Finite Group Databasebeta

← #80935

Subgroups — #80935

Order 384.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5778C211yesmaximal, characteristic, complemented
2#5775C211yesmaximal, characteristic, complemented
3#5762C211yesmaximal, characteristic, complemented
4#5751C211yesmaximal, characteristic, complemented
5C3×#471C211yesmaximal, characteristic, complemented
6#5205C211yesmaximal, characteristic, complemented
7#5198C211yesmaximal, characteristic, complemented
8#5175C211yesmaximal, characteristic, complemented
9#5144C211yesmaximal, characteristic, complemented
10#4898C211yesmaximal, characteristic, complemented
11#4895C211yesmaximal, characteristic, complemented
12#4754C211yesmaximal, characteristic, complemented
13#4752C211yesmaximal, characteristic, complemented
14#4748C211yesmaximal, characteristic, complemented
15#4747C211yesmaximal, characteristic, complemented
16#3291—31nomaximal, Sylow
17#1010C2211yescharacteristic
18#1009C2211yescharacteristic, complemented
19#1007C2211yescharacteristic
20#1004C2211yescharacteristic, complemented
21C3×#137C2211yescharacteristic, complemented
22C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×SD16C2211yescharacteristic, complemented
24C3×#131C2211yescharacteristic, complemented
25#950C2211yescharacteristic
26#944C2211yescharacteristic, complemented
27#942C2211yescharacteristic, complemented
28C2×#215C2211yescharacteristic, complemented
29#940C2211yescharacteristic
30C2×#214C2211yescharacteristic, complemented
31#932C2211yescharacteristic
32#919—21no—
33#918—21no—
34#916—21no—
35#915—21no—
36#915—21no—
37#914—21no—
38#914—21no—
39D3×SD16—21no—
40D3×SD16—21no—
41D3×SD16—21no—
42#912—21no—
43#911—21no—
44#909—21no—
45#909C2211yescharacteristic, complemented
46#909C2211yescharacteristic, complemented
47#908—21no—
48#908C2211yescharacteristic
49#908C2211yescharacteristic
50#907C2211yescharacteristic, complemented
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, complemented
62#825C2211yescharacteristic, complemented
63#825C2211yescharacteristic, complemented
64#824C2211yescharacteristic, complemented
65#823C2211yescharacteristic, complemented
66#822C2211yescharacteristic, complemented
67C8×Dic3C2211yescharacteristic, complemented
68#577—31no—
69#577—31no—
70#577—31no—
71#577—31no—
72#492—31no—
73#471—31no—
74#471—31no—
75#471—31no—
76#471D311yescharacteristic, complemented
77#456—31no—
78#456—31no—
79#453—31no—
80#453—31no—
81#443—31no—
82#443—31no—
83C3×#41C2311yescharacteristic
84C2×C3×Q8C2311yescharacteristic
85C2×C3×D4C2311yescharacteristic
86C2×#67—41no—
87C2×#67—41no—
88#239—21no—
89#239—21no—
90#239—21no—
91D3×Q8—21no—
92D3×Q8—21no—
93D3×Q8—21no—
94#237—21no—
95#237—21no—
96#237—21no—
97#237—41no—
98D3×D4—21no—
99D3×D4—21no—
100D3×D4—21no—
101D3×D4—41no—
102#235—21no—
103#235—21no—
104#235—41no—
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107#235C2311yescharacteristic
108C2×D12—21no—
109C2×D12C2311yescharacteristic
110C2×Dic6—21no—
111C2×Dic6C2311yescharacteristic
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#214—21no—
132#214—21no—
133#214D411yescharacteristic, complemented
134#213—21no—
135#213D411yescharacteristic, complemented
136Dic3⋊C4—41no—
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—
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×SD16—31no—
187C2×SD16—31no—
188C2×SD16—31no—
189C2×SD16—61no—
190C2×SD16—61no—
191C2×SD16—61no—
192C2×SD16—61no—
193C2×SD16C2×D311yescharacteristic, complemented
194#131—31no—
195#131—31no—
196#131—31no—
197#131C2×D311yescharacteristic, complemented
198C4⋊Q8—31no—
199#127—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—
232#67—82no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3—41no—
236C2×Dic3—41no—
237D12—21no—
238D12—21no—
239D12—41no—
240D12—41no—
241D12C2×D411yescharacteristic
242D12C2×D411yescharacteristic
243D12C2×D411yescharacteristic
