Finite Group Databasebeta

← #34068047

Subgroups — #34068047

Order 19328.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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, complemented
2#23752348C212yesmaximal, complemented
3#23752129C211yesmaximal, characteristic, complemented
4#23751947C212yesmaximal, complemented
5#324×C151C211yesmaximal, characteristic, complemented
6C2×#14559004—21no—
7C22×D604C2211yescharacteristic
8C2×D1208—22no—
9#18012719—22no—
10#18012714—22no—
11#18012713—21no—
12#18012713C2212yes—
13C2×(C2×D151)⋊C4—21no—
14C2×(C2×D151)⋊C4—21no—
15#18012661—22no—
16C151⋊#95C2211yescharacteristic
17C2×C4⋊C4×C151C2211yescharacteristic
18C22⋊C8×C151C2212yes—
19C23×D151—21no—
20#14559004—42no—
21#14559004—42no—
22C2×Dic302—21no—
23C2×D604—21no—
24C2×D604—21no—
25C2×D604—22no—
26C2×D604—42no—
27C2×D604D412yes—
28C2×C22⋊D151—22no—
29C22×Dic151—21no—
30C2×C4×D151—22no—
31D1208—44no—
32C4⋊Dic151—21no—
33C4⋊Dic151D412yes—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36(C2×D151)⋊C4—42no—
37(C2×D151)⋊C4—42no—
38C22×C4×C151D411yescharacteristic
39C22×C4×C151D411yescharacteristic
40C22×C4×C151C2311yescharacteristic
41C2×C8×C151—22no—
42C4⋊C4×C151—22no—
43C22×D151—22no—
44C22×D151—22no—
45C22×D151—41no—
46C22×D151—41no—
47C22×D151—41no—
48C22×D151—41no—
49C22×D151—41no—
50C22×D151—41no—
51Dic302—42no—
52D604—24no—
53D604—42no—
54D604—42no—
55D604—42no—
56D604—81no—
57C22⋊D151—42no—
58C22⋊D151—42no—
59C2×Dic151—22no—
60C2×Dic151—41no—
61C2×Dic151—41no—
62C2×Dic151—41no—
63C4×D151—44no—
64C23×C151C2×D411yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151—41no—
69C2×C4×C151—41no—
70C2×C4×C151D812yescomplemented
71C2×C4×C151C2×D412yes—
72C8×C151—42no—
73C22×C151—21no—
74C22×C151—21no—
75C22×C151#12011yescharacteristic
76C22×C151C2×D811yescharacteristic
77C22×C151AGL(1,ℤ/8)11yescharacteristic
78C2×D151—42no—
79C2×D151—42no—
80C2×D151—42no—
81C2×D151—42no—
82C2×D151—42no—
83C2×D151—42no—
84C2×D151—81no—
85C2×D151—81no—
86C2×D151—81no—
87C2×D151—81no—
88C4×C151—22no—
89C4×C151—22no—
90C4×C151—41no—
91Dic151—42no—
92Dic151—81no—
93C2×C151—21no—
94C2×C151—21no—
95C2×C151#44711yescharacteristic
96C2×C151#45411yescharacteristic
97C2×C151B(4,𝔽2)11yescharacteristic
98D151—82no—
99D151—82no—
100C151#159811yescharacteristic, complemented, Sylow
101#1598—1511nomaximal, Sylow
102#537—1511no—
103#447—1512no—
104#394—1511no—
105#327—1512no—
106#324D15111yescharacteristic, complemented
107C2×#41—3021no—
108C22×D4—1511no—
109C2×D8—3022no—
110C22⋊Q8—3022no—
111#121—3022no—
112#121—3021no—
113#121—1512no—
114C2×C4⋊C4C2×D15111yescharacteristic
115C2×C22⋊C4—3021no—
116C2×C22⋊C4—3021no—
117#102—3022no—
118C22⋊C8C2×D15112yes—
119#95—1511no—
120C24—3021no—
121#41—6042no—
122#41—6042no—
123C2×Q8—3021no—
124C2×D4—3021no—
125C2×D4—3021no—
126C2×D4—3022no—
127C2×D4—3022no—
128C2×D4—6042no—
129C2×D4—1512no—
130C22×C4—3022no—
131C22×C4—3021no—
132C22×C4D60411yescharacteristic
133C22×C4D60411yescharacteristic
134C22×C4C22×D15111yescharacteristic
135D8—6044no—
136C2×C8—22no—
137C4⋊C4—22no—
138C4⋊C4—3021no—
139C4⋊C4—1512no—
140C22⋊C4—3022no—
141C22⋊C4—3022no—
142C22⋊C4—6042no—
143C22⋊C4—6042no—
144C23—3022no—
145C23—3022no—
146C23—6041no—
147C23—6041no—
148C23—6041no—
149C23—6041no—
150C23—6041no—
151C23—6041no—
152C23C2×D60411yescharacteristic
153Q8—6042no—
154D4—3024no—
155D4—6042no—
156D4—6042no—
157D4—6042no—
158D4—6042no—
159D4—6042no—
160D4—12081no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—3022no—
167C2×C4—6044no—
168C2×C4—6041no—
169C2×C4—6041no—
170C2×C4—6041no—
171C2×C4D120812yescomplemented
172C2×C4D4×D15112yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—6042no—
177C22—6042no—
178C22—6042no—
179C22—6042no—
180C22—6042no—
181C22—6042no—
182C22—12081no—
183C22—12081no—
184C22—12081no—
185C22—12081no—
186C22#1801270911yescharacteristic
187C22C2×D120811yescharacteristic
188C22#1801276711yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—6042no—
193C4—12081no—
194C2—21no—
195C2—21no—
196C2—12082no—
197C2—12082no—
198C2#2375234811yescharacteristic
199C2#2375238711yescharacteristic
200C2#2375240011yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#324×C151C2
socleC22×C151#120
hypercenter#324D151
hypocenterC151#1598
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #23752793C2semidirect
2. #23752348C2semidirect
3. #23752129C2semidirect
4. #23751947C2semidirect
5. #324×C151C2semidirect
70. C2×C4×C151D8semidirect
100. C151#1598semidirect
106. #324D151semidirect
171. C2×C4D1208semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237523482
#237521292
#237519472
#324×C1512
#1598151