Finite Group Databasebeta

← #21425063

Subgroups — #21425063

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×#14273637C211yesmaximal, characteristic
3#16837271C211yesmaximal, 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×Dic59⋊C4—21no—
16C2×Dic59⋊C4—21no—
17C2×C4×Dic59C2211yescharacteristic
18#14273637—22no—
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×C59Q812yes—
32C4⋊C4×C59—21no—
33C4⋊C4×C59—21no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59C2×C412yes—
36C4⋊Dic59—21no—
37C4⋊Dic59—24no—
38C4⋊Dic59—21no—
39C4⋊Dic59—21no—
40C4⋊Dic59C2×C412yes—
41Dic59⋊C4—24no—
42Dic59⋊C4—42no—
43Dic59⋊C4—42no—
44C4×Dic59C2×C412yes—
45C4×Dic59D412yes—
46C2×C59⋊C8—21no—
47C2×C59⋊C8—21no—
48C2×C59⋊C8Q812yes—
49C23×C59C2×D411yescharacteristic
50C2×C4×C59—22no—
51C2×C4×C59—41no—
52C2×C4×C59—41no—
53C2×C4×C59—41no—
54C2×C4×C59—41no—
55C2×C4×C59—41no—
56C2×C4×C59C22×C411yescharacteristic
57C2×C4×C59C2×D411yescharacteristic
58C2×C4×C59C2×Q811yescharacteristic
59C2×C4×C59C2×Q811yescharacteristic
60C2×C4×C59#4111yescharacteristic
61C2×C4×C59#4111yescharacteristic
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59—21no—
65C2×Dic59—21no—
66C2×Dic59—22no—
67C2×Dic59—41no—
68C2×Dic59—41no—
69C2×Dic59—41no—
70C2×Dic59—41no—
71C2×Dic59—41no—
72C2×Dic59C22⋊C412yes—
73C2×Dic59C22⋊C412yes—
74C8×C59—22no—
75C59⋊C8—22no—
76C22×C59C2×C22⋊C411yescharacteristic
77C22×C59#12411yescharacteristic
78C22×C59C4⋊Q811yescharacteristic
79C22×C59AGL(1,ℤ/8)11yescharacteristic
80C22×C59AGL(1,ℤ/8)11yescharacteristic
81C22×C59#13711yescharacteristic
82C22×C59#13711yescharacteristic
83C4×C59—42no—
84C4×C59—81no—
85C4×C59C4×Q811yescharacteristic
86C4×C59C4×Q811yescharacteristic
87C4×C59C22⋊Q811yescharacteristic
88C4×C59C22⋊Q811yescharacteristic
89Dic59—22no—
90Dic59—22no—
91Dic59—42no—
92Dic59—81no—
93#1992—591nomaximal, Sylow
94C2×C59#39111yescharacteristic
95C2×C59#41711yescharacteristic
96C2×C59#41711yescharacteristic
97C2×C59#49011yescharacteristic
98C2×C59#49111yescharacteristic
99C2×C59#50111yescharacteristic
100C2×C59#50111yescharacteristic
101C2×#125—591no—
102C2×#97—591no—
103#384—591no—
104#340—591no—
105#340—591no—
106#340—591no—
107#340D5911yescharacteristic
108C59#199211yescharacteristic, complemented, Sylow
109C22×C8—591no—
110C22×C8C2×D5911yescharacteristic
111#125—594no—
112#125—1182no—
113C2×C4⋊C4—591no—
114C2×C4⋊C4—591no—
115C2×C4⋊C4—1181no—
116C2×C4⋊C4—1181no—
117C2×C4⋊C4—1181no—
118C2×C4⋊C4—1181no—
119C2×C4⋊C4C2×D5911yescharacteristic
120C2×C4⋊C4C2×D5911yescharacteristic
121C2×C42—591no—
122#97—1182no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—591no—
126C22×C4—591no—
127C22×C4—1181no—
128C22×C4—1181no—
129C22×C4C22×D5911yescharacteristic
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—592no—
133C2×C8—1181no—
134C2×C8—1181no—
135C2×C8Dic11812yes—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—592no—
140C4⋊C4—1184no—
141C4⋊C4—1184no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—2362no—
146C4⋊C4—2362no—
147C4⋊C4C4×D5912yes—
148C42—592no—
149C42—592no—
150C23D4×D5911yescharacteristic
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—592no—
158C2×C4—592no—
159C2×C4—1181no—
160C2×C4—1181no—
161C2×C4—1181no—
162C2×C4—1181no—
163C2×C4—1182no—
164C2×C4—2361no—
165C2×C4—2361no—
166C2×C4—2361no—
167C2×C4—2361no—
168C2×C4—2361no—
169C2×C4C2×Dic11811yescharacteristic
170C2×C4C2×C4×D5911yescharacteristic
171C2×C4#1174568511yescharacteristic
172C2×C4D4×D5911yescharacteristic
173C2×C4#1174568711yescharacteristic
174C2×C4Q8×D5911yescharacteristic
175C8—22no—
176C8—1182no—
177C22C22⋊C4×D5911yescharacteristic
178C22#1427371311yescharacteristic
179C22#1427372611yescharacteristic
180C22#1427375111yescharacteristic
181C22#1427375411yescharacteristic
182C22#1427375611yescharacteristic
183C22#1427375911yescharacteristic
184C4—42no—
185C4—81no—
186C4—1182no—
187C4—1182no—
188C4—4721no—
189C4—2362no—
190C4#1427369211yescharacteristic
191C4C4×Dic11811yescharacteristic
192C4#1427370411yescharacteristic
193C4#1427370511yescharacteristic
194C2#1683730611yescharacteristic
195C2#1683740011yescharacteristic
196C2#1683740211yescharacteristic
197C2#1683776511yescharacteristic
198C2#1683776911yescharacteristic
199C2#1683780911yescharacteristic
200C2#1683781011yescharacteristic
subgroupG/H
centerC23D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#340C2
socleC23×C59C2×D4
hypercenter#340D59
hypocenterC59#1992
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
108. C59#1992semidirect