Finite Group Databasebeta

← #34077148

Subgroups — #34077148

Order 19328.

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

normal subgroups only

This group has 444 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×#18012716C212yesmaximal
2#23752154C212yesmaximal, complemented
3#23752153C212yesmaximal, complemented
4#23752140C212yesmaximal
5#23752137C211yesmaximal, characteristic
6#23752133C212yesmaximal, complemented
7#23752132C212yesmaximal, complemented
8#23752073C211yesmaximal, characteristic
9#397×C151C211yesmaximal, characteristic
10C22×Dic302C2212yes—
11C23×Dic151C2211yescharacteristic
12#18012716—28no—
13C2×C4⋊Dic151C2212yes—
14C2×C4⋊Dic151C2211yescharacteristic
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×C22⋊Dic151C2212yes—
19C2×C22⋊Dic151C2211yescharacteristic
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2212yes—
25C151⋊#95C2211yescharacteristic
26C151⋊#95C2212yes—
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C22⋊C4×C151C2212yes—
29C2×C22⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31#95×C151C2211yescharacteristic
32C2×Dic302—24no—
33C2×Dic302—42no—
34C2×Dic302—42no—
35C22×Dic151—41no—
36C22×Dic151—41no—
37C22×Dic151D414yes—
38C22×Dic151C2312yes—
39C22×Dic151C2312yes—
40C22×Dic151C2312yes—
41C22×Dic151C2312yes—
42C4⋊Dic151—24no—
43C4⋊Dic151—41no—
44Dic151⋊C4—24no—
45Dic151⋊C4—24no—
46Dic151⋊C4—42no—
47C22⋊Dic151—24no—
48C22⋊Dic151—41no—
49C24×C151C2311yescharacteristic
50C22×C4×C151C2312yes—
51C22×C4×C151C2312yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2311yescharacteristic
54C4⋊C4×C151—41no—
55C22⋊C4×C151—24no—
56C22⋊C4×C151—41no—
57Dic302—48no—
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×Dic151—22no—
69C2×Dic151—44no—
70C2×Dic151C2×D414yes—
71C23×C151—21no—
72C23×C151—21no—
73C23×C151—22no—
74C23×C151—22no—
75C23×C151C2×D412yes—
76C23×C151C2411yescharacteristic
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—22no—
80C2×C4×C151—21no—
81C2×C4×C151—22no—
82C2×C4×C151—21no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C22×C151—22no—
88C22×C151—24no—
89C22×C151—41no—
90C22×C151—42no—
91C22×C151—41no—
92C22×C151C22×D411yescharacteristic
93C22×C151H(5,𝔽2)11yescharacteristic
94C22×C151H(5,𝔽2)11yescharacteristic
95C22×C1512−1+412yes—
96C22×C1512−1+412yes—
97C4×C151—42no—
98C4×C151—42no—
99C4×C151—41no—
100C4×C151—41no—
101Dic151—24no—
102Dic151—42no—
103Dic151—42no—
104Dic151—42no—
105C2×C151—42no—
106C2×C151#53411yescharacteristic
107C2×C151#53612yes—
108C2×C151#56311yescharacteristic
109C2×C151#56312yes—
110C2×C151#56311yescharacteristic
111C151#281711yescharacteristic, complemented, Sylow
112#2817—1511nomaximal, Sylow
113C2×C22⋊Q8—1512no—
114#400—1512no—
115#400—1512no—
116#397—1511no—
117#397—1512no—
118#397D15111yescharacteristic
119#395—1512no—
120#395—1512no—
121#381—1511no—
122C22×Q8—1512no—
123C23×C4—1511no—
124C22⋊Q8—3028no—
125C2×C4⋊C4—1512no—
126C2×C4⋊C4—1512no—
127C2×C4⋊C4—1512no—
128C2×C4⋊C4—1512no—
129C2×C4⋊C4—1511no—
130C2×C4⋊C4C2×D15111yescharacteristic
131C2×C22⋊C4—1512no—
132C2×C22⋊C4—1511no—
133C2×C22⋊C4C2×D15112yes—
134C2×C22⋊C4C2×D15111yescharacteristic
135#95—1512no—
136#95—1512no—
137#95—1512no—
138#95—1512no—
139#95—1512no—
140#95—1512no—
141#95—1511no—
142#95C2×D15112yes—
143#95C2×D15111yescharacteristic
144C24C22×D15111yescharacteristic
145C2×Q8—3024no—
146C2×Q8—6042no—
147C2×Q8—6042no—
148C22×C4—6041no—
149C22×C4—6041no—
150C22×C4—1512no—
151C22×C4—1512no—
152C22×C4—1512no—
153C22×C4—1512no—
154C22×C4—1514no—
155C22×C4C22×D15111yescharacteristic
156C22×C4C22×D15111yescharacteristic
157C22×C4C22×D15112yes—
158C22×C4C22×D15112yes—
159C4⋊C4—41no—
160C4⋊C4—3024no—
161C4⋊C4—3024no—
162C4⋊C4—3024no—
163C4⋊C4—6042no—
164C4⋊C4—6041no—
165C22⋊C4—24no—
166C22⋊C4—41no—
167C22⋊C4—3024no—
168C22⋊C4—6041no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23D4×D15112yes—
174C23C23×D15111yescharacteristic
175Q8—6048no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—3022no—
192C2×C4—3022no—
193C2×C4—3022no—
194C2×C4—3022no—
195C2×C4—3022no—
196C2×C4—3022no—
197C2×C4—6044no—
198C2×C4—1514no—
199C22—22no—
200C22—24no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22C2×D4×D15111yescharacteristic
205C22#1801278411yescharacteristic
206C22#1801278511yescharacteristic
207C22#1801278612yes—
208C22#1801278612yes—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—42no—
213C4—3024no—
214C4—6042no—
215C4—6042no—
216C4—6042no—
217C2—42no—
218C2#2375277011yescharacteristic
219C2#2375278412yes—
220C2#2375296211yescharacteristic
221C2#2375296412yes—
222C2#2375296511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#397×C151C2
prime radicalC24×C151C23
hypercenter#397D151
hypocenterC151#2817
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #23752154C2semidirect
3. #23752153C2semidirect
6. #23752133C2semidirect
7. #23752132C2semidirect
111. C151#2817semidirect

Maximal subgroups

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

subgroupindex
C2×#180127162
#237521542
#237521532
#237521402
#237521372
#237521332
#237521322
#237520732
#397×C1512
#2817151