Finite Group Databasebeta

← #11920236

Subgroups — #11920236

Order 1152.

381 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 381 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C4×#41⋊C9C211yesmaximal, characteristic
2#10589528C212yesmaximal
3#10589493C212yesmaximal, complemented
4#10589488C212yesmaximal, complemented
5#82508—31nomaximal
6C2×#41⋊C9C2211yescharacteristic
7#63431—41nomaximal
8C4×Q8⋊C9C2211yescharacteristic
9C4×Q8⋊C9C2211yescharacteristic
10#63421C2214yes—
11C3×C4×#41D311yescharacteristic
12C2×#869—31no—
13#5232—32no—
14#5021—32no—
15#5020—32no—
16#5008—32no—
17#5007—32no—
18#4995—32no—
19#4924—31no—
20C2×Dic18—42no—
21#41⋊C9Q812yescomplemented
22C2×Q8⋊C9C2311yescharacteristic
23C42×C9—41no—
24C4⋊Dic9—42no—
25C4⋊Dic9—42no—
26#3079—91noSylow
27C2×C3×#41C2×D311yescharacteristic
28C22×Dic6—61no—
29C3×C4×Q8C2×D311yescharacteristic
30C3×C4×Q8C2×D311yescharacteristic
31C3×C4×D4—31no—
32C3×C4×D4—31no—
33C3×#117—31no—
34C2×C3×C42—31no—
35C2×C4⋊Dic3—32no—
36C2×C4⋊Dic3—61no—
37C2×#208—32no—
38#869—32no—
39#869—32no—
40#869—61no—
41#869—61no—
42#835—34no—
43#832—34no—
44#808—34no—
45#807—34no—
46C4⋊(C3⋊C8)—32no—
47C4⋊(C3⋊C8)—32no—
48C2×C4×C9—41no—
49C2×C4×C9—41no—
50C2×C4×C9—41no—
51C2×Dic9—44no—
52Dic18—84no—
53Q8⋊C9C2×Q811yescharacteristic, complemented
54C2×C4⋊Q8—91no—
55C4×#41D911yescharacteristic
56#477—92no—
57#476—92no—
58#475—92no—
59#474—92no—
60#428—92no—
61#423—91no—
62#417—92no—
63C3×#41—32no—
64C3×#41Dic612yes—
65C2×C3×Q8C22×D311yescharacteristic
66C2×C3×D4—31no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4—31no—
70C22×Dic3—62no—
71C2×Dic6—62no—
72C2×Dic6—62no—
73C2×Dic6—124no—
74C3×C4⋊C4—31no—
75C3×C4⋊C4—31no—
76C3×C22⋊C4—61no—
77C3×C42—31no—
78C3×C42—31no—
79C3×C42—31no—
80C3×C42S411yescharacteristic
81C4⋊Dic3—34no—
82C4⋊Dic3—62no—
83C4⋊Dic3—62no—
84C4⋊Dic3—62no—
85#208—64no—
86C2×C3⋊C8—34no—
87C22×C9—41no—
88C4×C9—42no—
89C4×C9—42no—
90C4×C9—42no—
91Dic9—84no—
92C2×#41C2×D911yescharacteristic
93C22×Q8—181no—
94C2×M16—92no—
95C4⋊Q8—92no—
96C4⋊Q8—92no—
97C4⋊Q8—181no—
98C4⋊Q8—181no—
99C4×Q8C2×D911yescharacteristic
100C4×Q8C2×D911yescharacteristic
101C4×D4—31no—
102C4×D4—31no—
103#117—31no—
104C2×C4⋊C4—92no—
105C2×C4⋊C4—181no—
106C2×C42—31no—
107#107—94no—
108#106—94no—
109C4⋊C8—92no—
110C4⋊C8—92no—
111#103—94no—
112#102—94no—
113C23×C3—31no—
114C3×Q8—31no—
115C3×Q8C2×Dic611yescharacteristic
116C3×D4—32no—
117C3×D4—61no—
118C2×C3×C4—31no—
119C2×C3×C4—32no—
120C2×C3×C4—32no—
121C2×C3×C4—31no—
122C2×C3×C4—31no—
123C2×C3×C4—62no—
124C2×C3×C4—62no—
125C2×C3×C4C2×S411yescharacteristic
126C2×C3×C4C2×S411yescharacteristic
127C2×C3×C4C2×S411yescharacteristic
128C2×Dic3—64no—
129C2×Dic3—124no—
130Dic6—124no—
131Dic6—124no—
132C3⋊C8—64no—
133C2×C9—41no—
134C2×C9—41no—
135C2×C9—41no—
136#41—32no—
137#41Dic1812yescomplemented
138C2×Q8—182no—
139C2×Q8—182no—
140C2×Q8—364no—
141C2×Q8C22×D911yescharacteristic
142C2×D4—31no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—31no—
146C22×C4—182no—
147M16—184no—
148C2×C8—94no—
149C4⋊C4—31no—
150C4⋊C4—31no—
151C4⋊C4—94no—
152C4⋊C4—182no—
153C4⋊C4—182no—
154C4⋊C4—182no—
155C22⋊C4—61no—
156C42—31no—
157C42—31no—
158C42—31no—
159C42(C22⋊C9)⋊C211yescharacteristic
160C22×C3—32no—
161C22×C3—61no—
162C22×C3—61no—
163C22×C3C22×S411yescharacteristic
164C3×C4—31no—
165C3×C4—31no—
166C3×C4—61no—
167C3×C4—61no—
168C3×C4A4⋊Q812yes—
169C3×C4#98412yes—
170C3×C4#98612yes—
171Dic3—124no—
172C9—41noSylow
173C23—31no—
174Q8—31no—
175Q8—364no—
176Q8—364no—
177Q8C2×Dic1811yescharacteristic
178D4—32no—
179D4—61no—
180C2×C4—31no—
181C2×C4—32no—
182C2×C4—32no—
183C2×C4—31no—
184C2×C4—31no—
185C2×C4—62no—
186C2×C4—62no—
187C2×C4—184no—
188C2×C4—364no—
189C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
190C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
191C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
192C8—184no—
193C2×C3—62no—
194C2×C3C2×A4⋊Q811yescharacteristic
195C2×C3C2×#98411yescharacteristic
196C2×C3C2×#98611yescharacteristic
197C22—32no—
198C22—61no—
199C22—61no—
200C22C22×(C22⋊C9)⋊C211yescharacteristic
201C4—31no—
202C4—31no—
203C4—61no—
204C4—61no—
205C4—364no—
206C4(C22⋊C9)⋊Q812yes—
207C4#6369012yes—
208C4#6369212yes—
209C3#8533711yescharacteristic
210C2—62no—
211C2C2×(C22⋊C9)⋊Q811yescharacteristic
212C2C2×#6369011yescharacteristic
213C2C2×#6369211yescharacteristic
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC2×Q8⋊C9C23
Frattini, socleC22×C3C22×S4
FittingC3×C4×#41D3
prime radicalC2×C3×#41C2×D3
hypercenterC42(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×Q8
LCSG ▷ C2×Q8⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #10589493C2semidirect
4. #10589488C2semidirect
21. #41⋊C9Q8semidirect
53. Q8⋊C9C2×Q8semidirect
137. #41Dic18semidirect

Maximal subgroups

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

subgroupindex
C4×#41⋊C92
#105895282
#105894932
#105894882
#825083
#634314