Finite Group Databasebeta

← #34080887

Subgroups — #34080887

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#23753027C212yesmaximal, complemented
2#23753022C212yesmaximal, complemented
3#23752607C211yesmaximal, characteristic, complemented
4#23752486C212yesmaximal, complemented
5#23752473C212yesmaximal, complemented
6#23752396C212yesmaximal, complemented
7#23752389C211yesmaximal, characteristic, complemented
8#23752331C212yesmaximal, complemented
9#454×C151C211yesmaximal, characteristic, complemented
10#18012786C2212yes—
11#18012784C2211yescharacteristic
12#18012772C2212yes—
13#18012770—22no—
14#18012770C2212yes—
15#18012769—22no—
16#18012769C2212yescomplemented
17#18012768—22no—
18#18012763—22no—
19#18012759—22no—
20#18012759C2212yes—
21#18012758—22no—
22C2×#14558994—22no—
23C2×#14558994C2212yescomplemented
24C2×#14558992C2212yes—
25SD16×D151—22no—
26#18012747C2212yes—
27#18012746C2212yescomplemented
28#18012739C2211yescharacteristic, complemented
29#18012674C2212yescomplemented
30#18012667C2212yes—
31#18012657C2212yescomplemented
32#18012656C2211yescharacteristic
33#18012650C2211yescharacteristic, complemented
342−1+4×C151C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C151C2212yes—
36#124×C151C2211yescharacteristic
37#104×C151C2212yescomplemented
38#101×C151C2211yescharacteristic, complemented
39#14559004—22no—
40#14559004C2312yes—
41#14559003—22no—
42#14559003—22no—
43#14559003—42no—
44C2×Dic302—22no—
45C2×Dic302C2312yes—
46Q8×D151—22no—
47C2×C22⋊D151—41no—
48D4×D151—22no—
49Dic604—22no—
50#14558994—22no—
51#14558994—22no—
52#14558994—22no—
53#14558994—22no—
54#14558994D412yes—
55#14558993—22no—
56#14558992—22no—
57#14558992—22no—
58#14558992—22no—
59#14558992D412yes—
60#14558991—22no—
61#14558991D412yes—
62#14558989D412yes—
63#14558988—22no—
64#14558988C2312yes—
65#14558987—22no—
66C2×C151⋊C8—22no—
67C2×C151⋊C8C2312yes—
68C8×D151—22no—
69C4⋊Dic151—41no—
70#41×C151—22no—
71#41×C151—41no—
72#41×C151C2312yes—
73C2×Q8×C151—22no—
74C2×Q8×C151C2311yescharacteristic
75C2×D4×C151C2311yescharacteristic
76SD16×C151—22no—
77D8×C151—22no—
78M16×C151C2312yes—
79C22⋊C4×C151—41no—
80C42×C151C2311yescharacteristic
81C22×D151—41no—
82Dic302—22no—
83Dic302—22no—
84Dic302—42no—
85Dic302C2×D412yes—
86D604C2×D412yes—
87C22⋊D151—22no—
88C22⋊D151—42no—
89C22⋊D151—42no—
90C2×Dic151—22no—
91C2×Dic151—41no—
92C2×Dic151—42no—
93C4×D151—22no—
94C4×D151—42no—
95C151⋊C8—22no—
96C151⋊C8C2×D412yes—
97C151⋊C8C2×D412yes—
98C23×C151—21no—
99Q8×C151—22no—
100Q8×C151—41no—
101Q8×C151C2×D412yes—
102D4×C151—22no—
103D4×C151—22no—
104D4×C151—41no—
105D4×C151C2×D412yes—
106C2×C4×C151—22no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—42no—
110C2×C4×C151C2411yescharacteristic
111C8×C151—22no—
112C22×C151—22no—
113C22×C151—41no—
114C22×C151—81no—
115C22×C151H(5,𝔽2)11yescharacteristic
116C2×D151—22no—
117C2×D151—161no—
118C4×C151—22no—
119C4×C151—41no—
120C4×C151—41no—
121C4×C151C22×D412yes—
122Dic151—22no—
123Dic151—42no—
124C2×C151—21no—
125C2×C151—42no—
126C2×C151—81no—
127C2×C151D4211yescharacteristic
128D151—42no—
