Finite Group Databasebeta

← #21425499

Subgroups — #21425499

Order 7552.

274 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14273648C212yesmaximal
2#16837272C211yesmaximal, characteristic, complemented
3#16837164C212yesmaximal, complemented
4#16837157C211yesmaximal, characteristic, complemented
5C59×#390C211yesmaximal, characteristic
6C22×C59⋊C8C2212yes—
7C2×C4⋊Dic59—21no—
8C2×C4⋊Dic59—21no—
9C2×C4⋊Dic59C2212yes—
10#14273648—24no—
11C22×D4×C59C2211yescharacteristic
12C2×C4⋊C4×C59C2211yescharacteristic
13C2×C22⋊C4×C59—21no—
14C2×C22⋊C4×C59—21no—
15C2×C42×C59C2211yescharacteristic
16C24×C59—21no—
17C2×D4×C59—22no—
18C2×D4×C59—22no—
19C2×D4×C59—21no—
20C2×D4×C59D412yes—
21C22×C4×C59—21no—
22C22×C4×C59D411yescharacteristic
23C22×C4×C59D411yescharacteristic
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—22no—
26C4⋊C4×C59—22no—
27C22⋊C4×C59—42no—
28C22⋊C4×C59—42no—
29C42×C59—22no—
30C4⋊Dic59—22no—
31C4⋊Dic59—22no—
32C4⋊Dic59—42no—
33C4⋊Dic59—42no—
34C2×C59⋊C8—22no—
35C2×C59⋊C8—22no—
36C2×C59⋊C8—22no—
37C23×C59—22no—
38C23×C59—41no—
39C23×C59—41no—
40C23×C59—41no—
41C23×C59—41no—
42C23×C59—41no—
43C23×C59—41no—
44C23×C59C2×D411yescharacteristic
45D4×C59—24no—
46D4×C59—42no—
47C2×C4×C59—21no—
48C2×C4×C59—21no—
49C2×C4×C59—21no—
50C2×C4×C59—21no—
51C2×C4×C59—41no—
52C2×C4×C59—41no—
53C2×C4×C59—41no—
54C2×C4×C59D812yes—
55C2×C4×C59SD1612yes—
56C2×C4×C59C2×D411yescharacteristic
57C2×C4×C59#4111yescharacteristic
58C2×C4×C59#4112yes—
59C2×C4×C59#4112yes—
60C2×Dic59—42no—
61C2×Dic59—42no—
62C2×Dic59—42no—
63C59⋊C8—42no—
64C22×C59—42no—
65C22×C59—42no—
66C22×C59—42no—
67C22×C59—81no—
68C22×C59—81no—
69C22×C59—81no—
70C22×C59—81no—
71C22×C59#12111yescharacteristic
72C22×C59#12311yescharacteristic
73C22×C59#12411yescharacteristic
74C22×C59C2×D811yescharacteristic
75C22×C59C2×SD1611yescharacteristic
76C22×C59AGL(1,ℤ/8)11yescharacteristic
77C22×C59#13711yescharacteristic
78C4×C59—22no—
79C4×C59—22no—
80C4×C59—81no—
81C4×C59#12312yes—
82C4×C59#12612yes—
83Dic59—82no—
84#2071—591nomaximal, Sylow
85C2×C59—82no—
86C2×C59#39711yescharacteristic
87C2×C59#45911yescharacteristic
88C2×C59#46111yescharacteristic
89C2×C59#48011yescharacteristic
90C2×C59#48111yescharacteristic
91C2×C59#48611yescharacteristic
92C2×C59#48911yescharacteristic
93C2×#102—592no—
94#390D5911yescharacteristic
95#384—591no—
96#340—592no—
97#336—591no—
98C59#207111yescharacteristic, complemented, Sylow
99C22×D4C2×D5911yescharacteristic
100C22×C8—592no—
101C2×C4⋊C4—592no—
102C2×C4⋊C4—1181no—
103C2×C4⋊C4—1181no—
104C2×C4⋊C4C2×D5911yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107C2×C42C2×D5911yescharacteristic
108#102—1184no—
109C24—21no—
110C2×D4—21no—
111C2×D4—22no—
112C2×D4—22no—
113C2×D4D23612yes—
114C22×C4—21no—
115C22×C4—1182no—
116C22×C4C22⋊D5911yescharacteristic
117C22×C4C22⋊D5911yescharacteristic
118C22×C4C22×D5911yescharacteristic
119C2×C8—1182no—
120C2×C8—1182no—
121C2×C8—1182no—
122C4⋊C4—22no—
123C4⋊C4—1182no—
124C4⋊C4—1182no—
125C4⋊C4—2362no—
126C4⋊C4—2362no—
127C22⋊C4—42no—
128C22⋊C4—42no—
129C42—22no—
130C23—22no—
131C23—41no—
132C23—41no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23C2×C22⋊D5911yescharacteristic
138D4—24no—
139D4—42no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—2362no—
148C2×C4—2362no—
149C2×C4—2362no—
150C2×C4#1174566912yes—
151C2×C4#1174567012yes—
152C2×C4C2×D23611yescharacteristic
153C2×C4#1174568511yescharacteristic
154C2×C4#1174568712yes—
155C2×C4#1174568712yes—
156C8—2362no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—81no—
161C22—81no—
162C22—81no—
163C22—81no—
164C22#1427370111yescharacteristic
165C22#1427370811yescharacteristic
166C22#1427371411yescharacteristic
167C22C2×#1174566911yescharacteristic
168C22C2×#1174567011yescharacteristic
169C22#1427375211yescharacteristic
170C22#1427375711yescharacteristic
171C4—22no—
172C4—22no—
173C4—81no—
174C4—4722no—
175C4#1427371112yes—
176C4#1427372012yes—
177C2—82no—
178C2#1683732711yescharacteristic
179C2#1683759711yescharacteristic
180C2#1683760711yescharacteristic
181C2#1683771311yescharacteristic
182C2#1683771811yescharacteristic
183C2#1683774811yescharacteristic
184C2#1683776111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D59
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#390C2
socleC23×C59C2×D4
hypercenter#390D59
hypocenterC59#2071
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #16837272C2semidirect
3. #16837164C2semidirect
4. #16837157C2semidirect
98. C59#2071semidirect