Finite Group Databasebeta

← #80939

Subgroups — #80939

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#5775C211yesmaximal, characteristic, complemented
2#5774C211yesmaximal, characteristic, complemented
3#5757C211yesmaximal, characteristic, complemented
4#5751C211yesmaximal, characteristic, complemented
5C3×#472C211yesmaximal, characteristic, complemented
6#5201C211yesmaximal, characteristic, complemented
7#5198C211yesmaximal, characteristic, complemented
8#5154C211yesmaximal, characteristic, complemented
9#5145C211yesmaximal, characteristic, complemented
10#4898C211yesmaximal, characteristic, complemented
11#4894C211yesmaximal, characteristic, complemented
12#4749C211yesmaximal, characteristic, complemented
13#4748C211yesmaximal, characteristic, complemented
14#4747C211yesmaximal, characteristic, complemented
15#4746C211yesmaximal, characteristic, complemented
16#3288—31nomaximal, Sylow
17#1010C2211yescharacteristic, complemented
18#1009C2211yescharacteristic, complemented
19#1004C2211yescharacteristic
20#1004C2211yescharacteristic, complemented
21C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
22C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23C2×C3×D8C2211yescharacteristic, complemented
24C3×#131C2211yescharacteristic, complemented
25#950C2211yescharacteristic
26#940C2211yescharacteristic, complemented
27#936C2211yescharacteristic, complemented
28C2×#214C2211yescharacteristic, complemented
29#932C2211yescharacteristic
30#932C2211yescharacteristic, complemented
31C2×#213C2211yescharacteristic, complemented
32#916—21no—
33#915—21no—
34#914—21no—
35D3×SD16—21no—
36#912—21no—
37#912—21no—
38#911—21no—
39#911—21no—
40#911—21no—
41#911—21no—
42D3×D8—21no—
43D3×D8—21no—
44#909—21no—
45#909C2211yescharacteristic, complemented
46#909C2211yescharacteristic, complemented
47#908—21no—
48#908C2211yescharacteristic
49#908C2211yescharacteristic, complemented
50#907C2211yescharacteristic, complemented
51#907C2211yescharacteristic, complemented
52#904—21no—
53#904C2211yescharacteristic
54C2×#204—21no—
55C2×#204C2211yescharacteristic, complemented
56#901C2211yescharacteristic, complemented
57C3×#108C2211yescharacteristic, complemented
58C3×#100C2211yescharacteristic, complemented
59C3×#100C2211yescharacteristic, complemented
60#837C2211yescharacteristic, complemented
61#825C2211yescharacteristic, complemented
62#825C2211yescharacteristic, complemented
63#825C2211yescharacteristic, complemented
64#824C2211yescharacteristic, 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#472D311yescharacteristic, complemented
75#471—31no—
76#471—31no—
77#455—31no—
78#454—31no—
79#453—31no—
80#453—31no—
81#444—31no—
82#444—31no—
83C3×#41C2311yescharacteristic
84C2×C3×D4C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C2×#67—41no—
87C2×#67—41no—
88C2×#67—41no—
89#239—21no—
90D3×Q8—21no—
91#237—21no—
92#237—21no—
93#237—21no—
94#237—21no—
95#237—21no—
96#237—41no—
97D3×D4—21no—
98D3×D4—21no—
99D3×D4—21no—
100D3×D4—21no—
101D3×D4—21no—
102D3×D4—41no—
103#235—21no—
104#235—21no—
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107#235C2311yescharacteristic
108C2×D12—21no—
109C2×D12C2311yescharacteristic
110C2×Dic6—21no—
111C2×Dic6C2311yescharacteristic
112C3×SD16—21no—
113C3×SD16—21no—
114C3×D8—21no—
115C3×D8—21no—
116C3×D8—21no—
117C3×D8—21no—
118C3×M16—21no—
119C3×M16C2311yescharacteristic
120C3×M16C2311yescharacteristic
121C3×M16C2311yescharacteristic
122C2×C3×C8—21no—
123C2×C3×C8C2311yescharacteristic
124#217—41no—
125#216D411yescharacteristic, complemented
126#215D411yescharacteristic, complemented
127#214—21no—
128#214—21no—
129#214—21no—
130#214—21no—
131#214D411yescharacteristic, complemented
132#213—21no—
133#213—21no—
134#213—21no—
135#213—21no—
136#213D411yescharacteristic, complemented
137C4×Dic3C2311yescharacteristic
138#208C2311yescharacteristic
139C2×C3⋊C8C2311yescharacteristic
140Dic12—21no—
141Dic12—21no—
142Dic12D411yescharacteristic, complemented
143D24—21no—
144D24—21no—
145D24D411yescharacteristic, complemented
146#204—21no—
147#204—21no—
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—31no—
166#137—61no—
167#137—61no—
168AGL(1,ℤ/8)—31no—
169AGL(1,ℤ/8)—31no—
170AGL(1,ℤ/8)—31no—
171AGL(1,ℤ/8)—31no—
172AGL(1,ℤ/8)—61no—
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)C2×D311yescharacteristic, complemented
179AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
180#135—31no—
181#135—31no—
182#135—61no—
183#135—61no—
184#135—61no—
185#135—61no—
186C2×SD16—31no—
187C2×SD16—31no—
188C2×SD16—61no—
189C2×SD16—61no—
190C2×D8—31no—
191C2×D8—61no—
192C2×D8—61no—
193C2×D8C2×D311yescharacteristic, complemented
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#101—31no—
