Finite Group Databasebeta

← #34080892

Subgroups — #34080892

Order 19328.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#23753026C211yesmaximal, characteristic, complemented
2#23753023C212yesmaximal, complemented
3#23752595C211yesmaximal, characteristic, complemented
4#23752487C211yesmaximal, characteristic, complemented
5#23752479C211yesmaximal, characteristic, complemented
6#23752473C212yesmaximal, complemented
7#23752390C212yesmaximal, complemented
8#23752383C212yesmaximal, complemented
9#23752329C211yesmaximal, characteristic, complemented
10#23752327C211yesmaximal, characteristic, complemented
11#576×C151C211yesmaximal, characteristic, complemented
12#18012786C2212yescomplemented
13#18012769—22no—
14#18012769C2212yes—
15#18012769C2212yescomplemented
16#18012768—22no—
17#18012765—22no—
18#18012765C2212yescomplemented
19#18012759—22no—
20#18012759C2211yescharacteristic
21#18012758—21no—
22C2×Dic604C2211yescharacteristic, complemented
23Q16×D151—21no—
24C2×#14558992—22no—
25C2×#14558992C2212yescomplemented
26#18012746C2212yescomplemented
27#18012745C2211yescharacteristic, complemented
28#18012726C2212yescomplemented
29#18012675C2211yescharacteristic, complemented
30#18012674C2211yescharacteristic, complemented
31#18012666C2211yescharacteristic
32#18012666C2212yescomplemented
33#18012665C2211yescharacteristic, complemented
34#18012657C2212yescomplemented
35#18012656C2212yescomplemented
36C8×Dic151C2211yescharacteristic, complemented
37H(5,𝔽2)×C151C2212yes—
38AGL(1,ℤ/8)×C151—22no—
39AGL(1,ℤ/8)×C151C2212yes—
40#135×C151—21no—
41#135×C151C2211yescharacteristic
42C2×D8×C151—21no—
43C2×D8×C151C2211yescharacteristic
44#131×C151C2211yescharacteristic
45#14559004—22no—
46#14559004C2311yescharacteristic
47#14559003—22no—
48#14559003—42no—
49C2×Dic302—22no—
50C2×Dic302C2312yes—
51Q8×D151—22no—
52Dic604—21no—
53Dic604—21no—
54#14558994—22no—
55#14558994—22no—
56#14558994D411yescharacteristic
57#14558992—22no—
58#14558992—22no—
59#14558992—22no—
60#14558992—22no—
61#14558992—22no—
62#14558992D411yescharacteristic
63#14558991D411yescharacteristic
64#14558989—22no—
65#14558989D411yescharacteristic
66#14558988—22no—
67#14558988C2311yescharacteristic
68#14558988C2312yes—
69#14558987—21no—
70C2×C151⋊C8—22no—
71C2×C151⋊C8C2311yescharacteristic
72C8×D151—21no—
73C22⋊Dic151—42no—
74C4×Dic151C2311yescharacteristic
75#41×C151—22no—
76#41×C151—22no—
77#41×C151C2312yes—
78#41×C151C2311yescharacteristic
79C2×D4×C151—22no—
80C2×D4×C151—22no—
81C2×D4×C151—42no—
82C2×D4×C151C2312yes—
83Q16×C151D411yescharacteristic
84SD16×C151—22no—
85SD16×C151D412yes—
86D8×C151—22no—
87D8×C151—21no—
88D8×C151—21no—
89D8×C151D411yescharacteristic
90M16×C151—21no—
91M16×C151C2311yescharacteristic
92C2×C8×C151—21no—
93C2×C8×C151C2311yescharacteristic
94Dic302—22no—
95Dic302—22no—
96Dic302—42no—
97Dic302C2×D411yescharacteristic
98D604C2×D411yescharacteristic
99C22⋊D151—21no—
100C22⋊D151—42no—
101C2×Dic151—21no—
102C2×Dic151—22no—
103C2×Dic151—42no—
104C4×D151—21no—
105C4×D151—42no—
106C151⋊C8—21no—
107C151⋊C8—22no—
108C151⋊C8C2×D411yescharacteristic
109C151⋊C8C2×D411yescharacteristic
110C23×C151—22no—
111C23×C151—42no—
112Q8×C151C2×D411yescharacteristic
113Q8×C151C2×D412yes—
114D4×C151—22no—
115D4×C151—21no—
116D4×C151—22no—
117D4×C151—22no—
118D4×C151—42no—
119D4×C151—42no—
120D4×C151C2×D411yescharacteristic
121D4×C151C2×D412yes—
122C2×C4×C151—21no—
123C2×C4×C151—22no—
124C2×C4×C151—42no—
125C2×C4×C151C2411yescharacteristic
126C8×C151—21no—
127C8×C151C2×D411yescharacteristic
128C8×C151C2×D411yescharacteristic
129C22×C151—21no—
130C22×C151—22no—
131C22×C151—42no—
132C22×C151—82no—
133C22×C151—162no—
134C22×C151H(5,𝔽2)11yescharacteristic
135C2×D151—21no—
136C4×C151—21no—
137C4×C151—22no—
138C4×C151C22×D411yescharacteristic
139C4×C151C22×D411yescharacteristic
140Dic151—21no—
141Dic151—41no—
142Dic151—42no—
143C2×C151—21no—
