Finite Group Databasebeta

← C3⋊D3×#491 #11873595

Subgroups — C3⋊D3×#491 #11873595

Order 1152.

1152 conjugacy classes of subgroups; only the 225 normal subgroups are shown.

normal subgroups only

This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 225 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C3⋊D3×#125C211yesmaximal, characteristic
3C32×#491C211yesmaximal, characteristic, complemented
4#10592781C211yesmaximal, characteristic, complemented
5#10592768C211yesmaximal, characteristic, complemented
6C3⋊D3×#103C214yesmaximal
7#10592496C214yesmaximal, complemented
8C3⋊D3×#97C211yesmaximal, characteristic
9#10592402C211yesmaximal, characteristic, complemented
10D3×#491—34nomaximal
11C2×Q8×C3⋊D3C2212yes—
12C32×C4⋊Q8C2211yescharacteristic
13C32×#125C2211yescharacteristic
14#64153C2212yes—
15C2×C8×C3⋊D3C2212yes—
16C4⋊C4×C3⋊D3—22no—
17C4⋊C4×C3⋊D3—22no—
18C4⋊C4×C3⋊D3C2212yes—
19#64099C2212yes—
20#64098—22no—
21#64097—22no—
22C42×C3⋊D3C2211yescharacteristic
23#64079C2211yescharacteristic
24#64078C2211yescharacteristic
25C32×#103C2214yes—
26C32×#97C2211yescharacteristic
27#63662C2214yes—
28#63643C2214yes—
29#63642C2212yes—
30#63637C2214yes—
31#63630C2211yescharacteristic
32D3×C4⋊Q8—34no—
33D3×#125—34no—
34C3×#491D314yescomplemented
35#5082—34no—
36#5069—34no—
37D3×#103—316no—
38#4797—316no—
39D3×#97—34no—
40#4703—34no—
41C2×C32×Q8C2312yes—
42Q8×C3⋊D3—28no—
43C2×C4×C3⋊D3—22no—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3D412yes—
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×#634—22no—
48C2×#634C2312yes—
49C2×C32×C8C2312yes—
50C32×C4⋊C4—22no—
51C32×C4⋊C4—22no—
52C32×C4⋊C4C2312yes—
53C32×C42C2311yescharacteristic
54C4⋊(C3⋊Dic3)—22no—
55C4⋊(C3⋊Dic3)—22no—
56C4⋊(C3⋊Dic3)C2312yes—
57#3750—22no—
58#3750—24no—
59#3750—22no—
60#3750—22no—
61C4×C3⋊Dic3D412yes—
62C4×C3⋊Dic3C2311yescharacteristic
63C2×C3⋊(C3⋊C8)C2312yes—
64C8×C3⋊D3—24no—
65C2×#491—91noSylow
66C2×D3×Q8—38no—
67C3×C4⋊Q8C2×D314yes—
68C3×#125C2×D314yes—
69#944—38no—
70C2×D3×C8—38no—
71D3×C4⋊C4—38no—
72D3×C4⋊C4—68no—
73D3×C4⋊C4—68no—
74#890—38no—
75#889—68no—
76#888—68no—
77C42×D3—34no—
78#870—34no—
79#869—34no—
80C3×#103C2×D3116yes—
81C3×#97C2×D314yes—
82#835—316no—
83#816—316no—
84#815—38no—
85#810—316no—
86#803—34no—
87C22×C3⋊D3C2×D411yescharacteristic
88C32×Q8—24no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C2×D412yes—
92C2×C32×C4C2411yescharacteristic
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3C2×D412yes—
96C2×C3⋊Dic3C2×D411yescharacteristic
97C4×C3⋊D3—24no—
98C4×C3⋊D3—44no—
99C4×C3⋊D3—44no—
100C4×C3⋊D3#4114yes—
101#634—24no—
102#634—44no—
103C32×C8—22no—
104C3⋊(C3⋊C8)—22no—
105C2×C4⋊Q8—91no—
106C2×#125—91no—
107#491—91no—
108#491—91no—
109#491—94no—
110#491—91no—
111#491C3⋊D311yescharacteristic, direct product factor
112C2×#103—94no—
113C2×#97—91no—
114C2×C3×Q8C22×D318yes—
115D3×Q8—632no—
116C2×C4×D3—34no—
117C2×C4×D3—38no—
118C2×C4×D3—68no—
119C2×C4×D3—68no—
120C2×Dic6—38no—
121C2×Dic6—68no—
122C2×C3×C8C22×D318yes—
123C3×C4⋊C4—28no—
124C3×C4⋊C4—28no—
125C3×C4⋊C4C22×D318yes—
126C3×C42C22×D314yes—
127C4⋊Dic3—38no—
128C4⋊Dic3—68no—
