Finite Group Databasebeta

← #36375117

Subgroups — #36375117

Order 22336.

158 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 52 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×#19150242C211yesmaximal, characteristic, complemented
2C22×#14584102C211yesmaximal, characteristic, complemented
3#26013696C212yesmaximal, complemented
4C22⋊#14584102C212yesmaximal, complemented
5C2×#19150232C211yesmaximal, characteristic
6#19150242—22no—
7C2×#14584102—22no—
8C2×#14584102C2212yes—
9C2×#14584102C2212yes—
10#19150232—22no—
11#19150232—22no—
12C2×Dic698C411yescharacteristic
13C2×C22⋊D349C411yescharacteristic
14C2×C22⋊D349C411yescharacteristic
15C22×Dic349C2211yescharacteristic
16C22×Dic349C2211yescharacteristic
17C2×C4×D349C2211yescharacteristic
18C2×D4×C349C411yescharacteristic
19#14584102—22no—
20#14584102—22no—
21C22×D349C2×C411yescharacteristic
22Dic698—22no—
23C22⋊D349—22no—
24C22⋊D349—22no—
25C2×Dic349—21no—
26C2×Dic349—21no—
27C2×Dic349C2×C411yescharacteristic
28C2×Dic349C2×C411yescharacteristic
29C2×Dic349D412yes—
30C2×Dic349D412yes—
31C2×Dic349C2311yescharacteristic
32C4×D349—21no—
33C4×D349—21no—
34C23×C349C2×C411yescharacteristic
35C23×C349C2×C411yescharacteristic
36D4×C349—22no—
37C2×C4×C349C2×C411yescharacteristic
38C22×C349—22no—
39C22×C349—21no—
40C22×C349—22no—
41C22×C349C22⋊C412yes—
42C22×C349C22×C411yescharacteristic
43C2×D349—21no—
44C2×D349—22no—
45C4×C349—21no—
46Dic349—21no—
47Dic349C22⋊C412yes—
48Dic349C2×D411yescharacteristic
49Dic349C2×D411yescharacteristic
50C2×C349—22no—
51C2×C349—41no—
52C2×C349C2×C22⋊C411yescharacteristic
53C2×C349#13112yes—
54D349—41no—
55C349#40811yescharacteristic, complemented, Sylow
56#408—3491nomaximal, Sylow
57C2×#41—3491no—
58C2×M16—3491no—
59C22×C8—3491no—
60C22⋊C8—3492no—
61C22⋊C8—3492no—
62#41—6982no—
63#41—6982no—
64C2×Q8—3491no—
65C2×D4—3491no—
66C2×D4—3491no—
67C2×D4#1306370311yescharacteristic
68C22×C4—3491no—
69C22×C4—3491no—
70C22×C4—3491no—
71M16—6982no—
72C2×C8—3492no—
73C2×C8—3492no—
74C2×C8—6982no—
75C23—3491no—
76C23C2×#1306370311yescharacteristic
77C23C2×#1306370311yescharacteristic
78Q8—6982no—
79D4—22no—
80D4—6982no—
81D4—6982no—
82C2×C4—3492no—
83C2×C4—3492no—
84C2×C4—3491no—
85C2×C4—3491no—
86C2×C4—3491no—
87C2×C4—6981no—
88C2×C4—6981no—
89C2×C4—6981no—
90C2×C4—6981no—
91C2×C4C2×#1306370311yescharacteristic
92C8—6982no—
93C8—6982no—
94C22—22no—
95C22—21no—
96C22—22no—
97C22—6981no—
98C22—6982no—
99C22C22⋊#1306370312yes—
100C22C22×#1306370311yescharacteristic
101C4—21no—
102C4—3491no—
103C4—3491no—
104C4—3492no—
105C4—6981no—
106C2—22no—
107C2—41no—
108C2—13961no—
109C2C2×C22⋊#1306370311yescharacteristic
110C2#2601372612yes—
subgroupG/H
center, FrattiniC22C22×#13063703
commutator, socleC22×C349C22×C4
FittingC2×D4×C349C4
prime radicalC2×#19150232C2
cosocleC2×Dic349C23
hypercenterC2×D4#13063703
hypocenterC349#408
LCSG ▷ C22×C349 ▷ C349
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#19150242C2semidirect
2. C22×#14584102C2semidirect
3. #26013696C2semidirect
4. C22⋊#14584102C2semidirect
55. C349#408semidirect

Maximal subgroups

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

subgroupindex
C2×#191502422
C22×#145841022
#260136962
C22⋊#145841022
C2×#191502322
#408349