Finite Group Databasebeta

← C3×#71299 #11782690

Subgroups — C3×#71299 #11782690

Order 1152.

413 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 413 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C32×#494C211yesmaximal, characteristic
2C3×#5093C212yesmaximal
3C3×#5080C212yesmaximal
4C3×#4680C211yesmaximal, characteristic
5C3×#4455C211yesmaximal, characteristic
6C3×#1716—31nomaximal
7#71299C311yesmaximal, characteristic, direct product factor
8C2×C32×Q16—22no—
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C3×#869C2212yes—
12C32×C4×C8C2211yescharacteristic
13C3×#817—22no—
14C3×#810—24no—
15C3×#808—24no—
16C3×C4×C3⋊C8C2212yes—
17C3×#498—32no—
18C3×#498—31no—
19C3×#494—21no—
20C3×#494D311yescharacteristic
21C3×#494C2×C311yescharacteristic
22C3×#487—32no—
23#5093C2×C312yes—
24#5080C2×C312yes—
25#4680C2×C311yescharacteristic
26C3×#322—31no—
27#4455C2×C311yescharacteristic
28C2×C32×Q8—21no—
29C2×C32×Q8—21no—
30C2×C3×Dic6—22no—
31C32×Q16—44no—
32C2×C32×C8D412yes—
33C32×C4⋊C4—22no—
34C32×C4⋊C4—22no—
35C32×C42C2311yescharacteristic
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8D414yes—
39#1716—31noSylow
40C2×C3×Q16—24no—
41C2×C3×Q16—22no—
42C2×C3×Q16—22no—
43C3×C4⋊Q8—21no—
44C3×C4⋊Q8—21no—
45C3×C4⋊Q8—32no—
46C3×C4⋊Q8C2×D311yescharacteristic
47C3×C4⋊Q8C2×D311yescharacteristic
48C3×C4⋊Q8C22×C311yescharacteristic
49C3×C4⋊Q8C22×C311yescharacteristic
50#869C22×C312yes—
51C3×#106—64no—
52C3×#106—62no—
53C3×#103—64no—
54C3×C4×C8—21no—
55C3×C4×C8—32no—
56C3×C4×C8C2×D311yescharacteristic
57C3×C4×C8C22×C311yescharacteristic
58#817—22no—
59#810—24no—
60#808—24no—
61C4×C3⋊C8C22×C312yes—
62C32×Q8—42no—
63C32×Q8—42no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C2×D412yes—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3×Dic3—42no—
69C3×Dic6—44no—
70C32×C8SD1614yes—
71C3×C3⋊C8—24no—
72#498—32no—
73#498—31no—
74#494C3×D311yescharacteristic
75#487—32no—
76#322—31no—
77C2×C3×Q8—22no—
78C2×C3×Q8—22no—
79C2×C3×Q8—21no—
80C2×C3×Q8—21no—
81C2×C3×Q8—21no—
82C2×C3×Q8—21no—
83C2×C3×Q8—62no—
84C2×Dic6—22no—
85C3×Q16—48no—
86C3×Q16—44no—
87C3×Q16—44no—
88C2×C3×C8—22no—
89C2×C3×C8—34no—
90C2×C3×C8#6712yes—
91C2×C3×C8C3×D412yes—
92C3×C4⋊C4—22no—
93C3×C4⋊C4—22no—
94C3×C4⋊C4—22no—
95C3×C4⋊C4—22no—
96C3×C4⋊C4—42no—
97C3×C4⋊C4—42no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100C3×C42—21no—
101C3×C42C22×D311yescharacteristic
102C3×C42C23×C311yescharacteristic
103C4⋊Dic3—22no—
104C4⋊Dic3—22no—
105C2×C3⋊C8C3×D414yes—
106C22×C32#12711yescharacteristic
107C32×C4—81no—
108C32×C4—81no—
109C32×C4C2×SD1612yes—
110C32×C4#13714yes—
111C3×Dic3—82no—
112C2×Q16—22no—
113C4⋊Q8—32no—
114C4⋊Q8C2×C3×D311yescharacteristic
115C4⋊Q8C2×C3×D311yescharacteristic
116#106—64no—
117#106—62no—
118#103—64no—
119C4×C8—32no—
120C4×C8C2×C3×D311yescharacteristic
121C3×Q8—44no—
122C3×Q8—44no—
123C3×Q8—42no—
124C3×Q8—42no—
125C3×Q8—42no—
126C3×Q8—42no—
127C3×Q8—124no—
128C2×C3×C4—22no—
129C2×C3×C4—21no—
130C2×C3×C4—42no—
131C2×C3×C4—42no—
132C2×C3×C4—41no—
133C2×C3×C4—41no—
134C2×C3×C4—41no—
135C2×C3×C4—41no—
136C2×C3×C4—122no—
137C2×C3×C4D3×D412yes—
138C2×C3×C4C2×#6711yescharacteristic
139C2×C3×C4C2×C3×D412yes—
140C2×C3×C4C2×C3×D411yescharacteristic
141C2×Dic3—42no—
142Dic6—44no—
143C3×C8—24no—
144C3×C8—64no—
145C3×C8#21414yes—
146C3×C8C3×SD1614yes—
147C3⋊C8—24no—
148C2×C32#49211yescharacteristic
149C2×C32#49712yes—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—62no—
153Q16—44no—
154C2×C8—34no—
155C2×C8C3×#6712yes—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—62no—
159C4⋊C4—62no—
160C42C22×C3×D311yescharacteristic
161C22×C3—21no—
162C22×C3#94011yescharacteristic
163C22×C3C3×#12711yescharacteristic
164C3×C4—24no—
165C3×C4—22no—
166C3×C4—82no—
167C3×C4—82no—
168C3×C4—81no—
169C3×C4—81no—
170C3×C4—81no—
171C3×C4—81no—
172C3×C4—242no—
173C3×C4#91814yes—
174C3×C4C2×#21412yes—
175C3×C4C2×C3×SD1612yes—
176C3×C4C3×#13714yes—
177Dic3—82no—
178C32#171611yescharacteristic, complemented, Sylow
179Q8—42no—
180Q8—42no—
181Q8—124no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—122no—
185C2×C4C3×D3×D412yes—
186C2×C4C2×C3×#6711yescharacteristic
187C8—64no—
188C8C3×#21414yes—
189C2×C3—22no—
190C2×C3—21no—
191C2×C3#507611yescharacteristic
192C2×C3#519012yes—
193C2×C3C3×#49211yescharacteristic
194C2×C3C3×#49712yes—
195C22C3×#94011yescharacteristic
196C4—81no—
197C4—81no—
198C4—242no—
199C4C3×#91814yes—
200C4C2×C3×#21412yes—
201C3—21no—
202C3#7129911yescharacteristic, direct product factor
203C3C3×#171611yescharacteristic, complemented
204C2C3×#507611yescharacteristic
205C2C3×#519012yes—
subgroupG/H
centerC22×C3#940
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#494C2
socle, prime radicalC22×C32#127
hypercenterC3×#494D3
hypocenterC3C3×#1716
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
7. #71299C3direct (N × H)
178. C32#1716semidirect
202. C3#71299direct (N × H)
203. C3C3×#1716semidirect

Maximal subgroups

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

subgroupindex
C32×#4942
C3×#50932
C3×#50802
C3×#46802
C3×#44552
C3×#17163
#712993