Finite Group Databasebeta

← #34043874

Subgroups — #34043874

Order 19072.

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

normal subgroups only

This group has 212 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#23750361C211yesmaximal, characteristic
2#23749907C211yesmaximal, characteristic, complemented
3#23749832C211yesmaximal, characteristic, complemented
4#23749369C211yesmaximal, characteristic
5#23749357C211yesmaximal, characteristic, complemented
6#23749357C211yesmaximal, characteristic, complemented
7#486×C149C211yesmaximal, characteristic
8C2×#14558726—21no—
9#18011898—21no—
10#18011898—21no—
11#18011892—22no—
12C4×Dic298C2211yescharacteristic
13C4×Dic298C2211yescharacteristic
14D4×Dic149—21no—
15D4×Dic149—21no—
16#18011842—21no—
17C4⋊#11924746C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011835—21no—
20#18011834—21no—
21C4⋊Q8×C149C2211yescharacteristic
22#127×C149C2211yescharacteristic
23#102×C149—22no—
24C4×C8×C149C2211yescharacteristic
25C2×Dic298D411yescharacteristic
26C2×Dic298D411yescharacteristic
27C22×Dic149—22no—
28#14558726—42no—
29C2×#11924746—21no—
30C2×#11924746—21no—
31C4⋊Dic149D411yescharacteristic
32C4⋊Dic149D411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35C22⋊Dic149—22no—
36C22⋊Dic149—22no—
37C22⋊Dic149—22no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C2×Q8×C149—21no—
41C2×D4×C149—21no—
42C2×D4×C149—21no—
43C2×D4×C149D412yes—
44C2×C8×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C42×C149C2311yescharacteristic
48Dic298—21no—
49Dic298—21no—
50Dic298—21no—
51Dic298—21no—
52C2×Dic149—21no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—21no—
56C2×Dic149—82no—
57#11924746—41no—
58#11924746—41no—
59C23×C149—22no—
60Q8×C149—41no—
61Q8×C149—41no—
62D4×C149—42no—
63D4×C149—41no—
64D4×C149—41no—
65D4×C149—41no—
66D4×C149—41no—
67C2×C4×C149—41no—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C8×C149—41no—
72C22×C149—42no—
73C22×C149—42no—
74C22×C149—42no—
75C22×C149#12011yescharacteristic
76C4×C149—21no—
77C4×C149—81no—
78C4×C149#13511yescharacteristic
79C4×C149#13511yescharacteristic
80C4×C149AGL(1,ℤ/8)11yescharacteristic
81C4×C149#13711yescharacteristic
82Dic149—41no—
83Dic149—41no—
84Dic149—41no—
85Dic149—41no—
86C2×C149—82no—
87C2×C149#44911yescharacteristic
88C2×C149#45211yescharacteristic
89C2×C149#45511yescharacteristic
90C149#164011yescharacteristic, complemented, Sylow
91#1640—1491nomaximal, Sylow
92#559—1491no—
93#486D14911yescharacteristic
94#475—1491no—
95#462—1491no—
96#331—1491no—
97Q8⋊C8—1491no—
98Q8⋊C8—1491no—
99C2×Q16—2981no—
100C4⋊Q8C2×D14911yescharacteristic
101#127C2×D14911yescharacteristic
102#124—2981no—
103#124—2981no—
104#123—2982no—
105C4×Q8—1491no—
106C4×Q8—1491no—
107C4×D4—2981no—
108C4×D4—2981no—
109#106—2981no—
110C4⋊C8—1491no—
111C4⋊C8—1491no—
112#103—2981no—
113#103—2981no—
114#102—22no—
115C4×C8C2×D14911yescharacteristic
116C2×Q8—21no—
117C2×Q8—1491no—
118C2×Q8—1491no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D14912yes—
122C22×C4—2982no—
123Q16—5962no—
124C2×C8—21no—
125C2×C8—2981no—
126C2×C8—2981no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—1491no—
132C4⋊C4—1491no—
133C22⋊C4—2982no—
134C22⋊C4—2982no—
135C22⋊C4—2982no—
136C42—2981no—
137C42—2981no—
138C42C22×D14911yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—2981no—
143Q8—2981no—
144Q8—2981no—
145Q8—2981no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—11922no—
157C2×C4D4×D14911yescharacteristic
158C2×C4D4×D14911yescharacteristic
159C2×C4C2×C22⋊D14911yescharacteristic
160C8—41no—
161C8—5961no—
162C8—5961no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1801187911yescharacteristic
167C4—21no—
168C4—81no—
169C4—5961no—
170C4—5961no—
171C4—5961no—
172C4—5961no—
173C4#1801193011yescharacteristic
174C4#1801193211yescharacteristic
175C4#1801193511yescharacteristic
176C4#1801194011yescharacteristic
177C2—82no—
178C2#2374976711yescharacteristic
179C2#2374978411yescharacteristic
180C2#2374980211yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#486×C149C2
socleC22×C149#120
prime radical#127×C149C22
hypercenter#486D149
hypocenterC149#1640
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #23749907C2semidirect
3. #23749832C2semidirect
5. #23749357C2semidirect
6. #23749357C2semidirect
90. C149#1640semidirect

Maximal subgroups

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

subgroupindex
#237503612
#237499072
#237498322
#237493692
#237493572
#486×C1492
#1640149