Finite Group Databasebeta

← #34077383

Subgroups — #34077383

Order 19328.

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

normal subgroups only

This group has 356 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#23752153C212yesmaximal
2#23752152C212yesmaximal
3#23752151C211yesmaximal, characteristic
4#23752133C212yesmaximal
5#23752133C212yesmaximal
6#23752132C212yesmaximal
7#23752077C211yesmaximal, characteristic
8#23752076C212yesmaximal
9#400×C151C211yesmaximal, characteristic
10C22×Dic302C2212yes—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×C4×Dic151C2211yescharacteristic
18C151⋊#95C2212yes—
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28#95×C151C2212yes—
29#95×C151C2212yes—
30#95×C151C2211yescharacteristic
31C2×Dic302—42no—
32C2×Dic302—42no—
33C2×Dic302—42no—
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C4⋊Dic151—41no—
39C4⋊Dic151—42no—
40C4⋊Dic151—41no—
41Dic151⋊C4—42no—
42Dic151⋊C4—42no—
43Dic151⋊C4—42no—
44C4×Dic151Q814yescomplemented
45C22×C4×C151C2312yes—
46C22×C4×C151C2312yes—
47C22×C4×C151C2311yescharacteristic
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C4⋊C4×C151—41no—
51C4⋊C4×C151—41no—
52Dic302—48no—
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—22no—
63C2×Dic151—22no—
64C2×Dic151C2×Q814yes—
65C23×C151C2411yescharacteristic
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151—22no—
69C2×C4×C151—22no—
70C2×C4×C151—22no—
71C2×C4×C151—21no—
72C2×C4×C151—22no—
73C2×C4×C151—21no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151C2×Q812yes—
79C22×C151C22×Q811yescharacteristic
80C22×C151H(5,𝔽2)11yescharacteristic
81C22×C151H(5,𝔽2)12yes—
82C22×C1512−1+411yescharacteristic
83C22×C1512−1+412yes—
84C4×C151—22no—
85C4×C151—42no—
86C4×C151—42no—
87C4×C151—41no—
88C4×C151—41no—
89Dic151—24no—
90Dic151—42no—
91Dic151—42no—
92Dic151—42no—
93C2×C151#54411yescharacteristic
94C2×C151#54412yes—
95C2×C151H(3,𝔽4)11yescharacteristic
96C2×C151#56312yes—
97C2×C151#56311yescharacteristic
98C151#284411yescharacteristic, complemented, Sylow
99#2844—1511nomaximal, Sylow
100#400—1511no—
101#400—1512no—
102#400—1512no—
103#400D15111yescharacteristic
104#395—1512no—
105#395—1512no—
106#395—1512no—
107#382—1511no—
108#382—1512no—
109C22×Q8—1512no—
110C2×C4⋊C4—1512no—
111C2×C4⋊C4—1512no—
112C2×C4⋊C4—1512no—
113C2×C4⋊C4—1511no—
114C2×C4⋊C4—1511no—
115C2×C4⋊C4—1512no—
116C2×C4⋊C4C2×D15111yescharacteristic
117C2×C4⋊C4C2×D15111yescharacteristic
118C2×C42—1511no—
119#95—1512no—
120#95—1512no—
121#95—1512no—
122#95—1512no—
123#95—1512no—
124#95—1512no—
125#95—1512no—
126#95—1511no—
127#95C2×D15112yes—
128#95C2×D15112yes—
129#95C2×D15111yescharacteristic
130C2×Q8—6042no—
131C2×Q8—6042no—
132C2×Q8—6042no—
133C22×C4—1512no—
134C22×C4—1512no—
135C22×C4—1512no—
136C22×C4—1512no—
137C22×C4C22×D15111yescharacteristic
138C22×C4C22×D15111yescharacteristic
139C22×C4C22×D15112yes—
140C22×C4C22×D15112yes—
141C22×C4C22×D15111yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—6042no—
145C4⋊C4—6042no—
146C4⋊C4—6042no—
147C4⋊C4—6041no—
148C4⋊C4—6041no—
149C4⋊C4—6042no—
150C42—1514no—
151C23C23×D15111yescharacteristic
152Q8—6048no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—3022no—
166C2×C4—3022no—
167C2×C4—3022no—
168C2×C4—3022no—
169C2×C4—3022no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—3022no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—1514no—
177C2×C4Q8×D15112yes—
178C22C2×Q8×D15111yescharacteristic
179C22#1801278411yescharacteristic
180C22#1801278512yes—
181C22#1801278611yescharacteristic
182C22#1801278612yes—
183C4—22no—
184C4—42no—
185C4—41no—
186C4—41no—
187C4—42no—
188C4—3024no—
189C4—6042no—
190C4—6042no—
191C4—6042no—
192C2#2375284111yescharacteristic
193C2#2375284212yes—
194C2#2375295411yescharacteristic
195C2#2375296412yes—
196C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#400×C151C2
hypercenter#400D151
hypocenterC151#2844
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic151Q8semidirect
98. C151#2844semidirect

Maximal subgroups

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

subgroupindex
#237521532
#237521522
#237521512
#237521332
#237521322
#237520772
#237520762
#400×C1512
#2844151