Finite Group Databasebeta

← #36374315

Subgroups — #36374315

Order 22336.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#26013686C211yesmaximal, characteristic, complemented
2#26013665C211yesmaximal, characteristic, complemented
3#26013626C211yesmaximal, characteristic, complemented
4#26013566C211yesmaximal, characteristic, complemented
5#26013565C211yesmaximal, characteristic, complemented
6#26013557C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C349C211yesmaximal, characteristic, complemented
8#19150233—21no—
9#19150233C2211yescharacteristic
10#19150232—22no—
11#19150232—21no—
12C2×Dic698—21no—
13C2×Dic698C2211yescharacteristic
14Q8×D349—21no—
15#19150221—21no—
16#19150218—21no—
17#19150217C2211yescharacteristic
18C22⋊Dic349—22no—
19C4×Dic349C2211yescharacteristic
20#41×C349C2211yescharacteristic
21C2×D4×C349C2211yescharacteristic
22SD16×C349—21no—
23D8×C349—21no—
24M16×C349C2211yescharacteristic
25Dic698—22no—
26Dic698—21no—
27Dic698—21no—
28Dic698D411yescharacteristic
29D1396D411yescharacteristic
30C22⋊D349—22no—
31C22⋊D349—21no—
32C2×Dic349—22no—
33C2×Dic349—21no—
34C2×Dic349D412yes—
35C4×D349—22no—
36C4×D349—21no—
37#14584095—21no—
38C23×C349—21no—
39Q8×C349D411yescharacteristic
40D4×C349—21no—
41D4×C349—21no—
42D4×C349—21no—
43D4×C349D411yescharacteristic
44C2×C4×C349—21no—
45C2×C4×C349C2311yescharacteristic
46C8×C349—21no—
47C22×C349—21no—
48C22×C349—42no—
49C22×C349—41no—
50C22×C349C2×D411yescharacteristic
51C2×D349—21no—
52C4×C349—21no—
53C4×C349C2×D411yescharacteristic
54C4×C349C2×D411yescharacteristic
55Dic349—21no—
56Dic349—22no—
57Dic349—41no—
58C2×C349—21no—
59C2×C349—41no—
60C2×C349—81no—
61C2×C349#12011yescharacteristic
62D349—41no—
63C349#45411yescharacteristic, complemented, Sylow
64#454—3491nomaximal, Sylow
652−1+4—3491no—
66AGL(1,ℤ/8)—3491no—
67AGL(1,ℤ/8)D34911yescharacteristic, complemented
68#124—3491no—
69#104—3491no—
70#104—3491no—
71#101—3491no—
72#41—3491no—
73#41—6981no—
74#41—6982no—
75#41—6981no—
76#41C2×D34911yescharacteristic
77C2×Q8—3491no—
78C2×Q8—6981no—
79C2×Q8—6981no—
80C2×D4C2×D34911yescharacteristic
81SD16—21no—
82SD16—6981no—
83D8—21no—
84D8—6981no—
85M16—3491no—
86M16C2×D34911yescharacteristic
87C22⋊C4—6982no—
88C42—3491no—
89C23—21no—
90Q8—3491no—
91Q8—6982no—
92Q8—6981no—
93Q8—6981no—
94Q8C22⋊D34911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3491no—
99D4—6982no—
100D4—6981no—
101D4C22⋊D34911yescharacteristic
102C2×C4—21no—
103C2×C4—3492no—
104C2×C4—6982no—
105C2×C4—6981no—
106C2×C4—6982no—
107C2×C4—6981no—
108C2×C4C22×D34911yescharacteristic
109C8—21no—
110C8—6981no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—6981no—
115C22D4×D34911yescharacteristic
116C4—21no—
117C4—13961no—
118C4—6982no—
119C4—6981no—
120C4D4×D34911yescharacteristic
121C4C2×C22⋊D34911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—13961no—
126C2#2601360711yescharacteristic
subgroupG/H
centerC2#26013607
commutator, cosocleC2×C4×C349C23
FrattiniC2×C4C22×D349
FittingAGL(1,ℤ/8)×C349C2
socleC2×C349#120
hypercenterAGL(1,ℤ/8)D349
hypocenterC349#454
LCSG ▷ C2×C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #26013686C2semidirect
2. #26013665C2semidirect
3. #26013626C2semidirect
4. #26013566C2semidirect
5. #26013565C2semidirect
6. #26013557C2semidirect
7. AGL(1,ℤ/8)×C349C2semidirect
63. C349#454semidirect
67. AGL(1,ℤ/8)D349semidirect

Maximal subgroups

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

subgroupindex
#260136862
#260136652
#260136262
#260135662
#260135652
#260135572
AGL(1,ℤ/8)×C3492
#454349