Finite Group Databasebeta

← #34043785

Subgroups — #34043785

Order 19072.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750353C211yesmaximal, characteristic, complemented
2#23749971C211yesmaximal, characteristic
3#23749822C211yesmaximal, characteristic
4#23749372C211yesmaximal, characteristic, complemented
5Q8⋊#11924746C211yesmaximal, characteristic, complemented
6#23749355C211yesmaximal, characteristic, complemented
7#460×C149C211yesmaximal, characteristic
8C2×#14558724—21no—
9#18011911C2211yescharacteristic
10#18011909—21no—
11#18011903—21no—
12#18011901—22no—
13C4×Dic298—21no—
14C4×Dic298C2211yescharacteristic
15#18011876—21no—
16C4⋊#11924746C2211yescharacteristic
17#18011832—22no—
18#18011832—21no—
19C4×#11924746C2211yescharacteristic
20C2×SD16×C149—21no—
21#127×C149C2211yescharacteristic
22C4×Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24#102×C149—21no—
25C2×Dic298—21no—
26C2×Dic298D411yescharacteristic
27#14558724—42no—
28C2×#11924746—21no—
29C2×#11924746—21no—
30C4⋊Dic149—21no—
31C4⋊Dic149D412yes—
32C4⋊Dic149D411yescharacteristic
33#14558715—22no—
34#14558715—22no—
35#14558715—22no—
36#14558715—21no—
37C4×Dic149—22no—
38C4×Dic149—21no—
39C2×Q8×C149D411yescharacteristic
40C2×D4×C149—21no—
41C2×D4×C149—21no—
42C2×D4×C149—21no—
43SD16×C149—42no—
44C2×C8×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149D411yescharacteristic
47C42×C149—21no—
48C42×C149C2311yescharacteristic
49Dic298—21no—
50Dic298—41no—
51Dic298—41no—
52Dic298SD1612yescomplemented
53C2×Dic149—21no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56#11924746—41no—
57#11924746—41no—
58C23×C149—41no—
59Q8×C149—21no—
60Q8×C149—21no—
61D4×C149—42no—
62D4×C149—41no—
63D4×C149—41no—
64D4×C149—41no—
65D4×C149—41no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C8×C149—41no—
72C22×C149—81no—
73C22×C149—81no—
74C22×C149—81no—
75C22×C149#12011yescharacteristic
76C4×C149—21no—
77C4×C149—41no—
78C4×C149—41no—
79C4×C149C2×SD1611yescharacteristic
80C4×C149#13511yescharacteristic
81C4×C149AGL(1,ℤ/8)11yescharacteristic
82C4×C149#13711yescharacteristic
83Dic149—22no—
84Dic149—42no—
85Dic149—41no—
86C2×C149—161no—
87C2×C149#44811yescharacteristic
88C2×C149#44911yescharacteristic
89C2×C149#45411yescharacteristic
90C149#162611yescharacteristic, complemented, Sylow
91#1626—1491nomaximal, Sylow
92#557—1491no—
93#486—1491no—
94#460—1491no—
95#460D14911yescharacteristic
96#332—1491no—
97Q8⋊C8—1491no—
98Q8⋊C8—1491no—
99C2×SD16—21no—
100C2×SD16—2981no—
101C4⋊Q8—2981no—
102C4⋊Q8—1491no—
103#127C2×D14911yescharacteristic
104#125—2981no—
105#125—2982no—
106C4×Q8—2981no—
107C4×Q8—2981no—
108C4×Q8—1491no—
109C4×Q8C2×D14911yescharacteristic
110C4⋊C8—1491no—
111C4⋊C8C2×D14911yescharacteristic
112#102—21no—
113#102—2981no—
114#102—2982no—
115C4×C8—1491no—
116C2×Q8—2981no—
117C2×Q8—1491no—
118C2×Q8C22⋊D14911yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4—21no—
122SD16—42no—
123SD16—5962no—
124C2×C8—21no—
125C2×C8—2981no—
126C2×C8—2981no—
127C4⋊C4—21no—
128C4⋊C4—2982no—
129C4⋊C4—2982no—
130C4⋊C4—2982no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—1491no—
134C4⋊C4—1492no—
135C4⋊C4C22⋊D14911yescharacteristic
136C42—21no—
137C42—2982no—
138C42—2981no—
139C42C22×D14911yescharacteristic
140C23—41no—
141Q8—21no—
142Q8—21no—
143Q8—2981no—
144Q8—5961no—
145Q8—5961no—
146Q8—1492no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—2982no—
157C2×C4D4×D14911yescharacteristic
158C2×C4D4×D14911yescharacteristic
159C2×C4C2×C22⋊D14911yescharacteristic
160C8—41no—
161C8—5961no—
162C8—5961no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1801187911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—2982no—
171C4—5962no—
172C4—5961no—
173C4SD16×D14911yescharacteristic
174C4#1801193111yescharacteristic
175C4#1801193711yescharacteristic
176C4#1801194011yescharacteristic
177C2—161no—
178C2#2374976211yescharacteristic
179C2#2374976811yescharacteristic
180C2#2374979611yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#460×C149C2
socleC22×C149#120
prime radical#127×C149C22
hypercenter#460D149
hypocenterC149#1626
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23750353C2semidirect
4. #23749372C2semidirect
5. Q8⋊#11924746C2semidirect
6. #23749355C2semidirect
52. Dic298SD16semidirect
90. C149#1626semidirect

Maximal subgroups

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

subgroupindex
#237503532
#237499712
#237498222
#237493722
Q8⋊#119247462
#237493552
#460×C1492
#1626149