Finite Group Databasebeta

← #34068415

Subgroups — #34068415

Order 19328.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752954C211yesmaximal, characteristic
2#23752604C211yesmaximal, characteristic, complemented
3#23752574C211yesmaximal, characteristic, complemented
4#23751952C211yesmaximal, characteristic, complemented
5#23751951C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic, complemented
7#489×C151C211yesmaximal, characteristic, complemented
8C2×#14558994—21no—
9C2×#14558991—21no—
10#18012728—21no—
11#18012727C2211yescharacteristic
12#18012727C2211yescharacteristic
13#18012725—21no—
14#18012725—21no—
15#18012709—21no—
16#18012709—21no—
17#18012707—21no—
18#18012662—21no—
19#18012659—21no—
20#18012650C2211yescharacteristic, complemented
21#18012650C2211yescharacteristic, complemented
22C4⋊Q8×C151C2211yescharacteristic, complemented
23#124×C151C2211yescharacteristic
24#103×C151—21no—
25#102×C151—21no—
26#97×C151C2211yescharacteristic, complemented
27C23×D151—21no—
28C2×Dic302D411yescharacteristic
29C2×Dic302D411yescharacteristic
30C2×D604—21no—
31C2×D604D411yescharacteristic
32C2×D604D411yescharacteristic
33C2×C22⋊D151—21no—
34C2×C22⋊D151—21no—
35#14558994—42no—
36#14558991—42no—
37C2×C151⋊C8—21no—
38C2×C151⋊C8—21no—
39C22⋊Dic151—21no—
40(C2×D151)⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46C4×Dic151—21no—
47C2×Q8×C151—21no—
48C2×Q8×C151D411yescharacteristic
49C2×D4×C151D411yescharacteristic
50C2×C8×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C22⋊C4×C151—21no—
54C22⋊C4×C151—21no—
55C42×C151C2311yescharacteristic
56C22×D151—21no—
57C22×D151—21no—
58C22×D151—81no—
59C22×D151—81no—
60C22×D151—81no—
61Dic302—41no—
62Dic302—41no—
63D604—41no—
64D604—41no—
65D604—81no—
66C22⋊D151—81no—
67C22⋊D151—81no—
68C2×Dic151—21no—
69C2×Dic151—21no—
70C151⋊C8—22no—
71C151⋊C8—41no—
72C23×C151—21no—
73Q8×C151—41no—
74Q8×C151—41no—
75Q8×C151—41no—
76D4×C151—41no—
77C2×C4×C151—21no—
78C2×C4×C151—41no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C8×C151—41no—
83C22×C151—41no—
84C22×C151—41no—
85C22×C151—41no—
86C22×C151#12011yescharacteristic
87C2×D151—41no—
88C2×D151—41no—
89C2×D151—41no—
90C2×D151—41no—
91C2×D151—41no—
92C2×D151—41no—
93C2×D151—84no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—21no—
97C4×C151—41no—
98C4×C151—81no—
99Dic151—41no—
100Dic151—41no—
101C2×C151—81no—
102C2×C151#45311yescharacteristic
103C2×C151#45511yescharacteristic
104C2×C151#45511yescharacteristic
105D151—81no—
106D151—81no—
107C151#165911yescharacteristic, complemented, Sylow
108#1659—1511nomaximal, Sylow
109H(3,𝔽4)—1511no—
110#497—1511no—
111#489—1511no—
112#489D15111yescharacteristic, complemented
113#329—1511no—
114#329—1511no—
115#329—1511no—
116C2×Q16—3021no—
117C2×SD16—3021no—
118C4⋊Q8C2×D15111yescharacteristic, complemented
119#124—3021no—
120#124—3021no—
121#124—3021no—
122#124—1511no—
123#124—1511no—
124#124C2×D15111yescharacteristic
125#120—3021no—
126#120—3021no—
127#120—3021no—
128#103—21no—
129#103—3021no—
130#102—21no—
131#102—3021no—
132#97—1511no—
133#97—1511no—
134#97C2×D15111yescharacteristic, complemented
135C24—3021no—
136C2×Q8—21no—
137C2×Q8—1511no—
138C2×Q8—1511no—
139C2×Q8C22⋊D15111yescharacteristic
140C2×D4—3021no—
141C2×D4—3021no—
142C2×D4—3021no—
143C2×D4—1511no—
144C2×D4—1511no—
145C2×D4C22⋊D15111yescharacteristic
146Q16—6042no—
147SD16—6042no—
148C2×C8—21no—
149C2×C8—3021no—
150C2×C8—3021no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—3021no—
156C22⋊C4—3021no—
157C22⋊C4—3021no—
158C22⋊C4—3021no—
159C22⋊C4—3021no—
160C22⋊C4—3021no—
161C22⋊C4—3021no—
162C42—3021no—
163C42C22×D15111yescharacteristic
164C23—21no—
165C23—3021no—
166C23—3021no—
167C23—12081no—
168C23—12081no—
169C23—12081no—
170Q8—41no—
171Q8—41no—
172Q8—41no—
173Q8—6041no—
174Q8—6041no—
175D4—41no—
176D4—6041no—
177D4—6041no—
178D4—12081no—
179D4—12081no—
180D4—12081no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—3021no—
184C2×C4—3021no—
185C2×C4D4×D15111yescharacteristic
186C2×C4D4×D15111yescharacteristic
187C2×C4C2×C22⋊D15111yescharacteristic
188C8—41no—
189C8—3022no—
190C8—6041no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—6041no—
195C22—6041no—
196C22—6041no—
197C22—6041no—
198C22—6041no—
199C22—6041no—
200C22—12084no—
201C22#1801270711yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—81no—
207C4—6041no—
208C4—6041no—
209C2—81no—
210C2—12081no—
211C2—12081no—
212C2#2375237811yescharacteristic
213C2#2375238811yescharacteristic
214C2#2375238911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#489×C151C2
socleC22×C151#120
prime radical#23752954C2
hypercenter#489D151
hypocenterC151#1659
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #23752604C2semidirect
3. #23752574C2semidirect
4. #23751952C2semidirect
5. #23751951C2semidirect
6. #23751951C2semidirect
7. #489×C151C2semidirect
20. #18012650C22semidirect
21. #18012650C22semidirect
22. C4⋊Q8×C151C22semidirect
26. #97×C151C22semidirect
107. C151#1659semidirect
112. #489D151semidirect
118. C4⋊Q8C2×D151semidirect
134. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529542
#237526042
#237525742
#237519522
#237519512
#489×C1512
#1659151