Finite Group Databasebeta

← #34071064

Subgroups — #34071064

Order 19328.

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

normal subgroups only

This group has 220 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#23753014C211yesmaximal, characteristic, complemented
2C2×#18012680C211yesmaximal, characteristic, complemented
3#23752479C211yesmaximal, characteristic, complemented
4#23752026C211yesmaximal, characteristic, complemented
5#23752019C211yesmaximal, characteristic, complemented
6#23751997C211yesmaximal, characteristic, complemented
7#509×C151C211yesmaximal, characteristic, complemented
8#18012785—21no—
9#18012766—22no—
10#18012765—21no—
11#18012764—21no—
12#18012762—21no—
13C2×D1208C2211yescharacteristic
14D8×D151—21no—
15#18012745C2211yescharacteristic
16#18012680—22no—
17C2×C151⋊C16C2211yescharacteristic, complemented
18#18012675C2211yescharacteristic, complemented
19#18012656—21no—
20#135×C151C2211yescharacteristic
21C2×D8×C151C2211yescharacteristic, complemented
22SD32×C151—21no—
23D16×C151—21no—
24M32×C151C2211yescharacteristic, complemented
25#14559005—22no—
26#14559004—41no—
27#14559004D411yescharacteristic
28C2×D604—21no—
29C2×D604—41no—
30D4×D151—22no—
31D4×D151—42no—
32#14558992—41no—
33#14558991—22no—
34D1208—21no—
35D1208D412yes—
36#14558989—22no—
37#14558989—41no—
38#14558988—21no—
39#14558988D411yescharacteristic
40#14558987—21no—
41C8×D151—21no—
42C151⋊C16—21no—
43#41×C151—21no—
44C2×D4×C151—21no—
45Q16×C151D411yescharacteristic
46SD16×C151—21no—
47D8×C151—21no—
48D8×C151—21no—
49D8×C151D411yescharacteristic
50C2×C8×C151C2311yescharacteristic
51C16×C151—21no—
52C22×D151—42no—
53C22×D151—41no—
54Dic302D811yescharacteristic
55D604—22no—
56D604—42no—
57D604—41no—
58D604D811yescharacteristic
59C22⋊D151—21no—
60C22⋊D151—42no—
61C4×D151—21no—
62C4×D151—42no—
63C151⋊C8—21no—
64C151⋊C8—41no—
65C23×C151—41no—
66Q8×C151—21no—
67D4×C151—21no—
68D4×C151—41no—
69D4×C151—41no—
70D4×C151—41no—
71C2×C4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C8×C151C2×D411yescharacteristic
74C8×C151C2×D411yescharacteristic
75C22×C151—41no—
76C22×C151—81no—
77C22×C151—161no—
78C22×C151AGL(1,ℤ/8)11yescharacteristic
79C2×D151—21no—
80C2×D151—42no—
81C2×D151—162no—
82C2×D151—161no—
83C4×C151—41no—
84C4×C151#12011yescharacteristic
85C4×C151C2×D811yescharacteristic
86Dic151—21no—
87C2×C151—21no—
88C2×C151—81no—
89C2×C151—161no—
90C2×C151#44711yescharacteristic
91D151—41no—
92D151—82no—
93C151#219211yescharacteristic, complemented, Sylow
94#2192—1511nomaximal, Sylow
95#576—1511no—
96#509D15111yescharacteristic, complemented
97C2×D16—1511no—
98#472—1511no—
99#361—1511no—
100#359—1511no—
101#350—1511no—
102H(5,𝔽2)—3021no—
103AGL(1,ℤ/8)—3022no—
104AGL(1,ℤ/8)—3021no—
105AGL(1,ℤ/8)—3021no—
106#135—3021no—
107#135C2×D15111yescharacteristic
108C2×D8—3021no—
109C2×D8—1511no—
110C2×D8C2×D15111yescharacteristic, complemented
111#131—1511no—
112SD32—21no—
113D16—21no—
114D16—3022no—
115M32C2×D15111yescharacteristic, complemented
116C2×C16—1511no—
117#108—1511no—
118#100—3021no—
119#41—21no—
120#41—3022no—
121#41—6041no—
122#41—1511no—
123C2×D4—21no—
124C2×D4—3022no—
125C2×D4—3021no—
126C2×D4—6041no—
127C2×D4—6042no—
128Q16C22⋊D15111yescharacteristic
129SD16—21no—
130SD16—3022no—
131SD16—6041no—
132D8—21no—
133D8—21no—
134D8—3022no—
135D8—3021no—
136D8—6041no—
137D8—1512no—
138D8C22⋊D15111yescharacteristic
139M16—3021no—
140M16—3021no—
141M16—1511no—
142C2×C8—3021no—
143C2×C8C22×D15111yescharacteristic
144C16—21no—
145C16—3021no—
146C23—41no—
147C23—6042no—
148C23—6041no—
149Q8—21no—
150Q8—1511no—
151D4—21no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—3021no—
156D4—3022no—
157D4—6042no—
158D4—6042no—
159D4—6041no—
160D4—1511no—
161C2×C4—41no—
162C2×C4—3021no—
163C2×C4—6042no—
164C2×C4D4×D15111yescharacteristic
165C8—3021no—
166C8—6041no—
167C8D4×D15111yescharacteristic
168C8C2×C22⋊D15111yescharacteristic
169C22—41no—
170C22—81no—
171C22—161no—
172C22—3021no—
173C22—6042no—
174C22—24161no—
175C22—24162no—
176C22#1801276311yescharacteristic
177C4—41no—
178C4—3021no—
179C4#1801270711yescharacteristic
180C4D8×D15111yescharacteristic
181C2—21no—
182C2—81no—
183C2—161no—
184C2—6041no—
185C2—12082no—
186C2#2375234411yescharacteristic
subgroupG/H
centerC2#23752344
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#509×C151C2
socleC2×C151#447
hypercenter#509D151
hypocenterC151#2192
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23753014C2semidirect
2. C2×#18012680C2semidirect
3. #23752479C2semidirect
4. #23752026C2semidirect
5. #23752019C2semidirect
6. #23751997C2semidirect
7. #509×C151C2semidirect
17. C2×C151⋊C16C22semidirect
18. #18012675C22semidirect
21. C2×D8×C151C22semidirect
24. M32×C151C22semidirect
93. C151#2192semidirect
96. #509D151semidirect
110. C2×D8C2×D151semidirect
115. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530142
C2×#180126802
#237524792
#237520262
#237520192
#237519972
#509×C1512
#2192151