Finite Group Databasebeta

← #34079353

Subgroups — #34079353

Order 19328.

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

normal subgroups only

This group has 418 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#23752817C211yesmaximal, characteristic, complemented
2#23752536C212yesmaximal, complemented
3#23752512C212yesmaximal, complemented
4#23752407C212yesmaximal, complemented
5#23752346C212yesmaximal, complemented
6#23752322C212yesmaximal, complemented
7C4×#14558989C212yesmaximal, complemented
8#23752273C211yesmaximal, characteristic, complemented
9#518×C151C211yesmaximal, characteristic, complemented
10C2×#14558989C2212yes—
11C2×#14558989C2212yes—
12#18012736C2211yescharacteristic, complemented
13#18012731C2211yescharacteristic, complemented
14#18012724—22no—
15#18012713C2212yes—
16#18012712—22no—
17C4×D604C2212yescomplemented
18#18012672C2212yescomplemented
19#18012670C2212yescomplemented
20C4⋊(C151⋊C8)C2212yescomplemented
21#18012660C2212yes—
22#18012660C2212yes—
23#18012659C2212yescomplemented
24#18012659C2212yescomplemented
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×D604—22no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39#14558989—24no—
40#14558989—24no—
41C2×C151⋊C8C2312yes—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45(C2×D151)⋊C4—22no—
46(C2×D151)⋊C4—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
63C22×D151—22no—
64D604—22no—
65D604—22no—
66D604—82no—
67C22⋊D151—82no—
68C2×Dic151—22no—
69C4×D151—82no—
70C151⋊C8—22no—
71C151⋊C8—22no—
72C23×C151—24no—
73C23×C151—22no—
74C23×C151—82no—
75C23×C151C2×D411yescharacteristic
76D4×C151—24no—
77D4×C151—22no—
78D4×C151#4114yes—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—82no—
82C2×C4×C151—82no—
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2×D412yes—
85C2×C4×C151C2×D412yes—
86C2×C4×C151C2411yescharacteristic
87C22×C151—21no—
88C22×C151—24no—
89C22×C151—22no—
90C22×C151—42no—
91C22×C151—42no—
92C22×C151—84no—
93C22×C151C22×D411yescharacteristic
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—42no—
97C4×C151—21no—
98C4×C151—22no—
99C4×C151—22no—
100C4×C151—42no—
101C4×C151C2×#4112yes—
102Dic151—42no—
103C2×C151—41no—
104C2×C151—44no—
105C2×C151#52511yescharacteristic
106C2×C151#57612yes—
107D151—82no—
108C151#312211yescharacteristic, complemented, Sylow
109#3122—1511nomaximal, Sylow
110#540—1511no—
111#518D15111yescharacteristic, complemented
112#482—1512no—
113#478—1512no—
114#459—1512no—
115#447—1512no—
116#442—1512no—
117C4×D8—1512no—
118#433—1511no—
119C22×D4C2×D15111yescharacteristic
120C2×D8—1512no—
121C2×D8—1512no—
122#127—1511no—
123#125—1511no—
124#123—3022no—
125#121—3022no—
126#121—1512no—
127C4×D4—22no—
128C4×D4—1512no—
129C4×D4C2×D15112yes—
130C4×D4C2×D15112yes—
131#117C2×D15111yescharacteristic
132#117C2×D15111yescharacteristic
133C2×C22⋊C4—22no—
134#107—1512no—
135#106—1512no—
136C4⋊C8—1512no—
137#102—1512no—
138#102—1512no—
139#102—1512no—
140#102—1512no—
141C22⋊C8—1512no—
142#97—1511no—
143C4×C8—1511no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—3022no—
148C2×D4—3022no—
149C2×D4—1512no—
150C2×D4C22×D15112yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—3022no—
154C22×C4C22×D15111yescharacteristic
155D8—3024no—
156D8—3024no—
157C2×C8—1512no—
158C2×C8—1512no—
159C4⋊C4—3022no—
160C4⋊C4—1512no—
161C4⋊C4C22⋊D15112yes—
162C4⋊C4C22×D15112yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C22⋊C4C22⋊D15112yes—
169C42—21no—
170C42C22×D15111yescharacteristic
171C42C22×D15111yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—3022no—
176C23C2×C22⋊D15111yescharacteristic
177D4—24no—
178D4—22no—
179D4—3022no—
180D4—3022no—
181D4—12082no—
182D4—12082no—
183D4#1455900414yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—3022no—
189C2×C4—12082no—
190C2×C4C2×C22⋊D15111yescharacteristic
191C2×C4C2×C22⋊D15112yes—
192C2×C4C2×C22⋊D15112yes—
193C2×C4C23×D15111yescharacteristic
194C8—3022no—
195C8—3022no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—6042no—
203C22—6042no—
204C22—6042no—
205C22C22×C22⋊D15111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—6042no—
211C4C2×#1455900412yes—
212C2—41no—
213C2—44no—
214C2—12082no—
215C2#2375272311yescharacteristic
216C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#518×C151C2
socleC22×C151C22×D4
hypercenter#518D151
hypocenterC151#3122
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. #23752817C2semidirect
2. #23752536C2semidirect
3. #23752512C2semidirect
4. #23752407C2semidirect
5. #23752346C2semidirect
6. #23752322C2semidirect
7. C4×#14558989C2semidirect
8. #23752273C2semidirect
9. #518×C151C2semidirect
12. #18012736C22semidirect
13. #18012731C22semidirect
17. C4×D604C22semidirect
18. #18012672C22semidirect
19. #18012670C22semidirect
20. C4⋊(C151⋊C8)C22semidirect
23. #18012659C22semidirect
24. #18012659C22semidirect
26. #18012650C22semidirect
27. C4×C151⋊C8C22semidirect
108. C151#3122semidirect
111. #518D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237525362
#237525122
#237524072
#237523462
#237523222
C4×#145589892
#237522732
#518×C1512
#3122151