Finite Group Databasebeta

← #34071087

Subgroups — #34071087

Order 19328.

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

normal subgroups only

This group has 206 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
2#23752653C211yesmaximal, characteristic, complemented
3#23752484C211yesmaximal, characteristic, complemented
4#23752028C211yesmaximal, characteristic, complemented
5#23752020C211yesmaximal, characteristic, complemented
6#23751995C211yesmaximal, characteristic, complemented
7C2×Q32×C151C211yesmaximal, characteristic, complemented
8#18012787—21no—
9#18012771—22no—
10#18012770—21no—
11#18012770—21no—
12#18012762—21no—
13#18012761C2211yescharacteristic
14Q16×D151—21no—
15#18012745C2211yescharacteristic
16#18012685—21no—
17#18012682—21no—
18#18012679C2211yescharacteristic
19#18012675C2211yescharacteristic
20#18012658—21no—
21C2×Q16×C151C2211yescharacteristic
22C2×Q16×C151C2211yescharacteristic
23Q32×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#14558994—41no—
35#14558993—21no—
36#14558991—22no—
37#14558991—41no—
38D1208D411yescharacteristic
39#14558988—21no—
40#14558988D411yescharacteristic
41#14558987—21no—
42C8×D151—21no—
43C151⋊C16—21no—
44C2×Q8×C151—21no—
45C2×Q8×C151—21no—
46Q16×C151—21no—
47Q16×C151—21no—
48Q16×C151—21no—
49Q16×C151D412yes—
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—
66Q8×C151—22no—
67Q8×C151—41no—
68Q8×C151—41no—
69Q8×C151—41no—
70C2×C4×C151—41no—
71C2×C4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C8×C151C2×D411yescharacteristic
74C8×C151C2×D411yescharacteristic
75C22×C151AGL(1,ℤ/8)11yescharacteristic
76C2×D151—21no—
77C2×D151—41no—
78C4×C151—42no—
79C4×C151—81no—
80C4×C151#12011yescharacteristic
81C4×C151C2×D811yescharacteristic
82Dic151—21no—
83Dic151—41no—
84C2×C151—21no—
85C2×C151#44711yescharacteristic
86D151—41no—
87D151—81no—
88C151#219511yescharacteristic, complemented, Sylow
89#2195—1511nomaximal, Sylow
90#578—1511no—
91#510—1511no—
92C2×Q32D15111yescharacteristic, complemented
93#473—1511no—
94#362—1511no—
95#359—1511no—
96#350—1511no—
972−1+4—3021no—
98#137—3022no—
99#137—3021no—
100#137—3021no—
101#135—3021no—
102#135—1511no—
103C2×Q16—3021no—
104C2×Q16C2×D15111yescharacteristic
105C2×Q16C2×D15111yescharacteristic
106#131—1511no—
107Q32—22no—
108Q32—3021no—
109SD32—3021no—
110M32—1511no—
111C2×C16C2×D15111yescharacteristic
112#108—1511no—
113#101—3021no—
114#41—3022no—
115#41—3021no—
116#41—6042no—
117#41—6041no—
118#41—1511no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—3022no—
122C2×Q8—6041no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—3022no—
127Q16—6041no—
128Q16—1511no—
129Q16C22⋊D15112yes—
130SD16—3022no—
131SD16—3021no—
132SD16—6041no—
133D8—1511no—
134M16—3021no—
135M16—3021no—
136M16—1511no—
137C2×C8—3021no—
138C2×C8C22×D15111yescharacteristic
139C16—21no—
140C16—3021no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—3021no—
146Q8—6042no—
147Q8—1511no—
148D4—3021no—
149D4—3021no—
150D4—6042no—
151D4—6041no—
152D4—1511no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3021no—
156C2×C4—6042no—
157C2×C4—6042no—
158C2×C4—6041no—
159C2×C4D4×D15111yescharacteristic
160C8—3021no—
161C8—6041no—
162C8D4×D15111yescharacteristic
163C8C2×C22⋊D15111yescharacteristic
164C22—3021no—
165C22—6041no—
166C22#1801276311yescharacteristic
167C4—42no—
168C4—81no—
169C4—3021no—
170C4—6041no—
171C4#1801270711yescharacteristic
172C4D8×D15111yescharacteristic
173C2—21no—
174C2—6041no—
175C2—12081no—
176C2#2375234411yescharacteristic
subgroupG/H
centerC2#23752344
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
FittingC2×Q32×C151C2
socleC2×C151#447
prime radical#23753025C2
hypercenterC2×Q32D151
hypocenterC151#2195
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #23752653C2semidirect
3. #23752484C2semidirect
4. #23752028C2semidirect
5. #23752020C2semidirect
6. #23751995C2semidirect
7. C2×Q32×C151C2semidirect
88. C151#2195semidirect
92. C2×Q32D151semidirect

Maximal subgroups

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

subgroupindex
#237530252
#237526532
#237524842
#237520282
#237520202
#237519952
C2×Q32×C1512
#2195151