Finite Group Databasebeta

← #11878763

Subgroups — #11878763

Order 1152.

1314 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4#10592543C214yesmaximal, complemented
5#10592433C214yesmaximal, complemented
6#10592394C211yesmaximal, characteristic, complemented
7#10592393C211yesmaximal, characteristic, complemented
8#10592392C211yesmaximal, characteristic, complemented
9#10592380C211yesmaximal, characteristic, complemented
10#79304—34nomaximal
11C2×#3828—21no—
12C2×#3828C2212yes—
13C2×C32×C42C2211yescharacteristic
14#64139—21no—
15#64139—21no—
16#64139—21no—
17#64139C2212yes—
18C2×#3745C2214yes—
19C2×#3744C2214yes—
20#64084—21no—
21#64084C2212yes—
22#64083C2211yescharacteristic
23#64083C2211yescharacteristic
24C4×C4⋊(C3⋊D3)—21no—
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)—21no—
27C4×C4⋊(C3⋊D3)C2212yes—
28#64078C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×C4⋊C8C2212yes—
31C32×C22⋊C8C2212yes—
32C32×C4×C8C2211yescharacteristic
33C32×C4×C8C2211yescharacteristic
34#63648C2214yes—
35#63643C2214yes—
36#5477—34no—
37#5477—34no—
38C3×#431D314yescomplemented
39#4844—316no—
40#4734—316no—
41#4695—34no—
42#4694—34no—
43#4693—34no—
44#4681—34no—
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×#638—22no—
49C2×#638—22no—
50#3828—44no—
51#3828—44no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C2×C32×C8C2312yes—
63C2×C32×C8C2312yes—
64C32×C42D411yescharacteristic
65C32×C42D411yescharacteristic
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68#3752—22no—
69#3752—22no—
70#3752—22no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76#3745—44no—
77#3744—44no—
78#3207—91noSylow
79C2×#235—38no—
80C2×#235—64no—
81C2×C3×C42C2×D314yes—
82#930—38no—
83#930—64no—
84#930—64no—
85#930—64no—
86C2×D24—316no—
87C2×#204—316no—
88#875—38no—
89#875—64no—
90#874—34no—
91#874—34no—
92C4×D12—38no—
93C4×D12—64no—
94C4×D12—64no—
95C4×D12—64no—
96#869—34no—
97#869—34no—
98C3×C4⋊C8C2×D318yes—
99C3×C22⋊C8C2×D318yes—
100C3×C4×C8C2×D314yes—
101C3×C4×C8C2×D314yes—
102#821—316no—
103#816—316no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—22no—
106C22×C3⋊D3—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2411yescharacteristic
116#638—44no—
117#638—44no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—24no—
121C4⋊(C3⋊D3)—24no—
122C4⋊(C3⋊D3)—42no—
123C4⋊(C3⋊D3)—42no—
124C4⋊(C3⋊D3)—42no—
125C4⋊(C3⋊D3)—42no—
126C4×C3⋊D3—44no—
127C4×C3⋊D3—44no—
128#634—24no—
129#634—42no—
130C32×C8—22no—
131C32×C8—22no—
132#532—91no—
133#532—91no—
134#493—91no—
135#492—91no—
136#487—91no—
137#486—91no—
138#463—94no—
139#449—94no—
140#431C3⋊D311yescharacteristic, complemented
141C22×C3×C4D1214yes—
142C22×C3×C4D1214yes—
143C22×C3×C4C22×D314yes—
144C2×#67—68no—
145C2×#67—68no—
146#235—1216no—
147#235—1216no—
148C2×D12—38no—
149C2×D12—38no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×C4×D3—68no—
155C2×C4×D3—68no—
156C2×Dic6—38no—
157C2×Dic6—64no—
158C2×C3×C8C22×D318yes—
159C2×C3×C8C22×D318yes—
160C3×C42D1214yes—
161C3×C42D1214yes—
162C3×C42C22×D314yes—
163C3×C42C22×D314yes—
164(C2×D3)⋊C4—68no—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—68no—
167(C2×D3)⋊C4—68no—
168C4⋊Dic3—38no—
169C4⋊Dic3—64no—
170C4⋊Dic3—64no—
171C4⋊Dic3—64no—
172D24—1216no—
173#204—1216no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32C22×D411yescharacteristic
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4—21no—
187C32×C4#13512yes—
188C32×C4AGL(1,ℤ/8)12yes—
189C32×C4H(5,𝔽2)12yes—
190C3⋊Dic3—42no—
191C3⋊Dic3—42no—
192C2×#41—92no—
193C2×#41—181no—
194C2×SD16—94no—
195C2×D8—94no—
196C4⋊Q8—91no—
197C4⋊Q8—91no—
198#127—91no—
199#127—91no—
200#124—92no—
201#124—181no—
202#121—92no—
203#121—181no—
204#121—181no—
205#121—181no—
206C4×D4—92no—
207C4×D4—181no—
