Finite Group Databasebeta

← #80934

Subgroups — #80934

Order 384.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5779C211yesmaximal, characteristic, complemented
2#5774C211yesmaximal, characteristic, complemented
3#5762C211yesmaximal, characteristic, complemented
4#5751C211yesmaximal, characteristic, complemented
5C3×#471C211yesmaximal, characteristic, complemented
6#5202C211yesmaximal, characteristic, complemented
7#5201C211yesmaximal, characteristic, complemented
8#5168C211yesmaximal, characteristic, complemented
9#5144C211yesmaximal, characteristic, complemented
10#4898C211yesmaximal, characteristic, complemented
11#4895C211yesmaximal, characteristic, complemented
12#4755C211yesmaximal, characteristic, complemented
13#4753C211yesmaximal, characteristic, complemented
14#4749C211yesmaximal, characteristic, complemented
15#4746C211yesmaximal, characteristic, complemented
16#3290—31nomaximal, Sylow
17#1010C2211yescharacteristic, complemented
18#1009C2211yescharacteristic
19#1007C2211yescharacteristic, complemented
20#1004C2211yescharacteristic
21C3×#137C2211yescharacteristic, complemented
22C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×SD16C2211yescharacteristic, complemented
24C3×#131C2211yescharacteristic, complemented
25#950C2211yescharacteristic
26#947C2211yescharacteristic, complemented
27C2×#216C2211yescharacteristic, complemented
28#942C2211yescharacteristic
29#936C2211yescharacteristic, complemented
30#932C2211yescharacteristic, complemented
31C2×#213C2211yescharacteristic
32#918—21no—
33D3×Q16—21no—
34#916—21no—
35#916—21no—
36#916—21no—
37#915—21no—
38#915—21no—
39#914—21no—
40#914—21no—
41D3×SD16—21no—
42#911—21no—
43D3×D8—21no—
44#909—21no—
45#909C2211yescharacteristic
46#909C2211yescharacteristic, complemented
47#908—21no—
48#908C2211yescharacteristic
49#908C2211yescharacteristic, complemented
50#907C2211yescharacteristic
51#907C2211yescharacteristic, complemented
52#904—21no—
53#904C2211yescharacteristic
54C2×#204—21no—
55C2×#204C2211yescharacteristic, complemented
56#901C2211yescharacteristic, complemented
57C3×#108C2211yescharacteristic, complemented
58C3×#101C2211yescharacteristic, complemented
59C3×#100C2211yescharacteristic, complemented
60#837C2211yescharacteristic, complemented
61#825C2211yescharacteristic
62#825C2211yescharacteristic, complemented
63#825C2211yescharacteristic, complemented
64#824C2211yescharacteristic, complemented
65#823C2211yescharacteristic, complemented
66#822C2211yescharacteristic, complemented
67C8×Dic3C2211yescharacteristic, complemented
68#578—31no—
69#577—31no—
70#577—31no—
71#576—31no—
72#495—31no—
73#473—31no—
74#472—31no—
75#471—31no—
76#471D311yescharacteristic, complemented
77#455—31no—
78#455—31no—
79#454—31no—
80#454—31no—
81#443—31no—
82#443—31no—
83C3×#41C2311yescharacteristic
84C2×C3×Q8C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C2×#67—41no—
87#239—21no—
88#239—21no—
89#239—21no—
90D3×Q8—21no—
91D3×Q8—21no—
92D3×Q8—21no—
93#237—21no—
94#237—21no—
95#237—21no—
96#237—41no—
97D3×D4—21no—
98D3×D4—21no—
99D3×D4—21no—
100D3×D4—41no—
101#235—21no—
102#235—21no—
103#235—41no—
104#235C2311yescharacteristic
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107C2×D12—21no—
108C2×D12C2311yescharacteristic
109C2×Dic6—21no—
110C2×Dic6C2311yescharacteristic
111C3×Q16—21no—
112C3×SD16—21no—
113C3×SD16—21no—
114C3×SD16—21no—
115C3×SD16—21no—
116C3×D8—21no—
117C3×M16—21no—
