Finite Group Databasebeta

← #21425050

Subgroups — #21425050

Order 7552.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14273718C211yesmaximal, characteristic
2C2×Dic59⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic59C211yesmaximal, characteristic
4#16837165C211yesmaximal, characteristic
5#16837164C211yesmaximal, characteristic
6#16837164C211yesmaximal, characteristic
7C59×#340C211yesmaximal, characteristic
8C22×C59⋊C8C2211yescharacteristic
9#14273718—22no—
10#14273718C414yescomplemented
11C2×C4⋊Dic59—21no—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4—21no—
15C2×C4×Dic59—21no—
16C2×C4×Dic59C2211yescharacteristic
17Dic59⋊C8—22no—
18C59⋊#95—21no—
19C22×C8×C59C2211yescharacteristic
20C2×C4⋊C4×C59C2211yescharacteristic
21C2×C4⋊C4×C59C2211yescharacteristic
22C22×C4×C59—21no—
23C22×C4×C59—21no—
24C22×C4×C59C2311yescharacteristic
25C22×Dic59—21no—
26C22×Dic59—21no—
27C22×Dic59D411yescharacteristic
28C22×Dic59D411yescharacteristic
29C2×C8×C59—21no—
30C2×C8×C59—21no—
31C2×C8×C59—21no—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59C2×C412yes—
35C4⋊C4×C59Q812yes—
36C4⋊Dic59—21no—
37C4⋊Dic59—21no—
38C4⋊Dic59—24no—
39C4⋊Dic59C2×C412yes—
40C4⋊Dic59Q812yes—
41Dic59⋊C4—24no—
42C4×Dic59—42no—
43C4×Dic59C2×C412yes—
44C4×Dic59D412yes—
45C2×C59⋊C8—21no—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C23×C59C2×D411yescharacteristic
49C2×C4×C59—22no—
50C2×C4×C59—22no—
51C2×C4×C59—41no—
52C2×C4×C59—41no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59C22×C411yescharacteristic
56C2×C4×C59C2×D411yescharacteristic
57C2×C4×C59C2×Q811yescharacteristic
58C2×C4×C59C2×Q811yescharacteristic
59C2×C4×C59#4111yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×Dic59—21no—
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—22no—
66C2×Dic59—22no—
67C2×Dic59—41no—
68C2×Dic59—41no—
69C2×Dic59—41no—
70C2×Dic59—41no—
71C2×Dic59C22⋊C412yes—
72C2×Dic59C22⋊C412yes—
73C8×C59—41no—
74C59⋊C8—41no—
75C22×C59C2×C22⋊C411yescharacteristic
76C22×C59C22⋊Q811yescharacteristic
77C22×C59C22⋊Q811yescharacteristic
78C22×C59#13511yescharacteristic
79C22×C59#13511yescharacteristic
80C22×C59AGL(1,ℤ/8)11yescharacteristic
81C22×C59#13711yescharacteristic
82C4×C59—42no—
83C4×C59—42no—
84C4×C59C4×Q811yescharacteristic
85C4×C59C4×Q811yescharacteristic
86C4×C59#12411yescharacteristic
87C4×C59C4⋊Q811yescharacteristic
88Dic59—22no—
89Dic59—22no—
90Dic59—42no—
91Dic59—42no—
92#1989—591nomaximal, Sylow
93C2×C59#39111yescharacteristic
94C2×C59#41611yescharacteristic
95C2×C59#41711yescharacteristic
96C2×C59#47811yescharacteristic
97C2×C59#47811yescharacteristic
98C2×C59#47911yescharacteristic
99C2×C59#47911yescharacteristic
100C2×#125—591no—
101C2×C4⋊C8—591no—
102C4×C4⋊C4—591no—
103#340—591no—
104#340—591no—
105#340—591no—
106#340D5911yescharacteristic
107C59#198911yescharacteristic, complemented, Sylow
108C22×C8—591no—
109C22×C8C2×D5911yescharacteristic
110#125—594no—
111#125—1182no—
112C2×C4⋊C4—591no—
113C2×C4⋊C4—591no—
114C2×C4⋊C4—1181no—
115C2×C4⋊C4—1181no—
116C2×C4⋊C4C2×D5911yescharacteristic
117C2×C4⋊C4C2×D5911yescharacteristic
118C2×C42—591no—
119C2×C42—1181no—
120C4⋊C8—1182no—
121#95—1181no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—591no—
125C22×C4—591no—
126C22×C4—1181no—
127C22×C4—1181no—
128C22×C4C22×D5911yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1181no—
133C2×C8—1181no—
134C2×C8—1181no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—592no—
138C4⋊C4—592no—
139C4⋊C4—1184no—
140C4⋊C4—1184no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4Dic11812yes—
144C4⋊C4C4×D5912yes—
145C42—592no—
146C42—592no—
147C42—2362no—
148C23D4×D5911yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—592no—
156C2×C4—592no—
157C2×C4—1181no—
158C2×C4—1181no—
159C2×C4—1181no—
160C2×C4—1181no—
161C2×C4—1182no—
162C2×C4—1182no—
163C2×C4—2361no—
164C2×C4—2361no—
165C2×C4—2361no—
166C2×C4—2361no—
167C2×C4C2×Dic11811yescharacteristic
168C2×C4C2×C4×D5911yescharacteristic
169C2×C4#1174568511yescharacteristic
170C2×C4D4×D5911yescharacteristic
171C2×C4#1174568711yescharacteristic
172C2×C4Q8×D5911yescharacteristic
173C8—41no—
174C8—2361no—
175C22C22⋊C4×D5911yescharacteristic
176C22#1427370411yescharacteristic
177C22#1427370511yescharacteristic
178C22#1427374811yescharacteristic
179C22#1427375011yescharacteristic
180C22#1427375111yescharacteristic
181C22#1427375611yescharacteristic
182C4—42no—
183C4—42no—
184C4—1182no—
185C4—1182no—
186C4—2362no—
187C4—2362no—
188C4#1427369211yescharacteristic
189C4C4×Dic11811yescharacteristic
190C4#1427371311yescharacteristic
191C4#1427372611yescharacteristic
192C2#1683730611yescharacteristic
193C2#1683739711yescharacteristic
194C2#1683740011yescharacteristic
195C2#1683770411yescharacteristic
196C2#1683770511yescharacteristic
197C2#1683771111yescharacteristic
198C2#1683771211yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#1989
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
10. #14273718C4semidirect
107. C59#1989semidirect