Finite Group Databasebeta

← #21422636

Subgroups — #21422636

Order 7552.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#16837912C211yesmaximal, characteristic
2#16837364C211yesmaximal, characteristic, complemented
3#16837261C211yesmaximal, characteristic, complemented
4#16837140C211yesmaximal, characteristic, complemented
5#16837138C211yesmaximal, characteristic, complemented
6#16837136C211yesmaximal, characteristic, complemented
7C59×#327C211yesmaximal, characteristic, complemented
8C2×#11745687C411yescharacteristic, complemented
9C22×C4×D59C2211yescharacteristic
10C2×#11745659—21no—
11#14273709—21no—
12#14273707C411yescharacteristic, complemented
13#14273706C2211yescharacteristic
14#14273698C411yescharacteristic, complemented
15#14273695—21no—
16D4×Dic59—21no—
17(C22⋊D59)⋊C4—21no—
18#14273685C411yescharacteristic, complemented
19C2×Dic59⋊C4—21no—
20C2×(C2×D59)⋊C4—21no—
21C22⋊(C59⋊C8)C2211yescharacteristic
22(C2×D59)⋊C8—21no—
23C59⋊#95C2211yescharacteristic
24#121×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26#95×C59C2211yescharacteristic
27C23×D59D411yescharacteristic
28C2×D4×C59—21no—
29C2×D4×C59C2×C411yescharacteristic
30C22×C4×C59—21no—
31C22×C4×C59C2311yescharacteristic
32C2×C22⋊D59—21no—
33C2×C22⋊D59—21no—
34C22×Dic59—21no—
35C22×Dic59—21no—
36C22×Dic59D411yescharacteristic
37#11745687—42no—
38C2×C4×D59—42no—
39C2×C4×D59C2×C411yescharacteristic
40C2×C4×D59C2×C411yescharacteristic
41C2×C4×D59D411yescharacteristic
42C2×C4×D59D411yescharacteristic
43C2×Dic118C2×C411yescharacteristic
44C2×C8×C59—21no—
45C4⋊C4×C59C2×C411yescharacteristic
46C22⋊C4×C59—21no—
47C22⋊Dic59—21no—
48C22⋊Dic59—21no—
49(C2×D59)⋊C4—21no—
50(C2×D59)⋊C4—21no—
51(C2×D59)⋊C4—42no—
52C4⋊Dic59—21no—
53C4⋊Dic59C2×C411yescharacteristic
54Dic59⋊C4—21no—
55Dic59⋊C4—42no—
56C4×Dic59—21no—
57C2×C59⋊C8—21no—
58#11745659—42no—
59C23×C59—21no—
60C23×C59C2×D411yescharacteristic
61C22×D59—21no—
62C22×D59—21no—
63C22×D59—41no—
64C22×D59—41no—
65C22×D59C22⋊C411yescharacteristic
66C22×D59C22⋊C411yescharacteristic
67D4×C59—41no—
68D4×C59—41no—
69D4×C59—41no—
70C2×C4×C59—21no—
71C2×C4×C59—41no—
72C2×C4×C59—41no—
73C2×C4×C59—41no—
74C2×C4×C59—41no—
75C2×C4×C59C22×C411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C22⋊D59—42no—
78C22⋊D59—42no—
79C2×Dic59—22no—
80C2×Dic59—21no—
81C2×Dic59—21no—
82C2×Dic59—42no—
83C2×Dic59—41no—
84C2×Dic59—41no—
85C2×Dic59—41no—
86C2×Dic59C22⋊C411yescharacteristic
87C2×Dic59C22⋊C411yescharacteristic
88C4×D59—22no—
89C4×D59—22no—
90C4×D59—41no—
91C4×D59—41no—
92Dic118—41no—
93C8×C59—41no—
94C59⋊C8—41no—
95C22×C59—21no—
96C22×C59—21no—
97C22×C59—41no—
98C22×C59—41no—
99C22×C59—41no—
100C22×C59C2×C22⋊C411yescharacteristic
101C22×C59AGL(1,ℤ/8)11yescharacteristic
102C22×C59#13711yescharacteristic
103C2×D59—21no—
104C2×D59—21no—
105C2×D59—21no—
106C2×D59—21no—
107C2×D59—21no—
108C2×D59—21no—
109C2×D59—42no—
110C2×D59—42no—
111C4×C59—21no—
112C4×C59—21no—
113C4×C59—41no—
114C4×C59—81no—
115Dic59—21no—
116Dic59—41no—
