Finite Group Databasebeta

← #34071058

Subgroups — #34071058

Order 19328.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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#23753012C211yesmaximal, characteristic, complemented
2#23752650C212yesmaximal, complemented
3#23752465C211yesmaximal, characteristic, complemented
4#23752023C212yesmaximal, complemented
5#349×C151C211yesmaximal, characteristic, complemented
6C2×#14559004—21no—
7#18012772—22no—
8#18012767—22no—
9#18012761—21no—
10#18012761C2212yes—
11C2×D1208C2211yescharacteristic, complemented
12#18012713—21no—
13#18012684—22no—
14D2416—22no—
15#18012671C2211yescharacteristic, complemented
16#18012661—21no—
17C2×M16×C151C2211yescharacteristic
18M32×C151C2212yescomplemented
19#14559004—22no—
20#14559004—22no—
21#14559004—41no—
22#14559004—41no—
23C2×Dic302—21no—
24C2×D604—21no—
25C2×D604—21no—
26C2×C22⋊D151—41no—
27C2×C22⋊D151—41no—
28C2×C4×D151—41no—
29Dic604—21no—
30Dic604D412yescomplemented
31#14558993—22no—
32#14558993—22no—
33D1208—21no—
34D1208—22no—
35D1208D412yescomplemented
36C4⋊Dic151—21no—
37(C2×D151)⋊C4—41no—
38C22×C4×C151D411yescharacteristic
39M16×C151—22no—
40C2×C8×C151D411yescharacteristic
41C2×C8×C151C2311yescharacteristic
42C16×C151—22no—
43C22×D151—41no—
44C22×D151—41no—
45Dic302—22no—
46Dic302—41no—
47D604—22no—
48D604—41no—
49D604—41no—
50D604—41no—
51C22⋊D151—42no—
52C22⋊D151—42no—
53C22⋊D151—82no—
54C2×Dic151—41no—
55C2×Dic151—41no—
56C4×D151—42no—
57C4×D151—42no—
58C23×C151D811yescharacteristic
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151D811yescharacteristic
62C2×C4×C151C2×D411yescharacteristic
63C8×C151—21no—
64C8×C151C2×D412yes—
65C22×C151—21no—
66C22×C151—41no—
67C22×C151C2×D811yescharacteristic
68C2×D151—42no—
69C2×D151—82no—
70C2×D151—81no—
71C2×D151—81no—
72C2×D151—81no—
73C4×C151—21no—
74C4×C151#12011yescharacteristic
75C4×C151AGL(1,ℤ/8)11yescharacteristic
76Dic151—42no—
77Dic151—81no—
78C2×C151—21no—
79C2×C151—41no—
80C2×C151#44711yescharacteristic
81D151—82no—
82D151—161no—
83C151#219011yescharacteristic, complemented, Sylow
84#2190—1511nomaximal, Sylow
85#575—1511no—
86#509—1512no—
87#469—1511no—
88#360—1512no—
89#349D15111yescharacteristic, complemented
90C2×#41—3021no—
91#137—3022no—
92AGL(1,ℤ/8)—3022no—
93#135—3021no—
94#135—1512no—
95C2×D8—1511no—
96C2×M16C2×D15111yescharacteristic
97#121—3021no—
98SD32—3022no—
99D16—3022no—
100M32C2×D15112yescomplemented
101#106—1511no—
102#102—3021no—
103#41—3022no—
104#41—3022no—
105#41—6041no—
106#41—6041no—
107C2×Q8—3021no—
108C2×D4—3021no—
109C2×D4—3021no—
110C2×D4—6041no—
111C2×D4—6041no—
112C22×C4—6041no—
113C22×C4D60411yescharacteristic
114Q16—3021no—
115Q16—1512no—
116SD16—3022no—
117SD16—3022no—
118D8—3021no—
119D8—3022no—
120D8—1512no—
121M16—22no—
122C2×C8D60411yescharacteristic
123C2×C8C22×D15111yescharacteristic
124C4⋊C4—3021no—
125C22⋊C4—6041no—
126C16—22no—
127C23—6041no—
128C23—6041no—
129C23D120811yescharacteristic
130Q8—3022no—
131Q8—6041no—
132D4—3022no—
133D4—6041no—
134D4—6042no—
135D4—6042no—
136D4—6041no—
137D4—6041no—
138D4—12082no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—6042no—
142C2×C4—6041no—
143C2×C4—6042no—
144C2×C4—6041no—
145C2×C4D120811yescharacteristic
146C2×C4C2×D60411yescharacteristic
147C8—21no—
148C8D4×D15112yes—
149C22—21no—
150C22—41no—
151C22—6042no—
152C22—12081no—
153C22—12081no—
154C22—12082no—
155C22—12081no—
156C22C2×D120811yescharacteristic
157C4—21no—
158C4—6042no—
159C4—12081no—
160C4#1801270911yescharacteristic
161C4#1801276711yescharacteristic
162C2—21no—
163C2—41no—
164C2—24161no—
165C2—12082no—
166C2#2375234811yescharacteristic
subgroupG/H
centerC2#23752348
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#349×C151C2
socleC2×C151#447
hypercenter#349D151
hypocenterC151#2190
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #23753012C2semidirect
2. #23752650C2semidirect
3. #23752465C2semidirect
4. #23752023C2semidirect
5. #349×C151C2semidirect
11. C2×D1208C22semidirect
15. #18012671C22semidirect
18. M32×C151C22semidirect
30. Dic604D4semidirect
35. D1208D4semidirect
83. C151#2190semidirect
89. #349D151semidirect
100. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237526502
#237524652
#237520232
#349×C1512
#2190151