Finite Group Databasebeta

← #34068099

Subgroups — #34068099

Order 19328.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#23752837C211yesmaximal, characteristic
2#23752542C211yesmaximal, characteristic, complemented
3#23752138C211yesmaximal, characteristic
4#23751950C211yesmaximal, characteristic, complemented
5#23751949C211yesmaximal, characteristic, complemented
6#23751935C211yesmaximal, characteristic
7#483×C151C211yesmaximal, characteristic, complemented
8#18012719—21no—
9#18012718C2211yescharacteristic
10#18012717—21no—
11#18012717—21no—
12#18012716—21no—
13#18012715—21no—
14C2×(C2×D151)⋊C4—21no—
15C2×(C2×D151)⋊C4C2211yescharacteristic
16C22⋊C4×D151—21no—
17#18012670—21no—
18#18012662—21no—
19C22⋊(C151⋊C8)C2211yescharacteristic
20C151⋊#95—21no—
21C151⋊#95C2211yescharacteristic
22C22⋊Q8×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24#106×C151—21no—
25#103×C151—21no—
26C22⋊C8×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28C2×Dic302—21no—
29C2×Dic302D411yescharacteristic
30C22×Dic151—21no—
31C22×Dic151D411yescharacteristic
32C2×C4×D151—21no—
33C2×C4×D151—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—21no—
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40C22⋊Dic151—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—42no—
46C2×Q8×C151D411yescharacteristic
47C22×C4×C151—21no—
48C22×C4×C151C2311yescharacteristic
49C2×C8×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D411yescharacteristic
54C22⋊C4×C151—21no—
55C22×D151—21no—
56C22×D151—21no—
57C22×D151—41no—
58C22×D151—41no—
59C22×D151SD1612yes—
60Dic302—41no—
61Dic302—81no—
62C2×Dic151—21no—
63C2×Dic151—21no—
64C2×Dic151—21no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C2×Dic151—41no—
68C2×Dic151—41no—
69C4×D151—81no—
70C4×D151—81no—
71C151⋊C8—41no—
72C23×C151C2×D411yescharacteristic
73Q8×C151—41no—
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—41no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151—41no—
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C8×C151—41no—
83C22×C151—21no—
84C22×C151—21no—
85C22×C151#12011yescharacteristic
86C22×C151C2×SD1611yescharacteristic
87C22×C151#13711yescharacteristic
88C2×D151—22no—
89C2×D151—41no—
90C2×D151—41no—
91C2×D151—42no—
92C2×D151—81no—
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—41no—
96C4×C151—41no—
97C4×C151—81no—
98Dic151—41no—
99Dic151—41no—
100Dic151—41no—
101Dic151—81no—
102C2×C151—21no—
103C2×C151—21no—
104C2×C151#44811yescharacteristic
105C2×C151#45511yescharacteristic
106C2×C151#45811yescharacteristic
107D151—42no—
108C151#160811yescharacteristic, complemented, Sylow
109#1608—1511nomaximal, Sylow
110#543—1511no—
111#483—1511no—
112#483D15111yescharacteristic, complemented
113#397—1511no—
114#328—1511no—
115#328—1511no—
116#323—1511no—
117C22⋊Q8—3021no—
118C22⋊Q8—3021no—
119C22⋊Q8—3021no—
120C22⋊Q8—3021no—
121C22⋊Q8—3021no—
122C22⋊Q8—1511no—
123C22⋊Q8C2×D15111yescharacteristic
124C2×C4⋊C4C2×D15111yescharacteristic
125C2×C22⋊C4—3021no—
126C2×C22⋊C4—3021no—
127C2×C22⋊C4—1511no—
128#106—21no—
129#106—3021no—
130#103—21no—
131#103—3021no—
132C22⋊C8—1511no—
133C22⋊C8C2×D15111yescharacteristic
134#95—3021no—
135#95—1511no—
136C24—1511no—
137C2×Q8—3021no—
138C2×Q8—1511no—
139C2×Q8C22⋊D15111yescharacteristic
140C22×C4—21no—
141C22×C4—3021no—
142C22×C4—3021no—
143C22×C4—3021no—
144C22×C4—1511no—
145C22×C4C22×D15111yescharacteristic
146C2×C8—21no—
147C2×C8—3021no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—3021no—
152C4⋊C4—3021no—
153C4⋊C4—3021no—
154C4⋊C4—3021no—
155C4⋊C4—1511no—
156C4⋊C4C22⋊D15111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3021no—
159C22⋊C4—3021no—
160C22⋊C4—3021no—
161C22⋊C4—3021no—
162C22⋊C4—3021no—
163C22⋊C4—6042no—
164C23—3021no—
165C23—3021no—
166C23—6041no—
167C23—6041no—
168C23—1512no—
169C23D4×D15111yescharacteristic
170Q8—41no—
171Q8—6041no—
172Q8—12081no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—3021no—
180C2×C4—3021no—
181C2×C4—3021no—
182C2×C4—6041no—
183C2×C4—6041no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4—12081no—
187C2×C4—12081no—
188C2×C4D4×D15111yescharacteristic
189C2×C4C2×C22⋊D15111yescharacteristic
190C8—41no—
191C8—6041no—
192C22—21no—
193C22—21no—
194C22—3022no—
195C22—6042no—
196C22—6041no—
197C22—6041no—
198C22—12081no—
199C22#1801270711yescharacteristic
200C22SD16×D15111yescharacteristic
201C22#1801276811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—6041no—
208C4—6041no—
209C4—6041no—
210C4—12081no—
211C2—21no—
212C2—21no—
213C2—6042no—
214C2#2375234911yescharacteristic
215C2#2375238811yescharacteristic
216C2#2375240111yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#483×C151C2
socleC22×C151#120
prime radicalC23×D151D4
hypercenter#483D151
hypocenterC151#1608
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #23752542C2semidirect
4. #23751950C2semidirect
5. #23751949C2semidirect
7. #483×C151C2semidirect
108. C151#1608semidirect
112. #483D151semidirect

Maximal subgroups

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

subgroupindex
#237528372
#237525422
#237521382
#237519502
#237519492
#237519352
#483×C1512
#1608151