Finite Group Databasebeta

← #11782705

Subgroups — #11782705

Order 1152.

413 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 413 conjugacy classes of subgroups — too many to draw. Only its 116 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
1#10592398C211yesmaximal, characteristic
2C3×#4680C211yesmaximal, characteristic
3#10590303C212yesmaximal
4#10590287C212yesmaximal
5C3×#4455C211yesmaximal, characteristic
6#71338—31nomaximal
7#68095—31nomaximal
8C2×#3746—22no—
9#64078C2211yescharacteristic
10#64078C2211yescharacteristic
11C3×#869C2212yes—
12C32×C4×C8C2211yescharacteristic
13C3×#817—22no—
14C3×C4×C3⋊C8C2212yes—
15#63573—24no—
16#63566—24no—
17C3×#498—31no—
18#5080—32no—
19#5079—32no—
20#4699—31no—
21#4699—31no—
22#4699—61no—
23#4681—32no—
24#4680—32no—
25#4680D311yescharacteristic
26C3×#322—31no—
27#4455D311yescharacteristic
28C2×#634—21no—
29C2×#634—21no—
30C2×C3×Dic6—22no—
31C2×C32×C8D412yes—
32C32×C42C2311yescharacteristic
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35#3746—44no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8D414yes—
39#1716—91noSylow
40C3×C4⋊Q8—32no—
41C2×Dic12—64no—
42C2×Dic12—62no—
43C2×Dic12—62no—
44#869—31no—
45#869—31no—
46#869—31no—
47#869—31no—
48#869—61no—
49#869—61no—
50#869C2×D312yes—
51C3×#106—62no—
52C3×C4×C8—21no—
53C3×C4×C8—32no—
54C3×C4×C8C2×D311yescharacteristic
55C3×C4×C8C2×D311yescharacteristic
56#835—64no—
57#817—22no—
58#817—64no—
59#816—64no—
60#808—64no—
61C4×C3⋊C8C2×D312yes—
62C2×C32×C4C2×D412yes—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66#634—42no—
67#634—42no—
68C2×C3×Dic3—42no—
69C3×Dic6—44no—
70C32×C8SD1614yes—
71C3×C3⋊C8—24no—
72#498—31no—
73#498—92no—
74#494—91no—
75#487—92no—
76#322—31no—
77C2×C3×Q8—62no—
78C2×Dic6—22no—
79C2×Dic6—62no—
80C2×Dic6—62no—
81C2×Dic6—61no—
82C2×Dic6—61no—
83C2×Dic6—61no—
84C2×Dic6—61no—
85C2×C3×C8—22no—
86C2×C3×C8—34no—
87C2×C3×C8D1212yes—
88C2×C3×C8#6712yes—
89C3×C4⋊C4—62no—
90C3×C4⋊C4—62no—
91C3×C42—21no—
92C3×C42C22×D311yescharacteristic
93C3×C42C22×D311yescharacteristic
94C4⋊Dic3—22no—
95C4⋊Dic3—22no—
96C4⋊Dic3—62no—
97C4⋊Dic3—62no—
98C4⋊Dic3—62no—
99C4⋊Dic3—62no—
100C4⋊Dic3—122no—
101C4⋊Dic3—122no—
102C2×C3⋊C8D1214yes—
103Dic12—128no—
104Dic12—124no—
105Dic12—124no—
106C22×C32#12711yescharacteristic
107C32×C4C2×SD1612yes—
108C32×C4#13714yes—
109C3⋊Dic3—81no—
110C3⋊Dic3—81no—
111C3×Dic3—82no—
112C2×Q16—182no—
113C4⋊Q8—32no—
114C4⋊Q8—91no—
115C4⋊Q8—91no—
116#106—62no—
117#106—184no—
118#103—184no—
119C4×C8—32no—
120C4×C8D3211yescharacteristic
121C3×Q8—124no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—122no—
125C2×C3×C4C2×D1212yes—
126C2×C3×C4C2×D1211yescharacteristic
127C2×C3×C4D3×D412yes—
128C2×C3×C4C2×#6711yescharacteristic
129C2×Dic3—42no—
130C2×Dic3—122no—
131C2×Dic3—122no—
132C2×Dic3—121no—
133C2×Dic3—121no—
134C2×Dic3—121no—
135C2×Dic3—121no—
136Dic6—44no—
137Dic6—124no—
138Dic6—124no—
139Dic6—122no—
140Dic6—122no—
141Dic6—122no—
142Dic6—122no—
143C3×C8—24no—
144C3×C8—64no—
145C3×C8#20414yes—
146C3×C8#21514yes—
147C3⋊C8—24no—
148C2×C32#49211yescharacteristic
149C2×C32#49712yes—
150C2×Q8—62no—
151C2×Q8—181no—
152C2×Q8—181no—
153Q16—364no—
154C2×C8—34no—
155C2×C8#62612yes—
156C4⋊C4—62no—
157C4⋊C4—62no—
158C4⋊C4—182no—
159C4⋊C4—182no—
160C42C2×D3211yescharacteristic
161C22×C3—21no—
162C22×C3#87411yescharacteristic
163C22×C3#94011yescharacteristic
164C3×C4—24no—
165C3×C4—22no—
166C3×C4—242no—
167C3×C4C2×#20412yes—
168C3×C4#90914yes—
169C3×C4#91514yes—
170C3×C4C2×#21512yes—
171Dic3—82no—
172Dic3—242no—
173Dic3—242no—
174Dic3—241no—
175Dic3—241no—
176Dic3—241no—
177Dic3—241no—
178C32#171611yescharacteristic, complemented, Sylow
179Q8—124no—
180Q8—362no—
181Q8—362no—
182C2×C4—122no—
183C2×C4—361no—
184C2×C4—361no—
185C2×C4D3×D1212yes—
186C2×C4C2×#62611yescharacteristic
187C8—64no—
188C8#371714yes—
189C2×C3—21no—
190C2×C3—22no—
191C2×C3#469311yescharacteristic
192C2×C3#471512yes—
193C2×C3#508511yescharacteristic
194C2×C3#516712yes—
195C22#6391111yescharacteristic
196C4—242no—
197C4—721no—
198C4—721no—
199C4#6380014yes—
200C4C2×#371712yes—
201C3—21no—
202C3#6809511yescharacteristic, complemented
203C3#7133811yescharacteristic, complemented
204C2#1059037311yescharacteristic
205C2#1059089712yes—
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1716
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
178. C32#1716semidirect
202. C3#68095semidirect
203. C3#71338semidirect

Maximal subgroups

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

subgroupindex
#105923982
C3×#46802
#105903032
#105902872
C3×#44552
#713383
#680953