Finite Group Databasebeta

← #34080153

Subgroups — #34080153

Order 19328.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752816C211yesmaximal, characteristic, complemented
2#23752775C211yesmaximal, characteristic, complemented
3#23752599C211yesmaximal, characteristic, complemented
4#23752576C211yesmaximal, characteristic, complemented
5#23752567C211yesmaximal, characteristic, complemented
6#23752425C212yesmaximal, complemented
7#23752405C212yesmaximal, complemented
8#23752354C212yesmaximal, complemented
9#23752344C212yesmaximal, complemented
10#23752271C211yesmaximal, characteristic, complemented
11#493×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2211yescharacteristic
13C2×D4×D151C2211yescharacteristic
14C2×#14558992C2212yescomplemented
15C2×#14558989C2212yes—
16#18012735C2211yescharacteristic
17#18012731C2211yescharacteristic, complemented
18#18012727C2211yescharacteristic
19#18012726C2211yescharacteristic
20#18012720—22no—
21#18012711—22no—
22#18012711—22no—
23#18012710C2212yes—
24#18012707—22no—
25D4×Dic151C2212yescomplemented
26#18012696C2211yescharacteristic
27Dic151⋊C8C2212yescomplemented
28#18012664C2212yescomplemented
29#18012661C2212yes—
30#18012660C2212yes—
31#18012660C2212yescomplemented
32(C2×D151)⋊C8C2212yes—
33#18012650C2211yescharacteristic, complemented
34C2×D8×C151C2212yes—
35C2×D8×C151C2212yescomplemented
36#127×C151C2211yescharacteristic
37#127×C151C2211yescharacteristic, complemented
38C4×C8×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40#14559003—42no—
41C2×Dic302C2311yescharacteristic
42C2×D604C2311yescharacteristic
43C2×C22⋊D151—21no—
44C2×C22⋊D151—22no—
45C2×C22⋊D151—21no—
46C2×C22⋊D151—22no—
47D4×D151—42no—
48C22×Dic151—21no—
49C22×Dic151—22no—
50C2×C4×D151C2311yescharacteristic
51#14558992—42no—
52#14558989—42no—
53C2×C151⋊C8C2312yes—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—22no—
56Dic151⋊C4D412yes—
57C22⋊Dic151—22no—
58C22⋊Dic151—22no—
59C22⋊Dic151—22no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4D412yes—
62C4×Dic151C2311yescharacteristic
63C2×D4×C151—22no—
64C2×D4×C151—22no—
65C2×D4×C151C2312yes—
66C2×D4×C151C2311yescharacteristic
67C2×D4×C151C2311yescharacteristic
68D8×C151—42no—
69D8×C151—42no—
70C2×C8×C151C2312yes—
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—42no—
74C22×D151—82no—
75C22×D151C2×D411yescharacteristic
76Dic302—22no—
77D604—22no—
78C22⋊D151—42no—
79C22⋊D151—42no—
80C22⋊D151—82no—
81C22⋊D151—82no—
82C2×Dic151—21no—
83C2×Dic151—22no—
84C2×Dic151—42no—
85C2×Dic151—82no—
86C2×Dic151C2×D412yes—
87C2×Dic151C2×D411yescharacteristic
88C4×D151—22no—
89C151⋊C8—22no—
90C23×C151—22no—
91C23×C151—21no—
92C23×C151—21no—
93D4×C151—22no—
94D4×C151—22no—
95D4×C151—22no—
96D4×C151—22no—
97D4×C151—82no—
98D4×C151—82no—
99C2×C4×C151C2×D412yes—
100C2×C4×C151C2411yescharacteristic
101C8×C151—22no—
102C22×C151—42no—
103C22×C151—41no—
104C22×C151—41no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151—42no—
108C22×C151—42no—
109C22×C151C22×D411yescharacteristic
110C2×D151—21no—
111C2×D151—22no—
112C2×D151—41no—
113C2×D151—42no—
114C2×D151—84no—
115C4×C151—22no—
116C4×C151H(5,𝔽2)12yes—
117Dic151—21no—
118Dic151—22no—
119Dic151—41no—
120Dic151—42no—
121C2×C151—81no—
122C2×C151—82no—
123C2×C151—81no—
124C2×C151#53511yescharacteristic
125C2×C151#57612yes—
126D151—41no—
127D151—81no—
