Finite Group Databasebeta

← #33000236

Subgroups — #33000236

Order 18688.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#22612188C211yesmaximal, characteristic, complemented
2#22612007C211yesmaximal, characteristic
3#22611768C211yesmaximal, characteristic, complemented
4#22608006C211yesmaximal, characteristic, complemented
5#22607970C211yesmaximal, characteristic, complemented
6#22607967C211yesmaximal, characteristic, complemented
7C73×#2214C211yesmaximal, characteristic, complemented
8#17989022—21no—
9C2×#14556534—21no—
10C2×#14556534—21no—
11#17989004—21no—
12#17988964C2211yescharacteristic
13#17988408C2211yescharacteristic
14#17988408C2211yescharacteristic
15#17988399—21no—
16#17988371—21no—
17C4×#11924003C2211yescharacteristic
18#510×C73—21no—
19#494×C73C2211yescharacteristic
20#443×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#362×C73—21no—
23C2×D584—21no—
24C2×D584—21no—
25#14556588—21no—
26#14556534—42no—
27#14556534—41no—
28#14556534—41no—
29#14556534—41no—
30#14556532—41no—
31#14556531—21no—
32#14556531—21no—
33#14556531—41no—
34C2×#11924003—41no—
35C2×#11924003D411yescharacteristic
36C2×#11924003D411yescharacteristic
37#135×C73D411yescharacteristic
38C2×Q16×C73—21no—
39C2×Q16×C73—21no—
40#131×C73—21no—
41C4⋊Q8×C73—21no—
42Q32×C73—41no—
43SD32×C73—41no—
44M32×C73—21no—
45#108×C73D411yescharacteristic
46#104×C73—21no—
47C4×C8×C73C2311yescharacteristic
48C2×D292—41no—
49C2×D292—81no—
50D584—41no—
51D584—41no—
52D584—41no—
53D584—41no—
54#11924003—21no—
55#11924003—41no—
56#11924003—41no—
57#11924003D811yescharacteristic
58#11924003D811yescharacteristic
59#41×C73—21no—
60C2×Q8×C73—41no—
61Q16×C73—41no—
62Q16×C73—41no—
63Q16×C73—41no—
64Q16×C73—41no—
65Q16×C73D811yescharacteristic
66SD16×C73—21no—
67D8×C73D811yescharacteristic
68M16×C73—21no—
69M16×C73—41no—
70C2×C8×C73—41no—
71C2×C8×C73C2×D411yescharacteristic
72C2×C8×C73C2×D411yescharacteristic
73C4⋊C4×C73—81no—
74C42×C73#4111yescharacteristic
75C16×C73—41no—
76C22×D73—81no—
77Q8×C73—21no—
78Q8×C73—81no—
79Q8×C73—81no—
80D4×C73—21no—
81D4×C73—41no—
82C2×C4×C73—21no—
83C2×C4×C73—41no—
84C2×C4×C73—81no—
85C2×C4×C73#12111yescharacteristic
86D292—81no—
87D292—81no—
88D292—162no—
89C8×C73—41no—
90C8×C73C2×D811yescharacteristic
91C8×C73C2×D811yescharacteristic
92C8×C73#13511yescharacteristic
93C8×C73AGL(1,ℤ/8)11yescharacteristic
94C22×C73—41no—
95C22×C73#47211yescharacteristic
96C2×D73—162no—
97C2×D73—161no—
98C4×C73—22no—
99C4×C73—41no—
100C4×C73—161no—
101C4×C73#45911yescharacteristic
102C4×C73#46611yescharacteristic
103#12438—731nomaximal, Sylow
104C2×C73—21no—
105C2×C73—81no—
106C2×C73#166711yescharacteristic
107D73—321no—
108#2248—731no—
109#2214D7311yescharacteristic, complemented
110#2213—731no—
111#2170—731no—
112#1373—731no—
113#1358—731no—
114#1357—731no—
115C73#1243811yescharacteristic, complemented, Sylow
116#510—21no—
117#509—1461no—
118C2×SD32—1461no—
119C2×SD32—1461no—
120#504—1461no—
121#494C2×D7311yescharacteristic
122#493—731no—
123#443C2×D7311yescharacteristic
124#364—731no—
125#364—731no—
126#364C2×D7311yescharacteristic
127#362—21no—
128#361—1461no—
129#350—1461no—
130C4×C16—731no—
131#135C22⋊D7311yescharacteristic
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—1461no—
135C2×D8—1461no—
136#131—21no—
137C4⋊Q8—21no—
138#127—1461no—
139Q32—41no—
140SD32—41no—
141SD32—2921no—
142SD32—2921no—
143SD32—2921no—
144SD32—2922no—
145D16—2921no—
146M32—21no—
147M32—2921no—
148M32—1461no—
149M32—1461no—
150C2×C16—2921no—
151C2×C16—731no—
152C2×C16—731no—
153#108C22⋊D7311yescharacteristic
154#104—21no—
155C4×C8C22×D7311yescharacteristic
156#41—21no—
157C2×Q8—41no—
158C2×D4—2921no—
159C2×D4—5841no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16#1192401311yescharacteristic
165SD16—21no—
166D8—2921no—
167D8—2921no—
168D8—2921no—
169D8—2921no—
170D8#1192401311yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8D4×D7311yescharacteristic
175C2×C8C2×C22⋊D7311yescharacteristic
176C4⋊C4—81no—
177C42#1192402711yescharacteristic
178C16—41no—
179C16—2921no—
180C16—2921no—
181C16—731no—
182C16—731no—
183C16—1461no—
184C23—5841no—
185Q8—21no—
186Q8—81no—
187Q8—81no—
188D4—21no—
189D4—41no—
190D4—5841no—
191D4—5841no—
192D4—11682no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—81no—
196C2×C4#1455656311yescharacteristic
197C8—41no—
198C8D8×D7311yescharacteristic
199C8C2×#1192401311yescharacteristic
200C8#1455661111yescharacteristic
201C8#1455661511yescharacteristic
202C22—41no—
203C22—11682no—
204C22—11681no—
205C22#1798885511yescharacteristic
206C4—22no—
207C4—41no—
208C4—161no—
209C4#1798878011yescharacteristic
210C4#1798882111yescharacteristic
211C2—21no—
212C2—81no—
213C2—23361no—
214C2#2260928411yescharacteristic
subgroupG/H
centerC2#22609284
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2214C2
socleC2×C73#1667
prime radical#22612007C2
hypercenter#2214D73
hypocenterC73#12438
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #22612188C2semidirect
3. #22611768C2semidirect
4. #22608006C2semidirect
5. #22607970C2semidirect
6. #22607967C2semidirect
7. C73×#2214C2semidirect
109. #2214D73semidirect
115. C73#12438semidirect

Maximal subgroups

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

subgroupindex
#226121882
#226120072
#226117682
#226080062
#226079702
#226079672
C73×#22142
#1243873