Finite Group Databasebeta

← #34060216

Subgroups — #34060216

Order 19072.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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
2#23750643C211yesmaximal, characteristic
3#23750485C212yesmaximal, complemented
4#23750484C212yesmaximal, complemented
5#23750179C211yesmaximal, characteristic
6#18011978C2212yes—
7#18011978C2212yes—
8#18011968—21no—
9#18011968—21no—
10#18011966—21no—
11C4×#11924753—21no—
12#18011910C2211yescharacteristic
13#18011909C2211yescharacteristic
14#18011901—21no—
15#18011891C411yescharacteristic
16#18011889—21no—
17#18011887C411yescharacteristic
18C4×Dic298—21no—
19C4×Dic298C411yescharacteristic
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×Dic298—21no—
26C2×Dic298C2×C411yescharacteristic
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C411yescharacteristic
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558713—21no—
38#14558713—21no—
39C4×Dic149—21no—
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149C2311yescharacteristic
43C2×Q8×C149C2×C411yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149C2×C411yescharacteristic
46C42×C149—21no—
47C42×C149C2×C411yescharacteristic
48#11924753—42no—
49#11924753—42no—
50C22×D149C22⋊C411yescharacteristic
51Dic298—42no—
52Dic298—41no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C2×Dic149C2×D411yescharacteristic
58C4×D149—22no—
59C4×D149—22no—
60C4×D149—41no—
61Q8×C149—41no—
62C2×C4×C149—21no—
63C2×C4×C149—21no—
64C2×C4×C149C22⋊C411yescharacteristic
65C2×C4×C149C22⋊C411yescharacteristic
66C2×C4×C149C22×C411yescharacteristic
67C22×C149C2×C22⋊C411yescharacteristic
68C2×D149—21no—
69C2×D149—21no—
70C2×D149—21no—
71C4×C149—21no—
72C4×C149—21no—
73C4×C149—21no—
74C4×C149—41no—
75C4×C149—41no—
76Dic149—21no—
77Dic149—41no—
78Dic149—41no—
79Dic149#13512yes—
80Dic149#13712yes—
81C2×C149#41311yescharacteristic
82C2×C149#41611yescharacteristic
83C2×C149#41911yescharacteristic
84D149—41no—
85C149#155411yescharacteristic, complemented, Sylow
86#1554—1491nomaximal, Sylow
87#533—1491no—
88#432—1491no—
89#431—1491no—
90#333—1492no—
91#332—1492no—
92C4⋊Q8—1491no—
93C4⋊Q8—1491no—
94#125—2981no—
95C22⋊Q8—2981no—
96C22⋊Q8—1491no—
97C22⋊Q8—1491no—
98C4×Q8—2981no—
99C4×Q8—1491no—
100C4×Q8#1059701011yescharacteristic
101#117—2981no—
102C2×C42—1491no—
103C4⋊C8—1492no—
104C4⋊C8—1492no—
105C22⋊C8—2981no—
106C22⋊C8—2981no—
107#97—2981no—
108C4×C8—2981no—
109C2×Q8—2981no—
110C2×Q8—1491no—
111C2×Q8C2×#1059701011yescharacteristic
112C22×C4—1491no—
113C22×C4—1491no—
114C22×C4—1491no—
115C2×C8—2982no—
116C2×C8—2982no—
117C4⋊C4—21no—
118C4⋊C4—2981no—
119C4⋊C4—2981no—
120C4⋊C4—2981no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—1491no—
125C4⋊C4C2×#1059701011yescharacteristic
126C22⋊C4—2981no—
127C22⋊C4—2981no—
128C42—21no—
129C42—2981no—
130C42—1491no—
131C42—1491no—
132C42—1491no—
133C42C2×#1059701011yescharacteristic
134C23—1491no—
135Q8—41no—
136Q8—5961no—
137Q8—5962no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—2982no—
141C2×C4—2982no—
142C2×C4—2981no—
143C2×C4—2981no—
144C2×C4—5961no—
145C2×C4—1491no—
146C2×C4—1491no—
147C2×C4—1491no—
148C2×C4C22⋊#1059701011yescharacteristic
149C2×C4C22⋊#1059701011yescharacteristic
150C2×C4C22×#1059701011yescharacteristic
151C8—5962no—
152C8—5962no—
153C22—2981no—
154C22—2981no—
155C22—2981no—
156C22C2×C22⋊#1059701011yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—2981no—
163C4—5961no—
164C4—5961no—
165C4—1492no—
166C4—1492no—
167C2—5961no—
168C2#2375061111yescharacteristic
169C2#2375061511yescharacteristic
170C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1554
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23750485C2semidirect
4. #23750484C2semidirect
85. C149#1554semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237506432
#237504852
#237504842
#237501792
#1554149