Finite Group Databasebeta

← #21433605

Subgroups — #21433605

Order 7552.

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

normal subgroups only

This group has 494 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×#14273753C211yesmaximal, characteristic
2#16837976C211yesmaximal, characteristic, complemented
3#16837877C211yesmaximal, characteristic, complemented
4#16837619C214yesmaximal, complemented
5#16837605C214yesmaximal, complemented
6#16837428C211yesmaximal, characteristic, complemented
7#16837411C211yesmaximal, characteristic, complemented
8#16837399C211yesmaximal, characteristic, complemented
9C22×SD16×C59C211yesmaximal, characteristic, complemented
10C2×#11745685C2211yescharacteristic
11#14273753—24no—
12C2×#11745670C2212yes—
13C2×#11745669C2212yes—
14C2×#11745664C2211yescharacteristic
15#14273725C2212yescomplemented
16#14273716C2212yescomplemented
17#14273710—22no—
18#14273703—22no—
19D4×Dic59—22no—
20D4×Dic59C2214yes—
21#14273686C2211yescharacteristic
22#14273686C2211yescharacteristic
23C2×C22⋊Dic59—22no—
24Dic59⋊C8C2214yescomplemented
25#14273652C2212yescomplemented
26#14273651C2214yescomplemented
27#14273649C2212yescomplemented
28C22×Q8×C59C2211yescharacteristic
29C22×D4×C59C2211yescharacteristic
30C2×SD16×C59—24no—
31C2×SD16×C59C2214yes—
32C22×C8×C59C2211yescharacteristic
33C24×C59—21no—
34C2×Q8×C59—21no—
35C2×Q8×C59—22no—
36C2×Q8×C59—22no—
37C2×Q8×C59C2312yes—
38C2×D4×C59—21no—
39C2×D4×C59—22no—
40C2×D4×C59D414yes—
41C2×D4×C59C2312yes—
42C22×C4×C59—21no—
43C22×C4×C59C2311yescharacteristic
44C2×C22⋊D59—21no—
45C22×Dic59—24no—
46#11745685—22no—
47#11745685—22no—
48C2×D236C2311yescharacteristic
49C2×C4×D59—21no—
50C2×Dic118C2311yescharacteristic
51SD16×C59—28no—
52C2×C8×C59—22no—
53C2×C8×C59C2312yes—
54C22⋊Dic59—21no—
55C22⋊Dic59—24no—
56C22⋊Dic59D412yes—
57#11745670—24no—
58#11745669—24no—
59(C2×D59)⋊C4—24no—
60C4⋊Dic59D412yes—
61C4⋊Dic59C2312yes—
62Dic59⋊C4—24no—
63C4×Dic59—21no—
64C4×Dic59C2312yes—
65#11745664—22no—
66C2×C59⋊C8C2312yes—
67C23×C59—22no—
68C23×C59—24no—
69C23×C59—82no—
70C23×C59C2×D411yescharacteristic
71C22×D59—21no—
72Q8×C59—22no—
73Q8×C59—22no—
74Q8×C59—42no—
75D4×C59—24no—
76D4×C59—22no—
77D4×C59C2×D414yes—
78C2×C4×C59—22no—
79C2×C4×C59—42no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2×D412yes—
82C2×C4×C59#4112yes—
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—42no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59—84no—
88C2×Dic59C2×D414yes—
89D236—21no—
90D236—21no—
91C4×D59—42no—
92Dic118—21no—
93Dic118—21no—
94C8×C59—22no—
95C59⋊C8—22no—
96C22×C59—22no—
97C22×C59—24no—
98C22×C59—44no—
99C22×C59—84no—
100C22×C59#12112yes—
101C22×C59C22×D411yescharacteristic
102C2×D59—41no—
103C2×D59—42no—
104C4×C59—42no—
105C4×C59#12112yes—
106C4×C59C22×D411yescharacteristic
107C4×C59C2×#4111yescharacteristic
108Dic59—24no—
109Dic59—41no—
110Dic59—42no—