118C3×M16C2311yescharacteristic
119C3×M16C2311yescharacteristic
120C3×M16C2311yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8C2311yescharacteristic
123#217—41no—
124#216—21no—
125#216—21no—
126#216—21no—
127#216D411yescharacteristic
128#215—21no—
129#215D411yescharacteristic
130#214—21no—
131#214D411yescharacteristic
132#213—21no—
133#213—21no—
134#213—21no—
135#213D411yescharacteristic
136(C2×D3)⋊C4—41no—
137C4×Dic3C2311yescharacteristic
138#208C2311yescharacteristic
139C2×C3⋊C8C2311yescharacteristic
140Dic12—21no—
141Dic12—21no—
142Dic12D411yescharacteristic
143D24—21no—
144D24—21no—
145D24D411yescharacteristic
146#204—21no—
147#204—21no—
148#204—21no—
149#204—21no—
150#204—21no—
151#204—21no—
152#204D411yescharacteristic
153#204D411yescharacteristic
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—
1612−1+4—31no—
162H(5,𝔽2)—31no—
163H(5,𝔽2)—31no—
164#137—31no—
165#137—31no—
166#137—31no—
167#137—61no—
168#137—61no—
169#137—61no—
170#137—61no—
171#137C2×D311yescharacteristic, complemented
172AGL(1,ℤ/8)—31no—
173AGL(1,ℤ/8)—31no—
174AGL(1,ℤ/8)—31no—
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×Q16—31no—
187C2×Q16—61no—
188C2×SD16—31no—
189C2×SD16—61no—
190C2×SD16—61no—
191C2×SD16C2×D311yescharacteristic, complemented
192C2×D8—31no—
193C2×D8—61no—
194#131—31no—
195#131—31no—
196#131—31no—
197#131C2×D311yescharacteristic, complemented
198#124—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#101C2×D311yescharacteristic, complemented
208#100—31no—
209#100C2×D311yescharacteristic, complemented
210C4×C8—31no—
211C23×C3—21no—
212C22×D3—21no—
213C22×D3—41no—
214C22×D3—41no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8C2×D411yescharacteristic
218C3×D4—21no—
219C3×D4—21no—
220C3×D4—21no—
221C3×D4C2×D411yescharacteristic
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4C2411yescharacteristic
225#67—21no—
226#67—21no—
227#67—21no—
228#67—41no—
229#67—41no—
230#67—41no—
231#67—41no—
232C2×Dic3—21no—
233C2×Dic3—21no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236D12—21no—
237D12—21no—
238D12—41no—
239D12—41no—
240D12C2×D411yescharacteristic
241D12C2×D411yescharacteristic
242D12C2×D411yescharacteristic
243C4×D3—21no—
244C4×D3—21no—
245C4×D3—21no—
246C4×D3—41no—
247C4×D3—41no—
248C4×D3—41no—
249C4×D3—41no—
250Dic6—21no—
251Dic6—21no—
252Dic6—41no—
253Dic6—41no—
254Dic6C2×D411yescharacteristic
255Dic6C2×D411yescharacteristic
256Dic6C2×D411yescharacteristic
257C3×C8—21no—
258C3×C8—21no—
259C3×C8—21no—
260C3×C8C2×D411yescharacteristic
261C3×C8C2×D411yescharacteristic
262C3⋊C8—21no—
263C3⋊C8C2×D411yescharacteristic
264C3⋊C8C2×D411yescharacteristic
265#41—31no—
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#41—121no—
278#41C22×D311yescharacteristic
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8—61no—
282C2×Q8—61no—
283C2×Q8—61no—
284C2×Q8C22×D311yescharacteristic
285C2×D4—31no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—121no—
291C2×D4—121no—
292C2×D4C22×D311yescharacteristic
293Q16—21no—
294Q16—31no—
295Q16—31no—
296Q16—61no—
297Q16—61no—
298Q16—61no—
299Q16—61no—
300Q16—61no—
301SD16—21no—
302SD16—21no—
303SD16—21no—
304SD16—21no—
305SD16—31no—
306SD16—31no—
307SD16—31no—
308SD16—31no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312SD16—61no—
313SD16—61no—
314SD16—61no—
315SD16—61no—
316SD16—61no—
317D8—21no—
318D8—31no—
319D8—31no—
320D8—61no—
321D8—61no—
322D8—61no—
323D8—61no—
