Finite Group Databasebeta

← #34053601

Subgroups — #34053601

Order 19072.

458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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#23750392C212yesmaximal, complemented
2#23749747C214yesmaximal, complemented
3#23749742C214yesmaximal, complemented
4#23749674C211yesmaximal, characteristic, complemented
5C2×#18011838C212yesmaximal, complemented
6M16×Dic149C211yesmaximal, characteristic, complemented
7#575×C149C211yesmaximal, characteristic
8#18011918—24no—
9#18011918C2218yescomplemented
10C2×#14558720—24no—
11C2×#14558720C2212yes—
12C2×#14558720C2211yescharacteristic
13C2×C4×Dic149C2211yescharacteristic
14#18011847C2214yescomplemented
15#18011838C2214yescomplemented
16#18011838C2214yescomplemented
17#18011821C2212yescomplemented
18C8×Dic149C2212yescomplemented
19C2×#41×C149C2212yes—
20#137×C149C414yescomplemented
21AGL(1,ℤ/8)×C149C414yescomplemented
22#135×C149C2214yes—
23C2×M16×C149C2211yescharacteristic
24C22×Dic149—21no—
25#14558720—28no—
26#14558720—22no—
27#14558720D414yes—
28#14558720C2314yes—
29C2×#11924746—28no—
30C2×#11924746—22no—
31C2×#11924746C2312yes—
32C4×Dic149—21no—
33C4×Dic149C2311yescharacteristic
34C4×Dic149C2311yescharacteristic
35#41×C149—22no—
36#41×C149—22no—
37#41×C149C2×C414yes—
38#41×C149C2314yes—
39C2×Q8×C149C2×C412yes—
40C2×D4×C149—22no—
41C2×D4×C149C2×C412yes—
42C22×C4×C149—22no—
43C22×C4×C149C2311yescharacteristic
44Q16×C149C2×C414yescomplemented
45SD16×C149C2×C418yescomplemented
46D8×C149C2×C414yescomplemented
47M16×C149C2×C414yes—
48C2×C8×C149C2312yes—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149—42no—
52#11924746—24no—
53#11924746C2×D414yes—
54C23×C149—22no—
55C23×C149#4111yescharacteristic
56Q8×C149—22no—
57Q8×C149C22×C414yes—
58D4×C149—24no—
59D4×C149—24no—
60D4×C149—22no—
61D4×C149C22×C414yes—
62C2×C4×C149—22no—
63C2×C4×C149—24no—
64C2×C4×C149—24no—
65C2×C4×C149C22×C412yes—
66C2×C4×C149C2×D412yes—
67C2×C4×C149#4111yescharacteristic
68C2×C4×C149C2411yescharacteristic
69C8×C149C22×C414yes—
70C22×C149—24no—
71C22×C149—41no—
72C22×C149—82no—
73C22×C149C4×D412yes—
74C22×C149C2×#4111yescharacteristic
75C4×C149—24no—
76C4×C149C4×D412yes—
77C4×C149C23×C411yescharacteristic
78C4×C149C22×D411yescharacteristic
79Dic149—22no—
80Dic149—41no—
81C2×C149—21no—
82C2×C149—22no—
83C2×C149—44no—
84C2×C149C2×C4×D411yescharacteristic
85C149#295611yescharacteristic, complemented, Sylow
86#2956—1491nomaximal, Sylow
87#575D14911yescharacteristic
88#568—1492no—
89#444—1494no—
90#443—1494no—
91#430—1491no—
92C2×#104—1492no—
93C4×M16—1491no—
94C2×#41C2×D14912yes—
95#137Dic14914yescomplemented
96AGL(1,ℤ/8)Dic14914yescomplemented
97#135C2×D14914yes—
98#131—2984no—
99#131—1498no—
100C2×M16—2984no—
101C2×M16—1492no—
102C2×M16—1491no—
103C2×M16C2×D14911yescharacteristic
104C2×C42—1491no—
105#108—1494no—
106#104—1494no—
107#104—1494no—
108#97—1492no—
109C4×C8—1492no—
110#41—22no—
111#41—22no—
112#41C2×Dic14914yes—
113#41C22×D14914yes—
114C2×Q8C2×Dic14912yes—
115C2×D4—22no—
116C2×D4C2×Dic14912yes—
117C22×C4—22no—
118C22×C4—2981no—
119C22×C4C22×D14911yescharacteristic
120Q16C2×Dic14914yescomplemented
121SD16C2×Dic14918yescomplemented
122D8C2×Dic14914yescomplemented
123M16—2982no—
124M16—2988no—
125M16—1494no—
126M16—1494no—
127M16C2×Dic14914yes—
128C2×C8—2982no—
129C2×C8—2988no—
130C2×C8—1492no—
131C2×C8C22×D14912yes—
132C42—2981no—
133C42—1491no—
134C42—1491no—
135C23—22no—
136C23#1455873511yescharacteristic
137Q8—22no—
138Q8C22×Dic14914yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic14914yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—2981no—
147C2×C4—2981no—
148C2×C4—5962no—
149C2×C4C22×Dic14912yes—
150C2×C4D4×D14912yes—
151C2×C4#1455873511yescharacteristic
152C2×C4C23×D14911yescharacteristic
153C8—2984no—
154C8—1494no—
155C8C22×Dic14914yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic14912yes—
160C22C2×#1455873511yescharacteristic
161C4—24no—
162C4—2982no—
163C4—5961no—
164C4D4×Dic14912yes—
165C4C23×Dic14911yescharacteristic
166C4C2×D4×D14911yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic14911yescharacteristic
subgroupG/H
centerC4C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
Fitting, prime radical#575×C149C2
socleC2×C149C2×C4×D4
cosocleC2×C4×C149C24
hypercenter#575D149
hypocenterC149#2956
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23750392C2semidirect
2. #23749747C2semidirect
3. #23749742C2semidirect
4. #23749674C2semidirect
5. C2×#18011838C2semidirect
6. M16×Dic149C2semidirect
9. #18011918C22semidirect
14. #18011847C22semidirect
15. #18011838C22semidirect
16. #18011838C22semidirect
17. #18011821C22semidirect
18. C8×Dic149C22semidirect
20. #137×C149C4semidirect
21. AGL(1,ℤ/8)×C149C4semidirect
44. Q16×C149C2×C4semidirect
45. SD16×C149C2×C4semidirect
46. D8×C149C2×C4semidirect
85. C149#2956semidirect
95. #137Dic149semidirect
96. AGL(1,ℤ/8)Dic149semidirect
120. Q16C2×Dic149semidirect
121. SD16C2×Dic149semidirect
122. D8C2×Dic149semidirect

Maximal subgroups

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

subgroupindex
#237503922
#237497472
#237497422
#237496742
C2×#180118382
M16×Dic1492
#575×C1492
#2956149