Finite Group Databasebeta

← #34079505

Subgroups — #34079505

Order 19328.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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#23752763C211yesmaximal, characteristic
2C4⋊Q8×D151C211yesmaximal, characteristic, complemented
3#23752573C214yesmaximal, complemented
4#23752562C211yesmaximal, characteristic, complemented
5#23752560C211yesmaximal, characteristic, complemented
6#23752559C211yesmaximal, characteristic, complemented
7#23752212C214yesmaximal, complemented
8C4×#14558987C211yesmaximal, characteristic, complemented
9#487×C151C211yesmaximal, characteristic, complemented
10C2×#14559005C2212yes—
11C2×Q8×D151—21no—
12C2×#14558987C2212yes—
13#18012739C2211yescharacteristic
14#18012738—21no—
15#18012738C2212yes—
16#18012737—21no—
17#18012736C2211yescharacteristic
18#18012728C2212yes—
19#18012714—21no—
20#18012714—21no—
21#18012701—21no—
22#18012701—21no—
23C4⋊C4×D151—21no—
24C4⋊C4×D151C2212yes—
25C42×D151C2211yescharacteristic
26#18012663C2214yes—
27#18012661C2214yes—
28#18012659C2214yes—
29#18012649C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C4⋊Q8×C151C2211yescharacteristic
32C4⋊Q8×C151C2211yescharacteristic
33#103×C151C2214yes—
34C4×C8×C151C2211yescharacteristic
35#14559005—28no—
36C2×Dic302—22no—
37C2×Dic302—21no—
38Q8×D151—44no—
39C2×D604—22no—
40C2×D604—21no—
41C2×D604—21no—
42C2×D604C2312yes—
43C2×C4×D151—22no—
44C2×C4×D151—22no—
45C2×C4×D151D411yescharacteristic
46C2×C4×D151D411yescharacteristic
47C2×C4×D151C2311yescharacteristic
48#14558987—24no—
49C2×C151⋊C8C2312yes—
50C4⋊Dic151—21no—
51C4⋊Dic151C2312yes—
52Dic151⋊C4—22no—
53Dic151⋊C4—22no—
54(C2×D151)⋊C4—22no—
55(C2×D151)⋊C4—22no—
56C4×Dic151D411yescharacteristic
57C4×Dic151D411yescharacteristic
58C4×Dic151C2311yescharacteristic
59C2×Q8×C151—21no—
60C2×Q8×C151C2312yes—
61C2×C8×C151C2312yes—
62C4⋊C4×C151—21no—
63C4⋊C4×C151—21no—
64C4⋊C4×C151—21no—
65C4⋊C4×C151C2312yes—
66C42×C151C2311yescharacteristic
67C22×D151—22no—
68C22×D151C2×D411yescharacteristic
69Dic302—44no—
70Dic302—42no—
71D604—24no—
72D604—44no—
73D604—42no—
74D604—42no—
75C2×Dic151—22no—
76C2×Dic151C2×D411yescharacteristic
77C2×Dic151C2×D411yescharacteristic
78C2×Dic151C2×D411yescharacteristic
79C4×D151—22no—
80C4×D151—22no—
81C4×D151—44no—
82C4×D151—44no—
83C4×D151#4114yes—
84C151⋊C8—22no—
85Q8×C151—24no—
86Q8×C151—42no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151C2×D411yescharacteristic
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2411yescharacteristic
92C8×C151—22no—
93C22×C151C22×D411yescharacteristic
94C2×D151—21no—
95C2×D151—21no—
96C2×D151—42no—
97C2×D151—42no—
98C2×D151—42no—
99C2×D151#12412yes—
100C4×C151—42no—
101C4×C151—42no—
102C4×C151AGL(1,ℤ/8)12yes—
103C4×C151#13712yes—
104C4×C151C2×#4112yes—
105Dic151—21no—
106Dic151—21no—
107Dic151—42no—
108Dic151#12412yes—
109C2×C151C2×#12411yescharacteristic
