Finite Group Databasebeta

← #80296

Subgroups — #80296

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#5836C211yesmaximal, characteristic, complemented
2#5835C211yesmaximal, characteristic, complemented
3#5779C211yesmaximal, characteristic, complemented
4#5778C211yesmaximal, characteristic, complemented
5C3×#455C211yesmaximal, characteristic, complemented
6#5204C211yesmaximal, characteristic, complemented
7#5203C211yesmaximal, characteristic, complemented
8#5062C211yesmaximal, characteristic, complemented
9#5059C211yesmaximal, characteristic, complemented
10#4827C211yesmaximal, characteristic, complemented
11#4825C211yesmaximal, characteristic, complemented
12#4824C211yesmaximal, characteristic, complemented
13#4824C211yesmaximal, characteristic, complemented
14#4749C211yesmaximal, characteristic, complemented
15#4748C211yesmaximal, characteristic, complemented
16#3290—31nomaximal, Sylow
17C3×H(5,𝔽2)C2211yescharacteristic
18#1010C2211yescharacteristic, complemented
19#1009C2211yescharacteristic
20#1007C2211yescharacteristic, complemented
21C3×#137C2211yescharacteristic
22C3×#137C2211yescharacteristic, complemented
23C3×#124C2211yescharacteristic, complemented
24#951—21no—
25#951C2211yescharacteristic
26#950—21no—
27#950—21no—
28#950C2211yescharacteristic
29#950C2211yescharacteristic
30#949—21no—
31#949C2211yescharacteristic
32#948C2211yescharacteristic
33#948C2211yescharacteristic, complemented
34C2×#216C2211yescharacteristic, complemented
35C2×#215C2211yescharacteristic, complemented
36C2×#214—21no—
37C2×#214C2211yescharacteristic, complemented
38#932—21no—
39#932—21no—
40#932C2211yescharacteristic
41#932C2211yescharacteristic, complemented
42C2×#213—21no—
43C2×#213C2211yescharacteristic
44#919—21no—
45#918—21no—
46#918—21no—
47D3×Q16—21no—
48#916—21no—
49#915—21no—
50#914—21no—
51D3×SD16—21no—
52#909C2211yescharacteristic, complemented
53#908C2211yescharacteristic, complemented
54#907C2211yescharacteristic, complemented
55#907C2211yescharacteristic, complemented
56#875C2211yescharacteristic, complemented
57C3×#104C2211yescharacteristic
58C3×#104C2211yescharacteristic, complemented
59C3×#100C2211yescharacteristic, complemented
60#836C2211yescharacteristic, complemented
61#824C2211yescharacteristic, complemented
62#823C2211yescharacteristic, complemented
63#822C2211yescharacteristic, complemented
64#822C2211yescharacteristic, complemented
65#805C2211yescharacteristic, complemented
66#805C2211yescharacteristic, complemented
67C4×C3⋊C8C2211yescharacteristic, 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#471—31no—
77#455—31no—
78#455D311yescharacteristic, complemented
79#454—31no—
80#454—31no—
81#443—31no—
82#443—31no—
83C3×#41—21no—
84C3×#41—21no—
85C3×#41C2311yescharacteristic
86C3×#41C2311yescharacteristic
87C2×C3×Q8C2311yescharacteristic
88C2×C3×D4—21no—
89C2×C3×D4—21no—
90C2×C3×D4—41no—
91C2×C3×D4C2311yescharacteristic
92#239—21no—
93#239—21no—
94#239—21no—
95D3×Q8—21no—
96D3×Q8—21no—
97D3×Q8—21no—
98#237—21no—
99#237—41no—
100D3×D4—21no—
101D3×D4—41no—
102#235—21no—
103#235—21no—
104#235—41no—
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107C2×D12—21no—
108C2×D12C2311yescharacteristic
109C2×Dic6—21no—
110C2×Dic6C2311yescharacteristic
111C3×Q16—21no—
112C3×Q16—21no—
113C3×SD16—21no—
114C3×SD16—21no—
115C3×M16C2311yescharacteristic
116C3×M16C2311yescharacteristic
