Finite Group Databasebeta

← #34070334

Subgroups — #34070334

Order 19328.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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#23752793C211yesmaximal, characteristic
2C2×#18012667C212yesmaximal, complemented
3#23752211C212yesmaximal, complemented
4#23751981C211yesmaximal, characteristic, complemented
5#384×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7C2×#14558988C2212yes—
8#18012719—22no—
9#18012714—22no—
10#18012713—22no—
11#18012667—24no—
12#18012662—22no—
13#18012659—22no—
14C2×C4⋊C4×C151—22no—
15C2×C4⋊C4×C151C2211yescharacteristic
16C2×C4⋊C4×C151C2211yescharacteristic
17C2×C42×C151C2211yescharacteristic
18#14559004—22no—
19#14559004—22no—
20#14559004—22no—
21#14559004—22no—
22C2×Dic302D412yes—
23C2×D604—22no—
24C2×D604D412yes—
25C2×C22⋊D151—22no—
26C2×C4×D151—22no—
27#14558988—22no—
28#14558988—22no—
29C2×C151⋊C8—22no—
30C4⋊Dic151—22no—
31(C2×D151)⋊C4—24no—
32C22×C4×C151—21no—
33C22×C4×C151—21no—
34C22×C4×C151D412yes—
35C22×C4×C151C2311yescharacteristic
36C4⋊C4×C151—22no—
37C4⋊C4×C151—22no—
38C4⋊C4×C151—44no—
39C42×C151—21no—
40C42×C151D412yescomplemented
41C22×D151—22no—
42Dic302—22no—
43Dic302—22no—
44D604—22no—
45D604—22no—
46D604—82no—
47C22⋊D151—42no—
48C22⋊D151—42no—
49C2×Dic151—22no—
50C4×D151—42no—
51C4×D151—42no—
52C151⋊C8—42no—
53C23×C151C2×D411yescharacteristic
54C2×C4×C151—22no—
55C2×C4×C151—22no—
56C2×C4×C151—22no—
57C2×C4×C151—22no—
58C2×C4×C151—42no—
59C2×C4×C151—42no—
60C2×C4×C151—41no—
61C2×C4×C151C2×D412yes—
62C2×C4×C151C2×D411yescharacteristic
63C2×C4×C151#4111yescharacteristic
64C2×C4×C151#4112yes—
65C22×C151—21no—
66C22×C151—21no—
67C22×C151#12011yescharacteristic
68C22×C151#12111yescharacteristic
69C22×C151#12411yescharacteristic
70C2×D151—42no—
71C2×D151—42no—
72C2×D151—42no—
73C4×C151—24no—
74C4×C151—42no—
75C4×C151—81no—
76C4×C151#12112yes—
77C4×C151#12312yes—
78Dic151—42no—
79C2×C151—21no—
80C2×C151—21no—
81C2×C151#39411yescharacteristic
82C2×C151#45311yescharacteristic
83C2×C151#45611yescharacteristic
84D151—82no—
85C151#203911yescharacteristic, complemented, Sylow
86#2039—1511nomaximal, Sylow
87#537—1511no—
88C2×#104—1512no—
89#417—1512no—
90#384D15111yescharacteristic, complemented
91#343—1511no—
92C2×#41—1512no—
93C2×M16—1512no—
94C22⋊Q8—3022no—
95#121—3022no—
96#121—3022no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C2×D15111yescharacteristic
99C2×C4⋊C4C2×D15111yescharacteristic
100C2×C42C2×D15111yescharacteristic
101#104—3024no—
102#103—3022no—
103#102—3022no—
104#41—3022no—
105#41—3022no—
106#41—3022no—
107#41—3022no—
108C2×Q8—1512no—
109C2×D4—3022no—
110C2×D4—3022no—
111C2×D4—1512no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—3022no—
115C22×C4C22⋊D15112yes—
116C22×C4C22×D15111yescharacteristic
117M16—3022no—
118M16—3022no—
119C2×C8—3022no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—3022no—
124C22⋊C4—3024no—
125C42—21no—
126C42D60412yescomplemented
127C23—3022no—
128C23C2×C22⋊D15111yescharacteristic
129Q8—3022no—
130Q8—3022no—
131D4—3022no—
132D4—3022no—
133D4—6042no—
134D4—6042no—
135D4—12082no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—3022no—
144C2×C4—6042no—
145C2×C4—6042no—
146C2×C4D4×D15112yes—
147C2×C4C2×D60411yescharacteristic
148C2×C4#1455900411yescharacteristic
149C2×C4#1455900512yes—
150C8—6042no—
151C22—21no—
152C22—21no—
153C22—6042no—
154C22—6042no—
155C22—6042no—
156C22#1801270711yescharacteristic
157C22#1801271311yescharacteristic
158C22#1801272811yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—6042no—
163C4#1801271412yes—
164C4#1801272412yes—
165C2—21no—
166C2—21no—
167C2—12082no—
168C2#2375212911yescharacteristic
169C2#2375237911yescharacteristic
170C2#2375239411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#384×C151C2
socleC22×C151#120
prime radical#23752793C2
hypercenter#384D151
hypocenterC151#2039
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#18012667C2semidirect
3. #23752211C2semidirect
4. #23751981C2semidirect
5. #384×C151C2semidirect
40. C42×C151D4semidirect
85. C151#2039semidirect
90. #384D151semidirect
126. C42D604semidirect

Maximal subgroups

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

subgroupindex
#237527932
C2×#180126672
#237522112
#237519812
#384×C1512
#2039151