Finite Group Databasebeta

← #34080172

Subgroups — #34080172

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#23752818C211yesmaximal, characteristic, complemented
2#23752787C211yesmaximal, characteristic, complemented
3#23752601C211yesmaximal, characteristic, complemented
4#23752586C211yesmaximal, characteristic, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752430C212yesmaximal, complemented
7#23752416C212yesmaximal, complemented
8#23752360C212yesmaximal, complemented
9#23752352C212yesmaximal, complemented
10#23752274C211yesmaximal, characteristic, complemented
11#491×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×Q8×D151C2211yescharacteristic
14C2×#14558993C2212yes—
15C2×#14558991C2212yes—
16C2×#14558991C2212yes—
17C2×D1208C2212yes—
18#18012737C2211yescharacteristic
19#18012736C2211yescharacteristic
20#18012728C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012724—22no—
23#18012724—22no—
24#18012717—22no—
25#18012714—22no—
26#18012714C2212yes—
27#18012701C2212yes—
28#18012696C2211yescharacteristic
29Dic151⋊C8C2212yes—
30#18012662C2212yes—
31#18012659C2212yes—
32(C2×D151)⋊C8C2212yes—
33C4×C151⋊C8C2211yescharacteristic
34C4⋊Q8×C151C2211yescharacteristic
35#125×C151C2211yescharacteristic
36#103×C151C2212yes—
37#103×C151C2212yes—
38#97×C151C2211yescharacteristic
39#14559005—42no—
40C2×Dic302—21no—
41C2×Dic302C2311yescharacteristic
42Q8×D151—42no—
43C2×D604—21no—
44C2×D604—22no—
45C2×D604—22no—
46C2×D604C2312yes—
47C2×D604C2311yescharacteristic
48C2×C4×D151—21no—
49C2×C4×D151—21no—
50C2×C4×D151—22no—
51C2×C4×D151C2311yescharacteristic
52#14558993—42no—
53#14558991—42no—
54#14558991—42no—
55D1208—42no—
56C2×C151⋊C8C2312yes—
57Dic151⋊C4—22no—
58Dic151⋊C4D412yes—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63(C2×D151)⋊C4D412yes—
64C4×Dic151C2311yescharacteristic
65C2×Q8×C151C2311yescharacteristic
66C2×Q8×C151C2311yescharacteristic
67C2×C8×C151C2312yes—
68C4⋊C4×C151—22no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151C2312yes—
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—22no—
74C22×D151C2×D411yescharacteristic
75Dic302—22no—
76Dic302—42no—
77D604—22no—
78D604—22no—
79D604—22no—
80D604—42no—
81D604—82no—
82D604—82no—
83C2×Dic151—21no—
84C2×Dic151C2×D412yes—
85C2×Dic151C2×D411yescharacteristic
86C4×D151—22no—
87C4×D151—42no—
88C4×D151—42no—
89C4×D151—82no—
90C151⋊C8—22no—
91Q8×C151—22no—
92Q8×C151—22no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—22no—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2411yescharacteristic
98C8×C151—22no—
99C22×C151C22×D411yescharacteristic
100C2×D151—21no—
101C2×D151—22no—
102C2×D151—41no—
103C2×D151—42no—
104C2×D151—42no—
105C2×D151—42no—
106C2×D151—42no—
107C4×C151—22no—
108C4×C151—41no—
109C4×C151—41no—
110C4×C151—42no—
111C4×C151H(5,𝔽2)12yes—
112Dic151—21no—
113Dic151—22no—
114Dic151—41no—
115C2×C151#53511yescharacteristic
116C2×C151#57712yes—
117D151—41no—
118D151—81no—
119D151—82no—
120C151#322111yescharacteristic, complemented, Sylow
121#3221—1511nomaximal, Sylow
122#540—1511no—
123#536—1511no—
124#496—1511no—
125#492—1511no—
126#491D15111yescharacteristic, complemented
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×SD16—1512no—
138C2×D8—1512no—
139C4⋊Q8—1511no—
140C4⋊Q8C2×D15111yescharacteristic
141#127—1511no—
142#125C2×D15111yescharacteristic
143#124—1511no—
144#124—1511no—
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#103C2×D15112yes—
155#103C2×D15112yes—
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×Q8C22×D15111yescharacteristic
165C2×Q8C22×D15111yescharacteristic
166C2×D4—3021no—
167C2×D4—3022no—
168C2×D4—3022no—
169C2×D4—1511no—
170C2×D4—1512no—
171C22×C4—3021no—
172C22×C4—3021no—
173C22×C4—3022no—
174C22×C4—1511no—
175SD16—6042no—
176SD16—6042no—
177SD16—6042no—
178D8—6042no—
179C2×C8—1512no—
180C2×C8C22×D15112yes—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—3022no—
184C4⋊C4—1512no—
185C4⋊C4C22×D15112yes—
186C22⋊C4—3022no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C22⋊C4—3022no—
190C22⋊C4—1512no—
191C42—1511no—
192C42C22×D15111yescharacteristic
193C23—3021no—
194C23—3022no—
195C23—1511no—
196Q8—22no—
197Q8—22no—
198Q8—3022no—
199Q8—6042no—
200D4—3022no—
201D4—3022no—
202D4—3022no—
203D4—6042no—
204D4—12082no—
205D4—12082no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—3022no—
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—3022no—
221C22—3021no—
222C22—6042no—
223C22—6042no—
224C22—6042no—
225C22—6041no—
226C22—6042no—
227C22C2×D4×D15111yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—3022no—
233C4—3021no—
234C4—6041no—
235C4#1801278512yes—
236C2—6041no—
237C2—12082no—
238C2—12081no—
239C2#2375278011yescharacteristic
240C2#2375302112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#491×C151C2
socleC22×C151C22×D4
hypercenter#491D151
hypocenterC151#3221
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #23752818C2semidirect
2. #23752787C2semidirect
3. #23752601C2semidirect
4. #23752586C2semidirect
5. #23752569C2semidirect
6. #23752430C2semidirect
7. #23752416C2semidirect
8. #23752360C2semidirect
9. #23752352C2semidirect
10. #23752274C2semidirect
11. #491×C151C2semidirect
120. C151#3221semidirect
126. #491D151semidirect

Maximal subgroups

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

subgroupindex
#237528182
#237527872
#237526012
#237525862
#237525692
#237524302
#237524162
#237523602
#237523522
#237522742
#491×C1512
#3221151