Finite Group Databasebeta

← #34060868

Subgroups — #34060868

Order 19072.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14558746C211yesmaximal, characteristic
2C4×C4⋊#10597010C211yesmaximal, characteristic
3#23750495C212yesmaximal
4#23750495C212yesmaximal
5#23750181C211yesmaximal, characteristic
6C2×#14558746C2212yes—
7C2×C4⋊#10597010—21no—
8C2×C4×#10597010C2212yes—
9#18011966—21no—
10C4×#11924753—21no—
11(C2×#10597010)⋊C4—21no—
12#18011910C411yescharacteristic, complemented
13#18011910C411yescharacteristic, complemented
14#18011903C411yescharacteristic, complemented
15#18011889—21no—
16#18011889—21no—
17#18011876—21no—
18#18011876—21no—
19#18011869C2211yescharacteristic
20#18011869C2211yescharacteristic
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24#14558746—22no—
25#14558746Q814yescomplemented
26C2×#11924753—22no—
27C4⋊#10597010—24no—
28C4×#10597010—24no—
29C2×Dic298—21no—
30C2×Dic298—21no—
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149C2311yescharacteristic
34C4⋊Dic149C2×C411yescharacteristic
35C4⋊Dic149C2×C411yescharacteristic
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558713—21no—
41#14558713—21no—
42C4×Dic149—21no—
43C4×Dic149—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—24no—
56C22×D149C2×D411yescharacteristic
57Dic298—42no—
58Dic298—42no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C2×D411yescharacteristic
64C4×D149—22no—
65C4×D149—41no—
66C4×D149C2×Q812yes—
67C4×D149#4112yes—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22×C411yescharacteristic
73C22×C149C2×C22⋊C411yescharacteristic
74C2×D149—21no—
75C2×D149—21no—
76C2×D149#12411yescharacteristic
77C2×D149C4⋊Q811yescharacteristic
78#10597010—44no—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—41no—
82C4×C149—41no—
83C4×C149C4×Q812yes—
84Dic149—21no—
85Dic149—41no—
86Dic149—41no—
87Dic149#10412yes—
88Dic149C22⋊Q812yes—
89C2×C149#39111yescharacteristic
90C2×C149C2×#10411yescharacteristic
91C2×C149#42111yescharacteristic
92D149—21no—
93D149—21no—
94C149#198611yescharacteristic, complemented, Sylow
95#1986—1491nomaximal, Sylow
96#533—1491no—
97C4×M16—1491no—
98C4×C4⋊C4—1491no—
99#339—1492no—
100#339—1492no—
101C2×M16—1492no—
102C4⋊Q8—1491no—
103C4⋊Q8—1491no—
104#125—1491no—
105#125#1059701011yescharacteristic, complemented
106C22⋊Q8—2981no—
107C22⋊Q8—2981no—
108C4×Q8—2981no—
109C4×Q8—2981no—
110#117—1491no—
111#117—1491no—
112C2×C4⋊C4—2981no—
113C2×C42—1492no—
114C2×C42—1491no—
115#97—2981no—
116C4×C8—2981no—
117#95—2981no—
118C2×Q8—2981no—
119C2×Q8—2981no—
120C22×C4—2982no—
121C22×C4—1491no—
122C22×C4—1491no—
123C22×C4—1491no—
124M16—2982no—
125M16—1494no—
126C2×C8—2982no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2984no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—1491no—
135C4⋊C4—1491no—
136C4⋊C4C2×#1059701011yescharacteristic
137C4⋊C4C2×#1059701011yescharacteristic
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C42—2981no—
141C42—2981no—
142C42—2984no—
143C42—1491no—
144C42—1491no—
145C42—1491no—
146C42C2×#1059701011yescharacteristic
147C23—1491no—
148Q8—5962no—
149Q8—5962no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2982no—
153C2×C4—2984no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—5961no—
157C2×C4—5962no—
158C2×C4—5962no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4—1491no—
162C2×C4—1492no—
163C2×C4—1492no—
164C2×C4C22⋊#1059701011yescharacteristic
165C2×C4C22⋊#1059701011yescharacteristic
166C2×C4C22×#1059701011yescharacteristic
167C8—2984no—
168C22—2981no—
169C22—2981no—
170C22—1491no—
171C22—1491no—
172C22C2×C22⋊#1059701011yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—2981no—
178C4—5964no—
179C4—5961no—
180C4—5961no—
181C4—1492no—
182C4—1492no—
183C4Q8×#1059701012yes—
184C2—2981no—
185C2—2981no—
186C2(C2×#10597010)⋊Q811yescharacteristic
187C2D149⋊#10411yescharacteristic
188C2#2375062211yescharacteristic
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#1986
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. #18011910C4semidirect
13. #18011910C4semidirect
14. #18011903C4semidirect
22. #125×C149C4semidirect
25. #14558746Q8semidirect
94. C149#1986semidirect
105. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
C4×#145587462
C4×C4⋊#105970102
#237504952
#237501812
#1986149