
56#901C2211yescharacteristic, complemented
57C3×#108C2211yescharacteristic, complemented
58C3×#101C2211yescharacteristic, complemented
59C3×#100C2211yescharacteristic, complemented
60#837C2211yescharacteristic, complemented
61#825C2211yescharacteristic, complemented
62#825C2211yescharacteristic, complemented
63#825C2211yescharacteristic, complemented
64#823C2211yescharacteristic, complemented
65#823C2211yescharacteristic, complemented
66#822C2211yescharacteristic, complemented
67#815C2211yescharacteristic, complemented
68#577—31no—
69#577—31no—
70#576—31no—
71#576—31no—
72#496—31no—
73#472—31no—
74#472—31no—
75#471—31no—
76#471D311yescharacteristic, complemented
77#455—31no—
78#454—31no—
79#453—31no—
80#453—31no—
81#444—31no—
82#444—31no—
83C3×#41C2311yescharacteristic
84C2×C3×Q8C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C2×#67—41no—
87C2×#67—41no—
88#239—21no—
89#239—21no—
90#239—21no—
91#239—21no—
92D3×Q8—21no—
93D3×Q8—21no—
94#237—21no—
95#237—21no—
96D3×D4—21no—
97D3×D4—21no—
98D3×D4—21no—
99D3×D4—21no—
100D3×D4—41no—
101D3×D4—41no—
102#235—21no—
103#235—21no—
104#235—41no—
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107#235C2311yescharacteristic
108C2×D12—21no—
109C2×D12—21no—
110C2×D12C2311yescharacteristic
111C2×D12C2311yescharacteristic
112C3×Q16—21no—
113C3×SD16—21no—
114C3×SD16—21no—
115C3×SD16—21no—
116C3×SD16—21no—
117C3×D8—21no—
118C3×M16—21no—
119C3×M16C2311yescharacteristic
120C3×M16C2311yescharacteristic
121C3×M16C2311yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8C2311yescharacteristic
124#216—21no—
125#216D411yescharacteristic, complemented
126#215—21no—
127#215—21no—
128#215—21no—
129#215D411yescharacteristic, complemented
130#214—21no—
131#214D411yescharacteristic, complemented
132#213—21no—
133#213—21no—
134#213—21no—
135#213D411yescharacteristic, complemented
136(C2×D3)⋊C4—41no—
137C4×Dic3C2311yescharacteristic
138#208C2311yescharacteristic
139C2×C3⋊C8C2311yescharacteristic
140Dic12D411yescharacteristic, complemented
141D24—21no—
142D24—21no—
143D24—21no—
144D24—21no—
145D24—21no—
146D24—21no—
147D24D411yescharacteristic, complemented
148#204—21no—
149#204—21no—
150#204—21no—
151#204—21no—
152#204D411yescharacteristic, complemented
153#204D411yescharacteristic, complemented
154ΓL(1,𝔽25)—21no—
155ΓL(1,𝔽25)—21no—
156ΓL(1,𝔽25)—21no—
157D3×C8—21no—
158D3×C8—21no—
159D3×C8—21no—
1602−1+4—31no—
161H(5,𝔽2)—31no—
162H(5,𝔽2)—31no—
163H(5,𝔽2)—31no—
164#137—31no—
165#137—61no—
166#137—61no—
167#137C2×D311yescharacteristic, complemented
168AGL(1,ℤ/8)—31no—
169AGL(1,ℤ/8)—31no—
170AGL(1,ℤ/8)—31no—
171AGL(1,ℤ/8)—31no—
172AGL(1,ℤ/8)—31no—
173AGL(1,ℤ/8)—61no—
174AGL(1,ℤ/8)—61no—
175AGL(1,ℤ/8)—61no—
176AGL(1,ℤ/8)—61no—
177AGL(1,ℤ/8)—61no—
178AGL(1,ℤ/8)—61no—
179AGL(1,ℤ/8)C2×D311yescharacteristic
180#135—31no—
181#135—31no—
182#135—61no—
183#135—61no—
184#135—61no—
185#135—61no—
186C2×SD16—31no—
187C2×SD16—61no—
188C2×SD16—61no—
189C2×SD16C2×D311yescharacteristic, complemented
190C2×D8—31no—
191C2×D8—31no—
192C2×D8—61no—
