Finite Group Databasebeta

← #21423229

Subgroups — #21423229

Order 7552.

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

normal subgroups only

This group has 214 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#16838112C211yesmaximal, characteristic
2#16837781C211yesmaximal, characteristic, complemented
3#16837689C211yesmaximal, characteristic
4#16837150C211yesmaximal, characteristic, complemented
5Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic
7C59×#477C211yesmaximal, characteristic, complemented
8C2×#11745672—22no—
9#14273727C2211yescharacteristic
10#14273719—21no—
11#14273705—22no—
12#14273703—21no—
13C4×D236—21no—
14C4×D236C2211yescharacteristic
15C4⋊C4×D59—21no—
16#14273658—21no—
17C4⋊(C59⋊C8)C2211yescharacteristic
18#14273647—21no—
19C4×C59⋊C8C2211yescharacteristic
20C4⋊Q8×C59C2211yescharacteristic
21C4×Q8×C59C2211yescharacteristic
22#107×C59—21no—
23C4⋊C8×C59C2211yescharacteristic
24#103×C59—21no—
25C2×Q8×C59—21no—
26C2×Q8×C59D411yescharacteristic
27C2×D236D411yescharacteristic
28C2×C4×D59—21no—
29C2×C4×D59—22no—
30C2×Dic118D412yes—
31C2×C8×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59D411yescharacteristic
36C42×C59—21no—
37C42×C59C2311yescharacteristic
38#11745672—44no—
39(C2×D59)⋊C4—22no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59—21no—
43C4⋊Dic59D411yescharacteristic
44Dic59⋊C4—22no—
45Dic59⋊C4—22no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C22×D59—21no—
49Q8×C59—21no—
50Q8×C59—21no—
51Q8×C59—42no—
52C2×C4×C59—21no—
53C2×C4×C59—21no—
54C2×C4×C59—41no—
55C2×C4×C59C2×D411yescharacteristic
56C2×C4×C59C2×D411yescharacteristic
57C2×C4×C59C2×D411yescharacteristic
58C2×Dic59—21no—
59C2×Dic59—22no—
60D236—21no—
61D236Q1612yescomplemented
62C4×D59—41no—
63C4×D59—41no—
64C4×D59—82no—
65Dic118—42no—
66C8×C59—41no—
67C59⋊C8—22no—
68C59⋊C8—41no—
69C22×C59#12011yescharacteristic
70C2×D59—22no—
71C2×D59—41no—
72C2×D59—41no—
73C4×C59—21no—
74C4×C59—41no—
75C4×C59—41no—
76C4×C59—81no—
77C4×C59C2×Q1611yescharacteristic
78C4×C59#13511yescharacteristic
79C4×C59#13711yescharacteristic
80C4×C59#13711yescharacteristic
81Dic59—41no—
82Dic59—42no—
83#1632—591nomaximal, Sylow
84C2×C59#45111yescharacteristic
85C2×C59#45211yescharacteristic
86C2×C59#45311yescharacteristic
87D59—42no—
88#554—591no—
89#494—591no—
90#477D5911yescharacteristic, complemented
91#476—591no—
92#333—591no—
93Q8⋊C8—591no—
94D4⋊C8—591no—
95C59#163211yescharacteristic, complemented, Sylow
96C2×Q16—1182no—
97C4⋊Q8—591no—
98C4⋊Q8C2×D5911yescharacteristic
99#125—1181no—
100C22⋊Q8—1182no—
101C22⋊Q8—1181no—
102C4×Q8C2×D5911yescharacteristic
103C4×D4—591no—
104C4×D4—1181no—
105C2×C4⋊C4—1181no—
106#107—21no—
107#106—1181no—
108C4⋊C8—591no—
109C4⋊C8C2×D5911yescharacteristic
110#103—21no—
111#102—1181no—
112C4×C8—591no—
113C2×Q8—21no—
114C2×Q8—592no—
115C2×Q8C22⋊D5911yescharacteristic
116C2×D4—591no—
117C22×C4—1182no—
118C22×C4—1181no—
119Q16—2364no—
120C2×C8—21no—
121C2×C8—1181no—
122C2×C8—1181no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—591no—
127C4⋊C4—1182no—
128C4⋊C4—1182no—
129C4⋊C4—1181no—
130C4⋊C4—1181no—
131C4⋊C4C22⋊D5911yescharacteristic
132C22⋊C4—1182no—
133C22⋊C4—1181no—
134C42—21no—
135C42C22×D5911yescharacteristic
136C23—1181no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—2362no—
141D4—592no—
142D4—1181no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—1181no—
147C2×C4—1182no—
148C2×C4—4722no—
149C2×C4—2361no—
150C2×C4—2361no—
151C2×C4D4×D5911yescharacteristic
152C2×C4D4×D5911yescharacteristic
153C2×C4C2×C22⋊D5911yescharacteristic
154C8—41no—
155C8—1182no—
156C8—2361no—
157C22—1182no—
158C22—2361no—
159C22—2361no—
160C22#1427369511yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—2361no—
166C4—2362no—
167C4Q16×D5911yescharacteristic
168C4#1427374711yescharacteristic
169C4#1427375811yescharacteristic
170C4#1427375911yescharacteristic
171C2—2362no—
172C2#1683755611yescharacteristic
173C2#1683756211yescharacteristic
174C2#1683756811yescharacteristic
subgroupG/H
centerC22#14273695
commutatorC42×C59C23
FrattiniC42C22×D59
FittingC59×#477C2
socleC22×C59#120
hypercenter#477D59
hypocenterC59#1632
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #16837781C2semidirect
4. #16837150C2semidirect
5. Q8⋊(C59⋊C8)C2semidirect
7. C59×#477C2semidirect
61. D236Q16semidirect
90. #477D59semidirect
95. C59#1632semidirect