Finite Group Databasebeta

← #44486492

Subgroups — #44486492

Order 30592.

226 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 47 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#29505569C211yesmaximal, characteristic, complemented
2#29505208C211yesmaximal, characteristic, complemented
3#29505022C211yesmaximal, characteristic, complemented
4#29504583C211yesmaximal, characteristic, complemented
5#29504582C211yesmaximal, characteristic, complemented
6#29504553C211yesmaximal, characteristic, complemented
7#509×C239C211yesmaximal, characteristic, complemented
8#41×D239—21no—
9#21439992—21no—
10#21439989—21no—
11#21439987—21no—
12#21439984—21no—
13#21439982C2211yescharacteristic
14#21439980—21no—
15C2×#16838531C2211yescharacteristic
16#21439931—21no—
17#21439904—21no—
18#21439901—21no—
19#21439900C2211yescharacteristic, complemented
20#21439892C2211yescharacteristic, complemented
21#21439881—21no—
22#135×C239C2211yescharacteristic
23C2×D8×C239C2211yescharacteristic, complemented
24SD32×C239—21no—
25D16×C239—21no—
26M32×C239C2211yescharacteristic, complemented
27#16838549—21no—
28#16838548—21no—
29#16838548—41no—
30#16838547—21no—
31#16838547—41no—
32Q8×D239—21no—
33C2×C22⋊D239—41no—
34D4×D239—21no—
35D4×D239—41no—
36C2×C4×D239—41no—
37C2×C4×D239D411yescharacteristic
38Dic956D411yescharacteristic, complemented
39#16838538—21no—
40#16838537—21no—
41#16838536—21no—
42#16838535—21no—
43D1912D411yescharacteristic, complemented
44#16838533—21no—
45#16838531—21no—
46#16838531—21no—
47C2×C239⋊C8D411yescharacteristic
48C4⋊Dic239—21no—
49C22⋊Dic239—41no—
50C239⋊C16—21no—
51#41×C239—21no—
52C2×D4×C239—21no—
53Q16×C239D411yescharacteristic, complemented
54SD16×C239—21no—
55D8×C239—21no—
56D8×C239—21no—
57D8×C239D411yescharacteristic, complemented
58C2×C8×C239C2311yescharacteristic
59C16×C239—21no—
60C22×D239—41no—
61C22×D239D811yescharacteristic
62Dic478—21no—
63Dic478—41no—
64D956—21no—
65D956—41no—
66C22⋊D239—41no—
67C22⋊D239—41no—
68C22⋊D239—41no—
69C22⋊D239—82no—
70C2×Dic239—41no—
71C2×Dic239—41no—
72C2×Dic239D811yescharacteristic
73C4×D239—21no—
74C4×D239—21no—
75C4×D239—41no—
76C4×D239—41no—
77C4×D239—41no—
78C239⋊C8—21no—
79C23×C239—41no—
80Q8×C239—21no—
81D4×C239—21no—
82D4×C239—41no—
83D4×C239—41no—
84D4×C239—41no—
85C2×C4×C239—41no—
86C2×C4×C239C2×D411yescharacteristic
87C8×C239C2×D411yescharacteristic
88C8×C239C2×D411yescharacteristic
89C22×C239—41no—
90C22×C239—81no—
91C22×C239—81no—
92C22×C239—81no—
93C22×C239C2×D811yescharacteristic
94C2×D239—21no—
95C2×D239—41no—
96C2×D239—41no—
97C2×D239—82no—
98C4×C239—41no—
99C4×C239#12011yescharacteristic
100C4×C239AGL(1,ℤ/8)11yescharacteristic
101Dic239—21no—
102Dic239—41no—
103Dic239—81no—
104C2×C239—21no—
105C2×C239—81no—
106C2×C239—161no—
107C2×C239#44711yescharacteristic
108D239—41no—
109D239—81no—
110C239#219011yescharacteristic, complemented, Sylow
111#2190—2391nomaximal, Sylow
