Finite Group Databasebeta

← #34079362

Subgroups — #34079362

Order 19328.

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

normal subgroups only

This group has 394 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#23752824C211yesmaximal, characteristic, complemented
2#23752553C212yesmaximal, complemented
3#23752512C212yesmaximal, complemented
4#23752417C212yesmaximal, complemented
5#23752363C212yesmaximal
6#23752312C212yesmaximal, complemented
7C4×#14558992C212yesmaximal, complemented
8#23752273C211yesmaximal, characteristic, complemented
9#518×C151C211yesmaximal, characteristic
10C2×#14558992C2212yes—
11C2×#14558992C2212yes—
12#18012739C2211yescharacteristic, complemented
13#18012732—22no—
14#18012731C2211yescharacteristic, complemented
15#18012729—22no—
16#18012718C2212yes—
17C4×Dic302C2212yescomplemented
18#18012672C2212yescomplemented
19#18012670C2212yescomplemented
20C4⋊(C151⋊C8)C2212yescomplemented
21#18012662C2212yescomplemented
22#18012662C2212yescomplemented
23#18012660C2212yes—
24#18012660C2212yes—
25C22⋊(C151⋊C8)C2212yes—
26#18012650C2211yescharacteristic, complemented
27C4×C151⋊C8C2211yescharacteristic, complemented
28C22×D4×C151C2211yescharacteristic
29C4×D4×C151—22no—
30C4×D4×C151C2212yes—
31C4×D4×C151C2212yes—
32#117×C151C2211yescharacteristic
33#117×C151C2211yescharacteristic
34C2×C22⋊C4×C151—22no—
35C2×Dic302C2312yes—
36#14558992—24no—
37#14558992—24no—
38C2×C151⋊C8C2312yes—
39C2×C151⋊C8C2312yes—
40C4⋊Dic151—22no—
41C4⋊Dic151C2312yes—
42Dic151⋊C4—22no—
43Dic151⋊C4—22no—
44Dic151⋊C4—22no—
45C22⋊Dic151—22no—
46C4×Dic151—22no—
47C24×C151—21no—
48C2×D4×C151—24no—
49C2×D4×C151—21no—
50C2×D4×C151C2312yes—
51C22×C4×C151—22no—
52C22×C4×C151—22no—
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151D412yes—
55C4⋊C4×C151C2312yes—
56C22⋊C4×C151—21no—
57C22⋊C4×C151—22no—
58C22⋊C4×C151—22no—
59C22⋊C4×C151D412yes—
60C42×C151—21no—
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63Dic302—22no—
64Dic302—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C151⋊C8—22no—
68C151⋊C8—22no—
69C23×C151—24no—
70C23×C151—22no—
71C23×C151—82no—
72C23×C151C2×D411yescharacteristic
73D4×C151—24no—
74D4×C151—22no—
75D4×C151#4114yes—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—82no—
79C2×C4×C151—82no—
80C2×C4×C151C2×D412yes—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D412yes—
83C2×C4×C151C2411yescharacteristic
84C22×C151—21no—
85C22×C151—24no—
86C22×C151—22no—
87C22×C151—42no—
88C22×C151—42no—
89C22×C151—84no—
90C22×C151C22×D411yescharacteristic
91C4×C151—21no—
92C4×C151—22no—
93C4×C151—22no—
94C4×C151—42no—
95C4×C151C2×#4112yes—
96Dic151—42no—
97Dic151—42no—
98C2×C151—41no—
99C2×C151—44no—
100C2×C151#52511yescharacteristic
101C2×C151#57712yes—
102C151#312311yescharacteristic, complemented, Sylow
103#3123—1511nomaximal, Sylow
104#541—1511no—
105#518D15111yescharacteristic
106#485—1512no—
107#478—1512no—
108#461—1512no—
109#450—1512no—
110#440—1512no—
111C4×SD16—1512no—
112#433—1511no—
113C22×D4C2×D15111yescharacteristic
114C2×SD16—1512no—
115C2×SD16—1512no—
116C4⋊Q8—1511no—
117#126—3022no—
118#125—3022no—
119#125—1511no—
120C22⋊Q8—1512no—
121C4×Q8—1512no—
122C4×D4—22no—
123C4×D4C2×D15112yes—
124C4×D4C2×D15112yes—
125#117C2×D15111yescharacteristic
126#117C2×D15111yescharacteristic
127C2×C22⋊C4—22no—
128#107—1512no—
129#106—1512no—
130C4⋊C8—1512no—
131#103—1512no—
132#103—1512no—
133#102—1512no—
134#102—1512no—
135C22⋊C8—1512no—
136#97—1511no—
137C4×C8—1511no—
138C24—21no—
139C2×Q8—1512no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D15112yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D15111yescharacteristic
146SD16—3024no—
147SD16—3024no—
148C2×C8—1512no—
149C2×C8—1512no—
150C4⋊C4—3022no—
151C4⋊C4—3022no—
152C4⋊C4—3022no—
153C4⋊C4—3022no—
154C4⋊C4—1512no—
155C4⋊C4C22⋊D15112yes—
156C4⋊C4C22×D15112yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—3022no—
161C22⋊C4C22⋊D15112yes—
162C42—21no—
163C42—3022no—
164C42C22×D15111yescharacteristic
165C42C22×D15111yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D15111yescharacteristic
170Q8—3022no—
171Q8—3022no—
172D4—24no—
173D4—22no—
174D4#1455900414yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4C2×C22⋊D15111yescharacteristic
182C2×C4C2×C22⋊D15112yes—
183C2×C4C2×C22⋊D15112yes—
184C2×C4C23×D15111yescharacteristic
185C8—3022no—
186C8—3022no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D15111yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—6042no—
199C4—6042no—
200C4C2×#1455900412yes—
201C2—41no—
202C2—44no—
203C2#2375272311yescharacteristic
204C2#2375302312yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#518×C151C2
socleC22×C151C22×D4
prime radicalC22×D4×C151C22
hypercenter#518D151
hypocenterC151#3123
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #23752824C2semidirect
2. #23752553C2semidirect
3. #23752512C2semidirect
4. #23752417C2semidirect
6. #23752312C2semidirect
7. C4×#14558992C2semidirect
8. #23752273C2semidirect
12. #18012739C22semidirect
14. #18012731C22semidirect
17. C4×Dic302C22semidirect
18. #18012672C22semidirect
19. #18012670C22semidirect
20. C4⋊(C151⋊C8)C22semidirect
21. #18012662C22semidirect
22. #18012662C22semidirect
26. #18012650C22semidirect
27. C4×C151⋊C8C22semidirect
102. C151#3123semidirect

Maximal subgroups

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

subgroupindex
#237528242
#237525532
#237525122
#237524172
#237523632
#237523122
C4×#145589922
#237522732
#518×C1512
#3123151