Finite Group Databasebeta

← #36374116

Subgroups — #36374116

Order 22336.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#19150232C211yesmaximal, characteristic
2#26013595C212yesmaximal, complemented
3#26013554C211yesmaximal, characteristic, complemented
4#26013553C212yesmaximal, complemented
5#99×C349C211yesmaximal, characteristic, complemented
6#19150232—22no—
7#19150232—22no—
8C2×Dic698C411yescharacteristic, complemented
9C2×C22⋊D349C411yescharacteristic, complemented
10C2×C22⋊D349C2211yescharacteristic
11C22×Dic349C411yescharacteristic, complemented
12C22×Dic349C2211yescharacteristic
13C2×C4×D349C411yescharacteristic, complemented
14#19150212—22no—
15C22⋊Dic349C2212yes—
16C4×Dic349—22no—
17C2×D4×C349C2211yescharacteristic
18C22⋊C4×C349C2212yes—
19C22×D349C2×C411yescharacteristic
20Dic698—22no—
21C22⋊D349—22no—
22C22⋊D349—22no—
23C2×Dic349—21no—
24C2×Dic349—21no—
25C2×Dic349—22no—
26C2×Dic349C2×C411yescharacteristic
27C2×Dic349C2×C411yescharacteristic
28C2×Dic349C2×C411yescharacteristic
29C2×Dic349D412yes—
30C2×Dic349D412yes—
31C4×D349—21no—
32C4×D349—21no—
33C23×C349C2×C411yescharacteristic
34C23×C349C2311yescharacteristic
35D4×C349—22no—
36C2×C4×C349—22no—
37C2×C4×C349C2×C411yescharacteristic
38C22×C349—21no—
39C22×C349—41no—
40C22×C349—41no—
41C22×C349C22×C411yescharacteristic
42C22×C349C2×D412yes—
43C2×D349—21no—
44C2×D349—41no—
45C4×C349—21no—
46C4×C349—42no—
47Dic349—21no—
48Dic349—42no—
49Dic349C22⋊C411yescharacteristic
50Dic349C22⋊C411yescharacteristic
51Dic349C22⋊C412yes—
52C2×C349—22no—
53C2×C349—21no—
54C2×C349—41no—
55C2×C349C2×C22⋊C411yescharacteristic
56D349—41no—
57C349#41011yescharacteristic, complemented, Sylow
58#410—3491nomaximal, Sylow
59C2×#41—3491no—
60#117—3492no—
61#99—3491no—
62#99—3492no—
63#99D34911yescharacteristic, complemented
64#41—6982no—
65#41—6982no—
66C2×Q8—3491no—
67C2×D4—3491no—
68C2×D4—3491no—
69C2×D4C2×D34911yescharacteristic
70C22×C4—3491no—
71C22×C4—3491no—
72C22×C4—3491no—
73C4⋊C4—6982no—
74C22⋊C4—3492no—
75C22⋊C4C2×D34912yes—
76C42—6982no—
77C23—3491no—
78C23C4×D34911yescharacteristic
79C23C22×D34911yescharacteristic
80Q8—6982no—
81D4—22no—
82D4—6982no—
83D4—6982no—
84C2×C4—22no—
85C2×C4—3491no—
86C2×C4—3491no—
87C2×C4—3492no—
88C2×C4—3492no—
89C2×C4—3491no—
90C2×C4—6981no—
91C2×C4—6981no—
92C2×C4—6981no—
93C2×C4—6981no—
94C2×C4—6982no—
95C2×C4C4×D34911yescharacteristic
96C22—21no—
97C22—41no—
98C22—41no—
99C22—13961no—
100C22—6981no—
101C22C2×C4×D34911yescharacteristic
102C22D4×D34912yes—
103C4—21no—
104C4—42no—
105C4—3491no—
106C4—3491no—
107C4—3492no—
108C4—13962no—
109C4—6981no—
110C2—22no—
111C2—21no—
112C2—41no—
113C2—13961no—
114C2C22⋊C4×D34911yescharacteristic
subgroupG/H
centerC2C22⋊C4×D349
commutatorC22×C349C22×C4
FrattiniC23C22×D349
Fitting#99×C349C2
socleC2×C349C2×C22⋊C4
prime radicalC2×#19150232C2
cosocleC23×C349C23
hypercenter#99D349
hypocenterC349#410
LCSG ▷ C22×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #26013595C2semidirect
3. #26013554C2semidirect
4. #26013553C2semidirect
5. #99×C349C2semidirect
8. C2×Dic698C4semidirect
9. C2×C22⋊D349C4semidirect
11. C22×Dic349C4semidirect
13. C2×C4×D349C4semidirect
57. C349#410semidirect
63. #99D349semidirect

Maximal subgroups

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

subgroupindex
C2×#191502322
#260135952
#260135542
#260135532
#99×C3492
#410349