Finite Group Databasebeta

← #34079493

Subgroups — #34079493

Order 19328.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#23752768C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic
3#23752573C212yesmaximal, complemented
4#23752570C212yesmaximal, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752567C211yesmaximal, characteristic, complemented
7#23752566C211yesmaximal, characteristic, complemented
8#23752219C212yesmaximal, complemented
9#23752215C212yesmaximal
10C4×#14558987C211yesmaximal, characteristic, complemented
11#488×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151C2211yescharacteristic
13C2×D4×D151C2211yescharacteristic
14C2×#14558987C2212yes—
15#18012738C2212yescomplemented
16#18012731C2211yescharacteristic, complemented
17#18012728C2211yescharacteristic
18#18012727C2211yescharacteristic
19#18012726C2211yescharacteristic
20#18012725—22no—
21#18012717—22no—
22#18012704—22no—
23#18012697C2212yes—
24C22⋊C4×D151—22no—
25C42×D151C2211yescharacteristic
26#18012664C2212yescomplemented
27#18012663C2212yescomplemented
28#18012662C2212yescomplemented
29#18012661C2212yes—
30#18012660C2212yes—
31#18012659C2212yes—
32#18012649C2212yescomplemented
33C4×C151⋊C8C2211yescharacteristic, complemented
34#125×C151C2211yescharacteristic, complemented
35#124×C151C2211yescharacteristic
36#103×C151C2212yescomplemented
37#102×C151C2212yes—
38C4×C8×C151C2211yescharacteristic, complemented
39C23×D151—21no—
40C2×Dic302—22no—
41C2×Dic302—21no—
42C2×Dic302C2311yescharacteristic
43Q8×D151—24no—
44C2×D604C2311yescharacteristic
45C2×C22⋊D151—21no—
46D4×D151—24no—
47C2×C4×D151—21no—
48C2×C4×D151D412yes—
49C2×C4×D151C2311yescharacteristic
50#14558987—24no—
51C2×C151⋊C8C2312yes—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54Dic151⋊C4—22no—
55C22⋊Dic151—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C4×Dic151—22no—
60C4×Dic151D412yes—
61C4×Dic151C2311yescharacteristic
62C2×Q8×C151C2311yescharacteristic
63C2×D4×C151C2311yescharacteristic
64C2×C8×C151C2312yes—
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C42×C151C2311yescharacteristic
69C22×D151—21no—
70C22×D151—44no—
71C22×D151—42no—
72C22×D151C2×D411yescharacteristic
73Dic302—22no—
74Dic302—44no—
75Dic302—42no—
76D604—22no—
77C22⋊D151—42no—
78C2×Dic151—22no—
79C2×Dic151—21no—
80C2×Dic151C2×D412yes—
81C2×Dic151C2×D411yescharacteristic
82C4×D151—42no—
83C4×D151—42no—
84C4×D151#4114yes—
85C151⋊C8—22no—
86C23×C151—21no—
87Q8×C151—22no—
88D4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151C2×D412yes—
92C2×C4×C151C2411yescharacteristic
93C8×C151—22no—
94C22×C151—41no—
95C22×C151—42no—
96C22×C151C22×D411yescharacteristic
97C2×D151—22no—
98C2×D151—41no—
99C2×D151—42no—
100C2×D151—84no—
101C2×D151#12412yes—
102C4×C151—22no—
103C4×C151—41no—
104C4×C151—42no—
105C4×C151C2×#4112yes—
106Dic151—22no—
107Dic151—41no—
108Dic151—42no—
109Dic151#12412yes—
110C2×C151—81no—
111C2×C151C2×#12411yescharacteristic
112C2×C151#57512yes—
113D151—22no—
114D151—81no—
115C151#314011yescharacteristic, complemented, Sylow
116#3140—1511nomaximal, Sylow
