Finite Group Databasebeta

← #80945

Subgroups — #80945

Order 384.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5779C211yesmaximal, characteristic, complemented
2#5778C211yesmaximal, characteristic, complemented
3#5766C211yesmaximal, characteristic, complemented
4#5751C211yesmaximal, characteristic, complemented
5C3×#473C211yesmaximal, characteristic, complemented
6#5205C211yesmaximal, characteristic, complemented
7#5202C211yesmaximal, characteristic, complemented
8#5190C211yesmaximal, characteristic, complemented
9#5145C211yesmaximal, characteristic, complemented
10#4898C211yesmaximal, characteristic, complemented
11#4894C211yesmaximal, characteristic, complemented
12#4755C211yesmaximal, characteristic, complemented
13#4754C211yesmaximal, characteristic, complemented
14#4753C211yesmaximal, characteristic, complemented
15#4752C211yesmaximal, characteristic, complemented
16#3289—31nomaximal, Sylow
17#1010C2211yescharacteristic
18#1009C2211yescharacteristic
19#1007C2211yescharacteristic
20#1007C2211yescharacteristic, complemented
21C3×#137C2211yescharacteristic
22C3×#137C2211yescharacteristic
23C2×C3×Q16C2211yescharacteristic, complemented
24C3×#131C2211yescharacteristic
25#950C2211yescharacteristic
26#947C2211yescharacteristic
27#944C2211yescharacteristic, complemented
28C2×#216C2211yescharacteristic, complemented
29#942C2211yescharacteristic
30#942C2211yescharacteristic, complemented
31C2×#215C2211yescharacteristic
32#919—21no—
33#919—21no—
34#918—21no—
35#918—21no—
36#918—21no—
37#918—21no—
38D3×Q16—21no—
39D3×Q16—21no—
40#916—21no—
41#915—21no—
42#914—21no—
43D3×SD16—21no—
44#909—21no—
45#909C2211yescharacteristic
46#909C2211yescharacteristic, complemented
47#908—21no—
48#908C2211yescharacteristic
49#908C2211yescharacteristic
50#907C2211yescharacteristic
51#907C2211yescharacteristic, complemented
52#904—21no—
53#904C2211yescharacteristic
54C2×#204—21no—
55C2×#204C2211yescharacteristic
56#901C2211yescharacteristic, complemented
57C3×#108C2211yescharacteristic, complemented
58C3×#101C2211yescharacteristic, complemented
59C3×#101C2211yescharacteristic, complemented
60#837C2211yescharacteristic
61#825C2211yescharacteristic
62#825C2211yescharacteristic, complemented
63#825C2211yescharacteristic, complemented
64#824C2211yescharacteristic, complemented
65#823C2211yescharacteristic
66#822C2211yescharacteristic, complemented
67#815C2211yescharacteristic, complemented
68#578—31no—
69#578—31no—
70#577—31no—
71#577—31no—
72#497—31no—
73#473—31no—
74#473D311yescharacteristic, complemented
75#471—31no—
76#471—31no—
77#456—31no—
78#456—31no—
79#455—31no—
80#454—31no—
81#444—31no—
82#444—31no—
83C3×#41C2311yescharacteristic
84C2×C3×Q8C2311yescharacteristic
85C2×C3×Q8C2311yescharacteristic
86#239—21no—
87#239—21no—
88#239—21no—
89#239—21no—
90#239—21no—
91D3×Q8—21no—
92D3×Q8—21no—
93D3×Q8—21no—
94D3×Q8—21no—
95D3×Q8—21no—
96#237—21no—
97#237—41no—
98D3×D4—21no—
99D3×D4—41no—
100#235—21no—
101#235—21no—
102#235—41no—
103#235—41no—
104#235C2311yescharacteristic
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107C2×D12—21no—
108C2×D12C2311yescharacteristic
109C2×Dic6—21no—
110C2×Dic6C2311yescharacteristic
111C3×Q16—21no—
112C3×Q16—21no—
113C3×Q16—21no—
114C3×Q16—21no—
115C3×SD16—21no—
116C3×SD16—21no—
117C3×M16—21no—
118C3×M16C2311yescharacteristic
119C3×M16C2311yescharacteristic
120C3×M16C2311yescharacteristic
121C2×C3×C8—21no—
122C2×C3×C8C2311yescharacteristic
123#216—21no—
124#216—21no—
125#216—21no—
126#216—21no—
127#216D411yescharacteristic
128#215—21no—
129#215—21no—
130#215—21no—
131#215—21no—
132#215D411yescharacteristic
133#214D411yescharacteristic
134#213D411yescharacteristic
135(C2×D3)⋊C4—41no—
136Dic3⋊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—
1622−1+4—31no—
163H(5,𝔽2)—31no—
164#137—31no—
165#137—31no—
166#137—31no—
167#137—31no—
168#137—61no—
169#137—61no—
170#137—61no—
171#137—61no—
172#137—61no—
173#137—61no—
174#137C2×D311yescharacteristic
175#137C2×D311yescharacteristic
176AGL(1,ℤ/8)—31no—
177AGL(1,ℤ/8)—31no—
178AGL(1,ℤ/8)—61no—
179AGL(1,ℤ/8)—61no—
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×Q16—61no—
189C2×Q16C2×D311yescharacteristic, complemented
190C2×SD16—31no—
191C2×SD16—31no—
192C2×SD16—61no—
193C2×SD16—61no—
194#131—31no—
195#131—31no—
196#131—31no—
197#131C2×D311yescharacteristic
198C4⋊Q8—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#101C2×D311yescharacteristic, complemented