144C2×C151—42no—
145C2×C151—41no—
146C2×C151—82no—
147C2×C151D4211yescharacteristic
148D151—41no—
149C151#329011yescharacteristic, complemented, Sylow
150#3290—1511nomaximal, Sylow
151#578—1511no—
152#577—1512no—
153#576D15111yescharacteristic, complemented
154#495—1511no—
155#473—1511no—
156#472—1511no—
157#471—1512no—
158#455—1512no—
159#454—1512no—
160#443—1511no—
161#443—1511no—
1622−1+4—1512no—
163H(5,𝔽2)C2×D15112yes—
164#137—3022no—
165#137—3022no—
166#137—1512no—
167#137—1512no—
168AGL(1,ℤ/8)—22no—
169AGL(1,ℤ/8)—3022no—
170AGL(1,ℤ/8)—1512no—
171AGL(1,ℤ/8)C2×D15112yes—
172#135—21no—
173#135—3022no—
174#135—3021no—
175#135—1511no—
176#135C2×D15111yescharacteristic
177C2×Q16—3021no—
178C2×Q16—1511no—
179C2×SD16—3022no—
180C2×SD16—1512no—
181C2×D8—21no—
182C2×D8C2×D15111yescharacteristic
183#131—1512no—
184#131—1511no—
185#131C2×D15111yescharacteristic
186#124—1512no—
187#108—1511no—
188#108—1511no—
189#104—1512no—
190#104—1511no—
191#104—1511no—
192#101—1512no—
193#100—1512no—
194C4×C8—1511no—
195#41—22no—
196#41—22no—
197#41—3022no—
198#41—3022no—
199#41—6042no—
200#41—1511no—
201#41C22×D15111yescharacteristic
202#41C22×D15112yes—
203C2×Q8—3022no—
204C2×Q8—3022no—
205C2×Q8—1512no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D15112yes—
210Q16—3022no—
211Q16—3022no—
212Q16—3021no—
213Q16—3021no—
214Q16—1511no—
215Q16C22⋊D15111yescharacteristic
216SD16—22no—
217SD16—3022no—
218SD16—3022no—
219SD16—3022no—
220SD16—3022no—
221SD16—3022no—
222SD16—1511no—
223SD16—1511no—
224SD16C22⋊D15112yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—3022no—
229D8—1511no—
230D8C22⋊D15111yescharacteristic
231M16—21no—
232M16—3022no—
233M16—3021no—
234M16—1511no—
235M16—1512no—
236M16C22×D15111yescharacteristic
237C2×C8—21no—
238C2×C8—3022no—
239C2×C8—3021no—
240C2×C8—1511no—
241C2×C8C22×D15111yescharacteristic
242C22⋊C4—6042no—
243C42—1511no—
244C23—22no—
245C23—42no—
246Q8—3022no—
247Q8—3022no—
248Q8—6042no—
249Q8—1511no—
250Q8D4×D15111yescharacteristic
251Q8C2×C22⋊D15112yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—3021no—
259D4—6042no—
260D4—1511no—
261D4D4×D15111yescharacteristic
262D4C2×C22⋊D15112yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—3021no—
267C2×C4—3021no—
268C2×C4—3022no—
269C2×C4—6042no—
270C2×C4—6042no—
271C2×C4C23×D15111yescharacteristic
272C8—21no—
273C8—3022no—
274C8—3021no—
275C8—1511no—
276C8—1511no—
277C8C2×C22⋊D15111yescharacteristic
278C8C2×C22⋊D15111yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—3021no—
285C22#1801278411yescharacteristic
286C4—21no—
287C4—22no—
288C4—3021no—
289C4—6041no—
290C4—6042no—
291C4C2×D4×D15111yescharacteristic
292C4C22×C22⋊D15111yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—6041no—
298C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#576×C151C2
socleC2×C151D42
hypercenter#576D151
hypocenterC151#3290
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #23753026C2semidirect
2. #23753023C2semidirect
3. #23752595C2semidirect
4. #23752487C2semidirect
5. #23752479C2semidirect
6. #23752473C2semidirect
7. #23752390C2semidirect
8. #23752383C2semidirect
9. #23752329C2semidirect
10. #23752327C2semidirect
11. #576×C151C2semidirect
12. #18012786C22semidirect
15. #18012769C22semidirect
18. #18012765C22semidirect
22. C2×Dic604C22semidirect
25. C2×#14558992C22semidirect
26. #18012746C22semidirect
27. #18012745C22semidirect
28. #18012726C22semidirect
29. #18012675C22semidirect
30. #18012674C22semidirect
32. #18012666C22semidirect
33. #18012665C22semidirect
34. #18012657C22semidirect
35. #18012656C22semidirect
36. C8×Dic151C22semidirect
149. C151#3290semidirect
153. #576D151semidirect

Maximal subgroups

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

subgroupindex
#237530262
#237530232
#237525952
#237524872
#237524792
#237524732
#237523902
#237523832
#237523292
#237523272
#576×C1512
#3290151