Finite Group Databasebeta

← #32973476

Subgroups — #32973476

Order 18688.

268 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 39 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#22607867C211yesmaximal, characteristic, complemented
2#22607818C211yesmaximal, characteristic, complemented
3C73×#2010C211yesmaximal, characteristic
4C2×C22⋊#10596831—21no—
5#17988369—21no—
6#575×C73C411yescharacteristic
7#525×C73—21no—
8#421×C73—21no—
9#407×C73C2211yescharacteristic
10H(3,ℤ/4)×C73C411yescharacteristic
11C22×#10596831—41no—
12#14556531—41no—
13C22⋊#10596831—22no—
14C22⋊#10596831—41no—
15C2×#41×C73—21no—
16C23×C4×C73D411yescharacteristic
17#137×C73—41no—
18AGL(1,ℤ/8)×C73—41no—
19#135×C73—41no—
20C2×M16×C73C2×C411yescharacteristic
21C2×M16×C73D411yescharacteristic
22#123×C73—41no—
23C22⋊Q8×C73—41no—
24#121×C73—41no—
25#120×C73—41no—
26C4×D4×C73—42no—
27#117×C73—21no—
28#104×C73—42no—
29C22⋊C8×C73—41no—
30C2×#10596831—42no—
31C2×#10596831—81no—
32C2×#10596831—81no—
33#11924003—81no—
34C24×C73SD1611yescharacteristic
35#41×C73—41no—
36#41×C73—41no—
37#41×C73—41no—
38#41×C73—41no—
39C2×Q8×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73—42no—
42C2×D4×C73—41no—
43C22×C4×C73—21no—
44C22×C4×C73—21no—
45C22×C4×C73—41no—
46C22×C4×C73—41no—
47C22×C4×C73—41no—
48C22×C4×C73C22⋊C411yescharacteristic
49C22×C4×C73D811yescharacteristic
50Q16×C73—41no—
51SD16×C73—42no—
52D8×C73—41no—
53M16×C73—41no—
54M16×C73—41no—
55C2×C8×C73—21no—
56C2×C8×C73—21no—
57C4⋊C4×C73—41no—
58C4⋊C4×C73—42no—
59C22⋊C4×C73—42no—
60C22⋊C4×C73—42no—
61C22⋊C4×C73—41no—
62C42×C73—22no—
63C23×C73—21no—
64C23×C73—41no—
65C23×C73—42no—
66C23×C73—41no—
67C23×C73#10211yescharacteristic
68Q8×C73—41no—
69Q8×C73—41no—
70D4×C73—41no—
71D4×C73—41no—
72D4×C73—81no—
73D4×C73—84no—
74D4×C73—81no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—41no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—42no—
82C2×C4×C73—41no—
83C2×C4×C73—81no—
84C2×C4×C73—81no—
85C2×C4×C73—81no—
86C2×C4×C73#9911yescharacteristic
87C2×C4×C73#10411yescharacteristic
88C8×C73—41no—
89C8×C73—41no—
90#10596831—82no—
91C22×C73—22no—
92C22×C73—21no—
93C22×C73—41no—
94C22×C73—41no—
95C22×C73—42no—
96C22×C73—41no—
97C22×C73—81no—
98C22×C73—82no—
99C22×C73—81no—
100C22×C73#32711yescharacteristic
101C4×C73—21no—
102C4×C73—41no—
103C4×C73—82no—
104C4×C73—81no—
105C4×C73AΣL(1,𝔽16)11yescharacteristic
106C4×C73#35311yescharacteristic
107#7397—731nomaximal, Sylow
108C2×C73—21no—
109C2×C73—41no—
110C2×C73—42no—
111C2×C73—161no—
112C2×C73#134311yescharacteristic
113#2010D7311yescharacteristic
114#1320—731no—
115#1298—731no—
116C73#739711yescharacteristic, complemented, Sylow
117#575Dic7311yescharacteristic
118#525—21no—
119#421—21no—
120#407C2×D7311yescharacteristic
121C2×C22⋊C8—1461no—
122#349—1461no—
123H(3,ℤ/4)Dic7311yescharacteristic
124C2×#41—21no—
125C23×C4C22⋊D7311yescharacteristic
126#137—41no—
127AGL(1,ℤ/8)—41no—
128#135—41no—
129C2×M16C2×Dic7311yescharacteristic
130C2×M16C22⋊D7311yescharacteristic
131C22×C8—2921no—
132#123—41no—
133C22⋊Q8—41no—
134#121—41no—
135#120—41no—
136C4×D4—42no—
137#117—21no—
138M32—2921no—
139#104—42no—
140C22⋊C8—41no—
141C22⋊C8—2921no—
142C22⋊C8—1462no—
143C24#1192401611yescharacteristic
144#41—41no—
145#41—41no—
146#41—41no—
147#41—41no—
148C2×Q8—21no—
149C2×D4—21no—
150C2×D4—42no—
151C2×D4—41no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4C22⋊Dic7311yescharacteristic
158C22×C4#1192401311yescharacteristic
159Q16—41no—
160SD16—42no—
161D8—41no—
162M16—41no—
163M16—41no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—2922no—
167C2×C8—5841no—
168C2×C8—5841no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C22⋊C4—42no—
172C22⋊C4—42no—
173C22⋊C4—41no—
174C42—22no—
175C16—5841no—
176C23—21no—
177C23—41no—
178C23—42no—
179C23—41no—
180C23#1455651211yescharacteristic
181Q8—41no—
182Q8—41no—
183D4—41no—
184D4—41no—
185D4—81no—
186D4—84no—
187D4—81no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4#1455650611yescharacteristic
200C2×C4#1455651811yescharacteristic
201C8—41no—
202C8—41no—
203C8—5842no—
204C22—22no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—41no—
210C22—81no—
211C22—82no—
212C22—81no—
213C22#1798832111yescharacteristic
214C4—21no—
215C4—41no—
216C4—82no—
217C4—81no—
218C4#1798837411yescharacteristic
219C4#1798838011yescharacteristic
220C2—21no—
221C2—41no—
222C2—42no—
223C2—161no—
224C2#2260792811yescharacteristic
subgroupG/H
centerC4#17988380
commutatorC2×M16×C73C2×C4
Frattini#407C2×D73
Fitting, prime radicalC73×#2010C2
socleC2×C73#1343
cosocle#407×C73C22
hypercenter#2010D73
hypocenterC73#7397
LCSG ▷ C2×M16×C73 ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #2010

Complements

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

NH ≅ G/Ntype
1. #22607867C2semidirect
2. #22607818C2semidirect
116. C73#7397semidirect

Maximal subgroups

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

subgroupindex
#226078672
#226078182
C73×#20102
#739773