Finite Group Databasebeta

← #34071073

Subgroups — #34071073

Order 19328.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#23753025C211yesmaximal, characteristic, complemented
2#23752648C211yesmaximal, characteristic, complemented
3#23752479C211yesmaximal, characteristic, complemented
4#23752028C211yesmaximal, characteristic, complemented
5#23752020C211yesmaximal, characteristic, complemented
6#23751995C211yesmaximal, characteristic, complemented
7C2×SD32×C151C211yesmaximal, characteristic, complemented
8#18012787—21no—
9#18012771—22no—
10#18012770—21no—
11#18012765—21no—
12#18012762—21no—
13#18012761C2211yescharacteristic
14Q16×D151—21no—
15#18012745C2211yescharacteristic
16#18012683—21no—
17#18012680—21no—
18#18012679C2211yescharacteristic
19#18012675C2211yescharacteristic
20#18012656—21no—
21C2×Q16×C151C2211yescharacteristic
22C2×D8×C151C2211yescharacteristic
23SD32×C151—22no—
24C2×C16×C151C2211yescharacteristic
25#14559005—22no—
26#14559005—41no—
27#14559004—21no—
28#14559004—42no—
29#14559004D411yescharacteristic
30Q8×D151—22no—
31Q8×D151—41no—
32Dic604D411yescharacteristic
33#14558994—22no—
34#14558993—21no—
35#14558992—41no—
36#14558991—22no—
37D1208D411yescharacteristic
38#14558989—41no—
39#14558988—21no—
40#14558988D411yescharacteristic
41#14558987—21no—
42C8×D151—21no—
43C151⋊C16—21no—
44C2×Q8×C151—21no—
45C2×D4×C151—21no—
46Q16×C151—21no—
47Q16×C151D412yes—
48D8×C151—21no—
49D8×C151—21no—
50C2×C8×C151C2311yescharacteristic
51C16×C151—21no—
52Dic302—21no—
53Dic302—42no—
54Dic302D811yescharacteristic
55D604—21no—
56D604—42no—
57D604D811yescharacteristic
58C22⋊D151—21no—
59C22⋊D151—41no—
60C4×D151—21no—
61C4×D151—42no—
62C4×D151—42no—
63C4×D151—41no—
64C151⋊C8—21no—
65C151⋊C8—41no—
66C23×C151—41no—
67Q8×C151—22no—
68Q8×C151—41no—
69D4×C151—41no—
70D4×C151—41no—
71C2×C4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C8×C151C2×D411yescharacteristic
74C8×C151C2×D411yescharacteristic
75C22×C151—81no—
76C22×C151—161no—
77C22×C151AGL(1,ℤ/8)11yescharacteristic
78C2×D151—21no—
79C2×D151—41no—
80C4×C151—42no—
81C4×C151#12011yescharacteristic
82C4×C151C2×D811yescharacteristic
83Dic151—21no—
84Dic151—41no—
85C2×C151—21no—
86C2×C151—161no—
87C2×C151#44711yescharacteristic
88D151—41no—
89D151—81no—
90C151#219311yescharacteristic, complemented, Sylow
91#2193—1511nomaximal, Sylow
92#578—1511no—
93#509—1511no—
94C2×SD32D15111yescharacteristic, complemented
95#472—1511no—
96#362—1511no—
97#359—1511no—
98#350—1511no—
992−1+4—3021no—
100#137—3022no—
101#137—3021no—
102AGL(1,ℤ/8)—3021no—
103#135—3021no—
104#135—1511no—
105C2×Q16—3021no—
106C2×Q16C2×D15111yescharacteristic
107C2×D8C2×D15111yescharacteristic
108#131—1511no—
109SD32—22no—
110SD32—3021no—
111D16—3021no—
112M32—1511no—
113C2×C16C2×D15111yescharacteristic
114#108—1511no—
115#100—3021no—
116#41—3022no—
117#41—3021no—
118#41—6042no—
119#41—6041no—
120#41—1511no—
121C2×Q8—21no—
122C2×Q8—3022no—
123C2×Q8—6041no—
124C2×D4—21no—
125Q16—21no—
126Q16—3022no—
127Q16—1511no—
128Q16C22⋊D15112yes—
129SD16—3022no—
130SD16—3021no—
131SD16—6041no—
132D8—21no—
133D8—21no—
134D8—6041no—
135D8—1511no—
136M16—3021no—
137M16—3021no—
138M16—1511no—
139C2×C8—3021no—
140C2×C8C22×D15111yescharacteristic
141C16—21no—
142C16—3021no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—3021no—
147Q8—6042no—
148Q8—1511no—
149D4—41no—
150D4—41no—
151D4—3021no—
152D4—3021no—
153D4—6042no—
154D4—6041no—
155D4—1511no—
156C2×C4—41no—
157C2×C4—3021no—
158C2×C4—6042no—
159C2×C4—6042no—
160C2×C4—6041no—
161C2×C4D4×D15111yescharacteristic
162C8—3021no—
163C8—6041no—
164C8D4×D15111yescharacteristic
165C8C2×C22⋊D15111yescharacteristic
166C22—81no—
167C22—161no—
168C22—3021no—
169C22—6041no—
170C22#1801276311yescharacteristic
171C4—42no—
172C4—3021no—
173C4—6041no—
174C4#1801270711yescharacteristic
175C4D8×D15111yescharacteristic
176C2—21no—
177C2—161no—
178C2—6041no—
179C2—12081no—
180C2#2375234411yescharacteristic
subgroupG/H
centerC2#23752344
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
FittingC2×SD32×C151C2
socleC2×C151#447
hypercenterC2×SD32D151
hypocenterC151#2193
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #23753025C2semidirect
2. #23752648C2semidirect
3. #23752479C2semidirect
4. #23752028C2semidirect
5. #23752020C2semidirect
6. #23751995C2semidirect
7. C2×SD32×C151C2semidirect
90. C151#2193semidirect
94. C2×SD32D151semidirect

Maximal subgroups

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

subgroupindex
#237530252
#237526482
#237524792
#237520282
#237520202
#237519952
C2×SD32×C1512
#2193151