110C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C151C2×#13711yescharacteristic
112D151—22no—
113D151—82no—
114C151#314111yescharacteristic, complemented, Sylow
115#3141—1511nomaximal, Sylow
116#532—1511no—
117C2×C4⋊Q8—1511no—
118#489—1514no—
119#487—1511no—
120#487D15111yescharacteristic, complemented
121#486—1511no—
122#486—1511no—
123#417—1514no—
124C4×M16—1511no—
125C2×#41—1512no—
126C22×Q8—3021no—
127C2×M16—1512no—
128C4⋊Q8—3021no—
129C4⋊Q8—3021no—
130C4⋊Q8—1512no—
131C4⋊Q8—1511no—
132C4⋊Q8C2×D15111yescharacteristic
133C4⋊Q8C2×D15111yescharacteristic
134#127—1511no—
135#124—1512no—
136#121—3021no—
137#121—3021no—
138C4×D4—3021no—
139C4×D4—3021no—
140C2×C4⋊C4—3021no—
141C2×C4⋊C4—1512no—
142C2×C42—1511no—
143#103—1514no—
144#103C2×D15114yes—
145#102—1514no—
146#102—1514no—
147#97—1512no—
148C4×C8—1511no—
149C4×C8C2×D15111yescharacteristic
150#41—3028no—
151C2×Q8—21no—
152C2×Q8—3022no—
153C2×Q8—3021no—
154C2×Q8—6044no—
155C2×Q8C22×D15112yes—
156C2×D4—3022no—
157C2×D4—3021no—
158C2×D4—3021no—
159C2×D4—1512no—
160C22×C4—3022no—
161C22×C4—3022no—
162C22×C4—1511no—
163C22×C4—1511no—
164C22×C4—1511no—
165M16—3024no—
166C2×C8—1512no—
167C2×C8C22×D15112yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—3022no—
172C4⋊C4—3022no—
173C4⋊C4—3021no—
174C4⋊C4—1512no—
175C4⋊C4C22×D15112yes—
176C22⋊C4—3022no—
177C22⋊C4—3022no—
178C42—1511no—
179C42—1511no—
180C42—1511no—
181C42C22×D15111yescharacteristic
182C23—3022no—
183C23—1511no—
184Q8—24no—
185Q8—42no—
186Q8—6044no—
187Q8—6042no—
188D4—3024no—
189D4—6044no—
190D4—6042no—
191D4—6042no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—6044no—
198C2×C4—6044no—
199C2×C4—1511no—
200C2×C4—1511no—
201C2×C4—1511no—
202C2×C4—1514no—
203C2×C4D4×D15111yescharacteristic
204C2×C4D4×D15111yescharacteristic
205C2×C4C23×D15111yescharacteristic
206C8—22no—
207C8—3022no—
208C22—3021no—
209C22—3021no—
210C22—6042no—
211C22—6042no—
212C22—6042no—
213C22—1512no—
214C22C2×D4×D15111yescharacteristic
215C4—42no—
216C4—42no—
217C4—3021no—
218C4—3021no—
219C4—6042no—
220C4—1512no—
221C4#1801276612yes—
222C4#1801277112yes—
223C4#41×D15112yes—
224C2—3022no—
225C2—12082no—
226C2#124×D15111yescharacteristic
227C2C2×#1801276611yescharacteristic
228C2C2×#1801277111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#487×C151C2
socleC22×C151C22×D4
prime radical#23752763C2
hypercenter#487D151
hypocenterC151#3141
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D151C2semidirect
3. #23752573C2semidirect
4. #23752562C2semidirect
5. #23752560C2semidirect
6. #23752559C2semidirect
7. #23752212C2semidirect
8. C4×#14558987C2semidirect
9. #487×C151C2semidirect
114. C151#3141semidirect
120. #487D151semidirect

Maximal subgroups

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

subgroupindex
#237527632
C4⋊Q8×D1512
#237525732
#237525622
#237525602
#237525592
#237522122
C4×#145589872
#487×C1512
#3141151