Finite Group Databasebeta

← #34059793

Subgroups — #34059793

Order 19072.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#23750606C211yesmaximal, characteristic
2#23750600C211yesmaximal, characteristic
3#23749608C211yesmaximal, characteristic
4C2×#14558746C411yescharacteristic, complemented
5C2×D149⋊C8C411yescharacteristic, complemented
6#18011990—21no—
7#18011970—21no—
8#18011970C412yes—
9#18011968—21no—
10#18011968—21no—
11C2×#14558737C2211yescharacteristic
12M16×D149—21no—
13#18011830C411yescharacteristic, complemented
14#18011827—21no—
15#101×C149C411yescharacteristic, complemented
16#14558746—41no—
17D149⋊C8—41no—
18C2×#11924753—21no—
19C2×#11924753—21no—
20C4⋊#10597010—41no—
21C22⋊#10597010—22no—
22C4×#10597010—41no—
23#14558737—41no—
24#14558737—41no—
25C2×D596C2×C411yescharacteristic
26C2×D596D411yescharacteristic
27C2×D596Q811yescharacteristic
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31#14558720—21no—
32#14558719—41no—
33C8×D149—41no—
34C2×Q8×C149C2×C411yescharacteristic
35M16×C149—21no—
36C2×#10597010—42no—
37#11924753—41no—
38#11924753—41no—
39C22×D149C22⋊C411yescharacteristic
40C22×D149C4⋊C411yescharacteristic
41C22×D149C4⋊C411yescharacteristic
42D596—41no—
43D596—41no—
44D596—41no—
45C2×Dic149C22⋊C411yescharacteristic
46C4×D149—21no—
47C4×D149—21no—
48C4×D149—21no—
49C4×D149—21no—
50C4×D149—21no—
51C4×D149—21no—
52#11924746—41no—
53Q8×C149—41no—
54C2×C4×C149C4211yescharacteristic
55C2×C4×C149C22⋊C411yescharacteristic
56C2×C4×C149C4⋊C411yescharacteristic
57C8×C149—41no—
58C22×C149#9511yescharacteristic
59C2×D149—21no—
60C2×D149—21no—
61C2×D149—21no—
62C2×D149—41no—
63C2×D149—41no—
64C2×D149—41no—
65#10597010—82no—
66C4×C149—21no—
67C4×C149—21no—
68C4×C149—21no—
69Dic149#9911yescharacteristic
70Dic149#9911yescharacteristic
71C2×C149—21no—
72C2×C149#34211yescharacteristic
73D149—41no—
74D149—41no—
75D149—41no—
76C149#139511yescharacteristic, complemented, Sylow
77#1395—1491nomaximal, Sylow
78#413—1491no—
79#410—1491no—
80#408—1491no—
81C2×#41—1491no—
82C2×M16—2981no—
83C2×M16—1491no—
84C22×C8—1491no—
85#117—2981no—
86#101—1491no—
87#101#1059701011yescharacteristic, complemented
88#100—2981no—
89#99—2981no—
90#99—1492no—
91C22⋊C8—2981no—
92C22⋊C8—2981no—
93#41—5961no—
94#41—5961no—
95C2×Q8C2×#1059701011yescharacteristic
96C2×D4—1491no—
97C2×D4—1491no—
98C2×D4—1491no—
99C22×C4—1491no—
100C22×C4—1491no—
101C22×C4—1491no—
102M16—21no—
103M16—2981no—
104M16—5961no—
105M16—5961no—
106C2×C8—2981no—
107C2×C8—2981no—
108C2×C8—5961no—
109C2×C8—5961no—
110C4⋊C4—5961no—
111C22⋊C4—2982no—
112C42—5961no—
113C23—1491no—
114C23—1491no—
115C23—1491no—
116Q8—41no—
117D4—5961no—
118D4—5961no—
119D4—5961no—
120C2×C4—2981no—
121C2×C4—2981no—
122C2×C4—2981no—
123C2×C4—2981no—
124C2×C4—2981no—
125C2×C4—2981no—
126C2×C4—5962no—
127C2×C4—1491no—
128C2×C4C4×#1059701011yescharacteristic
129C2×C4C22⋊#1059701011yescharacteristic
130C2×C4C4⋊#1059701011yescharacteristic
131C8—41no—
132C8—5961no—
133C8—5961no—
134C8—5961no—
135C22—2981no—
136C22—2981no—
137C22—2981no—
138C22—5961no—
139C22—5961no—
140C22—5961no—
141C22(C2×#10597010)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—1491no—
146C4—1491no—
147C4—11922no—
148C2—21no—
149C2—5961no—
150C2—5961no—
151C2—5961no—
152C2#2375050211yescharacteristic
subgroupG/H
centerC2#23750502
commutatorC2×C4×C149C42
FrattiniC2×Q8C2×#10597010
Fitting#101×C149C4
socleC2×C149#342
prime radical, cosocleC2×#14558737C22
hypercenter#101#10597010
hypocenterC149#1395
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#14558746C4semidirect
5. C2×D149⋊C8C4semidirect
13. #18011830C4semidirect
15. #101×C149C4semidirect
76. C149#1395semidirect
87. #101#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506062
#237506002
#237496082
#1395149