Finite Group Databasebeta

← #21433673

Subgroups — #21433673

Order 7552.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C22×C8×D59C211yesmaximal, characteristic, complemented
2#16837909C212yesmaximal, complemented
3#16837640C212yesmaximal, complemented
4#16837635C212yesmaximal, complemented
5#16837628C214yesmaximal, complemented
6#16837440C211yesmaximal, characteristic, complemented
7#16837398C212yesmaximal, complemented
8C2×#135×C59C211yesmaximal, characteristic, complemented
9C22×C4×D59C2211yescharacteristic
10C22×C59⋊C8C2211yescharacteristic
11C2×C8×D59—24no—
12C2×C8×D59C2212yes—
13C2×C8×D59C2212yes—
14#14273708—22no—
15#14273703C2214yes—
16#14273698C2214yes—
17#14273695—22no—
18C4×C22⋊D59—24no—
19#14273686C2212yes—
20#14273661C2212yescomplemented
21#14273659C2212yescomplemented
22#14273651C2214yescomplemented
23#14273648C2214yescomplemented
24C2×#41×C59C2212yes—
25#135×C59—24no—
26C2×Q16×C59C2211yescharacteristic, complemented
27C2×SD16×C59C2212yescomplemented
28C2×D8×C59C2211yescharacteristic, complemented
29C22×C8×C59C2211yescharacteristic
30C23×D59D411yescharacteristic
31#41×C59—24no—
32#41×C59—24no—
33C2×Q8×C59C2312yes—
34C2×D4×C59—22no—
35C2×D4×C59C2312yes—
36C22×C4×C59—22no—
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—24no—
39C22×Dic59D411yescharacteristic
40C2×C4×D59—22no—
41C2×C4×D59—22no—
42C2×C4×D59D412yes—
43C2×C4×D59C2312yes—
44Q16×C59—22no—
45SD16×C59—24no—
46D8×C59—22no—
47C2×C8×C59D414yescomplemented
48C2×C8×C59C2311yescharacteristic
49C2×C8×C59C2311yescharacteristic
50C22⋊Dic59—22no—
51C22⋊Dic59—24no—
52(C2×D59)⋊C4—24no—
53C4⋊Dic59C2314yes—
54Dic59⋊C4—24no—
55C4×Dic59—22no—
56C2×C59⋊C8—22no—
57C2×C59⋊C8C2312yes—
58C8×D59—24no—
59C8×D59—24no—
60C23×C59—22no—
61C23×C59C2×D411yescharacteristic
62C22×D59—22no—
63C22×D59—24no—
64C22×D59C2×D412yes—
65Q8×C59—22no—
66Q8×C59—22no—
67D4×C59—22no—
68D4×C59—22no—
69D4×C59—44no—
70C2×C4×C59—22no—
71C2×C4×C59—44no—
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D412yes—
74C2×C4×C59#4112yes—
75C2×C4×C59C2411yescharacteristic
76C22⋊D59—48no—
77C2×Dic59—22no—
78C2×Dic59—24no—
79C2×Dic59C2×D412yes—
80C4×D59—24no—
81C4×D59—22no—
82C4×D59—22no—
83C8×C59C2×D412yes—
84C8×C59C2×D412yes—
85C59⋊C8—22no—
86C22×C59—22no—
87C22×C59—42no—
88C22×C59—44no—
89C22×C59#12112yes—
90C22×C59C22×D411yescharacteristic
91C2×D59—28no—
92C2×D59—22no—
93C2×D59—22no—
94C2×D59#13514yescomplemented
95C4×C59—42no—
96C4×C59#12112yes—
97C4×C59C22×D411yescharacteristic
98C4×C59C2×#4111yescharacteristic
99Dic59—22no—
100Dic59—44no—
101#3050—591nomaximal, Sylow
102C2×C59—22no—
103C2×C59—82no—
104C2×C59C2×#12111yescharacteristic
105C2×C59C2×#13512yes—
106D59—24no—
107C2×#135D5911yescharacteristic, complemented
108C23×C8—591no—
109#525—592no—
110#467—592no—
111#466—592no—
112#465—594no—
113#427—591no—
114#416—592no—
115C59#305011yescharacteristic, complemented, Sylow
116C2×#41C2×D5912yes—
117C23×C4—591no—
118#135—24no—
119C2×Q16C2×D5911yescharacteristic, complemented
120C2×SD16C2×D5912yescomplemented
121C2×D8C2×D5911yescharacteristic, complemented
122C22×C8—591no—
123C22×C8—592no—
124C22×C8—592no—
125C22×C8—1184no—
126C22×C8C2×D5911yescharacteristic
127#123—1182no—
128C22⋊Q8—594no—
129#121—594no—
130#120—1182no—
131C4×D4—1184no—
132#117—592no—
133#107—592no—
134#106—592no—
135#103—594no—
136#102—594no—
137C24—591no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D5912yes—
141C2×D4—22no—
142C2×D4—1184no—
143C2×D4C22×D5912yes—
144C22×C4—22no—
145C22×C4—591no—
146C22×C4—592no—
147C22×C4—592no—
148C22×C4—1182no—
149C22×C4—1182no—
150C22×C4C22×D5911yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—592no—
155C2×C8—1182no—
156C2×C8—1184no—
157C2×C8—1184no—
158C2×C8C22⋊D5914yescomplemented
159C2×C8C22×D5911yescharacteristic
160C2×C8C22×D5911yescharacteristic
161C4⋊C4—594no—
162C4⋊C4—1184no—
163C22⋊C4—1184no—
164C22⋊C4—1184no—
165C22⋊C4—1182no—
166C42—1182no—
167C23—22no—
168C23—592no—
169C23—1184no—
170C23—1182no—
171C23D4×D5911yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—2368no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—592no—
181C2×C4—1182no—
182C2×C4—1184no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1184no—
186C2×C4D4×D5911yescharacteristic
187C2×C4#1174568712yes—
188C2×C4C2×C22⋊D5912yes—
189C2×C4C23×D5911yescharacteristic
190C8—1182no—
191C8C2×C22⋊D5912yes—
192C8C2×C22⋊D5912yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—594no—
197C22—1188no—
198C22—1182no—
199C22—1182no—
200C22#1427369812yes—
201C22C2×D4×D5911yescharacteristic
202C4—42no—
203C4—1182no—
204C4—2364no—
205C4#1427369812yes—
206C4C22×C22⋊D5911yescharacteristic
207C4C2×#1174568711yescharacteristic
208C2—22no—
209C2—82no—
210C2—1184no—
211C2C2×#1427369811yescharacteristic
212C2#135×D5912yes—
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#135×C59C2
socleC22×C59C22×D4
hypercenterC2×#135D59
hypocenterC59#3050
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×C8×D59C2semidirect
2. #16837909C2semidirect
3. #16837640C2semidirect
4. #16837635C2semidirect
5. #16837628C2semidirect
6. #16837440C2semidirect
7. #16837398C2semidirect
8. C2×#135×C59C2semidirect
20. #14273661C22semidirect
21. #14273659C22semidirect
22. #14273651C22semidirect
23. #14273648C22semidirect
26. C2×Q16×C59C22semidirect
27. C2×SD16×C59C22semidirect
28. C2×D8×C59C22semidirect
47. C2×C8×C59D4semidirect
94. C2×D59#135semidirect
107. C2×#135D59semidirect
115. C59#3050semidirect
119. C2×Q16C2×D59semidirect
120. C2×SD16C2×D59semidirect
121. C2×D8C2×D59semidirect
158. C2×C8C22⋊D59semidirect