Finite Group Databasebeta

← #21423282

Subgroups — #21423282

Order 7552.

212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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#16837748C211yesmaximal, characteristic
2#16837687C211yesmaximal, characteristic, complemented
3#16837612C211yesmaximal, characteristic, complemented
4#16837146C211yesmaximal, characteristic
5Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
7C59×#559C211yesmaximal, characteristic
8C2×#11745672—21no—
9#14273727C2211yescharacteristic
10#14273658—21no—
11C4⋊(C59⋊C8)C2211yescharacteristic
12C4⋊(C59⋊C8)C2211yescharacteristic
13#14273651—21no—
14#14273650—21no—
15#14273648—22no—
16C4×C59⋊C8C2211yescharacteristic
17#127×C59C2211yescharacteristic
18#124×C59—21no—
19#124×C59—21no—
20#123×C59—22no—
21C4×Q8×C59C2211yescharacteristic
22C4×Q8×C59C2211yescharacteristic
23C4×D4×C59—21no—
24C4×D4×C59—21no—
25C2×Q8×C59D411yescharacteristic
26C2×Q8×C59D411yescharacteristic
27C2×D4×C59—21no—
28C2×D4×C59—21no—
29C2×D4×C59D412yes—
30C22×C4×C59—22no—
31C2×Dic118—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59D411yescharacteristic
35C4⋊C4×C59D411yescharacteristic
36C22⋊C4×C59—22no—
37C22⋊C4×C59—22no—
38C22⋊C4×C59—22no—
39C42×C59—21no—
40C42×C59—21no—
41C42×C59C2311yescharacteristic
42#11745672—42no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45C2×C59⋊C8—21no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C23×C59—22no—
49Q8×C59—21no—
50Q8×C59—21no—
51Q8×C59—21no—
52Q8×C59—21no—
53D4×C59—42no—
54D4×C59—41no—
55D4×C59—41no—
56D4×C59—41no—
57D4×C59—41no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—21no—
62C2×C4×C59—82no—
63C2×C4×C59C2×D411yescharacteristic
64C2×C4×C59C2×D411yescharacteristic
65C2×C4×C59C2×D411yescharacteristic
66C2×Dic59—41no—
67Dic118—41no—
68Dic118—41no—
69C59⋊C8—41no—
70C59⋊C8—41no—
71C59⋊C8—41no—
72C22×C59—42no—
73C22×C59—42no—
74C22×C59—42no—
75C22×C59#12011yescharacteristic
76C4×C59—21no—
77C4×C59—41no—
78C4×C59—41no—
79C4×C59—41no—
80C4×C59—41no—
81C4×C59#13511yescharacteristic
82C4×C59#13511yescharacteristic
83C4×C59AGL(1,ℤ/8)11yescharacteristic
84C4×C59#13711yescharacteristic
85Dic59—81no—
86#1640—591nomaximal, Sylow
87C2×C59—82no—
88C2×C59#44911yescharacteristic
89C2×C59#45211yescharacteristic
90C2×C59#45511yescharacteristic
91#559D5911yescharacteristic
92#486—591no—
93#475—591no—
94#462—591no—
95#331—591no—
96Q8⋊C8—591no—
97Q8⋊C8—591no—
98C59#164011yescharacteristic, complemented, Sylow
99C2×Q16—1181no—
100C4⋊Q8—591no—
101#127C2×D5911yescharacteristic
102#124—21no—
103#124—21no—
104#123—22no—
105C4×Q8C2×D5911yescharacteristic
106C4×Q8C2×D5911yescharacteristic
107C4×D4—21no—
108C4×D4—21no—
109#106—1181no—
110C4⋊C8—591no—
111C4⋊C8—591no—
112#103—1181no—
113#103—1181no—
114#102—1182no—
115C4×C8—591no—
116C2×Q8—1181no—
117C2×Q8C22⋊D5911yescharacteristic
118C2×Q8C22⋊D5911yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D5912yes—
122C22×C4—22no—
123Q16—2362no—
124C2×C8—1181no—
125C2×C8—1181no—
126C2×C8—1181no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C4⋊C4C22⋊D5911yescharacteristic
132C4⋊C4C22⋊D5911yescharacteristic
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C42C22×D5911yescharacteristic
139C23—22no—
140Q8—21no—
141Q8—21no—
142Q8—21no—
143Q8—21no—
144Q8—2361no—
145Q8—2361no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—82no—
156C2×C4—2361no—
157C2×C4C2×C22⋊D5911yescharacteristic
158C2×C4C2×C22⋊D5911yescharacteristic
159C2×C4C2×C22⋊D5911yescharacteristic
160C8—2361no—
161C8—2361no—
162C8—2361no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1427369611yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—4721no—
173C4#1427374711yescharacteristic
174C4#1427374711yescharacteristic
175C4#1427375211yescharacteristic
176C4#1427375711yescharacteristic
177C2—82no—
178C2#1683754711yescharacteristic
179C2#1683756411yescharacteristic
180C2#1683758011yescharacteristic
subgroupG/H
centerC22#14273696
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#559C2
socleC22×C59#120
hypercenter#559D59
hypocenterC59#1640
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #16837687C2semidirect
3. #16837612C2semidirect
5. Q8⋊(C59⋊C8)C2semidirect
6. Q8⋊(C59⋊C8)C2semidirect
98. C59#1640semidirect