Finite Group Databasebeta

← #34082522

Subgroups — #34082522

Order 19328.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#23752811C216yesmaximal, complemented
2#23752802C216yesmaximal, complemented
3#23752774C213yesmaximal, complemented
4#23752748C216yesmaximal, complemented
5#23752725C216yesmaximal, complemented
6C2×(C22⋊D151)⋊C4C213yesmaximal, complemented
7#543×C151C211yesmaximal, characteristic, complemented
8C2×#14559005C2212yescomplemented
9C22×C22⋊D151C2213yes—
10C23×Dic151C2211yescharacteristic
11C22×C4×D151C2213yescomplemented
12#18012734C22112yescomplemented
13#18012730C2216yescomplemented
14#18012728C2216yescomplemented
15#18012724C22112yescomplemented
16#18012723C22112yescomplemented
17#18012715C2216yescomplemented
18#18012714C2216yescomplemented
19#18012713C2216yes—
20#18012713C2216yes—
21#18012709C22112yescomplemented
22Q8×Dic151C2212yescomplemented
23#18012701C2216yescomplemented
24(C22⋊D151)⋊C4C22112yescomplemented
25(C22⋊D151)⋊C4C22112yescomplemented
26#18012697C2216yescomplemented
27C2×Dic151⋊C4C2213yescomplemented
28C2×(C2×D151)⋊C4C2213yescomplemented
29C2×C4×Dic151C2213yescomplemented
30C22⋊Q8×C151C2216yescomplemented
31C22⋊Q8×C151C2216yescomplemented
32C2×C22⋊C4×C151C2213yes—
33C23×D151C2313yes—
34#14559005—44no—
35C2×D604C2316yes—
36C2×D604C2316yes—
37C2×C22⋊D151—212no—
38C2×C22⋊D151C23112yes—
39C22×Dic151—42no—
40C22×Dic151C2313yes—
41C22×Dic151C2313yes—
42C22×Dic151C2313yes—
43C2×C4×D151—46no—
44C2×C4×D151C2316yes—
45C2×C4×D151C2316yes—
46C4⋊Dic151C2316yes—
47C4⋊Dic151C2316yes—
48Dic151⋊C4C23112yes—
49(C2×D151)⋊C4C23112yes—
50(C2×D151)⋊C4C23112yes—
51(C2×D151)⋊C4C23112yes—
52C4×Dic151C2316yes—
53C4×Dic151C2316yes—
54C24×C151C2311yescharacteristic
55C2×Q8×C151C2312yes—
56C2×Q8×C151C2312yes—
57C22×C4×C151C2313yes—
58C22×C4×C151C2313yes—
59C4⋊C4×C151C2316yes—
60C4⋊C4×C151C2316yes—
61C22⋊C4×C151C23112yes—
62C22×D151—26no—
63C22×D151—43no—
64C22×D151—43no—
65C22×D151C2416yes—
66D604—46no—
67D604—46no—
68C22⋊D151—224no—
69C2×Dic151—26no—
70C2×Dic151—26no—
71C2×Dic151—43no—
72C2×Dic151C2413yes—
73C2×Dic151C2416yes—
74C2×Dic151C2411yescharacteristic
75C4×D151—212no—
76C4×D151—46no—
77C23×C151—41no—
78C23×C151—41no—
79C23×C151#4114yescomplemented
80C23×C151C2413yes—
81Q8×C151—42no—
82Q8×C151—42no—
83C2×C4×C151—43no—
84C2×C4×C151—43no—
85C2×C4×C151C2416yes—
86C2×C4×C151C2416yes—
87C22×C151—23no—
88C22×C151—23no—
89C22×C151—44no—
90C22×C151C2×#4116yes—
91C22×C151C2511yescharacteristic
92C2×D151—26no—
93C2×D151—26no—
94C2×D151—26no—
95C2×D151—412no—
96C4×C151—26no—
97C4×C151—26no—
98Dic151—26no—
99Dic151—23no—
100Dic151H(5,𝔽2)12yes—
101C2×C151—26no—
102C2×C151C22×#4111yescharacteristic
103C2×C151C2×H(5,𝔽2)11yescharacteristic
104C2×C151#58511yescharacteristic
105D151—46no—
106C151#345911yescharacteristic, complemented, Sylow
107#3459—1511nomaximal, Sylow
108#543D15111yescharacteristic, complemented
109#539—1516no—
110#538—1516no—
111#534—1513no—
112#529—1516no—
113#525—1516no—
114C2×C4×D4—1513no—
115C2×#41—1512no—
116C22×D4—1513no—
117C23×C4—1511no—
118C23×C4—1513no—
