Finite Group Databasebeta

← #34069300

Subgroups — #34069300

Order 19328.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic151C211yesmaximal, characteristic
2C2×#18012673C212yesmaximal, complemented
3#23752072C211yesmaximal, characteristic
4#23751975C212yesmaximal, complemented
5C2×C22⋊C8×C151C211yesmaximal, characteristic
6C23×Dic151—21no—
7C2×C4⋊Dic151—21no—
8C2×C4⋊Dic151—24no—
9C2×C4⋊Dic151C2211yescharacteristic
10C2×C4⋊Dic151C2211yescharacteristic
11C2×C4⋊Dic151C2212yes—
12C2×C22⋊Dic151—21no—
13#18012673—24no—
14C151⋊#95—21no—
15C23×C4×C151C2211yescharacteristic
16C22×C8×C151C2212yes—
17C22⋊C8×C151C414yescomplemented
18C22×Dic151—24no—
19C22×Dic151—22no—
20C22×Dic151—21no—
21C22×Dic151—21no—
22C22×Dic151—42no—
23C22×Dic151—42no—
24C4⋊Dic151—24no—
25C4⋊Dic151—22no—
26C4⋊Dic151—22no—
27C4⋊Dic151—22no—
28C4⋊Dic151D414yes—
29C22⋊Dic151—42no—
30C24×C151D411yescharacteristic
31C22×C4×C151—22no—
32C22×C4×C151—22no—
33C22×C4×C151C2×C412yes—
34C22×C4×C151D411yescharacteristic
35C22×C4×C151Q812yes—
36C22×C4×C151C2311yescharacteristic
37C2×C8×C151—22no—
38C2×C8×C151—22no—
39C2×C8×C151C2×C414yescomplemented
40C2×Dic151—24no—
41C2×Dic151—48no—
42C2×Dic151—42no—
43C2×Dic151—42no—
44C2×Dic151—41no—
45C2×Dic151—41no—
46C2×Dic151—41no—
47C2×Dic151—41no—
48C2×Dic151—41no—
49C2×Dic151—41no—
50C23×C151—21no—
51C23×C151—21no—
52C23×C151—21no—
53C23×C151—21no—
54C23×C151C4⋊C412yes—
55C23×C151D812yes—
56C23×C151Q1612yes—
57C23×C151C2×D411yescharacteristic
58C2×C4×C151—21no—
59C2×C4×C151—21no—
60C2×C4×C151—24no—
61C2×C4×C151—24no—
62C2×C4×C151C4⋊C412yes—
63C2×C4×C151C22×C411yescharacteristic
64C2×C4×C151C2×D412yes—
65C2×C4×C151C2×Q811yescharacteristic
66C2×C4×C151#4112yes—
67C8×C151—24no—
68C22×C151—22no—
69C22×C151—22no—
70C22×C151—22no—
71C22×C151—22no—
72C22×C151—22no—
73C22×C151—22no—
74C22×C151#10714yescomplemented
75C22×C151C2×C4⋊C411yescharacteristic
76C22×C151#12011yescharacteristic
77C22×C151#12311yescharacteristic
78C22×C151C2×D811yescharacteristic
79C22×C151C2×Q1611yescharacteristic
80C22×C151AGL(1,ℤ/8)11yescharacteristic
81C22×C151#13711yescharacteristic
82C4×C151—22no—
83C4×C151C4×D412yes—
84C4×C151C22⋊Q812yes—
85Dic151—44no—
86Dic151—81no—
87Dic151—81no—
88C2×C151—24no—
89C2×C151#38511yescharacteristic
90C2×C151C2×#10711yescharacteristic
91C2×C151#42811yescharacteristic
92C2×C151#44711yescharacteristic
93C2×C151#45111yescharacteristic
94C2×C151#48011yescharacteristic
95C2×C151#48411yescharacteristic
96C151#185211yescharacteristic, complemented, Sylow
97#1852—1511nomaximal, Sylow
98C22×C4⋊C4—1511no—
99C2×#107—1512no—
100C2×C22⋊C8D15111yescharacteristic
101#380—1511no—
102#340—1512no—
103C23×C4—3021no—
104C23×C4C2×D15111yescharacteristic
105C22×C8C2×D15112yes—
106C2×C4⋊C4—3021no—
107C2×C4⋊C4—3024no—
108C2×C4⋊C4—1511no—
109C2×C4⋊C4—1511no—
110C2×C4⋊C4—1512no—
111C2×C22⋊C4—3021no—
112#107—3024no—
113C22⋊C8Dic15114yescomplemented
114#95—3021no—
115C24D60411yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—3024no—
119C22×C4—3022no—
120C22×C4—3021no—
121C22×C4—3021no—
122C22×C4—6042no—
123C22×C4—6042no—
124C22×C4C2×Dic15112yes—
125C22×C4D60411yescharacteristic
126C22×C4Dic30212yes—
127C22×C4C22×D15111yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic15114yescomplemented
131C4⋊C4—3024no—
132C4⋊C4—3022no—
133C4⋊C4—3022no—
134C4⋊C4—3022no—
135C4⋊C4—1514no—
136C22⋊C4—6042no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic15112yes—
142C23D120812yes—
143C23Dic60412yes—
144C23C2×D60411yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—3024no—
150C2×C4—6048no—
151C2×C4—6042no—
152C2×C4—6042no—
153C2×C4—6041no—
154C2×C4—6041no—
155C2×C4—6041no—
156C2×C4—6041no—
157C2×C4—6041no—
158C2×C4—6041no—
159C2×C4C4⋊Dic15112yes—
160C2×C4C22×Dic15111yescharacteristic
161C2×C4D4×D15112yes—
162C2×C4C2×Dic30211yescharacteristic
163C2×C4#1455900312yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1801267314yescomplemented
172C22C2×C4⋊Dic15111yescharacteristic
173C22#1801270911yescharacteristic
174C22#1801272311yescharacteristic
175C22C2×D120811yescharacteristic
176C22C2×Dic60411yescharacteristic
177C22#1801276711yescharacteristic
178C22#1801277211yescharacteristic
179C4—22no—
180C4—6044no—
181C4—12081no—
182C4—12081no—
183C4D4×Dic15112yes—
184C4#1801271612yes—
185C2—24no—
186C2#2375208711yescharacteristic
187C2C2×#1801267311yescharacteristic
188C2#2375225411yescharacteristic
189C2#2375234811yescharacteristic
190C2#2375237011yescharacteristic
191C2#2375252611yescharacteristic
192C2#2375254811yescharacteristic
subgroupG/H
centerC23C2×D604
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
FittingC2×C22⋊C8×C151C2
socleC23×C151C2×D4
prime radicalC24×C151D4
cosocleC22×C4×C151C23
hypercenterC2×C22⋊C8D151
hypocenterC151#1852
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#18012673C2semidirect
4. #23751975C2semidirect
17. C22⋊C8×C151C4semidirect
39. C2×C8×C151C2×C4semidirect
74. C22×C151#107semidirect
96. C151#1852semidirect
113. C22⋊C8Dic151semidirect
130. C2×C8C2×Dic151semidirect
171. C22#18012673semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1512
C2×#180126732
#237520722
#237519752
C2×C22⋊C8×C1512
#1852151