Finite Group Databasebeta

← #79677

Subgroups — #79677

Order 384.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5581C211yesmaximal, characteristic, complemented
2#5554C211yesmaximal, characteristic
3C3×C4×SD16C211yesmaximal, characteristic, complemented
4#5173C211yesmaximal, characteristic, complemented
5#5169C211yesmaximal, characteristic, complemented
6#5028C211yesmaximal, characteristic, complemented
7#5009C211yesmaximal, characteristic, complemented
8#4866C211yesmaximal, characteristic, complemented
9#4862C211yesmaximal, characteristic, complemented
10#4813C211yesmaximal, characteristic, complemented
11#4807C211yesmaximal, characteristic, complemented
12#4772C211yesmaximal, characteristic, complemented
13D3×#102C211yesmaximal, characteristic, complemented
14#4697C211yesmaximal, characteristic, complemented
15C8×D12C211yesmaximal, characteristic, complemented
16#3296—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×D3×D4C2211yescharacteristic
19C2×C3×SD16C2211yescharacteristic
20C3×C4×Q8C2211yescharacteristic, complemented
21C3×C4×D4C2211yescharacteristic
22#946C2211yescharacteristic
23#946C2211yescharacteristic, complemented
24C2×#216C2211yescharacteristic, complemented
25C2×#215C2211yescharacteristic
26#930—21no—
27C2×(C2×D3)⋊C4—21no—
28C2×D3×C8C2211yescharacteristic
29C2×D3×C8C2211yescharacteristic, complemented
30#897C2211yescharacteristic
31#895C2211yescharacteristic
32#894—21no—
33#892C2211yescharacteristic, complemented
34D3×C4⋊C4C2211yescharacteristic
35#889—21no—
36#886—21no—
37#882—21no—
38#876—21no—
39#875C2211yescharacteristic
40C4×D12C2211yescharacteristic
41#872—21no—
42#870C2211yescharacteristic, complemented
43C3×#106C2211yescharacteristic, complemented
44C3×#103C2211yescharacteristic, complemented
45C3×#102C2211yescharacteristic
46C3×C4×C8C2211yescharacteristic, complemented
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52(C2×D3)⋊C8C2211yescharacteristic, complemented
53#816C2211yescharacteristic, complemented
54#816C2211yescharacteristic, complemented
55#810C2211yescharacteristic, complemented
56#809C2211yescharacteristic
57#808C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59C4⋊(C3⋊C8)C2211yescharacteristic, complemented
60#552—31no—
61#546—31no—
62#488—31no—
63#483—31no—
64#482—31no—
65#478—31no—
66#467—31no—
67#465—31no—
68#464—31no—
69#452—31no—
70#450—31no—
71C4×SD16D311yescharacteristic, complemented
72C8×D4—31no—
73#416—31no—
74C2×#102—31no—
75C23×D3—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C2×#67—21no—
80C2×#67—21no—
81C22×Dic3—21no—
82#237—22no—
83#237—41no—
84D3×D4—22no—
85D3×D4—41no—
86C2×D12—21no—
87C2×D12D411yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3C2311yescharacteristic
91C2×C4×D3C2311yescharacteristic
92C2×Dic6C2311yescharacteristic
93C3×SD16—22no—
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C3×C4⋊C4—21no—
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C42—21no—
101C3×C42C2311yescharacteristic
102#216—41no—
103#215—41no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4D411yescharacteristic
112(C2×D3)⋊C4D411yescharacteristic
113C4⋊Dic3—21no—
114C4⋊Dic3D411yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125D3×C8—41no—
126D3×C8—41no—
127C2×#41—31no—
128C22×D4—31no—
129C2×Q16—31no—
130C2×SD16—31no—
131C2×SD16C2×D311yescharacteristic
132C22×C8—31no—
133C22×C8—31no—
134#126—61no—
135#125—31no—
136#125—61no—
137#124—31no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143#121—31no—
144#121—61no—
145#120—61no—
146C4×Q8C2×D311yescharacteristic, complemented
147C4×D4—31no—
148C4×D4C2×D311yescharacteristic
149#117—31no—
150#117—61no—
151C2×C4⋊C4—31no—
152C2×C22⋊C4—61no—
153#107—31no—
154#106—31no—
155#106C2×D311yescharacteristic, complemented
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103C2×D311yescharacteristic, complemented
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8—31no—
169C4×C8C2×D311yescharacteristic, complemented
170C23×C3—21no—
171C22×D3—21no—
172C22×D3—42no—
173C22×D3—42no—
174C22×D3—81no—
175C22×D3C2×D411yescharacteristic
176C22×D3C2×D411yescharacteristic
177C3×Q8—21no—
178C3×Q8—21no—
179C3×D4—21no—
