Finite Group Databasebeta

← #21425367

Subgroups — #21425367

Order 7552.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#14273753C211yesmaximal, characteristic
2#16837450C211yesmaximal, characteristic, complemented
3#16837420C211yesmaximal, characteristic, complemented
4#16837384C211yesmaximal, characteristic, complemented
5C2×#14273644C211yesmaximal, characteristic, complemented
6#16837172C211yesmaximal, characteristic, complemented
7C59×#418C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273753—22no—
10#14273753—22no—
11C2×#11745670—21no—
12C2×#11745669—21no—
13C2×#11745664C2211yescharacteristic
14C2×#11745664C2211yescharacteristic
15C2×#11745664C2211yescharacteristic
16#14273662—22no—
17#14273655—22no—
18#14273645—21no—
19#14273644—22no—
20#14273643—21no—
21C22×D4×C59C2211yescharacteristic
22C2×M16×C59C2211yescharacteristic
23#117×C59C2211yescharacteristic
24#102×C59—22no—
25C24×C59—21no—
26C2×D4×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59—21no—
29C2×D4×C59—21no—
30C2×D4×C59—21no—
31C2×D4×C59D412yes—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—21no—
34#11745685—21no—
35#11745685—21no—
36#11745685—21no—
37#11745685—21no—
38C2×D236D411yescharacteristic
39C2×C4×D59—21no—
40C2×Dic118D411yescharacteristic
41M16×C59—21no—
42M16×C59—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C42×C59—21no—
47#11745670—24no—
48#11745669—24no—
49#11745664—21no—
50#11745664—21no—
51#11745664—21no—
52#11745664—21no—
53#11745664D412yes—
54#11745664D412yes—
55C2×C59⋊C8—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58C23×C59—22no—
59C23×C59—41no—
60C23×C59—41no—
61C23×C59—82no—
62C23×C59#4111yescharacteristic
63C22×D59—21no—
64D4×C59—22no—
65D4×C59—22no—
66D4×C59—41no—
67D4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×C4×C59#4111yescharacteristic
75C22⋊D59—41no—
76C22⋊D59—41no—
77C2×Dic59—21no—
78D236—21no—
79D236—21no—
80C4×D59—41no—
81C4×D59—41no—
82Dic118—21no—
83Dic118—21no—
84C8×C59—41no—
85C59⋊C8—22no—
86C59⋊C8—22no—
87C59⋊C8—41no—
88C22×C59—41no—
89C22×C59—42no—
90C22×C59—82no—
91C22×C59—82no—
92C22×C59—82no—
93C22×C59#12111yescharacteristic
94C22×C59#12311yescharacteristic
95C22×C59#12411yescharacteristic
96C2×D59—41no—
97C2×D59—81no—
98C4×C59—81no—
99C4×C59#12011yescharacteristic
100C4×C59#12111yescharacteristic
101C4×C59#12111yescharacteristic
102C4×C59#12311yescharacteristic
103Dic59—41no—
104#2048—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—21no—
107C2×C59—21no—
108C2×C59—82no—
109C2×C59#39411yescharacteristic
110D59—81no—
111C2×AGL(1,ℤ/8)—591no—
112#430—591no—
113#421—591no—
114#418D5911yescharacteristic, complemented
115#413—591no—
116C2×#100—591no—
117#344—591no—
118C59#204811yescharacteristic, complemented, Sylow
119C2×#41—591no—
120C22×D4C2×D5911yescharacteristic
121AGL(1,ℤ/8)—1182no—
122AGL(1,ℤ/8)—1182no—
123C2×SD16—1181no—
124C2×D8—1181no—
125C2×M16—591no—
126C2×M16—591no—
127C2×M16—591no—
128C2×M16C2×D5911yescharacteristic
129#117C2×D5911yescharacteristic
130#108—1182no—
131#104—1182no—
132#102—22no—
133#101—1181no—
134#100—1181no—
135#100—1182no—
136C24—21no—
137#41—1181no—
138#41—1181no—
139#41—1181no—
140#41—1181no—
141C2×Q8—591no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—591no—
148C2×D4—1181no—
149C2×D4C22⋊D5912yes—
150C22×C4—1181no—
151C22×C4C22×D5911yescharacteristic
152SD16—1184no—
153D8—1184no—
154M16—21no—
155M16—21no—
156M16—592no—
157M16—592no—
158M16—1181no—
159M16—1181no—
160M16—1181no—
161M16—1181no—
162C2×C8—21no—
163C2×C8—1181no—
164C2×C8—1181no—
165C2×C8—1181no—
166C4⋊C4—21no—
167C22⋊C4—21no—
168C42—21no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—82no—
173C23—1181no—
174C23#1174568711yescharacteristic
175Q8—1181no—
176Q8—1181no—
177D4—22no—
178D4—22no—
179D4—41no—
180D4—41no—
181D4—1181no—
182D4—1181no—
183D4—2361no—
184D4—2361no—
185C2×C4—41no—
186C2×C4—1181no—
187C2×C4—2361no—
188C2×C4—2361no—
189C2×C4#1174568511yescharacteristic
190C2×C4#1174568511yescharacteristic
191C2×C4D4×D5911yescharacteristic
192C2×C4D4×D5911yescharacteristic
193C2×C4D4×D5911yescharacteristic
194C2×C4C2×C22⋊D5911yescharacteristic
195C8—41no—
196C8—1182no—
197C8—1182no—
198C8—2361no—
199C22—41no—
200C22—42no—
201C22—82no—
202C22—82no—
203C22—82no—
204C22—4721no—
205C22—2361no—
206C22#1427369911yescharacteristic
207C22#1427370911yescharacteristic
208C22#1427371311yescharacteristic
209C4—81no—
210C4—2361no—
211C4#1427369511yescharacteristic
212C4#1427370011yescharacteristic
213C4#1427370011yescharacteristic
214C4#1427371011yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—82no—
219C2—4721no—
220C2#1683731711yescharacteristic
subgroupG/H
centerC2#16837317
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#418C2
socleC2×C59#394
hypercenter#418D59
hypocenterC59#2048
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #16837450C2semidirect
3. #16837420C2semidirect
4. #16837384C2semidirect
5. C2×#14273644C2semidirect
6. #16837172C2semidirect
7. C59×#418C2semidirect
114. #418D59semidirect
118. C59#2048semidirect