Finite Group Databasebeta

← #79900

Subgroups — #79900

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#5770C211yesmaximal, characteristic, complemented
2#5769C211yesmaximal, characteristic, complemented
3#5752C211yesmaximal, characteristic, complemented
4#5751C211yesmaximal, characteristic, complemented
5C3×#444C211yesmaximal, characteristic, complemented
6#5142C211yesmaximal, characteristic, complemented
7#5141C211yesmaximal, characteristic, complemented
8#4898C211yesmaximal, characteristic, complemented
9#4897C211yesmaximal, characteristic, complemented
10#4827C211yesmaximal, characteristic, complemented
11#4825C211yesmaximal, characteristic, complemented
12#4822C211yesmaximal, characteristic, complemented
13#4822C211yesmaximal, characteristic, complemented
14#4717C211yesmaximal, characteristic, complemented
15#4712C211yesmaximal, characteristic, complemented
16#3288—31nomaximal, Sylow
17#1010C2211yescharacteristic, complemented
18#1009C2211yescharacteristic
19#1009C2211yescharacteristic, complemented
20#1009C2211yescharacteristic, complemented
21C3×#135C2211yescharacteristic
22C3×#131C2211yescharacteristic, complemented
23C3×#131C2211yescharacteristic, complemented
24#951C2211yescharacteristic, complemented
25#949C2211yescharacteristic
26#949C2211yescharacteristic, complemented
27#949C2211yescharacteristic, complemented
28#919—21no—
29#918—21no—
30#916—21no—
31#914—21no—
32#914—21no—
33D3×SD16—21no—
34#911—21no—
35D3×D8—21no—
36#909—21no—
37#909C2211yescharacteristic, complemented
38#908—21no—
39#908—21no—
40#908—21no—
41#908C2211yescharacteristic
42#908C2211yescharacteristic, complemented
43#908C2211yescharacteristic, complemented
44#904—21no—
45#904—21no—
46#904C2211yescharacteristic
47C2×D24—21no—
48C2×D24C2211yescharacteristic, complemented
49C2×D24C2211yescharacteristic, complemented
50C2×#204—21no—
51C2×#204C2211yescharacteristic, complemented
52C2×#204C2211yescharacteristic, complemented
53#901C2211yescharacteristic, complemented
54#901C2211yescharacteristic, complemented
55#875C2211yescharacteristic, complemented
56#874C2211yescharacteristic, complemented
57C3×#108C2211yescharacteristic, complemented
58C3×#104C2211yescharacteristic, complemented
59C3×#104C2211yescharacteristic, complemented
60C3×#97C2211yescharacteristic, complemented
61#824C2211yescharacteristic, complemented
62#823C2211yescharacteristic, complemented
63#823C2211yescharacteristic, complemented
64#823C2211yescharacteristic, complemented
65#819C2211yescharacteristic, complemented
66#805C2211yescharacteristic, complemented
67#805C2211yescharacteristic, 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#471—31no—
77#455—31no—
78#454—31no—
79#453—31no—
80#453—31no—
81#444—31no—
82#444D311yescharacteristic, complemented
83C3×#41C2311yescharacteristic
84C3×#41C2311yescharacteristic
85#239—21no—
86#239—21no—
87#239—21no—
88D3×Q8—21no—
89#237—21no—
90#237—41no—
91D3×D4—21no—
92D3×D4—21no—
93D3×D4—21no—
94D3×D4—41no—
95D3×D4—41no—
96D3×D4—41no—
97#235—21no—
98#235—21no—
99#235—21no—
100#235—21no—
101#235C2311yescharacteristic
102#235C2311yescharacteristic
103C2×D12—21no—
104C2×D12—21no—
105C2×D12—21no—
106C2×D12—41no—
107C2×D12C2311yescharacteristic
108C2×D12C2311yescharacteristic
109C2×D12C2311yescharacteristic
110C2×Dic6—21no—
111C2×Dic6C2311yescharacteristic
112C3×Q16D411yescharacteristic, complemented
113C3×SD16D411yescharacteristic, complemented
114C3×SD16D411yescharacteristic, complemented
115C3×D8D411yescharacteristic, complemented
116C3×M16—21no—
117C3×M16—21no—
118C3×M16C2311yescharacteristic
119C3×M16C2311yescharacteristic
120C2×C3×C8—21no—
121C2×C3×C8—21no—
122C2×C3×C8C2311yescharacteristic
