Finite Group Databasebeta

← #21429767

Subgroups — #21429767

Order 7552.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14273683C212yesmaximal, complemented
2#16837332C211yesmaximal, characteristic, complemented
3#16837325C212yesmaximal, complemented
4#16837295C212yesmaximal, complemented
5#16837284C212yesmaximal, complemented
6#16837282C212yesmaximal
7#16837274C212yesmaximal, complemented
8#16837267C211yesmaximal, characteristic, complemented
9C59×#394C211yesmaximal, characteristic
10C23×Dic59C2212yes—
11#14273683—28no—
12C2×C4⋊Dic59C2211yescharacteristic
13C2×C4⋊Dic59C2211yescharacteristic
14C2×Dic59⋊C4C2212yes—
15C2×Dic59⋊C4C2212yes—
16C2×Dic59⋊C4C2212yes—
17C2×C22⋊Dic59C2212yes—
18C2×C22⋊Dic59C2212yes—
19C2×C22⋊Dic59C2212yes—
20C2×C4×Dic59C2212yes—
21C2×C4×Dic59C2211yescharacteristic
22C59⋊#95C2212yes—
23C59⋊#95C2212yes—
24C59⋊#95C2211yescharacteristic
25C59⋊#95C2212yes—
26C59⋊#95C2212yes—
27C22×D4×C59C2211yescharacteristic
28C2×C4⋊C4×C59C2211yescharacteristic
29C2×C22⋊C4×C59C2212yes—
30C2×C22⋊C4×C59C2212yes—
31#95×C59C2211yescharacteristic
32C24×C59C2312yes—
33C2×D4×C59—24no—
34C2×D4×C59—41no—
35C22×C4×C59C2312yes—
36C22×C4×C59C2311yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×Dic59—24no—
40C22×Dic59—24no—
41C22×Dic59—24no—
42C22×Dic59C2312yes—
43C22×Dic59C2312yes—
44C22×Dic59C2312yes—
45C22×Dic59C2312yes—
46C4⋊C4×C59—41no—
47C22⋊C4×C59—24no—
48C22⋊C4×C59—24no—
49C22⋊Dic59—24no—
50C22⋊Dic59—24no—
51C22⋊Dic59—42no—
52C4⋊Dic59—41no—
53C4⋊Dic59—41no—
54Dic59⋊C4—24no—
55Dic59⋊C4—24no—
56Dic59⋊C4—24no—
57C4×Dic59—24no—
58C4×Dic59D414yescomplemented
59C23×C59—22no—
60C23×C59—22no—
61C23×C59—22no—
62C23×C59—22no—
63C23×C59—22no—
64C23×C59—22no—
65C23×C59#4114yes—
66C23×C59C2411yescharacteristic
67D4×C59—44no—
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—21no—
77C2×C4×C59C2×D412yes—
78C2×Dic59—216no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—22no—
83C2×Dic59—22no—
84C2×Dic59—22no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—22no—
89C2×Dic59C2×D414yes—
90C2×Dic59#4114yes—
91C22×C59—24no—
92C22×C59—24no—
93C22×C59—24no—
94C22×C59—42no—
95C22×C59—42no—
96C22×C59—42no—
97C22×C59—42no—
98C22×C59C22×D411yescharacteristic
99C22×C59C2×#4112yes—
100C22×C59C2×#4112yes—
101C22×C59H(5,𝔽2)11yescharacteristic
102C22×C592−1+411yescharacteristic
103C4×C59—22no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59—41no—
107Dic59—24no—
108Dic59—24no—
109Dic59—42no—
110Dic59—42no—
111#2609—591nomaximal, Sylow
112C2×C59—44no—
113C2×C59#52512yes—
114C2×C59#53711yescharacteristic
115C2×C59#55111yescharacteristic
116C2×C59#55212yes—
117C2×C59#55511yescharacteristic
118C2×#117—592no—
119#398—591no—
120#396—592no—
121#394D5911yescharacteristic
122#388—592no—
123#387—592no—
124#386—592no—
125#385—592no—
126#382—591no—
127C59#260911yescharacteristic, complemented, Sylow
128C22×D4C2×D5911yescharacteristic
129C23×C4—592no—
130#117—1188no—
131C2×C4⋊C4—592no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—591no—
136C2×C4⋊C4C2×D5911yescharacteristic
137C2×C22⋊C4—592no—
138C2×C22⋊C4—592no—
139C2×C22⋊C4—592no—
140C2×C22⋊C4C2×D5912yes—
141C2×C22⋊C4C2×D5912yes—
142C2×C42—591no—
143C2×C42—592no—
144#95—592no—
145#95—592no—
146#95—591no—
147#95—592no—
148#95—592no—
149#95C2×D5911yescharacteristic
150C24C22×D5912yes—
151C2×D4—24no—
152C2×D4—41no—
153C22×C4—592no—
154C22×C4—592no—
155C22×C4—592no—
156C22×C4—592no—
157C22×C4—1184no—
158C22×C4—1184no—
159C22×C4—1184no—
160C22×C4C22×D5911yescharacteristic
161C22×C4C22×D5911yescharacteristic
162C22×C4C22×D5912yes—
163C22×C4C22×D5911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—1184no—
166C4⋊C4—1184no—
167C4⋊C4—1184no—
168C4⋊C4—2361no—
169C4⋊C4—2361no—
170C22⋊C4—24no—
171C22⋊C4—24no—
172C22⋊C4—1184no—
173C22⋊C4—1184no—
174C22⋊C4—2362no—
175C42—594no—
176C42—1184no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23#1174568714yes—
184C23C23×D5911yescharacteristic
185D4—44no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—594no—
196C2×C4—594no—
197C2×C4—11816no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1182no—
201C2×C4—1182no—
202C2×C4—1182no—
203C2×C4—1182no—
204C2×C4—1182no—
205C2×C4—1182no—
206C2×C4—1182no—
207C2×C4—1182no—
208C2×C4D4×D5912yes—
209C22—24no—
210C22—24no—
211C22—24no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22C2×D4×D5911yescharacteristic
217C22#41×D5912yes—
218C22C2×#1174568712yes—
219C22#1427377211yescharacteristic
220C22#1427377411yescharacteristic
221C4—22no—
222C4—42no—
223C4—41no—
224C4—41no—
225C4—1184no—
226C4—1184no—
227C4—2362no—
228C4—2362no—
229C2—44no—
230C2#1683791212yes—
231C2#1683797911yescharacteristic
232C2#1683808311yescharacteristic
233C2#1683808912yes—
234C2#1683811411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2609
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273683C2semidirect
2. #16837332C2semidirect
3. #16837325C2semidirect
4. #16837295C2semidirect
5. #16837284C2semidirect
7. #16837274C2semidirect
8. #16837267C2semidirect
58. C4×Dic59D4semidirect
127. C59#2609semidirect