Finite Group Databasebeta

← #34068044

Subgroups — #34068044

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#23752346C212yesmaximal, complemented
3#23751945C212yesmaximal, complemented
4#23751938C211yesmaximal, characteristic, complemented
5#394×C151C211yesmaximal, characteristic, complemented
6C2×#14559004—21no—
7C2×#14558989—22no—
8#18012719—22no—
9#18012714—22no—
10#18012713—21no—
11#18012713C2212yes—
12#18012660—22no—
13C22⋊(C151⋊C8)C2212yes—
14C22×D4×C151C2211yescharacteristic
15C2×C4⋊C4×C151C2211yescharacteristic
16C2×C22⋊C4×C151—21no—
17C2×C22⋊C4×C151—21no—
18#95×C151C2211yescharacteristic
19#14559004—42no—
20#14559004—42no—
21C2×Dic302—21no—
22C2×D604—21no—
23C2×D604—21no—
24C2×D604D412yes—
25C2×C22⋊D151—22no—
26C2×C4×D151—22no—
27#14558989—44no—
28C2×C151⋊C8—22no—
29C4⋊Dic151—21no—
30C4⋊Dic151D412yes—
31(C2×D151)⋊C4—22no—
32(C2×D151)⋊C4—22no—
33C24×C151—21no—
34C2×D4×C151—22no—
35C2×D4×C151—42no—
36C22×C4×C151—21no—
37C22×C4×C151D411yescharacteristic
38C22×C4×C151D411yescharacteristic
39C22×C4×C151C2311yescharacteristic
40C4⋊C4×C151—22no—
41C22⋊C4×C151—42no—
42C22⋊C4×C151—42no—
43C22×D151—22no—
44Dic302—42no—
45D604—42no—
46D604—42no—
47D604—81no—
48C22⋊D151—42no—
49C22⋊D151—42no—
50C2×Dic151—22no—
51C4×D151—44no—
52C151⋊C8—42no—
53C23×C151—22no—
54C23×C151—41no—
55C23×C151—41no—
56C23×C151—41no—
57C23×C151—41no—
58C23×C151—41no—
59C23×C151—41no—
60C23×C151C2×D411yescharacteristic
61D4×C151—24no—
62D4×C151—42no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—21no—
66C2×C4×C151—41no—
67C2×C4×C151—41no—
68C2×C4×C151—41no—
69C2×C4×C151—41no—
70C2×C4×C151—41no—
71C2×C4×C151D812yescomplemented
72C2×C4×C151C2×D412yes—
73C22×C151—21no—
74C22×C151—21no—
75C22×C151—42no—
76C22×C151—42no—
77C22×C151—42no—
78C22×C151—81no—
79C22×C151—81no—
80C22×C151—81no—
81C22×C151—81no—
82C22×C151#12011yescharacteristic
83C22×C151C2×D811yescharacteristic
84C22×C151AGL(1,ℤ/8)11yescharacteristic
85C2×D151—42no—
86C2×D151—42no—
87C2×D151—42no—
88C4×C151—22no—
89C4×C151—22no—
90C4×C151—41no—
91C4×C151—81no—
92Dic151—42no—
93C2×C151—21no—
94C2×C151—21no—
95C2×C151—82no—
96C2×C151#44711yescharacteristic
97C2×C151#45411yescharacteristic
98C2×C151B(4,𝔽2)11yescharacteristic
99D151—82no—
100C151#159811yescharacteristic, complemented, Sylow
101#1598—1511nomaximal, Sylow
102#537—1511no—
103#447—1512no—
104#394D15111yescharacteristic, complemented
105#327—1512no—
106#324—1511no—
107C2×#41—3021no—
108C22×D4C2×D15111yescharacteristic
109C2×D8—3022no—
110C22⋊Q8—3022no—
111#121—3022no—
112#121—3021no—
113#121—1512no—
114C2×C4⋊C4C2×D15111yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—3022no—
118C22⋊C8—1512no—
119#95C2×D15111yescharacteristic
120C24—21no—
121#41—6042no—
122#41—6042no—
123C2×Q8—3021no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—3021no—
127C2×D4—3021no—
128C2×D4—3022no—
129C2×D4—1512no—
130C22×C4—21no—
131C22×C4—3022no—
132C22×C4C22⋊D15111yescharacteristic
133C22×C4C22⋊D15111yescharacteristic
134C22×C4C22×D15111yescharacteristic
135D8—6044no—
136C2×C8—3022no—
137C4⋊C4—22no—
138C4⋊C4—3021no—
139C4⋊C4—1512no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—3022no—
143C22⋊C4—3022no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—3022no—
152C23C2×C22⋊D15111yescharacteristic
153Q8—6042no—
154D4—24no—
155D4—42no—
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—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3022no—
170C2×C4—6044no—
171C2×C4#1455898912yescomplemented
172C2×C4D4×D15112yes—
173C8—6042no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—6042no—
184C22—6042no—
185C22—6042no—
186C22#1801270711yescharacteristic
187C22C2×#1455898911yescharacteristic
188C22#1801276411yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—6042no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—12082no—
198C2#2375234511yescharacteristic
199C2#2375238411yescharacteristic
200C2#2375239811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#394×C151C2
socleC22×C151#120
hypercenter#394D151
hypocenterC151#1598
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #23752793C2semidirect
2. #23752346C2semidirect
3. #23751945C2semidirect
4. #23751938C2semidirect
5. #394×C151C2semidirect
71. C2×C4×C151D8semidirect
100. C151#1598semidirect
104. #394D151semidirect
171. C2×C4#14558989semidirect

Maximal subgroups

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

subgroupindex
#237527932
#237523462
#237519452
#237519382
#394×C1512
#1598151