180C3×D4#4112yes—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—81no—
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—42no—
189#67—42no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—42no—
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196D12—22no—
197D12—21no—
198D12—21no—
199D12—81no—
200C4×D3—21no—
201C4×D3—21no—
202C4×D3—21no—
203C4×D3—21no—
204C4×D3—42no—
205Dic6—21no—
206Dic6—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3⋊C8—21no—
210C3⋊C8—21no—
211C24—61no—
212#41—62no—
213#41—121no—
214C2×Q8—31no—
215C2×Q8C22×D311yescharacteristic
216C2×D4—31no—
217C2×D4—31no—
218C2×D4—61no—
219C2×D4—61no—
220C2×D4—62no—
221C2×D4—61no—
222C2×D4—121no—
223C2×D4C22×D311yescharacteristic
224C22×C4—21no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—61no—
228C22×C4—61no—
229Q16—121no—
230SD16—22no—
231SD16—121no—
232C2×C8—31no—
233C2×C8—31no—
234C2×C8—121no—
235C2×C8—121no—
236C2×C8C22×D311yescharacteristic
237C2×C8C22×D311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—31no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4C22×D311yescharacteristic
249C4⋊C4C22×D311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—31no—
252C22⋊C4—31no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C42—21no—
261C42—61no—
262C42C22×D311yescharacteristic
263C22×C3—22no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3C22×D411yescharacteristic
267C2×D3—21no—
268C2×D3—21no—
269C2×D3—21no—
270C2×D3—21no—
271C2×D3—21no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—84no—
276C2×D3#13512yes—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4C2×#4111yescharacteristic
283C3×C4H(5,𝔽2)11yescharacteristic
284Dic3—21no—
285Dic3—21no—
286Dic3—41no—
287Dic3—41no—
288Dic3—41no—
289C23—21no—
290C23—31no—
291C23—31no—
292C23—61no—
293C23—122no—
294C23—122no—
295C23—241no—
296Q8—21no—
297Q8—21no—
298Q8—61no—
299Q8—61no—
300D4—21no—
301D4—62no—
302D4—61no—
303D4—61no—
304D4—122no—
305D4—122no—
306D4—241no—
307D4#23512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—81no—
321C2×C4—122no—
322C2×C4—122no—
323C2×C4D3×D411yescharacteristic
324C2×C4D3×D411yescharacteristic
325C2×C4C23×D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—61no—
329C8—61no—
330C2×C3—42no—
331C2×C3#54611yescharacteristic
332C2×C3C2×#13511yescharacteristic
333C2×C3#57711yescharacteristic
334D3—22no—
335D3—41no—
336D3—81no—
337C22—22no—
338C22—32no—
339C22—41no—
340C22—41no—
341C22—61no—
342C22—61no—
343C22—61no—
344C22—61no—
345C22—61no—
346C22—121no—
347C22—121no—
348C22—121no—
349C22—244no—
350C22C2×D3×D411yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—61no—
357C4—61no—
358C4—121no—
359C4—121no—
360C4—121no—
361C4C2×#23511yescharacteristic
362C4#100911yescharacteristic
363C3#329611yescharacteristic, complemented, Sylow
364C2—42no—
365C2—62no—
366C2—121no—
367C2—241no—
368C2#555011yescharacteristic
369C2#576211yescharacteristic
370C2D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×SD16C2
socleC22×C3C22×D4
prime radical#5554C2
hypercenterC4×SD16D3
hypocenterC3#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #5581C2semidirect
3. C3×C4×SD16C2semidirect
4. #5173C2semidirect
5. #5169C2semidirect
6. #5028C2semidirect
7. #5009C2semidirect
8. #4866C2semidirect
9. #4862C2semidirect
10. #4813C2semidirect
11. #4807C2semidirect
12. #4772C2semidirect
13. D3×#102C2semidirect
14. #4697C2semidirect
15. C8×D12C2semidirect
20. C3×C4×Q8C22semidirect
23. #946C22semidirect
24. C2×#216C22semidirect
29. C2×D3×C8C22semidirect
33. #892C22semidirect
42. #870C22semidirect
43. C3×#106C22semidirect
44. C3×#103C22semidirect
46. C3×C4×C8C22semidirect
52. (C2×D3)⋊C8C22semidirect
53. #816C22semidirect
54. #816C22semidirect
55. #810C22semidirect
57. #808C22semidirect
58. #807C22semidirect
59. C4⋊(C3⋊C8)C22semidirect
71. C4×SD16D3semidirect
146. C4×Q8C2×D3semidirect
155. #106C2×D3semidirect
160. #103C2×D3semidirect
169. C4×C8C2×D3semidirect
363. C3#3296semidirect

Maximal subgroups

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

subgroupindex
#55812
#55542
C3×C4×SD162
#51732
#51692
#50282
#50092
#48662
#48622
#48132
#48072
#47722
D3×#1022
#46972
C8×D122
#32963