324D8—61no—
325M16—21no—
326M16—31no—
327M16—61no—
328M16—61no—
329M16—61no—
330M16C22×D311yescharacteristic
331M16C22×D311yescharacteristic
332M16C22×D311yescharacteristic
333C2×C8—21no—
334C2×C8—31no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8C22×D311yescharacteristic
339C22⋊C4—121no—
340C22⋊C4—121no—
341C42—31no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—81no—
345C22×C3H(5,𝔽2)11yescharacteristic
346C2×D3—21no—
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—41no—
350C2×D3—81no—
351C2×D3—161no—
352C2×D3—161no—
353C3×C4—21no—
354C3×C4—41no—
355C3×C4C22×D411yescharacteristic
356C3×C4C22×D411yescharacteristic
357Dic3—21no—
358Dic3—21no—
359Dic3—21no—
360Dic3—41no—
361Dic3—41no—
362C23—21no—
363C23—61no—
364C23—121no—
365C23—121no—
366Q8—21no—
367Q8—21no—
368Q8—31no—
369Q8—31no—
370Q8—31no—
371Q8—61no—
372Q8—61no—
373Q8—121no—
374Q8—121no—
375Q8D3×D411yescharacteristic
376D4—21no—
377D4—21no—
378D4—21no—
379D4—31no—
380D4—31no—
381D4—31no—
382D4—61no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—121no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—121no—
392D4—121no—
393D4D3×D411yescharacteristic
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4C23×D311yescharacteristic
408C8—21no—
409C8—21no—
410C8—21no—
411C8—31no—
412C8—31no—
413C8—61no—
414C8D3×D411yescharacteristic
415C8D3×D411yescharacteristic
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—81no—
419C2×C3D4211yescharacteristic
420D3—41no—
421D3—41no—
422D3—41no—
423D3—81no—
424C22—21no—
425C22—41no—
426C22—61no—
427C22—61no—
428C22—61no—
429C22—81no—
430C22—121no—
431C22—241no—
432C22—481no—
433C22—481no—
434C22#100911yescharacteristic
435C4—21no—
436C4—41no—
437C4—61no—
438C4—61no—
439C4—61no—
440C4—121no—
441C4—121no—
442C4C2×D3×D411yescharacteristic
443C4C2×D3×D411yescharacteristic
444C3#329011yescharacteristic, complemented, Sylow
445C2—21no—
446C2—41no—
447C2—81no—
448C2—121no—
449C2—121no—
450C2—121no—
451C2—241no—
452C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#471C2
socleC2×C3D42
hypercenter#471D3
hypocenterC3#3290
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. #5779C2semidirect
2. #5774C2semidirect
3. #5762C2semidirect
4. #5751C2semidirect
5. C3×#471C2semidirect
6. #5202C2semidirect
7. #5201C2semidirect
8. #5168C2semidirect
9. #5144C2semidirect
10. #4898C2semidirect
11. #4895C2semidirect
12. #4755C2semidirect
13. #4753C2semidirect
14. #4749C2semidirect
15. #4746C2semidirect
17. #1010C22semidirect
19. #1007C22semidirect
21. C3×#137C22semidirect
23. C2×C3×SD16C22semidirect
24. C3×#131C22semidirect
26. #947C22semidirect
27. C2×#216C22semidirect
29. #936C22semidirect
30. #932C22semidirect
46. #909C22semidirect
49. #908C22semidirect
51. #907C22semidirect
55. C2×#204C22semidirect
56. #901C22semidirect
57. C3×#108C22semidirect
58. C3×#101C22semidirect
59. C3×#100C22semidirect
60. #837C22semidirect
62. #825C22semidirect
63. #825C22semidirect
64. #824C22semidirect
65. #823C22semidirect
66. #822C22semidirect
67. C8×Dic3C22semidirect
76. #471D3semidirect
171. #137C2×D3semidirect
191. C2×SD16C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
207. #101C2×D3semidirect
209. #100C2×D3semidirect
444. C3#3290semidirect

Maximal subgroups

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

subgroupindex
#57792
#57742
#57622
#57512
C3×#4712
#52022
#52012
#51682
#51442
#48982
#48952
#47552
#47532
#47492
#47462
#32903