Finite Group Databasebeta

← #80835

Subgroups — #80835

Order 384.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×SD16C211yesmaximal, characteristic, complemented
2C2×#909C211yesmaximal, characteristic, complemented
3#5632C211yesmaximal, characteristic, complemented
4#5612C211yesmaximal, characteristic
5C3×#468C211yesmaximal, characteristic, complemented
6#5167C211yesmaximal, characteristic, complemented
7#5127C211yesmaximal, characteristic, complemented
8#5047C211yesmaximal, characteristic, complemented
9#5040C211yesmaximal, characteristic, complemented
10#4889C211yesmaximal, characteristic, complemented
11#4887C211yesmaximal, characteristic, complemented
12#4818C211yesmaximal, characteristic, complemented
13#4809C211yesmaximal, characteristic, complemented
14#4776C211yesmaximal, characteristic, complemented
15#4767C211yesmaximal, characteristic, complemented
16#3266—31nomaximal, Sylow
17C2×D3×Q8C2211yescharacteristic
18C2×D3×D4C2211yescharacteristic
19C2×#235C2211yescharacteristic
20C22×Dic6C2211yescharacteristic, complemented
21C2×C3×SD16C2211yescharacteristic
22C2×C3×M16C2211yescharacteristic, complemented
23C3×C22⋊Q8C2211yescharacteristic, complemented
24C3×#121C2211yescharacteristic
25#944C2211yescharacteristic, complemented
26C2×#216C2211yescharacteristic, complemented
27C2×#215C2211yescharacteristic
28#938—21no—
29#937—21no—
30#936C2211yescharacteristic
31C2×#214C2211yescharacteristic
32C2×#214C2211yescharacteristic
33C4×#67C2211yescharacteristic
34D3×SD16—24no—
35#909—24no—
36C2×Dic12C2211yescharacteristic, complemented
37C2×Dic12C2211yescharacteristic, complemented
38C2×#204C2211yescharacteristic
39C2×#204C2211yescharacteristic
40C2×D3×C8C2211yescharacteristic
41#897C2211yescharacteristic
42#897C2211yescharacteristic
43#896—21no—
44#893C2211yescharacteristic
45#888—21no—
46#887C2211yescharacteristic, complemented
47#883—21no—
48#67⋊C4—21no—
49D3×C22⋊C4—21no—
50#878—21no—
51C3×#107C2211yescharacteristic, complemented
52C3×#103C2211yescharacteristic, complemented
53C3×#102C2211yescharacteristic
54#830C2211yescharacteristic, complemented
55(C2×D3)⋊C8C2211yescharacteristic
56#815C2211yescharacteristic, complemented
57Dic3⋊C8C2211yescharacteristic, complemented
58#810C2211yescharacteristic, complemented
59#810C2211yescharacteristic, complemented
60#810C2211yescharacteristic, complemented
61#809C2211yescharacteristic
62C2×#137—31no—
63C22×SD16—31no—
64D4×Q8—31no—
65#546—31no—
66#497—31no—
67#468D311yescharacteristic, complemented
68#467—31no—
69#464—31no—
70#461—31no—
71#452—31no—
72#451—31no—
73#450—31no—
74#448—31no—
75#440—31no—
76#435—31no—
77C23×D3—21no—
78C2×C3×Q8C2311yescharacteristic
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C2×#67—21no—
83C2×#67—21no—
84C2×#67D411yescharacteristic
85C22×Dic3—21no—
86D3×Q8—22no—
87D3×Q8—41no—
88D3×D4—22no—
89D3×D4—41no—
90#235—22no—
91#235—41no—
92C2×D12C2311yescharacteristic
93C2×C4×D3—21no—
94C2×C4×D3—21no—
95C2×C4×D3—21no—
96C2×C4×D3C2311yescharacteristic
97C2×Dic6—22no—
98C2×Dic6—21no—
99C2×Dic6—21no—
100C2×Dic6—41no—
101C2×Dic6C2311yescharacteristic
102C2×Dic6C2311yescharacteristic
103C2×Dic6C2311yescharacteristic
104C3×SD16—22no—
105C3×M16—22no—
106C2×C3×C8C2311yescharacteristic
107C2×C3×C8C2311yescharacteristic
