Finite Group Databasebeta

← #21424573

Subgroups — #21424573

Order 7552.

324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 79 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#16838168C211yesmaximal, characteristic, complemented
3#16837420C211yesmaximal, characteristic, complemented
4C2×#14273644C211yesmaximal, characteristic, complemented
5#16837172C211yesmaximal, characteristic, complemented
6C59⋊#338C211yesmaximal, characteristic, complemented
7C59×#418C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9#14273753—22no—
10#14273753—22no—
11C2×#11745670C412yescomplemented
12C2×#11745669C412yescomplemented
13#14273735—22no—
14#14273733—22no—
15C2×#11745664C2211yescharacteristic
16C2×#11745664C2211yescharacteristic
17C2×#11745664C2211yescharacteristic
18M16×D59—22no—
19#14273655—22no—
20#14273644—22no—
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×C59C2×C412yes—
32C22×C4×C59C2311yescharacteristic
33C2×C22⋊D59—21no—
34#11745685—21no—
35#11745685—21no—
36#11745685D412yes—
37#11745685D412yes—
38C2×D236C2×C411yescharacteristic
39C2×C4×D59—21no—
40C2×Dic118C2×C411yescharacteristic
41M16×C59—21no—
42M16×C59—21no—
43C2×C8×C59D412yes—
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#11745664—21no—
54#11745664D412yes—
55C2×C59⋊C8—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8C2×C412yes—
58#11745659—24no—
59C8×D59—24no—
60C23×C59—22no—
61C23×C59—41no—
62C23×C59—41no—
63C23×C59—82no—
64C23×C59#4111yescharacteristic
65C22×D59—21no—
66D4×C59—22no—
67D4×C59—22no—
68D4×C59—41no—
69D4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59C22×C411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59#4111yescharacteristic
77C22⋊D59—22no—
78C22⋊D59—22no—
79C2×Dic59—21no—
80D236—21no—
81D236C22⋊C412yes—
82C4×D59—22no—
83C4×D59—22no—
84Dic118—21no—
85Dic118C22⋊C412yes—
86C8×C59—22no—
87C59⋊C8—22no—
88C59⋊C8—22no—
89C59⋊C8—41no—
90C22×C59—41no—
91C22×C59—42no—
92C22×C59—82no—
93C22×C59—82no—
94C22×C59—82no—
95C22×C59C4×D411yescharacteristic
96C22×C59#12111yescharacteristic
97C22×C59#12311yescharacteristic
98C2×D59—22no—
99C2×D59—81no—
100C4×C59—81no—
101C4×C59C2×C22⋊C411yescharacteristic
102C4×C59C4×D411yescharacteristic
103C4×C59#12011yescharacteristic
104C4×C59#12111yescharacteristic
105Dic59—22no—
106#1903—591nomaximal, Sylow
107C2×C59—21no—
108C2×C59—21no—
109C2×C59—21no—
110C2×C59—82no—
111C2×C59#38611yescharacteristic
112D59—42no—
113C2×AGL(1,ℤ/8)—591no—
114#568—591no—
115#421—591no—
116#418D5911yescharacteristic, complemented
117C2×#100—591no—
118#344—591no—
119#338—591no—
120C59#190311yescharacteristic, complemented, Sylow
121C2×#41—591no—
122C22×D4C2×D5911yescharacteristic
123AGL(1,ℤ/8)—1182no—
124AGL(1,ℤ/8)—1182no—
125C2×SD16—592no—
126C2×D8—592no—
127#131—1182no—
128#131—1182no—
129C2×M16—591no—
130C2×M16—591no—
131C2×M16—591no—
132C2×M16—1182no—
133C2×M16C2×D5911yescharacteristic
134#117C2×D5911yescharacteristic
135#104—1182no—
136#102—22no—
137#100—1182no—
138C24—21no—
139#41—592no—
140#41—592no—
141#41—1181no—
142#41—1181no—
143C2×Q8—591no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—591no—
150C2×D4—1181no—
151C2×D4C4×D5912yes—
152C22×C4—1181no—
153C22×C4C22×D5911yescharacteristic
154SD16—1184no—
155D8—1184no—
156M16—21no—
157M16—21no—
158M16—592no—
159M16—1184no—
160M16—1181no—
161M16—1181no—
162M16—1181no—
163M16—1181no—
164M16—1181no—
165C2×C8—592no—
166C2×C8—1184no—
167C2×C8—1181no—
168C2×C8—1181no—
169C2×C8C22⋊D5912yes—
170C4⋊C4—21no—
171C22⋊C4—21no—
172C42—21no—
173C23—22no—
174C23—41no—
175C23—41no—
176C23—82no—
177C23—1181no—
178C23#1174568711yescharacteristic
179Q8—592no—
180Q8—1181no—
181D4—22no—
182D4—22no—
183D4—41no—
184D4—41no—
185D4—592no—
186D4—1182no—
187D4—1182no—
188D4—1181no—
189C2×C4—41no—
190C2×C4—1181no—
191C2×C4—1182no—
192C2×C4—1182no—
193C2×C4C2×C4×D5911yescharacteristic
194C2×C4#1174568511yescharacteristic
195C2×C4D4×D5911yescharacteristic
196C2×C4D4×D5911yescharacteristic
197C2×C4D4×D5911yescharacteristic
198C2×C4C2×C22⋊D5911yescharacteristic
199C8—22no—
200C8—1182no—
201C8—1182no—
202C8—2361no—
203C22—41no—
204C22—42no—
205C22—82no—
206C22—82no—
207C22—82no—
208C22—1182no—
209C22—4721no—
210C22(C22⋊D59)⋊C411yescharacteristic
211C22#1427369811yescharacteristic
212C22#1427370911yescharacteristic
213C4—81no—
214C4—1182no—
215C4C22⋊C4×D5911yescharacteristic
216C4C4×C22⋊D5911yescharacteristic
217C4#1427369511yescharacteristic
218C4#1427370011yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—82no—
223C2—2362no—
224C2#1683727811yescharacteristic
subgroupG/H
centerC2#16837278
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#418C2
socleC2×C59#386
hypercenter#418D59
hypocenterC59#1903
LCSG ▷ C2×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. #16838168C2semidirect
3. #16837420C2semidirect
4. C2×#14273644C2semidirect
5. #16837172C2semidirect
6. C59⋊#338C2semidirect
7. C59×#418C2semidirect
11. C2×#11745670C4semidirect
12. C2×#11745669C4semidirect
116. #418D59semidirect
120. C59#1903semidirect