193C2×D8—61no—
194#131—31no—
195#131—31no—
196#131—31no—
197#131C2×D311yescharacteristic, complemented
198#127—31no—
199#124—31no—
200#108—31no—
201#108C2×D311yescharacteristic, complemented
202#104—31no—
203#104—31no—
204#104—31no—
205#104—31no—
206#101C2×D311yescharacteristic, complemented
207#100—31no—
208#100—31no—
209#100C2×D311yescharacteristic, complemented
210#97—31no—
211C23×C3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—41no—
217C3×Q8—21no—
218C3×Q8—21no—
219C3×Q8C2×D411yescharacteristic
220C3×D4—21no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4C2×D411yescharacteristic
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4C2411yescharacteristic
227#67—21no—
228#67—21no—
229#67—21no—
230#67—41no—
231#67—41no—
232#67—41no—
233#67—41no—
234#67—82no—
235C2×Dic3—21no—
236C2×Dic3—41no—
237D12—21no—
238D12—21no—
239D12—21no—
240D12—21no—
241D12—41no—
242D12—41no—
243D12—41no—
244D12C2×D411yescharacteristic
245D12C2×D411yescharacteristic
246D12C2×D411yescharacteristic
247C4×D3—21no—
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—41no—
251C4×D3—41no—
252C4×D3—41no—
253C4×D3—41no—
254Dic6—41no—
255Dic6C2×D411yescharacteristic
256Dic6C2×D411yescharacteristic
257Dic6C2×D411yescharacteristic
258C3×C8—21no—
259C3×C8—21no—
260C3×C8—21no—
261C3×C8C2×D411yescharacteristic
262C3×C8C2×D411yescharacteristic
263C3⋊C8—21no—
264C3⋊C8C2×D411yescharacteristic
265C3⋊C8C2×D411yescharacteristic
266#41—31no—
267#41—31no—
268#41—31no—
269#41—61no—
270#41—61no—
271#41—61no—
272#41—61no—
273#41—61no—
274#41—61no—
275#41—61no—
276#41—61no—
277#41—121no—
278#41C22×D311yescharacteristic
279C2×Q8—61no—
280C2×Q8—61no—
281C2×Q8C22×D311yescharacteristic
282C2×D4—31no—
283C2×D4—31no—
284C2×D4—61no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—121no—
291C2×D4—121no—
292C2×D4—121no—
293C2×D4—121no—
294C2×D4C22×D311yescharacteristic
295Q16—21no—
296Q16—31no—
297Q16—31no—
298Q16—61no—
299SD16—21no—
300SD16—21no—
301SD16—21no—
302SD16—21no—
303SD16—31no—
304SD16—31no—
305SD16—31no—
306SD16—31no—
307SD16—61no—
308SD16—61no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312SD16—61no—
313SD16—61no—
314SD16—61no—
315D8—21no—
316D8—31no—
317D8—31no—
318D8—61no—
319D8—61no—
320D8—61no—
321D8—61no—
322D8—61no—
323D8—61no—
324D8—61no—
325D8—61no—
326D8—61no—
327M16—21no—
328M16—31no—
329M16—61no—
330M16—61no—
331M16—61no—
332M16C22×D311yescharacteristic
333M16C22×D311yescharacteristic
334M16C22×D311yescharacteristic
335C2×C8—21no—
336C2×C8—31no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—61no—
340C2×C8C22×D311yescharacteristic
341C22⋊C4—121no—
342C42—31no—
343C22×C3—21no—
344C22×C3—41no—
345C22×C3—81no—
346C22×C3H(5,𝔽2)11yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3—81no—
353C2×D3—81no—
354C2×D3—161no—
355C2×D3—161no—
356C2×D3—161no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4C22×D411yescharacteristic
360C3×C4C22×D411yescharacteristic
361Dic3—21no—
362Dic3—21no—
363Dic3—21no—
364Dic3—41no—
365C23—21no—
366C23—61no—
367C23—61no—
368C23—121no—
