Finite Group Databasebeta

← #18070033

Subgroups — #18070033

Order 4864.

258 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 37 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#14564744C211yesmaximal, characteristic
2#14561573C211yesmaximal, characteristic, complemented
3C19×#1391C211yesmaximal, characteristic, complemented
4C2×#10597395—21no—
5C22×D152C411yescharacteristic, complemented
6C2×#10597280—21no—
7#11926326—21no—
8#11926309C411yescharacteristic, complemented
9C19×#410—21no—
10C19×#408C2211yescharacteristic
11C2×#41×C19D411yescharacteristic
12C22×D76—21no—
13C2×M16×C19D411yescharacteristic
14C22×C8×C19C2×C411yescharacteristic
15C19×#117—41no—
16#10597395—42no—
17#10597395—42no—
18C2×#64527—41no—
19C2×#64525—41no—
20C2×#64520—21no—
21C2×D152—41no—
22C2×D152—42no—
23C19×#99—22no—
24C19×#99—41no—
25C19×C22⋊C8—41no—
26#10597280—42no—
27#10597269—41no—
28C23×D19—41no—
29#41×C19—41no—
30#41×C19—41no—
31C2×Q8×C19SD1611yescharacteristic
32C2×D4×C19—21no—
33C2×D4×C19D811yescharacteristic
34C22×C4×C19—21no—
35C22×C4×C19C22⋊C411yescharacteristic
36C2×D76—22no—
37C2×D76—41no—
38C2×D76—41no—
39C2×D76—41no—
40C2×D76—41no—
41C2×D76—41no—
42M16×C19—41no—
43C2×C8×C19—21no—
44C2×C8×C19—21no—
45C2×C8×C19—41no—
46C4⋊C4×C19—81no—
47C22⋊C4×C19—42no—
48C42×C19—81no—
49#64527—44no—
50#64525—44no—
51#64520—22no—
52#64520—41no—
53C2×C19⋊C8—41no—
54D152—42no—
55D152—42no—
56C19⋊C16—81no—
57#7398—191nomaximal, Sylow
58C23×C19—21no—
59C23×C19#10411yescharacteristic
60C22×D19—42no—
61C22×D19—81no—
62C22×D19—81no—
63C22×D19—162no—
64Q8×C19—41no—
65D4×C19—41no—
66D4×C19—81no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—41no—
71C2×C4×C19—41no—
72C2×C4×C19—82no—
73C2×C4×C19#9911yescharacteristic
74C2×C4×C19#10211yescharacteristic
75D76—42no—
76D76—42no—
77D76—81no—
78D76—81no—
79C8×C19—41no—
80C8×C19—41no—
81C19⋊C8—42no—
82#2018—191no—
83#1391D1911yescharacteristic, complemented
84#1321—191no—
85C22×C19—21no—
86C22×C19—41no—
87C22×C19—41no—
88C22×C19—81no—
89C22×C19#32711yescharacteristic
90C2×D19—82no—
91C2×D19—162no—
92C2×D19—162no—
93C2×D19—162no—
94C4×C19—21no—
95C4×C19—41no—
96C4×C19—162no—
97C4×C19AΣL(1,𝔽16)11yescharacteristic
98C4×C19#35311yescharacteristic
99C2×AGL(1,ℤ/8)—381no—
100C22×D8—191no—
101C2×#100—381no—
102#410—21no—
103#408C2×D1911yescharacteristic
104#349—381no—
105#341—191no—
106C2×C19—21no—
107C2×C19—41no—
108C2×C19—81no—
109C2×C19#134311yescharacteristic
110D19—162no—
111C2×#41C22⋊D1911yescharacteristic
112C22×D4—381no—
113AGL(1,ℤ/8)—762no—
114AGL(1,ℤ/8)—762no—
115C2×SD16—761no—
116C2×D8—761no—
117C2×D8—762no—
118C2×D8—761no—
119C2×M16—381no—
120C2×M16D7611yescharacteristic
121C22×C8C4×D1911yescharacteristic
122#117—41no—
123M32—761no—
124#100—762no—
125#99—22no—
126#99—41no—
127C22⋊C8—41no—
128C19#739811yescharacteristic, complemented, Sylow
129C24—761no—
130#41—41no—
131#41—41no—
132C2×Q8#6452711yescharacteristic
133C2×D4—21no—
134C2×D4—382no—
135C2×D4—761no—
136C2×D4—761no—
137C2×D4—761no—
138C2×D4—761no—
139C2×D4—761no—
140C2×D4#6452511yescharacteristic
141C22×C4—21no—
142C22×C4(C2×D19)⋊C411yescharacteristic
143SD16—764no—
144D8—762no—
145D8—762no—
146D8—764no—
147M16—41no—
148M16—382no—
149M16—761no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8—761no—
154C4⋊C4—81no—
155C22⋊C4—42no—
156C42—81no—
157C16—1521no—
158C23—21no—
159C23—3042no—
160C23—762no—
161C23—1521no—
162C23—1521no—
163C23#1059726211yescharacteristic
164Q8—41no—
165D4—41no—
166D4—81no—
167D4—762no—
168D4—762no—
169D4—1521no—
170D4—1521no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—82no—
177C2×C4#1059726311yescharacteristic
178C2×C4#1059726611yescharacteristic
179C8—41no—
180C8—41no—
181C8—762no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22—3042no—
187C22—3042no—
188C22—3042no—
189C22—1522no—
190C22#1192627711yescharacteristic
191C4—21no—
192C4—41no—
193C4—162no—
194C4#1192633011yescharacteristic
195C4#1192633611yescharacteristic
196C2—21no—
197C2—41no—
198C2—81no—
199C2—3042no—
200C2#1456163111yescharacteristic
subgroupG/H
centerC2#14561631
commutatorC22×C8×C19C2×C4
Frattini#408C2×D19
FittingC19×#1391C2
socleC2×C19#1343
prime radical#14564744C2
cosocleC19×#408C22
hypercenter#1391D19
hypocenterC19#7398
LCSG ▷ C22×C8×C19 ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1391

Complements

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

NH ≅ G/Ntype
2. #14561573C2semidirect
3. C19×#1391C2semidirect
5. C22×D152C4semidirect
8. #11926309C4semidirect
83. #1391D19semidirect
128. C19#7398semidirect

Maximal subgroups

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

subgroupindex
#145647442
#145615732
C19×#13912
#739819