Finite Group Databasebeta

← #34055434

Subgroups — #34055434

Order 19072.

358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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#23750180C212yesmaximal
2#23750023C211yesmaximal, characteristic, complemented
3#23749975C212yesmaximal, complemented
4#23749880C214yesmaximal
5#23749732C214yesmaximal, complemented
6C4×#14558719C211yesmaximal, characteristic
7#494×C149C211yesmaximal, characteristic, complemented
8C2×#14558719C2212yes—
9#18011911C2212yes—
10#18011902—22no—
11#18011891—22no—
12#18011887C2214yes—
13Q8×Dic149C2214yes—
14#18011876—22no—
15#18011869—22no—
16C42×D149C2211yescharacteristic
17#18011843C2214yes—
18#18011835C2218yes—
19#18011821C2212yes—
20C4×#11924746C2211yescharacteristic
21C2×Q16×C149C2214yes—
22C4⋊Q8×C149C2212yes—
23C4×C8×C149C2211yescharacteristic
24C2×Dic298—22no—
25C2×C4×D149D412yes—
26C2×C4×D149C2311yescharacteristic
27#14558719—24no—
28C2×#11924746C2312yes—
29C4⋊Dic149—24no—
30C4⋊Dic149—22no—
31C4⋊Dic149C2314yes—
32#14558715—24no—
33#14558713—24no—
34C4×Dic149—24no—
35C4×Dic149D412yes—
36C4×Dic149C2311yescharacteristic
37C2×Q8×C149C2314yes—
38Q16×C149—28no—
39C2×C8×C149C2312yes—
40C4⋊C4×C149—22no—
41C4⋊C4×C149—22no—
42C42×C149C2311yescharacteristic
43C22×D149C2×D411yescharacteristic
44Dic298—44no—
45C2×Dic149—24no—
46C2×Dic149C2×D412yes—
47C2×Dic149C2×D411yescharacteristic
48C4×D149—24no—
49C4×D149—22no—
50#11924746—22no—
51Q8×C149—28no—
52C2×C4×C149—24no—
53C2×C4×C149C2×D412yes—
54C2×C4×C149C2411yescharacteristic
55C8×C149#4114yes—
56C22×C149C22×D411yescharacteristic
57C2×D149—21no—
58C2×D149—22no—
59C4×C149—44no—
60C4×C149#13714yes—
61C4×C149C2×#4112yes—
62Dic149—21no—
63Dic149—22no—
64Dic149—44no—
65C2×C149#53211yescharacteristic
66C2×C149C2×#13712yes—
67D149—41no—
68C149#318511yescharacteristic, complemented, Sylow
69#3185—1491nomaximal, Sylow
70#533—1492no—
71#498—1491no—
72#494D14911yescharacteristic, complemented
73#487—1492no—
74#470—1494no—
75#441—1494no—
76C4×M16—1491no—
77C2×Q16C2×D14914yes—
78C2×M16—1492no—
79C4⋊Q8—1492no—
80C4⋊Q8C2×D14912yes—
81#125—2982no—
82C22⋊Q8—2982no—
83C22⋊Q8—1494no—
84C4×Q8—2982no—
85C4×Q8—1494no—
86#117—2982no—
87C2×C42—1491no—
88#106—1494no—
89#103—1498no—
90#97—1492no—
91C4×C8—1491no—
92C4×C8C2×D14911yescharacteristic
93C2×Q8—2982no—
94C2×Q8C22×D14914yes—
95C22×C4—1492no—
96C22×C4—1491no—
97Q16—28no—
98M16—2984no—
99C2×C8—1492no—
100C2×C8C22×D14912yes—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—2984no—
104C4⋊C4—2984no—
105C4⋊C4—2982no—
106C4⋊C4—1494no—
107C22⋊C4—2984no—
108C42—2984no—
109C42—1492no—
110C42—1491no—
111C42C22×D14911yescharacteristic
112C23—1491no—
113Q8—28no—
114Q8—5964no—
115C2×C4—24no—
116C2×C4—2984no—
117C2×C4—2982no—
118C2×C4—2984no—
119C2×C4—1492no—
120C2×C4—1491no—
121C2×C4D4×D14912yes—
122C2×C4C23×D14911yescharacteristic
123C8—2982no—
124C8#1455873514yes—
125C22—2982no—
126C22—2981no—
127C22C2×D4×D14911yescharacteristic
128C4—44no—
129C4—2982no—
130C4—2981no—
131C4—5964no—
132C4#1801194314yes—
133C4C2×#1455873512yes—
134C2—5961no—
135C2#2375017311yescharacteristic
136C2C2×#1801194312yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#494×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#494D149
hypocenterC149#3185
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #23750023C2semidirect
3. #23749975C2semidirect
5. #23749732C2semidirect
7. #494×C149C2semidirect
68. C149#3185semidirect
72. #494D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237500232
#237499752
#237498802
#237497322
C4×#145587192
#494×C1492
#3185149