Finite Group Databasebeta

← #36374159

Subgroups — #36374159

Order 22336.

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

normal subgroups only

This group has 154 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
1#41×D349C211yesmaximal, characteristic
2M16×D349C211yesmaximal, characteristic, complemented
3#26013596C211yesmaximal, characteristic, complemented
4#26013567C211yesmaximal, characteristic, complemented
5#26013566C211yesmaximal, characteristic, complemented
6#26013565C211yesmaximal, characteristic, complemented
7#104×C349C211yesmaximal, characteristic, complemented
8#19150234C411yescharacteristic, complemented
9#19150233—21no—
10#19150233C2211yescharacteristic
11#19150232—21no—
12#19150232C411yescharacteristic, complemented
13Q8×D349C411yescharacteristic, complemented
14D4×D349—21no—
15D4×D349C411yescharacteristic, complemented
16C2×C4×D349—21no—
17C2×C4×D349C2211yescharacteristic
18#19150217C2211yescharacteristic, complemented
19#19150216—21no—
20C8×D349—21no—
21#19150212—21no—
22#19150210—21no—
23C4×Dic349C2211yescharacteristic, complemented
24#41×C349C2211yescharacteristic
25M16×C349C2211yescharacteristic, complemented
26C42×C349C2211yescharacteristic, complemented
27C22×D349—21no—
28C22×D349D411yescharacteristic
29Dic698—21no—
30Dic698C2×C411yescharacteristic
31D1396—21no—
32D1396C2×C411yescharacteristic
33C22⋊D349—21no—
34C22⋊D349—21no—
35C22⋊D349—21no—
36C2×Dic349—21no—
37C2×Dic349—21no—
38C2×Dic349D411yescharacteristic
39C4×D349—21no—
40C4×D349—21no—
41C4×D349—21no—
42C4×D349C2×C411yescharacteristic
43C4×D349C2×C411yescharacteristic
44C4×D349D411yescharacteristic
45C4×D349D411yescharacteristic
46#14584095—21no—
47Q8×C349C2×C411yescharacteristic
48D4×C349—21no—
49D4×C349C2×C411yescharacteristic
50C2×C4×C349—21no—
51C2×C4×C349—21no—
52C2×C4×C349C2311yescharacteristic
53C8×C349—21no—
54C22×C349—21no—
55C22×C349C2×D411yescharacteristic
56C2×D349—21no—
57C2×D349—41no—
58C2×D349—42no—
59C2×D349C22⋊C411yescharacteristic
60C2×D349C22⋊C411yescharacteristic
61C4×C349—21no—
62C4×C349—41no—
63C4×C349C22×C411yescharacteristic
64C4×C349C2×D411yescharacteristic
65Dic349—21no—
66Dic349—41no—
67Dic349C22⋊C411yescharacteristic
68Dic349C22⋊C411yescharacteristic
69C2×C349—21no—
70C2×C349—41no—
71C2×C349C2×C22⋊C411yescharacteristic
72D349—21no—
73D349—21no—
74D349—41no—
75C349#42111yescharacteristic, complemented, Sylow
76#421—3491nomaximal, Sylow
77C2×#41—3491no—
78C2×M16—3491no—
79#117—3491no—
80#104—3491no—
81#104—3491no—
82#104—3491no—
83#104D34911yescharacteristic, complemented
84#41—3491no—
85#41—3491no—
86#41—3491no—
87#41—6981no—
88#41—6981no—
89#41C2×D34911yescharacteristic
90C2×Q8—3491no—
91C2×D4—3491no—
92C2×D4—6981no—
93C22×C4—3491no—
94C22×C4—6981no—
95M16—3491no—
96M16—6981no—
97M16C2×D34911yescharacteristic, complemented
98C2×C8—6981no—
99C4⋊C4—6981no—
100C22⋊C4—6981no—
101C42—3491no—
102C42C2×D34911yescharacteristic, complemented
103C23—3491no—
104C23—6981no—
105Q8—3491no—
106Q8—6981no—
107Q8C4×D34911yescharacteristic
108D4—21no—
109D4—3491no—
110D4—6981no—
111D4—6981no—
112D4—6981no—
113D4—6981no—
114D4C4×D34911yescharacteristic
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—3491no—
118C2×C4—3491no—
119C2×C4—3491no—
120C2×C4—3491no—
121C2×C4—3491no—
122C2×C4—6981no—
123C2×C4—6981no—
124C2×C4—6981no—
125C2×C4—6981no—
126C2×C4—6981no—
127C2×C4C22×D34911yescharacteristic
128C8—21no—
129C8—6981no—
130C22—21no—
131C22—3491no—
132C22—3491no—
133C22—13961no—
134C22—13962no—
135C22—6981no—
136C22D4×D34911yescharacteristic
137C4—21no—
138C4—41no—
139C4—3491no—
140C4—3491no—
141C4—13961no—
142C4—6981no—
143C4C2×C4×D34911yescharacteristic
144C4D4×D34911yescharacteristic
145C2—21no—
146C2—41no—
147C2—13961no—
148C2—6981no—
149C2—6981no—
150C2C22⋊C4×D34911yescharacteristic
subgroupG/H
centerC4D4×D349
commutatorC4×C349C22×C4
FrattiniC2×C4C22×D349
Fitting#104×C349C2
socleC2×C349C2×C22⋊C4
prime radical#41×D349C2
cosocleC2×C4×C349C23
hypercenter#104D349
hypocenterC349#421
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D349C2semidirect
3. #26013596C2semidirect
4. #26013567C2semidirect
5. #26013566C2semidirect
6. #26013565C2semidirect
7. #104×C349C2semidirect
8. #19150234C4semidirect
12. #19150232C4semidirect
13. Q8×D349C4semidirect
15. D4×D349C4semidirect
18. #19150217C22semidirect
23. C4×Dic349C22semidirect
25. M16×C349C22semidirect
26. C42×C349C22semidirect
75. C349#421semidirect
83. #104D349semidirect
97. M16C2×D349semidirect
102. C42C2×D349semidirect

Maximal subgroups

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

subgroupindex
#41×D3492
M16×D3492
#260135962
#260135672
#260135662
#260135652
#104×C3492
#421349