112#575—2391no—
113#509—2391no—
114#509D23911yescharacteristic, complemented
115#469—2391no—
116#360—2391no—
117#360—2391no—
118#349—2391no—
119C2×#41—4781no—
120#137—4781no—
121#137—4781no—
122AGL(1,ℤ/8)—4781no—
123AGL(1,ℤ/8)—4781no—
124#135—4781no—
125#135—2391no—
126#135C2×D23911yescharacteristic
127C2×D8C2×D23911yescharacteristic, complemented
128C2×M16—2391no—
129#121—4781no—
130SD32—21no—
131SD32—4781no—
132D16—21no—
133D16—4781no—
134M32—2391no—
135M32C2×D23911yescharacteristic, complemented
136#106—2391no—
137#102—4781no—
138#41—21no—
139#41—9561no—
140#41—9561no—
141#41—4781no—
142#41—4781no—
143#41—4781no—
144C2×Q8—4781no—
145C2×D4—21no—
146C2×D4—9561no—
147C2×D4—9561no—
148C2×D4—4781no—
149C22×C4—9561no—
150C22×C4—2391no—
151Q16—4781no—
152Q16—2391no—
153Q16C22⋊D23911yescharacteristic, complemented
154SD16—21no—
155SD16—4781no—
156SD16—4781no—
157SD16—4781no—
158D8—21no—
159D8—21no—
160D8—4781no—
161D8—2391no—
162D8C22⋊D23911yescharacteristic, complemented
163M16—4781no—
164M16—4781no—
165C2×C8—2391no—
166C2×C8C22×D23911yescharacteristic
167C4⋊C4—4781no—
168C22⋊C4—9561no—
169C16—21no—
170C16—4781no—
171C23—41no—
172C23—9561no—
173C23—2391no—
174Q8—21no—
175Q8—9561no—
176Q8—4781no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—19122no—
182D4—9561no—
183D4—9561no—
184D4—9561no—
185D4—9561no—
186D4—4781no—
187C2×C4—41no—
188C2×C4—9561no—
189C2×C4—9561no—
190C2×C4—9561no—
191C2×C4—9561no—
192C2×C4—9561no—
193C2×C4—4781no—
194C2×C4—4781no—
195C2×C4—2391no—
196C2×C4D4×D23911yescharacteristic
197C8—4781no—
198C8D4×D23911yescharacteristic
199C8C2×C22⋊D23911yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—19122no—
205C22—9561no—
206C22—9561no—
207C22—4781no—
208C22D8×D23911yescharacteristic
209C4—41no—
210C4—19121no—
211C4—9561no—
212C4—4781no—
213C4#2143992811yescharacteristic
214C4#2143998411yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—19121no—
219C2—9561no—
220C2#2950490411yescharacteristic
subgroupG/H
centerC2#29504904
commutator, cosocleC2×C8×C239C23
FrattiniC2×C8C22×D239
Fitting#509×C239C2
socleC2×C239#447
hypercenter#509D239
hypocenterC239#2190
LCSG ▷ C2×C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #29505569C2semidirect
2. #29505208C2semidirect
3. #29505022C2semidirect
4. #29504583C2semidirect
5. #29504582C2semidirect
6. #29504553C2semidirect
7. #509×C239C2semidirect
19. #21439900C22semidirect
20. #21439892C22semidirect
23. C2×D8×C239C22semidirect
26. M32×C239C22semidirect
38. Dic956D4semidirect
43. D1912D4semidirect
53. Q16×C239D4semidirect
57. D8×C239D4semidirect
110. C239#2190semidirect
114. #509D239semidirect
127. C2×D8C2×D239semidirect
135. M32C2×D239semidirect
153. Q16C22⋊D239semidirect
162. D8C22⋊D239semidirect

Maximal subgroups

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

subgroupindex
#295055692
#295052082
#295050222
#295045832
#295045822
#295045532
#509×C2392
#2190239