Finite Group Databasebeta

← #21434340

Subgroups — #21434340

Order 7552.

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

normal subgroups only

This group has 418 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#16838007C211yesmaximal, characteristic, complemented
2#16837876C211yesmaximal, characteristic, complemented
3#16837727C212yesmaximal, complemented
4#16837703C212yesmaximal, complemented
5#16837598C212yesmaximal, complemented
6#16837538C212yesmaximal, complemented
7#16837515C212yesmaximal, complemented
8C4×D472C212yesmaximal, complemented
9C59×#433C211yesmaximal, characteristic, complemented
10C22×D236C2211yescharacteristic
11C2×D472C2212yes—
12C2×D472C2212yes—
13#14273724C2211yescharacteristic, complemented
14#14273719C2211yescharacteristic, complemented
15#14273712—22no—
16#14273701C2212yes—
17#14273700—22no—
18C4×D236C2212yes—
19C4×D236C2212yes—
20C4×D236C2212yescomplemented
21#14273689—22no—
22#14273686C2211yescharacteristic
23C22⋊C4×D59—22no—
24#14273661C2212yescomplemented
25#14273659C2212yescomplemented
26#14273649C2212yes—
27#14273649C2212yes—
28#14273649C2212yescomplemented
29#14273649C2212yescomplemented
30#117×C59C2211yescharacteristic
31C4⋊C8×C59C2212yescomplemented
32C22⋊C8×C59C2212yes—
33#97×C59C2211yescharacteristic, complemented
34C4×C8×C59C2211yescharacteristic, complemented
35C23×D59—21no—
36C22×C4×C59C2311yescharacteristic
37C2×C22⋊D59—22no—
38C2×D236—21no—
39C2×D236—24no—
40C2×D236—22no—
41C2×D236C2312yes—
42C2×D236C2312yes—
43C2×C4×D59—22no—
44C2×C4×D59—22no—
45C2×C4×D59—22no—
46C2×C8×C59C2312yes—
47C2×C8×C59C2312yes—
48C4⋊C4×C59D412yes—
49C22⋊C4×C59D412yes—
50C42×C59C2311yescharacteristic
51C42×C59C2311yescharacteristic
52C22⋊Dic59—21no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57C4⋊Dic59C2312yes—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60C4×Dic59—21no—
61D472—24no—
62D472—24no—
63C23×C59C2×D411yescharacteristic
64C22×D59—22no—
65C22×D59—24no—
66C22×D59—22no—
67C22×D59—82no—
68C2×C4×C59—22no—
69C2×C4×C59C2×D411yescharacteristic
70C2×C4×C59C2×D412yes—
71C2×C4×C59C2×D412yes—
72C2×C4×C59C2411yescharacteristic
73C22⋊D59—82no—
74C2×Dic59—22no—
75C2×Dic59—22no—
76D236—24no—
77D236—22no—
78D236—22no—
79D236—22no—
80D236—82no—
81D236#4114yes—
82C4×D59—82no—
83C4×D59—82no—
84C4×D59—82no—
85C8×C59—22no—
86C8×C59—22no—
87C22×C59—21no—
88C22×C59—22no—
89C22×C59C22×D411yescharacteristic
90C2×D59—24no—
91C2×D59—42no—
92C2×D59—42no—
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—84no—
97C4×C59—21no—
98C4×C59—22no—
99C4×C59—22no—
100C4×C59C2×#4112yes—
101Dic59—42no—
102Dic59—42no—
103#3122—591nomaximal, Sylow
104C2×C59—41no—
105C2×C59#52511yescharacteristic
106C2×C59#57612yes—
107D59—44no—
108D59—82no—
109#540—591no—
110#518—591no—
111#482—592no—
112#478—592no—
113#459—592no—
114#447—592no—
115#442—592no—
116C4×D8—592no—
117#433D5911yescharacteristic, complemented
118C59#312211yescharacteristic, complemented, Sylow
119C22×D4—591no—
120C2×D8—592no—
121C2×D8—592no—
122#127—591no—
123#125—591no—
124#123—1182no—
125#121—592no—
126#121—1182no—
127C4×D4—592no—
128C4×D4—592no—
129C4×D4—592no—
130C4×D4—1182no—
131#117—591no—
132#117C2×D5911yescharacteristic
133C2×C22⋊C4—1182no—
134#107—592no—
135#106—592no—
136C4⋊C8C2×D5912yescomplemented
137#102—592no—
138#102—592no—
139#102—592no—
140#102—592no—
141C22⋊C8C2×D5912yes—
142#97C2×D5911yescharacteristic, complemented
143C4×C8C2×D5911yescharacteristic, complemented
144C24—1181no—
145C2×D4—592no—
146C2×D4—592no—
147C2×D4—1184no—
148C2×D4—1182no—
149C2×D4—1181no—
150C2×D4—1182no—
151C22×C4—1182no—
152C22×C4—1182no—
153C22×C4—1182no—
154C22×C4C22×D5911yescharacteristic
155D8—1184no—
156D8—1184no—
157C2×C8C22×D5912yes—
158C2×C8C22×D5912yes—
159C4⋊C4—592no—
160C4⋊C4—592no—
161C4⋊C4—1182no—
162C4⋊C4D23612yes—
163C22⋊C4—1181no—
164C22⋊C4—1182no—
165C22⋊C4—1182no—
166C22⋊C4—1182no—
167C22⋊C4—1182no—
168C22⋊C4D23612yes—
169C42—1181no—
170C42C22×D5911yescharacteristic
171C42C22×D5911yescharacteristic
172C23—1184no—
173C23—1182no—
174C23—1182no—
175C23—4722no—
176C23C2×D23611yescharacteristic
177D4—594no—
178D4—1184no—
179D4—1182no—
180D4—1182no—
181D4—1182no—
182D4—4722no—
183D4—4722no—
184C2×C4—22no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—4722no—
188C2×C4—4722no—
189C2×C4—4722no—
190C2×C4C2×D23611yescharacteristic
191C2×C4C2×D23612yes—
192C2×C4C2×D23612yes—
193C2×C4C23×D5911yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—1184no—
199C22—4724no—
200C22—2362no—
201C22—2362no—
202C22—2362no—
203C22—2362no—
204C22—2362no—
205C22C22×D23611yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—2362no—
210C4—2362no—
211C4#41×D5912yes—
212C2—41no—
213C2—4722no—
214C2—2364no—
215C2#1683791411yescharacteristic
216C2#1683820712yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3122
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838007C2semidirect
2. #16837876C2semidirect
3. #16837727C2semidirect
4. #16837703C2semidirect
5. #16837598C2semidirect
6. #16837538C2semidirect
7. #16837515C2semidirect
8. C4×D472C2semidirect
9. C59×#433C2semidirect
13. #14273724C22semidirect
14. #14273719C22semidirect
20. C4×D236C22semidirect
24. #14273661C22semidirect
25. #14273659C22semidirect
28. #14273649C22semidirect
29. #14273649C22semidirect
31. C4⋊C8×C59C22semidirect
33. #97×C59C22semidirect
34. C4×C8×C59C22semidirect
117. #433D59semidirect
118. C59#3122semidirect
136. C4⋊C8C2×D59semidirect
142. #97C2×D59semidirect
143. C4×C8C2×D59semidirect