Finite Group Databasebeta

← #21423355

Subgroups — #21423355

Order 7552.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#16838125C211yesmaximal, characteristic
2#16837807C211yesmaximal, characteristic, complemented
3#16837687C211yesmaximal, characteristic, complemented
4#16837608C211yesmaximal, characteristic
5#16837149C211yesmaximal, characteristic, complemented
6#16837131C211yesmaximal, characteristic
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745660—21no—
9#14273727C2211yescharacteristic
10#14273727C2211yescharacteristic
11#14273722—22no—
12#14273715—21no—
13#14273703—21no—
14C4×Dic118—21no—
15C4×D236C2211yescharacteristic
16#14273685—21no—
17#14273661—22no—
18#14273658—21no—
19C4⋊(C59⋊C8)C2211yescharacteristic
20#14273652—21no—
21#14273651—21no—
22C4×Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4×C8×C59C2211yescharacteristic
25C2×Q8×C59D411yescharacteristic
26C2×D236D411yescharacteristic
27C2×C4×D59—21no—
28C2×Dic118—21no—
29C2×Dic118—21no—
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59D411yescharacteristic
34C42×C59—21no—
35C42×C59C2311yescharacteristic
36(C2×D59)⋊C4—22no—
37(C2×D59)⋊C4—22no—
38(C2×D59)⋊C4—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59D411yescharacteristic
43C4⋊Dic59D412yes—
44Dic59⋊C4—22no—
45C4×Dic59—22no—
46C2×C59⋊C8—21no—
47#11745660—42no—
48C22×D59—21no—
49Q8×C59—21no—
50Q8×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59—21no—
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×C4×C59C2×D411yescharacteristic
56C2×Dic59—21no—
57C2×Dic59—22no—
58C2×Dic59—41no—
59D236—21no—
60D236—21no—
61C4×D59—41no—
62C4×D59—41no—
63Dic118—41no—
64Dic118—41no—
65Dic118—41no—
66Dic118—41no—
67C8×C59—22no—
68C8×C59—41no—
69C59⋊C8—41no—
70C22×C59#12011yescharacteristic
71C2×D59—41no—
72C2×D59—41no—
73C2×D59—41no—
74C4×C59—21no—
75C4×C59—41no—
76C4×C59—41no—
77C4×C59#13511yescharacteristic
78C4×C59#13511yescharacteristic
79C4×C59AGL(1,ℤ/8)11yescharacteristic
80C4×C59#13711yescharacteristic
81Dic59—42no—
82Dic59—41no—
83Dic59—81no—
84#1650—591nomaximal, Sylow
85C2×C59#44911yescharacteristic
86C2×C59#45211yescharacteristic
87C2×C59#45611yescharacteristic
88D59—81no—
89#556—591no—
90#500—591no—
91#475—591no—
92#461—591no—
93#332—591no—
94Q8⋊C8D5911yescharacteristic, complemented
95D4⋊C8—591no—
96C59#165011yescharacteristic, complemented, Sylow
97C2×SD16—1181no—
98C4⋊Q8—591no—
99C4⋊Q8—591no—
100#126—1182no—
101#124—1181no—
102C22⋊Q8—1181no—
103C4×Q8—1181no—
104C4×Q8C2×D5911yescharacteristic
105C4×D4—591no—
106#117—1181no—
107#107—1182no—
108#106—1181no—
109C4⋊C8—591no—
110C4⋊C8C2×D5911yescharacteristic
111#103—1181no—
112#103—1181no—
113C4×C8C2×D5911yescharacteristic
114C2×Q8—1181no—
115C2×Q8—1181no—
116C2×Q8D23611yescharacteristic
117C2×D4—591no—
118C22×C4—1181no—
119SD16—2362no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1181no—
123C4⋊C4—21no—
124C4⋊C4—591no—
125C4⋊C4—592no—
126C4⋊C4—1182no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C4⋊C4D23611yescharacteristic
131C22⋊C4—1182no—
132C22⋊C4—1182no—
133C22⋊C4—1181no—
134C42—21no—
135C42—1182no—
136C42C22×D5911yescharacteristic
137C23—1181no—
138Q8—21no—
139Q8—21no—
140Q8—2361no—
141Q8—2361no—
142Q8—2361no—
143Q8—2361no—
144D4—1181no—
145D4—1181no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1181no—
149C2×C4—1182no—
150C2×C4—2361no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4C2×D23611yescharacteristic
154C2×C4D4×D5911yescharacteristic
155C2×C4D4×D5911yescharacteristic
156C8—22no—
157C8—41no—
158C8—2361no—
159C22—2361no—
160C22—2361no—
161C22—2361no—
162C22#1427369711yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—4721no—
167C4—2362no—
168C4—2361no—
169C4#1427374911yescharacteristic
170C4#1427375011yescharacteristic
171C4#1427375411yescharacteristic
172C4#1427376011yescharacteristic
173C2—4721no—
174C2#1683755011yescharacteristic
175C2#1683756611yescharacteristic
176C2#1683758611yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59#120
hypercenterQ8⋊C8D59
hypocenterC59#1650
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837807C2semidirect
3. #16837687C2semidirect
5. #16837149C2semidirect
7. C59×Q8⋊C8C2semidirect
94. Q8⋊C8D59semidirect
96. C59#1650semidirect