Finite Group Databasebeta

← #34043380

Subgroups — #34043380

Order 19072.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#23750180C211yesmaximal, characteristic
2#23749647C211yesmaximal, characteristic
3C4⋊C8×D149C211yesmaximal, characteristic
4#23749373C211yesmaximal, characteristic, complemented
5#23749373C211yesmaximal, characteristic, complemented
6#23749371C211yesmaximal, characteristic, complemented
7#332×C149C211yesmaximal, characteristic, complemented
8C2×#14558719—21no—
9C2×C8×D149—21no—
10#18011911C2211yescharacteristic
11#18011902—21no—
12#18011891C412yes—
13#18011887—21no—
14Q8×Dic149—21no—
15#18011876C412yes—
16#18011869—21no—
17C42×D149C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19C4⋊#11924746C2211yescharacteristic
20#18011840—21no—
21#18011840—21no—
22C4⋊Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25C2×Dic298C2×C412yes—
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29#14558719—42no—
30C2×#11924746—21no—
31C2×#11924746—21no—
32C8×D149—42no—
33C4⋊Dic149—22no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36#14558715—22no—
37#14558713—22no—
38C4×Dic149—22no—
39C4×Dic149C2×C411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C2×Q8×C149—21no—
43C2×C8×C149—21no—
44C2×C8×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C412yes—
47C42×C149C2311yescharacteristic
48C22×D149C22⋊C411yescharacteristic
49Dic298—42no—
50C2×Dic149—22no—
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C22⋊C411yescharacteristic
53C2×Dic149C22⋊C411yescharacteristic
54C4×D149—21no—
55C4×D149—21no—
56C4×D149—41no—
57C4×D149SD1612yes—
58C4×D149Q1612yes—
59#11924746—41no—
60#11924746—41no—
61Q8×C149—41no—
62Q8×C149—41no—
63C2×C4×C149—22no—
64C2×C4×C149C22×C411yescharacteristic
65C2×C4×C149C2×D411yescharacteristic
66C2×C4×C149C2×D411yescharacteristic
67C8×C149—41no—
68C8×C149—41no—
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149#10312yes—
73C4×C149—21no—
74C4×C149—42no—
75C4×C149C2×SD1611yescharacteristic
76C4×C149C2×Q1611yescharacteristic
77C4×C149AGL(1,ℤ/8)11yescharacteristic
78C4×C149#13711yescharacteristic
79Dic149—21no—
80Dic149—21no—
81Dic149—42no—
82Dic149#10312yes—
83C2×C149#41311yescharacteristic
84C2×C149C2×#10311yescharacteristic
85C2×C149#41711yescharacteristic
86D149—22no—
87C149#155011yescharacteristic, complemented, Sylow
88#1550—1491nomaximal, Sylow
89#533—1491no—
90#423—1491no—
91C2×C4⋊C8—1491no—
92#333—1491no—
93#333—1491no—
94#332—1491no—
95#332D14911yescharacteristic, complemented
96C2×M16—2981no—
97C22×C8—2981no—
98C4⋊Q8—1491no—
99C4⋊Q8C2×D14911yescharacteristic
100#125—2981no—
101C22⋊Q8—2981no—
102C22⋊Q8—1492no—
103C4×Q8—2981no—
104C4×Q8—1492no—
105#117—2981no—
106C2×C42—1491no—
107C4⋊C8—2981no—
108C4⋊C8—2981no—
109C4⋊C8—1491no—
110C4⋊C8—1491no—
111C4⋊C8C2×D14911yescharacteristic
112C4⋊C8C2×D14911yescharacteristic
113C2×Q8—21no—
114C2×Q8—1492no—
115C22×C4—1491no—
116C22×C4—1491no—
117C22×C4—1491no—
118M16—5962no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—2981no—
122C2×C8—2981no—
123C2×C8—5962no—
124C4⋊C4—21no—
125C4⋊C4—2982no—
126C4⋊C4—2982no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4C4×D14912yes—
130C22⋊C4—2982no—
131C42—2982no—
132C42—1491no—
133C42—1491no—
134C42—1491no—
135C42C22×D14911yescharacteristic
136C23—1491no—
137Q8—41no—
138Q8—41no—
139Q8—5962no—
140C2×C4—22no—
141C2×C4—2981no—
142C2×C4—2981no—
143C2×C4—2982no—
144C2×C4—5961no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4—1492no—
149C2×C4—1492no—
150C2×C4C2×C4×D14911yescharacteristic
151C2×C4D4×D14911yescharacteristic
152C2×C4D4×D14911yescharacteristic
153C8—41no—
154C8—41no—
155C8—5961no—
156C8—5961no—
157C22—2981no—
158C22—2981no—
159C22—1492no—
160C22C22⋊C4×D14911yescharacteristic
161C4—21no—
162C4—42no—
163C4—2981no—
164C4—2981no—
165C4—5962no—
166C4—1492no—
167C4SD16×D14911yescharacteristic
168C4Q16×D14911yescharacteristic
169C4#1801193511yescharacteristic
170C4#1801194011yescharacteristic
171C2—2982no—
172C2#2374960811yescharacteristic
173C2#103×D14911yescharacteristic
174C2#2374962311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#332×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC42×C149C23
hypercenter#332D149
hypocenterC149#1550
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #23749373C2semidirect
5. #23749373C2semidirect
6. #23749371C2semidirect
7. #332×C149C2semidirect
87. C149#1550semidirect
95. #332D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237496472
C4⋊C8×D1492
#237493732
#237493712
#332×C1492
#1550149