Finite Group Databasebeta

← #34077165

Subgroups — #34077165

Order 19328.

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

normal subgroups only

This group has 464 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×#18012729C211yesmaximal, characteristic, complemented
2C2×#18012728C211yesmaximal, characteristic
3#23752147C212yesmaximal, complemented
4#23752141C212yesmaximal, complemented
5#23752136C212yesmaximal, complemented
6#23752134C212yesmaximal, complemented
7#23752131C211yesmaximal, characteristic, complemented
8#23752130C211yesmaximal, characteristic
9#23752129C211yesmaximal, characteristic
10#23752076C211yesmaximal, characteristic, complemented
11#395×C151C211yesmaximal, characteristic, complemented
12C22×D604C2211yescharacteristic
13#18012729—24no—
14#18012728—24no—
15C2×C4⋊Dic151C2211yescharacteristic
16C2×Dic151⋊C4C2211yescharacteristic
17C2×Dic151⋊C4C2211yescharacteristic
18C2×Dic151⋊C4C2211yescharacteristic
19C2×Dic151⋊C4C2211yescharacteristic
20C2×Dic151⋊C4C2212yes—
21C2×Dic151⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2212yes—
23C2×(C2×D151)⋊C4C2212yes—
24C2×(C2×D151)⋊C4C2212yes—
25C2×(C2×D151)⋊C4C2212yes—
26C2×(C2×D151)⋊C4C2212yes—
27C2×(C2×D151)⋊C4C2212yes—
28C2×C4×Dic151C2211yescharacteristic
29C151⋊#95C2211yescharacteristic
30C151⋊#95C2212yes—
31C151⋊#95C2212yes—
32C22×Q8×C151C2211yescharacteristic
33C2×C4⋊C4×C151C2211yescharacteristic
34C2×C4⋊C4×C151C2212yes—
35#95×C151C2211yescharacteristic
36#95×C151C2212yes—
37C23×D151C2312yes—
38C2×D604—22no—
39C2×D604—42no—
40C22×Dic151C2311yescharacteristic
41C22×Dic151C2311yescharacteristic
42C22×Dic151C2312yes—
43C22×Dic151C2311yescharacteristic
44C22×Dic151C2311yescharacteristic
45C4⋊Dic151—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48Dic151⋊C4—22no—
49Dic151⋊C4—22no—
50Dic151⋊C4—42no—
51Dic151⋊C4—42no—
52(C2×D151)⋊C4—24no—
53(C2×D151)⋊C4—24no—
54(C2×D151)⋊C4—42no—
55(C2×D151)⋊C4—42no—
56(C2×D151)⋊C4—42no—
57(C2×D151)⋊C4—42no—
58C4×Dic151D414yes—
59C2×Q8×C151—22no—
60C2×Q8×C151—42no—
61C22×C4×C151C2311yescharacteristic
62C22×C4×C151C2311yescharacteristic
63C22×C4×C151C2312yes—
64C22×C4×C151C2312yes—
65C22×C4×C151C2311yescharacteristic
66C4⋊C4×C151—22no—
67C4⋊C4×C151—42no—
68C22×D151—22no—
69C22×D151—22no—
70C22×D151—22no—
71C22×D151—22no—
72C22×D151—22no—
73C22×D151—22no—
74C22×D151—22no—
75D604—44no—
76C2×Dic151—21no—
77C2×Dic151—22no—
78C2×Dic151—21no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—22no—
83C2×Dic151—22no—
84C2×Dic151—22no—
85C2×Dic151—21no—
86C2×Dic151—22no—
87C2×Dic151C2×D412yes—
88C2×Dic151C2×D412yes—
89C23×C151C2411yescharacteristic
90Q8×C151—44no—
91C2×C4×C151—22no—
92C2×C4×C151—22no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—21no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—22no—
103C2×C4×C151C2×D412yes—
104C22×C151C22×D411yescharacteristic
105C22×C151H(5,𝔽2)12yes—
106C22×C151H(5,𝔽2)11yescharacteristic
107C22×C1512−1+412yes—
108C22×C1512−1+411yescharacteristic
109C2×D151—42no—
110C2×D151—42no—
111C2×D151—42no—
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—42no—
115C2×D151—42no—
116C4×C151—22no—
117C4×C151—41no—
118C4×C151—42no—
119C4×C151—41no—
120C4×C151—42no—
121Dic151—22no—
122Dic151—22no—
