Finite Group Databasebeta

← #21424510

Subgroups — #21424510

Order 7552.

386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 97 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
2C2×#14273642C211yesmaximal, characteristic
3#16837265C212yesmaximal, complemented
4#16837168C212yesmaximal, complemented
5C2×#123×C59C211yesmaximal, characteristic
6D4×Dic59—24no—
7#14273686—21no—
8C2×C22⋊Dic59—21no—
9C2×C22⋊Dic59C2212yes—
10C2×C22⋊Dic59C2212yes—
11#14273642—22no—
12C59⋊#95—24no—
13C22×D4×C59C2211yescharacteristic
14C23×C4×C59C2211yescharacteristic
15#123×C59—22no—
16#123×C59C414yescomplemented
17C2×C4⋊C4×C59—21no—
18C2×C22⋊C4×C59—21no—
19C2×C22⋊C4×C59C2211yescharacteristic
20C24×C59D411yescharacteristic
21C24×C59C2311yescharacteristic
22C2×D4×C59—22no—
23C2×D4×C59—22no—
24C2×D4×C59C2×C412yes—
25C2×D4×C59D412yes—
26C22×C4×C59—21no—
27C22×C4×C59—21no—
28C22×C4×C59—21no—
29C22×C4×C59—22no—
30C22×C4×C59—22no—
31C22×C4×C59C2×C412yescomplemented
32C22×C4×C59D411yescharacteristic
33C22×Dic59—22no—
34C22×Dic59—22no—
35C22×Dic59D414yes—
36C4⋊C4×C59—24no—
37C22⋊C4×C59—24no—
38C22⋊C4×C59—21no—
39C22⋊C4×C59C2×C412yescomplemented
40C22⋊Dic59—22no—
41C22⋊Dic59—22no—
42C22⋊Dic59—22no—
43C22⋊Dic59—22no—
44C22⋊Dic59—22no—
45C4⋊Dic59—22no—
46C4×Dic59—22no—
47C23×C59—21no—
48C23×C59—21no—
49C23×C59—42no—
50C23×C59—42no—
51C23×C59C22⋊C412yes—
52C23×C59C22×C411yescharacteristic
53C23×C59C2×D412yes—
54C23×C59C2×D411yescharacteristic
55C23×C59C2×D411yescharacteristic
56C23×C59#4112yes—
57D4×C59—24no—
58D4×C59—24no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—24no—
64C2×C4×C59—42no—
65C2×C4×C59—41no—
66C2×C4×C59—42no—
67C2×C4×C59—41no—
68C2×C4×C59C22⋊C412yes—
69C2×Dic59—24no—
70C2×Dic59—44no—
71C2×Dic59—44no—
72C2×Dic59—42no—
73C2×Dic59—82no—
74C22×C59—24no—
75C22×C59—22no—
76C22×C59—22no—
77C22×C59—41no—
78C22×C59—41no—
79C22×C59—42no—
80C22×C59—42no—
81C22×C59—42no—
82C22×C59—81no—
83C22×C59C2×C22⋊C411yescharacteristic
84C22×C59C4×D412yes—
85C22×C59#12011yescharacteristic
86C22×C59#12112yes—
87C22×C59#12311yescharacteristic
88C4×C59—22no—
89C4×C59—42no—
90C4×C59—42no—
91Dic59—44no—
92Dic59—82no—
93#1890—591nomaximal, Sylow
94C2×C59—22no—
95C2×C59—21no—
96C2×C59—21no—
97C2×C59—22no—
98C2×C59—42no—
99C2×C59#38611yescharacteristic
100C2×C59#45812yes—
101C2×#123D5911yescharacteristic
102#518—591no—
103C2×#99—591no—
104#381—592no—
105#342—592no—
106C59#189011yescharacteristic, complemented, Sylow
107C22×D4C2×D5911yescharacteristic
108C23×C4C2×D5911yescharacteristic
109#123—22no—
110#123Dic5914yescomplemented
111C4×D4—1184no—
112#117—1181no—
113C2×C4⋊C4—21no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—592no—
116C2×C22⋊C4—592no—
117C2×C22⋊C4—1181no—
118C2×C22⋊C4C2×D5911yescharacteristic
119#99—1182no—
120#95—1184no—
121C24C22⋊D5911yescharacteristic
122C24C22×D5911yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C2×Dic5912yes—
126C2×D4C22⋊D5912yes—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—594no—
133C22×C4—1182no—
134C22×C4—1182no—
135C22×C4C2×Dic5912yescomplemented
136C22×C4C22⋊D5911yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—1182no—
139C22⋊C4—24no—
140C22⋊C4—21no—
141C22⋊C4—1182no—
142C22⋊C4—1182no—
143C22⋊C4—1182no—
144C22⋊C4—1182no—
145C22⋊C4—1182no—
146C22⋊C4C2×Dic5912yescomplemented
147C42—1182no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23C22⋊Dic5912yes—
153C23D4×D5912yes—
154C23#1174568712yes—
155C23C22×Dic5911yescharacteristic
156C23C2×C22⋊D5911yescharacteristic
157C23C2×C22⋊D5911yescharacteristic
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—1184no—
170C2×C4—4722no—
171C2×C4—2364no—
172C2×C4—2362no—
173C2×C4—2364no—
174C2×C4C22⋊Dic5912yes—
175C22—22no—
176C22—24no—
177C22—22no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×C22⋊Dic5911yescharacteristic
185C22D4×Dic5912yes—
186C22#1427369511yescharacteristic
187C22#1427369912yes—
188C22#1427370811yescharacteristic
189C4—22no—
190C4—42no—
191C4—42no—
192C4—4722no—
193C4—2364no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1683728211yescharacteristic
200C2#1683759112yes—
subgroupG/H
centerC22#14273695
commutatorC23×C59C22×C4
FrattiniC24C22×D59
FittingC2×#123×C59C2
socleC22×C59#120
hypercenterC2×#123D59
hypocenterC59#1890
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #16837265C2semidirect
4. #16837168C2semidirect
16. #123×C59C4semidirect
31. C22×C4×C59C2×C4semidirect
39. C22⋊C4×C59C2×C4semidirect
106. C59#1890semidirect
110. #123Dic59semidirect
135. C22×C4C2×Dic59semidirect
146. C22⋊C4C2×Dic59semidirect