Finite Group Databasebeta

← #34033032

Subgroups — #34033032

Order 18688.

200 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 29 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#22626957C212yesmaximal
2#22625828C211yesmaximal, characteristic
3#17989672—22no—
4#17989530C411yescharacteristic
5#17989530C2211yescharacteristic
6#17989465—22no—
7C2×#14556548C411yescharacteristic
8C22⋊#10596842—42no—
9C2×C22⋊#64408—21no—
10C2×C22⋊#64408D412yes—
11(C2×#64408)⋊C4—41no—
12(C2×#64408)⋊C4—41no—
13C22×C4×D73C2×C411yescharacteristic
14#14556548—41no—
15#14556548—41no—
16C2×#11924007—21no—
17C2×#11924005—21no—
18C2×C4×Dic73C811yescharacteristic, complemented
19C2×C42×C73C811yescharacteristic, complemented
20C2×#10596842—82no—
21C22×#64408—22no—
22C22×#64408—41no—
23C22⋊#64408—42no—
24C22⋊#64408—42no—
25C23×D73C22⋊C411yescharacteristic
26C22×Dic73—21no—
27C22×Dic73M1611yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—42no—
31#11924007—42no—
32#11924005—41no—
33#11924005—41no—
34C4×Dic73—41no—
35C22×C4×C73—21no—
36C22×C4×C73C2×C811yescharacteristic
37C42×C73—41no—
38C23×C73C22⋊C811yescharacteristic
39C22×D73—22no—
40C22×D73—81no—
41C22×D73#9911yescharacteristic
42C22×D73#10011yescharacteristic
43C2×#64408—42no—
44C2×#64408—82no—
45C2×#64408—81no—
46C2×#64408—82no—
47#10596842—162no—
48C2×C4×C73—21no—
49C2×C4×C73—41no—
50C2×C4×C73—41no—
51C2×C4×C73—81no—
52C2×Dic73—21no—
53C2×Dic73—41no—
54C2×Dic73—41no—
55C2×Dic73—81no—
56C4×D73—42no—
57C4×D73—42no—
58C22×C73—21no—
59C22×C73—41no—
60C22×C73#32311yescharacteristic
61C2×D73—21no—
62C2×D73—41no—
63C2×D73—41no—
64C2×D73—82no—
65C2×D73#35212yes—
66#64408—82no—
67#64408—161no—
68C4×C73—41no—
69C4×C73—81no—
70Dic73—41no—
71Dic73—81no—
72#7348—731nomaximal, Sylow
73C2×C73—21no—
74C2×C73—41no—
75C2×C73#131711yescharacteristic
76D73—22no—
77D73—41no—
78#1820—731no—
79#1317—732no—
80C73#734811yescharacteristic, complemented, Sylow
81C2×#117—731no—
82#381—731no—
83#381—731no—
84#342—1462no—
85#323—1462no—
86C23×C4—731no—
87#117—2921no—
88#117—2921no—
89C2×C4⋊C4—1461no—
90C2×C22⋊C4—732no—
91C2×C22⋊C4—1461no—
92C2×C22⋊C4—1461no—
93C2×C42—731no—
94C2×C42#1059684211yescharacteristic, complemented
95C22⋊C8—2922no—
96#95—2921no—
97#95—2921no—
98C24—731no—
99C22×C4—21no—
100C22×C4—2922no—
101C22×C4—2921no—
102C22×C4—731no—
103C22×C4—1461no—
104C22×C4—1461no—
105C22×C4—1462no—
106C22×C4—1461no—
107C22×C4C2×#1059684211yescharacteristic
108C2×C8—5842no—
109C4⋊C4—2922no—
110C22⋊C4—2921no—
111C22⋊C4—2921no—
112C22⋊C4—2922no—
113C22⋊C4—2922no—
114C42—41no—
115C42—2921no—
116C23—5841no—
117C23—731no—
118C23—731no—
119C23—1462no—
120C23C22⋊#1059684211yescharacteristic
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—81no—
125C2×C4—2922no—
126C2×C4—2922no—
127C2×C4—2921no—
128C2×C4—2922no—
129C2×C4—2921no—
130C2×C4—5841no—
131C2×C4—5842no—
132C2×C4—5842no—
133C2×C4—5841no—
134C2×C4—1461no—
135C8—11682no—
136C22—21no—
137C22—41no—
138C22—2921no—
139C22—2921no—
140C22—5842no—
141C22—732no—
142C22—1461no—
143C22#1798967211yescharacteristic
144C4—41no—
145C4—81no—
146C4—2921no—
147C4—5841no—
148C4—5842no—
149C4—11681no—
150C2—21no—
151C2—41no—
152C2—2921no—
153C2—1462no—
154C2#2262695711yescharacteristic
subgroupG/H
centerC2#22626957
commutatorC22×C4×C73C2×C8
FrattiniC22×C4C2×#10596842
FittingC2×C42×C73C8
socleC2×C73#1317
prime radicalC23×D73C22⋊C4
cosocle#17989530C22
hypercenterC2×C42#10596842
hypocenterC73#7348
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
18. C2×C4×Dic73C8semidirect
19. C2×C42×C73C8semidirect
80. C73#7348semidirect
94. C2×C42#10596842semidirect

Maximal subgroups

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

subgroupindex
#226269572
#226258282
#734873