209#100—31no—
210#97—31no—
211C22×D3—21no—
212C22×D3—41no—
213C3×Q8—21no—
214C3×Q8—21no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8C2×D411yescharacteristic
218C3×D4—21no—
219C3×D4C2×D411yescharacteristic
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4C2411yescharacteristic
224#67—21no—
225#67—21no—
226#67—21no—
227#67—41no—
228#67—41no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—41no—
232D12—21no—
233D12—21no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12C2×D411yescharacteristic
238D12C2×D411yescharacteristic
239D12C2×D411yescharacteristic
240C4×D3—21no—
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—41no—
244C4×D3—41no—
245C4×D3—41no—
246C4×D3—41no—
247C4×D3—41no—
248C4×D3—41no—
249Dic6—21no—
250Dic6—21no—
251Dic6—41no—
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#41—121no—
279#41C22×D311yescharacteristic
280C2×Q8—31no—
281C2×Q8—61no—
282C2×Q8—61no—
283C2×Q8—61no—
284C2×Q8—61no—
285C2×Q8—61no—
286C2×Q8—61no—
287C2×Q8C22×D311yescharacteristic
288C2×Q8C22×D311yescharacteristic
289C2×D4—31no—
290C2×D4—61no—
291C2×D4—61no—
292C2×D4—121no—
293Q16—21no—
294Q16—21no—
295Q16—21no—
296Q16—21no—
297Q16—31no—
298Q16—31no—
299Q16—61no—
300Q16—61no—
301Q16—61no—
302Q16—61no—
303Q16—61no—
304Q16—61no—
305SD16—21no—
306SD16—21no—
307SD16—31no—
308SD16—31no—
309SD16—31no—
310SD16—31no—
311SD16—61no—
312SD16—61no—
313SD16—61no—
314SD16—61no—
315SD16—61no—
316SD16—61no—
317SD16—61no—
318SD16—61no—
319SD16—61no—
320SD16—61no—
321D8—31no—
322D8—31no—
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
339C4⋊C4—121no—
340C22⋊C4—121no—
341C42—31no—
342C22×C3—21no—
343C22×C3H(5,𝔽2)11yescharacteristic
344C2×D3—21no—
345C2×D3—21no—
346C2×D3—21no—
347C2×D3—41no—
348C2×D3—81no—
349C2×D3—161no—
350C3×C4—21no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4C22×D411yescharacteristic
354C3×C4C22×D411yescharacteristic
355Dic3—21no—
356Dic3—21no—
357Dic3—21no—
358Dic3—41no—
359Dic3—41no—
360C23—61no—
361C23—121no—
362Q8—21no—
363Q8—21no—
364Q8—21no—
365Q8—21no—
366Q8—31no—
367Q8—31no—
368Q8—31no—
369Q8—61no—
370Q8—61no—
371Q8—121no—
372Q8—121no—
373Q8—121no—
374Q8D3×D411yescharacteristic
375D4—21no—
376D4—31no—
377D4—31no—
378D4—31no—
379D4—61no—
380D4—61no—
381D4—61no—
382D4—61no—
383D4—61no—
384D4—121no—
385D4—121no—
386D4—121no—
387D4—121no—
388D4—121no—
389D4D3×D411yescharacteristic
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4C23×D311yescharacteristic
406C8—21no—
407C8—21no—
408C8—21no—
409C8—31no—
410C8—31no—
411C8—61no—
412C8D3×D411yescharacteristic
413C8D3×D411yescharacteristic
414C2×C3—21no—
415C2×C3—41no—
416C2×C3D4211yescharacteristic
417D3—41no—
418D3—41no—
419D3—41no—
420D3—81no—
421C22—21no—
422C22—61no—
423C22—61no—
424C22—61no—
425C22—121no—
426C22—241no—
427C22—481no—
428C22#100911yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—61no—
433C4—61no—
434C4—61no—
435C4—121no—
436C4—121no—
437C4C2×D3×D411yescharacteristic
438C4C2×D3×D411yescharacteristic
439C3#328911yescharacteristic, complemented, Sylow
440C2—21no—
441C2—41no—
442C2—121no—
443C2—121no—
444C2—121no—
445C2—241no—
446C2#560911yescharacteristic
subgroupG/H
centerC2#5609
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#473C2
socleC2×C3D42
hypercenter#473D3
hypocenterC3#3289
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #5779C2semidirect
2. #5778C2semidirect
3. #5766C2semidirect
4. #5751C2semidirect
5. C3×#473C2semidirect
6. #5205C2semidirect
7. #5202C2semidirect
8. #5190C2semidirect
9. #5145C2semidirect
10. #4898C2semidirect
11. #4894C2semidirect
12. #4755C2semidirect
13. #4754C2semidirect
14. #4753C2semidirect
15. #4752C2semidirect
20. #1007C22semidirect
23. C2×C3×Q16C22semidirect
27. #944C22semidirect
28. C2×#216C22semidirect
30. #942C22semidirect
46. #909C22semidirect
51. #907C22semidirect
56. #901C22semidirect
57. C3×#108C22semidirect
58. C3×#101C22semidirect
59. C3×#101C22semidirect
62. #825C22semidirect
63. #825C22semidirect
64. #824C22semidirect
66. #822C22semidirect
67. #815C22semidirect
74. #473D3semidirect
189. C2×Q16C2×D3semidirect
201. #108C2×D3semidirect
207. #101C2×D3semidirect
208. #101C2×D3semidirect
439. C3#3289semidirect

Maximal subgroups

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

subgroupindex
#57792
#57782
#57662
#57512
C3×#4732
#52052
#52022
#51902
#51452
#48982
#48942
#47552
#47542
#47532
#47522
#32893