Finite Group Databasebeta

← #80289

Subgroups — #80289

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#5838C211yesmaximal, characteristic, complemented
2#5837C211yesmaximal, characteristic, complemented
3#5775C211yesmaximal, characteristic, complemented
4#5774C211yesmaximal, characteristic, complemented
5C3×#454C211yesmaximal, characteristic, complemented
6#5200C211yesmaximal, characteristic, complemented
7#5199C211yesmaximal, characteristic, complemented
8#5061C211yesmaximal, characteristic, complemented
9#5059C211yesmaximal, characteristic, complemented
10#4827C211yesmaximal, characteristic, complemented
11#4825C211yesmaximal, characteristic, complemented
12#4824C211yesmaximal, characteristic, complemented
13#4824C211yesmaximal, characteristic, complemented
14#4755C211yesmaximal, characteristic, complemented
15#4754C211yesmaximal, characteristic, complemented
16#3290—31nomaximal, Sylow
17C3×2−1+4C2211yescharacteristic, complemented
18#1010C2211yescharacteristic, complemented
19#1009C2211yescharacteristic
20#1004C2211yescharacteristic
21C3×AGL(1,ℤ/8)C2211yescharacteristic
22C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23C3×#124C2211yescharacteristic, complemented
24#951—21no—
25#951C2211yescharacteristic, complemented
26#950—21no—
27#950—21no—
28#950C2211yescharacteristic
29#950C2211yescharacteristic
30#949—21no—
31#949C2211yescharacteristic, complemented
32#948C2211yescharacteristic, complemented
33#948C2211yescharacteristic, complemented
34C2×#216—21no—
35C2×#216C2211yescharacteristic, complemented
36#942—21no—
37#942—21no—
38#942C2211yescharacteristic
39#942C2211yescharacteristic, complemented
40C2×#215—21no—
41C2×#215C2211yescharacteristic, complemented
42C2×#214C2211yescharacteristic, complemented
43C2×#213C2211yescharacteristic
44#916—21no—
45#915—21no—
46#914—21no—
47D3×SD16—21no—
48#912—21no—
49#911—21no—
50#911—21no—
51D3×D8—21no—
52#909C2211yescharacteristic
53#908C2211yescharacteristic
54#907C2211yescharacteristic
55#907C2211yescharacteristic, complemented
56#875C2211yescharacteristic, complemented
57C3×#104C2211yescharacteristic, complemented
58C3×#104C2211yescharacteristic, complemented
59C3×#101C2211yescharacteristic, complemented
60#833C2211yescharacteristic, complemented
61#824C2211yescharacteristic, complemented
62#823C2211yescharacteristic, complemented
63#822C2211yescharacteristic, complemented
64#822C2211yescharacteristic, complemented
65#805C2211yescharacteristic
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#455—31no—
79#454—31no—
80#454D311yescharacteristic, complemented
81#443—31no—
82#443—31no—
83C3×#41—21no—
84C3×#41—21no—
85C3×#41—41no—
86C3×#41C2311yescharacteristic
87C3×#41C2311yescharacteristic
88C2×C3×Q8—21no—
89C2×C3×Q8—21no—
90C2×C3×Q8C2311yescharacteristic
91C2×C3×D4C2311yescharacteristic
92C2×#67—41no—
93#239—21no—
94D3×Q8—21no—
95#237—21no—
96#237—21no—
97#237—21no—
98#237—41no—
99D3×D4—21no—
100D3×D4—21no—
101D3×D4—21no—
102D3×D4—41no—
103#235—21no—
104#235—21no—
105#235C2311yescharacteristic
106#235C2311yescharacteristic
107C2×D12—21no—
108C2×D12C2311yescharacteristic
109C2×Dic6—21no—
110C2×Dic6C2311yescharacteristic
111C3×SD16—21no—
112C3×SD16—21no—
113C3×D8—21no—
114C3×D8—21no—
115C3×M16C2311yescharacteristic
116C3×M16C2311yescharacteristic
117C3×C22⋊C4—41no—
118C3×C42C2311yescharacteristic
119#216—21no—
120#216—21no—
121#216—21no—
122#216—21no—
123#216—21no—
124#216D411yescharacteristic
125#216D411yescharacteristic
126#215—21no—
127#215—21no—
128#215—21no—
129#215—21no—
130#215—21no—
131#215D411yescharacteristic
132#215D411yescharacteristic
133#214—21no—
134#214—21no—
135#214—21no—
136#214D411yescharacteristic
137#214D411yescharacteristic
