Finite Group Databasebeta

← #37566050

Subgroups — #37566050

Order 24256.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#27131379C211yesmaximal, characteristic, complemented
2#27131376C211yesmaximal, characteristic, complemented
3#27131362C211yesmaximal, characteristic, complemented
4#27131360C212yesmaximal, complemented
5#27131358C212yesmaximal, complemented
6#27131357C211yesmaximal, characteristic, complemented
7#27131353C211yesmaximal, characteristic, complemented
8#27131352C212yesmaximal, complemented
9SD16×D379C212yesmaximal, complemented
10#27131337C211yesmaximal, characteristic, complemented
11C2×SD16×C379C211yesmaximal, characteristic, complemented
12#20258607—21no—
13#20258607C2212yescomplemented
14#20258606—22no—
15#20258606C2211yescharacteristic
16#20258606C2211yescharacteristic
17#20258606C2211yescharacteristic, complemented
18#20258605—21no—
19#20258605C2212yes—
20Q8×D379—21no—
21Q8×D379C2212yescomplemented
22C2×C22⋊D379—22no—
23D4×D379—21no—
24D4×D379C2212yes—
25Dic1516C2211yescharacteristic, complemented
26#20258596C2212yescomplemented
27#20258595C2211yescharacteristic, complemented
28#20258595C2211yescharacteristic, complemented
29#20258594C2212yescomplemented
30#20258593C2212yescomplemented
31D3032C2211yescharacteristic, complemented
32#20258591C2212yescomplemented
33#20258590C2211yescharacteristic, complemented
34#20258589C2212yescomplemented
35C8×D379C2212yescomplemented
36C2×Q8×C379C2211yescharacteristic, complemented
37C2×D4×C379C2211yescharacteristic
38SD16×C379C2212yescomplemented
39SD16×C379C2212yescomplemented
40C2×C8×C379C2211yescharacteristic, complemented
41C22×D379—22no—
42Dic758—22no—
43Dic758D411yescharacteristic
44Dic758C2311yescharacteristic
45Dic758C2311yescharacteristic
46D1516—22no—
47D1516D411yescharacteristic
48D1516C2311yescharacteristic
49D1516C2311yescharacteristic
50C22⋊D379—21no—
51C22⋊D379—21no—
52C22⋊D379—22no—
53C22⋊D379—22no—
54C22⋊D379D412yes—
55C2×Dic379—22no—
56C4×D379—22no—
57C4×D379—21no—
58C4×D379—21no—
59C4×D379—22no—
60C4×D379C2312yes—
61C379⋊C8C2312yes—
62C23×C379—21no—
63Q8×C379—21no—
64Q8×C379C2312yes—
65D4×C379—21no—
66D4×C379C2312yes—
67C2×C4×C379—21no—
68C2×C4×C379C2311yescharacteristic
69C8×C379C2311yescharacteristic
70C8×C379C2311yescharacteristic
71C22×C379—22no—
72C22×C379—81no—
73C22×C379C2×D411yescharacteristic
74C2×D379—21no—
75C2×D379—21no—
76C2×D379—82no—
77C2×D379C2×D412yes—
78C4×C379—22no—
79C4×C379C2×D411yescharacteristic
80C4×C379C2411yescharacteristic
81Dic379—21no—
82Dic379—21no—
83Dic379C2×D412yes—
84C2×C379—21no—
85C2×C379—42no—
86C2×C379C22×D411yescharacteristic
87D379—22no—
88D379—41no—
89D379—41no—
90C379#57711yescharacteristic, complemented, Sylow
91#577—3791nomaximal, Sylow
922−1+4—3791no—
93H(5,𝔽2)—3791no—
94#137—3791no—
95#137—3792no—
96AGL(1,ℤ/8)—3791no—
97AGL(1,ℤ/8)—3792no—
98#135—3792no—
99#135—3791no—
