Finite Group Databasebeta

← #34000814

Subgroups — #34000814

Order 18688.

202 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 36 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#22624877C212yesmaximal, complemented
2#22610763C211yesmaximal, characteristic
3#17989483—22no—
4#17989137C411yescharacteristic
5#17988611C2211yescharacteristic
6C2×#14556519—22no—
7#376×C73C411yescharacteristic
8#14556665—42no—
9C2×#11924028—21no—
10C2×#11924012D412yes—
11#14556591C811yescharacteristic
12#14556588C811yescharacteristic
13#14556579—21no—
14#14556565—41no—
15C4×D292—41no—
16C4⋊#10596831—41no—
17#14556519—44no—
18C2×C42×C73—21no—
19C2×C42×C73C2×C411yescharacteristic
20#95×C73—41no—
21#11924031—82no—
22#11924028—42no—
23#11924028—42no—
24C2×Dic146—21no—
25C2×D292—21no—
26C2×D292—41no—
27C2×C22⋊D73—41no—
28C2×C4×D73—41no—
29#11924012—42no—
30C2×#10596831—22no—
31C4⋊Dic73—41no—
32#11924005—42no—
33C22×C4×C73—21no—
34C22×C4×C73—41no—
35C22×C4×C73C22⋊C411yescharacteristic
36C42×C73—21no—
37C42×C73—22no—
38C42×C73—41no—
39C42×C73C2×C811yescharacteristic
40C42×C73M1611yescharacteristic
41C23×C73#10011yescharacteristic
42C22×D73—41no—
43C2×C4×C73—21no—
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73—21no—
47C2×C4×C73—42no—
48C2×C4×C73—81no—
49C2×C4×C73—82no—
50C2×C4×C73C22⋊C811yescharacteristic
51C2×C4×C73#9911yescharacteristic
52C22⋊D73—82no—
53C2×Dic73—41no—
54D292—42no—
55D292—82no—
56C4×D73—81no—
57C4×D73—81no—
58Dic146—42no—
59#10596831—42no—
60C22×C73—21no—
61C22×C73—41no—
62C22×C73#32311yescharacteristic
63C2×D73—82no—
64C2×D73—81no—
65C4×C73—21no—
66C4×C73—41no—
67C4×C73—41no—
68C4×C73—82no—
69C4×C73#35311yescharacteristic
70C4×C73#35511yescharacteristic
71Dic73—81no—
72#7356—731nomaximal, Sylow
73C2×C73—21no—
74C2×C73—41no—
75C2×C73#131811yescharacteristic
76D73—161no—
77#1963—731no—
78#1327—732no—
79C73#735611yescharacteristic, complemented, Sylow
80#532—731no—
81#423—731no—
82C2×#104—1462no—
83#376#6440811yescharacteristic
84#349—1462no—
85C2×#41—1461no—
86C2×M16—732no—
87C4⋊Q8—731no—
88#127—731no—
89#124—1461no—
90#121—2921no—
91C4×D4—2921no—
92C2×C42—21no—
93C2×C42C2×#6440811yescharacteristic
94M32—2922no—
95C4⋊C8—2921no—
96#104—2924no—
97#95—41no—
98#41—2922no—
99#41—2922no—
100C2×Q8—1461no—
101C2×D4—2921no—
102C2×D4—2921no—
103C2×D4—1461no—
104C22×C4—21no—
105C22×C4—41no—
106C22×C4—2921no—
107C22×C4C22⋊#6440811yescharacteristic
108M16—2922no—
109C2×C8—1462no—
110C4⋊C4—2921no—
111C22⋊C4—2922no—
112C42—21no—
113C42—22no—
114C42—41no—
115C42#1192403611yescharacteristic
116C42#1192403811yescharacteristic
117C16—5842no—
118C23—2921no—
119C23#1455665111yescharacteristic
120Q8—2922no—
121D4—2922no—
122D4—5842no—
123D4—5842no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—81no—
130C2×C4—82no—
131C2×C4—2921no—
132C2×C4—5841no—
133C2×C4—5841no—
134C2×C4#1455664811yescharacteristic
135C2×C4#1455665011yescharacteristic
136C8—2922no—
137C22—21no—
138C22—41no—
139C22—5842no—
140C22—5841no—
141C22#1798943111yescharacteristic
142C4—21no—
143C4—41no—
144C4—41no—
145C4—82no—
146C4—5841no—
147C4#1798949211yescharacteristic
148C4#1798949611yescharacteristic
149C2—21no—
150C2—41no—
151C2—11681no—
152C2#2262486011yescharacteristic
subgroupG/H
centerC4#17989492
commutatorC42×C73C2×C8
FrattiniC2×C42C2×#64408
Fitting#376×C73C4
socleC2×C73#1318
prime radical#17989137C4
cosocle#17988611C22
hypercenter#376#64408
hypocenterC73#7356
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #22624877C2semidirect
79. C73#7356semidirect

Maximal subgroups

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

subgroupindex
#226248772
#226107632
#735673