Finite Group Databasebeta

← #21434744

Subgroups — #21434744

Order 7552.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838003C212yesmaximal, complemented
2#16837802C211yesmaximal, characteristic, complemented
3#16837777C211yesmaximal, characteristic, complemented
4#16837765C212yesmaximal, complemented
5#16837656C211yesmaximal, characteristic, complemented
6#16837652C211yesmaximal, characteristic, complemented
7#16837637C212yesmaximal, complemented
8#16837515C211yesmaximal, characteristic, complemented
9C4×#11745669C212yesmaximal, complemented
10#16837359C211yesmaximal, characteristic, complemented
11C59×#442C211yesmaximal, characteristic, complemented
12C2×D472C2211yescharacteristic
13C2×#11745669C2212yes—
14C2×#11745659C2211yescharacteristic
15C2×C8×D59C2211yescharacteristic
16#14273723C2212yes—
17#14273718C2212yes—
18#14273710—22no—
19#14273709—22no—
20#14273702C2212yes—
21#14273701—22no—
22#14273700—22no—
23#14273698C2212yes—
24C4×D236C2212yes—
25#14273684C2211yescharacteristic
26#14273660C2212yes—
27#14273659C2211yescharacteristic
28#14273649C2212yes—
29#14273648C2212yes—
30#14273647C2212yes—
31#14273637C2211yescharacteristic
32C4×C59⋊C8C2211yescharacteristic
33C8×Dic59C2211yescharacteristic
34C2×D8×C59C2211yescharacteristic
35C4×D4×C59C2212yes—
36#106×C59C2211yescharacteristic
37#102×C59C2212yes—
38#97×C59C2211yescharacteristic
39C2×D4×C59C2312yes—
40C22×C4×C59—22no—
41C2×C22⋊D59—22no—
42C2×C22⋊D59—22no—
43C2×C22⋊D59—22no—
44C2×D236—22no—
45C2×D236C2312yes—
46C2×C4×D59—22no—
47C2×C4×D59C2311yescharacteristic
48D8×C59—22no—
49C2×C8×C59C2311yescharacteristic
50C2×C8×C59C2311yescharacteristic
51C4⋊C4×C59C2312yes—
52C22⋊C4×C59—22no—
53C42×C59C2311yescharacteristic
54C22⋊Dic59—22no—
55#11745669—24no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58(C2×D59)⋊C4D412yes—
59C4⋊Dic59—22no—
60C4⋊Dic59C2312yes—
61Dic59⋊C4—22no—
62Dic59⋊C4D412yes—
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66D472—22no—
67#11745659—22no—
68C8×D59—22no—
69C23×C59—22no—
70C22×D59—22no—
71C22×D59C2×D411yescharacteristic
72D4×C59—22no—
73D4×C59—22no—
74C2×C4×C59—22no—
75C2×C4×C59—82no—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2411yescharacteristic
78C22⋊D59—82no—
79C22⋊D59—82no—
80C22⋊D59—82no—
81C2×Dic59—22no—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D411yescharacteristic
84D236—22no—
85D236—22no—
86D236—82no—
87C4×D59—21no—
88C4×D59—21no—
89C4×D59—82no—
90C8×C59—21no—
91C8×C59#4112yes—
92C59⋊C8—21no—
93C59⋊C8#4112yes—
94C22×C59—42no—
95C22×C59—42no—
96C22×C59—42no—
97C22×C59C22×D411yescharacteristic
98C2×D59—21no—
99C2×D59—22no—
100C2×D59—42no—
101C2×D59—42no—
102C2×D59—42no—
103C4×C59—22no—
104C4×C59—42no—
105C4×C59C2×#4111yescharacteristic
106C4×C59C2×#4111yescharacteristic
107Dic59—21no—
108Dic59—22no—
109Dic59—42no—
110#3176—591nomaximal, Sylow
111C2×C59—82no—
112C2×C59#53211yescharacteristic
113C2×C59#57612yes—
114D59—41no—
115D59—82no—
116#540—592no—
117#499—591no—
118#493—591no—
119#490—592no—
120#469—591no—
121#469—591no—
122#466—592no—
123#442—591no—
124#442D5911yescharacteristic, complemented
125C4×D8—592no—
126#405—591no—
127C59#317611yescharacteristic, complemented, Sylow
128C2×D8—592no—
129C2×D8—591no—
130C2×D8C2×D5911yescharacteristic
131C2×M16—591no—
132C22×C8—591no—
133#127—592no—
134#125—592no—
135#123—1182no—
136#123—1182no—
137#121—592no—
138#121—592no—
139#121—1182no—
140#121—1182no—
141C4×D4—592no—
142C4×D4C2×D5912yes—
143#117—591no—
144#107—592no—
145#106—591no—
146#106C2×D5911yescharacteristic
147#102—592no—
148#102—592no—
149#102—592no—
150#102C2×D5912yes—
151#97—591no—
152#97C2×D5911yescharacteristic
153C4×C8—591no—
154C4×C8—591no—
155C2×D4—592no—
156C2×D4—1182no—
157C2×D4—1182no—
158C2×D4—1182no—
159C2×D4—1182no—
160C2×D4C22×D5912yes—
161C22×C4—22no—
162C22×C4—591no—
163C22×C4—1182no—
164D8—22no—
165D8—1184no—
166D8—1182no—
167M16—1182no—
168C2×C8—591no—
169C2×C8—591no—
170C2×C8—1182no—
171C2×C8C22×D5911yescharacteristic
172C2×C8C22×D5911yescharacteristic
173C4⋊C4—592no—
174C4⋊C4—592no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4C22×D5912yes—
178C22⋊C4—22no—
179C22⋊C4—592no—
180C22⋊C4—1182no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C42—591no—
184C42C22×D5911yescharacteristic
185C23—22no—
186C23—591no—
187C23—1182no—
188D4—22no—
189D4—22no—
190D4—1182no—
191D4—1182no—
192D4—4722no—
193D4—4722no—
194D4—4722no—
195D4—4722no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—592no—
199C2×C4—591no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1182no—
203C2×C4—4722no—
204C2×C4D4×D5912yes—
205C2×C4C23×D5911yescharacteristic
206C8—21no—
207C8—592no—
208C8—1181no—
209C8#1174568512yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—1181no—
214C22—1182no—
215C22—2362no—
216C22—2362no—
217C22—2362no—
218C22C2×D4×D5911yescharacteristic
219C4—22no—
220C4—42no—
221C4—1181no—
222C4—1182no—
223C4—2362no—
224C4#41×D5911yescharacteristic
225C4C2×#1174568511yescharacteristic
226C2—82no—
227C2—4722no—
228C2—2361no—
229C2#1683794911yescharacteristic
230C2#1683820612yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#442C2
socleC22×C59C22×D4
hypercenter#442D59
hypocenterC59#3176
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16838003C2semidirect
2. #16837802C2semidirect
3. #16837777C2semidirect
4. #16837765C2semidirect
5. #16837656C2semidirect
6. #16837652C2semidirect
7. #16837637C2semidirect
8. #16837515C2semidirect
9. C4×#11745669C2semidirect
10. #16837359C2semidirect
11. C59×#442C2semidirect
124. #442D59semidirect
127. C59#3176semidirect