Finite Group Databasebeta

← #21430043

Subgroups — #21430043

Order 7552.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14273726C211yesmaximal, characteristic
2C2×#14273717C211yesmaximal, characteristic
3#16837344C212yesmaximal
4#16837343C212yesmaximal
5#16837342C211yesmaximal, characteristic
6#16837341C211yesmaximal, characteristic
7#16837340C211yesmaximal, characteristic
8#16837306C212yesmaximal
9#16837306C212yesmaximal
10#16837247C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic
12C22×Dic118C2212yes—
13#14273726—24no—
14#14273717—24no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×C4×Dic59C2212yes—
23C2×C4×Dic59C2211yescharacteristic
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2211yescharacteristic
35#95×C59C2212yes—
36#95×C59C2212yes—
37C22×C4×C59C2312yes—
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×Dic59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×Dic118—24no—
49C2×Dic118—28no—
50C4⋊C4×C59—22no—
51C4⋊C4×C59—22no—
52C4⋊Dic59—22no—
53C4⋊Dic59—22no—
54Dic59⋊C4—22no—
55Dic59⋊C4—22no—
56Dic59⋊C4—22no—
57Dic59⋊C4—22no—
58Dic59⋊C4—24no—
59C4×Dic59—24no—
60C4×Dic59D414yes—
61C23×C59C2411yescharacteristic
62C2×C4×C59—22no—
63C2×C4×C59—21no—
64C2×C4×C59—21no—
65C2×C4×C59—22no—
66C2×C4×C59—22no—
67C2×C4×C59—24no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—21no—
73C2×C4×C59C2×D412yes—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80C2×Dic59—24no—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59C2×D412yes—
87C2×Dic59C2×D412yes—
88C2×Dic59#4114yes—
89Dic118—48no—
90C22×C59C22×D411yescharacteristic
91C22×C59C2×#4112yes—
92C22×C592−1+412yes—
93C22×C592−1+411yescharacteristic
94C22×C592−1+411yescharacteristic
95C4×C59—22no—
96C4×C59—42no—
97C4×C59—41no—
98C4×C59—41no—
99C4×C59—42no—
100Dic59—22no—
101Dic59—42no—
102Dic59—41no—
103Dic59—41no—
104Dic59—42no—
105Dic59#12414yes—
106#2642—591nomaximal, Sylow
107C2×C59C2×#12411yescharacteristic
108C2×C59#53611yescharacteristic
109C2×C59#53611yescharacteristic
110C2×C59#54112yes—
111C2×C59#54112yes—
112C2×C4⋊Q8—591no—
113C2×#125—591no—
114#400—591no—
115#400—591no—
116#400—591no—
117#400—592no—
118#400—592no—
119#400D5911yescharacteristic
120#391—592no—
121#391—592no—
122#376—591no—
123C59#264211yescharacteristic, complemented, Sylow
124C22×Q8—592no—
125C4⋊Q8—1184no—
126#125—1184no—
127C2×C4⋊C4—591no—
128C2×C4⋊C4—591no—
129C2×C4⋊C4—591no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4—591no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—591no—
134C2×C4⋊C4C2×D5911yescharacteristic
135C2×C4⋊C4C2×D5911yescharacteristic
136C2×C42—591no—
137C2×C42—592no—
138#95—592no—
139#95—591no—
140#95—592no—
141#95—592no—
142#95—592no—
143#95—592no—
144#95—592no—
145#95—592no—
146#95C2×D5911yescharacteristic
147#95C2×D5912yes—
148#95C2×D5912yes—
149C2×Q8—1184no—
150C2×Q8—1188no—
151C22×C4—591no—
152C22×C4—591no—
153C22×C4—592no—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—592no—
157C22×C4C22×D5912yes—
158C22×C4C22×D5911yescharacteristic
159C22×C4C22×D5911yescharacteristic
160C22×C4C22×D5912yes—
161C22×C4C22×D5911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1184no—
169C4⋊C4—1182no—
170C4⋊C4—1182no—
171C42—594no—
172C42—1184no—
173C23C23×D5911yescharacteristic
174Q8—2368no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—592no—
187C2×C4—594no—
188C2×C4—592no—
189C2×C4—1181no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1181no—
193C2×C4—1182no—
194C2×C4—1182no—
195C2×C4—1184no—
196C2×C4—1182no—
197C2×C4—1181no—
198C2×C4—1182no—
199C2×C4—1181no—
200C2×C4—1182no—
201C2×C4D4×D5912yes—
202C22C2×D4×D5911yescharacteristic
203C22#41×D5912yes—
204C22#1427377412yes—
205C22#1427377411yescharacteristic
206C22#1427377511yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—594no—
213C4—1182no—
214C4—2362no—
215C4—2361no—
216C4—2361no—
217C4—2362no—
218C2#124×D5911yescharacteristic
219C2#1683797411yescharacteristic
220C2#1683797511yescharacteristic
221C2#1683800912yes—
222C2#1683801112yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2642
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
123. C59#2642semidirect