128C151#322011yescharacteristic, complemented, Sylow
129#3220—1511nomaximal, Sylow
130#540—1511no—
131#535—1511no—
132#496—1511no—
133#493D15111yescharacteristic, complemented
134#490—1511no—
135#488—1511no—
136#463—1512no—
137#459—1512no—
138#449—1512no—
139#447—1512no—
140#433—1511no—
141C2×#41—1511no—
142C22×D4—1511no—
143C2×SD16—1512no—
144C2×D8—1512no—
145C2×D8C2×D15112yes—
146C2×D8C2×D15112yescomplemented
147#127—1511no—
148#127C2×D15111yescharacteristic
149#127C2×D15111yescharacteristic, complemented
150#125—1511no—
151#124—1511no—
152#124—1511no—
153#123—3022no—
154#121—3022no—
155#121—3022no—
156#121—1512no—
157#120—3022no—
158C4×D4—1512no—
159#117—1511no—
160C4⋊C8—1512no—
161#103—1512no—
162#102—1512no—
163#102—1512no—
164#102—1512no—
165C22⋊C8—1512no—
166#97—1511no—
167C4×C8C2×D15111yescharacteristic, complemented
168C24—3021no—
169#41—6042no—
170C2×Q8—1511no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—3021no—
174C2×D4—3022no—
175C2×D4—3021no—
176C2×D4—3022no—
177C2×D4—6042no—
178C2×D4—1511no—
179C2×D4C22×D15111yescharacteristic
180C2×D4C22×D15111yescharacteristic
181C2×D4C22×D15112yes—
182C22×C4—3021no—
183C22×C4—3022no—
184C22×C4—1511no—
185SD16—6042no—
186D8—42no—
187D8—42no—
188D8—6042no—
189C2×C8—1512no—
190C2×C8C22×D15112yes—
191C4⋊C4—3022no—
192C4⋊C4—1512no—
193C4⋊C4—1512no—
194C22⋊C4—3022no—
195C22⋊C4—3022no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4—1512no—
199C42—1511no—
200C42C22×D15111yescharacteristic
201C23—22no—
202C23—21no—
203C23—21no—
204C23—3021no—
205C23—6042no—
206C23—1511no—
207C23—12082no—
208Q8—3022no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—22no—
213D4—82no—
214D4—82no—
215D4—3022no—
216D4—6042no—
217D4—6042no—
218D4—12082no—
219D4—12082no—
220C2×C4—3022no—
221C2×C4—3021no—
222C2×C4—3022no—
223C2×C4—6042no—
224C2×C4—1512no—
225C2×C4—1511no—
226C2×C4—12082no—
227C2×C4D4×D15112yes—
228C2×C4C23×D15111yescharacteristic
229C8—22no—
230C8—3022no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—42no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22—3022no—
239C22—3021no—
240C22—6042no—
241C22—6041no—
242C22—12084no—
243C22C2×D4×D15111yescharacteristic
244C4—22no—
245C4—3022no—
246C4—3021no—
247C4—6042no—
248C4—6041no—
249C4#1801278412yes—
250C2—81no—
251C2—82no—
252C2—81no—
253C2—6041no—
254C2—12081no—
255C2#2375277511yescharacteristic
256C2#2375301312yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#493×C151C2
socleC22×C151C22×D4
hypercenter#493D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23752816C2semidirect
2. #23752775C2semidirect
3. #23752599C2semidirect
4. #23752576C2semidirect
5. #23752567C2semidirect
6. #23752425C2semidirect
7. #23752405C2semidirect
8. #23752354C2semidirect
9. #23752344C2semidirect
10. #23752271C2semidirect
11. #493×C151C2semidirect
14. C2×#14558992C22semidirect
17. #18012731C22semidirect
25. D4×Dic151C22semidirect
27. Dic151⋊C8C22semidirect
28. #18012664C22semidirect
31. #18012660C22semidirect
33. #18012650C22semidirect
35. C2×D8×C151C22semidirect
37. #127×C151C22semidirect
38. C4×C8×C151C22semidirect
128. C151#3220semidirect
133. #493D151semidirect
146. C2×D8C2×D151semidirect
149. #127C2×D151semidirect
167. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237527752
#237525992
#237525762
#237525672
#237524252
#237524052
#237523542
#237523442
#237522712
#493×C1512
#3220151