Finite Group Databasebeta

← #34080166

Subgroups — #34080166

Order 19328.

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

normal subgroups only

This group has 388 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#23752782C211yesmaximal, characteristic, complemented
3#23752584C211yesmaximal, characteristic, complemented
4#23752581C211yesmaximal, characteristic, complemented
5#23752566C211yesmaximal, characteristic, complemented
6#23752425C212yesmaximal, complemented
7#23752415C212yesmaximal, complemented
8#23752354C212yesmaximal, complemented
9#23752349C212yesmaximal, complemented
10#23752274C211yesmaximal, characteristic, complemented
11#496×C151C211yesmaximal, characteristic, complemented
12C2×#14559003C2211yescharacteristic
13C2×Q8×D151C2211yescharacteristic
14C2×#14558992C2212yes—
15C2×#14558992C2212yes—
16#18012739C2211yescharacteristic
17#18012737C2211yescharacteristic
18#18012731C2211yescharacteristic
19#18012726C2211yescharacteristic
20#18012721—22no—
21#18012720—22no—
22#18012716—22no—
23#18012711—22no—
24#18012710C2212yes—
25D4×Dic151C2212yes—
26#18012696C2211yescharacteristic
27Dic151⋊C8C2212yes—
28#18012664C2212yes—
29#18012664C2212yes—
30#18012663C2212yes—
31#18012660C2212yes—
32(C2×D151)⋊C8C2212yes—
33C4×C151⋊C8C2211yescharacteristic
34C2×SD16×C151C2212yes—
35C2×D8×C151C2212yes—
36#127×C151C2211yescharacteristic
37#124×C151C2211yescharacteristic
38#97×C151C2211yescharacteristic
39#14559003—42no—
40C2×Dic302—21no—
41C2×Dic302C2311yescharacteristic
42C2×Dic302C2311yescharacteristic
43Q8×D151—42no—
44C2×C22⋊D151—21no—
45C2×C22⋊D151—22no—
46C22×Dic151—21no—
47C22×Dic151—22no—
48C2×C4×D151—21no—
49C2×C4×D151C2311yescharacteristic
50#14558992—42no—
51#14558992—42no—
52C2×C151⋊C8C2312yes—
53C4⋊Dic151—22no—
54C4⋊Dic151C2312yes—
55Dic151⋊C4—22no—
56Dic151⋊C4—22no—
57Dic151⋊C4D412yes—
58C22⋊Dic151—22no—
59C22⋊Dic151—22no—
60C22⋊Dic151—22no—
61(C2×D151)⋊C4D412yes—
62C4×Dic151C2311yescharacteristic
63C2×Q8×C151C2311yescharacteristic
64C2×D4×C151—22no—
65C2×D4×C151C2312yes—
66C2×D4×C151C2311yescharacteristic
67SD16×C151—42no—
68D8×C151—42no—
69C2×C8×C151C2312yes—
70C22⋊C4×C151—22no—
71C42×C151C2311yescharacteristic
72C22×D151C2×D411yescharacteristic
73Dic302—22no—
74Dic302—22no—
75Dic302—42no—
76C22⋊D151—42no—
77C22⋊D151—82no—
78C2×Dic151—22no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—42no—
82C2×Dic151—82no—
83C2×Dic151C2×D412yes—
84C2×Dic151C2×D411yescharacteristic
85C4×D151—22no—
86C4×D151—42no—
87C151⋊C8—22no—
88C23×C151—21no—
89C23×C151—22no—
90Q8×C151—22no—
91D4×C151—22no—
92D4×C151—22no—
93D4×C151—22no—
94D4×C151—82no—
95C2×C4×C151—21no—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2411yescharacteristic
98C8×C151—22no—
99C22×C151—42no—
100C22×C151—41no—
101C22×C151—42no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151C22×D411yescharacteristic
105C2×D151—21no—
106C2×D151—22no—
107C4×C151—22no—
108C4×C151—41no—
109C4×C151H(5,𝔽2)12yes—
110Dic151—21no—
111Dic151—22no—
112Dic151—41no—
113Dic151—41no—