108C3×C4⋊C4—21no—
109C3×C4⋊C4C2311yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C22⋊C4—21no—
112C3×C22⋊C4—21no—
113#217—21no—
114#217—21no—
115#217D411yescharacteristic
116#216—41no—
117#215—22no—
118#214—22no—
119#214—41no—
120(C2×D3)⋊C4—21no—
121(C2×D3)⋊C4—21no—
122(C2×D3)⋊C4—21no—
123(C2×D3)⋊C4D411yescharacteristic
124C4⋊Dic3—21no—
125C4⋊Dic3—21no—
126Dic3⋊C4—21no—
127Dic3⋊C4—21no—
128Dic3⋊C4—21no—
129Dic3⋊C4D411yescharacteristic
130C4×Dic3—21no—
131C4×Dic3C2311yescharacteristic
132C2×C3⋊C8C2311yescharacteristic
133C2×C3⋊C8C2311yescharacteristic
134Dic12—22no—
135Dic12—22no—
136#204—22no—
137#204D414yescomplemented
138D3×C8—22no—
139C2×#41—31no—
140C22×Q8—31no—
141C22×Q8—31no—
142C22×D4—31no—
143#137—64no—
144C2×Q16—31no—
145C2×Q16—31no—
146C2×Q16—31no—
147C2×SD16—31no—
148C2×SD16—31no—
149C2×SD16—31no—
150C2×SD16—31no—
151C2×SD16—31no—
152C2×SD16—64no—
153C2×SD16C2×D311yescharacteristic
154C2×M16C2×D311yescharacteristic, complemented
155C22×C8—31no—
156C4⋊Q8—31no—
157C4⋊Q8—61no—
158#124—31no—
159#123—61no—
160C22⋊Q8—31no—
161C22⋊Q8—31no—
162C22⋊Q8—61no—
163C22⋊Q8—61no—
164C22⋊Q8C2×D311yescharacteristic, complemented
165#121—61no—
166#121C2×D311yescharacteristic
167#120—61no—
168C4×Q8—31no—
169C4×D4—31no—
170C4×D4—31no—
171C4×D4—61no—
172C2×C22⋊C4—61no—
173#107C2×D311yescharacteristic, complemented
174C4⋊C8—31no—
175#103—31no—
176#103—31no—
177#103—31no—
178#103C2×D311yescharacteristic, complemented
179#102—31no—
180#102C2×D311yescharacteristic
181C22⋊C8—31no—
182C22⋊C8—31no—
183#97—31no—
184C23×C3—21no—
185C23×C3C2×D411yescharacteristic
186C22×D3—21no—
187C22×D3—42no—
188C22×D3—42no—
189C22×D3—81no—
190C22×D3C2×D411yescharacteristic
191C3×Q8—21no—
192C3×Q8—21no—
193C3×D4—21no—
194C3×D4—21no—
195C3×D4—81no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2411yescharacteristic
203#67—22no—
204#67—42no—
205#67—42no—
206C2×Dic3—21no—
207C2×Dic3—21no—
208C2×Dic3—21no—
209C2×Dic3—42no—
210C2×Dic3C2×D411yescharacteristic
211C2×Dic3C2×D411yescharacteristic
212C2×Dic3C2×D411yescharacteristic
213D12—21no—
214D12C2×D412yes—
215C4×D3—21no—
216C4×D3—21no—
217C4×D3—42no—
218C4×D3—42no—
219C4×D3—81no—
220Dic6—21no—
221Dic6—21no—
222Dic6—21no—
223Dic6—21no—
224Dic6—21no—
225Dic6—42no—
226Dic6—42no—
227Dic6C2×D412yes—
228C3×C8—21no—
229C3×C8C2×D412yes—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C24—61no—
233#41—62no—
234#41—121no—
235C2×Q8—31no—
236C2×Q8—31no—
237C2×Q8—31no—
238C2×Q8—61no—
239C2×Q8—62no—
240C2×Q8—61no—
241C2×Q8—62no—
242C2×Q8—121no—
243C2×Q8—121no—
244C2×Q8C22×D311yescharacteristic
245C2×D4—21no—
246C2×D4—31no—
247C2×D4—31no—
248C2×D4—61no—
249C2×D4—62no—
250C2×D4—61no—
251C2×D4—121no—
252C2×D4C22×D311yescharacteristic
253C22×C4—31no—
254C22×C4—61no—
255C22×C4—61no—
256C22×C4—61no—
257C22×C4—61no—
258C22×C4C22×D311yescharacteristic
259Q16—62no—
260Q16—62no—
261Q16—121no—
262SD16—22no—
263SD16—34no—
264SD16—62no—
265SD16—62no—
266SD16—62no—
267SD16—121no—
268M16—22no—
269C2×C8—31no—
270C2×C8—31no—
271C2×C8—62no—
272C2×C8C22×D311yescharacteristic
273C2×C8C22×D311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—31no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4C22×D311yescharacteristic
282C4⋊C4C22×D311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—31no—