208C4×D4—181no—
209C4×D4—181no—
210C2×C42C2×C3⋊D311yescharacteristic
211C4⋊C8C2×C3⋊D312yes—
212#103—94no—
213#102—94no—
214C22⋊C8C2×C3⋊D312yes—
215C4×C8C2×C3⋊D311yescharacteristic
216C4×C8C2×C3⋊D311yescharacteristic
217C23×C3C2×D1214yes—
218C22×D3—68no—
219C22×D3—68no—
220C2×C3×C4—28no—
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4C2×D1214yes—
224C2×C3×C4C2×D1214yes—
225C2×C3×C4C2×D1214yes—
226C2×C3×C4C2×D1214yes—
227C2×C3×C4C2×D1214yes—
228C2×C3×C4C23×D314yes—
229#67—1216no—
230#67—1216no—
231C2×Dic3—68no—
232C2×Dic3—68no—
233D12—616no—
234D12—616no—
235D12—128no—
236D12—128no—
237D12—128no—
238D12—128no—
239C4×D3—1216no—
240C4×D3—1216no—
241Dic6—616no—
242Dic6—128no—
243C3×C8—28no—
244C3×C8—28no—
245C2×C32—41no—
246C2×C32#53511yescharacteristic
247C2×C32C2×#13511yescharacteristic
248C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
249C3⋊D3—82no—
250C3⋊D3—82no—
251#41—364no—
252#41—364no—
253C2×Q8—92no—
254C2×Q8—181no—
255C2×D4—92no—
256C2×D4—92no—
257C2×D4—182no—
258C2×D4—182no—
259C2×D4—181no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—182no—
264C22×C4—182no—
265C22×C4C4⋊(C3⋊D3)11yescharacteristic
266C22×C4C4⋊(C3⋊D3)11yescharacteristic
267C22×C4C22×C3⋊D311yescharacteristic
268SD16—364no—
269D8—364no—
270C2×C8C22×C3⋊D312yes—
271C2×C8C22×C3⋊D312yes—
272C4⋊C4—92no—
273C4⋊C4—181no—
274C4⋊C4—181no—
275C4⋊C4—181no—
276C22⋊C4—182no—
277C22⋊C4—182no—
278C22⋊C4—182no—
279C22⋊C4—182no—
280C42C4⋊(C3⋊D3)11yescharacteristic
281C42C4⋊(C3⋊D3)11yescharacteristic
282C42C22×C3⋊D311yescharacteristic
283C42C22×C3⋊D311yescharacteristic
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—24no—
287C22×C3C22×D1214yes—
288C2×D3—128no—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C2×D3—128no—
293C2×D3—128no—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—24no—
297C3×C4#90418yes—
298C3×C4#90818yes—
299C3×C4#100918yes—
300Dic3—128no—
301Dic3—128no—
302C32#320711yescharacteristic, complemented, Sylow
303C23—182no—
304C23—182no—
305C23C2×C4⋊(C3⋊D3)11yescharacteristic
306Q8—184no—
307Q8—362no—
308D4—184no—
309D4—184no—
310D4—364no—
311D4—364no—
312D4—362no—
313D4—362no—
314D4—362no—
315D4—362no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—182no—
320C2×C4—182no—
321C2×C4—364no—
322C2×C4—364no—
323C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
324C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
325C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
326C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
327C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—22no—
330C8—22no—
331C2×C3—44no—
332C2×C3#552514yes—
333C2×C3C2×#90414yes—
334C2×C3C2×#90814yes—
335D3—248no—
336D3—248no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—362no—
341C22—362no—
342C22—362no—
343C22—362no—
344C22—362no—
345C22—362no—
346C22C22×C4⋊(C3⋊D3)11yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—362no—
351C4—362no—
352C4#6411312yes—
353C4#6411712yes—
354C4#6436612yes—
355C3#7930414yescomplemented
356C2—41no—
357C2—722no—
358C2—722no—
359C2#1059599611yescharacteristic
360C2C2×#6411311yescharacteristic
361C2C2×#6411711yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C22×D4
hypercenter#431C3⋊D3
hypocenterC32#3207
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. #10595948C2semidirect
3. C32×#431C2semidirect
4. #10592543C2semidirect
5. #10592433C2semidirect
6. #10592394C2semidirect
7. #10592393C2semidirect
8. #10592392C2semidirect
9. #10592380C2semidirect
38. C3×#431D3semidirect
140. #431C3⋊D3semidirect
302. C32#3207semidirect
355. C3#79304semidirect

Maximal subgroups

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

subgroupindex
#105959482
C32×#4312
#105925432
#105924332
#105923942
#105923932
#105923922
#105923802
#793043