Finite Group Databasebeta

← #34079498

Subgroups — #34079498

Order 19328.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752765C211yesmaximal, characteristic, complemented
2C2×#18012728C211yesmaximal, characteristic
3#23752573C214yesmaximal, complemented
4#23752568C214yesmaximal, complemented
5#23752221C211yesmaximal, characteristic, complemented
6#23752218C211yesmaximal, characteristic
7#23752216C211yesmaximal, characteristic
8M16×Dic151C211yesmaximal, characteristic, complemented
9#419×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C2×#14558988C2211yescharacteristic
12#18012738C2212yescomplemented
13#18012730C2212yescomplemented
14#18012728—22no—
15#18012728C2212yes—
16#18012728C2212yes—
17#18012716—22no—
18C4×Dic302—22no—
19#18012698C2211yescharacteristic
20C2×(C2×D151)⋊C4—22no—
21C2×C4×Dic151C2211yescharacteristic
22#18012663C2214yescomplemented
23#18012661C2214yes—
24#18012659C2214yes—
25#18012649C2212yescomplemented
26C8×Dic151C2212yescomplemented
27C22×Q8×C151C2211yescharacteristic
28C2×M16×C151C2211yescharacteristic
29#117×C151C2211yescharacteristic
30#103×C151C2214yescomplemented
31C23×D151—21no—
32C2×Dic302—22no—
33C2×D604—21no—
34C2×D604—22no—
35C2×D604—22no—
36C2×D604C2312yes—
37C22×Dic151D412yes—
38#14558988—22no—
39C2×C151⋊C8C2312yes—
40C4⋊Dic151—22no—
41C4⋊Dic151C2312yes—
42Dic151⋊C4—22no—
43Dic151⋊C4—22no—
44C22⋊Dic151—21no—
45(C2×D151)⋊C4—24no—
46(C2×D151)⋊C4—24no—
47C4×Dic151—21no—
48C4×Dic151D412yes—
49C4×Dic151C2311yescharacteristic
50C4×Dic151C2311yescharacteristic
51C2×Q8×C151—21no—
52C2×Q8×C151—22no—
53C2×Q8×C151—22no—
54C2×Q8×C151C2312yes—
55C22×C4×C151—21no—
56C22×C4×C151C2311yescharacteristic
57M16×C151—22no—
58C2×C8×C151C2312yes—
59C4⋊C4×C151C2312yes—
60C22⋊C4×C151—21no—
61C42×C151—21no—
62C22×D151—22no—
63C22×D151—44no—
64C22×D151—42no—
65Dic302—44no—
66D604—22no—
67D604—22no—
68D604—42no—
69C2×Dic151—22no—
70C2×Dic151—42no—
71C2×Dic151C2×D412yes—
72C2×Dic151C2×D412yes—
73C151⋊C8—22no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—22no—
76Q8×C151—22no—
77Q8×C151—42no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—42no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151#4112yes—
83C2×C4×C151#4112yes—
84C2×C4×C151C2411yescharacteristic
85C8×C151—22no—
86C22×C151—22no—
87C22×C151#12412yes—
88C22×C151C22×D411yescharacteristic
89C2×D151—42no—
90C2×D151—44no—
91C2×D151—84no—
92C4×C151—42no—
93C4×C151—42no—
94C4×C151#12412yes—
95C4×C151C2×#4111yescharacteristic
96C4×C151C2×#4111yescharacteristic
97Dic151—22no—
98Dic151—22no—
99Dic151—42no—
100C2×C151—22no—
101C2×C151C2×#12411yescharacteristic
102C2×C151#57512yes—
103D151—82no—
104C151#314011yescharacteristic, complemented, Sylow
105#3140—1511nomaximal, Sylow
106#533—1511no—
107C2×#124—1511no—
108#489—1514no—
109#488—1514no—
110#419—1511no—
111#419D15111yescharacteristic, complemented
112#418—1511no—
113#418—1511no—
114C4×M16—1511no—
115C22×Q8C2×D15111yescharacteristic
116C22×D4—1511no—
117C2×M16—1511no—
118C2×M16C2×D15111yescharacteristic
119C4⋊Q8—1512no—
120#125—1512no—
121#124—3022no—
122#124—1512no—
123#124—1512no—
124C22⋊Q8—3022no—
125C4×Q8—3022no—
126#117—1511no—
127#117C2×D15111yescharacteristic
128C2×C22⋊C4—3022no—
129C2×C42—1511no—
130#103—1514no—
131#103C2×D15114yescomplemented
132#102—1514no—
133#102—1514no—
134#97—1512no—
135C4×C8—1512no—
136C24—3021no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—3022no—
141C2×Q8C22×D15112yes—
142C2×D4—3021no—
143C2×D4—3022no—
144C2×D4—3022no—
145C2×D4—1512no—
146C22×C4—21no—
147C22×C4—1512no—
148C22×C4C22×D15111yescharacteristic
149M16—22no—
150M16—3022no—
151C2×C8—1512no—
152C2×C8C22×D15112yes—
153C4⋊C4—3022no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—1512no—
157C4⋊C4C22×D15112yes—
158C22⋊C4—21no—
159C22⋊C4—3024no—
160C22⋊C4—3024no—
161C22⋊C4—3021no—
162C42—21no—
163C42—3021no—
164C42—1512no—
165C42—1511no—
166C42—1511no—
167C23—3022no—
168C23—6044no—
169C23—6042no—
170C23D4×D15111yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—6044no—
175D4—3022no—
176D4—3022no—
177D4—6042no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—3022no—
182C2×C4—6042no—
183C2×C4—1512no—
184C2×C4—1512no—
185C2×C4D4×D15111yescharacteristic
186C2×C4#1455900312yes—
187C2×C4#1455900412yes—
188C2×C4C23×D15111yescharacteristic
189C8—22no—
190C8—3022no—
191C22—22no—
192C22—6042no—
193C22—6044no—
194C22—12084no—
195C22#1801272512yes—
196C22C2×D4×D15111yescharacteristic
197C4—42no—
198C4—42no—
199C4—3022no—
200C4—3022no—
201C4—6042no—
202C4#1801272512yes—
203C4C2×#1455900311yescharacteristic
204C4C2×#1455900411yescharacteristic
205C2—22no—
206C2—12082no—
207C2C2×#1801272511yescharacteristic
208C2#2375301112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#419×C151C2
socleC22×C151C22×D4
prime radicalC22×D604C22
hypercenter#419D151
hypocenterC151#3140
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #23752765C2semidirect
3. #23752573C2semidirect
4. #23752568C2semidirect
5. #23752221C2semidirect
8. M16×Dic151C2semidirect
9. #419×C151C2semidirect
12. #18012738C22semidirect
13. #18012730C22semidirect
22. #18012663C22semidirect
25. #18012649C22semidirect
26. C8×Dic151C22semidirect
30. #103×C151C22semidirect
104. C151#3140semidirect
111. #419D151semidirect
131. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527652
C2×#180127282
#237525732
#237525682
#237522212
#237522182
#237522162
M16×Dic1512
#419×C1512
#3140151