117C3×C22⋊C4—41no—
118C3×C42C2311yescharacteristic
119#216—21no—
120#216—21no—
121#216—21no—
122#216D411yescharacteristic
123#216D411yescharacteristic
124#215—21no—
125#215—21no—
126#215—21no—
127#215D411yescharacteristic
128#215D411yescharacteristic
129#214—21no—
130#214—21no—
131#214—21no—
132#214—21no—
133#214—21no—
134#214D411yescharacteristic
135#214D411yescharacteristic
136#213—21no—
137#213—21no—
138#213—21no—
139#213—21no—
140#213—21no—
141#213D411yescharacteristic
142#213D411yescharacteristic
143(C2×D3)⋊C4—41no—
144#208—21no—
145#208—21no—
146#208C2311yescharacteristic
147#208C2311yescharacteristic
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8C2311yescharacteristic
151C2×C3⋊C8C2311yescharacteristic
152Dic12—21no—
153D24—21no—
154#204—21no—
155#204—21no—
156ΓL(1,𝔽25)—21no—
157ΓL(1,𝔽25)—21no—
158D3×C8—21no—
159D3×C8—21no—
1602−1+4—31no—
1612−1+4—31no—
162H(5,𝔽2)—31no—
163H(5,𝔽2)C2×D311yescharacteristic
164#137—31no—
165#137—31no—
166#137—61no—
167#137—61no—
168#137—61no—
169#137—61no—
170#137C2×D311yescharacteristic
171#137C2×D311yescharacteristic, complemented
172AGL(1,ℤ/8)—31no—
173AGL(1,ℤ/8)—31no—
174AGL(1,ℤ/8)—31no—
175AGL(1,ℤ/8)—31no—
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—31no—
182#135—61no—
183#135—61no—
184#135—61no—
185#135—61no—
186C2×Q16—31no—
187C2×Q16—61no—
188C2×SD16—31no—
189C2×SD16—31no—
190C2×SD16—61no—
191C2×SD16—61no—
192C2×D8—31no—
193C2×D8—61no—
194#131—31no—
195#131—31no—
196#131—31no—
197#131—31no—
198#124—31no—
199#124C2×D311yescharacteristic, complemented
200#108—31no—
201#108—31no—
202#104—31no—
203#104—31no—
204#104C2×D311yescharacteristic
205#104C2×D311yescharacteristic, complemented
206#101—31no—
207#101—31no—
208#100—31no—
209#100C2×D311yescharacteristic, complemented
210C4×C8—31no—
211C23×C3—21no—
212C23×C3—41no—
213C22×D3—21no—
214C22×D3—41no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8C2×D411yescharacteristic
218C3×Q8C2×D411yescharacteristic
219C3×D4—21no—
220C3×D4—21no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4C2×D411yescharacteristic
226C3×D4C2×D411yescharacteristic
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—41no—
232C2×C3×C4C2411yescharacteristic
233#67—21no—
234#67—21no—
235#67—41no—
236#67—41no—
237C2×Dic3—21no—
238C2×Dic3—41no—
239D12—21no—
240D12—21no—
241D12—41no—
242D12—41no—
243D12C2×D411yescharacteristic
244D12C2×D411yescharacteristic
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
257C3×C8—21no—
258C3×C8—21no—
259C3⋊C8—21no—
260C3⋊C8—21no—
261C3⋊C8C2×D411yescharacteristic
262C3⋊C8C2×D411yescharacteristic
263C3⋊C8C2×D411yescharacteristic
264C3⋊C8C2×D411yescharacteristic
265#41—21no—
266#41—21no—
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—121no—
276#41—121no—
277#41C22×D311yescharacteristic
278#41C22×D311yescharacteristic
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8—61no—
282C2×Q8—61no—
283C2×Q8—61no—
284C2×Q8C22×D311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—31no—
288C2×D4—41no—
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—121no—
292C2×D4C22×D311yescharacteristic
293Q16—21no—
294Q16—21no—
295Q16—31no—
296Q16—31no—
297Q16—61no—
298Q16—61no—
299Q16—61no—
300Q16—61no—
301SD16—21no—
302SD16—21no—
303SD16—31no—
304SD16—31no—
305SD16—31no—
306SD16—31no—
307SD16—61no—
308SD16—61no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312SD16—61no—
313SD16—61no—
