Finite Group Databasebeta

← #34080885

Subgroups — #34080885

Order 19328.

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

normal subgroups only

This group has 448 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#23753025C212yesmaximal, complemented
2#23753018C212yesmaximal, complemented
3#23752484C212yesmaximal, complemented
4#23752472C212yesmaximal, complemented
5#23752394C212yesmaximal, complemented
6#23752389C211yesmaximal, characteristic, complemented
7#23752384C211yesmaximal, characteristic, complemented
8#23752335C212yesmaximal, complemented
9#497×C151C211yesmaximal, characteristic, complemented
10#18012787C2212yes—
11#18012787C2211yescharacteristic, complemented
12#18012784C2211yescharacteristic
13#18012771—22no—
14#18012771—22no—
15#18012770C2212yes—
16#18012770C2212yes—
17#18012770C2212yescomplemented
18#18012768—22no—
19#18012766—22no—
20#18012765C2212yes—
21#18012762—22no—
22#18012761C2212yes—
23#18012760—22no—
24Q16×D151—22no—
25SD16×D151—22no—
26#18012745C2212yes—
27#18012745C2212yescomplemented
28#18012675C2212yescomplemented
29#18012667C2212yes—
30#18012667C2212yescomplemented
31#18012658C2212yescomplemented
32#18012658C2211yescharacteristic, complemented
33#18012656C2211yescharacteristic
34C2×Q16×C151C2212yescomplemented
35C2×SD16×C151C2212yes—
36C4⋊Q8×C151C2211yescharacteristic, complemented
37#124×C151C2211yescharacteristic
38#97×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559005—22no—
41#14559005—22no—
42#14559004—42no—
43#14559004—41no—
44#14559004C2312yes—
45#14559004C2312yes—
46#14559003—22no—
47Q8×D151—22no—
48Q8×D151—22no—
49Q8×D151—22no—
50C2×C22⋊D151—41no—
51D4×D151—22no—
52Dic604D412yes—
53#14558994—22no—
54#14558994—22no—
55#14558994—22no—
56#14558993D412yes—
57#14558993D412yes—
58#14558992—22no—
59#14558991—22no—
60#14558991—22no—
61#14558991—22no—
62D1208D412yes—
63#14558989—22no—
64#14558988C2312yes—
65#14558988C2312yes—
66#14558987—22no—
67#14558987—22no—
68C8×D151—22no—
69C8×D151—22no—
70C2×Q8×C151C2311yescharacteristic
71C2×Q8×C151C2312yes—
72C2×D4×C151C2311yescharacteristic
73Q16×C151—22no—
74Q16×C151—22no—
75SD16×C151—22no—
76SD16×C151—22no—
77C2×C8×C151C2312yes—
78C4⋊C4×C151—41no—
79C22⋊C4×C151—41no—
80C42×C151C2311yescharacteristic
81C22×D151—41no—
82Dic302—41no—
83Dic302—42no—
84Dic302C2×D412yes—
85Dic302C2×D412yes—
86D604—41no—
87D604—42no—
88D604C2×D412yes—
89D604C2×D412yes—
90C22⋊D151—22no—
91C22⋊D151—22no—
92C22⋊D151—42no—
93C2×Dic151—41no—
94C4×D151—22no—
95C4×D151—22no—
96C4×D151—42no—
97C4×D151—42no—
98C4×D151—42no—
99C151⋊C8—22no—
100C151⋊C8—22no—
101C23×C151—21no—
102Q8×C151—22no—
103Q8×C151—22no—
104Q8×C151—22no—
105D4×C151—22no—
106C2×C4×C151—21no—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151C2411yescharacteristic
110C8×C151C2×D412yes—
111C8×C151C2×D412yes—
112C22×C151—41no—
113C22×C151—81no—
114C22×C151H(5,𝔽2)11yescharacteristic
115C2×D151—22no—
116C2×D151—22no—
117C2×D151—161no—
118C4×C151—41no—
119C4×C151—41no—
120C4×C151—42no—
121C4×C151C22×D412yes—
122Dic151—22no—
123Dic151—22no—
124C2×C151—21no—
125C2×C151—81no—
126C2×C151D4211yescharacteristic
127D151—42no—
128D151—42no—
129C151#328911yescharacteristic, complemented, Sylow
130#3289—1511nomaximal, Sylow
