Finite Group Databasebeta

← #34032765

Subgroups — #34032765

Order 18688.

194 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 37 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#22626953C212yesmaximal
2#22625825C211yesmaximal, characteristic
3C22⋊#11924040—22no—
4C2×#14556648C411yescharacteristic
5C2×#14556648C2211yescharacteristic
6#17989453—22no—
7C2×#14556549C411yescharacteristic
8C2×#11924040—42no—
9C22×#10596833—21no—
10C22×#10596833D412yes—
11#14556648—41no—
12#14556648—41no—
13C22×C4×D73C2×C411yescharacteristic
14#14556549—41no—
15#14556549—41no—
16C2×C4⋊Dic73C811yescharacteristic
17C2×#11924005—21no—
18C2×C4×Dic73—21no—
19C2×C4⋊C4×C73C811yescharacteristic
20#11924040—82no—
21C2×#10596833—22no—
22C2×#10596833—42no—
23C2×#10596833—42no—
24C2×#10596833—41no—
25C23×D73M1611yescharacteristic
26C22×Dic73—21no—
27C22×Dic73C22⋊C411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—42no—
31C4⋊Dic73—41no—
32#11924005—42no—
33C4×Dic73—41no—
34C4×Dic73—41no—
35C22×C4×C73—21no—
36C22×C4×C73C2×C811yescharacteristic
37C4⋊C4×C73—41no—
38C23×C73C22⋊C811yescharacteristic
39C22×D73—21no—
40C22×D73—22no—
41C22×D73—41no—
42C22×D73—41no—
43C2×C4×C73—21no—
44C2×C4×C73—41no—
45C2×C4×C73—41no—
46C2×C4×C73—42no—
47C2×Dic73—22no—
48C2×Dic73—42no—
49C2×Dic73—41no—
50C2×Dic73#9911yescharacteristic
51C2×Dic73#10011yescharacteristic
52C4×D73—42no—
53C4×D73—42no—
54#10596833—42no—
55#10596833—81no—
56C22×C73—21no—
57C22×C73—21no—
58C22×C73#32311yescharacteristic
59C22×C73#35012yes—
60C2×D73—41no—
61C2×D73—41no—
62C2×D73—41no—
63C2×D73—82no—
64C4×C73—41no—
65C4×C73—81no—
66Dic73—21no—
67Dic73—81no—
68Dic73#35212yes—
69#7059—731nomaximal, Sylow
70C2×C73—22no—
71C2×C73#131511yescharacteristic
72C2×C73#131711yescharacteristic
73C2×C73#132111yescharacteristic
74D73—81no—
75#1818—731no—
76#1314—732no—
77C73#705911yescharacteristic, complemented, Sylow
78C2×#117—731no—
79C2×C22⋊C8—731no—
80C2×C22⋊C8—731no—
81C22⋊C16—1462no—
82#336—1462no—
83C23×C4—731no—
84C22×C8—732no—
85C22×C8—1461no—
86#117—2921no—
87#117—2921no—
88C2×C4⋊C4—731no—
89C2×C4⋊C4#1059684211yescharacteristic
90C2×C22⋊C4—1461no—
91C2×C42—1461no—
92C2×C16—2922no—
93C22⋊C8—2921no—
94C22⋊C8—2921no—
95C24—731no—
96C22×C4—21no—
97C22×C4—2922no—
98C22×C4—731no—
99C22×C4—1461no—
100C22×C4—1461no—
101C22×C4—1461no—
102C22×C4C2×#1059684211yescharacteristic
103C2×C8—2922no—
104C2×C8—2921no—
105C2×C8—2922no—
106C2×C8—1462no—
107C4⋊C4—41no—
108C4⋊C4—2921no—
109C22⋊C4—2922no—
110C42—2921no—
111C42—2921no—
112C16—5842no—
113C23—2921no—
114C23—2921no—
115C23—1461no—
116C23—1462no—
117C23C22⋊#1059684211yescharacteristic
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—2922no—
123C2×C4—2922no—
124C2×C4—2922no—
125C2×C4—2921no—
126C2×C4—731no—
127C2×C4—731no—
128C2×C4—1462no—
129C8—2922no—
130C8—5841no—
131C22—21no—
132C22—21no—
133C22—2921no—
134C22—2921no—
135C22—2921no—
136C22—5842no—
137C22#1798967211yescharacteristic
138C22#1798968712yes—
139C4—41no—
140C4—81no—
141C4—5841no—
142C4—732no—
143C4—1461no—
144C2—22no—
145C2—5841no—
146C2#2262695411yescharacteristic
147C2#2262695711yescharacteristic
148C2#2262696311yescharacteristic
subgroupG/H
centerC22#17989672
commutatorC22×C4×C73C2×C8
FrattiniC22×C4C2×#10596842
FittingC2×C4⋊C4×C73C8
socleC22×C73#323
prime radicalC23×D73M16
cosocleC2×#14556648C22
hypercenterC2×C4⋊C4#10596842
hypocenterC73#7059
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
77. C73#7059semidirect

Maximal subgroups

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

subgroupindex
#226269532
#226258252
#705973