Finite Group Databasebeta

← #21423304

Subgroups — #21423304

Order 7552.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#16838113C211yesmaximal, characteristic
2#16837752C211yesmaximal, characteristic, complemented
3#16837688C211yesmaximal, characteristic, complemented
4#16837608C211yesmaximal, characteristic
5#16837132C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic
7C59×#333C211yesmaximal, characteristic, complemented
8C2×#11745660—21no—
9#14273727C2211yescharacteristic
10#14273718—21no—
11#14273707—21no—
12#14273703—22no—
13C4×Dic118C2211yescharacteristic
14C4×D236C2211yescharacteristic
15#14273689—21no—
16C4⋊C4×D59—21no—
17#14273659—21no—
18#14273652—21no—
19#14273652—21no—
20#14273651—22no—
21C4×C59⋊C8C2211yescharacteristic
22C4⋊Q8×C59C2211yescharacteristic
23C4⋊C8×C59C2211yescharacteristic
24C4⋊C8×C59C2211yescharacteristic
25C2×Q8×C59D412yes—
26C2×D236D411yescharacteristic
27C2×C4×D59—21no—
28C2×C4×D59—22no—
29C2×Dic118—21no—
30C2×Dic118D411yescharacteristic
31C2×C8×C59—21no—
32C2×C8×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C42×C59C2311yescharacteristic
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—22no—
44Dic59⋊C4—21no—
45C4×Dic59—21no—
46C2×C59⋊C8—21no—
47#11745660—42no—
48C22×D59—21no—
49Q8×C59—42no—
50C2×C4×C59—22no—
51C2×C4×C59C2×D411yescharacteristic
52C2×C4×C59C2×D411yescharacteristic
53C2×C4×C59C2×D411yescharacteristic
54C2×Dic59—21no—
55C2×Dic59—21no—
56C2×Dic59—21no—
57C2×Dic59—41no—
58D236—21no—
59D236SD1612yes—
60C4×D59—41no—
61C4×D59—41no—
62C4×D59—82no—
63Dic118—21no—
64Dic118—21no—
65Dic118—41no—
66Dic118—41no—
67C8×C59—41no—
68C8×C59—41no—
69C59⋊C8—41no—
70C22×C59#12011yescharacteristic
71C2×D59—22no—
72C2×D59—41no—
73C2×D59—41no—
74C4×C59—21no—
75C4×C59—42no—
76C4×C59C2×SD1611yescharacteristic
77C4×C59#13511yescharacteristic
78C4×C59#13711yescharacteristic
79C4×C59#13711yescharacteristic
80Dic59—41no—
81Dic59—41no—
82Dic59—41no—
83Dic59—81no—
84#1643—591nomaximal, Sylow
85C2×C59#44811yescharacteristic
86C2×C59#45211yescharacteristic
87C2×C59#45511yescharacteristic
88D59—42no—
89#554—591no—
90#487—591no—
91#475—591no—
92#461—591no—
93#333D5911yescharacteristic, complemented
94Q8⋊C8—591no—
95D4⋊C8—591no—
96C59#164311yescharacteristic, complemented, Sylow
97C2×SD16—1181no—
98C4⋊Q8—591no—
99C4⋊Q8C2×D5911yescharacteristic
100#125—1181no—
101C22⋊Q8—1181no—
102C22⋊Q8—1182no—
103C4×Q8—591no—
104C4×D4—591no—
105C4×D4—1181no—
106C2×C4⋊C4—1181no—
107#106—1181no—
108C4⋊C8C2×D5911yescharacteristic
109C4⋊C8C2×D5911yescharacteristic
110#103—1181no—
111#103—1181no—
112#103—1182no—
113C4×C8—591no—
114C2×Q8—591no—
115C2×Q8—1181no—
116C2×Q8D23612yes—
117C2×D4—591no—
118C22×C4—1182no—
119C22×C4—1181no—
120SD16—2362no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—1181no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—591no—
127C4⋊C4—591no—
128C4⋊C4—1182no—
129C4⋊C4—1182no—
130C4⋊C4—1181no—
131C4⋊C4—1181no—
132C4⋊C4—1181no—
133C22⋊C4—1182no—
134C22⋊C4—1181no—
135C42—1181no—
136C42C22×D5911yescharacteristic
137C23—1181no—
138Q8—42no—
139Q8—1181no—
140Q8—1181no—
141Q8—2361no—
142Q8—2361no—
143D4—592no—
144D4—1181no—
145C2×C4—22no—
146C2×C4—1181no—
147C2×C4—1181no—
148C2×C4—1181no—
149C2×C4—4722no—
150C2×C4—2361no—
151C2×C4—2361no—
152C2×C4—2361no—
153C2×C4C2×D23611yescharacteristic
154C2×C4D4×D5911yescharacteristic
155C2×C4D4×D5911yescharacteristic
156C8—41no—
157C8—41no—
158C8—2361no—
159C22—1182no—
160C22—2361no—
161C22—2361no—
162C22#1427369711yescharacteristic
163C4—21no—
164C4—42no—
165C4—4721no—
166C4—2361no—
167C4—2361no—
168C4—2361no—
169C4SD16×D5911yescharacteristic
170C4#1427374811yescharacteristic
171C4#1427375911yescharacteristic
172C4#1427375911yescharacteristic
173C2—2362no—
174C2#1683754211yescharacteristic
175C2#1683756711yescharacteristic
176C2#1683758211yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#333C2
socleC22×C59#120
hypercenter#333D59
hypocenterC59#1643
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #16837752C2semidirect
3. #16837688C2semidirect
5. #16837132C2semidirect
7. C59×#333C2semidirect
93. #333D59semidirect
96. C59#1643semidirect