Finite Group Databasebeta

← #34068115

Subgroups — #34068115

Order 19328.

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

normal subgroups only

This group has 254 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#23752526C212yesmaximal, complemented
3#23752142C211yesmaximal, 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
12C2×Dic151⋊C4—21no—
13#18012673—22no—
14#18012661—22no—
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—
32Dic151⋊C4—42no—
33(C2×D151)⋊C4—22no—
34(C2×D151)⋊C4—22no—
35C22×C4×C151D411yescharacteristic
36C22×C4×C151D411yescharacteristic
37C22×C4×C151C2311yescharacteristic
38C2×C8×C151—22no—
39C4⋊C4×C151—22no—
40C22×D151—22no—
41Dic302—42no—
42D604—42no—
43D604—42no—
44D604—81no—
45C22⋊D151—42no—
46C22⋊D151—42no—
47C2×Dic151—22no—
48C2×Dic151—22no—
49C2×Dic151—41no—
50C2×Dic151—41no—
51C2×Dic151—41no—
52C2×Dic151—41no—
53C2×Dic151—41no—
54C4×D151—44no—
55C23×C151C2×D411yescharacteristic
56C2×C4×C151—21no—
57C2×C4×C151—21no—
58C2×C4×C151—21no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151D812yes—
62C2×C4×C151C2×D412yes—
63C8×C151—42no—
64C22×C151—21no—
65C22×C151—21no—
66C22×C151#12011yescharacteristic
67C22×C151C2×D811yescharacteristic
68C22×C151AGL(1,ℤ/8)11yescharacteristic
69C2×D151—42no—
70C2×D151—42no—
71C2×D151—42no—
72C4×C151—22no—
73C4×C151—22no—
74C4×C151—41no—
75Dic151—42no—
76Dic151—42no—
77Dic151—81no—
78C2×C151—21no—
79C2×C151—21no—
80C2×C151#44711yescharacteristic
81C2×C151#45611yescharacteristic
82C2×C151#45811yescharacteristic
83D151—82no—
84C151#161011yescharacteristic, complemented, Sylow
85#1610—1511nomaximal, Sylow
86#537—1511no—
87#480—1512no—
88#398—1511no—
89#327—1512no—
90#324D15111yescharacteristic, complemented
91C2×#41—3021no—
92C22⋊Q8—3022no—
93#121—3022no—
94#121—3021no—
95#121—1512no—
96C2×C4⋊C4—3021no—
97C2×C4⋊C4—1511no—
98C2×C4⋊C4C2×D15111yescharacteristic
99#107—3022no—
100#102—3022no—
101C22⋊C8C2×D15112yes—
102#95—3021no—
103#95—1511no—
104#41—6042no—
105#41—6042no—
106C2×Q8—3021no—
107C2×D4—3021no—
108C2×D4—3021no—
109C2×D4—3022no—
110C2×D4—1512no—
111C22×C4—3022no—
112C22×C4—3021no—
113C22×C4—3021no—
114C22×C4D60411yescharacteristic
115C22×C4D60411yescharacteristic
116C22×C4C22×D15111yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—3021no—
120C4⋊C4—3022no—
121C4⋊C4—6042no—
122C4⋊C4—1512no—
123C22⋊C4—3022no—
124C22⋊C4—3022no—
125C23—3022no—
126C23C2×D60411yescharacteristic
127Q8—6042no—
128D4—6042no—
129D4—6042no—
130D4—6042no—
131D4—6042no—
132D4—12081no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—3022no—
139C2×C4—3022no—
140C2×C4—6044no—
141C2×C4—6041no—
142C2×C4—6041no—
143C2×C4—6041no—
144C2×C4—6041no—
145C2×C4—6041no—
146C2×C4D120812yes—
147C2×C4D4×D15112yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—6042no—
152C22—6042no—
153C22—6042no—
154C22#1801270911yescharacteristic
155C22C2×D120811yescharacteristic
156C22#1801276711yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—6042no—
161C4—6042no—
162C4—12081no—
163C2—21no—
164C2—21no—
165C2—12082no—
166C2#2375234811yescharacteristic
167C2#2375239711yescharacteristic
168C2#2375240311yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#324D151
hypocenterC151#1610
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. #23752526C2semidirect
3. #23752142C2semidirect
4. #23751947C2semidirect
5. #324×C151C2semidirect
84. C151#1610semidirect
90. #324D151semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237525262
#237521422
#237519472
#324×C1512
#1610151