Finite Group Databasebeta

← #34060974

Subgroups — #34060974

Order 19072.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#23750606C212yesmaximal
2#23750532C212yesmaximal, complemented
3#23750531C212yesmaximal, complemented
4#23750200C211yesmaximal, characteristic
5#18011990—22no—
6#18011970—22no—
7#18011970C2214yes—
8C2×#14558737C2211yescharacteristic
9C2×Q8×D149C411yescharacteristic, complemented
10#18011909C411yescharacteristic, complemented
11#18011900C2211yescharacteristic
12#18011899C2211yescharacteristic
13#18011896—22no—
14#18011889—22no—
15#18011868C411yescharacteristic, complemented
16C4⋊Q8×C149C411yescharacteristic, complemented
17C4⋊#10597010—42no—
18C22⋊#10597010—24no—
19C4×#10597010—42no—
20#14558737—42no—
21C2×Dic298—21no—
22C2×Dic298C2×C411yescharacteristic
23Q8×D149—42no—
24C2×D596D412yes—
25C2×D596C2311yescharacteristic
26C2×C4×D149—21no—
27C2×C4×D149C2×C411yescharacteristic
28C2×C4×D149D412yes—
29#14558715—21no—
30#14558715—22no—
31#14558713—21no—
32#14558713—22no—
33#14558713—22no—
34C4×Dic149C2×C411yescharacteristic
35C2×Q8×C149C2×C411yescharacteristic
36C2×Q8×C149C2×C411yescharacteristic
37C4⋊C4×C149—22no—
38C42×C149C2×C411yescharacteristic
39C2×#10597010—44no—
40C22×D149C22⋊C411yescharacteristic
41C22×D149C2×D412yes—
42Dic298—42no—
43Dic298—41no—
44D596—42no—
45D596—41no—
46C2×Dic149—21no—
47C2×Dic149—21no—
48C2×Dic149C22⋊C411yescharacteristic
49C4×D149—22no—
50C4×D149—22no—
51C4×D149—22no—
52C4×D149—42no—
53Q8×C149—41no—
54Q8×C149—41no—
55C2×C4×C149—21no—
56C2×C4×C149—21no—
57C2×C4×C149C22⋊C412yes—
58C2×C4×C149C22×C411yescharacteristic
59C22×C149C2×C22⋊C411yescharacteristic
60C2×D149—21no—
61C2×D149—22no—
62C2×D149—41no—
63C2×D149—42no—
64#10597010—84no—
65C4×C149—22no—
66C4×C149—21no—
67C4×C149—41no—
68C4×C149—41no—
69Dic149—41no—
70Dic149—41no—
71Dic149#9912yes—
72C2×C149—21no—
73C2×C149C2×#9911yescharacteristic
74D149—42no—
75D149—41no—
76C149#212911yescharacteristic, complemented, Sylow
77#2129—1491nomaximal, Sylow
78#536—1491no—
79#410—1492no—
80#354—1492no—
81#354—1492no—
82C2×#41—1491no—
83C22×Q8—1491no—
84C4⋊Q8—1491no—
85C4⋊Q8#1059701011yescharacteristic, complemented
86#124—1491no—
87#124—1491no—
88#123—2982no—
89C22⋊Q8—2982no—
90#117—2982no—
91#117—1491no—
92#99—2982no—
93#99—1494no—
94#41—5962no—
95C2×Q8—2981no—
96C2×Q8—5962no—
97C2×Q8—1491no—
98C2×Q8C2×#1059701011yescharacteristic
99C2×Q8C2×#1059701011yescharacteristic
100C2×D4—1492no—
101C2×D4—1491no—
102C22×C4—2981no—
103C22×C4—1492no—
104C22×C4—1491no—
105C4⋊C4—22no—
106C4⋊C4—2981no—
107C4⋊C4—2982no—
108C4⋊C4—5962no—
109C22⋊C4—2981no—
110C22⋊C4—2982no—
111C22⋊C4—2982no—
112C22⋊C4—2984no—
113C42—5962no—
114C42—1491no—
115C42C2×#1059701011yescharacteristic
116C23—1491no—
117C23—1492no—
118Q8—41no—
119Q8—41no—
120Q8—5961no—
121Q8—5962no—
122D4—5962no—
123D4—5961no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—2982no—
127C2×C4—2982no—
128C2×C4—2982no—
129C2×C4—2981no—
130C2×C4—2981no—
131C2×C4—5962no—
132C2×C4—5964no—
133C2×C4—1491no—
134C2×C4C22⋊#1059701012yes—
135C2×C4C22×#1059701011yescharacteristic
136C22—2982no—
137C22—2981no—
138C22—5962no—
139C22—5961no—
140C22C2×C22⋊#1059701011yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—5961no—
146C4—5961no—
147C4—1492no—
148C4—11924no—
149C2—21no—
150C2—5962no—
151C2—5961no—
152C2D149⋊#9911yescharacteristic
subgroupG/H
centerC2D149⋊#99
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC2×C149C2×#99
prime radicalC2×#14558737C22
cosocleC2×D596C23
hypercenterC4⋊Q8#10597010
hypocenterC149#2129
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23750532C2semidirect
3. #23750531C2semidirect
9. C2×Q8×D149C4semidirect
10. #18011909C4semidirect
15. #18011868C4semidirect
16. C4⋊Q8×C149C4semidirect
76. C149#2129semidirect
85. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506062
#237505322
#237505312
#237502002
#2129149