Finite Group Databasebeta

← #34045798

Subgroups — #34045798

Order 19072.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#18011937C212yesmaximal, complemented
2C2×#18011828C212yesmaximal, complemented
3#23749591C211yesmaximal, characteristic, complemented
4#23749390C211yesmaximal, characteristic, complemented
5C22×D8×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7#18011937—24no—
8#18011937—24no—
9C2×#14558724—22no—
10C2×#14558721—22no—
11C2×#14558720C2211yescharacteristic
12C2×#14558720C2212yes—
13#18011828—24no—
14#18011823—22no—
15C22×D4×C149C2212yes—
16C2×D8×C149—24no—
17C2×D8×C149—22no—
18C22×C8×C149C2211yescharacteristic
19#14558736—22no—
20#14558736—22no—
21C2×Dic298D411yescharacteristic
22C2×D596D411yescharacteristic
23C2×C22⋊D149—21no—
24C2×C4×D149—21no—
25#14558724—28no—
26#14558721—28no—
27#14558720—22no—
28#14558720—22no—
29#14558720D414yes—
30C2×#11924746—22no—
31C2×#11924746—21no—
32C24×C149—22no—
33C2×D4×C149—22no—
34C2×D4×C149—22no—
35C2×D4×C149—22no—
36C2×D4×C149—22no—
37C2×D4×C149—22no—
38C2×D4×C149D414yes—
39C22×C4×C149C2311yescharacteristic
40D8×C149—28no—
41C2×C8×C149—22no—
42C2×C8×C149D412yes—
43C22×D149—21no—
44Dic298—22no—
45D596—22no—
46C22⋊D149—42no—
47C2×Dic149—21no—
48C4×D149—41no—
49C4×D149—41no—
50#11924746—24no—
51#11924746—41no—
52C23×C149—24no—
53C23×C149—42no—
54C23×C149—42no—
55C23×C149—84no—
56C23×C149#4111yescharacteristic
57D4×C149—24no—
58D4×C149—24no—
59D4×C149—42no—
60D4×C149—42no—
61C2×C4×C149C2×D411yescharacteristic
62C2×C4×C149C2×D412yes—
63C2×C4×C149C2×D412yes—
64C2×C4×C149C2×D411yescharacteristic
65C8×C149—22no—
66C22×C149—22no—
67C22×C149—44no—
68C22×C149—84no—
69C22×C149—84no—
70C22×C149—84no—
71C22×C149#12111yescharacteristic
72C22×C149#12112yes—
73C2×D149—41no—
74C2×D149—42no—
75C4×C149#12012yes—
76C4×C149#12011yescharacteristic
77C4×C149#12711yescharacteristic
78Dic149—41no—
79C2×C149—22no—
80C2×C149—84no—
81C2×C149#39211yescharacteristic
82C2×C149#47212yes—
83D149—81no—
84C149#201811yescharacteristic, complemented, Sylow
85#2018—1491nomaximal, Sylow
86C2×AGL(1,ℤ/8)—1492no—
87C22×D8D14911yescharacteristic, complemented
88C2×#100—1492no—
89#408—1491no—
90#341—1491no—
91C2×#41—1491no—
92C22×D4C2×D14912yes—
93AGL(1,ℤ/8)—2984no—
94AGL(1,ℤ/8)—2984no—
95C2×SD16—2982no—
96C2×D8—24no—
97C2×D8—22no—
98C2×D8—2982no—
99C2×M16—1491no—
100C2×M16—1492no—
101C22×C8C2×D14911yescharacteristic
102#100—2984no—
103C22⋊C8—2982no—
104C24—22no—
105#41—2982no—
106#41—2982no—
107C2×Q8—1491no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—22no—
113C2×D4—2981no—
114C2×D4—1491no—
115C2×D4C22⋊D14914yes—
116C22×C4—2981no—
117C22×C4C22×D14911yescharacteristic
118SD16—2988no—
119D8—28no—
120D8—2988no—
121M16—2982no—
122M16—2982no—
123M16—1494no—
124C2×C8—22no—
125C2×C8—2982no—
126C2×C8—2981no—
127C2×C8C22⋊D14912yes—
128C23—24no—
129C23—42no—
130C23—42no—
131C23—84no—
132C23—2981no—
133C23#1455873511yescharacteristic
134Q8—2982no—
135D4—24no—
136D4—24no—
137D4—42no—
138D4—42no—
139D4—2982no—
140D4—5962no—
141C2×C4—2981no—
142C2×C4—5961no—
143C2×C4—5961no—
144C2×C4D4×D14912yes—
145C2×C4D4×D14911yescharacteristic
146C2×C4C2×C22⋊D14911yescharacteristic
147C2×C4C2×C22⋊D14912yes—
148C8—22no—
149C8—2984no—
150C8—5961no—
151C22—22no—
152C22—44no—
153C22—84no—
154C22—84no—
155C22—84no—
156C22—5962no—
157C22—5961no—
158C22#1801188211yescharacteristic
159C22#1801188312yes—
160C4—5961no—
161C4#1801187912yes—
162C4#1801188011yescharacteristic
163C4#1801190711yescharacteristic
164C2—22no—
165C2—84no—
166C2—11921no—
167C2#2374953311yescharacteristic
168C2#2374989212yes—
subgroupG/H
centerC22#18011882
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC22×D8×C149C2
socleC22×C149#121
hypercenterC22×D8D149
hypocenterC149#2018
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#18011937C2semidirect
2. C2×#18011828C2semidirect
3. #23749591C2semidirect
4. #23749390C2semidirect
5. C22×D8×C149C2semidirect
84. C149#2018semidirect
87. C22×D8D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119372
C2×#180118282
#237495912
#237493902
C22×D8×C1492
#2018149