Finite Group Databasebeta

← #33000231

Subgroups — #33000231

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#22612009C211yesmaximal, characteristic, complemented
2#22612004C211yesmaximal, characteristic
3#22611769C211yesmaximal, characteristic, complemented
4#22608007C211yesmaximal, characteristic, complemented
5#22607970C211yesmaximal, characteristic, complemented
6#22607968C211yesmaximal, characteristic, complemented
7C73×#2248C211yesmaximal, characteristic, complemented
8#17989028—21no—
9#17989023—21no—
10#17989003—21no—
11#17988705C2211yescharacteristic
12#17988408C2211yescharacteristic
13#17988408C2211yescharacteristic
14#17988408C2211yescharacteristic
15#17988403—21no—
16#17988400—21no—
17#17988370—21no—
18C2×SD32×C73—21no—
19C2×SD32×C73—21no—
20#494×C73C2211yescharacteristic
21#493×C73C2211yescharacteristic
22C4×C16×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24#14556597—21no—
25#14556537—41no—
26#14556535—41no—
27#14556534—41no—
28#14556532—41no—
29#14556531—21no—
30#14556531—21no—
31#14556531—21no—
32#14556530—41no—
33C16×D73—41no—
34#14556527D411yescharacteristic
35#14556519—21no—
36C2×Q16×C73—21no—
37C2×Q16×C73—21no—
38C2×D8×C73—21no—
39C2×D8×C73—21no—
40C4⋊Q8×C73—21no—
41#127×C73—21no—
42SD32×C73—42no—
43SD32×C73—41no—
44SD32×C73—41no—
45C2×C16×C73D411yescharacteristic
46C2×C16×C73D411yescharacteristic
47C4×C8×C73C2311yescharacteristic
48#11924028—21no—
49Dic292D811yescharacteristic
50#11924017—21no—
51D584D811yescharacteristic
52#11924012—21no—
53#11924011—41no—
54C8×D73—41no—
55#11924003—41no—
56#11924003—41no—
57#11924003—41no—
58C2×Q8×C73—41no—
59C2×D4×C73—41no—
60C2×D4×C73—81no—
61Q16×C73—41no—
62Q16×C73—41no—
63Q16×C73—41no—
64Q16×C73—41no—
65D8×C73—41no—
66D8×C73—41no—
67D8×C73—41no—
68D8×C73—41no—
69C2×C8×C73C2×D411yescharacteristic
70C2×C8×C73C2×D411yescharacteristic
71C4⋊C4×C73—81no—
72C42×C73#4111yescharacteristic
73C16×C73—21no—
74C16×C73D811yescharacteristic
75C16×C73D811yescharacteristic
76C23×C73—81no—
77Q8×C73—81no—
78Q8×C73—81no—
79D4×C73—81no—
80D4×C73—81no—
81D4×C73—162no—
82C2×C4×C73—21no—
83C2×C4×C73—81no—
84C2×C4×C73#12111yescharacteristic
85C22⋊D73—41no—
86D292—21no—
87C4×D73—41no—
88Dic146—21no—
89C8×C73C2×D811yescharacteristic
90C8×C73C2×D811yescharacteristic
91C8×C73#13511yescharacteristic
92C8×C73AGL(1,ℤ/8)11yescharacteristic
93#10596831—41no—
94C22×C73—162no—
95C22×C73—161no—
96C22×C73#47211yescharacteristic
97C2×D73—41no—
98C4×C73—22no—
99C4×C73—161no—
100C4×C73#45911yescharacteristic
101C4×C73#46611yescharacteristic
102Dic73—41no—
103#12438—731nomaximal, Sylow
104C2×C73—21no—
105C2×C73—321no—
106C2×C73#166711yescharacteristic
107D73—81no—
108#2248D7311yescharacteristic, complemented
109#2214—731no—
110#2213—731no—
111#2170—731no—
112#1373—731no—
113#1358—731no—
114#1357—731no—
115C73#1243811yescharacteristic, complemented, Sylow
116#510—1461no—
117#509—1461no—
118C2×SD32—21no—
119C2×SD32—21no—
120#504—1461no—
121#494C2×D7311yescharacteristic
122#493C2×D7311yescharacteristic
123#443—731no—
124#364—731no—
125#364—731no—
126#364—731no—
127#362—1461no—
128#361—1461no—
129#350—1461no—
130C4×C16C2×D7311yescharacteristic
131#135—731no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—21no—
135C2×D8—21no—
136#131—1461no—
137C4⋊Q8—21no—
138#127—21no—
139Q32—2921no—
140SD32—42no—
141SD32—41no—
142SD32—41no—
143SD32—2921no—
144SD32—2921no—
145D16—2921no—
146M32—2921no—
147M32—1461no—
148M32—1461no—
149M32—1461no—
150C2×C16—2921no—
151C2×C16C22⋊D7311yescharacteristic
152C2×C16C22⋊D7311yescharacteristic
153#108—731no—
154#104—1461no—
155C4×C8C22×D7311yescharacteristic
156#41—1461no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—731no—
165SD16—1461no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—731no—
171M16—2921no—
172M16—1461no—
173C2×C8—2921no—
174C2×C8D4×D7311yescharacteristic
175C2×C8C2×C22⋊D7311yescharacteristic
176C4⋊C4—81no—
177C42#1192402711yescharacteristic
178C16—21no—
179C16—2921no—
180C16—2921no—
181C16—2921no—
182C16#1192401311yescharacteristic
183C16#1192401311yescharacteristic
184C23—81no—
185Q8—81no—
186Q8—81no—
187Q8—1461no—
188D4—81no—
189D4—81no—
190D4—162no—
191D4—2921no—
192D4—1461no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—2921no—
196C2×C4#1455656211yescharacteristic
197C8—2921no—
198C8D8×D7311yescharacteristic
199C8C2×#1192401311yescharacteristic
200C8#1455661011yescharacteristic
201C8#1455661711yescharacteristic
202C22—162no—
203C22—161no—
204C22—2921no—
205C22#1798885411yescharacteristic
206C4—22no—
207C4—161no—
208C4—2921no—
209C4#1798877911yescharacteristic
210C4#1798882011yescharacteristic
211C2—21no—
212C2—321no—
213C2—5841no—
214C2#2260928311yescharacteristic
subgroupG/H
centerC2#22609283
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2248C2
socleC2×C73#1667
prime radical#22612004C2
hypercenter#2248D73
hypocenterC73#12438
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #22612009C2semidirect
3. #22611769C2semidirect
4. #22608007C2semidirect
5. #22607970C2semidirect
6. #22607968C2semidirect
7. C73×#2248C2semidirect
108. #2248D73semidirect
115. C73#12438semidirect

Maximal subgroups

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

subgroupindex
#226120092
#226120042
#226117692
#226080072
#226079702
#226079682
C73×#22482
#1243873