Finite Group Databasebeta

← #34069640

Subgroups — #34069640

Order 19328.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#23752779C211yesmaximal, characteristic
2#23752687C211yesmaximal, characteristic, complemented
3#23752228C212yesmaximal, complemented
4#23751969C212yesmaximal, complemented
5C2×#100×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7#18012735C412yescomplemented
8#18012726C412yescomplemented
9#18012710—22no—
10#18012708—22no—
11D4×Dic151—24no—
12#18012698C2211yescharacteristic
13#18012698C2212yes—
14C2×C22⋊Dic151—22no—
15#18012665—24no—
16C22×D4×C151C2211yescharacteristic
17C2×M16×C151C2212yes—
18#100×C151—22no—
19#14559004—22no—
20#14559004—22no—
21C2×Dic302C2×C411yescharacteristic, complemented
22C2×D604C2×C411yescharacteristic, complemented
23C2×C22⋊D151—24no—
24C2×C22⋊D151—21no—
25C22×Dic151—24no—
26C2×C4×D151—21no—
27C4⋊Dic151—22no—
28C4⋊Dic151—21no—
29C22⋊Dic151—24no—
30C22⋊Dic151—24no—
31C22⋊Dic151—22no—
32C22⋊Dic151—21no—
33C4×Dic151C2×C412yescomplemented
34C4×Dic151D414yescomplemented
35C24×C151D412yes—
36C2×D4×C151—22no—
37C2×D4×C151—22no—
38C2×D4×C151C2×C412yes—
39C2×D4×C151D412yes—
40C22×C4×C151C2311yescharacteristic
41M16×C151—22no—
42M16×C151—22no—
43C2×C8×C151—22no—
44C22×D151—21no—
45Dic302—22no—
46D604—22no—
47C22⋊D151—41no—
48C22⋊D151—41no—
49C22⋊D151—84no—
50C2×Dic151—22no—
51C2×Dic151—21no—
52C2×Dic151—24no—
53C2×Dic151—84no—
54C4×D151—42no—
55C23×C151—22no—
56C23×C151—22no—
57C23×C151—82no—
58C23×C151C22⋊C414yes—
59C23×C151C2×D411yescharacteristic
60D4×C151—24no—
61D4×C151—24no—
62C2×C4×C151C22×C411yescharacteristic
63C2×C4×C151C2×D412yes—
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151#4112yes—
66C8×C151—42no—
67C22×C151—24no—
68C22×C151—41no—
69C22×C151—44no—
70C22×C151—44no—
71C22×C151—82no—
72C22×C151C2×C22⋊C411yescharacteristic
73C22×C151#12011yescharacteristic
74C22×C151#12311yescharacteristic
75C2×D151—42no—
76C2×D151—41no—
77C4×C151C4×D412yes—
78C4×C151#12112yes—
79Dic151—44no—
80Dic151—42no—
81Dic151—41no—
82C2×C151—21no—
83C2×C151—21no—
84C2×C151—21no—
85C2×C151—44no—
86C2×C151#38611yescharacteristic
87D151—81no—
88C151#191111yescharacteristic, complemented, Sylow
89#1911—1511nomaximal, Sylow
90#535—1511no—
91#518—1511no—
92#421—1512no—
93C2×#100D15111yescharacteristic, complemented
94H(3,ℤ/4)—1512no—
95C2×#41—1511no—
96C22×D4C2×D15111yescharacteristic
97C2×M16C2×D15112yes—
98#127—1512no—
99#124—1512no—
100#121—3022no—
101#120—3022no—
102C4×D4—3024no—
103#117—1512no—
104#117—1511no—
105C2×C22⋊C4—3022no—
106#104—3024no—
107#100—22no—
108C24D60412yes—
109#41—3022no—
110#41—3022no—
111C2×Q8—1511no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—3021no—
115C2×D4—3024no—
116C2×D4—1511no—
117C2×D4C4×D15112yes—
118C2×D4C22⋊D15112yes—
119C22×C4—3024no—
120C22×C4—3021no—
121C22×C4C22×D15111yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—3022no—
126C4⋊C4—3021no—
127C22⋊C4—3024no—
128C22⋊C4—3024no—
129C22⋊C4—3022no—
130C22⋊C4—3021no—
131C42—1512no—
132C42—1514no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—3021no—
137C23(C2×D151)⋊C414yes—
138C23C2×D60411yescharacteristic
139Q8—3022no—
140D4—24no—
141D4—24no—
142D4—3022no—
143D4—6041no—
144D4—6041no—
145D4—12084no—
146C2×C4—3022no—
147C2×C4—3021no—
148C2×C4—3024no—
149C2×C4—6042no—
150C2×C4—12084no—
151C2×C4C2×C4×D15111yescharacteristic
152C2×C4D4×D15112yes—
153C2×C4C2×C22⋊D15111yescharacteristic
154C2×C4#1455900312yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—6042no—
162C22—6041no—
163C22C2×(C2×D151)⋊C411yescharacteristic
164C22#1801270911yescharacteristic
165C22#1801272311yescharacteristic
166C4—6044no—
167C4—6042no—
168C4—6041no—
169C4(C22⋊D151)⋊C412yes—
170C4#1801271112yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—12081no—
176C2#2375208911yescharacteristic
subgroupG/H
centerC2#23752089
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×#100×C151C2
socleC2×C151#386
prime radical#23752779C2
cosocleC22×C4×C151C23
hypercenterC2×#100D151
hypocenterC151#1911
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #23752687C2semidirect
3. #23752228C2semidirect
4. #23751969C2semidirect
5. C2×#100×C151C2semidirect
7. #18012735C4semidirect
8. #18012726C4semidirect
21. C2×Dic302C2×C4semidirect
22. C2×D604C2×C4semidirect
33. C4×Dic151C2×C4semidirect
34. C4×Dic151D4semidirect
88. C151#1911semidirect
93. C2×#100D151semidirect

Maximal subgroups

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

subgroupindex
#237527792
#237526872
#237522282
#237519692
C2×#100×C1512
#1911151