Finite Group Databasebeta

← #104×D541 #46830186

Subgroups — #104×D541 #46830186

Order 34624.

170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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#41×D541C211yesmaximal, characteristic
2M16×D541C211yesmaximal, characteristic, complemented
3C42×D541C211yesmaximal, characteristic, complemented
4#31772556C211yesmaximal, characteristic, complemented
5#31772555C211yesmaximal, characteristic, complemented
6#31772554C211yesmaximal, characteristic, complemented
7#104×C541C211yesmaximal, characteristic, complemented
8#22575837C411yescharacteristic, complemented
9#22575836—21no—
10#22575836C2211yescharacteristic
11#22575835—21no—
12#22575835C411yescharacteristic, complemented
13Q8×D541C411yescharacteristic, complemented
14D4×D541—21no—
15D4×D541C411yescharacteristic, complemented
16C2×C4×D541—21no—
17C2×C4×D541—21no—
18C2×C4×D541C2211yescharacteristic
19#22575820C2211yescharacteristic, complemented
20#22575819—21no—
21C8×D541—21no—
22C4×Dic541—21no—
23C4×Dic541C2211yescharacteristic, complemented
24#41×C541C2211yescharacteristic
25M16×C541C2211yescharacteristic, complemented
26C42×C541C2211yescharacteristic, complemented
27C22×D541—21no—
28C22×D541D411yescharacteristic
29Dic1082—21no—
30Dic1082C2×C411yescharacteristic, complemented
31D2164—21no—
32D2164C2×C411yescharacteristic, complemented
33C22⋊D541—21no—
34C22⋊D541—21no—
35C22⋊D541—21no—
36C2×Dic541—21no—
37C2×Dic541—21no—
38C2×Dic541D411yescharacteristic
39C4×D541—24no—
40C4×D541—21no—
41C4×D541—21no—
42C4×D541—21no—
43C4×D541C2×C411yescharacteristic
44C4×D541C2×C411yescharacteristic
45C4×D541D411yescharacteristic
46C4×D541D411yescharacteristic
47#16864513—21no—
48Q8×C541C2×C411yescharacteristic, complemented
49D4×C541—21no—
50D4×C541C2×C411yescharacteristic, complemented
51C2×C4×C541—21no—
52C2×C4×C541—21no—
53C2×C4×C541C2311yescharacteristic
54C8×C541—21no—
55C22×C541—21no—
56C22×C541C2×D411yescharacteristic
57C2×D541—22no—
58C2×D541—21no—
59C2×D541—42no—
60C2×D541C22⋊C411yescharacteristic
61C2×D541C22⋊C411yescharacteristic
62C4×C541—22no—
63C4×C541—21no—
64C4×C541C22×C411yescharacteristic
65C4×C541C2×D411yescharacteristic
66Dic541—22no—
67Dic541—21no—
68Dic541C22⋊C411yescharacteristic
69Dic541C22⋊C411yescharacteristic
70C2×C541—21no—
71C2×C541—41no—
72C2×C541C2×C22⋊C411yescharacteristic
73D541—21no—
74D541—41no—
75D541#10412yesdirect product factor
76C541C2×#10411yescharacteristic, complemented, Sylow
77C2×#104—5411nomaximal, Sylow
78C2×#41—5411no—
79C2×M16—5411no—
80C2×C42—5411no—
81#104—5411no—
82#104—5411no—
83#104—5411no—
84#104D54111yescharacteristic, direct product factor
85#41—5411no—
86#41—5411no—
87#41—5411no—
88#41—10821no—
89#41—10821no—
90#41C2×D54111yescharacteristic
91C2×Q8—5411no—
92C2×D4—5411no—
93C2×D4—10821no—
94C22×C4—5411no—
95C22×C4—10821no—
96C22×C4—10821no—
97M16—5411no—
98M16—10821no—
99M16C2×D54111yescharacteristic, complemented
100C2×C8—10821no—
101C42—5411no—
102C42—10821no—
103C42C2×D54111yescharacteristic, complemented
104C23—5411no—
105C23—10821no—
106Q8—5411no—
107Q8—10821no—
108Q8C4×D54111yescharacteristic, complemented
109D4—21no—
110D4—5411no—
111D4—10821no—
112D4—10821no—
113D4—10821no—
114D4—10821no—
115D4C4×D54111yescharacteristic, complemented
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—5411no—
119C2×C4—5411no—
120C2×C4—5411no—
121C2×C4—5411no—
122C2×C4—5411no—
123C2×C4—10821no—
124C2×C4—10821no—
125C2×C4—10824no—
126C2×C4—10821no—
127C2×C4—10821no—
128C2×C4—10821no—
129C2×C4C22×D54111yescharacteristic
130C8—21no—
131C8—10821no—
132C22—21no—
133C22—5411no—
134C22—5411no—
135C22—10822no—
136C22—10821no—
137C22—21642no—
138C22D4×D54111yescharacteristic
139C4—22no—
140C4—21no—
141C4—5411no—
142C4—5411no—
143C4—10822no—
144C4—10821no—
145C4C2×C4×D54111yescharacteristic
146C4D4×D54111yescharacteristic
147C2—21no—
148C2—41no—
149C2—5412no—
150C2—10821no—
151C2—21641no—
152C2C22⋊C4×D54111yescharacteristic
subgroupG/H
centerC4D4×D541
commutatorC4×C541C22×C4
FrattiniC2×C4C22×D541
Fitting#104×C541C2
socleC2×C541C2×C22⋊C4
prime radical#41×D541C2
cosocleC2×C4×C541C23
hypercenter#104D541
hypocenterC541C2×#104
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D541C2semidirect
3. C42×D541C2semidirect
4. #31772556C2semidirect
5. #31772555C2semidirect
6. #31772554C2semidirect
7. #104×C541C2semidirect
8. #22575837C4semidirect
12. #22575835C4semidirect
13. Q8×D541C4semidirect
15. D4×D541C4semidirect
19. #22575820C22semidirect
23. C4×Dic541C22semidirect
25. M16×C541C22semidirect
26. C42×C541C22semidirect
30. Dic1082C2×C4semidirect
32. D2164C2×C4semidirect
48. Q8×C541C2×C4semidirect
50. D4×C541C2×C4semidirect
75. D541#104direct (N × H)
76. C541C2×#104semidirect
84. #104D541direct (N × H)
99. M16C2×D541semidirect
103. C42C2×D541semidirect
108. Q8C4×D541semidirect
115. D4C4×D541semidirect

Maximal subgroups

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

subgroupindex
#41×D5412
M16×D5412
C42×D5412
#317725562
#317725552
#317725542
#104×C5412
C2×#104541