Finite Group Databasebeta

← #21430219

Subgroups — #21430219

Order 7552.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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#16837334C211yesmaximal, characteristic
4#16837333C211yesmaximal, characteristic
5#16837332C211yesmaximal, characteristic
6#16837323C212yesmaximal
7#16837322C212yesmaximal
8#16837271C212yesmaximal
9#16837266C212yesmaximal
10#16837247C211yesmaximal, characteristic
11C59×#398C211yesmaximal, characteristic
12C22×Dic118C2212yes—
13#14273726—24no—
14#14273717—24no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2212yes—
23C2×Dic59⋊C4C2212yes—
24C2×Dic59⋊C4C2212yes—
25C2×C4×Dic59C2211yescharacteristic
26C2×C4×Dic59C2212yes—
27C59⋊#95C2212yes—
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C22×C4×C59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×Dic59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C2×Dic118—24no—
49C2×Dic118—42no—
50C2×Dic118—42no—
51C4⋊C4×C59—22no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—42no—
54C4⋊Dic59—22no—
55C4⋊Dic59—22no—
56C4⋊Dic59—42no—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—24no—
62Dic59⋊C4—42no—
63Dic59⋊C4—42no—
64C4×Dic59D414yes—
65C4×Dic59Q818yescomplemented
66C23×C59C2411yescharacteristic
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59—21no—
71C2×C4×C59—21no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—21no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59C2×D412yes—
79C2×C4×C59C2×Q814yes—
80C2×Dic59—22no—
81C2×Dic59—21no—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—22no—
87C2×Dic59—21no—
88C2×Dic59—22no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—22no—
92C2×Dic59C2×D412yes—
93C2×Dic59C2×D412yes—
94C2×Dic59C2×Q814yes—
95C2×Dic59C2×Q814yes—
96Dic118—48no—
97C22×C59C22×D411yescharacteristic
98C22×C59C22×Q812yes—
99C22×C59H(5,𝔽2)11yescharacteristic
100C22×C59H(5,𝔽2)11yescharacteristic
101C22×C592−1+412yes—
102C4×C59—22no—
103C4×C59—24no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59—41no—
107Dic59—22no—
108Dic59—24no—
109Dic59—42no—
110Dic59—41no—
111Dic59—41no—
112Dic59C4⋊Q814yes—
113#2660—591nomaximal, Sylow
114C2×C59C2×C4⋊Q811yescharacteristic
115C2×C59#53511yescharacteristic
116C2×C59#53611yescharacteristic
117C2×C59#54412yes—
118C2×C59#54412yes—
119C2×C4⋊Q8—591no—
120C2×#125—591no—
121#398—591no—
122#398—591no—
123#398—591no—
124#398D5911yescharacteristic
125#395—592no—
126#395—592no—
127#384—592no—
128#382—592no—
129#376—591no—
130C59#266011yescharacteristic, complemented, Sylow
131C22×Q8—592no—
132C4⋊Q8—1184no—
133#125—1184no—
134C2×C4⋊C4—591no—
135C2×C4⋊C4—591no—
136C2×C4⋊C4—591no—
137C2×C4⋊C4—591no—
138C2×C4⋊C4—591no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—591no—
141C2×C4⋊C4—592no—
142C2×C4⋊C4—592no—
143C2×C4⋊C4—592no—
144C2×C4⋊C4C2×D5911yescharacteristic
145C2×C4⋊C4C2×D5911yescharacteristic
146C2×C4⋊C4C2×D5912yes—
147C2×C42—591no—
148C2×C42—592no—
149#95—592no—
150#95—591no—
151#95—592no—
152#95—592no—
153#95—592no—
154#95C2×D5911yescharacteristic
155#95C2×D5912yes—
156C2×Q8—1184no—
157C2×Q8—2362no—
158C2×Q8—2362no—
159C22×C4—591no—
160C22×C4—592no—
161C22×C4—591no—
162C22×C4—591no—
163C22×C4—592no—
164C22×C4—591no—
165C22×C4C22×D5911yescharacteristic
166C22×C4C22×D5912yes—
167C22×C4C22×D5911yescharacteristic
168C22×C4C22×D5911yescharacteristic
169C22×C4C22×D5912yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—1184no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—2362no—
181C4⋊C4—2362no—
182C4⋊C4—2362no—
183C42—594no—
184C42—598no—
185C23C23×D5911yescharacteristic
186Q8—2368no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—592no—
199C2×C4—594no—
200C2×C4—592no—
201C2×C4—594no—
202C2×C4—1181no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—1182no—
206C2×C4—1181no—
207C2×C4—1181no—
208C2×C4—1182no—
209C2×C4—1181no—
210C2×C4—1182no—
211C2×C4—1181no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4D4×D5912yes—
215C2×C4Q8×D5914yes—
216C22C2×D4×D5911yescharacteristic
217C22C2×Q8×D5912yes—
218C22#1427377211yescharacteristic
219C22#1427377311yescharacteristic
220C22#1427377412yes—
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—594no—
227C4—1182no—
228C4—1184no—
229C4—2362no—
230C4—2361no—
231C4—2361no—
232C2C4⋊Q8×D5911yescharacteristic
233C2#1683796811yescharacteristic
234C2#1683797411yescharacteristic
235C2#1683803112yes—
236C2#1683803212yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2660
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. C4×Dic59Q8semidirect
130. C59#2660semidirect