123C2×C3×C8C2311yescharacteristic
124C3×C42C2311yescharacteristic
125#216—21no—
126#215—21no—
127#215—21no—
128#215—21no—
129#214—21no—
130#213—21no—
131#213—21no—
132#213—21no—
133(C2×D3)⋊C4—41no—
134#208C2311yescharacteristic
135#208C2311yescharacteristic
136Dic12—21no—
137Dic12D411yescharacteristic, complemented
138D24—21no—
139D24—21no—
140D24—21no—
141D24—21no—
142D24—21no—
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#204—21no—
153#204—21no—
154#204D411yescharacteristic, complemented
155#204D411yescharacteristic, complemented
156ΓL(1,𝔽25)—21no—
157ΓL(1,𝔽25)—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)—31no—
173AGL(1,ℤ/8)—31no—
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)—61no—
180#135—31no—
181#135—61no—
182#135—61no—
183#135—61no—
184#135—61no—
185#135C2×D311yescharacteristic
186C2×SD16—31no—
187C2×SD16—31no—
188C2×SD16—61no—
189C2×SD16—61no—
190C2×D8—31no—
191C2×D8—31no—
192C2×D8—61no—
193C2×D8—61no—
194#131—31no—
195#131—31no—
196#131C2×D311yescharacteristic, complemented
197#131C2×D311yescharacteristic, complemented
198#127—31no—
199#124—31no—
200#108—31no—
201#108C2×D311yescharacteristic, complemented
202#104—31no—
203#104—31no—
204#104C2×D311yescharacteristic, complemented
205#104C2×D311yescharacteristic, complemented
206#101—31no—
207#100—31no—
208#100—31no—
209#100—31no—
210#97C2×D311yescharacteristic, complemented
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—41no—
217C3×Q8C2×D411yescharacteristic
218C3×Q8C2×D411yescharacteristic
219C3×D4—21no—
220C3×D4—21no—
221C3×D4C2×D411yescharacteristic
222C3×D4C2×D411yescharacteristic
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4C2411yescharacteristic
227#67—21no—
228#67—21no—
229#67—41no—
230#67—41no—
231#67—41no—
232#67—41no—
233C2×Dic3—21no—
234C2×Dic3—41no—
235D12—21no—
236D12—21no—
237D12—21no—
238D12—21no—
239D12—21no—
240D12—21no—
241D12—41no—
242D12—41no—
243D12—41no—
244D12—82no—
245D12C2×D411yescharacteristic
246D12C2×D411yescharacteristic
247C4×D3—21no—
248C4×D3—21no—
249C4×D3—41no—
250C4×D3—41no—
251C4×D3—41no—
252C4×D3—41no—
253Dic6—21no—
254Dic6—21no—
255Dic6—41no—
256Dic6C2×D411yescharacteristic
257Dic6C2×D411yescharacteristic
258C3×C8—21no—
259C3×C8—21no—
260C3×C8C2×D411yescharacteristic
261C3×C8C2×D411yescharacteristic
262C3×C8C2×D411yescharacteristic
263C3×C8C2×D411yescharacteristic
264C3⋊C8—21no—
265C3⋊C8—21no—
266#41—31no—
267#41—31no—
268#41—61no—
269#41—61no—
270#41—61no—
271#41—61no—
272#41—61no—
273#41—61no—
274#41—61no—
275#41—61no—
276#41—121no—
277#41C22×D311yescharacteristic
278#41C22×D311yescharacteristic
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8—61no—
282C2×D4—31no—
283C2×D4—31no—
284C2×D4—31no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—121no—
292C2×D4—121no—
293C2×D4—121no—
294C2×D4—121no—
295Q16—31no—
296Q16—61no—
297Q16—61no—
298Q16D1211yescharacteristic, complemented
299SD16—31no—
300SD16—31no—
301SD16—61no—
302SD16—61no—
303SD16—61no—
304SD16—61no—
305SD16—61no—
306SD16—61no—
307SD16—61no—
308SD16—61no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312SD16—61no—
313SD16D1211yescharacteristic, complemented
314SD16D1211yescharacteristic, complemented
315D8—31no—
316D8—61no—
317D8—61no—
318D8—61no—
319D8—61no—
320D8—61no—
321D8—61no—
322D8—61no—
323D8—61no—
324D8—61no—
325D8—61no—
326D8D1211yescharacteristic, complemented
327M16—21no—
328M16—21no—
329M16—31no—
330M16—31no—
331M16—61no—
332M16—61no—
333M16C22×D311yescharacteristic
334M16C22×D311yescharacteristic
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8C22×D311yescharacteristic
340C2×C8C22×D311yescharacteristic
341C22⋊C4—121no—
342C42C22×D311yescharacteristic
