Finite Group Databasebeta

← #34077069

Subgroups — #34077069

Order 19328.

392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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#23752146C212yesmaximal
2#23752146C212yesmaximal
3#23752131C212yesmaximal
4#23752118C211yesmaximal, characteristic
5#23752116C212yesmaximal
6#23752110C211yesmaximal, characteristic
7#23752107C212yesmaximal
8#23752097C212yesmaximal
9#391×C151C211yesmaximal, characteristic
10C22×Dic302C2211yescharacteristic
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2211yescharacteristic
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×Dic151⋊C4C2212yes—
19C2×C4×Dic151C2212yes—
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—
31C2×Dic302—41no—
32C2×Dic302—41no—
33C2×Dic302Q814yescomplemented
34C22×Dic151C2312yes—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C4⋊Dic151—41no—
39C4⋊Dic151—41no—
40C4⋊Dic151Q814yescomplemented
41Dic151⋊C4—24no—
42Dic151⋊C4—42no—
43Dic151⋊C4—42no—
44Dic151⋊C4—42no—
45Dic151⋊C4—42no—
46C4×Dic151—42no—
47C2×Q8×C151—22no—
48C2×Q8×C151—41no—
49C2×Q8×C151—41no—
50C22×C4×C151C2312yes—
51C22×C4×C151C2312yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C22×C4×C151C2311yescharacteristic
55C4⋊C4×C151—41no—
56C42×C151—41no—
57Dic302—44no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C2×Dic151—22no—
68C2×Dic151C2×Q814yes—
69C2×Dic151C2×Q814yes—
70C23×C151C2411yescharacteristic
71Q8×C151—44no—
72C2×C4×C151—21no—
73C2×C4×C151—21no—
74C2×C4×C151—21no—
75C2×C4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151C2×Q812yes—
85C2×C4×C151C2×Q812yes—
86C2×C4×C151#4112yes—
87C22×C151C22×Q811yescharacteristic
88C22×C151C22×Q811yescharacteristic
89C22×C151C2×#4111yescharacteristic
90C22×C151H(5,𝔽2)11yescharacteristic
91C22×C151H(5,𝔽2)11yescharacteristic
92C22×C151H(5,𝔽2)11yescharacteristic
93C22×C1512−1+411yescharacteristic
94C4×C151—22no—
95C4×C151—22no—
96C4×C151—22no—
97C4×C151—42no—
98C4×C151—42no—
99Dic151—24no—
100Dic151—24no—
101Dic151—42no—
102Dic151—42no—
103C2×C151#53811yescharacteristic
104C2×C151#54311yescharacteristic
105C2×C151#54411yescharacteristic
106C2×C151#55411yescharacteristic
107C2×C151#55711yescharacteristic
108C2×C151Q8211yescharacteristic
109C2×C151#56211yescharacteristic
110C151#280611yescharacteristic, complemented, Sylow
111#2806—1511nomaximal, Sylow
112#398—1512no—
113#398—1512no—
114#395—1512no—
115#391—1511no—
116#391—1512no—
117#391D15111yescharacteristic
118#389—1512no—
119#389—1511no—
120#387—1512no—
121C22×Q8—1511no—
122C22×Q8C2×D15111yescharacteristic
123C2×C4⋊C4—1512no—
124C2×C4⋊C4—1512no—
125C2×C4⋊C4—1512no—
126C2×C4⋊C4—1512no—
127C2×C4⋊C4—1512no—
128C2×C4⋊C4—1511no—
129C2×C4⋊C4—1511no—
130C2×C4⋊C4—1511no—
131C2×C4⋊C4C2×D15111yescharacteristic
132C2×C42—1512no—
133C2×C42C2×D15111yescharacteristic
134#95—1512no—
135#95—1512no—
136#95—1512no—
137#95—1512no—
138#95—1512no—
139#95—1512no—
140#95C2×D15112yes—
141#95C2×D15112yes—
142C2×Q8—22no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—6041no—
146C2×Q8—6041no—
147C2×Q8—1514no—
148C22×C4—1512no—
149C22×C4—1512no—
150C22×C4—1512no—
151C22×C4—1512no—
152C22×C4C22×D15112yes—
153C22×C4C22×D15112yes—
154C22×C4C22×D15111yescharacteristic
155C22×C4C22×D15111yescharacteristic
156C22×C4C22×D15111yescharacteristic
157C4⋊C4—41no—
158C4⋊C4—3024no—
159C4⋊C4—6042no—
160C4⋊C4—6042no—
161C4⋊C4—6042no—
162C4⋊C4—6042no—
163C4⋊C4—6041no—
164C4⋊C4—6041no—
165C4⋊C4—1514no—
166C42—41no—
167C42—6042no—
168C23C23×D15111yescharacteristic
169Q8—44no—
170Q8—6044no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—3022no—
192C2×C4—3022no—
193C2×C4—1514no—
194C2×C4—1514no—
195C2×C4Q8×D15112yes—
196C2×C4Q8×D15112yes—
197C2×C4#1455900412yes—
198C22C2×Q8×D15111yescharacteristic
199C22C2×Q8×D15111yescharacteristic
200C22C2×#1455900411yescharacteristic
201C22#1801278411yescharacteristic
202C22#1801278411yescharacteristic
203C22#1801278511yescharacteristic
204C22#1801278611yescharacteristic
205C4—22no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—42no—
210C4—3024no—
211C4—3024no—
212C4—6042no—
213C4—6042no—
214C2#2375280011yescharacteristic
215C2#2375283711yescharacteristic
216C2#2375284111yescharacteristic
217C2#2375292211yescharacteristic
218C2#2375294011yescharacteristic
219C2#2375294211yescharacteristic
220C2#2375295611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, prime radical, cosocleC23×C151C24
Fitting#391×C151C2
hypercenter#391D151
hypocenterC151#2806
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
33. C2×Dic302Q8semidirect
40. C4⋊Dic151Q8semidirect
110. C151#2806semidirect

Maximal subgroups

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

subgroupindex
#237521462
#237521312
#237521182
#237521162
#237521102
#237521072
#237520972
#391×C1512
#2806151