123Dic151—41no—
124Dic151—41no—
125Dic151—42no—
126C2×C151#53511yescharacteristic
127C2×C151#53611yescharacteristic
128C2×C151#53711yescharacteristic
129C2×C151#56212yes—
130C2×C151#56312yes—
131D151—82no—
132C151#282011yescharacteristic, complemented, Sylow
133#2820—1511nomaximal, Sylow
134C2×#125—1511no—
135C2×#124—1511no—
136#399—1512no—
137#397—1512no—
138#396—1512no—
139#396—1512no—
140#395—1511no—
141#395D15111yescharacteristic, complemented
142#394—1511no—
143#394—1511no—
144#382—1511no—
145C22×Q8C2×D15111yescharacteristic
146C22×D4—1511no—
147#125—3024no—
148#124—3024no—
149C2×C4⋊C4—1511no—
150C2×C4⋊C4—1511no—
151C2×C4⋊C4—1511no—
152C2×C4⋊C4—1511no—
153C2×C4⋊C4—1511no—
154C2×C4⋊C4—1512no—
155C2×C4⋊C4—1512no—
156C2×C4⋊C4C2×D15111yescharacteristic
157C2×C4⋊C4C2×D15112yes—
158C2×C22⋊C4—1512no—
159C2×C22⋊C4—1512no—
160C2×C22⋊C4—1512no—
161C2×C22⋊C4—1512no—
162C2×C22⋊C4—1512no—
163C2×C22⋊C4—1512no—
164C2×C42—1511no—
165#95—1511no—
166#95—1512no—
167#95—1512no—
168#95C2×D15111yescharacteristic
169#95C2×D15112yes—
170C24—1512no—
171C2×Q8—22no—
172C2×Q8—42no—
173C2×D4—3022no—
174C2×D4—6042no—
175C22×C4—1512no—
176C22×C4—1511no—
177C22×C4—1511no—
178C22×C4—1511no—
179C22×C4—1511no—
180C22×C4C22×D15112yes—
181C22×C4C22×D15112yes—
182C22×C4C22×D15111yescharacteristic
183C22×C4C22×D15111yescharacteristic
184C22×C4C22×D15111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—3022no—
188C4⋊C4—3022no—
189C4⋊C4—3022no—
190C4⋊C4—3022no—
191C4⋊C4—3022no—
192C4⋊C4—6042no—
193C4⋊C4—6042no—
194C22⋊C4—3024no—
195C22⋊C4—3024no—
196C22⋊C4—6042no—
197C22⋊C4—6042no—
198C22⋊C4—6042no—
199C22⋊C4—6042no—
200C42—1514no—
201C23—3022no—
202C23—3022no—
203C23—3022no—
204C23—3022no—
205C23—3022no—
206C23—3022no—
207C23—3022no—
208C23C23×D15111yescharacteristic
209Q8—44no—
210D4—6044no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—3021no—
224C2×C4—3022no—
225C2×C4—3021no—
226C2×C4—3021no—
227C2×C4—3021no—
228C2×C4—3022no—
229C2×C4—3022no—
230C2×C4—3021no—
231C2×C4—3022no—
232C2×C4—3021no—
233C2×C4—3022no—
234C2×C4—1512no—
235C2×C4—1512no—
236C2×C4D4×D15112yes—
237C22—6042no—
238C22—6042no—
239C22—6042no—
240C22—6042no—
241C22—6042no—
242C22—6042no—
243C22—6042no—
244C22C2×D4×D15111yescharacteristic
245C22#1801278412yes—
246C22#1801278511yescharacteristic
247C22#1801278711yescharacteristic
248C22#1801278712yes—
249C4—22no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—3022no—
255C4—3022no—
256C4—6041no—
257C4—6041no—
258C4—6042no—
259C2—12082no—
260C2#2375277711yescharacteristic
261C2#2375278711yescharacteristic
262C2#2375279211yescharacteristic
263C2#2375295812yes—
264C2#2375296112yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#395×C151C2
prime radicalC22×D604C22
hypercenter#395D151
hypocenterC151#2820
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#18012729C2semidirect
3. #23752147C2semidirect
4. #23752141C2semidirect
5. #23752136C2semidirect
6. #23752134C2semidirect
7. #23752131C2semidirect
10. #23752076C2semidirect
11. #395×C151C2semidirect
132. C151#2820semidirect
141. #395D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127292
C2×#180127282
#237521472
#237521412
#237521362
#237521342
#237521312
#237521302
#237521292
#237520762
#395×C1512
#2820151