Finite Group Databasebeta

← #11792272

Subgroups — #11792272

Order 1152.

1110 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C2×#64118C212yesmaximal, complemented
2#10595981C211yesmaximal, characteristic
3C2×#63652C212yesmaximal, complemented
4#10592672C211yesmaximal, characteristic, complemented
5C32×#343C211yesmaximal, characteristic, complemented
6#69009—34nomaximal
7C2×#3828C2212yes—
8C22×#634C2211yescharacteristic
9C2×C32×M16C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—22no—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64118—24no—
14#64118—24no—
15C2×#3746—22no—
16C2×#3744—22no—
17#64106—22no—
18#64104—22no—
19#63658—22no—
20#63652—24no—
21C2×#909—38no—
22#5510—34no—
23C2×#825—38no—
24#4973—34no—
25C3×#343D314yescomplemented
26C22×C32×C4D412yes—
27C22×C32×C4C2311yescharacteristic
28C2×#638—22no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31#3828—22no—
32#3828—22no—
33#3828—22no—
34#3828—22no—
35C2×C4⋊(C3⋊D3)—22no—
36C2×C4⋊(C3⋊D3)D412yes—
37C2×C4×C3⋊D3—22no—
38C2×#634—22no—
39C2×#634—22no—
40C2×#634—21no—
41C2×#634D412yes—
42C2×#634D412yescomplemented
43C32×M16—22no—
44C32×M16D414yescomplemented
45C2×C32×C8—22no—
46C32×C4⋊C4—22no—
47#3752—24no—
48C4⋊(C3⋊Dic3)—22no—
49C4×C3⋊Dic3—22no—
50#3746—28no—
51#3744—28no—
52#2007—91noSylow
53C2×#235—38no—
54C22×Dic6—34no—
55C2×C3×M16C2×D318yes—
56C2×C3×C4⋊C4C2×D314yes—
57#930—68no—
58C2×C4×Dic3—34no—
59#909—616no—
60#909—616no—
61C2×Dic12—68no—
62C2×#204—68no—
63#897—68no—
64#895—68no—
65C3⋊#95—68no—
66#825—616no—
67C23×C32C2×D411yescharacteristic
68C22×C3⋊D3—22no—
69C2×C32×C4—22no—
70C2×C32×C4—42no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D412yes—
74C2×C32×C4#4111yescharacteristic
75#638—42no—
76#638—42no—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—22no—
80C2×C3⋊Dic3—41no—
81C2×C3⋊Dic3—41no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3—41no—
84C4⋊(C3⋊D3)—22no—
85C4⋊(C3⋊D3)—22no—
86C4⋊(C3⋊D3)—82no—
87C4×C3⋊D3—42no—
88C4×C3⋊D3—42no—
89#634—24no—
90#634—22no—
91#634—22no—
92#634—42no—
93C32×C8—24no—
94C2×#137—92no—
95#537—91no—
96C2×#104—92no—
97#391—91no—
98#343C3⋊D311yescharacteristic, complemented
99C22×C3×C4D1218yes—
100C22×C3×C4C22×D314yes—
101C2×#67—68no—
102C22×Dic3—64no—
103C22×Dic3—64no—
104#235—68no—
105#235—68no—
106#235—68no—
107#235—68no—
108C2×D12—38no—
109C2×D12—68no—
110C2×C4×D3—68no—
111C2×Dic6—38no—
112C2×Dic6—38no—
113C2×Dic6—68no—
114C2×Dic6—68no—
115C2×Dic6—64no—
116C3×M16—28no—
117C3×M16D12116yescomplemented
118C2×C3×C8—28no—
119C3×C4⋊C4—28no—
120(C2×D3)⋊C4—616no—
121C4⋊Dic3—68no—
122C4×Dic3—68no—
123Dic12—632no—
124#204—632no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32#12011yescharacteristic
128C22×C32#12111yescharacteristic
129C22×C32#12711yescharacteristic
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—42no—
133C32×C4—42no—
134C32×C4#12012yes—
135C32×C4#12112yes—
136C3⋊Dic3—42no—
137C3⋊Dic3—42no—
138C3⋊Dic3—42no—
139C2×#41—92no—
140C22×Q8—91no—
141#137—184no—
142#137—184no—
143C2×Q16—182no—
144C2×SD16—182no—
