Finite Group Databasebeta

← #21434479

Subgroups — #21434479

Order 7552.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837958C211yesmaximal, characteristic, complemented
2#124×D59C211yesmaximal, characteristic
3#16837763C212yesmaximal, complemented
4#16837760C212yesmaximal, complemented
5#16837759C211yesmaximal, characteristic, complemented
6#16837757C211yesmaximal, characteristic, complemented
7#16837756C211yesmaximal, characteristic, complemented
8#16837409C212yesmaximal, complemented
9#16837405C212yesmaximal
10C4×#11745659C211yesmaximal, characteristic, complemented
11C59×#488C211yesmaximal, characteristic, complemented
12C2×Q8×D59C2211yescharacteristic
13C2×D4×D59C2211yescharacteristic
14C2×#11745659C2212yes—
15#14273726C2212yescomplemented
16#14273719C2211yescharacteristic, complemented
17#14273716C2211yescharacteristic
18#14273715C2211yescharacteristic
19#14273714C2211yescharacteristic
20#14273713—22no—
21#14273705—22no—
22#14273692—22no—
23#14273685C2212yes—
24C22⋊C4×D59—22no—
25C42×D59C2211yescharacteristic
26#14273652C2212yescomplemented
27#14273651C2212yescomplemented
28#14273650C2212yescomplemented
29#14273649C2212yes—
30#14273648C2212yes—
31#14273647C2212yes—
32#14273637C2212yescomplemented
33C4×C59⋊C8C2211yescharacteristic, complemented
34#125×C59C2211yescharacteristic, complemented
35#124×C59C2211yescharacteristic
36#103×C59C2212yescomplemented
37#102×C59C2212yes—
38C4×C8×C59C2211yescharacteristic, complemented
39C23×D59—21no—
40C2×Q8×C59C2311yescharacteristic
41C2×D4×C59C2311yescharacteristic
42C2×C22⋊D59—21no—
43Q8×D59—24no—
44D4×D59—24no—
45C2×D236C2311yescharacteristic
46C2×C4×D59—21no—
47C2×C4×D59D412yes—
48C2×C4×D59C2311yescharacteristic
49C2×Dic118—22no—
50C2×Dic118—21no—
51C2×Dic118C2311yescharacteristic
52C2×C8×C59C2312yes—
53C4⋊C4×C59—22no—
54C4⋊C4×C59C2312yes—
55C22⋊C4×C59—22no—
56C42×C59C2311yescharacteristic
57C22⋊Dic59—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61C4⋊Dic59C2312yes—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64C4×Dic59—22no—
65C4×Dic59D412yes—
66C4×Dic59C2311yescharacteristic
67C2×C59⋊C8C2312yes—
68#11745659—24no—
69C23×C59—21no—
70C22×D59—21no—
71C22×D59—44no—
72C22×D59—42no—
73C22×D59C2×D411yescharacteristic
74Q8×C59—22no—
75D4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—21no—
78C2×C4×C59C2×D412yes—
79C2×C4×C59C2411yescharacteristic
80C22⋊D59—42no—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59C2×D412yes—
84C2×Dic59C2×D411yescharacteristic
85D236—22no—
86C4×D59—42no—
87C4×D59—42no—
88C4×D59#4114yes—
89Dic118—22no—
90Dic118—44no—
91Dic118—42no—
92C8×C59—22no—
93C59⋊C8—22no—
94C22×C59—41no—
95C22×C59—42no—
96C22×C59C22×D411yescharacteristic
97C2×D59—22no—
98C2×D59—41no—
99C2×D59—42no—
100C2×D59—84no—
101C2×D59#12412yes—
102C4×C59—22no—
103C4×C59—41no—
104C4×C59—42no—
105C4×C59C2×#4112yes—
106Dic59—22no—
107Dic59—41no—
108Dic59—42no—
109Dic59#12412yes—
110#3140—591nomaximal, Sylow
111C2×C59—81no—
