Finite Group Databasebeta

← #34060988

Subgroups — #34060988

Order 19072.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×#18011972C212yesmaximal, complemented
2#23750536C212yesmaximal, complemented
3#23750534C212yesmaximal, complemented
4#23750201C211yesmaximal, characteristic
5C2×#14558745—22no—
6#18011972—22no—
7#18011972C2214yes—
8C2×#14558736C411yescharacteristic
9C22×Dic298C2211yescharacteristic
10#18011911C411yescharacteristic
11#18011911C2211yescharacteristic
12#18011899C411yescharacteristic
13#18011899C2211yescharacteristic
14#18011895—22no—
15#18011891—22no—
16#117×C149C411yescharacteristic
17#14558745—24no—
18#14558745—42no—
19C2×#11924753—42no—
20#14558736—42no—
21C2×Dic298—42no—
22C2×Dic298C2×C411yescharacteristic
23C2×Dic298C2×C411yescharacteristic
24C2×Dic298D412yes—
25C2×Dic298C2311yescharacteristic
26C2×D596C2×C411yescharacteristic
27C2×C22⋊D149—21no—
28C22×Dic149D412yes—
29C2×C4×D149—21no—
30C4⋊Dic149—22no—
31C4⋊Dic149—22no—
32#14558713—22no—
33#14558713—22no—
34C22×C4×C149C2×C411yescharacteristic
35C4⋊C4×C149—21no—
36C22⋊C4×C149—21no—
37C42×C149C2×C411yescharacteristic
38C42×C149C2×C411yescharacteristic
39#11924753—44no—
40C22×D149—21no—
41Dic298—41no—
42Dic298—42no—
43Dic298—41no—
44Dic298—41no—
45D596—41no—
46C22⋊D149—42no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—21no—
50C2×Dic149C22⋊C412yes—
51C2×Dic149C2×D412yes—
52C4×D149—42no—
53C23×C149C22⋊C411yescharacteristic
54C2×C4×C149—22no—
55C2×C4×C149—21no—
56C2×C4×C149—21no—
57C2×C4×C149C22⋊C411yescharacteristic
58C2×C4×C149C22×C411yescharacteristic
59C22×C149—41no—
60C22×C149#9912yes—
61C22×C149C2×C22⋊C411yescharacteristic
62C2×D149—42no—
63C2×D149—41no—
64C4×C149—21no—
65C4×C149—21no—
66C4×C149—41no—
67C4×C149—41no—
68Dic149—22no—
69Dic149—22no—
70Dic149—41no—
71C2×C149—21no—
72C2×C149—22no—
73C2×C149C2×#9911yescharacteristic
74D149—81no—
75C149#213311yescharacteristic, complemented, Sylow
76#2133—1491nomaximal, Sylow
77#536—1491no—
78C2×#101—1492no—
79#356—1492no—
80#355—1492no—
81C2×#41—1491no—
82C22×Q8—1491no—
83C2×M16—2982no—
84C4⋊Q8—1491no—
85C4⋊Q8—1491no—
86#124—1491no—
87#124—1491no—
88#123—2982no—
89C22⋊Q8—2982no—
90#117#1059701011yescharacteristic
91#101—2982no—
92#101—1494no—
93#41—5962no—
94C2×Q8—5962no—
95C2×Q8—1491no—
96C2×Q8—1492no—
97C2×Q8—1491no—
98C2×Q8—1491no—
99C2×D4—2981no—
100C2×D4—1491no—
101C22×C4—2981no—
102C22×C4—1492no—
103C22×C4C2×#1059701011yescharacteristic
104M16—2984no—
105M16—5962no—
106C2×C8—5962no—
107C4⋊C4—21no—
108C4⋊C4—2982no—
109C4⋊C4—2982no—
110C22⋊C4—21no—
111C22⋊C4—2982no—
112C22⋊C4—2982no—
113C42C2×#1059701011yescharacteristic
114C42C2×#1059701011yescharacteristic
115C23—2981no—
116C23C22⋊#1059701011yescharacteristic
117Q8—5962no—
118Q8—5961no—
119Q8—5961no—
120Q8—5961no—
121D4—5961no—
122D4—5962no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—2982no—
127C2×C4—2982no—
128C2×C4—2981no—
129C2×C4—5962no—
130C2×C4—1492no—
131C2×C4—1492no—
132C2×C4C22⋊#1059701011yescharacteristic
133C2×C4C22×#1059701011yescharacteristic
134C8—5964no—
135C22—41no—
136C22—5962no—
137C22—5961no—
138C22#1801197012yes—
139C22C2×C22⋊#1059701011yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—2982no—
145C4—2982no—
146C4—5961no—
147C2—21no—
148C2—22no—
149C2—11921no—
150C2C2×#1801197011yescharacteristic
subgroupG/H
centerC2C2×#18011970
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#117×C149C4
socleC2×C149C2×#99
prime radicalC2×#14558736C4
cosocleC2×Dic298C23
hypercenter#117#10597010
hypocenterC149#2133
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#18011972C2semidirect
2. #23750536C2semidirect
3. #23750534C2semidirect
75. C149#2133semidirect

Maximal subgroups

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

subgroupindex
C2×#180119722
#237505362
#237505342
#237502012
#2133149