Finite Group Databasebeta

← #21423271

Subgroups — #21423271

Order 7552.

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

normal subgroups only

This group has 194 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#16837753C211yesmaximal, characteristic, complemented
3#16837697C211yesmaximal, characteristic, complemented
4#16837693C211yesmaximal, characteristic
5#16837149C211yesmaximal, characteristic, complemented
6#16837131C211yesmaximal, characteristic
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8#14273727C2211yescharacteristic
9#14273727C2211yescharacteristic
10#14273722—22no—
11#14273715—21no—
12#14273703—21no—
13C4×Dic118—21no—
14C4×D236C2211yescharacteristic
15#14273685—21no—
16#14273660—21no—
17#14273659—21no—
18C4⋊(C59⋊C8)C2211yescharacteristic
19#14273652—22no—
20#14273651—21no—
21#14273649—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⋊Dic59D412yes—
43C4⋊Dic59D411yescharacteristic
44Dic59⋊C4—22no—
45C4×Dic59—22no—
46C2×C59⋊C8—21no—
47C22×D59—21no—
48Q8×C59—21no—
49Q8×C59—21no—
50C2×C4×C59—21no—
51C2×C4×C59—21no—
52C2×C4×C59C2×D411yescharacteristic
53C2×C4×C59C2×D411yescharacteristic
54C2×C4×C59C2×D411yescharacteristic
55C2×Dic59—21no—
56C2×Dic59—22no—
57C2×Dic59—41no—
58D236—21no—
59D236—21no—
60C4×D59—41no—
61C4×D59—41no—
62Dic118—41no—
63Dic118—41no—
64Dic118—42no—
65C8×C59—41no—
66C8×C59—41no—
67C59⋊C8—41no—
68C22×C59#12011yescharacteristic
69C2×D59—41no—
70C2×D59—41no—
71C2×D59—41no—
72C4×C59—21no—
73C4×C59—41no—
74C4×C59—41no—
75C4×C59#13511yescharacteristic
76C4×C59#13511yescharacteristic
77C4×C59#13711yescharacteristic
78C4×C59#13711yescharacteristic
79Dic59—42no—
80Dic59—41no—
81Dic59—81no—
82#1638—591nomaximal, Sylow
83C2×C59#45211yescharacteristic
84C2×C59#45211yescharacteristic
85C2×C59#45411yescharacteristic
86D59—81no—
87#556—591no—
88#487—591no—
89#477—591no—
90#476—591no—
91#332—591no—
92Q8⋊C8D5911yescharacteristic, complemented
93D4⋊C8—591no—
94C59#163811yescharacteristic, complemented, Sylow
95C4⋊Q8—591no—
96C4⋊Q8—591no—
97#126—1182no—
98#124—1181no—
99C22⋊Q8—1181no—
100C4×Q8—1181no—
101C4×Q8C2×D5911yescharacteristic
102C4×D4—591no—
103#117—1181no—
104#107—1181no—
105#106—1181no—
106C4⋊C8—591no—
107C4⋊C8C2×D5911yescharacteristic
108#103—1182no—
109#103—1181no—
110#102—1181no—
111C4×C8C2×D5911yescharacteristic
112C2×Q8—1181no—
113C2×Q8—1181no—
114C2×Q8D23611yescharacteristic
115C2×D4—591no—
116C22×C4—1181no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—1181no—
120C4⋊C4—21no—
121C4⋊C4—592no—
122C4⋊C4—591no—
123C4⋊C4—1182no—
124C4⋊C4—1181no—
125C4⋊C4—1181no—
126C4⋊C4—1181no—
127C4⋊C4D23611yescharacteristic
128C22⋊C4—1182no—
129C22⋊C4—1182no—
130C22⋊C4—1181no—
131C42—21no—
132C42—1182no—
133C42C22×D5911yescharacteristic
134C23—1181no—
135Q8—21no—
136Q8—21no—
137Q8—2362no—
138Q8—2361no—
139Q8—2361no—
140D4—1181no—
141D4—1181no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—1181no—
145C2×C4—1182no—
146C2×C4—2361no—
147C2×C4—2361no—
148C2×C4—2361no—
149C2×C4C2×D23611yescharacteristic
150C2×C4D4×D5911yescharacteristic
151C2×C4D4×D5911yescharacteristic
152C8—41no—
153C8—41no—
154C8—2361no—
155C22—2361no—
156C22—2361no—
157C22—2361no—
158C22#1427369711yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—4721no—
163C4—2361no—
164C4—2362no—
165C4#1427374811yescharacteristic
166C4#1427374911yescharacteristic
167C4#1427375911yescharacteristic
168C4#1427376011yescharacteristic
169C2—4721no—
170C2#1683756611yescharacteristic
171C2#1683756711yescharacteristic
172C2#1683757611yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59#120
hypercenterQ8⋊C8D59
hypocenterC59#1638
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. #16837753C2semidirect
3. #16837697C2semidirect
5. #16837149C2semidirect
7. C59×Q8⋊C8C2semidirect
92. Q8⋊C8D59semidirect
94. C59#1638semidirect