Finite Group Databasebeta

← #2064×C151 #34065396

Subgroups — #2064×C151 #34065396

Order 19328.

208 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 84 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×#108×C151C211yesmaximal, characteristic
2#428×C151C211yesmaximal, characteristic
3#424×C151C211yesmaximal, characteristic
4#419×C151C211yesmaximal, characteristic
5C2×#103×C151C211yesmaximal, characteristic
6C2×#101×C151C211yesmaximal, characteristic
7#343×C151C211yesmaximal, characteristic
8C22×Q8×C151C2211yescharacteristic
9C2×M16×C151C2211yescharacteristic
10C2×M16×C151C2211yescharacteristic
11C2×M16×C151C2211yescharacteristic
12C22×C8×C151C2211yescharacteristic
13#117×C151C2211yescharacteristic
14C2×C4⋊C4×C151C2211yescharacteristic
15#108×C151—22no—
16#107×C151—21no—
17#106×C151—21no—
18C4⋊C8×C151—22no—
19#103×C151—22no—
20#103×C151—21no—
21#103×C151—21no—
22#101×C151—22no—
23C2×Q8×C151—21no—
24C2×Q8×C151—21no—
25C2×Q8×C151—21no—
26C2×Q8×C151—21no—
27C2×Q8×C151—21no—
28C2×Q8×C151Q812yes—
29C22×C4×C151—21no—
30C22×C4×C151—21no—
31C22×C4×C151C2311yescharacteristic
32M16×C151—21no—
33M16×C151—21no—
34M16×C151—21no—
35M16×C151—21no—
36M16×C151—21no—
37M16×C151D412yes—
38C2×C8×C151—21no—
39C2×C8×C151—21no—
40C2×C8×C151—21no—
41C2×C8×C151—21no—
42C2×C8×C151—21no—
43C2×C8×C151D412yes—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151D411yescharacteristic
47C4⋊C4×C151D411yescharacteristic
48C22⋊C4×C151—21no—
49C42×C151—21no—
50C23×C151#4111yescharacteristic
51Q8×C151—22no—
52Q8×C151—22no—
53Q8×C151—41no—
54Q8×C151—41no—
55C2×C4×C151—21no—
56C2×C4×C151—21no—
57C2×C4×C151—22no—
58C2×C4×C151—41no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151—81no—
62C2×C4×C151C2×D411yescharacteristic
63C2×C4×C151C2×D411yescharacteristic
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151C2×Q811yescharacteristic
66C2×C4×C151#4111yescharacteristic
67C2×C4×C151#4111yescharacteristic
68C8×C151—22no—
69C8×C151—22no—
70C8×C151—41no—
71C8×C151—41no—
72C22×C151—21no—
73C22×C151—21no—
74C22×C151#12111yescharacteristic
75C22×C151C22⋊Q811yescharacteristic
76C22×C151#12611yescharacteristic
77C4×C151—42no—
78C4×C151—41no—
79C4×C151—41no—
80C4×C151—81no—
81C4×C151#12111yescharacteristic
82C4×C151#12111yescharacteristic
83C4×C151C22⋊Q811yescharacteristic
84C4×C151C22⋊Q811yescharacteristic
85C2×C151—21no—
86C2×C151—21no—
87C2×C151#39611yescharacteristic
88C2×C151#47111yescharacteristic
89C2×C151#47311yescharacteristic
90C151#206411yescharacteristic, direct product factor, Sylow
91#2064C15111yesmaximal, characteristic, direct product factor, Sylow
92C2×#108C2×C15111yescharacteristic
93#428C2×C15111yescharacteristic
94#424C2×C15111yescharacteristic
95#419C2×C15111yescharacteristic
96C2×#103C2×C15111yescharacteristic
97C2×#101C2×C15111yescharacteristic
98#343C2×C15111yescharacteristic
99C22×Q8C22×C15111yescharacteristic
100C2×M16C22×C15111yescharacteristic
101C2×M16C22×C15111yescharacteristic
102C2×M16C22×C15111yescharacteristic
103C22×C8C22×C15111yescharacteristic
104#117C22×C15111yescharacteristic
105C2×C4⋊C4C22×C15111yescharacteristic
106#108—22no—
107#107—21no—
108#106—21no—
109C4⋊C8—22no—
110#103—22no—
111#103—21no—
112#103—21no—
113#101—22no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Q8×C15112yes—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4C23×C15111yescharacteristic
123M16—21no—
124M16—21no—
125M16—21no—
126M16—21no—
127M16—21no—
128M16D4×C15112yes—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8D4×C15112yes—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4D4×C15111yescharacteristic
138C4⋊C4D4×C15111yescharacteristic
139C22⋊C4—21no—
140C42—21no—
141C23#41×C15111yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4C2×D4×C15111yescharacteristic
154C2×C4C2×D4×C15111yescharacteristic
155C2×C4C2×D4×C15111yescharacteristic
156C2×C4C2×Q8×C15111yescharacteristic
157C2×C4#41×C15111yescharacteristic
158C2×C4#41×C15111yescharacteristic
159C8—22no—
160C8—22no—
161C8—41no—
162C8—41no—
163C22—21no—
164C22—21no—
165C22#121×C15111yescharacteristic
166C22C22⋊Q8×C15111yescharacteristic
167C22#126×C15111yescharacteristic
168C4—42no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4#121×C15111yescharacteristic
173C4#121×C15111yescharacteristic
174C4C22⋊Q8×C15111yescharacteristic
175C4C22⋊Q8×C15111yescharacteristic
176C2—21no—
177C2—21no—
178C2#396×C15111yescharacteristic
179C2#471×C15111yescharacteristic
180C2#473×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#121
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC23×C151#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
90. C151#2064direct (N × H)
91. #2064C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#108×C1512
#428×C1512
#424×C1512
#419×C1512
C2×#103×C1512
C2×#101×C1512
#343×C1512
#2064151