343C22×C3—21no—
344C22×C3—21no—
345C22×C3H(5,𝔽2)11yescharacteristic
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—81no—
352C2×D3—81no—
353C2×D3—81no—
354C2×D3—161no—
355C2×D3—161no—
356C2×D3—161no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4C22×D411yescharacteristic
361C3×C4C22×D411yescharacteristic
362Dic3—21no—
363Dic3—21no—
364Dic3—41no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—121no—
369C23—121no—
370C23—121no—
371Q8—31no—
372Q8—31no—
373Q8—61no—
374Q8—61no—
375Q8—121no—
376Q8C2×D1211yescharacteristic
377Q8C2×D1211yescharacteristic
378D4—21no—
379D4—21no—
380D4—31no—
381D4—31no—
382D4—61no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—61no—
389D4—61no—
390D4—121no—
391D4—121no—
392D4—121no—
393D4—121no—
394D4—121no—
395D4—121no—
396D4—121no—
397D4—242no—
398D4C2×D1211yescharacteristic
399D4C2×D1211yescharacteristic
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
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—61no—
415C8—61no—
416C8C2×D1211yescharacteristic
417C8C2×D1211yescharacteristic
418C8D3×D411yescharacteristic
419C8D3×D411yescharacteristic
420C2×C3—21no—
421C2×C3—41no—
422C2×C3—41no—
423C2×C3D4211yescharacteristic
424D3—41no—
425D3—41no—
426D3—81no—
427D3—81no—
428D3—81no—
429C22—21no—
430C22—21no—
431C22—61no—
432C22—61no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22—241no—
437C22—241no—
438C22—241no—
439C22—481no—
440C22—481no—
441C22—481no—
442C22#100911yescharacteristic
443C4—21no—
444C4—21no—
445C4—41no—
446C4—61no—
447C4—61no—
448C4—121no—
449C4C22×D1211yescharacteristic
450C4C2×D3×D411yescharacteristic
451C3#328811yescharacteristic, complemented, Sylow
452C2—21no—
453C2—41no—
454C2—41no—
455C2—121no—
456C2—121no—
457C2—241no—
458C2—241no—
459C2—241no—
460C2D4×D1211yescharacteristic
subgroupG/H
centerC2D4×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#444C2
socleC2×C3D42
hypercenter#444D3
hypocenterC3#3288
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #5770C2semidirect
2. #5769C2semidirect
3. #5752C2semidirect
4. #5751C2semidirect
5. C3×#444C2semidirect
6. #5142C2semidirect
7. #5141C2semidirect
8. #4898C2semidirect
9. #4897C2semidirect
10. #4827C2semidirect
11. #4825C2semidirect
12. #4822C2semidirect
13. #4822C2semidirect
14. #4717C2semidirect
15. #4712C2semidirect
17. #1010C22semidirect
19. #1009C22semidirect
20. #1009C22semidirect
22. C3×#131C22semidirect
23. C3×#131C22semidirect
24. #951C22semidirect
26. #949C22semidirect
27. #949C22semidirect
37. #909C22semidirect
42. #908C22semidirect
43. #908C22semidirect
48. C2×D24C22semidirect
49. C2×D24C22semidirect
51. C2×#204C22semidirect
52. C2×#204C22semidirect
53. #901C22semidirect
54. #901C22semidirect
55. #875C22semidirect
56. #874C22semidirect
57. C3×#108C22semidirect
58. C3×#104C22semidirect
59. C3×#104C22semidirect
60. C3×#97C22semidirect
61. #824C22semidirect
62. #823C22semidirect
63. #823C22semidirect
64. #823C22semidirect
65. #819C22semidirect
66. #805C22semidirect
67. #805C22semidirect
82. #444D3semidirect
112. C3×Q16D4semidirect
113. C3×SD16D4semidirect
114. C3×SD16D4semidirect
115. C3×D8D4semidirect
137. Dic12D4semidirect
145. D24D4semidirect
154. #204D4semidirect
155. #204D4semidirect
196. #131C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
204. #104C2×D3semidirect
205. #104C2×D3semidirect
210. #97C2×D3semidirect
298. Q16D12semidirect
313. SD16D12semidirect
314. SD16D12semidirect
326. D8D12semidirect
451. C3#3288semidirect

Maximal subgroups

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

subgroupindex
#57702
#57692
#57522
#57512
C3×#4442
#51422
#51412
#48982
#48972
#48272
#48252
#48222
#47172
#47122
#32883