Finite Group Databasebeta

← #21435150

Subgroups — #21435150

Order 7552.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#16838006C211yesmaximal, characteristic, complemented
2#16837977C211yesmaximal, characteristic, complemented
3#16837789C211yesmaximal, characteristic, complemented
4#16837770C211yesmaximal, characteristic, complemented
5#16837757C211yesmaximal, characteristic, complemented
6#16837619C212yesmaximal, complemented
7#16837605C212yesmaximal, complemented
8#16837546C212yesmaximal, complemented
9#16837539C212yesmaximal, complemented
10#16837461C211yesmaximal, characteristic, complemented
11C59×#492C211yesmaximal, characteristic, complemented
12C2×#11745689C2211yescharacteristic
13C2×Q8×D59C2211yescharacteristic
14C2×#11745670C2212yes—
15C2×#11745669C2212yes—
16#14273725C2211yescharacteristic
17#14273719C2211yescharacteristic
18#14273716C2211yescharacteristic
19#14273715C2211yescharacteristic
20#14273712—22no—
21#14273708—22no—
22#14273705—22no—
23#14273699—22no—
24#14273698C2212yes—
25D4×Dic59C2212yes—
26#14273684C2211yescharacteristic
27Dic59⋊C8C2212yes—
28#14273652C2212yes—
29#14273651C2212yes—
30#14273651C2212yes—
31#14273649C2212yes—
32(C2×D59)⋊C8C2212yes—
33#14273638C2211yescharacteristic
34C2×SD16×C59C2212yes—
35C2×SD16×C59C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37#127×C59C2211yescharacteristic
38C4×C8×C59C2211yescharacteristic
39C2×Q8×C59C2311yescharacteristic
40C2×Q8×C59C2311yescharacteristic
41C2×D4×C59—22no—
42C2×D4×C59C2312yes—
43C2×C22⋊D59—22no—
44C22×Dic59—22no—
45#11745689—42no—
46Q8×D59—42no—
47C2×D236—21no—
48C2×D236C2311yescharacteristic
49C2×C4×D59—21no—
50C2×C4×D59—21no—
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53C2×Dic118C2311yescharacteristic
54SD16×C59—42no—
55SD16×C59—42no—
56C2×C8×C59C2312yes—
57C4⋊C4×C59—22no—
58C42×C59C2311yescharacteristic
59C22⋊Dic59—22no—
60C22⋊Dic59—22no—
61#11745670—42no—
62#11745669—42no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4D412yes—
66C4⋊Dic59C2312yes—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4D412yes—
70C4×Dic59C2311yescharacteristic
71C2×C59⋊C8C2312yes—
72C23×C59—22no—
73C22×D59—21no—
74C22×D59C2×D411yescharacteristic
75Q8×C59—22no—
76Q8×C59—22no—
77D4×C59—22no—
78D4×C59—22no—
79D4×C59—82no—
80C2×C4×C59—21no—
81C2×C4×C59—21no—
82C2×C4×C59C2×D412yes—
83C2×C4×C59C2411yescharacteristic
84C22⋊D59—82no—
85C2×Dic59—22no—
86C2×Dic59—21no—
87C2×Dic59—82no—
88C2×Dic59C2×D412yes—
89C2×Dic59C2×D411yescharacteristic
90D236—22no—
91D236—42no—
92C4×D59—22no—
93C4×D59—42no—
94C4×D59—42no—
95Dic118—22no—
96Dic118—42no—
97C8×C59—22no—
98C59⋊C8—22no—
99C22×C59—42no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59C22×D411yescharacteristic
103C2×D59—21no—
104C2×D59—22no—
105C2×D59—41no—
106C2×D59—42no—
107C4×C59—22no—
108C4×C59—41no—
109C4×C59—41no—
110C4×C59H(5,𝔽2)12yes—
111Dic59—21no—
112Dic59—22no—
113Dic59—41no—
114Dic59—42no—
115#3221—591nomaximal, Sylow
116C2×C59—82no—
117C2×C59#53511yescharacteristic
118C2×C59#57712yes—
119D59—41no—
120D59—81no—
121#540—591no—
122#536—591no—
123#496—591no—
124#492D5911yescharacteristic, complemented
125#491—591no—
126#488—591no—
127#463—592no—
128#461—592no—
129#449—592no—
130#448—592no—
131#433—591no—
132C59#322111yescharacteristic, complemented, Sylow
133C2×#41—591no—
134C22×Q8—591no—
135C2×SD16—592no—
136C2×SD16C2×D5912yes—
137C2×SD16C2×D5912yes—
138C2×D8—592no—
139C4⋊Q8—591no—
140C4⋊Q8C2×D5911yescharacteristic
141#127C2×D5911yescharacteristic
142#125—591no—
143#124—591no—
144#124—591no—
145#123—1182no—
146#123—1182no—
147C22⋊Q8—1182no—
148#121—592no—
149#121—1182no—
150C4×D4—592no—
151#117—591no—
152C4⋊C8—592no—
153#103—592no—
154#103—592no—
155#103—592no—
156#102—592no—
157C22⋊C8—592no—
158#97—591no—
159C4×C8C2×D5911yescharacteristic
160#41—2362no—
161C2×Q8—591no—
162C2×Q8—1181no—
163C2×Q8—2362no—
164C2×Q8C22×D5911yescharacteristic
165C2×Q8C22×D5911yescharacteristic
166C2×D4—22no—
167C2×D4—591no—
168C2×D4—1181no—
169C2×D4—1182no—
170C2×D4C22×D5912yes—
171C22×C4—591no—
172C22×C4—1181no—
173C22×C4—1181no—
174C22×C4—1182no—
175SD16—42no—
176SD16—42no—
177SD16—2362no—
178D8—2362no—
179C2×C8—592no—
180C2×C8C22×D5912yes—
181C4⋊C4—22no—
182C4⋊C4—592no—
183C4⋊C4—592no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C22⋊C4—592no—
187C22⋊C4—1182no—
188C22⋊C4—1182no—
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C42—591no—
192C42C22×D5911yescharacteristic
193C23—22no—
194C23—591no—
195C23—1181no—
196Q8—22no—
197Q8—22no—
198Q8—1182no—
199Q8—2362no—
200D4—22no—
201D4—22no—
202D4—82no—
203D4—1182no—
204D4—4722no—
205D4—2362no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—592no—
209C2×C4—591no—
210C2×C4—1182no—
211C2×C4—1182no—
212C2×C4—1181no—
213C2×C4—4722no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4D4×D5912yes—
217C2×C4C23×D5911yescharacteristic
218C8—22no—
219C8—1182no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—1182no—
224C22—1181no—
225C22—2362no—
226C22—2361no—
227C22C2×D4×D5911yescharacteristic
228C4—22no—
229C4—41no—
230C4—41no—
231C4—1182no—
232C4—1181no—
233C4—2362no—
234C4—2361no—
235C4#1427377212yes—
236C2—82no—
237C2—4721no—
238C2—2361no—
239C2#1683796511yescharacteristic
240C2#1683820812yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#492C2
socleC22×C59C22×D4
hypercenter#492D59
hypocenterC59#3221
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16838006C2semidirect
2. #16837977C2semidirect
3. #16837789C2semidirect
4. #16837770C2semidirect
5. #16837757C2semidirect
6. #16837619C2semidirect
7. #16837605C2semidirect
8. #16837546C2semidirect
9. #16837539C2semidirect
10. #16837461C2semidirect
11. C59×#492C2semidirect
124. #492D59semidirect
132. C59#3221semidirect