Finite Group Databasebeta

← #34045859

Subgroups — #34045859

Order 19072.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#23750251C211yesmaximal, characteristic
2#23749486C212yesmaximal
3#23749486C211yesmaximal, characteristic
4#23749391C212yesmaximal
5#342×C149C211yesmaximal, characteristic
6C23×Dic149C2211yescharacteristic
7#18011890—22no—
8#18011888—24no—
9C2×C22⋊Dic149C2211yescharacteristic
10C2×C22⋊Dic149C2212yes—
11#18011818—22no—
12#18011818—24no—
13C2×C22⋊C4×C149C2212yes—
14C2×C22⋊C4×C149C2211yescharacteristic
15C2×Dic298—22no—
16C22×Dic149—22no—
17C22×Dic149—21no—
18C22×Dic149—21no—
19C22×Dic149—21no—
20C22×Dic149—22no—
21C22×Dic149D414yes—
22C22×Dic149Q812yescomplemented
23C4⋊Dic149—22no—
24#14558715—24no—
25C22⋊Dic149—22no—
26C22⋊Dic149—22no—
27C22⋊Dic149—22no—
28C24×C149C2311yescharacteristic
29C22×C4×C149—22no—
30C22×C4×C149D412yes—
31C22⋊C4×C149—22no—
32C22⋊C4×C149—22no—
33C22⋊C4×C149—22no—
34Dic298—82no—
35C2×Dic149—24no—
36C2×Dic149—24no—
37C2×Dic149—22no—
38C2×Dic149—41no—
39C2×Dic149—42no—
40C2×Dic149—41no—
41C2×Dic149—44no—
42C2×Dic149—42no—
43C2×Dic149—41no—
44C23×C149—42no—
45C23×C149C2×D412yes—
46C23×C149C2×D411yescharacteristic
47C23×C149C2×Q811yescharacteristic
48C23×C149#4111yescharacteristic
49C23×C149#4112yes—
50C2×C4×C149—22no—
51C2×C4×C149—42no—
52C2×C4×C149—44no—
53C2×C4×C149—42no—
54C22×C149—24no—
55C22×C149—22no—
56C22×C149—41no—
57C22×C149—41no—
58C22×C149—42no—
59C22×C149#12011yescharacteristic
60C22×C149C22⋊Q812yes—
61C22×C149C22⋊Q811yescharacteristic
62C22×C149#12412yes—
63C22×C149#12411yescharacteristic
64C4×C149—42no—
65C4×C149—82no—
66Dic149—42no—
67Dic149—44no—
68Dic149—81no—
69C2×C149—21no—
70C2×C149—22no—
71C2×C149—22no—
72C2×C149—21no—
73C2×C149#39311yescharacteristic
74C2×C149#45812yes—
75C149#203011yescharacteristic, complemented, Sylow
76#2030—1491nomaximal, Sylow
77#543—1491no—
78#381—1492no—
79#381—1491no—
80#342—1492no—
81#342D14911yescharacteristic
82C23×C4—1491no—
83C22⋊Q8—2984no—
84C22⋊Q8—2982no—
85C2×C22⋊C4—1491no—
86C2×C22⋊C4—1492no—
87C2×C22⋊C4C2×D14912yes—
88C2×C22⋊C4C2×D14911yescharacteristic
89#95—2984no—
90#95—2982no—
91C24C22×D14911yescharacteristic
92C2×Q8—2982no—
93C22×C4—22no—
94C22×C4—2982no—
95C22×C4—2981no—
96C22×C4—2981no—
97C22×C4—2982no—
98C22×C4—2981no—
99C22×C4—1492no—
100C22×C4—1494no—
101C22×C4D59612yes—
102C4⋊C4—2984no—
103C4⋊C4—2982no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—2982no—
108C22⋊C4—2982no—
109C22⋊C4—2982no—
110C23—42no—
111C23D4×D14912yes—
112C23C2×D59611yescharacteristic
113C23Q8×D14911yescharacteristic
114C23#1455873511yescharacteristic
115C23#1455873612yes—
116Q8—11922no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—2984no—
122C2×C4—2984no—
123C2×C4—2982no—
124C2×C4—5961no—
125C2×C4—5962no—
126C2×C4—5961no—
127C2×C4—5964no—
128C2×C4—5962no—
129C2×C4—5961no—
130C22—24no—
131C22—22no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1801188111yescharacteristic
136C22#1801188912yes—
137C22#1801189111yescharacteristic
138C22#1801189712yes—
139C22#1801189911yescharacteristic
140C4—42no—
141C4—82no—
142C4—5962no—
143C4—5964no—
144C4—11921no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#2374953811yescharacteristic
150C2#2374981612yes—
subgroupG/H
centerC22#18011881
commutator, prime radical, cosocleC24×C149C23
FrattiniC24C22×D149
Fitting#342×C149C2
socleC22×C149#120
hypercenter#342D149
hypocenterC149#2030
LCSG ▷ C24×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
22. C22×Dic149Q8semidirect
75. C149#2030semidirect

Maximal subgroups

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

subgroupindex
#237502512
#237494862
#237493912
#342×C1492
#2030149