112C2×C59C2×#12411yescharacteristic
113C2×C59#57512yes—
114D59—22no—
115D59—81no—
116#533—591no—
117C2×#124—591no—
118#489—592no—
119#489—592no—
120#488—591no—
121#488—591no—
122#488—591no—
123#488D5911yescharacteristic, complemented
124#419—592no—
125#418—592no—
126C4×M16—591no—
127C59#314011yescharacteristic, complemented, Sylow
128C22×Q8—591no—
129C22×D4—591no—
130C2×M16—592no—
131C4⋊Q8—592no—
132#125—591no—
133#125C2×D5911yescharacteristic, complemented
134#124—591no—
135#124—591no—
136#124—591no—
137#124—1182no—
138#124C2×D5911yescharacteristic
139C22⋊Q8—1182no—
140C4×Q8—1182no—
141#117—592no—
142C2×C22⋊C4—1182no—
143C2×C42—591no—
144#103—592no—
145#103—592no—
146#103—592no—
147#103C2×D5912yescomplemented
148#102—592no—
149#102—592no—
150#102—592no—
151#102C2×D5912yes—
152#97—592no—
153C4×C8—591no—
154C4×C8C2×D5911yescharacteristic, complemented
155C24—1181no—
156C2×Q8—591no—
157C2×Q8—1182no—
158C2×Q8—1181no—
159C2×Q8—1184no—
160C2×Q8C22×D5911yescharacteristic
161C2×D4—591no—
162C2×D4—1184no—
163C2×D4—1181no—
164C2×D4C22×D5911yescharacteristic
165C22×C4—591no—
166C22×C4—592no—
167C22×C4—1181no—
168M16—1184no—
169C2×C8—592no—
170C2×C8C22×D5912yes—
171C4⋊C4—22no—
172C4⋊C4—592no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4C22×D5912yes—
176C22⋊C4—22no—
177C22⋊C4—1182no—
178C22⋊C4—1182no—
179C22⋊C4—1182no—
180C22⋊C4—1182no—
181C42—592no—
182C42—591no—
183C42—1182no—
184C42C22×D5911yescharacteristic
185C23—21no—
186C23—591no—
187C23—1181no—
188C23—2362no—
189C23—2364no—
190Q8—22no—
191Q8—1182no—
192Q8—2362no—
193Q8—2364no—
194D4—22no—
195D4—1182no—
196D4—2362no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—591no—
200C2×C4—594no—
201C2×C4—592no—
202C2×C4—1182no—
203C2×C4—1181no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4D4×D5912yes—
207C2×C4C23×D5911yescharacteristic
208C8—22no—
209C8—1182no—
210C22—41no—
211C22—42no—
212C22—592no—
213C22—1182no—
214C22—4724no—
215C22—2361no—
216C22—2362no—
217C22C2×D4×D5911yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—592no—
222C4—1182no—
223C4—2361no—
224C4—2362no—
225C4#41×D5912yes—
226C2—81no—
227C2—1182no—
228C2—4721no—
229C2#124×D5911yescharacteristic
230C2#1683819912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#488C2
socleC22×C59C22×D4
hypercenter#488D59
hypocenterC59#3140
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #16837958C2semidirect
3. #16837763C2semidirect
4. #16837760C2semidirect
5. #16837759C2semidirect
6. #16837757C2semidirect
7. #16837756C2semidirect
8. #16837409C2semidirect
10. C4×#11745659C2semidirect
11. C59×#488C2semidirect
15. #14273726C22semidirect
16. #14273719C22semidirect
26. #14273652C22semidirect
27. #14273651C22semidirect
28. #14273650C22semidirect
32. #14273637C22semidirect
33. C4×C59⋊C8C22semidirect
34. #125×C59C22semidirect
36. #103×C59C22semidirect
38. C4×C8×C59C22semidirect
123. #488D59semidirect
127. C59#3140semidirect
133. #125C2×D59semidirect
147. #103C2×D59semidirect
154. C4×C8C2×D59semidirect