Finite Group Databasebeta

← #34080031

Subgroups — #34080031

Order 19328.

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

normal subgroups only

This group has 428 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#23752760C211yesmaximal, characteristic
2C4⋊Q8×D151C211yesmaximal, characteristic, complemented
3#23752584C211yesmaximal, characteristic, complemented
4#23752563C211yesmaximal, characteristic, complemented
5#23752562C211yesmaximal, characteristic, complemented
6#23752415C214yesmaximal, complemented
7#23752349C214yesmaximal, complemented
8#23752263C211yesmaximal, characteristic, complemented
9#492×C151C211yesmaximal, characteristic, complemented
10C2×#14559003—21no—
11C2×Q8×D151C2212yes—
12C2×#14558992C2214yes—
13#18012739C2211yescharacteristic
14#18012739C2211yescharacteristic
15#18012738—21no—
16#18012738—21no—
17#18012737C2212yes—
18#18012726—21no—
19#18012710—21no—
20#18012710C2212yes—
21D4×Dic151—21no—
22D4×Dic151C2212yes—
23C4⋊C4×D151—21no—
24C4⋊C4×D151—21no—
25C42×D151C2211yescharacteristic
26Dic151⋊C8C2212yes—
27#18012664C2214yes—
28#18012663C2214yes—
29(C2×D151)⋊C8C2212yes—
30C4×C151⋊C8C2211yescharacteristic
31C2×SD16×C151C2214yes—
32C4⋊Q8×C151C2211yescharacteristic
33#127×C151C2211yescharacteristic
34C4×C8×C151C2211yescharacteristic
35#14559003—44no—
36C2×Dic302—22no—
37C2×Dic302—21no—
38C2×Dic302C2312yes—
39Q8×D151—44no—
40C2×C22⋊D151—22no—
41C22×Dic151—22no—
42C2×C4×D151—22no—
43C2×C4×D151D411yescharacteristic
44C2×C4×D151D411yescharacteristic
45C2×C4×D151C2311yescharacteristic
46#14558992—44no—
47C2×C151⋊C8C2312yes—
48C4⋊Dic151—21no—
49C4⋊Dic151—21no—
50C4⋊Dic151—21no—
51C4⋊Dic151C2312yes—
52Dic151⋊C4—22no—
53Dic151⋊C4—22no—
54C22⋊Dic151—22no—
55C22⋊Dic151—22no—
56C4×Dic151D411yescharacteristic
57C4×Dic151D411yescharacteristic
58C4×Dic151C2311yescharacteristic
59C2×Q8×C151C2312yes—
60C2×D4×C151—21no—
61C2×D4×C151—21no—
62C2×D4×C151C2312yes—
63SD16×C151—44no—
64C2×C8×C151C2312yes—
65C4⋊C4×C151—21no—
66C4⋊C4×C151—21no—
67C42×C151C2311yescharacteristic
68C22×D151C2×D411yescharacteristic
69Dic302—24no—
70Dic302—44no—
71Dic302—42no—
72C22⋊D151—44no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151—44no—
76C2×Dic151C2×D411yescharacteristic
77C2×Dic151C2×D411yescharacteristic
78C2×Dic151C2×D411yescharacteristic
79C4×D151—22no—
80C4×D151—22no—
81C4×D151—44no—
82C4×D151SD1614yescomplemented
83C151⋊C8—22no—
84C23×C151—22no—
85Q8×C151—24no—
86D4×C151—24no—
87D4×C151—42no—
88D4×C151—42no—
89C2×C4×C151—22no—
90C2×C4×C151C2×D411yescharacteristic
91C2×C4×C151C2×D411yescharacteristic
92C2×C4×C151C2411yescharacteristic
93C8×C151—22no—
94C22×C151—42no—
95C22×C151—42no—
96C22×C151—42no—
97C22×C151C22×D411yescharacteristic
98C2×D151—21no—
99C2×D151—21no—
100C2×D151C2×SD1612yes—
101C4×C151—42no—
102C4×C151C2×SD1612yes—
103C4×C151#13712yes—
104C4×C151H(5,𝔽2)12yes—
105Dic151—21no—
106Dic151—21no—
107Dic151—42no—
108Dic151—42no—
109Dic151C2×SD1612yes—
110C2×C151—82no—