314SD16—61no—
315SD16—61no—
316SD16—61no—
317D8—31no—
318D8—31no—
319D8—61no—
320D8—61no—
321D8—61no—
322D8—61no—
323D8—61no—
324D8—61no—
325M16—31no—
326M16—31no—
327M16—61no—
328M16—61no—
329M16—61no—
330M16—61no—
331M16C22×D311yescharacteristic
332M16C22×D311yescharacteristic
333C2×C8—31no—
334C2×C8—31no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C22⋊C4—41no—
340C22⋊C4—121no—
341C42C22×D311yescharacteristic
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—41no—
345C22×C3—81no—
346C22×C3—161no—
347C22×C3H(5,𝔽2)11yescharacteristic
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—41no—
351C2×D3—81no—
352C2×D3—161no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4C22×D411yescharacteristic
358C3×C4C22×D411yescharacteristic
359Dic3—21no—
360Dic3—21no—
361Dic3—41no—
362C23—21no—
363C23—41no—
364C23—61no—
365C23—121no—
366Q8—21no—
367Q8—21no—
368Q8—31no—
369Q8—31no—
370Q8—61no—
371Q8—61no—
372Q8—121no—
373Q8—121no—
374Q8D3×D411yescharacteristic
375Q8D3×D411yescharacteristic
376D4—21no—
377D4—21no—
378D4—21no—
379D4—21no—
380D4—31no—
381D4—31no—
382D4—41no—
383D4—41no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—121no—
389D4—121no—
390D4—121no—
391D4—121no—
392D4D3×D411yescharacteristic
393D4D3×D411yescharacteristic
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4C23×D311yescharacteristic
408C8—21no—
409C8—21no—
410C8—31no—
411C8—31no—
412C8—31no—
413C8—31no—
414C8—61no—
415C8—61no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—81no—
420C2×C3D4211yescharacteristic
421D3—41no—
422D3—41no—
423D3—81no—
424C22—21no—
425C22—21no—
426C22—41no—
427C22—61no—
428C22—61no—
429C22—81no—
430C22—121no—
431C22—161no—
432C22—241no—
433C22—481no—
434C22#100411yescharacteristic
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—61no—
440C4—61no—
441C4—121no—
442C4C2×D3×D411yescharacteristic
443C4C2×D3×D411yescharacteristic
444C3#329011yescharacteristic, complemented, Sylow
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—121no—
450C2—121no—
451C2—241no—
452C2#559011yescharacteristic
subgroupG/H
centerC2#5590
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#455C2
socleC2×C3D42
hypercenter#455D3
hypocenterC3#3290
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #5836C2semidirect
2. #5835C2semidirect
3. #5779C2semidirect
4. #5778C2semidirect
5. C3×#455C2semidirect
6. #5204C2semidirect
7. #5203C2semidirect
8. #5062C2semidirect
9. #5059C2semidirect
10. #4827C2semidirect
11. #4825C2semidirect
12. #4824C2semidirect
13. #4824C2semidirect
14. #4749C2semidirect
15. #4748C2semidirect
18. #1010C22semidirect
20. #1007C22semidirect
22. C3×#137C22semidirect
23. C3×#124C22semidirect
33. #948C22semidirect
34. C2×#216C22semidirect
35. C2×#215C22semidirect
37. C2×#214C22semidirect
41. #932C22semidirect
52. #909C22semidirect
53. #908C22semidirect
54. #907C22semidirect
55. #907C22semidirect
56. #875C22semidirect
58. C3×#104C22semidirect
59. C3×#100C22semidirect
60. #836C22semidirect
61. #824C22semidirect
62. #823C22semidirect
63. #822C22semidirect
64. #822C22semidirect
65. #805C22semidirect
66. #805C22semidirect
67. C4×C3⋊C8C22semidirect
78. #455D3semidirect
171. #137C2×D3semidirect
199. #124C2×D3semidirect
205. #104C2×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
#58362
#58352
#57792
#57782
C3×#4552
#52042
#52032
#50622
#50592
#48272
#48252
#48242
#47492
#47482
#32903