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+4C2×D311yescharacteristic, complemented
162H(5,𝔽2)—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—
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)C2×D311yescharacteristic
179AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
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, complemented
205#104C2×D311yescharacteristic, complemented
206#101—31no—
207#101C2×D311yescharacteristic, complemented
208#100—31no—
209#100—31no—
210C4×C8—31no—
211C23×C3—21no—
212C22×D3—21no—
213C22×D3—41no—
214C22×D3—41no—
215C3×Q8—21no—
216C3×Q8—21no—
217C3×Q8—41no—
218C3×Q8C2×D411yescharacteristic
219C3×Q8C2×D411yescharacteristic
220C3×D4—21no—
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—21no—
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×C4—41no—
233C2×C3×C4C2411yescharacteristic
234#67—21no—
235#67—21no—
236#67—41no—
237#67—41no—
238#67—41no—
239#67—41no—
240C2×Dic3—21no—
241C2×Dic3—41no—
242C2×Dic3—41no—
243D12—21no—
244D12—21no—
245D12—41no—
246D12C2×D411yescharacteristic
247D12C2×D411yescharacteristic
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—41no—
251C4×D3—41no—
252Dic6—21no—
253Dic6—21no—
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—41no—
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—21no—
280C2×Q8—21no—
281C2×Q8—31no—
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—31no—
294Q16—31no—
295Q16—61no—
296Q16—61no—
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—21no—
318D8—21no—
319D8—31no—
320D8—31no—
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×C3H(5,𝔽2)11yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—41no—
350C2×D3—81no—
351C2×D3—161no—
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—61no—
364C23—121no—
365C23—121no—
366Q8—21no—
367Q8—21no—
368Q8—31no—
369Q8—31no—
370Q8—41no—
371Q8—61no—
372Q8—61no—
373Q8—121no—
374Q8D3×D411yescharacteristic
375Q8D3×D411yescharacteristic
376D4—21no—
377D4—21no—
378D4—21no—
379D4—21no—
380D4—31no—
381D4—31no—
382D4—41no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—121no—
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—41no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
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—241no—
432C22—481no—
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×#454C2
socleC2×C3D42
hypercenter#454D3
hypocenterC3#3290
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #5838C2semidirect
2. #5837C2semidirect
3. #5775C2semidirect
4. #5774C2semidirect
5. C3×#454C2semidirect
6. #5200C2semidirect
7. #5199C2semidirect
8. #5061C2semidirect
9. #5059C2semidirect
10. #4827C2semidirect
11. #4825C2semidirect
12. #4824C2semidirect
13. #4824C2semidirect
14. #4755C2semidirect
15. #4754C2semidirect
17. C3×2−1+4C22semidirect
18. #1010C22semidirect
22. C3×AGL(1,ℤ/8)C22semidirect
23. C3×#124C22semidirect
25. #951C22semidirect
31. #949C22semidirect
32. #948C22semidirect
33. #948C22semidirect
35. C2×#216C22semidirect
39. #942C22semidirect
41. C2×#215C22semidirect
42. C2×#214C22semidirect
55. #907C22semidirect
56. #875C22semidirect
57. C3×#104C22semidirect
58. C3×#104C22semidirect
59. C3×#101C22semidirect
60. #833C22semidirect
61. #824C22semidirect
62. #823C22semidirect
63. #822C22semidirect
64. #822C22semidirect
66. #805C22semidirect
67. C4×C3⋊C8C22semidirect
80. #454D3semidirect
161. 2−1+4C2×D3semidirect
179. AGL(1,ℤ/8)C2×D3semidirect
199. #124C2×D3semidirect
204. #104C2×D3semidirect
205. #104C2×D3semidirect
207. #101C2×D3semidirect
444. C3#3290semidirect

Maximal subgroups

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

subgroupindex
#58382
#58372
#57752
#57742
C3×#4542
#52002
#51992
#50612
#50592
#48272
#48252
#48242
#47552
#47542
#32903