111C2×C151#53511yescharacteristic
112C2×C151C22×SD1611yescharacteristic
113C2×C151C2×#13711yescharacteristic
114D151—22no—
115C151#320611yescharacteristic, complemented, Sylow
116#3206—1511nomaximal, Sylow
117#532—1511no—
118C2×C4⋊Q8—1511no—
119#492—1511no—
120#492D15111yescharacteristic, complemented
121#487—1511no—
122#487—1511no—
123#461—1514no—
124#448—1514no—
125#431—1511no—
126C2×#41—3021no—
127C22×Q8—1512no—
128C2×SD16—1514no—
129C2×SD16C2×D15114yes—
130C4⋊Q8—3021no—
131C4⋊Q8—3021no—
132C4⋊Q8—1512no—
133C4⋊Q8—1511no—
134C4⋊Q8—1511no—
135C4⋊Q8C2×D15111yescharacteristic
136#127C2×D15111yescharacteristic
137#124—3021no—
138#121—3021no—
139#121—1512no—
140C4×D4—3021no—
141C4×D4—1512no—
142C2×C4⋊C4—3021no—
143C2×C4⋊C4—3021no—
144C2×C42—1511no—
145C4⋊C8—1512no—
146#103—1514no—
147#103—1514no—
148C22⋊C8—1512no—
149C4×C8—1511no—
150C4×C8C2×D15111yescharacteristic
151#41—6044no—
152C2×Q8—3022no—
153C2×Q8—3021no—
154C2×Q8—6044no—
155C2×Q8—1512no—
156C2×Q8C22×D15112yes—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—3022no—
160C2×D4C22×D15112yes—
161C22×C4—3022no—
162C22×C4—3022no—
163C22×C4—1511no—
164C22×C4—1511no—
165C22×C4—1511no—
166SD16—44no—
167SD16—6044no—
168C2×C8—1512no—
169C2×C8C22×D15112yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—3022no—
173C4⋊C4—3022no—
174C4⋊C4—3021no—
175C4⋊C4—3021no—
176C4⋊C4—3021no—
177C4⋊C4—1512no—
178C22⋊C4—3022no—
179C22⋊C4—3022no—
180C42—1511no—
181C42—1511no—
182C42—1511no—
183C42C22×D15111yescharacteristic
184C23—22no—
185C23—1511no—
186Q8—24no—
187Q8—3024no—
188Q8—6044no—
189Q8—6042no—
190D4—24no—
191D4—42no—
192D4—42no—
193D4—6044no—
194C2×C4—22no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—6044no—
200C2×C4—6044no—
201C2×C4—1511no—
202C2×C4—1511no—
203C2×C4—1511no—
204C2×C4—1514no—
205C2×C4D4×D15111yescharacteristic
206C2×C4D4×D15111yescharacteristic
207C2×C4C23×D15111yescharacteristic
208C8—22no—
209C8—3022no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—3021no—
214C22—3021no—
215C22—1512no—
216C22C2×D4×D15111yescharacteristic
217C4—42no—
218C4—3021no—
219C4—3021no—
220C4—6042no—
221C4—6042no—
222C4—1512no—
223C4SD16×D15112yes—
224C4#1801276812yes—
225C4#1801278412yes—
226C2—82no—
227C2—3022no—
228C2#2375277511yescharacteristic
229C2C2×SD16×D15111yescharacteristic
230C2C2×#1801276811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#492×C151C2
socleC22×C151C22×D4
prime radical#23752760C2
hypercenter#492D151
hypocenterC151#3206
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D151C2semidirect
3. #23752584C2semidirect
4. #23752563C2semidirect
5. #23752562C2semidirect
6. #23752415C2semidirect
7. #23752349C2semidirect
8. #23752263C2semidirect
9. #492×C151C2semidirect
82. C4×D151SD16semidirect
115. C151#3206semidirect
120. #492D151semidirect

Maximal subgroups

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

subgroupindex
#237527602
C4⋊Q8×D1512
#237525842
#237525632
#237525622
#237524152
#237523492
#237522632
#492×C1512
#3206151