Finite Group Databasebeta

← #34080580

Subgroups — #34080580

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#23752829C212yesmaximal, complemented
2#23752500C212yesmaximal, complemented
3#23752496C212yesmaximal, complemented
4#23752470C211yesmaximal, characteristic, complemented
5#23752439C212yesmaximal, complemented
6#23752433C212yesmaximal, complemented
7#23752425C212yesmaximal, complemented
8#23752240C211yesmaximal, characteristic, complemented
9#469×C151C211yesmaximal, characteristic
10C2×Dic604C2211yescharacteristic
11C2×#14558992C2212yes—
12C22×C151⋊C8C2211yescharacteristic
13#18012738C2212yes—
14#18012732—22no—
15#18012726—22no—
16#18012726C2212yes—
17#18012720—22no—
18#18012718C2212yes—
19#18012716—22no—
20#18012704C2212yes—
21D4×Dic151C2212yes—
22#18012698C2211yescharacteristic
23#18012671C2211yescharacteristic
24#18012670C2212yes—
25Dic151⋊C8C2212yes—
26Dic151⋊C8C2212yes—
27#18012664C2212yes—
28#18012662C2212yes—
29#18012660C2212yes—
30C2×D8×C151C2211yescharacteristic
31C2×M16×C151C2211yescharacteristic
32#121×C151C2212yes—
33#106×C151C2211yescharacteristic
34#102×C151C2212yes—
35C2×Dic302—22no—
36C2×Dic302C2312yes—
37C22×Dic151—22no—
38Dic604—41no—
39#14558992—42no—
40C2×C151⋊C8—41no—
41C2×C151⋊C8C2312yes—
42C4⋊Dic151D412yes—
43C4⋊Dic151C2312yes—
44Dic151⋊C4—22no—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47C22⋊Dic151—22no—
48C22⋊Dic151—22no—
49C22⋊Dic151—22no—
50C22⋊Dic151—22no—
51C22⋊Dic151D411yescharacteristic
52C22⋊Dic151D411yescharacteristic
53C4×Dic151—22no—
54C4×Dic151C2312yes—
55C2×D4×C151—22no—
56C2×D4×C151C2312yes—
57C22×C4×C151C2311yescharacteristic
58D8×C151—41no—
59M16×C151—41no—
60C2×C8×C151C2311yescharacteristic
61C2×C8×C151C2311yescharacteristic
62C4⋊C4×C151C2312yes—
63C22⋊C4×C151—22no—
64Dic302—22no—
65Dic302—22no—
66Dic302—82no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—82no—
70C2×Dic151C2×D412yes—
71C2×Dic151C2×D412yes—
72C151⋊C8—22no—
73C23×C151—22no—
74C23×C151C2×D411yescharacteristic
75D4×C151—22no—
76D4×C151—22no—
77D4×C151—82no—
78C2×C4×C151—21no—
79C2×C4×C151—21no—
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2411yescharacteristic
83C8×C151—21no—
84C8×C151—21no—
85C22×C151—21no—
86C22×C151—22no—
87C22×C151—42no—
88C22×C151—42no—
89C22×C151—42no—
90C22×C151C22×D411yescharacteristic
91C4×C151—21no—
92C4×C151—42no—
93C4×C151H(5,𝔽2)11yescharacteristic
94C4×C1512−1+411yescharacteristic
95Dic151—22no—
96Dic151—22no—
97Dic151—42no—
98Dic151—42no—
99C2×C151—41no—
100C2×C151—82no—
101C2×C151#53711yescharacteristic
102C2×C151#57712yes—
103C151#326311yescharacteristic, complemented, Sylow
104#3263—1511nomaximal, Sylow
105#542—1512no—
106#476—1512no—
107#475—1512no—
108#470—1511no—
109#469D15111yescharacteristic
110#465—1512no—
111#464—1512no—
112#463—1512no—
113#424—1511no—
114C2×Q16—1511no—
115C2×SD16—1512no—
116C2×D8C2×D15111yescharacteristic
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⋊Q8—1512no—
126#121C2×D15112yes—
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#103—1512no—
137#102—1512no—
138#102C2×D15112yes—
139C2×Q8—3022no—
140C2×Q8—1512no—
141C2×D4—22no—
142C2×D4C22×D15112yes—
143C22×C4—3022no—
144C22×C4C22×D15111yescharacteristic
145Q16—6041no—
146SD16—6042no—
147D8—41no—
148M16—41no—
149C2×C8—6041no—
150C2×C8—1512no—
151C2×C8C22×D15111yescharacteristic
152C2×C8C22×D15111yescharacteristic
153C4⋊C4—3022no—
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—22no—
169C23D4×D15111yescharacteristic
170Q8—3022no—
171Q8—3022no—
172Q8—12082no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—3022no—
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—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D15111yescharacteristic
195C4—21no—
196C4—42no—
197C4—3022no—
198C4—3022no—
199C4—6042no—
200C4—6042no—
201C4#1801278411yescharacteristic
202C4#1801278611yescharacteristic
203C2—41no—
204C2—82no—
205C2#2375278911yescharacteristic
206C2#2375302212yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting, prime radical#469×C151C2
socleC22×C151C22×D4
hypercenter#469D151
hypocenterC151#3263
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23752829C2semidirect
2. #23752500C2semidirect
3. #23752496C2semidirect
4. #23752470C2semidirect
5. #23752439C2semidirect
6. #23752433C2semidirect
7. #23752425C2semidirect
8. #23752240C2semidirect
103. C151#3263semidirect

Maximal subgroups

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

subgroupindex
#237528292
#237525002
#237524962
#237524702
#237524392
#237524332
#237524252
#237522402
#469×C1512
#3263151