100C2×SD16—3792no—
101C2×SD16D37911yescharacteristic, complemented
102#131—3791no—
103#41—3791no—
104#41—3792no—
105#41—3792no—
106#41—3791no—
107#41—3791no—
108#41—7582no—
109#41—7581no—
110#41—7581no—
111C2×Q8—3792no—
112C2×Q8—7581no—
113C2×Q8C2×D37911yescharacteristic, complemented
114C2×D4—3792no—
115C2×D4—7581no—
116C2×D4—7582no—
117C2×D4C2×D37911yescharacteristic
118Q16—3792no—
119Q16—3791no—
120SD16—3792no—
121SD16—3792no—
122SD16—3791no—
123SD16—3791no—
124SD16C2×D37912yescomplemented
125SD16C2×D37912yescomplemented
126D8—3792no—
127D8—3791no—
128M16—3791no—
129M16—3792no—
130C2×C8—3792no—
131C2×C8C2×D37911yescharacteristic, complemented
132C23—21no—
133C23—7582no—
134Q8—21no—
135Q8—3791no—
136Q8—3791no—
137Q8—3791no—
138Q8—7582no—
139Q8C22×D37912yes—
140D4—21no—
141D4—3792no—
142D4—3791no—
143D4—3791no—
144D4—3791no—
145D4—7582no—
146D4—7582no—
147D4—7582no—
148D4—7581no—
149D4—7581no—
150D4C22×D37912yes—
151C2×C4—21no—
152C2×C4—3792no—
153C2×C4—7582no—
154C2×C4—7582no—
155C2×C4—7582no—
156C2×C4—7581no—
157C2×C4—7581no—
158C2×C4C22×D37911yescharacteristic
159C8—3792no—
160C8C22×D37911yescharacteristic
161C8C22×D37911yescharacteristic
162C22—22no—
163C22—81no—
164C22—3792no—
165C22—30322no—
166C22—7581no—
167C22—7581no—
168C22D4×D37911yescharacteristic
169C4—22no—
170C4—3792no—
171C4—7581no—
172C4—7581no—
173C4D4×D37911yescharacteristic
174C4C23×D37911yescharacteristic
175C2—21no—
176C2—42no—
177C2—15161no—
178C2—15161no—
179C2—7582no—
180C2C2×D4×D37911yescharacteristic
subgroupG/H
centerC2C2×D4×D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingC2×SD16×C379C2
socleC2×C379C22×D4
hypercenterC2×SD16D379
hypocenterC379#577
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #27131379C2semidirect
2. #27131376C2semidirect
3. #27131362C2semidirect
4. #27131360C2semidirect
5. #27131358C2semidirect
6. #27131357C2semidirect
7. #27131353C2semidirect
8. #27131352C2semidirect
9. SD16×D379C2semidirect
10. #27131337C2semidirect
11. C2×SD16×C379C2semidirect
13. #20258607C22semidirect
17. #20258606C22semidirect
21. Q8×D379C22semidirect
25. Dic1516C22semidirect
26. #20258596C22semidirect
27. #20258595C22semidirect
28. #20258595C22semidirect
29. #20258594C22semidirect
30. #20258593C22semidirect
31. D3032C22semidirect
32. #20258591C22semidirect
33. #20258590C22semidirect
34. #20258589C22semidirect
35. C8×D379C22semidirect
36. C2×Q8×C379C22semidirect
38. SD16×C379C22semidirect
39. SD16×C379C22semidirect
40. C2×C8×C379C22semidirect
90. C379#577semidirect
101. C2×SD16D379semidirect
113. C2×Q8C2×D379semidirect
124. SD16C2×D379semidirect
125. SD16C2×D379semidirect
131. C2×C8C2×D379semidirect

Maximal subgroups

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

subgroupindex
#271313792
#271313762
#271313622
#271313602
#271313582
#271313572
#271313532
#271313522
SD16×D3792
#271313372
C2×SD16×C3792
#577379