Finite Group Databasebeta

← #34070177

Subgroups — #34070177

Order 19328.

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

normal subgroups only

This group has 394 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#23753012C211yesmaximal, characteristic, complemented
2#23752723C212yesmaximal, complemented
3#23752228C212yesmaximal, complemented
4#23751969C211yesmaximal, characteristic, complemented
5#407×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7#18012772—22no—
8#18012767—22no—
9#18012761—22no—
10#18012722—22no—
11#18012718—22no—
12#18012713—22no—
13#18012708—22no—
14C4×C22⋊D151—24no—
15#18012698C2212yes—
16#18012665—24no—
17C23×C4×C151C2211yescharacteristic
18C2×M16×C151C2211yescharacteristic
19C2×M16×C151C2211yescharacteristic
20C22⋊C8×C151—22no—
21#14559004—22no—
22#14559004—22no—
23#14559004—22no—
24#14559004—22no—
25C2×Dic302D412yescomplemented
26C2×D604D412yescomplemented
27C2×C22⋊D151—24no—
28C2×C22⋊D151—22no—
29C2×C4×D151—22no—
30Dic604—22no—
31#14558993—24no—
32D1208—22no—
33C4⋊Dic151—22no—
34Dic151⋊C4—24no—
35C22⋊Dic151—24no—
36C22⋊Dic151—22no—
37(C2×D151)⋊C4—24no—
38C4×Dic151D414yescomplemented
39C24×C151D411yescharacteristic
40C22×C4×C151—22no—
41C22×C4×C151—22no—
42C22×C4×C151—21no—
43C22×C4×C151—21no—
44C22×C4×C151D411yescharacteristic
45C22×C4×C151C2311yescharacteristic
46M16×C151—22no—
47M16×C151—22no—
48C2×C8×C151—21no—
49C2×C8×C151D412yescomplemented
50C22×D151—22no—
51Dic302—22no—
52Dic302—22no—
53D604—22no—
54D604—22no—
55C22⋊D151—48no—
56C22⋊D151—42no—
57C22⋊D151—42no—
58C2×Dic151—24no—
59C2×Dic151—22no—
60C4×D151—42no—
61C4×D151—42no—
62C23×C151—22no—
63C23×C151—21no—
64C23×C151—42no—
65C23×C151C2×D411yescharacteristic
66C2×C4×C151—22no—
67C2×C4×C151—21no—
68C2×C4×C151—41no—
69C2×C4×C151—42no—
70C2×C4×C151—41no—
71C2×C4×C151C2×D412yes—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151#4111yescharacteristic
75C8×C151—22no—
76C8×C151—41no—
77C22×C151—22no—
78C22×C151—24no—
79C22×C151—41no—
80C22×C151—42no—
81C22×C151—41no—
82C22×C151—41no—
83C22×C151#12012yes—
84C22×C151#12111yescharacteristic
85C2×D151—44no—
86C2×D151—42no—
87C4×C151—41no—
88C4×C151#12011yescharacteristic
89C4×C151#12112yes—
90C4×C151#12711yescharacteristic
91Dic151—44no—
92Dic151—42no—
93C2×C151—22no—
94C2×C151—21no—
95C2×C151—42no—
96C2×C151#39211yescharacteristic
97D151—82no—
98C151#201011yescharacteristic, complemented, Sylow
99#2010—1511nomaximal, Sylow
100#575—1511no—
101#525—1512no—
102#421—1512no—
103#407D15111yescharacteristic, complemented
104H(3,ℤ/4)—1511no—
105C2×#41—1512no—
106C23×C4C2×D15111yescharacteristic
107#137—3022no—
108AGL(1,ℤ/8)—3022no—
109#135—3022no—
110C2×M16C2×D15111yescharacteristic
111C2×M16C2×D15111yescharacteristic
112#123—3022no—
113C22⋊Q8—3022no—
114#121—3022no—
115#120—3022no—
116C4×D4—3024no—
117#117—1512no—
118#104—3024no—
119C22⋊C8—22no—
120C24D60411yescharacteristic
121#41—3022no—
122#41—3022no—
123#41—3022no—
124#41—3022no—
125C2×Q8—1512no—
126C2×D4—3024no—
127C2×D4—3022no—
128C2×D4—1512no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—3022no—
134C22×C4D60411yescharacteristic
135C22×C4C22×D15111yescharacteristic
136Q16—3022no—
137SD16—3024no—
138D8—3022no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D15112yescomplemented
143C4⋊C4—3024no—
144C4⋊C4—3022no—
145C22⋊C4—3024no—
146C22⋊C4—3024no—
147C22⋊C4—3022no—
148C42—1514no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—3022no—
153C23C2×D60411yescharacteristic
154Q8—3022no—
155Q8—3022no—
156D4—3022no—
157D4—3022no—
158D4—6048no—
159D4—6042no—
160D4—6042no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—3024no—
167C2×C4—3022no—
168C2×C4—6042no—
169C2×C4—6042no—
170C2×C4D4×D15112yes—
171C2×C4D4×D15112yes—
172C2×C4C2×C22⋊D15111yescharacteristic
173C2×C4#1455900411yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—6044no—
183C22—6042no—
184C22#1801270912yes—
185C22#1801271311yescharacteristic
186C4—41no—
187C4—6044no—
188C4—6042no—
189C4#1801270711yescharacteristic
190C4#1801271212yes—
191C4#1801273511yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—12082no—
196C2#2375212111yescharacteristic
subgroupG/H
centerC4#18012735
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#407×C151C2
socleC2×C151#392
hypercenter#407D151
hypocenterC151#2010
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #23753012C2semidirect
2. #23752723C2semidirect
3. #23752228C2semidirect
4. #23751969C2semidirect
5. #407×C151C2semidirect
25. C2×Dic302D4semidirect
26. C2×D604D4semidirect
38. C4×Dic151D4semidirect
49. C2×C8×C151D4semidirect
98. C151#2010semidirect
103. #407D151semidirect
142. C2×C8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237527232
#237522282
#237519692
#407×C1512
#2010151