Finite Group Databasebeta

← #21423353

Subgroups — #21423353

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#16838126C211yesmaximal, characteristic
2#16837805C211yesmaximal, characteristic, complemented
3#16837688C211yesmaximal, characteristic, complemented
4#16837608C211yesmaximal, characteristic
5#16837132C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic
7C59×#332C211yesmaximal, characteristic, complemented
8C2×#11745660—21no—
9#14273727C2211yescharacteristic
10#14273722—22no—
11#14273716—21no—
12#14273707—21no—
13Q8×Dic59—21no—
14C4×Dic118C2211yescharacteristic
15C4×D236C2211yescharacteristic
16#14273685—21no—
17#14273660—22no—
18#14273659—21no—
19#14273652—21no—
20#14273652—21no—
21C4×C59⋊C8C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×Q8×C59—21no—
26C2×D236D411yescharacteristic
27C2×C4×D59—21no—
28C2×Dic118—21no—
29C2×Dic118D411yescharacteristic
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59D412yes—
34C42×C59C2311yescharacteristic
35(C2×D59)⋊C4—22no—
36(C2×D59)⋊C4—22no—
37(C2×D59)⋊C4—21no—
38C4⋊Dic59—22no—
39C4⋊Dic59—21no—
40C4⋊Dic59—21no—
41C4⋊Dic59D411yescharacteristic
42C4⋊Dic59D411yescharacteristic
43Dic59⋊C4—21no—
44C4×Dic59—22no—
45C4×Dic59—21no—
46C2×C59⋊C8—21no—
47#11745660—42no—
48C22×D59—21no—
49Q8×C59—41no—
50Q8×C59—41no—
51C2×C4×C59—22no—
52C2×C4×C59C2×D411yescharacteristic
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×Dic59—21no—
56C2×Dic59—21no—
57C2×Dic59—21no—
58C2×Dic59—41no—
59D236—21no—
60D236—21no—
61C4×D59—41no—
62C4×D59—41no—
63Dic118—21no—
64Dic118—21no—
65Dic118—41no—
66Dic118—41no—
67C8×C59—41no—
68C8×C59—41no—
69C59⋊C8—22no—
70C22×C59#12011yescharacteristic
71C2×D59—41no—
72C2×D59—41no—
73C2×D59—41no—
74C4×C59—21no—
75C4×C59—42no—
76C4×C59#13511yescharacteristic
77C4×C59#13511yescharacteristic
78C4×C59AGL(1,ℤ/8)11yescharacteristic
79C4×C59#13711yescharacteristic
80Dic59—41no—
81Dic59—41no—
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#332D5911yescharacteristic, complemented
94Q8⋊C8—591no—
95D4⋊C8—591no—
96C59#165011yescharacteristic, complemented, Sylow
97C2×SD16—1181no—
98C4⋊Q8—591no—
99C4⋊Q8C2×D5911yescharacteristic
100#126—1182no—
101#124—1181no—
102C22⋊Q8—1181no—
103C4×Q8—591no—
104C4×Q8—1181no—
105C4×D4—591no—
106#117—1181no—
107#107—1182no—
108#106—1181no—
109C4⋊C8C2×D5911yescharacteristic
110C4⋊C8C2×D5911yescharacteristic
111#103—1181no—
112#103—1181no—
113C4×C8—591no—
114C2×Q8—21no—
115C2×Q8—591no—
116C2×Q8—1181no—
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—591no—
126C4⋊C4—1182no—
127C4⋊C4—1181no—
128C4⋊C4—1181no—
129C4⋊C4—1181no—
130C4⋊C4D23612yes—
131C22⋊C4—1182no—
132C22⋊C4—1182no—
133C22⋊C4—1181no—
134C42—1182no—
135C42—1181no—
136C42C22×D5911yescharacteristic
137C23—1181no—
138Q8—41no—
139Q8—41no—
140Q8—1181no—
141Q8—1181no—
142Q8—2361no—
143Q8—2361no—
144D4—1181no—
145D4—1181no—
146C2×C4—22no—
147C2×C4—1181no—
148C2×C4—1181no—
149C2×C4—1181no—
150C2×C4—2361no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4C2×D23611yescharacteristic
154C2×C4D4×D5911yescharacteristic
155C2×C4D4×D5911yescharacteristic
156C8—41no—
157C8—41no—
158C8—1182no—
159C22—2361no—
160C22—2361no—
161C22—2361no—
162C22#1427369711yescharacteristic
163C4—21no—
164C4—42no—
165C4—4721no—
166C4—2361no—
167C4—2361no—
168C4—2361no—
169C4#1427374811yescharacteristic
170C4#1427374811yescharacteristic
171C4#1427375111yescharacteristic
172C4#1427375911yescharacteristic
173C2—4721no—
174C2#1683754811yescharacteristic
175C2#1683756711yescharacteristic
176C2#1683758711yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#332C2
socleC22×C59#120
hypercenter#332D59
hypocenterC59#1650
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #16837805C2semidirect
3. #16837688C2semidirect
5. #16837132C2semidirect
7. C59×#332C2semidirect
93. #332D59semidirect
96. C59#1650semidirect