Finite Group Databasebeta

← #11779303

Subgroups — #11779303

Order 1152.

942 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2#10592707C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4#10592392C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6#10589351C211yesmaximal, characteristic, complemented
7#10589325C211yesmaximal, characteristic, complemented
8#68195—34nomaximal
9C2×D4×C3⋊D3—21no—
10C22×C4⋊(C3⋊D3)—21no—
11C32×C4×D4C2211yescharacteristic
12#64139—21no—
13C2×#3744—22no—
14#64104—21no—
15#64091—22no—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18#64078C2211yescharacteristic, complemented
19C32×C4⋊C8C2211yescharacteristic, complemented
20C32×C4×C8C2211yescharacteristic, complemented
21#63659—21no—
22#63648—21no—
23#63644—21no—
24#63635—21no—
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
26D4×D12—34no—
27#5008—34no—
28#4842—34no—
29#4693—34no—
30C3×D4⋊C8D314yescomplemented
31#4485—34no—
32#4459—34no—
33C23×C3⋊D3—22no—
34C2×C32×D4D411yescharacteristic
35C22×C32×C4—21no—
36C2×#638—22no—
37D4×C3⋊D3—42no—
38D4×C3⋊D3—42no—
39C2×C4⋊(C3⋊D3)—22no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—42no—
43C2×C4⋊(C3⋊D3)—42no—
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×C4⋊(C3⋊D3)D412yes—
46C2×C4×C3⋊D3—21no—
47C2×#634—21no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53#3752—22no—
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59#3744—44no—
60#1629—91noSylow
61C2×D3×D4—64no—
62C22×D12—64no—
63C3×C4×D4C2×D314yes—
64#930—64no—
65C2×#204—68no—
66#895—64no—
67#882—68no—
68#874—34no—
69C4×D12—34no—
70#869—34no—
71C3×C4⋊C8C2×D314yescomplemented
72C3×C4×C8C2×D314yescomplemented
73#832—64no—
74#821—64no—
75#817—64no—
76#808—64no—
77C4⋊(C3⋊C8)—34no—
78C23×C32—21no—
79C22×C3⋊D3—21no—
80C22×C3⋊D3—22no—
81C22×C3⋊D3—44no—
82C22×C3⋊D3—44no—
83C22×C3⋊D3—82no—
84C32×D4—21no—
85C32×D4SD1612yescomplemented
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92#638—44no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—41no—
95C4⋊(C3⋊D3)—21no—
96C4⋊(C3⋊D3)—42no—
97C4⋊(C3⋊D3)—44no—
98C4⋊(C3⋊D3)—41no—
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)SD1612yescomplemented
103C4×C3⋊D3—41no—
104C4×C3⋊D3—41no—
105#634—42no—
106C32×C8—22no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—41no—
109D42—91no—
110#492—91no—
111#476—91no—
112#476—91no—
113#331—91no—
114D4⋊C8—91no—
115D4⋊C8C3⋊D311yescharacteristic, complemented
116C23×D3—68no—
117C2×C3×D4D1214yes—
118C22×C3×C4—24no—
119C2×#67—68no—
120D3×D4—128no—
121D3×D4—128no—
122C2×D12—34no—
123C2×D12—38no—
124C2×D12—68no—
125C2×D12—64no—
126C2×D12—64no—
127C2×D12—128no—
128C2×D12—128no—
129C2×C4×D3—64no—
130C2×Dic6—64no—
131C2×C3×C8—24no—
132C2×C3×C8—24no—
133C3×C4⋊C4D1214yes—
134C3×C22⋊C4—24no—
135C3×C42C22×D314yes—
136(C2×D3)⋊C4—68no—
137(C2×D3)⋊C4—64no—
138C4⋊Dic3—34no—
139C4⋊Dic3—64no—
140C4⋊Dic3—64no—
141C2×C3⋊C8—64no—
142#204—1216no—
143C22×C32—22no—
144C22×C32—41no—
145C22×C32—41no—
146C22×C32#12011yescharacteristic
147C2×C3⋊D3—22no—
148C2×C3⋊D3—41no—
149C2×C3⋊D3—41no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3—42no—
152C2×C3⋊D3—42no—
153C2×C3⋊D3—88no—
154C32×C4—21no—
155C32×C4—41no—
156C32×C4C2×SD1611yescharacteristic
157C32×C4C2×SD1611yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C32×C4AGL(1,ℤ/8)11yescharacteristic
160C3⋊Dic3—41no—
161C3⋊Dic3—81no—
162C22×D4—181no—
163C22×D4—181no—
164C2×SD16—182no—
165C4⋊Q8—91no—
166#127—91no—
167#121—181no—
168#121—181no—
169#120—182no—
170C4×D4—91no—
171C4×D4C2×C3⋊D311yescharacteristic
172#106—181no—
173#106—181no—
174C4⋊C8—91no—
175C4⋊C8C2×C3⋊D311yescharacteristic, complemented
