Finite Group Databasebeta

← #34071063

Subgroups — #34071063

Order 19328.

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

normal subgroups only

This group has 216 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
2#23752655C212yesmaximal, complemented
3#23752470C211yesmaximal, 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×Dic604C2211yescharacteristic, complemented
12#18012718—21no—
13Dic1208—22no—
14#18012684—22no—
15#18012671C2211yescharacteristic, complemented
16#18012664—21no—
17C2×M16×C151C2211yescharacteristic
18M32×C151C2212yescomplemented
19#14559004—22no—
20#14559004—22no—
21#14559004—41no—
22#14559004—41no—
23C2×Dic302—21no—
24C2×Dic302—21no—
25C2×D604—21no—
26C2×C22⋊D151—41no—
27C2×C4×D151—41no—
28Dic604—21no—
29Dic604—22no—
30Dic604D412yes—
31#14558993—22no—
32#14558993—22no—
33D1208—21no—
34D1208D412yes—
35C4⋊Dic151—21no—
36Dic151⋊C4—41no—
37C22⋊Dic151—41no—
38C22×C4×C151D411yescharacteristic
39M16×C151—22no—
40C2×C8×C151D411yescharacteristic
41C2×C8×C151C2311yescharacteristic
42C16×C151—22no—
43C22×D151—41no—
44Dic302—22no—
45Dic302—41no—
46Dic302—41no—
47Dic302—41no—
48D604—22no—
49D604—41no—
50C22⋊D151—42no—
51C22⋊D151—42no—
52C2×Dic151—41no—
53C2×Dic151—41no—
54C2×Dic151—41no—
55C4×D151—42no—
56C4×D151—42no—
57C23×C151D811yescharacteristic
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151D811yescharacteristic
61C2×C4×C151C2×D411yescharacteristic
62C8×C151—21no—
63C8×C151C2×D412yes—
64C22×C151—21no—
65C22×C151—41no—
66C22×C151C2×D811yescharacteristic
67C2×D151—42no—
68C2×D151—82no—
69C4×C151—21no—
70C4×C151#12011yescharacteristic
71C4×C151AGL(1,ℤ/8)11yescharacteristic
72Dic151—42no—
73Dic151—81no—
74Dic151—81no—
75C2×C151—21no—
76C2×C151—41no—
77C2×C151#44711yescharacteristic
78D151—82no—
79C151#219111yescharacteristic, complemented, Sylow
80#2191—1511nomaximal, Sylow
81#575—1511no—
82#510—1512no—
83#470—1511no—
84#360—1512no—
85#349D15111yescharacteristic, complemented
86C2×#41—3021no—
87#137—3022no—
88AGL(1,ℤ/8)—3022no—
89#135—3021no—
90#135—1512no—
91C2×Q16—1511no—
92C2×M16C2×D15111yescharacteristic
93C22⋊Q8—3021no—
94Q32—3022no—
95SD32—3022no—
96M32C2×D15112yescomplemented
97#106—1511no—
98#103—3021no—
99#41—3022no—
100#41—3022no—
101#41—6041no—
102#41—6041no—
103C2×Q8—3021no—
104C2×Q8—3021no—
105C2×D4—3021no—
106C2×D4—6041no—
107C22×C4—6041no—
108C22×C4D60411yescharacteristic
109Q16—3021no—
110Q16—3022no—
111Q16—1512no—
112SD16—3022no—
113SD16—3022no—
114D8—3021no—
115D8—1512no—
116M16—22no—
117C2×C8D60411yescharacteristic
118C2×C8C22×D15111yescharacteristic
119C4⋊C4—3021no—
120C4⋊C4—6041no—
121C22⋊C4—6041no—
122C16—22no—
123C23—6041no—
124C23D120811yescharacteristic
125Q8—3022no—
126Q8—6041no—
127Q8—6041no—
128Q8—6041no—
129D4—3022no—
130D4—6041no—
131D4—6042no—
132D4—6042no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—6042no—
136C2×C4—6041no—
137C2×C4—6042no—
138C2×C4—6041no—
139C2×C4—6041no—
140C2×C4D120811yescharacteristic
141C2×C4C2×D60411yescharacteristic
142C8—21no—
143C8D4×D15112yes—
144C22—21no—
145C22—41no—
146C22—6042no—
147C22—12082no—
148C22C2×D120811yescharacteristic
149C4—21no—
150C4—6042no—
151C4—12081no—
152C4—12081no—
153C4#1801270911yescharacteristic
154C4#1801276711yescharacteristic
155C2—21no—
156C2—41no—
157C2—12082no—
158C2#2375234811yescharacteristic
subgroupG/H
centerC2#23752348
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#349×C151C2
socleC2×C151#447
prime radical#23753012C2
hypercenter#349D151
hypocenterC151#2191
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
2. #23752655C2semidirect
3. #23752470C2semidirect
4. #23752023C2semidirect
5. #349×C151C2semidirect
11. C2×Dic604C22semidirect
15. #18012671C22semidirect
18. M32×C151C22semidirect
79. C151#2191semidirect
85. #349D151semidirect
96. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237526552
#237524702
#237520232
#349×C1512
#2191151