Finite Group Databasebeta

← #21426040

Subgroups — #21426040

Order 7552.

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#16838199C211yesmaximal, characteristic, complemented
2#16837838C211yesmaximal, characteristic, complemented
3#16837652C211yesmaximal, characteristic, complemented
4#16837213C211yesmaximal, characteristic, complemented
5#16837212C211yesmaximal, characteristic, complemented
6#16837183C211yesmaximal, characteristic, complemented
7C59×#509C211yesmaximal, characteristic, complemented
8#41×D59—21no—
9#14273759—21no—
10#14273756—21no—
11#14273754—21no—
12#14273751—21no—
13#14273749C2211yescharacteristic
14#14273747—21no—
15C2×#11745659C2211yescharacteristic
16#14273698—21no—
17#14273671—21no—
18#14273668—21no—
19#14273667C2211yescharacteristic, complemented
20#14273659C2211yescharacteristic, complemented
21#14273648—21no—
22#135×C59C2211yescharacteristic
23C2×D8×C59C2211yescharacteristic, complemented
24SD32×C59—21no—
25D16×C59—21no—
26M32×C59C2211yescharacteristic, complemented
27#41×C59—21no—
28C2×D4×C59—21no—
29C2×C22⋊D59—41no—
30#11745689—21no—
31Q8×D59—21no—
32#11745687—21no—
33#11745687—41no—
34D4×D59—21no—
35D4×D59—41no—
36#11745685—21no—
37#11745685—41no—
38C2×C4×D59—41no—
39C2×C4×D59D411yescharacteristic
40Q16×C59D411yescharacteristic, complemented
41SD16×C59—21no—
42D8×C59—21no—
43D8×C59—21no—
44D8×C59D411yescharacteristic, complemented
45C2×C8×C59C2311yescharacteristic
46C22⋊Dic59—41no—
47#11745672—21no—
48#11745671—21no—
49#11745670—21no—
50#11745669—21no—
51C4⋊Dic59—21no—
52C2×C59⋊C8D411yescharacteristic
53Dic236D411yescharacteristic, complemented
54D472D411yescharacteristic, complemented
55#11745660—21no—
56#11745659—21no—
57#11745659—21no—
58C16×C59—21no—
59C59⋊C16—21no—
60C23×C59—41no—
61C22×D59—41no—
62C22×D59D811yescharacteristic
63Q8×C59—21no—
64D4×C59—21no—
65D4×C59—41no—
66D4×C59—41no—
67D4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59C2×D411yescharacteristic
70C22⋊D59—41no—
71C22⋊D59—41no—
72C22⋊D59—41no—
73C22⋊D59—82no—
74C2×Dic59—41no—
75C2×Dic59—41no—
76C2×Dic59D811yescharacteristic
77D236—21no—
78D236—41no—
79C4×D59—21no—
80C4×D59—21no—
81C4×D59—41no—
82C4×D59—41no—
83C4×D59—41no—
84Dic118—21no—
85Dic118—41no—
86C8×C59C2×D411yescharacteristic
87C8×C59C2×D411yescharacteristic
88C59⋊C8—21no—
89C22×C59—41no—
90C22×C59—81no—
91C22×C59—81no—
92C22×C59—81no—
93C22×C59C2×D811yescharacteristic
94C2×D59—21no—
95C2×D59—41no—
96C2×D59—41no—
97C2×D59—82no—
98C4×C59—41no—
99C4×C59#12011yescharacteristic
100C4×C59AGL(1,ℤ/8)11yescharacteristic
101Dic59—21no—
102Dic59—41no—
103Dic59—81no—
104#2190—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—81no—
107C2×C59—161no—
108C2×C59#44711yescharacteristic
109D59—41no—
110D59—81no—
111#575—591no—
112#509—591no—
113#509D5911yescharacteristic, complemented
114#469—591no—
115#360—591no—
116#360—591no—
117#349—591no—
118C59#219011yescharacteristic, complemented, Sylow
119C2×#41—1181no—
120#137—1181no—
121#137—1181no—
122AGL(1,ℤ/8)—1181no—
123AGL(1,ℤ/8)—1181no—
124#135—591no—
125#135—1181no—
126#135C2×D5911yescharacteristic
127C2×D8C2×D5911yescharacteristic, complemented
128C2×M16—591no—
129#121—1181no—
130SD32—21no—
131SD32—1181no—
132D16—21no—
133D16—1181no—
134M32—591no—
135M32C2×D5911yescharacteristic, complemented
136#106—591no—
137#102—1181no—
138#41—21no—
139#41—1181no—
140#41—1181no—
141#41—1181no—
142#41—2361no—
143#41—2361no—
144C2×Q8—1181no—
145C2×D4—21no—
146C2×D4—1181no—
147C2×D4—2361no—
148C2×D4—2361no—
149C22×C4—591no—
150C22×C4—2361no—
151Q16—591no—
152Q16—1181no—
153Q16C22⋊D5911yescharacteristic, complemented
154SD16—21no—
155SD16—1181no—
156SD16—1181no—
157SD16—1181no—
158D8—21no—
159D8—21no—
160D8—591no—
161D8—1181no—
162D8C22⋊D5911yescharacteristic, complemented
163M16—1181no—
164M16—1181no—
165C2×C8—591no—
166C2×C8C22×D5911yescharacteristic
167C4⋊C4—1181no—
168C22⋊C4—2361no—
169C16—21no—
170C16—1181no—
171C23—41no—
172C23—591no—
173C23—2361no—
174Q8—21no—
175Q8—1181no—
176Q8—2361no—
177D4—21no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—1181no—
182D4—4722no—
183D4—2361no—
184D4—2361no—
185D4—2361no—
186D4—2361no—
187C2×C4—41no—
188C2×C4—591no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4—2361no—
192C2×C4—2361no—
193C2×C4—2361no—
194C2×C4—2361no—
195C2×C4—2361no—
196C2×C4D4×D5911yescharacteristic
197C8—1181no—
198C8D4×D5911yescharacteristic
199C8C2×C22⋊D5911yescharacteristic
200C22—41no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—1181no—
205C22—4722no—
206C22—2361no—
207C22—2361no—
208C22D8×D5911yescharacteristic
209C4—41no—
210C4—1181no—
211C4—4721no—
212C4—2361no—
213C4#1427369511yescharacteristic
214C4#1427375111yescharacteristic
215C2—21no—
216C2—81no—
217C2—161no—
218C2—4721no—
219C2—2361no—
220C2#1683753411yescharacteristic
subgroupG/H
centerC2#16837534
commutatorC2×C8×C59C23
FrattiniC2×C8C22×D59
FittingC59×#509C2
socleC2×C59#447
hypercenter#509D59
hypocenterC59#2190
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #16838199C2semidirect
2. #16837838C2semidirect
3. #16837652C2semidirect
4. #16837213C2semidirect
5. #16837212C2semidirect
6. #16837183C2semidirect
7. C59×#509C2semidirect
19. #14273667C22semidirect
20. #14273659C22semidirect
23. C2×D8×C59C22semidirect
26. M32×C59C22semidirect
40. Q16×C59D4semidirect
44. D8×C59D4semidirect
53. Dic236D4semidirect
54. D472D4semidirect
113. #509D59semidirect
118. C59#2190semidirect
127. C2×D8C2×D59semidirect
135. M32C2×D59semidirect
153. Q16C22⋊D59semidirect
162. D8C22⋊D59semidirect