176#102—181no—
177#102—181no—
178C4×C8C2×C3⋊D311yescharacteristic, complemented
179C23×C3—24no—
180C22×D3—64no—
181C22×D3—68no—
182C22×D3—1216no—
183C22×D3—1216no—
184C22×D3—248no—
185C3×D4—24no—
186C3×D4#20418yescomplemented
187C2×C3×C4—24no—
188C2×C3×C4—44no—
189C2×C3×C4—44no—
190C2×C3×C4C2×D1214yes—
191C2×C3×C4D3×D414yes—
192C2×C3×C4D3×D414yes—
193#67—1216no—
194C2×Dic3—64no—
195C2×Dic3—124no—
196D12—38no—
197D12—64no—
198D12—128no—
199D12—1216no—
200D12—124no—
201D12—124no—
202D12—124no—
203D12—124no—
204C4×D3—124no—
205C4×D3—124no—
206Dic6—128no—
207C3×C8—28no—
208C3×C8—44no—
209C3⋊C8—124no—
210C2×C32—42no—
211C2×C32#45011yescharacteristic
212C2×C32#45011yescharacteristic
213C2×C32#45311yescharacteristic
214C3⋊D3—42no—
215C3⋊D3—82no—
216C24—182no—
217C2×Q8—181no—
218C2×D4—91no—
219C2×D4—92no—
220C2×D4—182no—
221C2×D4—182no—
222C2×D4—181no—
223C2×D4—181no—
224C2×D4—362no—
225C2×D4—362no—
226C2×D4—362no—
227C2×D4—362no—
228C2×D4C4⋊(C3⋊D3)11yescharacteristic
229C22×C4—21no—
230C22×C4—181no—
231SD16—364no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—181no—
235C4⋊C4—91no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—182no—
241C22⋊C4—181no—
242C42C22×C3⋊D311yescharacteristic
243C22×C3—28no—
244C22×C3—44no—
245C22×C3—44no—
246C22×C3#88214yes—
247C2×D3—68no—
248C2×D3—124no—
249C2×D3—124no—
250C2×D3—128no—
251C2×D3—128no—
252C2×D3—128no—
253C2×D3—2432no—
254C3×C4—24no—
255C3×C4—44no—
256C3×C4C2×#20414yes—
257C3×C4#90814yes—
258C3×C4#91114yes—
259C3×C4D3×SD1614yes—
260Dic3—124no—
261Dic3—244no—
262C32#162911yescharacteristic, complemented, Sylow
263C23—21no—
264C23—181no—
265C23—182no—
266C23—364no—
267C23—364no—
268C23—722no—
269Q8—362no—
270D4—21no—
271D4—92no—
272D4—181no—
273D4—362no—
274D4—364no—
275D4—364no—
276D4—361no—
277D4—361no—
278D4—361no—
279D4—361no—
280D4#374412yescomplemented
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—181no—
285C2×C4—361no—
286C2×C4—361no—
287C2×C4—361no—
288C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
289C2×C4D4×C3⋊D311yescharacteristic
290C2×C4D4×C3⋊D311yescharacteristic
291C8—22no—
292C8—41no—
293C8—361no—
294C2×C3—48no—
295C2×C3#473114yes—
296C2×C3#477614yes—
297C2×C3#482214yes—
298D3—128no—
299D3—248no—
300C22—22no—
301C22—41no—
302C22—41no—
303C22—182no—
304C22—361no—
305C22—361no—
306C22—362no—
307C22—362no—
308C22—362no—
309C22—728no—
310C22#6409111yescharacteristic
311C4—21no—
312C4—41no—
313C4—361no—
314C4—721no—
315C4C2×#374411yescharacteristic
316C4#6411711yescharacteristic
317C4#6412011yescharacteristic
318C4SD16×C3⋊D311yescharacteristic
319C3#6819514yescomplemented
320C2—42no—
321C2—362no—
322C2—722no—
323C2#1059243011yescharacteristic
324C2#1059247511yescharacteristic
325C2#1059252111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalD4×C4⋊(C3⋊D3)C2
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1629
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592707C2semidirect
3. #10592541C2semidirect
4. #10592392C2semidirect
5. C32×D4⋊C8C2semidirect
6. #10589351C2semidirect
7. #10589325C2semidirect
18. #64078C22semidirect
19. C32×C4⋊C8C22semidirect
20. C32×C4×C8C22semidirect
25. C4⋊(C3⋊(C3⋊C8))C22semidirect
30. C3×D4⋊C8D3semidirect
71. C3×C4⋊C8C2×D3semidirect
72. C3×C4×C8C2×D3semidirect
85. C32×D4SD16semidirect
102. C4⋊(C3⋊D3)SD16semidirect
115. D4⋊C8C3⋊D3semidirect
175. C4⋊C8C2×C3⋊D3semidirect
178. C4×C8C2×C3⋊D3semidirect
186. C3×D4#204semidirect
262. C32#1629semidirect
280. D4#3744semidirect
319. C3#68195semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
#105927072
#105925412
#105923922
C32×D4⋊C82
#105893512
#105893252
#681953