Finite Group Databasebeta

← #34000450

Subgroups — #34000450

Order 18688.

180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 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#22625862C211yesmaximal, characteristic
2#22625151C211yesmaximal, characteristic
3#22611741C211yesmaximal, characteristic
4#17989606—21no—
5#17989469—21no—
6#17989458—21no—
7#17989456C411yescharacteristic
8#17989455C411yescharacteristic
9#17989429—21no—
10#17989428C411yescharacteristic, complemented
11C8×#10596833C411yescharacteristic, complemented
12#17988539C2211yescharacteristic
13#17988407—21no—
14#17988368—21no—
15#17988365C411yescharacteristic, complemented
16#347×C73C411yescharacteristic, complemented
17D73⋊M16—21no—
18#14556670—21no—
19C4⋊#10596833—22no—
20#14556648—22no—
21C4×#10596833—21no—
22C4×#10596833—21no—
23C2×#11924011C2×C411yescharacteristic
24C2×#11924011D411yescharacteristic
25C42×D73D411yescharacteristic
26#14556531—21no—
27#14556502Q811yescharacteristic
28C8×Dic73C2×C411yescharacteristic
29C8×Dic73D411yescharacteristic
30M32×C73—21no—
31#97×C73C2×C411yescharacteristic
32#11924038—41no—
33#11924037—41no—
34#11924036—41no—
35C2×#10596833—22no—
36C2×#10596833—22no—
37C4⋊#64408—41no—
38C22⋊#64408—41no—
39C4×#64408—41no—
40C2×C4×D73—21no—
41C2×C4×D73C22⋊C411yescharacteristic
42#11924011—41no—
43#11924011—41no—
44C2×#10596831C4⋊C411yescharacteristic
45C2×#10596831C4⋊C411yescharacteristic
46C4×Dic73—21no—
47C4×Dic73C22⋊C411yescharacteristic
48#11924003—41no—
49C2×C8×C73C4211yescharacteristic
50C2×C8×C73C22⋊C411yescharacteristic
51C42×C73C4⋊C411yescharacteristic
52C16×C73—41no—
53C22×D73#10411yescharacteristic
54C2×#64408—81no—
55C2×C4×C73—21no—
56C2×C4×C73#9511yescharacteristic
57C2×Dic73—21no—
58C2×Dic73#10411yescharacteristic
59C4×D73—21no—
60C4×D73—21no—
61C4×D73—42no—
62#10596833—42no—
63#10596833—42no—
64#10596833—81no—
65C8×C73—21no—
66C8×C73—21no—
67#10596831—21no—
68#10596831—21no—
69C22×C73#33911yescharacteristic
70C2×D73—21no—
71C2×D73—41no—
72#64408—161no—
73C4×C73—41no—
74C4×C73H(3,ℤ/4)11yescharacteristic
75C4×C73#34411yescharacteristic
76Dic73—22no—
77Dic73—21no—
78#7226—731nomaximal, Sylow
79C2×C73—21no—
80C2×C73#128811yescharacteristic
81D73—41no—
82#2165—731no—
83#1841—731no—
84#1453—731no—
85C73#722611yescharacteristic, complemented, Sylow
86#431—1461no—
87C4×M16—731no—
88#364—1461no—
89#349—1461no—
90#347—731no—
91#347#6440811yescharacteristic, complemented
92#344—1461no—
93#339—1461no—
94#338—731no—
95H(3,ℤ/4)—731no—
96#322—731no—
97#322—1461no—
98C82—731no—
99C2×M16—731no—
100C2×M16—731no—
101C2×M16—1461no—
102#117—1461no—
103C2×C42—731no—
104M32—21no—
105M32—1461no—
106C4⋊C8—1462no—
107C22⋊C8—1462no—
108#97—731no—
109#97C2×#6440811yescharacteristic
110C4×C8—731no—
111C4×C8—731no—
112C4×C8—1461no—
113C4×C8—1461no—
114C22×C4—731no—
115C22×C4—1461no—
116M16—2921no—
117M16—2921no—
118M16—2921no—
119M16—2921no—
120C2×C8—2921no—
121C2×C8—731no—
122C2×C8—731no—
123C2×C8—1462no—
124C2×C8—1462no—
125C2×C8C4×#6440811yescharacteristic
126C2×C8C22⋊#6440811yescharacteristic
127C4⋊C4—2921no—
128C22⋊C4—2921no—
129C42—2921no—
130C42—731no—
131C42—1461no—
132C42C4⋊#6440811yescharacteristic
133C16—41no—
134C16—2921no—
135C23—731no—
136C2×C4—21no—
137C2×C4—2922no—
138C2×C4—5841no—
139C2×C4—731no—
140C2×C4—1461no—
141C2×C4—1461no—
142C2×C4—1461no—
143C2×C4(C2×#64408)⋊C411yescharacteristic
144C8—21no—
145C8—21no—
146C8—2922no—
147C8—2922no—
148C8—5841no—
149C8—1461no—
150C8—1461no—
151C22—2921no—
152C22—1461no—
153C22#1798945911yescharacteristic
154C4—41no—
155C4—11681no—
156C4—1462no—
157C4—1461no—
158C4#1798945411yescharacteristic
159C4#1798947011yescharacteristic
160C2—21no—
161C2—2921no—
162C2#2262479211yescharacteristic
subgroupG/H
centerC4#17989454
commutatorC2×C8×C73C42
Frattini#97C2×#64408
Fitting#347×C73C4
socleC2×C73#1288
prime radicalC22×D73#104
cosocle#17988539C22
hypercenter#347#64408
hypocenterC73#7226
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C8 ◁ #347

Complements

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

NH ≅ G/Ntype
10. #17989428C4semidirect
11. C8×#10596833C4semidirect
15. #17988365C4semidirect
16. #347×C73C4semidirect
85. C73#7226semidirect
91. #347#64408semidirect

Maximal subgroups

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

subgroupindex
#226258622
#226251512
#226117412
#722673