Finite Group Databasebeta

← #34045852

Subgroups — #34045852

Order 19072.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750256C211yesmaximal, characteristic
2#23749634C212yesmaximal
3#23749394C211yesmaximal, characteristic
4#23749385C212yesmaximal
5#391×C149C211yesmaximal, characteristic
6C2×#14558720C2212yes—
7#18011910—22no—
8#18011902—22no—
9#18011890—22no—
10#18011870C2212yes—
11#18011835—22no—
12#18011835—22no—
13C22×Q8×C149C2211yescharacteristic
14C2×C4⋊C4×C149C2211yescharacteristic
15C2×C42×C149C2211yescharacteristic
16#95×C149—22no—
17C2×Dic298—22no—
18#14558720—22no—
19#14558720—22no—
20C2×#11924746—22no—
21C4⋊Dic149—22no—
22C4⋊Dic149D412yes—
23C4⋊Dic149D412yes—
24#14558715—24no—
25C22⋊Dic149—22no—
26C4×Dic149—22no—
27C2×Q8×C149—21no—
28C2×Q8×C149—22no—
29C2×Q8×C149—22no—
30C2×Q8×C149Q812yescomplemented
31C22×C4×C149—21no—
32C22×C4×C149—21no—
33C22×C4×C149D412yes—
34C22×C4×C149C2311yescharacteristic
35C4⋊C4×C149—22no—
36C42×C149—22no—
37Dic298—82no—
38C2×Dic149—22no—
39C2×Dic149—22no—
40#11924746—42no—
41C23×C149C2×D411yescharacteristic
42Q8×C149—24no—
43Q8×C149—42no—
44C2×C4×C149—22no—
45C2×C4×C149—22no—
46C2×C4×C149—22no—
47C2×C4×C149—41no—
48C2×C4×C149—41no—
49C2×C4×C149—41no—
50C2×C4×C149—41no—
51C2×C4×C149—42no—
52C2×C4×C149C2×D412yes—
53C2×C4×C149C2×Q811yescharacteristic
54C2×C4×C149#4112yes—
55C2×C4×C149#4111yescharacteristic
56C22×C149—21no—
57C22×C149—21no—
58C22×C149#12011yescharacteristic
59C22×C149C22⋊Q811yescharacteristic
60C22×C149#12411yescharacteristic
61C4×C149—42no—
62C4×C149—42no—
63C4×C149—42no—
64C4×C149C22⋊Q812yes—
65C4×C149#12412yes—
66Dic149—42no—
67Dic149—42no—
68C2×C149—21no—
69C2×C149—21no—
70C2×C149#39311yescharacteristic
71C2×C149#45511yescharacteristic
72C2×C149#45611yescharacteristic
73C149#202811yescharacteristic, complemented, Sylow
74#2028—1491nomaximal, Sylow
75#544—1491no—
76#419—1492no—
77#391D14911yescharacteristic
78#343—1491no—
79#339—1492no—
80C22×Q8C2×D14911yescharacteristic
81C2×M16—1492no—
82C4⋊Q8—2982no—
83#125—2982no—
84C22⋊Q8—2982no—
85#117—1492no—
86C2×C4⋊C4C2×D14911yescharacteristic
87C2×C42C2×D14911yescharacteristic
88#103—2982no—
89#103—2982no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—2982no—
95C2×Q8Dic29812yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D14912yes—
99C22×C4C22×D14911yescharacteristic
100M16—2982no—
101M16—2982no—
102C2×C8—2982no—
103C4⋊C4—22no—
104C4⋊C4—2982no—
105C4⋊C4—2984no—
106C4⋊C4—1492no—
107C4⋊C4—1492no—
108C22⋊C4—2982no—
109C42—22no—
110C42—2982no—
111C23C2×C22⋊D14911yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—11922no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—2982no—
124C2×C4—2982no—
125C2×C4D4×D14912yes—
126C2×C4C2×Dic29811yescharacteristic
127C2×C4#1455873512yes—
128C2×C4#1455873611yescharacteristic
129C8—5962no—
130C22—21no—
131C22—21no—
132C22#1801187911yescharacteristic
133C22#1801189011yescharacteristic
134C22#1801189811yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—5962no—
139C4—5962no—
140C4#1801188812yes—
141C4#1801189712yes—
142C2—21no—
143C2—21no—
144C2#2374953711yescharacteristic
145C2#2374980211yescharacteristic
146C2#2374980711yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#391×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#391D149
hypocenterC149#2028
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C149Q8semidirect
73. C149#2028semidirect
95. C2×Q8Dic298semidirect

Maximal subgroups

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

subgroupindex
#237502562
#237496342
#237493942
#237493852
#391×C1492
#2028149