111#3042—591nomaximal, Sylow
112C2×C59—22no—
113C2×C59—44no—
114C2×C59C2×#12111yescharacteristic
115C2×C59#57712yes—
116D59—81no—
117C2×AGL(1,ℤ/8)—591no—
118C22×SD16D5911yescharacteristic, complemented
119#536—591no—
120#518—591no—
121#463—594no—
122#461—594no—
123#424—591no—
124#419—591no—
125#416—591no—
126C59#304211yescharacteristic, complemented, Sylow
127C2×#41—591no—
128C22×Q8C2×D5911yescharacteristic
129C22×D4C2×D5911yescharacteristic
130AGL(1,ℤ/8)—1184no—
131C2×SD16—24no—
132C2×SD16—592no—
133C2×SD16C2×D5914yes—
134C2×D8—592no—
135C2×M16—591no—
136C22×C8C2×D5911yescharacteristic
137C4⋊Q8—592no—
138#124—592no—
139#123—1182no—
140C22⋊Q8—1182no—
141C4×D4—594no—
142C4×D4—1182no—
143#117—591no—
144#117—591no—
145C2×C22⋊C4—1182no—
146C4⋊C8—594no—
147#103—594no—
148#103—592no—
149#102—592no—
150C24—21no—
151#41—1182no—
152#41—1182no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—591no—
157C2×Q8C22×D5912yes—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4—591no—
161C2×D4—1181no—
162C2×D4C22⋊D5914yes—
163C2×D4C22×D5912yes—
164C22×C4—21no—
165C22×C4—1184no—
166C22×C4—1181no—
167C22×C4C22×D5911yescharacteristic
168SD16—28no—
169SD16—1184no—
170D8—1184no—
171M16—1182no—
172C2×C8—22no—
173C2×C8—592no—
174C2×C8C22×D5912yes—
175C4⋊C4—592no—
176C4⋊C4—592no—
177C4⋊C4—1184no—
178C22⋊C4—592no—
179C22⋊C4—1184no—
180C22⋊C4—1184no—
181C22⋊C4—1181no—
182C42—592no—
183C42—1181no—
184C23—22no—
185C23—24no—
186C23—82no—
187C23—1181no—
188C23D4×D5911yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—1181no—
193Q8—1181no—
194D4—24no—
195D4—22no—
196D4—1181no—
197D4—1181no—
198D4—2362no—
199D4C2×C22⋊D5914yes—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—594no—
203C2×C4—1182no—
204C2×C4—1181no—
205C2×C4—4724no—
206C2×C4—2362no—
207C2×C4D4×D5911yescharacteristic
208C2×C4#1174568712yes—
209C2×C4C2×C22⋊D5912yes—
210C2×C4C23×D5911yescharacteristic
211C8—22no—
212C8—1182no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—84no—
217C22—2361no—
218C22—2362no—
219C22#1427369912yes—
220C22C2×D4×D5911yescharacteristic
221C4—42no—
222C4—1184no—
223C4—2361no—
224C4—2362no—
225C4#1427369912yes—
226C4C22×C22⋊D5911yescharacteristic
227C4C2×#1174568711yescharacteristic
228C2—22no—
229C2—44no—
230C2—4721no—
231C2C2×#1427369911yescharacteristic
232C2#1683820812yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC22×SD16×C59C2
socleC22×C59C22×D4
hypercenterC22×SD16D59
hypocenterC59#3042
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #16837976C2semidirect
3. #16837877C2semidirect
4. #16837619C2semidirect
5. #16837605C2semidirect
6. #16837428C2semidirect
7. #16837411C2semidirect
8. #16837399C2semidirect
9. C22×SD16×C59C2semidirect
15. #14273725C22semidirect
16. #14273716C22semidirect
24. Dic59⋊C8C22semidirect
25. #14273652C22semidirect
26. #14273651C22semidirect
27. #14273649C22semidirect
118. C22×SD16D59semidirect
126. C59#3042semidirect