286C22⋊C4—31no—
287C22⋊C4—61no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4—61no—
291C22⋊C4—61no—
292C42—31no—
293C42—61no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3C22×D411yescharacteristic
301C2×D3—21no—
302C2×D3—21no—
303C2×D3—22no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—84no—
307C2×D3#13712yescomplemented
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4C22×D411yescharacteristic
313C3×C4H(5,𝔽2)11yescharacteristic
314Dic3—22no—
315Dic3—21no—
316Dic3—21no—
317Dic3—21no—
318Dic3—41no—
319Dic3—41no—
320C23—21no—
321C23—31no—
322C23—61no—
323C23—122no—
324C23—122no—
325C23—241no—
326C23D3×D411yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—32no—
330Q8—61no—
331Q8—61no—
332Q8—61no—
333Q8—61no—
334Q8—61no—
335Q8—122no—
336Q8—122no—
337D4—21no—
338D4—21no—
339D4—32no—
340D4—62no—
341D4—61no—
342D4—81no—
343D4—122no—
344D4—122no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—31no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—61no—
354C2×C4—61no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—122no—
359C2×C4—122no—
360C2×C4—122no—
361C2×C4—241no—
362C2×C4D3×D411yescharacteristic
363C2×C4C23×D311yescharacteristic
364C8—21no—
365C8—61no—
366C8—61no—
367C8D3×D412yes—
368C2×C3—41no—
369C2×C3—81no—
370C2×C3D4211yescharacteristic
371C2×C3C2×#13711yescharacteristic
372C2×C3#57711yescharacteristic
373D3—22no—
374D3—42no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—32no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—61no—
383C22—61no—
384C22—62no—
385C22—121no—
386C22—121no—
387C22—244no—
388C22C2×D3×D411yescharacteristic
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—61no—
394C4—61no—
395C4—61no—
396C4—62no—
397C4—121no—
398C4—121no—
399C4C2×D3×D411yescharacteristic
400C4#100911yescharacteristic
401C3#326611yescharacteristic, complemented, Sylow
402C2—41no—
403C2—62no—
404C2—81no—
405C2—122no—
406C2#560911yescharacteristic
407C2#577511yescharacteristic
408C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#468C2
socleC22×C3C22×D4
prime radical#5612C2
hypercenter#468D3
hypocenterC3#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×D3×SD16C2semidirect
2. C2×#909C2semidirect
3. #5632C2semidirect
5. C3×#468C2semidirect
6. #5167C2semidirect
7. #5127C2semidirect
8. #5047C2semidirect
9. #5040C2semidirect
10. #4889C2semidirect
11. #4887C2semidirect
12. #4818C2semidirect
13. #4809C2semidirect
14. #4776C2semidirect
15. #4767C2semidirect
20. C22×Dic6C22semidirect
22. C2×C3×M16C22semidirect
23. C3×C22⋊Q8C22semidirect
25. #944C22semidirect
26. C2×#216C22semidirect
36. C2×Dic12C22semidirect
37. C2×Dic12C22semidirect
46. #887C22semidirect
51. C3×#107C22semidirect
52. C3×#103C22semidirect
54. #830C22semidirect
56. #815C22semidirect
57. Dic3⋊C8C22semidirect
58. #810C22semidirect
59. #810C22semidirect
60. #810C22semidirect
67. #468D3semidirect
137. #204D4semidirect
154. C2×M16C2×D3semidirect
164. C22⋊Q8C2×D3semidirect
173. #107C2×D3semidirect
178. #103C2×D3semidirect
307. C2×D3#137semidirect
401. C3#3266semidirect

Maximal subgroups

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

subgroupindex
C2×D3×SD162
C2×#9092
#56322
#56122
C3×#4682
#51672
#51272
#50472
#50402
#48892
#48872
#48182
#48092
#47762
#47672
#32663