Finite Group Databasebeta

← #1815×C151 #34065147

Subgroups — #1815×C151 #34065147

Order 19328.

264 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C2×#131×C151C211yesmaximal, characteristic
2C2×#108×C151C211yesmaximal, characteristic, complemented
3C2×#106×C151C211yesmaximal, characteristic, complemented
4#417×C151C212yesmaximal
5#343×C151C212yesmaximal, complemented
6C2×#41×C151C2211yescharacteristic
7#131×C151—22no—
8#131×C151C414yescomplemented
9C2×M16×C151—21no—
10C2×M16×C151C2212yes—
11C2×M16×C151C2211yescharacteristic
12C22×C8×C151—21no—
13C22×C8×C151C2211yescharacteristic
14C2×C4⋊C4×C151C2212yes—
15#108×C151—22no—
16#106×C151—21no—
17#106×C151—21no—
18#103×C151—22no—
19#102×C151—22no—
20#41×C151—21no—
21#41×C151—21no—
22#41×C151C2×C412yes—
23#41×C151Q812yes—
24C2×Q8×C151D411yescharacteristic
25C2×D4×C151—21no—
26C2×D4×C151D411yescharacteristic
27C22×C4×C151—21no—
28C22×C4×C151—22no—
29C22×C4×C151C2311yescharacteristic
30M16×C151—21no—
31M16×C151—24no—
32M16×C151—22no—
33M16×C151—22no—
34M16×C151C2×C412yes—
35C2×C8×C151—21no—
36C2×C8×C151—24no—
37C2×C8×C151—22no—
38C2×C8×C151C2×C412yes—
39C2×C8×C151D411yescharacteristic
40C2×C8×C151D411yescharacteristic
41C2×C8×C151D412yes—
42C4⋊C4×C151—22no—
43C4⋊C4×C151—22no—
44C23×C151—21no—
45C23×C151#4111yescharacteristic
46Q8×C151—21no—
47Q8×C151C4⋊C412yes—
48D4×C151—22no—
49D4×C151—22no—
50D4×C151—21no—
51D4×C151C4⋊C412yes—
52C2×C4×C151—21no—
53C2×C4×C151—22no—
54C2×C4×C151—22no—
55C2×C4×C151—42no—
56C2×C4×C151—82no—
57C2×C4×C151C22×C411yescharacteristic
58C2×C4×C151C2×D411yescharacteristic
59C2×C4×C151C2×D411yescharacteristic
60C2×C4×C151C2×D411yescharacteristic
61C2×C4×C151C2×Q811yescharacteristic
62C2×C4×C151#4111yescharacteristic
63C8×C151—22no—
64C8×C151—42no—
65C8×C151C22⋊C412yes—
66C8×C151C22⋊C412yes—
67C22×C151—22no—
68C22×C151—22no—
69C22×C151—42no—
70C22×C151#11711yescharacteristic
71C22×C151#12111yescharacteristic
72C22×C151C22⋊Q811yescharacteristic
73C4×C151—22no—
74C4×C151—82no—
75C4×C151C2×C22⋊C411yescharacteristic
76C4×C151C2×C4⋊C411yescharacteristic
77C4×C151#12111yescharacteristic
78C4×C151C22⋊Q811yescharacteristic
79C2×C151—21no—
80C2×C151—21no—
81C2×C151—42no—
82C2×C151#38011yescharacteristic
83C2×C151#47112yes—
84C151#181511yescharacteristic, direct product factor, Sylow
85#1815C15111yesmaximal, characteristic, direct product factor, Sylow
86C2×#131C2×C15111yescharacteristic
87C2×#108C2×C15111yescharacteristic, complemented
88C2×#106C2×C15111yescharacteristic, complemented
89#417C2×C15112yes—
90#343C2×C15112yescomplemented
91C2×#41C22×C15111yescharacteristic
92#131—22no—
93#131C4×C15114yescomplemented
94C2×M16—21no—
95C2×M16C22×C15112yes—
96C2×M16C22×C15111yescharacteristic
97C22×C8—21no—
98C22×C8C22×C15111yescharacteristic
99C2×C4⋊C4C22×C15112yes—
100#108—22no—
101#106—21no—
102#106—21no—
103#103—22no—
104#102—22no—
105#41—21no—
106#41—21no—
107#41C2×C4×C15112yes—
108#41Q8×C15112yes—
109C2×Q8D4×C15111yescharacteristic
110C2×D4—21no—
111C2×D4D4×C15111yescharacteristic
112C22×C4—21no—
113C22×C4—22no—
114C22×C4C23×C15111yescharacteristic
115M16—21no—
116M16—24no—
117M16—22no—
118M16—22no—
119M16C2×C4×C15112yes—
120C2×C8—21no—
121C2×C8—24no—
122C2×C8—22no—
123C2×C8C2×C4×C15112yes—
124C2×C8D4×C15111yescharacteristic
125C2×C8D4×C15111yescharacteristic
126C2×C8D4×C15112yes—
127C4⋊C4—22no—
128C4⋊C4—22no—
129C23—21no—
130C23#41×C15111yescharacteristic
131Q8—21no—
132Q8C4⋊C4×C15112yes—
133D4—22no—
134D4—22no—
135D4—21no—
136D4C4⋊C4×C15112yes—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—82no—
142C2×C4C22×C4×C15111yescharacteristic
143C2×C4C2×D4×C15111yescharacteristic
144C2×C4C2×D4×C15111yescharacteristic
145C2×C4C2×D4×C15111yescharacteristic
146C2×C4C2×Q8×C15111yescharacteristic
147C2×C4#41×C15111yescharacteristic
148C8—22no—
149C8—42no—
150C8C22⋊C4×C15112yes—
151C8C22⋊C4×C15112yes—
152C22—22no—
153C22—22no—
154C22—42no—
155C22#117×C15111yescharacteristic
156C22#121×C15111yescharacteristic
157C22C22⋊Q8×C15111yescharacteristic
158C4—22no—
159C4—82no—
160C4C2×C22⋊C4×C15111yescharacteristic
161C4C2×C4⋊C4×C15111yescharacteristic
162C4#121×C15111yescharacteristic
163C4C22⋊Q8×C15111yescharacteristic
164C2—21no—
165C2—21no—
166C2—42no—
167C2#380×C15111yescharacteristic
168C2#471×C15112yes—
subgroupG/H
center, socleC22×C151#121
commutatorC2×C4C22×C4×C151
Frattini, cosocleC22×C4C23×C151
prime radicalC2×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#108×C151C2semidirect
3. C2×#106×C151C2semidirect
5. #343×C151C2semidirect
8. #131×C151C4semidirect
84. C151#1815direct (N × H)
85. #1815C151direct (N × H)
87. C2×#108C2×C151semidirect
88. C2×#106C2×C151semidirect
90. #343C2×C151semidirect
93. #131C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#131×C1512
C2×#108×C1512
C2×#106×C1512
#417×C1512
#343×C1512
#1815151