Finite Group Databasebeta

← #34001195

Subgroups — #34001195

Order 18688.

266 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 46 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#22626224C212yesmaximal
2#22610762C211yesmaximal, characteristic
3#17989573—22no—
4#17989498—22no—
5#17989496C414yescomplemented
6#17989137C2211yescharacteristic
7C2×#14556517—22no—
8#17988433C411yescharacteristic
9#423×C73C411yescharacteristic
10D73⋊M16—42no—
11#14556652—24no—
12#14556651—42no—
13C2×#11924028D412yes—
14#14556591D411yescharacteristic
15#14556588Q811yescharacteristic
16#14556579C2×C412yes—
17#14556565—41no—
18C4×D292—41no—
19C2×C4×Dic73—21no—
20#14556517—44no—
21#14556498—41no—
22C2×M16×C73—21no—
23C2×C42×C73C2×C411yescharacteristic
24C4⋊C8×C73—41no—
25#11924038—82no—
26#11924037—44no—
27#11924036—82no—
28#11924028—42no—
29#11924028—42no—
30C2×Dic146C22⋊C412yes—
31C2×D292—41no—
32C2×D292C4⋊C412yes—
33C2×C22⋊D73—22no—
34C22×Dic73—41no—
35C2×C4×D73—22no—
36C4⋊Dic73—41no—
37#11924005—42no—
38C4×Dic73—22no—
39C4×Dic73—41no—
40C22×C4×C73—21no—
41C22×C4×C73C22⋊C411yescharacteristic
42M16×C73—42no—
43C2×C8×C73—41no—
44C42×C73—21no—
45C42×C73C4211yescharacteristic
46C42×C73C4⋊C411yescharacteristic
47C23×C73#9911yescharacteristic
48C22×D73—22no—
49C2×C4×C73—21no—
50C2×C4×C73—21no—
51C2×C4×C73—21no—
52C2×C4×C73—21no—
53C2×C4×C73—81no—
54C2×C4×C73#9511yescharacteristic
55C2×C4×C73#9911yescharacteristic
56C22⋊D73—82no—
57C2×Dic73—22no—
58C2×Dic73—42no—
59C2×Dic73—82no—
60D292—42no—
61D292—82no—
62C4×D73—42no—
63C4×D73—42no—
64Dic146—42no—
65#10596833—84no—
66C8×C73—81no—
67C22×C73—21no—
68C22×C73—41no—
69C22×C73#34211yescharacteristic
70C2×D73—42no—
71C2×D73—82no—
72C4×C73—21no—
73C4×C73—41no—
74C4×C73—41no—
75C4×C73#35311yescharacteristic
76C4×C73#35411yescharacteristic
77Dic73—42no—
78Dic73—82no—
79#7507—731nomaximal, Sylow
80C2×C73—21no—
81C2×C73—41no—
82C2×C73#139311yescharacteristic
83D73—82no—
84#2132—732no—
85#1963—731no—
86C73#750711yescharacteristic, complemented, Sylow
87#532—731no—
88#423#6440811yescharacteristic
89C2×#104—1462no—
90#413—1462no—
91#376—731no—
92#356—1462no—
93#355—734no—
94C2×#41—732no—
95C2×M16—21no—
96C2×M16—2922no—
97C4⋊Q8—731no—
98#127—731no—
99#124—732no—
100#121—2921no—
101C4×D4—2921no—
102C2×C42—1461no—
103C2×C42C2×#6440811yescharacteristic
104C4⋊C8—41no—
105#104—2924no—
106#101—1464no—
107#100—2922no—
108#95—2921no—
109#41—2922no—
110#41—2922no—
111C2×Q8—732no—
112C2×D4—2921no—
113C2×D4—732no—
114C2×D4—1462no—
115C22×C4—21no—
116C22×C4—2921no—
117C22×C4—1462no—
118C22×C4C22⋊#6440811yescharacteristic
119M16—42no—
120M16—2924no—
121M16—5842no—
122C2×C8—41no—
123C2×C8—5842no—
124C4⋊C4—2921no—
125C22⋊C4—2922no—
126C42—21no—
127C42—2921no—
128C42—1462no—
129C42C4×#6440811yescharacteristic
130C42C4⋊#6440811yescharacteristic
131C23—1462no—
132C23#1455665011yescharacteristic
133Q8—2922no—
134D4—2922no—
135D4—5842no—
136D4—5842no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—81no—
142C2×C4—2922no—
143C2×C4—2922no—
144C2×C4—2922no—
145C2×C4—5842no—
146C2×C4—1462no—
147C2×C4(C2×#64408)⋊C411yescharacteristic
148C2×C4#1455664911yescharacteristic
149C8—81no—
150C8—5844no—
151C22—21no—
152C22—41no—
153C22—2922no—
154C22—5842no—
155C22#1798946511yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—2922no—
160C4—5842no—
161C4#1798949111yescharacteristic
162C4#1798949311yescharacteristic
163C2—21no—
164C2—41no—
165C2—5842no—
166C2#2262502611yescharacteristic
subgroupG/H
centerC4#17989491
commutatorC42×C73C42
FrattiniC2×C42C2×#64408
Fitting#423×C73C4
socleC2×C73#1393
prime radical, cosocle#17989137C22
hypercenter#423#64408
hypocenterC73#7507
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
5. #17989496C4semidirect
86. C73#7507semidirect

Maximal subgroups

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

subgroupindex
#226262242
#226107622
#750773