Finite Group Databasebeta

← #34060871

Subgroups — #34060871

Order 19072.

260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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
1D149⋊(C4⋊C8)C211yesmaximal, characteristic
2C4×C4⋊#10597010C211yesmaximal, characteristic
3#23750498C212yesmaximal
4#23750498C212yesmaximal
5#125×D149C211yesmaximal, characteristic
6C2×D149⋊C8C2212yes—
7C2×C4⋊#10597010C2212yes—
8C2×C4×#10597010—21no—
9#18011978—21no—
10C4⋊#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12#18011903C411yescharacteristic, complemented
13#18011902C411yescharacteristic, complemented
14#18011902C411yescharacteristic, complemented
15#18011901—21no—
16#18011901—21no—
17C4⋊C4×D149—21no—
18C4⋊C4×D149—21no—
19C4⋊C4×D149C2211yescharacteristic
20C4⋊C4×D149C2211yescharacteristic
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24D149⋊C8—24no—
25C2×#11924753—22no—
26C4⋊#10597010—22no—
27C4⋊#10597010Q814yes—
28C4×#10597010—42no—
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149C2311yescharacteristic
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149C2×C411yescharacteristic
37C4⋊Dic149C2×C411yescharacteristic
38#14558715—21no—
39#14558715—21no—
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43#14558715—21no—
44C4×Dic149C2×C411yescharacteristic
45C4×Dic149D411yescharacteristic
46C4×Dic149D411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149—21no—
49C4⋊C4×C149C2×C411yescharacteristic
50C4⋊C4×C149C2×C411yescharacteristic
51C42×C149C2×C411yescharacteristic
52C2×#10597010—24no—
53C2×#10597010—42no—
54C2×#10597010—42no—
55#11924753—42no—
56C22×D149C2×D411yescharacteristic
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—22no—
63C4×D149—21no—
64C4×D149—21no—
65C4×D149—42no—
66C4×D149—41no—
67C4×D149—41no—
68C4×D149C2×Q812yes—
69C4×D149#4112yes—
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22×C411yescharacteristic
75C22×C149C2×C22⋊C411yescharacteristic
76C2×D149C22⋊Q812yes—
77C2×D149#13512yes—
78C2×D149AGL(1,ℤ/8)11yescharacteristic
79C2×D149#13711yescharacteristic
80#10597010—44no—
81C4×C149—21no—
82C4×C149—21no—
83C4×C149—41no—
84C4×C149—41no—
85C4×C149C4×Q812yes—
86Dic149—21no—
87Dic149—21no—
88Dic149—41no—
89Dic149—41no—
90Dic149#12411yescharacteristic
91Dic149C4⋊Q811yescharacteristic
92C2×C149#39111yescharacteristic
93C2×C149#41611yescharacteristic
94C2×C149#41711yescharacteristic
95D149#47812yes—
96D149#47912yes—
97C149#198911yescharacteristic, complemented, Sylow
98#1989—1491nomaximal, Sylow
99C2×#125—1491no—
100C2×C4⋊C8—1491no—
101C4×C4⋊C4—1491no—
102#340—1492no—
103#340—1492no—
104C22×C8—1492no—
105#125—2981no—
106#125—2981no—
107#125—1491no—
108#125—1491no—
109#125—1491no—
110#125#1059701011yescharacteristic, complemented
111C2×C4⋊C4—2981no—
112C2×C4⋊C4—2981no—
113C2×C4⋊C4—1492no—
114C2×C4⋊C4—1491no—
115C2×C4⋊C4—1491no—
116C2×C42—2981no—
117C2×C42—1491no—
118C4⋊C8—2981no—
119C4⋊C8—2981no—
120#95—2981no—
121C22×C4—2981no—
122C22×C4—2981no—
123C22×C4—2982no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4—1491no—
127C2×C8—2982no—
128C2×C8—2984no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2982no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—1494no—
141C4⋊C4—1491no—
142C4⋊C4—1491no—
143C4⋊C4C2×#1059701011yescharacteristic
144C4⋊C4C2×#1059701011yescharacteristic
145C42—5962no—
146C42—1491no—
147C42—1491no—
148C42—1491no—
149C42C2×#1059701011yescharacteristic
150C23—1491no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2981no—
154C2×C4—2982no—
155C2×C4—2981no—
156C2×C4—2984no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—5962no—
160C2×C4—5961no—
161C2×C4—5961no—
162C2×C4—5962no—
163C2×C4—5962no—
164C2×C4—1491no—
165C2×C4—1491no—
166C2×C4—1491no—
167C2×C4—1492no—
168C2×C4—1492no—
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C22⋊#1059701011yescharacteristic
171C2×C4C22×#1059701011yescharacteristic
172C8—5962no—
173C22—1492no—
174C22—1492no—
175C22—1491no—
176C22—1491no—
177C22C2×C22⋊#1059701011yescharacteristic
178C4—21no—
179C4—21no—
180C4—41no—
181C4—41no—
182C4—2981no—
183C4—2981no—
184C4—5964no—
185C4—5961no—
186C4—5961no—
187C4—1491no—
188C4—1491no—
189C4Q8×#1059701012yes—
190C2—1492no—
191C2—1492no—
192C2(C2×#10597010)⋊Q811yescharacteristic
193C2#2375061511yescharacteristic
194C2#2375061611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenter#125#10597010
hypocenterC149#1989
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #18011903C4semidirect
13. #18011902C4semidirect
14. #18011902C4semidirect
22. #125×C149C4semidirect
97. C149#1989semidirect
110. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C4⋊C8)2
C4×C4⋊#105970102
#237504982
#125×D1492
#1989149