Finite Group Databasebeta

← #34080576

Subgroups — #34080576

Order 19328.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752835C212yesmaximal, complemented
2#23752501C212yesmaximal, complemented
3#23752495C212yesmaximal, complemented
4#23752465C211yesmaximal, characteristic
5#23752443C212yesmaximal, complemented
6#23752436C212yesmaximal, complemented
7#23752430C212yesmaximal, complemented
8#23752240C211yesmaximal, characteristic, complemented
9#470×C151C211yesmaximal, characteristic, complemented
10C2×#14558991C2212yes—
11C2×D1208C2211yescharacteristic
12C22×C151⋊C8C2211yescharacteristic
13#18012738C2212yes—
14#18012734—22no—
15#18012728C2212yes—
16#18012725—22no—
17#18012721—22no—
18#18012719—22no—
19#18012713C2212yes—
20Q8×Dic151C2212yes—
21#18012701C2212yes—
22#18012698C2211yescharacteristic
23#18012671C2211yescharacteristic
24#18012670C2212yes—
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012663C2212yes—
28#18012661C2212yes—
29#18012659C2212yes—
30C2×Q16×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#106×C151C2211yescharacteristic
34#103×C151C2212yes—
35C2×Dic302—22no—
36C2×D604C2312yes—
37C2×C22⋊D151—22no—
38C2×C4×D151—22no—
39#14558991—42no—
40D1208—41no—
41C2×C151⋊C8—41no—
42C2×C151⋊C8C2312yes—
43C4⋊Dic151—22no—
44C4⋊Dic151D412yes—
45C4⋊Dic151C2312yes—
46Dic151⋊C4—22no—
47C22⋊Dic151D411yescharacteristic
48C22⋊Dic151D411yescharacteristic
49(C2×D151)⋊C4—22no—
50(C2×D151)⋊C4—22no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53C4×Dic151—22no—
54C4×Dic151C2312yes—
55C2×Q8×C151C2312yes—
56C22×C4×C151C2311yescharacteristic
57Q16×C151—41no—
58M16×C151—41no—
59C2×C8×C151C2311yescharacteristic
60C2×C8×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64C22×D151—22no—
65Dic302—82no—
66D604—22no—
67D604—22no—
68C22⋊D151—82no—
69C2×Dic151—22no—
70C2×Dic151C2×D412yes—
71C2×Dic151C2×D412yes—
72C4×D151—82no—
73C151⋊C8—22no—
74C23×C151C2×D411yescharacteristic
75Q8×C151—22no—
76Q8×C151—22no—
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2411yescharacteristic
83C8×C151—21no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151C22×D411yescharacteristic
88C2×D151—42no—
89C2×D151—42no—
90C2×D151—42no—
91C4×C151—21no—
92C4×C151—42no—
93C4×C151—42no—
94C4×C151H(5,𝔽2)11yescharacteristic
95C4×C1512−1+411yescharacteristic
96Dic151—22no—
97Dic151—22no—
98Dic151—42no—
99C2×C151—41no—
100C2×C151#53711yescharacteristic
101C2×C151#57712yes—
102D151—82no—
103C151#326311yescharacteristic, complemented, Sylow
104#3263—1511nomaximal, Sylow
105#542—1512no—
106#476—1512no—
107#475—1512no—
108#470D15111yescharacteristic, complemented
109#469—1511no—
110#465—1512no—
111#464—1512no—
112#463—1512no—
113#424—1511no—
114C2×Q16C2×D15111yescharacteristic
115C2×SD16—1512no—
116C2×D8—1511no—
117C2×M16C2×D15111yescharacteristic
118C22×C8—1511no—
119C4⋊Q8—1512no—
120#126—3022no—
121#124—3022no—
122#124—1512no—
123#123—3022no—
124C22⋊Q8—3022no—
125C22⋊Q8C2×D15112yes—
126#121—1512no—
127C4×Q8—1512no—
128C4×D4—1512no—
129#117—1511no—
130#106—1511no—
131#106—1512no—
132#106C2×D15111yescharacteristic
133C4⋊C8—1512no—
134C4⋊C8—1512no—
135#103—1512no—
136#103C2×D15112yes—
137#102—1512no—
138#102—1512no—
139C2×Q8—3022no—
140C2×Q8C22×D15112yes—
141C2×D4—3022no—
142C2×D4—1512no—
143C22×C4—3022no—
144C22×C4C22×D15111yescharacteristic
145Q16—41no—
146SD16—6042no—
147D8—6041no—
148M16—41no—
149C2×C8—6041no—
150C2×C8—1512no—
151C2×C8C22×D15111yescharacteristic
152C2×C8C22×D15111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—3022no—
155C4⋊C4—3022no—
156C4⋊C4—1512no—
157C4⋊C4—1512no—
158C4⋊C4C22×D15112yes—
159C22⋊C4—22no—
160C22⋊C4—3022no—
161C22⋊C4—3022no—
162C22⋊C4—3022no—
163C22⋊C4—3022no—
164C22⋊C4—1511no—
165C22⋊C4—1511no—
166C42—3022no—
167C42—1512no—
168C23—3022no—
169C23D4×D15111yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—12082no—
173D4—3022no—
174D4—3022no—
175D4—12082no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—3022no—
181C2×C4—1512no—
182C2×C4—1512no—
183C2×C4—12082no—
184C2×C4D4×D15111yescharacteristic
185C2×C4C23×D15111yescharacteristic
186C8—21no—
187C8—21no—
188C8—3022no—
189C22—22no—
190C22—21no—
191C22—6042no—
192C22—6042no—
193C22—6042no—
194C22C2×D4×D15111yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—3022no—
199C4—3022no—
200C4—6042no—
201C4#1801278411yescharacteristic
202C4#1801278611yescharacteristic
203C2—41no—
204C2—12082no—
205C2#2375278911yescharacteristic
206C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#470×C151C2
socleC22×C151C22×D4
prime radical#23752465C2
hypercenter#470D151
hypocenterC151#3263
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23752835C2semidirect
2. #23752501C2semidirect
3. #23752495C2semidirect
5. #23752443C2semidirect
6. #23752436C2semidirect
7. #23752430C2semidirect
8. #23752240C2semidirect
9. #470×C151C2semidirect
103. C151#3263semidirect
108. #470D151semidirect

Maximal subgroups

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

subgroupindex
#237528352
#237525012
#237524952
#237524652
#237524432
#237524362
#237524302
#237522402
#470×C1512
#3263151