Finite Group Databasebeta

← #21434339

Subgroups — #21434339

Order 7552.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#16838007C211yesmaximal, characteristic, complemented
2#16837726C212yesmaximal, complemented
3#16837702C212yesmaximal, complemented
4#16837597C212yesmaximal, complemented
5#16837536C212yesmaximal, complemented
6#16837512C212yesmaximal, complemented
7C4×#11745669C212yesmaximal, complemented
8#16837463C211yesmaximal, characteristic, complemented
9C59×#518C211yesmaximal, characteristic, complemented
10C2×#11745669C2212yes—
11C2×#11745669C2212yes—
12#14273724C2211yescharacteristic, complemented
13#14273719C2211yescharacteristic, complemented
14#14273712—22no—
15#14273701C2212yes—
16#14273700—22no—
17C4×D236C2212yescomplemented
18#14273660C2212yescomplemented
19#14273658C2212yescomplemented
20C4⋊(C59⋊C8)C2212yescomplemented
21#14273648C2212yes—
22#14273648C2212yes—
23#14273647C2212yescomplemented
24#14273647C2212yescomplemented
25C22⋊(C59⋊C8)C2212yes—
26#14273638C2211yescharacteristic, complemented
27C4×C59⋊C8C2211yescharacteristic, complemented
28C22×D4×C59C2211yescharacteristic
29C4×D4×C59—22no—
30C4×D4×C59C2212yes—
31C4×D4×C59C2212yes—
32#117×C59C2211yescharacteristic
33#117×C59C2211yescharacteristic
34C2×C22⋊C4×C59—22no—
35C24×C59—21no—
36C2×D4×C59—24no—
37C2×D4×C59—21no—
38C2×D4×C59C2312yes—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2311yescharacteristic
42C2×C22⋊D59—22no—
43C2×D236—22no—
44C2×D236C2312yes—
45C2×C4×D59—22no—
46C4⋊C4×C59D412yes—
47C4⋊C4×C59C2312yes—
48C22⋊C4×C59—21no—
49C22⋊C4×C59—22no—
50C22⋊C4×C59—22no—
51C22⋊C4×C59D412yes—
52C42×C59—21no—
53C42×C59C2311yescharacteristic
54C42×C59C2311yescharacteristic
55#11745669—24no—
56#11745669—24no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—22no—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61C2×C59⋊C8C2312yes—
62C2×C59⋊C8C2312yes—
63C23×C59—24no—
64C23×C59—22no—
65C23×C59—82no—
66C23×C59C2×D411yescharacteristic
67C22×D59—22no—
68D4×C59—24no—
69D4×C59—22no—
70D4×C59#4114yes—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—82no—
74C2×C4×C59—82no—
75C2×C4×C59C2×D412yes—
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D412yes—
78C2×C4×C59C2411yescharacteristic
79C22⋊D59—82no—
80C2×Dic59—22no—
81D236—22no—
82D236—22no—
83D236—82no—
84C4×D59—82no—
85C59⋊C8—22no—
86C59⋊C8—22no—
87C22×C59—21no—
88C22×C59—24no—
89C22×C59—22no—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—84no—
93C22×C59C22×D411yescharacteristic
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C4×C59—21no—
98C4×C59—22no—
99C4×C59—22no—
100C4×C59—42no—
101C4×C59C2×#4112yes—
102Dic59—42no—
103#3122—591nomaximal, Sylow
104C2×C59—41no—
105C2×C59—44no—
106C2×C59#52511yescharacteristic
107C2×C59#57612yes—
108D59—82no—
109#540—591no—
110#518D5911yescharacteristic, complemented
111#482—592no—
112#478—592no—
113#459—592no—
114#447—592no—
115#442—592no—
116C4×D8—592no—
117#433—591no—
118C59#312211yescharacteristic, complemented, Sylow
119C22×D4C2×D5911yescharacteristic
120C2×D8—592no—
121C2×D8—592no—
122#127—591no—
123#125—591no—
124#123—1182no—
125#121—592no—
126#121—1182no—
127C4×D4—22no—
128C4×D4—592no—
129C4×D4C2×D5912yes—
130C4×D4C2×D5912yes—
131#117C2×D5911yescharacteristic
132#117C2×D5911yescharacteristic
133C2×C22⋊C4—22no—
134#107—592no—
135#106—592no—
136C4⋊C8—592no—
137#102—592no—
138#102—592no—
139#102—592no—
140#102—592no—
141C22⋊C8—592no—
142#97—591no—
143C4×C8—591no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—592no—
148C2×D4—1182no—
149C2×D4—1182no—
150C2×D4C22×D5912yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—1182no—
154C22×C4C22×D5911yescharacteristic
155D8—1184no—
156D8—1184no—
157C2×C8—592no—
158C2×C8—592no—
159C4⋊C4—592no—
160C4⋊C4—1182no—
161C4⋊C4C22⋊D5912yes—
162C4⋊C4C22×D5912yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—1182no—
167C22⋊C4—1182no—
168C22⋊C4C22⋊D5912yes—
169C42—21no—
170C42C22×D5911yescharacteristic
171C42C22×D5911yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—1182no—
176C23C2×C22⋊D5911yescharacteristic
177D4—24no—
178D4—22no—
179D4—1182no—
180D4—1182no—
181D4—4722no—
182D4—4722no—
183D4#1174568514yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—1182no—
189C2×C4—4722no—
190C2×C4C2×C22⋊D5911yescharacteristic
191C2×C4C2×C22⋊D5912yes—
192C2×C4C2×C22⋊D5912yes—
193C2×C4C23×D5911yescharacteristic
194C8—1182no—
195C8—1182no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—2362no—
203C22—2362no—
204C22—2362no—
205C22C22×C22⋊D5911yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—2362no—
211C4C2×#1174568512yes—
212C2—41no—
213C2—44no—
214C2—4722no—
215C2#1683791311yescharacteristic
216C2#1683820512yes—
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#518C2
socleC22×C59C22×D4
hypercenter#518D59
hypocenterC59#3122
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #16838007C2semidirect
2. #16837726C2semidirect
3. #16837702C2semidirect
4. #16837597C2semidirect
5. #16837536C2semidirect
6. #16837512C2semidirect
7. C4×#11745669C2semidirect
8. #16837463C2semidirect
9. C59×#518C2semidirect
12. #14273724C22semidirect
13. #14273719C22semidirect
17. C4×D236C22semidirect
18. #14273660C22semidirect
19. #14273658C22semidirect
20. C4⋊(C59⋊C8)C22semidirect
23. #14273647C22semidirect
24. #14273647C22semidirect
26. #14273638C22semidirect
27. C4×C59⋊C8C22semidirect
110. #518D59semidirect
118. C59#3122semidirect