Finite Group Databasebeta

← #34068149

Subgroups — #34068149

Order 19328.

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

normal subgroups only

This group has 246 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#23752793C211yesmaximal, characteristic
2#23752531C212yesmaximal, complemented
3#23752151C211yesmaximal, characteristic, complemented
4#23751947C212yesmaximal, complemented
5#324×C151C211yesmaximal, characteristic, complemented
6C2×#14559004—21no—
7#18012719—22no—
8#18012714—22no—
9#18012713—21no—
10#18012713C2212yes—
11C2×C4⋊Dic151C2211yescharacteristic
12#18012671—22no—
13#18012661—22no—
14C151⋊#95—21no—
15C151⋊#95—21no—
16C151⋊#95C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yes—
19#14559004—42no—
20#14559004—42no—
21C2×Dic302—21no—
22C2×D604—21no—
23C2×D604—21no—
24C2×D604D412yes—
25C2×C22⋊D151—22no—
26C22×Dic151—21no—
27C22×Dic151—21no—
28C2×C4×D151—22no—
29C4⋊Dic151—21no—
30C4⋊Dic151—22no—
31C4⋊Dic151D412yes—
32(C2×D151)⋊C4—22no—
33(C2×D151)⋊C4—22no—
34C22×C4×C151D411yescharacteristic
35C22×C4×C151D411yescharacteristic
36C22×C4×C151C2311yescharacteristic
37C2×C8×C151—22no—
38C4⋊C4×C151—22no—
39C22×D151—22no—
40Dic302—42no—
41D604—42no—
42D604—42no—
43D604—81no—
44C22⋊D151—42no—
45C22⋊D151—42no—
46C2×Dic151—22no—
47C2×Dic151—41no—
48C2×Dic151—41no—
49C2×Dic151—42no—
50C2×Dic151—41no—
51C2×Dic151—41no—
52C4×D151—44no—
53C23×C151C2×D411yescharacteristic
54C2×C4×C151—21no—
55C2×C4×C151—21no—
56C2×C4×C151—21no—
57C2×C4×C151—41no—
58C2×C4×C151—41no—
59C2×C4×C151SD1612yes—
60C2×C4×C151C2×D412yes—
61C8×C151—42no—
62C22×C151—21no—
63C22×C151—21no—
64C22×C151#12011yescharacteristic
65C22×C151C2×SD1611yescharacteristic
66C22×C151AGL(1,ℤ/8)11yescharacteristic
67C2×D151—42no—
68C2×D151—42no—
69C2×D151—42no—
70C4×C151—22no—
71C4×C151—22no—
72C4×C151—41no—
73Dic151—42no—
74Dic151—81no—
75Dic151—81no—
76C2×C151—21no—
77C2×C151—21no—
78C2×C151#45011yescharacteristic
79C2×C151#45411yescharacteristic
80C2×C151#45811yescharacteristic
81D151—82no—
82C151#161611yescharacteristic, complemented, Sylow
83#1616—1511nomaximal, Sylow
84#537—1511no—
85#481—1512no—
86#400—1511no—
87#327—1512no—
88#324D15111yescharacteristic, complemented
89C2×#41—3021no—
90C22⋊Q8—3022no—
91#121—3022no—
92#121—3021no—
93#121—1512no—
94C2×C4⋊C4—1511no—
95C2×C4⋊C4C2×D15111yescharacteristic
96#106—3022no—
97#102—3022no—
98C22⋊C8C2×D15112yes—
99#95—3021no—
100#95—3021no—
101#95—1511no—
102#41—6042no—
103#41—6042no—
104C2×Q8—3021no—
105C2×D4—3021no—
106C2×D4—3021no—
107C2×D4—3022no—
108C2×D4—1512no—
109C22×C4—3022no—
110C22×C4—3021no—
111C22×C4—3021no—
112C22×C4D60411yescharacteristic
113C22×C4D60411yescharacteristic
114C22×C4C22×D15111yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—3021no—
118C4⋊C4—3022no—
119C4⋊C4—1512no—
120C22⋊C4—3022no—
121C22⋊C4—3022no—
122C23—3022no—
123C23C2×D60411yescharacteristic
124Q8—6042no—
125D4—6042no—
126D4—6042no—
127D4—6042no—
128D4—6042no—
129D4—12081no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—3022no—
136C2×C4—6044no—
137C2×C4—6041no—
138C2×C4—6041no—
139C2×C4—6042no—
140C2×C4—6041no—
141C2×C4—6041no—
142C2×C4#1455899312yes—
143C2×C4D4×D15112yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—6042no—
148C22—6042no—
149C22—6042no—
150C22#1801270911yescharacteristic
151C22C2×#1455899311yescharacteristic
152C22#1801276711yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—6042no—
157C4—12081no—
158C4—12081no—
159C2—21no—
160C2—21no—
161C2—12082no—
162C2#2375236511yescharacteristic
163C2#2375238711yescharacteristic
164C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#324D151
hypocenterC151#1616
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23752531C2semidirect
3. #23752151C2semidirect
4. #23751947C2semidirect
5. #324×C151C2semidirect
82. C151#1616semidirect
88. #324D151semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237525312
#237521512
#237519472
#324×C1512
#1616151