207#100—31no—
208#100C2×D311yescharacteristic, complemented
209#100C2×D311yescharacteristic, complemented
210#97—31no—
211C23×C3—21no—
212C23×C3—21no—
213C22×D3—21no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—41no—
217C3×Q8C2×D411yescharacteristic
218C3×D4—21no—
219C3×D4—21no—
220C3×D4—21no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4C2×D411yescharacteristic
224C2×C3×C4—21no—
225C2×C3×C4C2411yescharacteristic
226#67—21no—
227#67—21no—
228#67—21no—
229#67—41no—
230#67—41no—
231#67—41no—
232#67—41no—
233#67—41no—
234#67—41no—
235#67—82no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—41no—
239C2×Dic3—41no—
240C2×Dic3—41no—
241D12—21no—
242D12—21no—
243D12—41no—
244D12C2×D411yescharacteristic
245D12C2×D411yescharacteristic
246D12C2×D411yescharacteristic
247C4×D3—21no—
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—41no—
251C4×D3—41no—
252Dic6—21no—
253Dic6—21no—
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—31no—
280C2×Q8—61no—
281C2×Q8—61no—
282C2×D4—31no—
283C2×D4—61no—
284C2×D4—61no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—121no—
290C2×D4—121no—
291C2×D4—121no—
292C2×D4—121no—
293C2×D4C22×D311yescharacteristic
294C2×D4C22×D311yescharacteristic
295Q16—31no—
296Q16—31no—
297Q16—61no—
298Q16—61no—
299SD16—21no—
300SD16—21no—
301SD16—31no—
302SD16—31no—
303SD16—31no—
304SD16—31no—
305SD16—61no—
306SD16—61no—
307SD16—61no—
308SD16—61no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312SD16—61no—
313SD16—61no—
314SD16—61no—
315D8—21no—
316D8—21no—
317D8—21no—
318D8—21no—
319D8—31no—
320D8—31no—
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—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3H(5,𝔽2)11yescharacteristic
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—41no—
353C2×D3—81no—
354C2×D3—161no—
355C2×D3—161no—
356C2×D3—161no—
357C3×C4—21no—
358C3×C4C22×D411yescharacteristic
359C3×C4C22×D411yescharacteristic
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—41no—
364Dic3—41no—
365C23—21no—
366C23—21no—
367C23—61no—
368C23—121no—
369C23—121no—
370C23—121no—
371Q8—31no—
372Q8—31no—
373Q8—31no—
374Q8—61no—
375Q8—61no—
376Q8—121no—
377Q8D3×D411yescharacteristic
378D4—21no—
379D4—21no—
380D4—21no—
381D4—21no—
382D4—21no—
383D4—31no—
384D4—31no—
385D4—31no—
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—61no—
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×C3—81no—
424C2×C3D4211yescharacteristic
425D3—41no—
426D3—41no—
427D3—41no—
428D3—81no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—61no—
433C22—61no—
434C22—61no—
435C22—81no—
436C22—81no—
437C22—121no—
438C22—241no—
439C22—481no—
440C22—481no—
441C22—481no—
442C22#100911yescharacteristic
443C4—21no—
444C4—61no—
445C4—61no—
446C4—61no—
447C4—121no—
448C4—121no—
449C4C2×D3×D411yescharacteristic
450C4C2×D3×D411yescharacteristic
451C3#328811yescharacteristic, complemented, Sylow
452C2—21no—
453C2—41no—
454C2—81no—
455C2—81no—
456C2—121no—
457C2—121no—
458C2—121no—
459C2—241no—
460C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#472C2
socleC2×C3D42
hypercenter#472D3
hypocenterC3#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #5775C2semidirect
2. #5774C2semidirect
3. #5757C2semidirect
4. #5751C2semidirect
5. C3×#472C2semidirect
6. #5201C2semidirect
7. #5198C2semidirect
8. #5154C2semidirect
9. #5145C2semidirect
10. #4898C2semidirect
11. #4894C2semidirect
12. #4749C2semidirect
13. #4748C2semidirect
14. #4747C2semidirect
15. #4746C2semidirect
17. #1010C22semidirect
18. #1009C22semidirect
20. #1004C22semidirect
21. C3×AGL(1,ℤ/8)C22semidirect
22. C3×AGL(1,ℤ/8)C22semidirect
23. C2×C3×D8C22semidirect
24. C3×#131C22semidirect
26. #940C22semidirect
27. #936C22semidirect
28. C2×#214C22semidirect
30. #932C22semidirect
31. C2×#213C22semidirect
45. #909C22semidirect
46. #909C22semidirect
49. #908C22semidirect
50. #907C22semidirect
51. #907C22semidirect
55. C2×#204C22semidirect
56. #901C22semidirect
57. C3×#108C22semidirect
58. C3×#100C22semidirect
59. C3×#100C22semidirect
60. #837C22semidirect
61. #825C22semidirect
62. #825C22semidirect
63. #825C22semidirect
64. #824C22semidirect
65. #823C22semidirect
66. #822C22semidirect
67. #815C22semidirect
74. #472D3semidirect
125. #216D4semidirect
126. #215D4semidirect
131. #214D4semidirect
136. #213D4semidirect
142. Dic12D4semidirect
145. D24D4semidirect
152. #204D4semidirect
153. #204D4semidirect
178. AGL(1,ℤ/8)C2×D3semidirect
179. AGL(1,ℤ/8)C2×D3semidirect
193. C2×D8C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
208. #100C2×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
#57752
#57742
#57572
#57512
C3×#4722
#52012
#51982
#51542
#51452
#48982
#48942
#47492
#47482
#47472
#47462
#32883