Finite Group Databasebeta

← #21425270

Subgroups — #21425270

Order 7552.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#16837955C211yesmaximal, characteristic, complemented
2#16837419C211yesmaximal, characteristic
3C2×#14273654C211yesmaximal, characteristic
4#16837172C211yesmaximal, characteristic, complemented
5#16837161C211yesmaximal, characteristic, complemented
6#16837158C211yesmaximal, characteristic, complemented
7C59×#410C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10#14273726—21no—
11#14273718—21no—
12#14273704—22no—
13C4×Dic118—22no—
14#14273686C2211yescharacteristic
15C2×C4×Dic59C2211yescharacteristic
16#14273654—21no—
17#14273654—21no—
18#14273654—22no—
19C2×#41×C59C2211yescharacteristic
20#117×C59C2211yescharacteristic
21#117×C59C2211yescharacteristic
22#99×C59—22no—
23#41×C59—21no—
24#41×C59—21no—
25#41×C59—21no—
26#41×C59—21no—
27C2×Q8×C59Q811yescharacteristic, complemented
28C2×D4×C59—21no—
29C2×D4×C59Q811yescharacteristic, complemented
30C22×C4×C59—21no—
31C22×C4×C59C2311yescharacteristic
32C22×Dic59—21no—
33C2×Dic118—22no—
34C4⋊C4×C59—21no—
35C4⋊C4×C59—21no—
36C22⋊C4×C59—21no—
37C22⋊C4×C59D412yes—
38C42×C59—21no—
39C42×C59—21no—
40C22⋊Dic59—21no—
41C4⋊Dic59—22no—
42C4⋊Dic59—21no—
43Dic59⋊C4—22no—
44Dic59⋊C4—22no—
45C4×Dic59—21no—
46C4×Dic59D411yescharacteristic
47C4×Dic59D411yescharacteristic
48C4×Dic59D412yes—
49#11745664—21no—
50#11745664—21no—
51#11745664—21no—
52#11745664—21no—
53C2×C59⋊C8—21no—
54C2×C59⋊C8—21no—
55C23×C59—21no—
56C23×C59C2×D411yescharacteristic
57Q8×C59—21no—
58Q8×C59—21no—
59D4×C59—21no—
60D4×C59—21no—
61D4×C59—41no—
62D4×C59—41no—
63C2×C4×C59—22no—
64C2×C4×C59—21no—
65C2×C4×C59—41no—
66C2×C4×C59—41no—
67C2×C4×C59—41no—
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×Q811yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C2×C4×C59#4111yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—22no—
77C2×Dic59—42no—
78Dic118—44no—
79C59⋊C8—41no—
80C59⋊C8—41no—
81C22×C59—41no—
82C22×C59—41no—
83C22×C59—81no—
84C22×C59#12011yescharacteristic
85C22×C59C22⋊Q811yescharacteristic
86C22×C59#12411yescharacteristic
87C4×C59—42no—
88C4×C59—41no—
89C4×C59—81no—
90C4×C59C22⋊Q811yescharacteristic
91C4×C59C22⋊Q811yescharacteristic
92C4×C59#12411yescharacteristic
93C4×C59#12411yescharacteristic
94Dic59—22no—
95Dic59—42no—
96Dic59—41no—
97#2031—591nomaximal, Sylow
98C2×C59—21no—
99C2×C59—21no—
100C2×C59—21no—
101C2×C59—81no—
102C2×C59#39311yescharacteristic
103#533—591no—
104#421—591no—
105C2×#104—591no—
106#410D5911yescharacteristic
107#344—591no—
108#339—591no—
109H(3,ℤ/4)—591no—
110C59#203111yescharacteristic, complemented, Sylow
111C2×#41C2×D5911yescharacteristic
112C2×M16—591no—
113C2×M16—591no—
114C4⋊Q8—1181no—
115#125—1181no—
116C22⋊Q8—1182no—
117C4×Q8—1182no—
118#117—591no—
119#117C2×D5911yescharacteristic
120#117C2×D5911yescharacteristic
121C2×C42—591no—
122#104—1181no—
123#104—1181no—
124#104—1182no—
125#99—22no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—1182no—
131C2×Q8Dic11811yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic11811yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—1181no—
136C22×C4C22×D5911yescharacteristic
137M16—1181no—
138M16—1181no—
139M16—1181no—
140M16—1181no—
141C2×C8—1181no—
142C2×C8—1181no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1182no—
146C4⋊C4—1182no—
147C4⋊C4—1182no—
148C4⋊C4—1181no—
149C22⋊C4—21no—
150C22⋊C4—1181no—
151C22⋊C4C22⋊D5912yes—
152C42—21no—
153C42—21no—
154C42—591no—
155C42—591no—
156C42—592no—
157C42—1181no—
158C23—21no—
159C23C2×C22⋊D5911yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—2364no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—1181no—
173C2×C4—1181no—
174C2×C4—1182no—
175C2×C4—2362no—
176C2×C4C2×Dic11811yescharacteristic
177C2×C4#1174568511yescharacteristic
178C2×C4D4×D5911yescharacteristic
179C2×C4D4×D5911yescharacteristic
180C2×C4#1174568711yescharacteristic
181C2×C4#1174568711yescharacteristic
182C8—2361no—
183C8—2361no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#1427369511yescharacteristic
188C22#1427370611yescharacteristic
189C22#1427371411yescharacteristic
190C4—42no—
191C4—41no—
192C4—81no—
193C4—1182no—
194C4—2361no—
195C4—2362no—
196C4#1427370411yescharacteristic
197C4#1427370411yescharacteristic
198C4#1427371311yescharacteristic
199C4#1427371311yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1683731411yescharacteristic
subgroupG/H
centerC4#14273713
commutatorC22×C4×C59C23
FrattiniC22×C4C22×D59
FittingC59×#410C2
socleC2×C59#393
hypercenter#410D59
hypocenterC59#2031
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #16837955C2semidirect
4. #16837172C2semidirect
5. #16837161C2semidirect
6. #16837158C2semidirect
27. C2×Q8×C59Q8semidirect
29. C2×D4×C59Q8semidirect
110. C59#2031semidirect
131. C2×Q8Dic118semidirect
133. C2×D4Dic118semidirect