Finite Group Databasebeta

← #34077176

Subgroups — #34077176

Order 19328.

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

normal subgroups only

This group has 380 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
1C2×#18012729C212yesmaximal
2#23752154C212yesmaximal
3#23752153C212yesmaximal
4#23752146C212yesmaximal
5#23752145C212yesmaximal
6#23752145C212yesmaximal
7#23752142C211yesmaximal, characteristic
8#23752077C211yesmaximal, characteristic
9#398×C151C211yesmaximal, characteristic
10#18012729—28no—
11C2×C4⋊Dic151C2212yes—
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×Dic151⋊C4C2212yes—
19C2×C4×Dic151C2211yescharacteristic
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2211yescharacteristic
24C151⋊#95C2212yes—
25C151⋊#95C2212yes—
26C151⋊#95C2212yes—
27C2×C4⋊C4×C151C2212yes—
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31#95×C151C2211yescharacteristic
32C22×Dic151C2312yes—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C4⋊Dic151—24no—
37C4⋊Dic151—41no—
38C4⋊Dic151—41no—
39Dic151⋊C4—24no—
40Dic151⋊C4—24no—
41Dic151⋊C4—24no—
42Dic151⋊C4—24no—
43Dic151⋊C4—42no—
44C4×Dic151D414yes—
45C22×C4×C151C2312yes—
46C22×C4×C151C2312yes—
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—24no—
51C4⋊C4×C151—41no—
52C4⋊C4×C151—41no—
53C2×Dic151—22no—
54C2×Dic151—22no—
55C2×Dic151—22no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—24no—
63C2×Dic151C2×D414yes—
64C23×C151C2411yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—22no—
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151—21no—
71C2×C4×C151—21no—
72C2×C4×C151—22no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151C2×D412yes—
78C22×C151C22×D411yescharacteristic
79C22×C151H(5,𝔽2)11yescharacteristic
80C22×C1512−1+412yes—
81C22×C1512−1+411yescharacteristic
82C22×C1512−1+412yes—
83C4×C151—22no—
84C4×C151—42no—
85C4×C151—42no—
86C4×C151—41no—
87C4×C151—41no—
88Dic151—24no—
89Dic151—42no—
90Dic151—42no—
91Dic151—42no—
92C2×C151#53612yes—
93C2×C151#53711yescharacteristic
94C2×C151#56311yescharacteristic
95C2×C151#56311yescharacteristic
96C2×C151#56412yes—
97C151#282211yescharacteristic, complemented, Sylow
98#2822—1511nomaximal, Sylow
99C2×#125—1512no—
100#400—1512no—
101#400—1512no—
102#398—1511no—
103#398—1512no—
104#398—1512no—
105#398—1512no—
106#398D15111yescharacteristic
107#382—1511no—
108#125—3028no—
109C2×C4⋊C4—1512no—
110C2×C4⋊C4—1512no—
111C2×C4⋊C4—1512no—
112C2×C4⋊C4—1512no—
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1512no—
115C2×C4⋊C4—1511no—
116C2×C4⋊C4—1511no—
117C2×C4⋊C4C2×D15112yes—
118C2×C4⋊C4C2×D15111yescharacteristic
119C2×C4⋊C4C2×D15111yescharacteristic
120C2×C42—1511no—
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1512no—
125#95—1512no—
126#95—1512no—
127#95—1511no—
128#95C2×D15112yes—
129#95C2×D15111yescharacteristic
130C22×C4—1512no—
131C22×C4—1512no—
132C22×C4—1512no—
133C22×C4—1512no—
134C22×C4C22×D15111yescharacteristic
135C22×C4C22×D15111yescharacteristic
136C22×C4C22×D15112yes—
137C22×C4C22×D15112yes—
138C22×C4C22×D15111yescharacteristic
139C4⋊C4—24no—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—3024no—
143C4⋊C4—3024no—
144C4⋊C4—3024no—
145C4⋊C4—3024no—
146C4⋊C4—3024no—
147C4⋊C4—6042no—
148C4⋊C4—6041no—
149C4⋊C4—6041no—
150C42—1514no—
151C23C23×D15111yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—3022no—
165C2×C4—3022no—
166C2×C4—3022no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4—3022no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—3024no—
173C2×C4—3022no—
174C2×C4—1514no—
175C2×C4D4×D15112yes—
176C22C2×D4×D15111yescharacteristic
177C22#1801278411yescharacteristic
178C22#1801278612yes—
179C22#1801278611yescharacteristic
180C22#1801278712yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—3024no—
187C4—6042no—
188C4—6042no—
189C4—6042no—
190C2#2375278512yes—
191C2#2375278911yescharacteristic
192C2#2375296111yescharacteristic
193C2#2375296511yescharacteristic
194C2C151⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#398×C151C2
hypercenter#398D151
hypocenterC151#2822
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
97. C151#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180127292
#237521542
#237521532
#237521462
#237521452
#237521422
#237520772
#398×C1512
#2822151