Finite Group Databasebeta

← #34059669

Subgroups — #34059669

Order 19072.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#23750503C211yesmaximal, characteristic, complemented
2#23750469C211yesmaximal, characteristic, complemented
3#23749533C211yesmaximal, characteristic
4C2×C22⋊#10597010—21no—
5C22⋊#11924753—21no—
6C22×C22⋊D149—21no—
7C2×C22⋊Dic149—21no—
8C2×#14558713C2211yescharacteristic
9#18011818C411yescharacteristic, complemented
10C22×D4×C149C411yescharacteristic, complemented
11C22×#10597010—41no—
12C2×#11924753—41no—
13C22⋊#10597010—22no—
14C22⋊#10597010—41no—
15C23×D149D411yescharacteristic
16C2×C22⋊D149—42no—
17C2×C22⋊D149—42no—
18C2×C22⋊D149—41no—
19C2×C22⋊D149—41no—
20C22×Dic149—21no—
21C22×Dic149D411yescharacteristic
22C22⋊Dic149—42no—
23#14558713—41no—
24C24×C149—21no—
25C2×D4×C149—41no—
26C2×D4×C149—42no—
27C22×C4×C149C2×C411yescharacteristic
28C2×#10597010—42no—
29C2×#10597010—81no—
30C2×#10597010—81no—
31#11924753—81no—
32C22×D149—21no—
33C22×D149—21no—
34C22×D149—41no—
35C22×D149—41no—
36C22×D149D811yescharacteristic
37C22×D149SD1611yescharacteristic
38C22⋊D149—44no—
39C22⋊D149—44no—
40C2×Dic149—22no—
41C2×Dic149—21no—
42C2×Dic149—41no—
43C2×Dic149—41no—
44C2×Dic149—41no—
45C23×C149—22no—
46C23×C149—41no—
47C23×C149—41no—
48C23×C149—41no—
49C23×C149—41no—
50C23×C149—41no—
51C23×C149—41no—
52C23×C149C22⋊C411yescharacteristic
53D4×C149—42no—
54D4×C149—42no—
55C2×C4×C149—21no—
56C2×C4×C149—41no—
57C22×C149—21no—
58C22×C149—21no—
59C22×C149—42no—
60C22×C149—42no—
61C22×C149—42no—
62C22×C149—81no—
63C22×C149—81no—
64C22×C149—81no—
65C22×C149—81no—
66C22×C149#9911yescharacteristic
67C22×C149#10211yescharacteristic
68C22×C149#10411yescharacteristic
69C2×D149—21no—
70C2×D149—21no—
71C2×D149—41no—
72C2×D149—41no—
73C2×D149—41no—
74C2×D149—41no—
75C2×D149—81no—
76#10597010—82no—
77C4×C149—41no—
78Dic149—42no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—21no—
82C2×C149—82no—
83C2×C149#32711yescharacteristic
84C2×C149AΣL(1,𝔽16)11yescharacteristic
85C2×C149#35311yescharacteristic
86D149—41no—
87D149—41no—
88C149#134311yescharacteristic, complemented, Sylow
89#1343—1491nomaximal, Sylow
90#392—1491no—
91#342—1491no—
92#323—1491no—
93C22×D4—2981no—
94C22×D4#1059701011yescharacteristic, complemented
95C2×C22⋊C4—2981no—
96C2×C22⋊C4—2981no—
97C2×C22⋊C4—1491no—
98C22⋊C8—2981no—
99#95—1491no—
100C24—21no—
101C24—1491no—
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—5962no—
105C2×D4—5962no—
106C2×D4—5961no—
107C2×D4—5961no—
108C22×C4—2981no—
109C22×C4—5961no—
110C22×C4—1491no—
111C22×C4C2×#1059701011yescharacteristic
112C2×C8—5961no—
113C22⋊C4—2982no—
114C22⋊C4—5961no—
115C22⋊C4—5962no—
116C22⋊C4—5961no—
117C23—22no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—2981no—
125C23—2981no—
126C23—5961no—
127C23—5961no—
128C23—1491no—
129C23—1491no—
130C23C22⋊#1059701011yescharacteristic
131D4—42no—
132D4—42no—
133D4—5964no—
134D4—5964no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—2982no—
138C2×C4—2981no—
139C2×C4—5961no—
140C2×C4—5961no—
141C2×C4—5961no—
142C2×C4—5962no—
143C2×C4—11921no—
144C2×C4—11921no—
145C8—11921no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—2981no—
156C22—2981no—
157C22—5961no—
158C22—5961no—
159C22—5961no—
160C22—5961no—
161C22—11921no—
162C22#1801196911yescharacteristic
163C22#1801197311yescharacteristic
164C22#1801197511yescharacteristic
165C4—41no—
166C4—5962no—
167C4—5961no—
168C4—11922no—
169C2—21no—
170C2—21no—
171C2—82no—
172C2—5961no—
173C2—5961no—
174C2#2375047611yescharacteristic
175C2#2375052511yescharacteristic
176C2#2375052911yescharacteristic
subgroupG/H
centerC22#18011969
commutatorC22×C4×C149C2×C4
FrattiniC22×C4C2×#10597010
FittingC22×D4×C149C4
socleC22×C149#99
prime radical#23749533C2
cosocleC2×#14558713C22
hypercenterC22×D4#10597010
hypocenterC149#1343
LCSG ▷ C22×C4×C149 ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750503C2semidirect
2. #23750469C2semidirect
9. #18011818C4semidirect
10. C22×D4×C149C4semidirect
88. C149#1343semidirect
94. C22×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505032
#237504692
#237495332
#1343149