117#533—1511no—
118C2×#124—1511no—
119#489—1512no—
120#489—1512no—
121#488—1511no—
122#488—1511no—
123#488—1511no—
124#488D15111yescharacteristic, complemented
125#419—1512no—
126#418—1512no—
127C4×M16—1511no—
128C22×Q8—1511no—
129C22×D4—1511no—
130C2×M16—1512no—
131C4⋊Q8—1512no—
132#125—1511no—
133#125C2×D15111yescharacteristic, complemented
134#124—3022no—
135#124—1511no—
136#124—1511no—
137#124—1511no—
138#124C2×D15111yescharacteristic
139C22⋊Q8—3022no—
140C4×Q8—3022no—
141#117—1512no—
142C2×C22⋊C4—3022no—
143C2×C42—1511no—
144#103—1512no—
145#103—1512no—
146#103—1512no—
147#103C2×D15112yescomplemented
148#102—1512no—
149#102—1512no—
150#102—1512no—
151#102C2×D15112yes—
152#97—1512no—
153C4×C8—1511no—
154C4×C8C2×D15111yescharacteristic, complemented
155C24—3021no—
156C2×Q8—3022no—
157C2×Q8—3021no—
158C2×Q8—3024no—
159C2×Q8—1511no—
160C2×Q8C22×D15111yescharacteristic
161C2×D4—3024no—
162C2×D4—3021no—
163C2×D4—1511no—
164C2×D4C22×D15111yescharacteristic
165C22×C4—3021no—
166C22×C4—1512no—
167C22×C4—1511no—
168M16—3024no—
169C2×C8—1512no—
170C2×C8C22×D15112yes—
171C4⋊C4—22no—
172C4⋊C4—3022no—
173C4⋊C4—3022no—
174C4⋊C4—1512no—
175C4⋊C4C22×D15112yes—
176C22⋊C4—22no—
177C22⋊C4—3022no—
178C22⋊C4—3022no—
179C22⋊C4—3022no—
180C22⋊C4—3022no—
181C42—3022no—
182C42—1512no—
183C42—1511no—
184C42C22×D15111yescharacteristic
185C23—21no—
186C23—3021no—
187C23—6044no—
188C23—6042no—
189C23—1511no—
190Q8—22no—
191Q8—3022no—
192Q8—6044no—
193Q8—6042no—
194D4—22no—
195D4—3022no—
196D4—6042no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—3022no—
200C2×C4—3021no—
201C2×C4—6042no—
202C2×C4—6042no—
203C2×C4—1512no—
204C2×C4—1511no—
205C2×C4—1514no—
206C2×C4D4×D15112yes—
207C2×C4C23×D15111yescharacteristic
208C8—22no—
209C8—3022no—
210C22—41no—
211C22—42no—
212C22—3022no—
213C22—6041no—
214C22—6042no—
215C22—1512no—
216C22—12084no—
217C22C2×D4×D15111yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—3022no—
222C4—6041no—
223C4—6042no—
224C4—1512no—
225C4#41×D15112yes—
226C2—81no—
227C2—3022no—
228C2—12081no—
229C2#124×D15111yescharacteristic
230C2#2375300912yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#488×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#488D151
hypocenterC151#3140
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #23752768C2semidirect
3. #23752573C2semidirect
4. #23752570C2semidirect
5. #23752569C2semidirect
6. #23752567C2semidirect
7. #23752566C2semidirect
8. #23752219C2semidirect
10. C4×#14558987C2semidirect
11. #488×C151C2semidirect
15. #18012738C22semidirect
16. #18012731C22semidirect
26. #18012664C22semidirect
27. #18012663C22semidirect
28. #18012662C22semidirect
32. #18012649C22semidirect
33. C4×C151⋊C8C22semidirect
34. #125×C151C22semidirect
36. #103×C151C22semidirect
38. C4×C8×C151C22semidirect
115. C151#3140semidirect
124. #488D151semidirect
133. #125C2×D151semidirect
147. #103C2×D151semidirect
154. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527682
#124×D1512
#237525732
#237525702
#237525692
#237525672
#237525662
#237522192
#237522152
C4×#145589872
#488×C1512
#3140151