Finite Group Databasebeta

← #21428576

Subgroups — #21428576

Order 7552.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273705C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic
3#16837342C211yesmaximal, characteristic, complemented
4#16837341C211yesmaximal, characteristic, complemented
5#16837340C211yesmaximal, characteristic, complemented
6#16837306C212yesmaximal, complemented
7#16837266C212yesmaximal, complemented
8#16837264C212yesmaximal
9#16837264C212yesmaximal
10#16837249C211yesmaximal, characteristic
11C59×#400C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C4×D59C2212yes—
14C22×C4×D59C2211yescharacteristic
15#14273705—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C4⋊C4×D59—24no—
21C2×(C2×D59)⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊C4C2211yescharacteristic
23C2×(C2×D59)⋊C4C2212yes—
24C2×C4×Dic59C2212yes—
25C59⋊#95C2211yescharacteristic
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—
37C23×D59C2311yescharacteristic
38C22×C4×C59C2312yes—
39C22×C4×C59C2311yescharacteristic
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×Dic59C2312yes—
44C22×Dic59C2311yescharacteristic
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—24no—
49C2×C4×D59—24no—
50C2×C4×D59—28no—
51C2×C4×D59D414yes—
52C2×Dic118—22no—
53C2×Dic118—24no—
54C4⋊C4×C59—22no—
55C4⋊C4×C59—22no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4—24no—
59C4⋊Dic59—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4—24no—
62Dic59⋊C4—22no—
63C4×Dic59—24no—
64C23×C59C2411yescharacteristic
65C22×D59—22no—
66C22×D59—21no—
67C22×D59—21no—
68C22×D59C2×D412yes—
69C22×D59#4114yes—
70C2×C4×C59—22no—
71C2×C4×C59—21no—
72C2×C4×C59—22no—
73C2×C4×C59—21no—
74C2×C4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—24no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—21no—
81C2×C4×C59C2×D412yes—
82C2×Dic59—21no—
83C2×Dic59—22no—
84C2×Dic59—21no—
85C2×Dic59—22no—
86C2×Dic59—22no—
87C2×Dic59—22no—
88C2×Dic59—24no—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59C2×D412yes—
93C2×Dic59#4114yes—
94C4×D59—28no—
95C4×D59—48no—
96Dic118—44no—
97C22×C59C22×D411yescharacteristic
98C22×C59C2×#4112yes—
99C22×C59C2×#4112yes—
100C22×C592−1+411yescharacteristic
101C22×C592−1+411yescharacteristic
102C2×D59—22no—
103C2×D59—22no—
104C2×D59—24no—
105C2×D59—24no—
106C2×D59#12414yes—
107C4×C59—22no—
108C4×C59—41no—
109C4×C59—42no—
110C4×C59—41no—
111C4×C59—42no—
112Dic59—41no—
113Dic59—42no—
114Dic59—41no—
115Dic59—42no—
116Dic59#12314yes—
117#2503—591nomaximal, Sylow
118C2×C59C2×#12311yescharacteristic
119C2×C59C2×#12411yescharacteristic
120C2×C59#53611yescharacteristic
121C2×C59#55212yes—
122C2×C59#55212yes—
123D59—24no—
124C2×C22⋊Q8—591no—
125C22×C4⋊C4—591no—
126#400—591no—
127#400—591no—
128#400—591no—
129#400D5911yescharacteristic, complemented
130#391—592no—
131#382—592no—
132#381—592no—
133#381—592no—
134C4×C22⋊C4—591no—
135C59#250311yescharacteristic, complemented, Sylow
136C22×Q8—591no—
137C23×C4—591no—
138C23×C4—592no—
139C22⋊Q8—1184no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—591no—
142C2×C4⋊C4—591no—
143C2×C4⋊C4—591no—
144C2×C4⋊C4—1184no—
145C2×C4⋊C4C2×D5911yescharacteristic
146C2×C4⋊C4C2×D5911yescharacteristic
147C2×C22⋊C4—591no—
148C2×C22⋊C4—591no—
149C2×C22⋊C4—592no—
150C2×C42—592no—
151#95—591no—
152#95—592no—
153#95—592no—
154#95—592no—
155#95—592no—
156#95—592no—
157#95—592no—
158#95C2×D5911yescharacteristic
159#95C2×D5912yes—
160#95C2×D5912yes—
161C24—591no—
162C2×Q8—1182no—
163C2×Q8—1184no—
164C22×C4—591no—
165C22×C4—594no—
166C22×C4—592no—
167C22×C4—591no—
168C22×C4—591no—
169C22×C4—592no—
170C22×C4—1184no—
171C22×C4—1184no—
172C22×C4—1188no—
173C22×C4C22×D5912yes—
174C22×C4C22×D5911yescharacteristic
175C22×C4C22×D5911yescharacteristic
176C22×C4C22×D5912yes—
177C22×C4C22×D5911yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—1184no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—1184no—
187C42—1184no—
188C23—592no—
189C23—594no—
190C23—1182no—
191C23—1181no—
192C23—1181no—
193C23C23×D5911yescharacteristic
194Q8—2364no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—592no—
207C2×C4—594no—
208C2×C4—1188no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—1182no—
212C2×C4—1182no—
213C2×C4—1182no—
214C2×C4—1184no—
215C2×C4—1182no—
216C2×C4—1181no—
217C2×C4—1181no—
218C2×C4—1182no—
219C2×C4—2368no—
220C2×C4D4×D5912yes—
221C22—594no—
222C22—1182no—
223C22—1182no—
224C22—1184no—
225C22—1184no—
226C22C2×D4×D5911yescharacteristic
227C22#41×D5912yes—
228C22#41×D5912yes—
229C22#1427377411yescharacteristic
230C22#1427377511yescharacteristic
231C4—22no—
232C4—41no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—594no—
237C4—2361no—
238C4—2362no—
239C4—2361no—
240C4—2362no—
241C2—1184no—
242C2#123×D5911yescharacteristic
243C2#124×D5911yescharacteristic
244C2#1683797511yescharacteristic
245C2#1683808412yes—
246C2#1683808812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2503
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #16837342C2semidirect
4. #16837341C2semidirect
5. #16837340C2semidirect
6. #16837306C2semidirect
7. #16837266C2semidirect
11. C59×#400C2semidirect
129. #400D59semidirect
135. C59#2503semidirect