Finite Group Databasebeta

← #34055064

Subgroups — #34055064

Order 19072.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750181C211yesmaximal, characteristic, complemented
2#127×D149C211yesmaximal, characteristic
3#23749991C211yesmaximal, characteristic, complemented
4#23749990C211yesmaximal, characteristic, complemented
5#23749989C211yesmaximal, characteristic, complemented
6#23749970C214yesmaximal, complemented
7#23749628C214yesmaximal, complemented
8#23749577C211yesmaximal, characteristic, complemented
9#490×C149C211yesmaximal, characteristic, complemented
10C2×D4×D149—22no—
11C2×D4×D149C2212yes—
12C2×#14558719C2212yes—
13#18011910C2212yescomplemented
14#18011908C2211yescharacteristic
15#18011907—22no—
16#18011907C2212yes—
17#18011903C2211yescharacteristic, complemented
18#18011889—22no—
19#18011876—22no—
20#18011869C2212yes—
21C42×D149C2211yescharacteristic
22#18011833C2214yescomplemented
23#18011832C2214yescomplemented
24#18011831C2214yescomplemented
25#18011822C2211yescharacteristic, complemented
26C8×Dic149C2212yescomplemented
27#127×C149C2211yescharacteristic
28#125×C149C2211yescharacteristic, complemented
29#102×C149C2214yescomplemented
30#97×C149C2211yescharacteristic, complemented
31C23×D149—22no—
32C2×Dic298—22no—
33C2×D596—22no—
34C2×D596C2312yes—
35C2×C22⋊D149—22no—
36C2×C22⋊D149—24no—
37D4×D149—28no—
38D4×D149—48no—
39C2×C4×D149D412yes—
40C2×C4×D149C2311yescharacteristic
41#14558719—24no—
42C2×#11924746C2312yes—
43C4⋊Dic149C2312yes—
44#14558715—22no—
45#14558715—22no—
46#14558713—22no—
47C4×Dic149—22no—
48C4×Dic149D412yes—
49C4×Dic149C2311yescharacteristic
50C2×D4×C149—22no—
51C2×D4×C149C2312yes—
52C2×C8×C149C2312yes—
53C4⋊C4×C149—22no—
54C4⋊C4×C149C2312yes—
55C42×C149C2311yescharacteristic
56C22×D149—22no—
57C22×D149—48no—
58C22×D149—44no—
59C22×D149C2×D411yescharacteristic
60Dic298—44no—
61D596—24no—
62D596—44no—
63C22⋊D149—44no—
64C22⋊D149—48no—
65C2×Dic149—22no—
66C2×Dic149C2×D411yescharacteristic
67C2×Dic149C2×D412yes—
68C4×D149—24no—
69C4×D149#4114yes—
70#11924746—22no—
71C23×C149—22no—
72D4×C149—24no—
73D4×C149—44no—
74C2×C4×C149—22no—
75C2×C4×C149C2×D412yes—
76C2×C4×C149C2411yescharacteristic
77C8×C149—22no—
78C22×C149—42no—
79C22×C149—44no—
80C22×C149C22×D411yescharacteristic
81C2×D149—22no—
82C2×D149—42no—
83C2×D149—44no—
84C2×D149—88no—
85C2×D149#12412yes—
86C4×C149—22no—
87C4×C149—42no—
88C4×C149C2×#4112yes—
89Dic149—42no—
90Dic149#12412yes—
91Dic149AGL(1,ℤ/8)14yes—
92C2×C149—82no—
93C2×C149C2×#12411yescharacteristic
94C2×C149C2×AGL(1,ℤ/8)12yes—
95D149—22no—
96D149—82no—
97C149#313811yescharacteristic, complemented, Sylow
98#3138—1491nomaximal, Sylow
99#533—1491no—
100C2×#127—1491no—
101#490—1491no—
102#490—1491no—
103#490—1491no—
104#490D14911yescharacteristic, complemented
105#486—1494no—
106#418—1494no—
107C4×M16—1491no—
108C22×D4—2982no—
109C22×D4—1492no—
110C2×M16—1492no—
111C4⋊Q8—1492no—
112#127—2982no—
113#127—1492no—
114#127—1491no—
115#127C2×D14911yescharacteristic
116#125—1491no—
117#125C2×D14911yescharacteristic, complemented
118C22⋊Q8—2982no—
119C4×Q8—2982no—
120#117—1492no—
121C2×C42—1491no—
122#102—1494no—
123#102—1494no—
124#102—1494no—
125#102C2×D14914yescomplemented
126#97—1491no—
127#97C2×D14911yescharacteristic, complemented
128C4×C8—1492no—
129C24—2982no—
130C2×Q8—2982no—
131C2×D4—22no—
132C2×D4—2988no—
133C2×D4—2982no—
134C2×D4—2984no—
135C2×D4—2982no—
136C2×D4—5968no—
137C2×D4—1492no—
138C2×D4C22×D14912yes—
139C22×C4—1492no—
140C22×C4—1491no—
141M16—2984no—
142C2×C8—1492no—
143C2×C8C22×D14912yes—
144C4⋊C4—22no—
145C4⋊C4—2982no—
146C4⋊C4—2982no—
147C4⋊C4—1492no—
148C4⋊C4C22×D14912yes—
149C22⋊C4—2982no—
150C42—2982no—
151C42—1492no—
152C42—1491no—
153C42C22×D14911yescharacteristic
154C23—22no—
155C23—2982no—
156C23—5968no—
157C23—5964no—
158C23—1491no—
159Q8—5964no—
160D4—24no—
161D4—44no—
162D4—2984no—
163D4—5964no—
164D4—5964no—
165D4—5968no—
166C2×C4—22no—
167C2×C4—2984no—
168C2×C4—2982no—
169C2×C4—1491no—
170C2×C4—1492no—
171C2×C4—1494no—
172C2×C4D4×D14912yes—
173C2×C4C23×D14911yescharacteristic
174C8—22no—
175C8—2982no—
176C22—44no—
177C22—42no—
178C22—2982no—
179C22—5964no—
180C22—5962no—
181C22—1492no—
182C22—11928no—
183C22C2×D4×D14911yescharacteristic
184C4—22no—
185C4—42no—
186C4—5962no—
187C4—1494no—
188C4—1492no—
189C4#41×D14912yes—
190C2—82no—
191C2—2982no—
192C2—11922no—
193C2#124×D14911yescharacteristic
194C2AGL(1,ℤ/8)×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#490×C149C2
socleC22×C149C22×D4
prime radical#127×D149C2
hypercenter#490D149
hypocenterC149#3138
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23750181C2semidirect
3. #23749991C2semidirect
4. #23749990C2semidirect
5. #23749989C2semidirect
6. #23749970C2semidirect
7. #23749628C2semidirect
8. #23749577C2semidirect
9. #490×C149C2semidirect
13. #18011910C22semidirect
17. #18011903C22semidirect
22. #18011833C22semidirect
23. #18011832C22semidirect
24. #18011831C22semidirect
25. #18011822C22semidirect
26. C8×Dic149C22semidirect
28. #125×C149C22semidirect
29. #102×C149C22semidirect
30. #97×C149C22semidirect
97. C149#3138semidirect
104. #490D149semidirect
117. #125C2×D149semidirect
125. #102C2×D149semidirect
127. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501812
#127×D1492
#237499912
#237499902
#237499892
#237499702
#237496282
#237495772
#490×C1492
#3138149