129C151#328911yescharacteristic, complemented, Sylow
130#3289—1511nomaximal, Sylow
131#578—1512no—
132#577—1512no—
133#497—1511no—
134#473—1512no—
135#471—1512no—
136#456—1512no—
137#455—1511no—
138#454D15111yescharacteristic, complemented
139#444—1512no—
1402−1+4—1512no—
1412−1+4C2×D15111yescharacteristic, complemented
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)C2×D15112yes—
151#135—3022no—
152#135—3022no—
153#135—1512no—
154C2×Q16—3022no—
155C2×Q16—1512no—
156C2×SD16—3022no—
157C2×SD16—1512no—
158#131—1512no—
159#131—1512no—
160C4⋊Q8—1511no—
161#124C2×D15111yescharacteristic
162#108—1512no—
163#104—1512no—
164#104C2×D15112yescomplemented
165#101—1512no—
166#101C2×D15111yescharacteristic, complemented
167#100—1511no—
168#97—1511no—
169#41—22no—
170#41—41no—
171#41—3022no—
172#41—3022no—
173#41—3022no—
174#41—6042no—
175#41—1512no—
176#41C22×D15112yes—
177C2×Q8—22no—
178C2×Q8—3022no—
179C2×Q8—3022no—
180C2×Q8—1512no—
181C2×Q8C22×D15111yescharacteristic
182C2×D4—3022no—
183C2×D4—6041no—
184C2×D4C22×D15111yescharacteristic
185Q16—3022no—
186Q16—3022no—
187Q16—3022no—
188Q16—3022no—
189Q16—3022no—
190Q16—1512no—
191SD16—22no—
192SD16—3022no—
193SD16—3022no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—1512no—
198SD16—1512no—
199D8—22no—
200D8—1512no—
201M16—3022no—
202M16—3022no—
203M16—1512no—
204M16C22×D15112yes—
205C2×C8—3022no—
206C2×C8—3022no—
207C2×C8—1512no—
208C4⋊C4—6041no—
209C22⋊C4—41no—
210C42C22×D15111yescharacteristic
211C23—21no—
212C23—6041no—
213Q8—22no—
214Q8—41no—
215Q8—3022no—
216Q8—3022no—
217Q8—6042no—
218Q8—1512no—
219Q8D4×D15112yes—
220D4—22no—
221D4—22no—
222D4—41no—
223D4—3022no—
224D4—6042no—
225D4—6042no—
226D4—1512no—
227D4D4×D15112yes—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—3022no—
233C2×C4—3022no—
234C2×C4—6042no—
235C2×C4—6041no—
236C2×C4—6042no—
237C2×C4C23×D15111yescharacteristic
238C8—22no—
239C8—3022no—
240C8—1512no—
241C8—1512no—
242C22—22no—
243C22—41no—
244C22—81no—
245C22—3022no—
246C22—24161no—
247C22#1801278411yescharacteristic
248C4—22no—
249C4—41no—
250C4—41no—
251C4—3022no—
252C4—6042no—
253C4C2×D4×D15112yes—
254C2—21no—
255C2—42no—
256C2—81no—
257C2—6042no—
258C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#454×C151C2
socleC2×C151D42
hypercenter#454D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #23753027C2semidirect
2. #23753022C2semidirect
3. #23752607C2semidirect
4. #23752486C2semidirect
5. #23752473C2semidirect
6. #23752396C2semidirect
7. #23752389C2semidirect
8. #23752331C2semidirect
9. #454×C151C2semidirect
16. #18012769C22semidirect
23. C2×#14558994C22semidirect
27. #18012746C22semidirect
28. #18012739C22semidirect
29. #18012674C22semidirect
31. #18012657C22semidirect
33. #18012650C22semidirect
34. 2−1+4×C151C22semidirect
37. #104×C151C22semidirect
38. #101×C151C22semidirect
129. C151#3289semidirect
138. #454D151semidirect
141. 2−1+4C2×D151semidirect
164. #104C2×D151semidirect
166. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530272
#237530222
#237526072
#237524862
#237524732
#237523962
#237523892
#237523312
#454×C1512
#3289151