Finite Group Databasebeta

← #104×D379 #37565255

Subgroups — #104×D379 #37565255

Order 24256.

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×D379C211yesmaximal, characteristic
2M16×D379C211yesmaximal, characteristic, complemented
3C42×D379C211yesmaximal, characteristic, complemented
4#27131259C211yesmaximal, characteristic, complemented
5#27131258C211yesmaximal, characteristic, complemented
6#27131257C211yesmaximal, characteristic, complemented
7#104×C379C211yesmaximal, characteristic, complemented
8#20258607C411yescharacteristic, complemented
9#20258606—21no—
10#20258606C2211yescharacteristic
11#20258605—21no—
12#20258605C411yescharacteristic, complemented
13Q8×D379C411yescharacteristic, complemented
14D4×D379—21no—
15D4×D379C411yescharacteristic, complemented
16C2×C4×D379—21no—
17C2×C4×D379—21no—
18C2×C4×D379C2211yescharacteristic
19#20258590C2211yescharacteristic, complemented
20#20258589—21no—
21C8×D379—21no—
22C4×Dic379—21no—
23C4×Dic379C2211yescharacteristic, complemented
24#41×C379C2211yescharacteristic
25M16×C379C2211yescharacteristic, complemented
26C42×C379C2211yescharacteristic, complemented
27C22×D379—21no—
28C22×D379D411yescharacteristic
29Dic758—21no—
30Dic758C2×C411yescharacteristic, complemented
31D1516—21no—
32D1516C2×C411yescharacteristic, complemented
33C22⋊D379—21no—
34C22⋊D379—21no—
35C22⋊D379—21no—
36C2×Dic379—21no—
37C2×Dic379—21no—
38C2×Dic379D411yescharacteristic
39C4×D379—24no—
40C4×D379—21no—
41C4×D379—21no—
42C4×D379—21no—
43C4×D379C2×C411yescharacteristic
44C4×D379C2×C411yescharacteristic
45C4×D379D411yescharacteristic
46C4×D379D411yescharacteristic
47C379⋊C8—21no—
48Q8×C379C2×C411yescharacteristic, complemented
49D4×C379—21no—
50D4×C379C2×C411yescharacteristic, complemented
51C2×C4×C379—21no—
52C2×C4×C379—21no—
53C2×C4×C379C2311yescharacteristic
54C8×C379—21no—
55C22×C379—21no—
56C22×C379C2×D411yescharacteristic
57C2×D379—22no—
58C2×D379—21no—
59C2×D379—42no—
60C2×D379C22⋊C411yescharacteristic
61C2×D379C22⋊C411yescharacteristic
62C4×C379—22no—
63C4×C379—21no—
64C4×C379C22×C411yescharacteristic
65C4×C379C2×D411yescharacteristic
66Dic379—22no—
67Dic379—21no—
68Dic379C22⋊C411yescharacteristic
69Dic379C22⋊C411yescharacteristic
70C2×C379—21no—
71C2×C379—41no—
72C2×C379C2×C22⋊C411yescharacteristic
73D379—21no—
74D379—41no—
75D379#10412yesdirect product factor
76C379C2×#10411yescharacteristic, complemented, Sylow
77C2×#104—3791nomaximal, Sylow
78C2×#41—3791no—
79C2×M16—3791no—
80C2×C42—3791no—
81#104—3791no—
82#104—3791no—
83#104—3791no—
84#104D37911yescharacteristic, direct product factor
85#41—3791no—
86#41—3791no—
87#41—3791no—
88#41—7581no—
89#41—7581no—
90#41C2×D37911yescharacteristic
91C2×Q8—3791no—
92C2×D4—3791no—
93C2×D4—7581no—
94C22×C4—3791no—
95C22×C4—7581no—
96C22×C4—7581no—
97M16—3791no—
98M16—7581no—
99M16C2×D37911yescharacteristic, complemented
100C2×C8—7581no—
101C42—3791no—
102C42—7581no—
103C42C2×D37911yescharacteristic, complemented
104C23—3791no—
105C23—7581no—
106Q8—3791no—
107Q8—7581no—
108Q8C4×D37911yescharacteristic, complemented
109D4—21no—
110D4—3791no—
111D4—7581no—
112D4—7581no—
113D4—7581no—
114D4—7581no—
115D4C4×D37911yescharacteristic, complemented
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—3791no—
119C2×C4—3791no—
120C2×C4—3791no—
121C2×C4—3791no—
122C2×C4—3791no—
123C2×C4—7581no—
124C2×C4—7581no—
125C2×C4—7584no—
126C2×C4—7581no—
127C2×C4—7581no—
128C2×C4—7581no—
129C2×C4C22×D37911yescharacteristic
130C8—21no—
131C8—7581no—
132C22—21no—
133C22—3791no—
134C22—3791no—
135C22—15162no—
136C22—7582no—
137C22—7581no—
138C22D4×D37911yescharacteristic
139C4—22no—
140C4—21no—
141C4—3791no—
142C4—3791no—
143C4—7582no—
144C4—7581no—
145C4C2×C4×D37911yescharacteristic
146C4D4×D37911yescharacteristic
147C2—21no—
148C2—41no—
149C2—3792no—
150C2—15161no—
151C2—7581no—
152C2C22⋊C4×D37911yescharacteristic
subgroupG/H
centerC4D4×D379
commutatorC4×C379C22×C4
FrattiniC2×C4C22×D379
Fitting#104×C379C2
socleC2×C379C2×C22⋊C4
prime radical#41×D379C2
cosocleC2×C4×C379C23
hypercenter#104D379
hypocenterC379C2×#104
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D379C2semidirect
3. C42×D379C2semidirect
4. #27131259C2semidirect
5. #27131258C2semidirect
6. #27131257C2semidirect
7. #104×C379C2semidirect
8. #20258607C4semidirect
12. #20258605C4semidirect
13. Q8×D379C4semidirect
15. D4×D379C4semidirect
19. #20258590C22semidirect
23. C4×Dic379C22semidirect
25. M16×C379C22semidirect
26. C42×C379C22semidirect
30. Dic758C2×C4semidirect
32. D1516C2×C4semidirect
48. Q8×C379C2×C4semidirect
50. D4×C379C2×C4semidirect
75. D379#104direct (N × H)
76. C379C2×#104semidirect
84. #104D379direct (N × H)
99. M16C2×D379semidirect
103. C42C2×D379semidirect
108. Q8C4×D379semidirect
115. D4C4×D379semidirect

Maximal subgroups

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

subgroupindex
#41×D3792
M16×D3792
C42×D3792
#271312592
#271312582
#271312572
#104×C3792
C2×#104379