Finite Group Databasebeta

← #21424639

Subgroups — #21424639

Order 7552.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#16837877C211yesmaximal, characteristic, complemented
2C2×#14273642C212yesmaximal, complemented
3C2×#14273642C211yesmaximal, characteristic, complemented
4#16837168C212yesmaximal, complemented
5C59×#534C211yesmaximal, characteristic
6D4×Dic59—24no—
7#14273686—21no—
8C2×C22⋊Dic59—21no—
9C2×C22⋊Dic59C2212yes—
10C2×C22⋊Dic59C2212yes—
11#14273642—22no—
12#14273642—24no—
13C22×D4×C59C2211yescharacteristic
14C22×D4×C59C2211yescharacteristic
15#123×C59—21no—
16#123×C59C412yescomplemented
17#121×C59—22no—
18#120×C59—21no—
19#120×C59C412yescomplemented
20C2×C22⋊C4×C59C2211yescharacteristic
21C24×C59C2×C411yescharacteristic, complemented
22C24×C59D411yescharacteristic
23C24×C59C2311yescharacteristic
24C2×D4×C59—22no—
25C2×D4×C59—22no—
26C2×D4×C59—21no—
27C2×D4×C59—21no—
28C2×D4×C59—22no—
29C2×D4×C59—22no—
30C2×D4×C59—22no—
31C2×D4×C59C2×C412yes—
32C2×D4×C59D412yes—
33C22×C4×C59—21no—
34C22×C4×C59C2×C411yescharacteristic, complemented
35C22×C4×C59D411yescharacteristic
36C22×Dic59—22no—
37C22×Dic59—22no—
38C22×Dic59—22no—
39C4⋊C4×C59—22no—
40C22⋊C4×C59—22no—
41C22⋊C4×C59—21no—
42C22⋊C4×C59—22no—
43C22⋊C4×C59C2×C412yescomplemented
44C22⋊Dic59—22no—
45C22⋊Dic59—22no—
46C22⋊Dic59—22no—
47C22⋊Dic59—22no—
48C22⋊Dic59D414yescomplemented
49C4⋊Dic59—22no—
50C4×Dic59—22no—
51C23×C59—21no—
52C23×C59—21no—
53C23×C59—21no—
54C23×C59—22no—
55C23×C59—81no—
56C23×C59—81no—
57C23×C59—81no—
58C23×C59C22⋊C412yes—
59C23×C59C22×C411yescharacteristic
60C23×C59C2×D412yes—
61C23×C59C2×D411yescharacteristic
62C23×C59C2×D411yescharacteristic
63C23×C59#4112yes—
64D4×C59—24no—
65D4×C59—24no—
66D4×C59—41no—
67D4×C59—42no—
68D4×C59—41no—
69D4×C59—82no—
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—81no—
76C2×C4×C59C22⋊C412yes—
77C2×Dic59—24no—
78C2×Dic59—42no—
79C2×Dic59—82no—
80C2×Dic59—82no—
81C2×Dic59—82no—
82C22×C59—22no—
83C22×C59—42no—
84C22×C59—42no—
85C22×C59—41no—
86C22×C59—41no—
87C22×C59—41no—
88C22×C59—42no—
89C22×C59—42no—
90C22×C59—42no—
91C22×C59—41no—
92C22×C59—81no—
93C22×C59—82no—
94C22×C59C2×C22⋊C411yescharacteristic
95C22×C59C4×D412yes—
96C22×C59#12011yescharacteristic
97C22×C59#12112yes—
98C22×C59#12311yescharacteristic
99C4×C59—22no—
100C4×C59—42no—
101C4×C59—41no—
102Dic59—44no—
103Dic59—82no—
104#1913—591nomaximal, Sylow
105C2×C59—21no—
106C2×C59—22no—
107C2×C59—21no—
108C2×C59—22no—
109C2×C59—21no—
110C2×C59—42no—
111C2×C59—81no—
112C2×C59#38611yescharacteristic
113#534D5911yescharacteristic
114#518—591no—
115C2×#99—592no—
116C2×#99—591no—
117#342—592no—
118C59#191311yescharacteristic, complemented, Sylow
119C22×D4C2×D5911yescharacteristic
120C22×D4C2×D5911yescharacteristic
121#123—21no—
122#123Dic5912yescomplemented
123#121—22no—
124#120—21no—
125#120Dic5912yescomplemented
126C4×D4—1184no—
127#117—1181no—
128C2×C22⋊C4—592no—
129C2×C22⋊C4—592no—
130C2×C22⋊C4—1181no—
131C2×C22⋊C4C2×D5911yescharacteristic
132#99—1184no—
133#99—1182no—
134C24C2×Dic5911yescharacteristic, complemented
135C24C22⋊D5911yescharacteristic
136C24C22×D5911yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4C2×Dic5912yes—
145C2×D4C22⋊D5912yes—
146C22×C4—21no—
147C22×C4—1182no—
148C22×C4—1182no—
149C22×C4—1182no—
150C22×C4C2×Dic5911yescharacteristic, complemented
151C22×C4C22⋊D5911yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—1182no—
154C22⋊C4—22no—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C22⋊C4—594no—
158C22⋊C4—1182no—
159C22⋊C4—1182no—
160C22⋊C4—1182no—
161C22⋊C4—1182no—
162C22⋊C4C2×Dic5912yescomplemented
163C42—1182no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C22⋊Dic5912yes—
172C23D4×D5912yes—
173C23#1174568712yes—
174C23C22×Dic5911yescharacteristic
175C23C2×C22⋊D5911yescharacteristic
176C23C2×C22⋊D5911yescharacteristic
177D4—24no—
178D4—24no—
179D4—41no—
180D4—42no—
181D4—41no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—81no—
189C2×C4—1184no—
190C2×C4—4722no—
191C2×C4—4722no—
192C2×C4—4722no—
193C2×C4—2362no—
194C2×C4C22⋊Dic5912yes—
195C22—22no—
196C22—41no—
197C22—42no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22C2×C22⋊Dic5911yescharacteristic
208C22D4×Dic5912yes—
209C22#1427369511yescharacteristic
210C22#1427369912yes—
211C22#1427370811yescharacteristic
212C4—22no—
213C4—42no—
214C4—41no—
215C4—4722no—
216C4—2364no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2#1683728211yescharacteristic
subgroupG/H
centerC2#16837282
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC59×#534C2
socleC2×C59#386
hypercenter#534D59
hypocenterC59#1913
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #16837877C2semidirect
2. C2×#14273642C2semidirect
3. C2×#14273642C2semidirect
4. #16837168C2semidirect
16. #123×C59C4semidirect
19. #120×C59C4semidirect
21. C24×C59C2×C4semidirect
34. C22×C4×C59C2×C4semidirect
43. C22⋊C4×C59C2×C4semidirect
48. C22⋊Dic59D4semidirect
118. C59#1913semidirect
122. #123Dic59semidirect
125. #120Dic59semidirect
134. C24C2×Dic59semidirect
150. C22×C4C2×Dic59semidirect
162. C22⋊C4C2×Dic59semidirect