Finite Group Databasebeta

← #34045997

Subgroups — #34045997

Order 19072.

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

normal subgroups only

This group has 264 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
1#23750425C211yesmaximal, characteristic
2#23749622C212yesmaximal, complemented
3#23749598C212yesmaximal, complemented
4#23749382C211yesmaximal, characteristic, complemented
5#424×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7#18011944—22no—
8#18011939—22no—
9#18011933—22no—
10#18011870C2212yes—
11#18011836—22no—
12#18011833—22no—
13#18011825—24no—
14C2×M16×C149C2211yescharacteristic
15C22×C8×C149C2211yescharacteristic
16#117×C149C2211yescharacteristic
17C4⋊C8×C149—22no—
18#14558736—22no—
19#14558736—22no—
20#14558736—22no—
21#14558736—22no—
22C2×Dic298D412yes—
23C2×D596D412yes—
24C2×C22⋊D149—22no—
25C2×C4×D149—22no—
26Dic596—22no—
27#14558725—24no—
28D1192—22no—
29C4⋊Dic149—22no—
30C22⋊Dic149—22no—
31C4×Dic149—22no—
32C22×C4×C149C2311yescharacteristic
33M16×C149—22no—
34C2×C8×C149—21no—
35C2×C8×C149—22no—
36C2×C8×C149D412yes—
37C4⋊C4×C149—21no—
38C22⋊C4×C149D412yes—
39C42×C149—21no—
40C22×D149—22no—
41Dic298—22no—
42Dic298—22no—
43D596—22no—
44D596—22no—
45C22⋊D149—42no—
46C22⋊D149—42no—
47C2×Dic149—22no—
48C2×Dic149—42no—
49C4×D149—42no—
50C4×D149—42no—
51C23×C149C2×D411yescharacteristic
52C2×C4×C149—22no—
53C2×C4×C149C2×D412yes—
54C2×C4×C149C2×D411yescharacteristic
55C2×C4×C149#4111yescharacteristic
56C2×C4×C149#4112yes—
57C8×C149—22no—
58C8×C149—41no—
59C22×C149—41no—
60C22×C149#12111yescharacteristic
61C22×C149#12112yes—
62C2×D149—42no—
63C2×D149—82no—
64C4×C149—42no—
65C4×C149#12011yescharacteristic
66C4×C149#12312yes—
67C4×C149#12411yescharacteristic
68Dic149—42no—
69Dic149—82no—
70C2×C149—22no—
71C2×C149—21no—
72C2×C149#39411yescharacteristic
73D149—82no—
74C149#205311yescharacteristic, complemented, Sylow
75#2053—1491nomaximal, Sylow
76#575—1491no—
77#424D14911yescharacteristic, complemented
78#416—1492no—
79#410—1492no—
80H(3,ℤ/4)—1491no—
81C2×#41—1492no—
82#137—2982no—
83AGL(1,ℤ/8)—2982no—
84#135—2982no—
85C2×M16C2×D14911yescharacteristic
86C22×C8C2×D14911yescharacteristic
87#117—1492no—
88#117C2×D14911yescharacteristic
89C4⋊C8—22no—
90#103—2982no—
91#102—2982no—
92#99—2984no—
93#41—2982no—
94#41—2982no—
95#41—2982no—
96#41—2982no—
97C2×Q8—1492no—
98C2×D4—2982no—
99C2×D4—1492no—
100C22×C4—2982no—
101C22×C4C22×D14911yescharacteristic
102Q16—2982no—
103SD16—2984no—
104D8—2982no—
105M16—22no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8C22⋊D14912yes—
109C4⋊C4—21no—
110C4⋊C4—2982no—
111C22⋊C4—2982no—
112C22⋊C4D59612yes—
113C42—21no—
114C42—2982no—
115C23—2982no—
116C23C2×D59611yescharacteristic
117Q8—2982no—
118Q8—2982no—
119D4—2982no—
120D4—2982no—
121D4—5962no—
122D4—5962no—
123C2×C4—22no—
124C2×C4—2982no—
125C2×C4—5962no—
126C2×C4—5962no—
127C2×C4—5962no—
128C2×C4D4×D14912yes—
129C2×C4C2×C22⋊D14911yescharacteristic
130C2×C4#1455873611yescharacteristic
131C2×C4#1455873712yes—
132C8—22no—
133C8—41no—
134C22—41no—
135C22—5962no—
136C22—11922no—
137C22#1801188511yescharacteristic
138C22#1801188612yes—
139C4—42no—
140C4—5962no—
141C4—11922no—
142C4#1801187911yescharacteristic
143C4#1801189612yes—
144C4#1801190011yescharacteristic
145C2—21no—
146C2—22no—
147C2—11922no—
148C2#2374954211yescharacteristic
subgroupG/H
centerC4#18011900
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#424×C149C2
socleC2×C149#394
prime radical#23750425C2
hypercenter#424D149
hypocenterC149#2053
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #23749622C2semidirect
3. #23749598C2semidirect
4. #23749382C2semidirect
5. #424×C149C2semidirect
74. C149#2053semidirect
77. #424D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237496222
#237495982
#237493822
#424×C1492
#2053149