Finite Group Databasebeta

← #34043701

Subgroups — #34043701

Order 19072.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#23749956C212yesmaximal
3#23749555C211yesmaximal, characteristic
4#23749363C212yesmaximal
5#324×C149C211yesmaximal, characteristic
6#18011910—22no—
7#18011902—22no—
8#18011890—21no—
9#18011890C2212yes—
10#18011870—21no—
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715—21no—
13#18011843—22no—
14#18011836—22no—
15#18011818—21no—
16#18011818C2211yescharacteristic
17C2×C4⋊C4×C149C2211yescharacteristic
18C22⋊C8×C149C2212yes—
19C2×Dic298—21no—
20C2×Dic298D412yes—
21C22×Dic149—21no—
22C22×Dic149—21no—
23C4⋊Dic149—21no—
24C4⋊Dic149—21no—
25C4⋊Dic149—21no—
26C4⋊Dic149—22no—
27C4⋊Dic149D412yes—
28#14558715—22no—
29#14558715—22no—
30#14558715—42no—
31C22⋊Dic149—22no—
32C4×Dic149—22no—
33C22×C4×C149D411yescharacteristic
34C22×C4×C149D411yescharacteristic
35C22×C4×C149C2311yescharacteristic
36C2×C8×C149—22no—
37C4⋊C4×C149—22no—
38Dic298—42no—
39Dic298—81no—
40C2×Dic149—22no—
41C2×Dic149—22no—
42C2×Dic149—22no—
43C2×Dic149—41no—
44C2×Dic149—41no—
45C2×Dic149—41no—
46C2×Dic149—41no—
47C2×Dic149—41no—
48C23×C149C2×D411yescharacteristic
49C2×C4×C149—21no—
50C2×C4×C149—21no—
51C2×C4×C149—21no—
52C2×C4×C149—41no—
53C2×C4×C149—41no—
54C2×C4×C149SD1612yes—
55C2×C4×C149C2×D412yes—
56C8×C149—42no—
57C22×C149—21no—
58C22×C149—21no—
59C22×C149#12011yescharacteristic
60C22×C149C2×SD1611yescharacteristic
61C22×C149#13711yescharacteristic
62C4×C149—22no—
63C4×C149—22no—
64C4×C149—41no—
65Dic149—42no—
66Dic149—42no—
67Dic149—42no—
68Dic149—81no—
69C2×C149—21no—
70C2×C149—21no—
71C2×C149#44811yescharacteristic
72C2×C149#45611yescharacteristic
73C2×C149#45811yescharacteristic
74C149#161111yescharacteristic, complemented, Sylow
75#1611—1491nomaximal, Sylow
76#544—1491no—
77#483—1492no—
78#398—1491no—
79#328—1492no—
80#324D14911yescharacteristic
81C4⋊Q8—2982no—
82#125—2982no—
83C22⋊Q8—2981no—
84C22⋊Q8—1492no—
85#117—2981no—
86C2×C4⋊C4—2981no—
87C2×C4⋊C4—1491no—
88C2×C4⋊C4C2×D14911yescharacteristic
89#106—2982no—
90#103—2982no—
91C22⋊C8C2×D14912yes—
92#95—2981no—
93#95—1491no—
94C2×Q8—2981no—
95C2×Q8—1492no—
96C22×C4—2981no—
97C22×C4—2981no—
98C22×C4D59611yescharacteristic
99C22×C4D59611yescharacteristic
100C22×C4C22×D14911yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—2981no—
104C4⋊C4—2981no—
105C4⋊C4—2981no—
106C4⋊C4—2982no—
107C4⋊C4—2982no—
108C4⋊C4—2982no—
109C4⋊C4—5962no—
110C4⋊C4—1492no—
111C22⋊C4—2982no—
112C42—2982no—
113C23C2×D59611yescharacteristic
114Q8—5962no—
115Q8—11921no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2982no—
122C2×C4—2982no—
123C2×C4—2982no—
124C2×C4—5961no—
125C2×C4—5961no—
126C2×C4—5961no—
127C2×C4—5961no—
128C2×C4—5961no—
129C2×C4#1455872512yes—
130C2×C4D4×D14912yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1801188111yescharacteristic
135C22C2×#1455872511yescharacteristic
136C22#1801194411yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—5962no—
141C4—5962no—
142C4—5962no—
143C4—11921no—
144C2—21no—
145C2—21no—
146C2#2374976611yescharacteristic
147C2#2374981011yescharacteristic
148C2#2374981611yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#324×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#324D149
hypocenterC149#1611
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
74. C149#1611semidirect

Maximal subgroups

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

subgroupindex
#237502562
#237499562
#237495552
#237493632
#324×C1492
#1611149