Finite Group Databasebeta

← #34060213

Subgroups — #34060213

Order 19072.

208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750648C211yesmaximal, characteristic
2D149⋊(C4⋊C8)C211yesmaximal, characteristic
3#23750484C212yesmaximal, complemented
4#23750484C212yesmaximal, complemented
5#23750181C211yesmaximal, characteristic
6C2×D149⋊C8—21no—
7#18011978C2212yes—
8#18011978C2212yes—
9C4⋊#11924753—21no—
10#18011968—21no—
11#18011966—21no—
12#18011910C2211yescharacteristic
13#18011910C2211yescharacteristic
14#18011903C411yescharacteristic
15#18011889—21no—
16#18011889—21no—
17#18011876—21no—
18#18011876—21no—
19#18011869C411yescharacteristic
20#18011869C411yescharacteristic
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic
23D149⋊C8—42no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—21no—
27C2×Dic298—21no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C4⋊Dic149C2×C411yescharacteristic
32C4⋊Dic149C2×C411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558713—21no—
38#14558713—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149C2×C411yescharacteristic
49#11924753—42no—
50#11924753—42no—
51C22×D149C22⋊C411yescharacteristic
52Dic298—42no—
53Dic298—41no—
54Dic298—41no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—22no—
62C4×D149—21no—
63C4×D149—21no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22×C411yescharacteristic
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149#10112yes—
73C4×C149—21no—
74C4×C149—21no—
75C4×C149—21no—
76C4×C149—41no—
77C4×C149—41no—
78Dic149—21no—
79Dic149—41no—
80Dic149—41no—
81Dic149#13512yes—
82Dic149AGL(1,ℤ/8)11yescharacteristic
83Dic149#13711yescharacteristic
84C2×C149C2×#10111yescharacteristic
85C2×C149#41611yescharacteristic
86C2×C149#41711yescharacteristic
87D149—22no—
88C149#155211yescharacteristic, complemented, Sylow
89#1552—1491nomaximal, Sylow
90#533—1491no—
91#432—1491no—
92C2×C4⋊C8—1491no—
93#332—1492no—
94#332—1492no—
95C22×C8—2981no—
96C4⋊Q8—1491no—
97C4⋊Q8—1491no—
98#125—1491no—
99#125#1059701011yescharacteristic
100C22⋊Q8—2981no—
101C22⋊Q8—2981no—
102C4×Q8—2981no—
103C4×Q8—2981no—
104#117—1491no—
105#117—1491no—
106C2×C42—1491no—
107C4⋊C8—2981no—
108C4⋊C8—1492no—
109C4⋊C8—1492no—
110C22⋊C8—2981no—
111#97—2981no—
112C2×Q8—2981no—
113C2×Q8—2981no—
114C22×C4—1491no—
115C22×C4—1491no—
116C22×C4—1491no—
117C2×C8—2982no—
118C2×C8—2982no—
119C2×C8—5962no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—1491no—
127C4⋊C4—1491no—
128C4⋊C4C2×#1059701011yescharacteristic
129C4⋊C4C2×#1059701011yescharacteristic
130C22⋊C4—2981no—
131C22⋊C4—2981no—
132C42—2981no—
133C42—2981no—
134C42—1491no—
135C42—1491no—
136C42—1491no—
137C42C2×#1059701011yescharacteristic
138C23—1491no—
139Q8—5962no—
140Q8—5961no—
141Q8—5961no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—2982no—
145C2×C4—2981no—
146C2×C4—2982no—
147C2×C4—2981no—
148C2×C4—2981no—
149C2×C4—2981no—
150C2×C4—1491no—
151C2×C4—1491no—
152C2×C4—1491no—
153C2×C4C22⋊#1059701011yescharacteristic
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22×#1059701011yescharacteristic
156C8—5962no—
157C8—5962no—
158C22—2981no—
159C22—2981no—
160C22—1492no—
161C22C2×C22⋊#1059701011yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—2981no—
168C4—5961no—
169C4—5961no—
170C4—1492no—
171C4—1491no—
172C4—1491no—
173C2—2982no—
174C2D149⋊#10111yescharacteristic
175C2#2375061511yescharacteristic
176C2#2375061611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenter#125#10597010
hypocenterC149#1552
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #23750484C2semidirect
4. #23750484C2semidirect
88. C149#1552semidirect

Maximal subgroups

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

subgroupindex
#237506482
D149⋊(C4⋊C8)2
#237504842
#237501812
#1552149