369C23—121no—
370C23—121no—
371Q8—21no—
372Q8—21no—
373Q8—31no—
374Q8—31no—
375Q8—31no—
376Q8—121no—
377Q8D3×D411yescharacteristic
378D4—21no—
379D4—21no—
380D4—21no—
381D4—31no—
382D4—31no—
383D4—31no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—61no—
389D4—61no—
390D4—61no—
391D4—121no—
392D4—121no—
393D4—121no—
394D4—121no—
395D4—121no—
396D4—121no—
397D4—121no—
398D4—242no—
399D4D3×D411yescharacteristic
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4C23×D311yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—31no—
416C8—31no—
417C8—61no—
418C8D3×D411yescharacteristic
419C8D3×D411yescharacteristic
420C2×C3—21no—
421C2×C3—41no—
422C2×C3—81no—
423C2×C3D4211yescharacteristic
424D3—41no—
425D3—41no—
426D3—41no—
427D3—81no—
428D3—81no—
429C22—21no—
430C22—41no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—81no—
435C22—121no—
436C22—121no—
437C22—241no—
438C22—241no—
439C22—481no—
440C22—481no—
441C22—481no—
442C22#100911yescharacteristic
443C4—21no—
444C4—41no—
445C4—61no—
446C4—61no—
447C4—61no—
448C4—121no—
449C4C2×D3×D411yescharacteristic
450C4C2×D3×D411yescharacteristic
451C3#328811yescharacteristic, complemented, Sylow
452C2—21no—
453C2—41no—
454C2—81no—
455C2—121no—
456C2—121no—
457C2—121no—
458C2—241no—
459C2—241no—
460C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#471C2
socleC2×C3D42
hypercenter#471D3
hypocenterC3#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #5778C2semidirect
2. #5774C2semidirect
3. #5762C2semidirect
4. #5752C2semidirect
5. C3×#471C2semidirect
6. #5202C2semidirect
7. #5198C2semidirect
8. #5176C2semidirect
9. #5145C2semidirect
10. #4897C2semidirect
11. #4894C2semidirect
12. #4754C2semidirect
13. #4753C2semidirect
14. #4749C2semidirect
15. #4747C2semidirect
18. #1009C22semidirect
19. #1007C22semidirect
20. #1004C22semidirect
21. C3×#137C22semidirect
23. C2×C3×SD16C22semidirect
24. C3×#131C22semidirect
26. #947C22semidirect
27. #942C22semidirect
28. C2×#215C22semidirect
29. #940C22semidirect
30. #932C22semidirect
31. C2×#213C22semidirect
47. #908C22semidirect
48. #908C22semidirect
49. #908C22semidirect
50. #907C22semidirect
51. #907C22semidirect
55. C2×D24C22semidirect
56. #901C22semidirect
57. C3×#108C22semidirect
58. C3×#101C22semidirect
59. C3×#100C22semidirect
60. #837C22semidirect
61. #825C22semidirect
62. #825C22semidirect
63. #825C22semidirect
64. #823C22semidirect
65. #823C22semidirect
66. #822C22semidirect
67. #815C22semidirect
76. #471D3semidirect
125. #216D4semidirect
129. #215D4semidirect
131. #214D4semidirect
135. #213D4semidirect
140. Dic12D4semidirect
147. D24D4semidirect
152. #204D4semidirect
153. #204D4semidirect
167. #137C2×D3semidirect
189. C2×SD16C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
206. #101C2×D3semidirect
209. #100C2×D3semidirect
451. C3#3288semidirect

Maximal subgroups

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

subgroupindex
#57782
#57742
#57622
#57522
C3×#4712
#52022
#51982
#51762
#51452
#48972
#48942
#47542
#47532
#47492
#47472
#32883