Finite Group Databasebeta

← #34001165

Subgroups — #34001165

Order 18688.

348 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C2×#17989492C212yesmaximal
2#22610737C211yesmaximal, characteristic
3C2×#14556650—22no—
4#17989492—22no—
5#17989492C414yescomplemented
6C2×#14556588C2211yescharacteristic
7C2×#14556513—22no—
8#17988457C411yescharacteristic, complemented
9C2×C4×C8×C73C411yescharacteristic, complemented
10C2×C22⋊#64408—42no—
11#14556650—24no—
12#14556650—42no—
13C22×D292—41no—
14C22×D292D412yes—
15#14556588—41no—
16#14556588C2×C412yes—
17#14556588D411yescharacteristic
18#14556588Q811yescharacteristic
19C2×C4⋊Dic73—21no—
20C2×C4⋊Dic73—41no—
21#14556513—44no—
22C22×C8×C73—21no—
23C2×C42×C73C2×C411yescharacteristic
24C4×C8×C73—41no—
25C22×#64408—82no—
26C22⋊#64408—44no—
27C22⋊#64408—82no—
28C23×D73—22no—
29C2×D292—22no—
30C2×D292—42no—
31C2×D292—42no—
32C2×D292—42no—
33C2×D292—41no—
34C2×D292—41no—
35C2×D292—82no—
36C2×D292—82no—
37C2×D292C22⋊C412yes—
38C2×D292C4⋊C412yes—
39C22×Dic73—41no—
40C4⋊Dic73—42no—
41C4⋊Dic73—82no—
42C22×C4×C73—21no—
43C22×C4×C73C22⋊C411yescharacteristic
44C2×C8×C73—22no—
45C2×C8×C73—41no—
46C2×C8×C73—41no—
47C42×C73—21no—
48C42×C73C4211yescharacteristic
49C42×C73C4⋊C411yescharacteristic
50C23×C73#9911yescharacteristic
51C22×D73—22no—
52C22×D73—22no—
53C22×D73—42no—
54C22×D73—42no—
55C22×D73—82no—
56C22×D73—82no—
57C2×#64408—84no—
58C2×#64408—162no—
59C2×#64408—162no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73#9511yescharacteristic
67C2×C4×C73#9911yescharacteristic
68C2×Dic73—82no—
69C2×Dic73—81no—
70D292—42no—
71D292—42no—
72D292—82no—
73D292—84no—
74D292—82no—
75D292—82no—
76C8×C73—42no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73#34211yescharacteristic
80C22×C73#35311yescharacteristic
81C22×C73#35411yescharacteristic
82C2×D73—42no—
83C2×D73—42no—
84C2×D73—82no—
85C2×D73—82no—
86C2×D73—82no—
87C2×D73—82no—
88C2×D73—162no—
89#64408—164no—
90C4×C73—22no—
91C4×C73—22no—
92C4×C73—21no—
93C4×C73—21no—
94Dic73—161no—
95#7498—731nomaximal, Sylow
96C2×C73—21no—
97C2×C73—21no—
98C2×C73#139311yescharacteristic
99C2×C73#140811yescharacteristic
100C2×C73#140911yescharacteristic
101D73—82no—
102D73—82no—
103C2×#353—732no—
104#1957—731no—
105C73#749811yescharacteristic, complemented, Sylow
106C2×#127—731no—
107C2×#102—1462no—
108C2×#99—1462no—
109C2×C4×C8#6440811yescharacteristic, complemented
110#384—731no—
111#353—734no—
112#353—1462no—
113C22×D4—2921no—
114C22×D4—732no—
115C22×C8—21no—
116#127—2921no—
117#127—732no—
118#127—731no—
119#127—731no—
120C2×C4⋊C4—2921no—
121C2×C4⋊C4—1461no—
122C2×C22⋊C4—2922no—
123C2×C42C2×#6440811yescharacteristic
124#102—2924no—
125#99—2922no—
126#99—1464no—
127C4×C8—41no—
128C24—1462no—
129C2×D4—2922no—
130C2×D4—2922no—
131C2×D4—2922no—
132C2×D4—2921no—
133C2×D4—2921no—
134C2×D4—5842no—
135C2×D4—5842no—
136C2×D4—732no—
137C2×D4—732no—
138C2×D4—1462no—
139C22×C4—21no—
140C22×C4—2921no—
141C22×C4—5842no—
142C22×C4C22⋊#6440811yescharacteristic
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C4⋊C4—2922no—
147C4⋊C4—5842no—
148C22⋊C4—2924no—
149C22⋊C4—5842no—
150C42—21no—
151C42C4×#6440811yescharacteristic
152C42C4⋊#6440811yescharacteristic
153C23—2922no—
154C23—2922no—
155C23—5842no—
156C23—5842no—
157C23—1462no—
158C23—1462no—
159C23#1455665011yescharacteristic
160D4—2922no—
161D4—2922no—
162D4—5842no—
163D4—5844no—
164D4—5842no—
165D4—5842no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—5842no—
173C2×C4—5844no—
174C2×C4—5841no—
175C2×C4—11682no—
176C2×C4—11682no—
177C2×C4(C2×#64408)⋊C411yescharacteristic
178C2×C4#1455664911yescharacteristic
179C8—42no—
180C22—21no—
181C22—21no—
182C22—2922no—
183C22—2922no—
184C22—5842no—
185C22—5842no—
186C22—5842no—
187C22—5842no—
188C22—11682no—
189C22#1798946511yescharacteristic
190C22#1798949211yescharacteristic
191C22#1798949411yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—11684no—
197C4—11681no—
198C2—21no—
199C2—21no—
200C2—5842no—
201C2—5842no—
202C2#2262502511yescharacteristic
203C2#2262506311yescharacteristic
204C2#2262506511yescharacteristic
subgroupG/H
centerC22#17989492
commutatorC42×C73C42
FrattiniC2×C42C2×#64408
FittingC2×C4×C8×C73C4
socleC22×C73#353
prime radical, cosocleC2×#14556588C22
hypercenterC2×C4×C8#64408
hypocenterC73#7498
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
5. #17989492C4semidirect
8. #17988457C4semidirect
9. C2×C4×C8×C73C4semidirect
105. C73#7498semidirect
109. C2×C4×C8#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179894922
#226107372
#749873