117Dic59—41no—
118Dic59—81no—
119Dic59#9912yes—
120#1513—591nomaximal, Sylow
121C2×C59—21no—
122C2×C59—21no—
123C2×C59—81no—
124C2×C59C2×#9911yescharacteristic
125C2×C59#41711yescharacteristic
126C2×C59#42111yescharacteristic
127D59—41no—
128D59—41no—
129#525—591no—
130#407—591no—
131#380—591no—
132#328—591no—
133#328—591no—
134#327—591no—
135#327D5911yescharacteristic, complemented
136C59#151311yescharacteristic, complemented, Sylow
137C2×#41—591no—
138C23×C4—591no—
139C2×M16—1181no—
140#123—1181no—
141C22⋊Q8—591no—
142C22⋊Q8—591no—
143#121—591no—
144#121C2×D5911yescharacteristic
145#120—1181no—
146C4×D4—1181no—
147C4×D4—1181no—
148#117—591no—
149C2×C4⋊C4—1181no—
150C2×C22⋊C4—1181no—
151C22⋊C8—591no—
152C22⋊C8—1181no—
153C22⋊C8C2×D5911yescharacteristic
154#95—591no—
155#95C2×D5911yescharacteristic
156C24—591no—
157#41—2362no—
158C2×Q8—591no—
159C2×D4—21no—
160C2×D4—1181no—
161C2×D4—1181no—
162C2×D4C4×D5911yescharacteristic
163C22×C4—21no—
164C22×C4—591no—
165C22×C4—591no—
166C22×C4—591no—
167C22×C4—591no—
168C22×C4—591no—
169C22×C4—1181no—
170C22×C4—1181no—
171C22×C4—2362no—
172C22×C4C22×D5911yescharacteristic
173M16—2362no—
174C2×C8—21no—
175C2×C8—1181no—
176C4⋊C4—591no—
177C4⋊C4—1181no—
178C4⋊C4—1181no—
179C4⋊C4—2362no—
180C4⋊C4C4×D5911yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—1181no—
183C22⋊C4—1181no—
184C22⋊C4—1181no—
185C22⋊C4—1181no—
186C22⋊C4—2362no—
187C42—1181no—
188C23—21no—
189C23—591no—
190C23—591no—
191C23—1181no—
192C23—1181no—
193C23—2361no—
194C23—2361no—
195C23D4×D5911yescharacteristic
196Q8—2361no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—2362no—
201D4—2362no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—591no—
208C2×C4—591no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1181no—
213C2×C4—1181no—
214C2×C4—2361no—
215C2×C4—2361no—
216C2×C4—2362no—
217C2×C4—2361no—
218C2×C4—2361no—
219C2×C4—2361no—
220C2×C4C2×C4×D5911yescharacteristic
221C2×C4D4×D5911yescharacteristic
222C8—41no—
223C8—2361no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—1181no—
230C22—1181no—
231C22—1181no—
232C22—1181no—
233C22—1181no—
234C22—1181no—
235C22—2362no—
236C22—2362no—
237C22C22⋊C4×D5911yescharacteristic
238C22#1427375111yescharacteristic
239C22#1427375611yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—81no—
244C4—592no—
245C4—1181no—
246C4—4721no—
247C4—2361no—
248C4—2361no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—2361no—
253C2—2361no—
254C2#99×D5911yescharacteristic
255C2#1683740011yescharacteristic
256C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#327C2
socleC22×C59C2×C22⋊C4
hypercenter#327D59
hypocenterC59#1513
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #16837364C2semidirect
3. #16837261C2semidirect
4. #16837140C2semidirect
5. #16837138C2semidirect
6. #16837136C2semidirect
7. C59×#327C2semidirect
8. C2×#11745687C4semidirect
12. #14273707C4semidirect
14. #14273698C4semidirect
18. #14273685C4semidirect
135. #327D59semidirect
136. C59#1513semidirect