Finite Group Databasebeta

← #34079507

Subgroups — #34079507

Order 19328.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752761C211yesmaximal, characteristic
2#125×D151C211yesmaximal, characteristic, complemented
3#23752579C212yesmaximal, complemented
4#23752575C212yesmaximal, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752567C211yesmaximal, characteristic, complemented
7#23752566C211yesmaximal, characteristic, complemented
8#23752212C212yesmaximal, complemented
9#23752210C212yesmaximal, complemented
10C4×#14558987C211yesmaximal, characteristic, complemented
11#488×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×#14559003C2211yescharacteristic
14C2×#14558987C2212yes—
15#18012737C2211yescharacteristic
16#18012735C2211yescharacteristic
17#18012731C2211yescharacteristic
18#18012730C2212yes—
19#18012729—22no—
20#18012727C2211yescharacteristic
21#18012712—22no—
22(C22⋊D151)⋊C4—22no—
23C4⋊C4×D151—22no—
24C4⋊C4×D151C2212yes—
25C42×D151C2211yescharacteristic
26#18012664C2212yes—
27#18012663C2212yes—
28#18012662C2212yes—
29#18012661C2212yes—
30#18012660C2212yes—
31#18012659C2212yes—
32#18012649C2212yes—
33C4×C151⋊C8C2211yescharacteristic
34#125×C151C2211yescharacteristic
35#124×C151C2211yescharacteristic
36#103×C151C2212yes—
37#102×C151C2212yes—
38C4×C8×C151C2211yescharacteristic
39#14559005—24no—
40#14559003—24no—
41C2×Dic302C2311yescharacteristic
42C2×D604—21no—
43C2×D604C2311yescharacteristic
44C2×C22⋊D151—21no—
45C2×C22⋊D151—22no—
46C22×Dic151—21no—
47C2×C4×D151—22no—
48C2×C4×D151—21no—
49C2×C4×D151D412yes—
50C2×C4×D151C2311yescharacteristic
51#14558987—24no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—22no—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—22no—
56Dic151⋊C4—22no—
57Dic151⋊C4—22no—
58Dic151⋊C4—22no—
59(C2×D151)⋊C4—22no—
60C4×Dic151D412yes—
61C4×Dic151C2311yescharacteristic
62C2×Q8×C151C2311yescharacteristic
63C2×D4×C151C2311yescharacteristic
64C2×C8×C151C2312yes—
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C42×C151C2311yescharacteristic
69C22×D151—21no—
70C22×D151C2×D411yescharacteristic
71Dic302—22no—
72D604—22no—
73D604—42no—
74C22⋊D151—44no—
75C22⋊D151—42no—
76C2×Dic151—21no—
77C2×Dic151—22no—
78C2×Dic151—42no—
79C2×Dic151C2×D412yes—
80C2×Dic151C2×D411yescharacteristic
81C4×D151—42no—
82C4×D151—44no—
83C4×D151—42no—
84C4×D151#4114yes—
85C151⋊C8—22no—
86C23×C151—21no—
87Q8×C151—22no—
88D4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151C2×D412yes—
92C2×C4×C151C2411yescharacteristic
93C8×C151—22no—
94C22×C151—41no—
95C22×C151—42no—
96C22×C151C22×D411yescharacteristic
97C2×D151—22no—
98C2×D151—41no—
99C2×D151—42no—
100C2×D151#12412yes—
101C4×C151—22no—
102C4×C151—41no—
103C4×C151—42no—
104C4×C151C2×#4112yes—
105Dic151—22no—
106Dic151—41no—
107Dic151—42no—
108Dic151#12412yes—
109C2×C151—81no—
110C2×C151C2×#12411yescharacteristic
111C2×C151#57512yes—
112D151—22no—
113D151—81no—
114C151#314211yescharacteristic, complemented, Sylow
115#3142—1511nomaximal, Sylow
116#532—1511no—
117C2×#125—1511no—
118#491—1512no—
119#490—1512no—
120#488—1511no—
121#488—1511no—
122#488—1511no—
123#488D15111yescharacteristic, complemented
124#417—1512no—
125#417—1512no—
126C4×M16—1511no—
127C2×#41—1511no—
128C2×#41—1511no—
129C2×M16—1512no—
130C4⋊Q8—1511no—
131#127—1511no—
132#125—3022no—
133#125—1512no—
134#125—1511no—
135#125C2×D15111yescharacteristic
136#124—1511no—
137#124C2×D15111yescharacteristic
138#121—3022no—
139C4×D4—3022no—
140C2×C4⋊C4—3022no—
141C2×C4⋊C4—1512no—
142C2×C42—1511no—
143#103—1512no—
144#103—1512no—
145#103—1512no—
146#103C2×D15112yes—
147#102—1512no—
148#102—1512no—
149#102—1512no—
150#102C2×D15112yes—
151#97—1512no—
152C4×C8—1511no—
153C4×C8C2×D15111yescharacteristic
154#41—3024no—
155#41—3024no—
156C2×Q8—1511no—
157C2×Q8C22×D15111yescharacteristic
158C2×D4—3021no—
159C2×D4—3021no—
160C2×D4—3022no—
161C2×D4—1511no—
162C2×D4C22×D15111yescharacteristic
163C22×C4—3022no—
164C22×C4—3021no—
165C22×C4—3021no—
166C22×C4—1512no—
167C22×C4—1511no—
168M16—3024no—
169C2×C8—1512no—
170C2×C8C22×D15112yes—
171C4⋊C4—22no—
172C4⋊C4—3022no—
173C4⋊C4—3022no—
174C4⋊C4—3022no—
175C4⋊C4—3022no—
176C4⋊C4—3022no—
177C4⋊C4—1512no—
178C4⋊C4C22×D15112yes—
179C22⋊C4—22no—
180C22⋊C4—3022no—
181C42—1512no—
182C42—1511no—
183C42C22×D15111yescharacteristic
184C23—21no—
185C23—3021no—
186C23—1511no—
187Q8—22no—
188Q8—3022no—
189D4—22no—
190D4—3022no—
191D4—6042no—
192D4—6044no—
193D4—6042no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—3021no—
197C2×C4—3022no—
198C2×C4—6042no—
199C2×C4—6044no—
200C2×C4—6042no—
201C2×C4—6042no—
202C2×C4—1512no—
203C2×C4—1511no—
204C2×C4—1514no—
205C2×C4D4×D15112yes—
206C2×C4C23×D15111yescharacteristic
207C8—22no—
208C8—3022no—
209C22—41no—
210C22—42no—
211C22—3022no—
212C22—6041no—
213C22—6042no—
214C22—1512no—
215C22C2×D4×D15111yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—3022no—
220C4—6041no—
221C4—6042no—
222C4—1512no—
223C4#41×D15112yes—
224C2—81no—
225C2—3022no—
226C2—12081no—
227C2#124×D15111yescharacteristic
228C2#2375300912yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#488×C151C2
socleC22×C151C22×D4
prime radical#23752761C2
hypercenter#488D151
hypocenterC151#3142
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D151C2semidirect
3. #23752579C2semidirect
4. #23752575C2semidirect
5. #23752569C2semidirect
6. #23752567C2semidirect
7. #23752566C2semidirect
8. #23752212C2semidirect
9. #23752210C2semidirect
10. C4×#14558987C2semidirect
11. #488×C151C2semidirect
114. C151#3142semidirect
123. #488D151semidirect

Maximal subgroups

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

subgroupindex
#237527612
#125×D1512
#237525792
#237525752
#237525692
#237525672
#237525662
#237522122
#237522102
C4×#145589872
#488×C1512
#3142151