Finite Group Databasebeta

← #11920238

Subgroups — #11920238

Order 1152.

343 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 343 conjugacy classes of subgroups — too many to draw. Only its 57 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#10589491C214yesmaximal, complemented
4#82509—31nomaximal
5C2×#41⋊C9C2211yescharacteristic
6#63432—41nomaximal
7C4×Q8⋊C9C2212yes—
8#63421C2214yes—
9C3×C4×#41D311yescharacteristic
10C2×#870—31no—
11#5232—32no—
12#5022—34no—
13#5009—34no—
14#4995—32no—
15#4924—31no—
16#41⋊C9Q812yes—
17C2×Q8⋊C9C2311yescharacteristic
18C42×C9—41no—
19C4⋊Dic9—42no—
20Dic9⋊C4—44no—
21#3080—91noSylow
22C2×C3×#41C2×D311yescharacteristic
23C3×C4×Q8C2×D312yes—
24C3×C4×D4—32no—
25C3×#117—31no—
26C2×C3×C42—31no—
27C2×C4⋊Dic3—32no—
28C2×Dic3⋊C4—62no—
29C2×#208—32no—
30#870—34no—
31#870—61no—
32#870—61no—
33#835—34no—
34#832—34no—
35#808—34no—
36#807—34no—
37C4⋊(C3⋊C8)—34no—
38C2×C4×C9—41no—
39C2×C4×C9—42no—
40C2×Dic9—44no—
41Q8⋊C9C2×Q811yescharacteristic
42C2×#125—91no—
43C4×#41D911yescharacteristic
44#479—94no—
45#478—94no—
46#428—92no—
47#423—91no—
48#417—92no—
49C3×#41—32no—
50C3×#41Dic612yes—
51C2×C3×Q8C22×D311yescharacteristic
52C2×C3×D4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—32no—
55C22×Dic3—62no—
56C3×C4⋊C4—32no—
57C3×C22⋊C4—61no—
58C3×C42—32no—
59C3×C42—31no—
60C3×C42S411yescharacteristic
61C4⋊Dic3—34no—
62C4⋊Dic3—62no—
63Dic3⋊C4—64no—
64Dic3⋊C4—64no—
65#208—64no—
66C2×C3⋊C8—34no—
67C22×C9—41no—
68C4×C9—42no—
69C4×C9—82no—
70Dic9—84no—
71C2×#41C2×D911yescharacteristic
72C2×M16—92no—
73#125—94no—
74#125—181no—
75#125—181no—
76C4×Q8C2×D912yes—
77C4×D4—32no—
78#117—31no—
79C2×C4⋊C4—92no—
80C2×C4⋊C4—182no—
81C2×C42—31no—
82#107—94no—
83#106—94no—
84C4⋊C8—94no—
85#103—94no—
86#102—94no—
87C23×C3—31no—
88C3×Q8—31no—
89C3×Q8C2×Dic611yescharacteristic
90C3×D4—32no—
91C3×D4—61no—
92C2×C3×C4—31no—
93C2×C3×C4—32no—
94C2×C3×C4—32no—
95C2×C3×C4—32no—
96C2×C3×C4—122no—
97C2×C3×C4C2×S412yes—
98C2×C3×C4C2×S411yescharacteristic
99C2×Dic3—64no—
100C2×Dic3—124no—
101C3⋊C8—64no—
102C2×C9—41no—
103C2×C9—42no—
104#41—32no—
105#41Dic1812yes—
106C2×Q8C22×D911yescharacteristic
107C2×D4—31no—
108C22×C4—31no—
109C22×C4—32no—
110C22×C4—182no—
111M16—184no—
112C2×C8—94no—
113C4⋊C4—32no—
114C4⋊C4—94no—
115C4⋊C4—184no—
116C4⋊C4—182no—
117C4⋊C4—184no—
118C22⋊C4—61no—
119C42—32no—
120C42—31no—
121C42(C22⋊C9)⋊C211yescharacteristic
122C22×C3—32no—
123C22×C3—62no—
124C22×C3C22×S411yescharacteristic
125C3×C4—22no—
126C3×C4—31no—
127C3×C4—31no—
128C3×C4—62no—
129C3×C4A4⋊Q812yes—
130Dic3—124no—
131C9—41noSylow
132C23—31no—
133Q8—31no—
134Q8C2×Dic1811yescharacteristic
135D4—32no—
136D4—61no—
137C2×C4—31no—
138C2×C4—32no—
139C2×C4—32no—
140C2×C4—32no—
141C2×C4—122no—
142C2×C4—184no—
143C2×C4—364no—
144C2×C4C2×(C22⋊C9)⋊C212yes—
145C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
146C8—184no—
147C2×C3—62no—
148C2×C3C2×A4⋊Q811yescharacteristic
149C2×C3#592312yes—
150C22—32no—
151C22—62no—
152C22C22×(C22⋊C9)⋊C211yescharacteristic
153C4—22no—
154C4—31no—
155C4—31no—
156C4—62no—
157C4—364no—
158C4(C22⋊C9)⋊Q812yes—
159C3#8533911yescharacteristic
160C2—62no—
161C2C2×(C22⋊C9)⋊Q811yescharacteristic
162C2#1059309812yes—
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. #10589491C2semidirect

Maximal subgroups

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

subgroupindex
C4×#41⋊C92
#105895282
#105894912
#825093
#634324