131#578—1512no—
132#577—1512no—
133#497D15111yescharacteristic, complemented
134#473—1512no—
135#471—1512no—
136#456—1512no—
137#455—1511no—
138#454—1511no—
139#444—1512no—
1402−1+4—1512no—
1412−1+4—1511no—
142H(5,𝔽2)—1511no—
143#137—3022no—
144#137—3022no—
145#137—3022no—
146#137—1512no—
147#137—1512no—
148#137—1512no—
149AGL(1,ℤ/8)—3022no—
150AGL(1,ℤ/8)—1512no—
151#135—3022no—
152#135—3022no—
153#135—1512no—
154C2×Q16—3022no—
155C2×Q16C2×D15112yescomplemented
156C2×SD16—3022no—
157C2×SD16C2×D15112yes—
158#131—1512no—
159#131—1512no—
160C4⋊Q8C2×D15111yescharacteristic, complemented
161#124C2×D15111yescharacteristic
162#108—1512no—
163#104—1512no—
164#104—1512no—
165#101—1511no—
166#101—1512no—
167#100—1511no—
168#97C2×D15111yescharacteristic, complemented
169#41—3022no—
170#41—3022no—
171#41—3022no—
172#41—3022no—
173#41—6041no—
174#41—6042no—
175#41—1512no—
176#41—1512no—
177C2×Q8—3022no—
178C2×Q8—3022no—
179C2×Q8—3022no—
180C2×Q8C22×D15111yescharacteristic
181C2×Q8C22×D15112yes—
182C2×D4—3022no—
183C2×D4—6041no—
184C2×D4C22×D15111yescharacteristic
185Q16—22no—
186Q16—22no—
187Q16—3022no—
188Q16—3022no—
189Q16—3022no—
190Q16—1512no—
191SD16—22no—
192SD16—22no—
193SD16—3022no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—1512no—
198SD16—1512no—
199D8—3022no—
200D8—1512no—
201M16—3022no—
202M16—3022no—
203M16—1512no—
204M16—1512no—
205C2×C8—3022no—
206C2×C8—3022no—
207C2×C8C22×D15112yes—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C42C22×D15111yescharacteristic
211C23—21no—
212C23—6041no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—6042no—
217Q8—6041no—
218Q8—1512no—
219Q8—1512no—
220D4—22no—
221D4—3022no—
222D4—3022no—
223D4—6041no—
224D4—6042no—
225D4—6042no—
226D4—1512no—
227D4—1512no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—3022no—
232C2×C4—3022no—
233C2×C4—6042no—
234C2×C4—6042no—
235C2×C4—6042no—
236C2×C4—6041no—
237C2×C4C23×D15111yescharacteristic
238C8—3022no—
239C8—3022no—
240C8D4×D15112yes—
241C8D4×D15112yes—
242C22—41no—
243C22—81no—
244C22—3022no—
245C22—3022no—
246C22—24161no—
247C22#1801278411yescharacteristic
248C4—41no—
249C4—41no—
250C4—42no—
251C4—3022no—
252C4—3022no—
253C4C2×D4×D15112yes—
254C2—21no—
255C2—81no—
256C2—6042no—
257C2—6042no—
258C2#2375284711yescharacteristic
subgroupG/H
centerC2#23752847
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#497×C151C2
socleC2×C151D42
hypercenter#497D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #23753025C2semidirect
2. #23753018C2semidirect
3. #23752484C2semidirect
4. #23752472C2semidirect
5. #23752394C2semidirect
6. #23752389C2semidirect
7. #23752384C2semidirect
8. #23752335C2semidirect
9. #497×C151C2semidirect
11. #18012787C22semidirect
17. #18012770C22semidirect
27. #18012745C22semidirect
28. #18012675C22semidirect
30. #18012667C22semidirect
31. #18012658C22semidirect
32. #18012658C22semidirect
34. C2×Q16×C151C22semidirect
36. C4⋊Q8×C151C22semidirect
38. #97×C151C22semidirect
129. C151#3289semidirect
133. #497D151semidirect
155. C2×Q16C2×D151semidirect
160. C4⋊Q8C2×D151semidirect
168. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530252
#237530182
#237524842
#237524722
#237523942
#237523892
#237523842
#237523352
#497×C1512
#3289151