Finite Group Databasebeta

← #34077096

Subgroups — #34077096

Order 19328.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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#23752154C212yesmaximal
2#23752146C212yesmaximal
3#23752145C212yesmaximal
4#23752119C211yesmaximal, characteristic
5#23752119C211yesmaximal, characteristic
6#23752109C212yesmaximal
7#23752096C212yesmaximal
8#23752095C212yesmaximal
9#391×C151C211yesmaximal, characteristic
10C2×C4⋊Dic151C2212yes—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2211yescharacteristic
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×C4×Dic151C2211yescharacteristic
18C2×C4×Dic151C2211yescharacteristic
19C151⋊#95C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2212yes—
26C22×Q8×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C42×C151C2211yescharacteristic
29#95×C151C2212yes—
30#95×C151C2212yes—
31C22×Dic151C2312yes—
32C22×Dic151C2312yes—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C4⋊Dic151—24no—
36C4⋊Dic151—41no—
37C4⋊Dic151—41no—
38Dic151⋊C4—24no—
39Dic151⋊C4—24no—
40Dic151⋊C4—42no—
41Dic151⋊C4—42no—
42C4×Dic151—41no—
43C4×Dic151—41no—
44C2×Q8×C151—41no—
45C2×Q8×C151—41no—
46C2×Q8×C151Q814yes—
47C22×C4×C151C2312yes—
48C22×C4×C151C2312yes—
49C22×C4×C151C2311yescharacteristic
50C22×C4×C151C2311yescharacteristic
51C22×C4×C151C2311yescharacteristic
52C4⋊C4×C151—41no—
53C42×C151—41no—
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—24no—
64C2×Dic151#4114yes—
65C23×C151C2411yescharacteristic
66Q8×C151—44no—
67C2×C4×C151—21no—
68C2×C4×C151—21no—
69C2×C4×C151—21no—
70C2×C4×C151—21no—
71C2×C4×C151—21no—
72C2×C4×C151—21no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151C2×Q812yes—
80C2×C4×C151C2×Q812yes—
81C2×C4×C151C2×Q812yes—
82C22×C151C22×Q811yescharacteristic
83C22×C151C2×#4112yes—
84C22×C151H(5,𝔽2)11yescharacteristic
85C22×C151H(5,𝔽2)11yescharacteristic
86C22×C1512−1+412yes—
87C4×C151—22no—
88C4×C151—22no—
89C4×C151—22no—
90C4×C151—42no—
91C4×C151—42no—
92Dic151—24no—
93Dic151—42no—
94Dic151—42no—
95Dic151—42no—
96C2×C151#53912yes—
97C2×C151#54311yescharacteristic
98C2×C151#55511yescharacteristic
99C2×C151#55712yes—
100C2×C151#56311yescharacteristic
101C151#280911yescharacteristic, complemented, Sylow
102#2809—1511nomaximal, Sylow
103#400—1512no—
104#398—1512no—
105#398—1512no—
106#391—1511no—
107#391—1511no—
108#391D15111yescharacteristic
109#389—1512no—
110#387—1512no—
111#387—1512no—
112C22×Q8C2×D15111yescharacteristic
113C2×C4⋊C4—1512no—
114C2×C4⋊C4—1512no—
115C2×C4⋊C4—1512no—
116C2×C4⋊C4—1512no—
117C2×C4⋊C4—1512no—
118C2×C4⋊C4—1511no—
119C2×C4⋊C4—1511no—
120C2×C4⋊C4C2×D15111yescharacteristic
121C2×C42—1511no—
122C2×C42—1511no—
123C2×C42C2×D15111yescharacteristic
124#95—1512no—
125#95—1512no—
126#95—1512no—
127#95—1512no—
128#95—1512no—
129#95—1512no—
130#95—1512no—
131#95C2×D15112yes—
132#95C2×D15112yes—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8Dic30214yes—
136C22×C4—1512no—
137C22×C4—1512no—
138C22×C4—1512no—
139C22×C4—1512no—
140C22×C4C22×D15112yes—
141C22×C4C22×D15112yes—
142C22×C4C22×D15111yescharacteristic
143C22×C4C22×D15111yescharacteristic
144C22×C4C22×D15111yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—3024no—
147C4⋊C4—3024no—
148C4⋊C4—3024no—
149C4⋊C4—6042no—
150C4⋊C4—6042no—
151C4⋊C4—6041no—
152C4⋊C4—6041no—
153C42—41no—
154C42—6041no—
155C42—6041no—
156C23C23×D15111yescharacteristic
157Q8—44no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—3022no—
171C2×C4—3022no—
172C2×C4—3022no—
173C2×C4—3022no—
174C2×C4—3022no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—3022no—
178C2×C4—3024no—
179C2×C4—3022no—
180C2×C4—1514no—
181C2×C4C2×Dic30212yes—
182C2×C4C2×Dic30212yes—
183C2×C4C2×Dic30212yes—
184C22C22×Dic30211yescharacteristic
185C22#41×D15112yes—
186C22#1801278411yescharacteristic
187C22#1801278411yescharacteristic
188C22#1801278712yes—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—3024no—
195C4—6042no—
196C4—6042no—
197C4—6042no—
198C2#2375280812yes—
199C2#2375283811yescharacteristic
200C2#2375292411yescharacteristic
201C2#2375293812yes—
202C2#2375296111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#391×C151C2
hypercenter#391D151
hypocenterC151#2809
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
101. C151#2809semidirect

Maximal subgroups

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

subgroupindex
#237521542
#237521462
#237521452
#237521192
#237521092
#237520962
#237520952
#391×C1512
#2809151