244C4×D3—21no—
245C4×D3—21no—
246C4×D3—21no—
247C4×D3—41no—
248C4×D3—41no—
249C4×D3—41no—
250C4×D3—41no—
251Dic6—21no—
252Dic6—21no—
253Dic6—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#41—121no—
279#41C22×D311yescharacteristic
280C2×Q8—31no—
281C2×Q8—61no—
282C2×Q8—61no—
283C2×Q8—61no—
284C2×Q8—61no—
285C2×Q8C22×D311yescharacteristic
286C2×D4—31no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—121no—
292C2×D4—121no—
293C2×D4—121no—
294C2×D4C22×D311yescharacteristic
295Q16—21no—
296Q16—31no—
297Q16—31no—
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—
317SD16—61no—
318SD16—61no—
319SD16—61no—
320SD16—61no—
321D8—21no—
322D8—31no—
323D8—31no—
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
341C4⋊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—81no—
352C2×D3—161no—
353C2×D3—161no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4C22×D411yescharacteristic
357C3×C4C22×D411yescharacteristic
358Dic3—22no—
359Dic3—21no—
360Dic3—21no—
361Dic3—21no—
362Dic3—41no—
363C23—21no—
364C23—61no—
365C23—121no—
366C23—121no—
367Q8—21no—
368Q8—21no—
369Q8—31no—
370Q8—31no—
371Q8—31no—
372Q8—61no—
373Q8—61no—
374Q8—121no—
375Q8—121no—
376Q8D3×D411yescharacteristic
377D4—21no—
378D4—21no—
379D4—21no—
380D4—31no—
381D4—31no—
382D4—31no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—121no—
392D4—121no—
393D4—121no—
394D4—242no—
395D4D3×D411yescharacteristic
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4C23×D311yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—31no—
414C8—31no—
415C8—61no—
416C8D3×D411yescharacteristic
417C8D3×D411yescharacteristic
418C2×C3—21no—
419C2×C3—41no—
420C2×C3—81no—
421C2×C3D4211yescharacteristic
422D3—41no—
423D3—41no—
424D3—41no—
425D3—81no—
426C22—21no—
427C22—41no—
428C22—61no—
429C22—61no—
430C22—61no—
431C22—81no—
432C22—121no—
433C22—241no—
434C22—481no—
435C22—481no—
436C22#100911yescharacteristic
437C4—21no—
438C4—41no—
439C4—62no—
440C4—61no—
441C4—61no—
442C4—61no—
443C4—121no—
444C4C2×D3×D411yescharacteristic
445C4C2×D3×D411yescharacteristic
446C3#329111yescharacteristic, complemented, Sylow
447C2—21no—
448C2—41no—
449C2—81no—
450C2—121no—
451C2—121no—
452C2—121no—
453C2—241no—
454C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#471C2
socleC2×C3D42
hypercenter#471D3
hypocenterC3#3291
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. #5775C2semidirect
3. #5762C2semidirect
4. #5751C2semidirect
5. C3×#471C2semidirect
6. #5205C2semidirect
7. #5198C2semidirect
8. #5175C2semidirect
9. #5144C2semidirect
10. #4898C2semidirect
11. #4895C2semidirect
12. #4754C2semidirect
13. #4752C2semidirect
14. #4748C2semidirect
15. #4747C2semidirect
18. #1009C22semidirect
20. #1004C22semidirect
21. C3×#137C22semidirect
23. C2×C3×SD16C22semidirect
24. C3×#131C22semidirect
26. #944C22semidirect
27. #942C22semidirect
28. C2×#215C22semidirect
30. C2×#214C22semidirect
45. #909C22semidirect
46. #909C22semidirect
50. #907C22semidirect
51. #907C22semidirect
55. C2×#204C22semidirect
56. #901C22semidirect
57. C3×#108C22semidirect
58. C3×#101C22semidirect
59. C3×#100C22semidirect
60. #837C22semidirect
61. #825C22semidirect
62. #825C22semidirect
63. #825C22semidirect
64. #824C22semidirect
65. #823C22semidirect
66. #822C22semidirect
67. C8×Dic3C22semidirect
76. #471D3semidirect
125. #216D4semidirect
129. #215D4semidirect
133. #214D4semidirect
135. #213D4semidirect
142. Dic12D4semidirect
145. D24D4semidirect
152. #204D4semidirect
153. #204D4semidirect
171. #137C2×D3semidirect
193. C2×SD16C2×D3semidirect
197. #131C2×D3semidirect
201. #108C2×D3semidirect
207. #101C2×D3semidirect
209. #100C2×D3semidirect
446. C3#3291semidirect

Maximal subgroups

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

subgroupindex
#57782
#57752
#57622
#57512
C3×#4712
#52052
#51982
#51752
#51442
#48982
#48952
#47542
#47522
#47482
#47472
#32913