Finite Group Databasebeta

← #34068145

Subgroups — #34068145

Order 19328.

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

normal subgroups only

This group has 246 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#23752789C211yesmaximal, characteristic
2#23752530C211yesmaximal, characteristic, complemented
3#23752150C211yesmaximal, characteristic, complemented
4#23751947C211yesmaximal, characteristic, complemented
5#23751946C211yesmaximal, characteristic, complemented
6#23751937C211yesmaximal, characteristic, complemented
7#481×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9#18012717—21no—
10#18012716—21no—
11#18012713C2211yescharacteristic
12#18012712—21no—
13#18012711—21no—
14#18012711—21no—
15C2×Dic151⋊C4C2211yescharacteristic
16#18012670—21no—
17#18012659—21no—
18C22⋊(C151⋊C8)C2211yescharacteristic
19C151⋊#95—21no—
20C151⋊#95—21no—
21C151⋊#95C2211yescharacteristic
22#121×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24#106×C151—21no—
25#102×C151—21no—
26C22⋊C8×C151C2211yescharacteristic
27#14559003—42no—
28#14559003—42no—
29C2×Dic302—21no—
30C2×D604D411yescharacteristic
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34C22×Dic151—21no—
35C22×Dic151—21no—
36C22×Dic151D411yescharacteristic
37C22×Dic151D411yescharacteristic
38C2×C4×D151—21no—
39C2×C151⋊C8—21no—
40C4⋊Dic151D411yescharacteristic
41Dic151⋊C4—21no—
42Dic151⋊C4—21no—
43Dic151⋊C4—21no—
44C22⋊Dic151—21no—
45(C2×D151)⋊C4—21no—
46(C2×D151)⋊C4—21no—
47C2×D4×C151—21no—
48C2×D4×C151D411yescharacteristic
49C22×C4×C151—21no—
50C22×C4×C151C2311yescharacteristic
51C2×C8×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151D411yescharacteristic
55C22⋊C4×C151—21no—
56C22×D151—21no—
57Dic302—42no—
58D604—41no—
59C22⋊D151—42no—
60C22⋊D151—41no—
61C22⋊D151—41no—
62C22⋊D151—81no—
63C2×Dic151—21no—
64C2×Dic151—21no—
65C2×Dic151—21no—
66C2×Dic151—21no—
67C2×Dic151—42no—
68C2×Dic151—41no—
69C2×Dic151—41no—
70C2×Dic151—41no—
71C2×Dic151—41no—
72C2×Dic151SD1612yes—
73C4×D151—42no—
74C151⋊C8—41no—
75C23×C151—21no—
76C23×C151C2×D411yescharacteristic
77D4×C151—41no—
78D4×C151—41no—
79D4×C151—41no—
80C2×C4×C151—21no—
81C2×C4×C151—41no—
82C2×C4×C151—42no—
83C2×C4×C151—41no—
84C2×C4×C151C2×D411yescharacteristic
85C2×C4×C151C2×D411yescharacteristic
86C8×C151—41no—
87C22×C151—21no—
88C22×C151—21no—
89C22×C151—41no—
90C22×C151—41no—
91C22×C151—41no—
92C22×C151#12011yescharacteristic
93C22×C151C2×SD1611yescharacteristic
94C22×C151AGL(1,ℤ/8)11yescharacteristic
95C2×D151—41no—
96C2×D151—41no—
97C2×D151—41no—
98C4×C151—21no—
99C4×C151—21no—
100C4×C151—41no—
101C4×C151—81no—
102Dic151—22no—
103Dic151—41no—
104Dic151—41no—
105Dic151—81no—
106C2×C151—21no—
107C2×C151—21no—
108C2×C151—81no—
109C2×C151#45011yescharacteristic
110C2×C151#45411yescharacteristic
111C2×C151#45811yescharacteristic
112D151—81no—
113C151#161611yescharacteristic, complemented, Sylow
114#1616—1511nomaximal, Sylow
115#537—1511no—
116#481—1511no—
117#481D15111yescharacteristic, complemented
118#400—1511no—
119#327—1511no—
120#327—1511no—
121#324—1511no—
122C2×#41—3021no—
123C22⋊Q8—3021no—
124C22⋊Q8—3021no—
125#121—3021no—
126#121—3021no—
127#121—3021no—
128#121—1511no—
129#121C2×D15111yescharacteristic
130C2×C4⋊C4—1511no—
131C2×C4⋊C4C2×D15111yescharacteristic
132#106—21no—
133#106—3021no—
134#102—21no—
135#102—3021no—
136C22⋊C8—1511no—
137C22⋊C8C2×D15111yescharacteristic
138#95—3021no—
139#95—3021no—
140#95—1511no—
141#41—6042no—
142#41—6042no—
143C2×Q8—3021no—
144C2×D4—21no—
145C2×D4—3021no—
146C2×D4—3021no—
147C2×D4—3021no—
148C2×D4—1511no—
149C2×D4C22⋊D15111yescharacteristic
150C22×C4—21no—
151C22×C4—3021no—
152C22×C4—3021no—
153C22×C4—3021no—
154C22×C4—1511no—
155C22×C4—1511no—
156C22×C4C22×D15111yescharacteristic
157C2×C8—21no—
158C2×C8—3021no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—3021no—
162C4⋊C4—3021no—
163C4⋊C4—3021no—
164C4⋊C4—1511no—
165C4⋊C4C22⋊D15111yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—3021no—
168C22⋊C4—3021no—
169C22⋊C4—3021no—
170C23—21no—
171C23—3021no—
172C23D4×D15111yescharacteristic
173Q8—6042no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—6041no—
178D4—6042no—
179D4—6041no—
180D4—6041no—
181D4—12081no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—41no—
186C2×C4—3021no—
187C2×C4—3021no—
188C2×C4—3021no—
189C2×C4—3021no—
190C2×C4—6042no—
191C2×C4—6042no—
192C2×C4—6041no—
193C2×C4—6041no—
194C2×C4—6041no—
195C2×C4—6041no—
196C2×C4—1512no—
197C2×C4D4×D15111yescharacteristic
198C2×C4C2×C22⋊D15111yescharacteristic
199C8—41no—
200C8—6041no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—6041no—
207C22—6041no—
208C22—6041no—
209C22#1801270711yescharacteristic
210C22SD16×D15111yescharacteristic
211C22#1801276611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—3022no—
217C4—6041no—
218C4—6041no—
219C4—12081no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—12081no—
224C2#2375236111yescharacteristic
225C2#2375238311yescharacteristic
226C2#2375240111yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#481×C151C2
socleC22×C151#120
prime radical#23752789C2
hypercenter#481D151
hypocenterC151#1616
LCSG ▷ C22×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #23752530C2semidirect
3. #23752150C2semidirect
4. #23751947C2semidirect
5. #23751946C2semidirect
6. #23751937C2semidirect
7. #481×C151C2semidirect
113. C151#1616semidirect
117. #481D151semidirect

Maximal subgroups

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

subgroupindex
#237527892
#237525302
#237521502
#237519472
#237519462
#237519372
#481×C1512
#1616151