145C2×M16C2×C3⋊D312yes—
146C22⋊Q8—182no—
147#121—182no—
148#121—182no—
149C2×C4⋊C4C2×C3⋊D311yescharacteristic
150C2×C42—91no—
151#104—184no—
152#95—182no—
153C23×C3C2×D1214yes—
154C22×D3—68no—
155C2×C3×C4—28no—
156C2×C3×C4—48no—
157C2×C3×C4C2×D1218yes—
158C2×C3×C4D3×D414yes—
159C2×C3×C4D3×D418yes—
160C2×C3×C4#23914yes—
161#67—128no—
162#67—128no—
163C2×Dic3—68no—
164C2×Dic3—68no—
165C2×Dic3—68no—
166C2×Dic3—124no—
167C2×Dic3—124no—
168C2×Dic3—124no—
169C2×Dic3—124no—
170D12—68no—
171D12—68no—
172D12—248no—
173C4×D3—128no—
174C4×D3—128no—
175Dic6—616no—
176Dic6—68no—
177Dic6—68no—
178Dic6—128no—
179C3×C8—216no—
180C2×C32—21no—
181C2×C32—21no—
182C2×C32#39211yescharacteristic
183C2×C32#45511yescharacteristic
184C2×C32#45611yescharacteristic
185C3⋊D3—82no—
186#41—182no—
187#41—182no—
188#41—182no—
189#41—182no—
190C2×Q8—92no—
191C2×Q8—92no—
192C2×Q8—181no—
193C2×Q8—182no—
194C2×Q8—182no—
195C2×D4—92no—
196C2×D4—182no—
197C2×D4—182no—
198C22×C4—181no—
199C22×C4—181no—
200C22×C4—182no—
201C22×C4C4⋊(C3⋊D3)12yes—
202C22×C4C22×C3⋊D311yescharacteristic
203Q16—188no—
204SD16—188no—
205M16—22no—
206M16C4⋊(C3⋊D3)14yescomplemented
207C2×C8—22no—
208C4⋊C4—22no—
209C4⋊C4—182no—
210C22⋊C4—184no—
211C42—182no—
212C22×C3—24no—
213C22×C3—24no—
214C22×C3#87414yes—
215C22×C3#88214yes—
216C22×C3#89514yes—
217C2×D3—128no—
218C2×D3—128no—
219C2×D3—128no—
220C3×C4—48no—
221C3×C4#88218yes—
222C3×C4#89518yes—
223Dic3—128no—
224Dic3—128no—
225Dic3—128no—
226C32#200711yescharacteristic, complemented, Sylow
227C23—182no—
228C23C2×C4⋊(C3⋊D3)11yescharacteristic
229Q8—184no—
230Q8—182no—
231Q8—182no—
232Q8—362no—
233D4—182no—
234D4—182no—
235D4—362no—
236D4—362no—
237D4—722no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—182no—
243C2×C4—361no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—362no—
248C2×C4—362no—
249C2×C4C2×C4⋊(C3⋊D3)12yes—
250C2×C4D4×C3⋊D311yescharacteristic
251C2×C4D4×C3⋊D312yes—
252C2×C4#383211yescharacteristic
253C8—24no—
254C2×C3—24no—
255C2×C3—24no—
256C2×C3#467114yes—
257C2×C3#474614yes—
258C2×C3#475214yes—
259D3—248no—
260C22—21no—
261C22—21no—
262C22—362no—
263C22—362no—
264C22—362no—
265C22#6408311yescharacteristic
266C22#6409111yescharacteristic
267C22#6410411yescharacteristic
268C4—42no—
269C4—362no—
270C4—362no—
271C4—362no—
272C4#6409112yes—
273C4#6410412yes—
274C3#6900914yescomplemented
275C2—21no—
276C2—21no—
277C2—722no—
278C2#1059237011yescharacteristic
279C2#1059244511yescharacteristic
280C2#1059245111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#343C3⋊D3
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#64118C2semidirect
3. C2×#63652C2semidirect
4. #10592672C2semidirect
5. C32×#343C2semidirect
25. C3×#343D3semidirect
42. C2×#634D4semidirect
44. C32×M16D4semidirect
98. #343C3⋊D3semidirect
117. C3×M16D12semidirect
206. M16C4⋊(C3⋊D3)semidirect
226. C32#2007semidirect
274. C3#69009semidirect

Maximal subgroups

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

subgroupindex
C2×#641182
#105959812
C2×#636522
#105926722
C32×#3432
#690093