Finite Group Databasebeta

← #36375135

Subgroups — #36375135

Order 22336.

162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D349⋊M16C211yesmaximal, characteristic, complemented
2C2×C4⋊#13063703C211yesmaximal, characteristic, complemented
3#26013702C212yesmaximal, complemented
4#26013701C212yesmaximal, complemented
5#41×D349C211yesmaximal, characteristic
6C22×#13063703—21no—
7#19150243—21no—
8#19150242—21no—
9D349⋊C8C2212yes—
10C4⋊#13063703—21no—
11C4⋊#13063703C2212yes—
12#19150234C411yescharacteristic, complemented
13#19150233—21no—
14#19150233C411yescharacteristic, complemented
15#19150232—21no—
16#19150232C411yescharacteristic, complemented
17Q8×D349C2211yescharacteristic
18D4×D349—21no—
19D4×D349C2211yescharacteristic
20C2×C4×D349—21no—
21C2×C4×D349C2211yescharacteristic
22#41×C349C411yescharacteristic, complemented
23C2×#13063703—22no—
24C2×#13063703—42no—
25#14584102—22no—
26C22×D349—21no—
27C22×D349D411yescharacteristic
28Dic698—21no—
29Dic698C2×C411yescharacteristic, complemented
30D1396—21no—
31D1396C2×C411yescharacteristic, complemented
32C22⋊D349—21no—
33C22⋊D349—21no—
34C22⋊D349—21no—
35C2×Dic349—21no—
36C2×Dic349D411yescharacteristic
37C4×D349—21no—
38C4×D349—21no—
39C4×D349—21no—
40C4×D349C2×C411yescharacteristic
41C4×D349D411yescharacteristic
42C4×D349D411yescharacteristic
43C4×D349C2311yescharacteristic
44Q8×C349C2×C411yescharacteristic, complemented
45D4×C349—21no—
46D4×C349C2×C411yescharacteristic, complemented
47C2×C4×C349—21no—
48C2×C4×C349C2×C411yescharacteristic
49C22×C349—21no—
50C22×C349C22⋊C411yescharacteristic
51C2×D349—21no—
52C2×D349—21no—
53C2×D349—21no—
54C2×D349—41no—
55C2×D349—41no—
56C2×D349C22⋊C411yescharacteristic
57C2×D349C2×D411yescharacteristic
58#13063703—42no—
59C4×C349—21no—
60C4×C349C22⋊C411yescharacteristic
61C4×C349C22×C411yescharacteristic
62Dic349—21no—
63Dic349C22⋊C411yescharacteristic
64Dic349C2×D411yescharacteristic
65C2×C349—21no—
66C2×C349—41no—
67C2×C349C2×C22⋊C411yescharacteristic
68D349—21no—
69D349—41no—
70D349AGL(1,ℤ/8)11yescharacteristic
71D349#13711yescharacteristic
72C349#41711yescharacteristic, complemented, Sylow
73#417—3491nomaximal, Sylow
74C2×#41—3491no—
75C2×M16—3491no—
76C2×C4⋊C4—3491no—
77#103—3492no—
78#102—3492no—
79#41—3491no—
80#41—3491no—
81#41—3491no—
82#41—6981no—
83#41—6981no—
84#41#1306370311yescharacteristic, complemented
85C2×Q8—3491no—
86C2×D4—3491no—
87C2×D4—6981no—
88C22×C4—3491no—
89C22×C4—6981no—
90C22×C4—6981no—
91M16—6981no—
92M16—6981no—
93C2×C8—3492no—
94C4⋊C4—3492no—
95C4⋊C4—6981no—
96C23—3491no—
97C23—6981no—
98Q8—3491no—
99Q8—6981no—
100Q8C2×#1306370311yescharacteristic, complemented
101D4—21no—
102D4—3491no—
103D4—6981no—
104D4—6981no—
105D4—6981no—
106D4—6981no—
107D4C2×#1306370311yescharacteristic, complemented
108C2×C4—21no—
109C2×C4—3491no—
110C2×C4—3491no—
111C2×C4—3491no—
112C2×C4—3491no—
113C2×C4—3491no—
114C2×C4—13962no—
115C2×C4—6981no—
116C2×C4—6981no—
117C2×C4—6981no—
118C2×C4—6982no—
119C2×C4—6981no—
120C2×C4C2×#1306370311yescharacteristic
121C8—6982no—
122C22—21no—
123C22—3491no—
124C22—3491no—
125C22—13961no—
126C22—13961no—
127C22—6981no—
128C22—6981no—
129C22—6981no—
130C22C22⋊#1306370311yescharacteristic
131C4—21no—
132C4—3491no—
133C4—3491no—
134C4—13962no—
135C4—6981no—
136C4C22⋊#1306370311yescharacteristic
137C4C22×#1306370311yescharacteristic
138C2—21no—
139C2—41no—
140C2—3491no—
141C2—3491no—
142C2—13961no—
143C2—6981no—
144C2C2×C22⋊#1306370311yescharacteristic
subgroupG/H
centerC2C2×C22⋊#13063703
commutatorC4×C349C22×C4
FrattiniC4C22×#13063703
Fitting#41×C349C4
socleC2×C349C2×C22⋊C4
prime radical#41×D349C2
cosocleC4×D349C23
hypercenter#41#13063703
hypocenterC349#417
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. D349⋊M16C2semidirect
2. C2×C4⋊#13063703C2semidirect
3. #26013702C2semidirect
4. #26013701C2semidirect
12. #19150234C4semidirect
14. #19150233C4semidirect
16. #19150232C4semidirect
22. #41×C349C4semidirect
29. Dic698C2×C4semidirect
31. D1396C2×C4semidirect
44. Q8×C349C2×C4semidirect
46. D4×C349C2×C4semidirect
72. C349#417semidirect
84. #41#13063703semidirect
100. Q8C2×#13063703semidirect
107. D4C2×#13063703semidirect

Maximal subgroups

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

subgroupindex
D349⋊M162
C2×C4⋊#130637032
#260137022
#260137012
#41×D3492
#417349