129C4⋊Dic3—68no—
130Dic3⋊C4—616no—
131Dic3⋊C4—68no—
132Dic3⋊C4—68no—
133Dic3⋊C4—68no—
134C4×Dic3—38no—
135C4×Dic3—34no—
136C2×C3⋊C8—38no—
137D3×C8—616no—
138C22×C32C22×D411yescharacteristic
139C2×C3⋊D3#12412yes—
140C2×C3⋊D3#13714yes—
141C32×C4—22no—
142C32×C4—42no—
143C32×C4—42no—
144C32×C4C2×#4112yes—
145C3⋊Dic3—22no—
146C3⋊Dic3—42no—
147C3⋊Dic3—42no—
148C3⋊Dic3#12412yes—
149C22×Q8—92no—
150C22×C8—92no—
151C4⋊Q8—92no—
152C4⋊Q8—91no—
153C4⋊Q8—182no—
154C4⋊Q8C2×C3⋊D311yescharacteristic
155#125—92no—
156#125—91no—
157#125—182no—
158#125C2×C3⋊D311yescharacteristic
159C2×C4⋊C4—92no—
160C2×C4⋊C4—182no—
161C2×C4⋊C4—182no—
162C2×C42—91no—
163#103—94no—
164#103—94no—
165#103—94no—
166#103C2×C3⋊D314yes—
167#97—92no—
168#97—91no—
169#97C2×C3⋊D311yescharacteristic
170C22×D3—34no—
171C3×Q8—216no—
172C2×C3×C4—28no—
173C2×C3×C4—28no—
174C2×C3×C4D3×D418yes—
175C2×C3×C4C23×D314yes—
176C2×Dic3—34no—
177C2×Dic3—38no—
178C2×Dic3—68no—
179C2×Dic3—68no—
180C4×D3—316no—
181C4×D3—616no—
182C4×D3—1216no—
183C4×D3—1216no—
184Dic6—616no—
185Dic6—1216no—
186C3×C8—28no—
187C3⋊C8—68no—
188C2×C32C2×#12411yescharacteristic
189C2×C32C2×#13712yes—
190C3⋊D3#49114yesdirect product factor
191C2×Q8—92no—
192C2×Q8—182no—
193C2×Q8—188no—
194C2×Q8C22×C3⋊D312yes—
195C22×C4—91no—
196C22×C4—92no—
197C22×C4—182no—
198C22×C4—182no—
199C2×C8—92no—
200C2×C8—184no—
201C2×C8C22×C3⋊D312yes—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—92no—
205C4⋊C4—182no—
206C4⋊C4—182no—
207C4⋊C4—182no—
208C4⋊C4—184no—
209C4⋊C4—182no—
210C4⋊C4—182no—
211C4⋊C4C22×C3⋊D312yes—
212C42—91no—
213C42—92no—
214C42C22×C3⋊D311yescharacteristic
215C22×C3C2×D3×D414yes—
216C2×D3—38no—
217C2×D3—316no—
218C3×C4—28no—
219C3×C4—48no—
220C3×C4—48no—
221C3×C4D3×#4118yes—
222Dic3—38no—
223Dic3—68no—
224Dic3—128no—
225Dic3—128no—
226C32C2×#49111yescharacteristic, complemented, Sylow
227C23—91no—
228Q8—24no—
229Q8—184no—
230Q8—364no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—91no—
234C2×C4—94no—
235C2×C4—92no—
236C2×C4—184no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—364no—
240C2×C4—364no—
241C2×C4D4×C3⋊D312yes—
242C2×C4C23×C3⋊D311yescharacteristic
243C8—22no—
244C8—182no—
245C2×C3D3×#12414yes—
246C2×C3D3×#13718yes—
247D3—316no—
248C22—92no—
249C22—94no—
250C22C2×D4×C3⋊D311yescharacteristic
251C4—22no—
252C4—42no—
253C4—42no—
254C4—92no—
255C4—182no—
256C4—362no—
257C4—362no—
258C4#41×C3⋊D312yes—
259C3D3×#49114yescomplemented
260C2—94no—
261C2C3⋊D3×#12411yescharacteristic
262C2C3⋊D3×#13712yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#491C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#491C3⋊D3
hypocenterC32C2×#491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
3. C32×#491C2semidirect
4. #10592781C2semidirect
5. #10592768C2semidirect
7. #10592496C2semidirect
9. #10592402C2semidirect
34. C3×#491D3semidirect
111. #491C3⋊D3direct (N × H)
190. C3⋊D3#491direct (N × H)
226. C32C2×#491semidirect
259. C3D3×#491semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C3⋊D3×#1252
C32×#4912
#105927812
#105927682
C3⋊D3×#1032
#105924962
C3⋊D3×#972
#105924022
D3×#4913