119#126—15112no—
120#125—1516no—
121#124—1516no—
122#123—15112no—
123#123—15112no—
124C22⋊Q8—1516no—
125C22⋊Q8C2×D15116yescomplemented
126C22⋊Q8C2×D15116yescomplemented
127#121—1516no—
128#121—1516no—
129#121—1516no—
130#120—15112no—
131C4×Q8—1512no—
132C4×D4—1516no—
133C4×D4—15112no—
134C4×D4—15112no—
135#117—1516no—
136C2×C4⋊C4—1513no—
137C2×C22⋊C4—1513no—
138C2×C22⋊C4C2×D15113yes—
139C2×C42—1513no—
140C24—1513no—
141C24C22×D15111yescharacteristic
142#41—6044no—
143C2×Q8C22×D15112yes—
144C2×Q8C22×D15112yes—
145C2×D4—30212no—
146C2×D4—15112no—
147C2×D4—1516no—
148C2×D4—1516no—
149C22×C4—6046no—
150C22×C4—6042no—
151C22×C4—1513no—
152C22×C4—1513no—
153C22×C4—1516no—
154C22×C4—1513no—
155C22×C4—1516no—
156C22×C4C22×D15113yes—
157C22×C4C22×D15113yes—
158C4⋊C4—15112no—
159C4⋊C4—1516no—
160C4⋊C4—1516no—
161C4⋊C4C22×D15116yes—
162C4⋊C4C22×D15116yes—
163C22⋊C4—15112no—
164C22⋊C4—15112no—
165C22⋊C4—15112no—
166C22⋊C4C22×D151112yes—
167C42—1516no—
168C42—1516no—
169C23—41no—
170C23—41no—
171C23—3026no—
172C23—6043no—
173C23—6043no—
174C23—1516no—
175C23#1455900514yescomplemented
176C23C23×D15113yes—
177Q8—42no—
178Q8—42no—
179D4—30224no—
180D4—6046no—
181D4—6046no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—30212no—
185C2×C4—3026no—
186C2×C4—3026no—
187C2×C4—6046no—
188C2×C4—6043no—
189C2×C4—1516no—
190C2×C4—1513no—
191C2×C4—1511no—
192C2×C4C23×D15116yes—
193C2×C4C23×D15116yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—3026no—
198C22—3026no—
199C22—3026no—
200C22—60412no—
201C22C2×#1455900516yes—
202C22C24×D15111yescharacteristic
203C4—26no—
204C4—26no—
205C4—3026no—
206C4—3023no—
207C4—1512no—
208C2—26no—
209C2—6046no—
210C2C22×#1455900511yescharacteristic
211C2H(5,𝔽2)×D15111yescharacteristic
212C2#2375304711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D151
commutator, socle, cosocleC22×C151C25
Fitting#543×C151C2
hypercenter#543D151
hypocenterC151#3459
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #23752811C2semidirect
2. #23752802C2semidirect
3. #23752774C2semidirect
4. #23752748C2semidirect
5. #23752725C2semidirect
6. C2×(C22⋊D151)⋊C4C2semidirect
7. #543×C151C2semidirect
8. C2×#14559005C22semidirect
11. C22×C4×D151C22semidirect
12. #18012734C22semidirect
13. #18012730C22semidirect
14. #18012728C22semidirect
15. #18012724C22semidirect
16. #18012723C22semidirect
17. #18012715C22semidirect
18. #18012714C22semidirect
21. #18012709C22semidirect
22. Q8×Dic151C22semidirect
23. #18012701C22semidirect
24. (C22⋊D151)⋊C4C22semidirect
25. (C22⋊D151)⋊C4C22semidirect
26. #18012697C22semidirect
27. C2×Dic151⋊C4C22semidirect
28. C2×(C2×D151)⋊C4C22semidirect
29. C2×C4×Dic151C22semidirect
30. C22⋊Q8×C151C22semidirect
31. C22⋊Q8×C151C22semidirect
79. C23×C151#41semidirect
106. C151#3459semidirect
108. #543D151semidirect
125. C22⋊Q8C2×D151semidirect
126. C22⋊Q8C2×D151semidirect
175. C23#14559005semidirect

Maximal subgroups

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

subgroupindex
#237528112
#237528022
#237527742
#237527482
#237527252
C2×(C22⋊D151)⋊C42
#543×C1512
#3459151