Finite Group Databasebeta

← #21424060

Subgroups — #21424060

Order 7552.

548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837419C212yesmaximal, complemented
2#16837398C212yesmaximal, complemented
3#16837376C211yesmaximal, characteristic, complemented
4#16837369C211yesmaximal, characteristic, complemented
5C59×#585C211yesmaximal, characteristic
6C2×#11745664C2211yescharacteristic, complemented
7C22×C59⋊C8C2211yescharacteristic, complemented
8#14273686C2212yescomplemented
9#14273654—24no—
10#14273651—22no—
11#14273648—22no—
12#14273642—22no—
13C22⋊(C59⋊C8)—22no—
142−1+4×C59—22no—
152−1+4×C59C412yescomplemented
16H(5,𝔽2)×C59—22no—
17H(5,𝔽2)×C59—22no—
18H(5,𝔽2)×C59C412yescomplemented
19C2×#41×C59—24no—
20C2×#41×C59—22no—
21C2×#41×C59C2212yes—
22C2×#41×C59C2211yescharacteristic
23#41×C59—24no—
24#41×C59—28no—
25#41×C59—24no—
26#41×C59—24no—
27#41×C59—24no—
28#41×C59—24no—
29#41×C59—22no—
30#41×C59—22no—
31#41×C59—22no—
32#41×C59—22no—
33#41×C59C2×C414yes—
34#41×C59D414yes—
35C2×Q8×C59—22no—
36C2×Q8×C59—24no—
37C2×Q8×C59C2×C411yescharacteristic
38C2×Q8×C59D412yes—
39C2×D4×C59—28no—
40C2×D4×C59—22no—
41C2×D4×C59—24no—
42C2×D4×C59—22no—
43C2×D4×C59—24no—
44C2×D4×C59C2×C411yescharacteristic
45C2×D4×C59D412yes—
46C2×D4×C59D412yes—
47C22×C4×C59—24no—
48C22×C4×C59—22no—
49C22×C4×C59D412yes—
50C22×C4×C59C2311yescharacteristic
51C22⋊Dic59—22no—
52C4⋊Dic59—22no—
53C4×Dic59—22no—
54#11745664—22no—
55C2×C59⋊C8—21no—
56C2×C59⋊C8—21no—
57C2×C59⋊C8—22no—
58C23×C59—24no—
59C23×C59—22no—
60C23×C59C22⋊C412yes—
61C23×C59C2×D411yescharacteristic
62Q8×C59—24no—
63Q8×C59—22no—
64Q8×C59—22no—
65Q8×C59C22⋊C414yes—
66D4×C59—28no—
67D4×C59—24no—
68D4×C59—24no—
69D4×C59—24no—
70D4×C59—24no—
71D4×C59—22no—
72D4×C59—22no—
73D4×C59C22⋊C414yes—
74C2×C4×C59—24no—
75C2×C4×C59—28no—
76C2×C4×C59—22no—
77C2×C4×C59—24no—
78C2×C4×C59—24no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59C22⋊C412yes—
82C2×C4×C59C22×C411yescharacteristic
83C2×C4×C59C2×D412yes—
84C2×C4×C59C2×D412yes—
85C2×C4×C59C2×D411yescharacteristic
86C2×Dic59—42no—
87C59⋊C8—41no—
88C59⋊C8—41no—
89C22×C59—22no—
90C22×C59—24no—
91C22×C59—41no—
92C22×C59—42no—
93C22×C59—82no—
94C22×C59—84no—
95C22×C59C2×C22⋊C411yescharacteristic
96C22×C59#12012yes—
97C4×C59—24no—
98C4×C59—22no—
99C4×C59C2×C22⋊C412yes—
100C4×C59#12011yescharacteristic
101C4×C59#12011yescharacteristic
102Dic59—82no—
103#1794—591nomaximal, Sylow
104C2×C59—22no—
105C2×C59—21no—
106C2×C59—42no—
107C2×C59—44no—
108C2×C59#37911yescharacteristic
109#585D5911yescharacteristic
110#421—592no—
111#416—592no—
112#410—591no—
113#408—591no—
114C59#179411yescharacteristic, complemented, Sylow
1152−1+4—22no—
1162−1+4Dic5912yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)Dic5912yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C2×D5912yes—
123C2×#41C2×D5911yescharacteristic
124C2×M16—591no—
125C22×C8—591no—
126#117—592no—
127#104—1184no—
128#103—1182no—
129#102—1182no—
130#99—1182no—
131C22⋊C8—1182no—
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—24no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—22no—
142#41C2×Dic5914yes—
143#41C22⋊D5914yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×Dic5911yescharacteristic
147C2×Q8C22⋊D5912yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×Dic5911yescharacteristic
154C2×D4C22⋊D5912yes—
155C2×D4C22⋊D5912yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4C22⋊D5912yes—
159C22×C4C22×D5911yescharacteristic
160M16—1182no—
161C2×C8—1181no—
162C2×C8—1181no—
163C2×C8—1182no—
164C4⋊C4—1182no—
165C22⋊C4—1182no—
166C42—1182no—
167C23—24no—
168C23—22no—
169C23C22⋊Dic5912yes—
170C23C2×C22⋊D5911yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊Dic5914yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊Dic5914yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—2362no—
191C2×C4C22⋊Dic5912yes—
192C2×C4C22×Dic5911yescharacteristic
193C2×C4C2×C22⋊D5912yes—
194C2×C4C2×C22⋊D5912yes—
195C2×C4C2×C22⋊D5911yescharacteristic
196C8—2361no—
197C8—2361no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊Dic5911yescharacteristic
205C22#1427369612yes—
206C4—24no—
207C4—22no—
208C4—4722no—
209C4C2×C22⋊Dic5912yes—
210C4#1427369611yescharacteristic
211C4#1427369611yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#1683725811yescharacteristic
subgroupG/H
centerC4#14273696
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#585C2
socleC2×C59#379
hypercenter#585D59
hypocenterC59#1794
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #16837419C2semidirect
2. #16837398C2semidirect
3. #16837376C2semidirect
4. #16837369C2semidirect
6. C2×#11745664C22semidirect
7. C22×C59⋊C8C22semidirect
8. #14273686C22semidirect
15. 2−1+4×C59C4semidirect
18. H(5,𝔽2)×C59C4semidirect
114. C59#1794semidirect
116. 2−1+4Dic59semidirect
119. H(5,𝔽2)Dic59semidirect