Finite Group Databasebeta

← #2023×C151 #34065355

Subgroups — #2023×C151 #34065355

Order 19328.

326 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊Q8×C151C211yesmaximal, characteristic, complemented
2C2×#102×C151C212yesmaximal
3#390×C151C211yesmaximal, characteristic
4#340×C151C212yesmaximal, complemented
5#336×C151C211yesmaximal, characteristic, complemented
6C22×Q8×C151—21no—
7C22×D4×C151C2211yescharacteristic
8C22×C8×C151C2212yes—
9C4⋊Q8×C151—24no—
10C2×C4⋊C4×C151—21no—
11C2×C4⋊C4×C151C2211yescharacteristic
12C2×C4⋊C4×C151C2212yes—
13C2×C22⋊C4×C151—21no—
14C2×C22⋊C4×C151—21no—
15C2×C42×C151C2211yescharacteristic
16#102×C151—24no—
17C24×C151—21no—
18C2×Q8×C151—24no—
19C2×Q8×C151—42no—
20C2×Q8×C151—42no—
21C2×D4×C151—22no—
22C2×D4×C151—22no—
23C2×D4×C151—21no—
24C2×D4×C151Q812yescomplemented
25C22×C4×C151—22no—
26C22×C4×C151—21no—
27C22×C4×C151D411yescharacteristic
28C22×C4×C151D411yescharacteristic
29C22×C4×C151C2311yescharacteristic
30C2×C8×C151—22no—
31C2×C8×C151—22no—
32C2×C8×C151—22no—
33C4⋊C4×C151—24no—
34C4⋊C4×C151—22no—
35C4⋊C4×C151—22no—
36C4⋊C4×C151D414yes—
37C22⋊C4×C151—42no—
38C22⋊C4×C151—42no—
39C42×C151—22no—
40C23×C151—22no—
41C23×C151—41no—
42C23×C151—41no—
43C23×C151—41no—
44C23×C151—41no—
45C23×C151—41no—
46C23×C151—41no—
47C23×C151C2×D411yescharacteristic
48Q8×C151—48no—
49D4×C151—24no—
50D4×C151—42no—
51C2×C4×C151—21no—
52C2×C4×C151—21no—
53C2×C4×C151—21no—
54C2×C4×C151—21no—
55C2×C4×C151—24no—
56C2×C4×C151—42no—
57C2×C4×C151—42no—
58C2×C4×C151—41no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151D812yes—
62C2×C4×C151SD1612yes—
63C2×C4×C151C2×D412yes—
64C2×C4×C151C2×Q811yescharacteristic
65C2×C4×C151#4112yes—
66C2×C4×C151#4111yescharacteristic
67C8×C151—42no—
68C22×C151—42no—
69C22×C151—42no—
70C22×C151—42no—
71C22×C151—81no—
72C22×C151—81no—
73C22×C151—81no—
74C22×C151—81no—
75C22×C151#12011yescharacteristic
76C22×C151C22⋊Q811yescharacteristic
77C22×C151#12411yescharacteristic
78C22×C151C2×D811yescharacteristic
79C22×C151C2×SD1611yescharacteristic
80C22×C151AGL(1,ℤ/8)11yescharacteristic
81C22×C151#13711yescharacteristic
82C4×C151—22no—
83C4×C151—22no—
84C4×C151—44no—
85C4×C151—81no—
86C4×C151C22⋊Q812yes—
87C4×C151#12412yes—
88C2×C151—82no—
89C2×C151#39311yescharacteristic
90C2×C151#44711yescharacteristic
91C2×C151#44811yescharacteristic
92C2×C151#47411yescharacteristic
93C2×C151#47611yescharacteristic
94C2×C151#48611yescharacteristic
95C2×C151#48911yescharacteristic
96C151#202311yescharacteristic, direct product factor, Sylow
97#2023C15111yesmaximal, characteristic, direct product factor, Sylow
98C2×C4⋊Q8C2×C15111yescharacteristic, complemented
99C2×#102C2×C15112yes—
100#390C2×C15111yescharacteristic
101#340C2×C15112yescomplemented
102#336C2×C15111yescharacteristic, complemented
103C22×Q8—21no—
104C22×D4C22×C15111yescharacteristic
105C22×C8C22×C15112yes—
106C4⋊Q8—24no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C22×C15111yescharacteristic
109C2×C4⋊C4C22×C15112yes—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C42C22×C15111yescharacteristic
113#102—24no—
114C24—21no—
115C2×Q8—24no—
116C2×Q8—42no—
117C2×Q8—42no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4Q8×C15112yescomplemented
122C22×C4—22no—
123C22×C4—21no—
124C22×C4D4×C15111yescharacteristic
125C22×C4D4×C15111yescharacteristic
126C22×C4C23×C15111yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C4⋊C4—24no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4D4×C15114yes—
134C22⋊C4—42no—
135C22⋊C4—42no—
136C42—22no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C2×D4×C15111yescharacteristic
145Q8—48no—
146D4—24no—
147D4—42no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—24no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4D8×C15112yes—
159C2×C4SD16×C15112yes—
160C2×C4C2×D4×C15112yes—
161C2×C4C2×Q8×C15111yescharacteristic
162C2×C4#41×C15112yes—
163C2×C4#41×C15111yescharacteristic
164C8—42no—
165C22—42no—
166C22—42no—
167C22—42no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22#120×C15111yescharacteristic
173C22C22⋊Q8×C15111yescharacteristic
174C22#124×C15111yescharacteristic
175C22C2×D8×C15111yescharacteristic
176C22C2×SD16×C15111yescharacteristic
177C22AGL(1,ℤ/8)×C15111yescharacteristic
178C22#137×C15111yescharacteristic
179C4—22no—
180C4—22no—
181C4—44no—
182C4—81no—
183C4C22⋊Q8×C15112yes—
184C4#124×C15112yes—
185C2—82no—
186C2#393×C15111yescharacteristic
187C2#447×C15111yescharacteristic
188C2#448×C15111yescharacteristic
189C2#474×C15111yescharacteristic
190C2#476×C15111yescharacteristic
191C2#486×C15111yescharacteristic
192C2#489×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×D4
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC22×D4×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×C151C2semidirect
4. #340×C151C2semidirect
5. #336×C151C2semidirect
24. C2×D4×C151Q8semidirect
96. C151#2023direct (N × H)
97. #2023C151direct (N × H)
98. C2×C4⋊Q8C2×C151semidirect
101. #340C2×C151semidirect
102. #336C2×C151semidirect
121. C2×D4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×C1512
C2×#102×C1512
#390×C1512
#340×C1512
#336×C1512
#2023151