114Dic151—42no—
115C2×C151—82no—
116C2×C151—81no—
117C2×C151#53511yescharacteristic
118C2×C151#57712yes—
119D151—41no—
120C151#322111yescharacteristic, complemented, Sylow
121#3221—1511nomaximal, Sylow
122#540—1511no—
123#536—1511no—
124#496D15111yescharacteristic, complemented
125#492—1511no—
126#491—1511no—
127#488—1511no—
128#463—1512no—
129#461—1512no—
130#449—1512no—
131#448—1512no—
132#433—1511no—
133C2×#41—1511no—
134C22×Q8—1511no—
135C2×SD16—1512no—
136C2×SD16—1512no—
137C2×SD16C2×D15112yes—
138C2×D8C2×D15112yes—
139C4⋊Q8—1511no—
140C4⋊Q8—1511no—
141#127C2×D15111yescharacteristic
142#125—1511no—
143#124—1511no—
144#124C2×D15111yescharacteristic
145#123—3022no—
146#123—3022no—
147C22⋊Q8—3022no—
148#121—3022no—
149#121—1512no—
150C4×D4—1512no—
151#117—1511no—
152C4⋊C8—1512no—
153#103—1512no—
154#103—1512no—
155#103—1512no—
156#102—1512no—
157C22⋊C8—1512no—
158#97C2×D15111yescharacteristic
159C4×C8—1511no—
160#41—6042no—
161C2×Q8—3021no—
162C2×Q8—6042no—
163C2×Q8—1511no—
164C2×Q8—1511no—
165C2×Q8C22×D15111yescharacteristic
166C2×D4—22no—
167C2×D4—3021no—
168C2×D4—3022no—
169C2×D4C22×D15111yescharacteristic
170C2×D4C22×D15112yes—
171C22×C4—3021no—
172C22×C4—3021no—
173C22×C4—3022no—
174C22×C4—1511no—
175SD16—42no—
176SD16—6042no—
177SD16—6042no—
178D8—42no—
179C2×C8—1512no—
180C2×C8C22×D15112yes—
181C4⋊C4—3022no—
182C4⋊C4—3022no—
183C4⋊C4—3022no—
184C4⋊C4—1512no—
185C4⋊C4—1512no—
186C22⋊C4—22no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—1512no—
191C42—1511no—
192C42C22×D15111yescharacteristic
193C23—21no—
194C23—22no—
195C23—1511no—
196Q8—22no—
197Q8—3022no—
198Q8—3022no—
199Q8—6042no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—6042no—
205D4—12082no—
206C2×C4—21no—
207C2×C4—3022no—
208C2×C4—3022no—
209C2×C4—3021no—
210C2×C4—3021no—
211C2×C4—6042no—
212C2×C4—6042no—
213C2×C4—1512no—
214C2×C4—1511no—
215C2×C4—12082no—
216C2×C4D4×D15112yes—
217C2×C4C23×D15111yescharacteristic
218C8—22no—
219C8—3022no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—41no—
224C22—42no—
225C22—3022no—
226C22—3021no—
227C22C2×D4×D15111yescharacteristic
228C4—22no—
229C4—41no—
230C4—3022no—
231C4—3021no—
232C4—6042no—
233C4—6041no—
234C4—6041no—
235C4#1801278412yes—
236C2—82no—
237C2—81no—
238C2—6041no—
239C2#2375277511yescharacteristic
240C2#2375302212yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC22×C151C22×D4
hypercenter#496D151
hypocenterC151#3221
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23752816C2semidirect
2. #23752782C2semidirect
3. #23752584C2semidirect
4. #23752581C2semidirect
5. #23752566C2semidirect
6. #23752425C2semidirect
7. #23752415C2semidirect
8. #23752354C2semidirect
9. #23752349C2semidirect
10. #23752274C2semidirect
11. #496×C151C2semidirect
120. C151#3221semidirect
124. #496D151semidirect

Maximal subgroups

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

subgroupindex
#237528162
#237527822
#237525842
#237525812
#237525662
#237524252
#237524152
#237523542
#237523492
#237522742
#496×C1512
#3221151