Finite Group Databasebeta

← #34077185

Subgroups — #34077185

Order 19328.

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

normal subgroups only

This group has 456 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×#18012734C212yesmaximal, complemented
2#23752146C212yesmaximal, complemented
3#23752136C212yesmaximal, complemented
4#23752134C212yesmaximal, complemented
5#23752134C212yesmaximal, complemented
6#23752130C212yesmaximal
7#23752129C211yesmaximal, characteristic
8#23752081C211yesmaximal, characteristic, complemented
9#398×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11#18012734—28no—
12C2×C4⋊Dic151C2212yes—
13C2×C4⋊Dic151C2211yescharacteristic
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×Dic151⋊C4C2212yes—
18C2×(C2×D151)⋊C4C2212yes—
19C2×(C2×D151)⋊C4C2212yes—
20C2×(C2×D151)⋊C4C2212yes—
21C2×(C2×D151)⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2212yes—
23C2×(C2×D151)⋊C4C2212yes—
24C2×C4×Dic151C2211yescharacteristic
25C151⋊#95C2211yescharacteristic
26C151⋊#95C2212yes—
27C2×C4⋊C4×C151C2212yes—
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31#95×C151C2211yescharacteristic
32C23×D151C2312yes—
33C2×D604—42no—
34C2×D604—41no—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2312yes—
38C4⋊Dic151—24no—
39C4⋊Dic151—41no—
40Dic151⋊C4—24no—
41Dic151⋊C4—42no—
42Dic151⋊C4—42no—
43Dic151⋊C4—42no—
44(C2×D151)⋊C4—24no—
45(C2×D151)⋊C4—24no—
46(C2×D151)⋊C4—24no—
47(C2×D151)⋊C4—42no—
48(C2×D151)⋊C4—42no—
49(C2×D151)⋊C4—42no—
50C4×Dic151D414yescomplemented
51C22×C4×C151C2312yes—
52C22×C4×C151C2311yescharacteristic
53C22×C4×C151C2312yes—
54C22×C4×C151C2311yescharacteristic
55C22×C4×C151C2311yescharacteristic
56C4⋊C4×C151—24no—
57C4⋊C4×C151—41no—
58C4⋊C4×C151—41no—
59C22×D151—22no—
60C22×D151—22no—
61C22×D151—22no—
62C22×D151—22no—
63C22×D151—22no—
64C22×D151—22no—
65C22×D151—22no—
66D604—44no—
67C2×Dic151—22no—
68C2×Dic151—22no—
69C2×Dic151—22no—
70C2×Dic151—22no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—22no—
75C2×Dic151C2×D414yes—
76C23×C151C2411yescharacteristic
77C2×C4×C151—21no—
78C2×C4×C151—21no—
79C2×C4×C151—22no—
80C2×C4×C151—22no—
81C2×C4×C151—22no—
82C2×C4×C151—22no—
83C2×C4×C151—22no—
84C2×C4×C151—22no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151C2×D412yes—
90C22×C151C22×D411yescharacteristic
91C22×C151H(5,𝔽2)11yescharacteristic
92C22×C151H(5,𝔽2)12yes—
93C22×C1512−1+411yescharacteristic
94C22×C1512−1+412yes—
95C2×D151—42no—
96C2×D151—42no—
97C2×D151—42no—
98C2×D151—42no—
99C2×D151—42no—
100C2×D151—42no—
101C2×D151—42no—
102C4×C151—22no—
103C4×C151—42no—
104C4×C151—42no—
105C4×C151—41no—
106C4×C151—41no—
107Dic151—24no—
108Dic151—42no—
109Dic151—42no—
110C2×C151#53711yescharacteristic
111C2×C151#53712yes—
112C2×C151#56011yescharacteristic
113C2×C151#56311yescharacteristic
114C2×C151#56312yes—
115D151—82no—
116C151#282311yescharacteristic, complemented, Sylow
117#2823—1511nomaximal, Sylow
118C2×#126—1512no—
119#398—1512no—
120#398D15111yescharacteristic, complemented
121#396—1512no—
122#396—1512no—
123#396—1512no—
124#394—1511no—
125#394—1512no—
126#384—1511no—
127C22×D4—1511no—
128#126—3028no—
129C2×C4⋊C4—1512no—
130C2×C4⋊C4—1512no—
131C2×C4⋊C4—1512no—
132C2×C4⋊C4—1512no—
133C2×C4⋊C4—1512no—
134C2×C4⋊C4—1511no—
135C2×C4⋊C4C2×D15112yes—
136C2×C4⋊C4C2×D15111yescharacteristic
137C2×C4⋊C4C2×D15111yescharacteristic
138C2×C22⋊C4—1512no—
139C2×C22⋊C4—1512no—
140C2×C22⋊C4—1512no—
141C2×C22⋊C4—1512no—
142C2×C22⋊C4—1512no—
143C2×C22⋊C4—1512no—
144C2×C42—1511no—
145#95—1511no—
146#95—1512no—
147#95C2×D15112yes—
148#95C2×D15111yescharacteristic
149C24—1512no—
150C2×D4—6041no—
151C2×D4—6042no—
152C22×C4—1512no—
153C22×C4—1512no—
154C22×C4—1512no—
155C22×C4C22×D15111yescharacteristic
156C22×C4C22×D15112yes—
157C22×C4C22×D15112yes—
158C22×C4C22×D15111yescharacteristic
159C22×C4C22×D15111yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—3024no—
164C4⋊C4—3024no—
165C4⋊C4—6042no—
166C4⋊C4—6042no—
167C4⋊C4—6042no—
168C4⋊C4—6041no—
169C22⋊C4—3024no—
170C22⋊C4—3024no—
171C22⋊C4—3024no—
172C22⋊C4—6042no—
173C22⋊C4—6042no—
174C22⋊C4—6042no—
175C42—1514no—
176C23—3022no—
177C23—3022no—
178C23—3022no—
179C23—3022no—
180C23—3022no—
181C23—3022no—
182C23—3022no—
183C23C23×D15111yescharacteristic
184D4—6044no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—3022no—
198C2×C4—3022no—
199C2×C4—3022no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—1514no—
206C2×C4D4×D15112yes—
207C22—6042no—
208C22—6042no—
209C22—6042no—
210C22—6042no—
211C22—6042no—
212C22—6042no—
213C22—6042no—
214C22C2×D4×D15111yescharacteristic
215C22#1801278411yescharacteristic
216C22#1801278512yes—
217C22#1801278611yescharacteristic
218C22#1801278712yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—3024no—
225C4—6042no—
226C4—6042no—
227C2—12082no—
228C2#2375278911yescharacteristic
229C2#2375279212yes—
230C2#2375295211yescharacteristic
231C2#2375296111yescharacteristic
232C2#2375296612yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#398×C151C2
prime radicalC22×D604C22
hypercenter#398D151
hypocenterC151#2823
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#18012734C2semidirect
2. #23752146C2semidirect
3. #23752136C2semidirect
4. #23752134C2semidirect
5. #23752134C2semidirect
8. #23752081C2semidirect
9. #398×C151C2semidirect
50. C4×Dic151D4semidirect
116. C151#2823semidirect
120. #398D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127342
#237521462
#237521362
#237521342
#237521302
#237521292
#237520812
#398×C1512
#2823151