Finite Group Databasebeta

← #21435152

Subgroups — #21435152

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#16837972C211yesmaximal, characteristic, complemented
3#16837774C211yesmaximal, characteristic, complemented
4#16837771C211yesmaximal, characteristic, complemented
5#16837756C211yesmaximal, characteristic, complemented
6#16837615C212yesmaximal, complemented
7#16837605C212yesmaximal, complemented
8#16837544C212yesmaximal, complemented
9#16837539C212yesmaximal, complemented
10#16837464C211yesmaximal, characteristic, complemented
11C59×#496C211yesmaximal, characteristic, complemented
12C2×#11745687C2211yescharacteristic
13C2×Q8×D59C2211yescharacteristic
14C2×#11745670C2212yes—
15C2×#11745670C2212yes—
16#14273727C2211yescharacteristic
17#14273725C2211yescharacteristic
18#14273719C2211yescharacteristic
19#14273714C2211yescharacteristic
20#14273709—22no—
21#14273708—22no—
22#14273704—22no—
23#14273699—22no—
24#14273698C2212yes—
25D4×Dic59C2212yes—
26#14273684C2211yescharacteristic
27Dic59⋊C8C2212yes—
28#14273652C2212yes—
29#14273652C2212yes—
30#14273651C2212yes—
31#14273648C2212yes—
32(C2×D59)⋊C8C2212yes—
33C4×C59⋊C8C2211yescharacteristic
34C2×SD16×C59C2212yes—
35C2×D8×C59C2212yes—
36#127×C59C2211yescharacteristic
37#124×C59C2211yescharacteristic
38#97×C59C2211yescharacteristic
39C2×Q8×C59C2311yescharacteristic
40C2×D4×C59—22no—
41C2×D4×C59C2311yescharacteristic
42C2×D4×C59C2312yes—
43C2×C22⋊D59—21no—
44C2×C22⋊D59—22no—
45C22×Dic59—21no—
46C22×Dic59—22no—
47Q8×D59—42no—
48#11745687—42no—
49C2×C4×D59—21no—
50C2×C4×D59C2311yescharacteristic
51C2×Dic118—21no—
52C2×Dic118C2311yescharacteristic
53C2×Dic118C2311yescharacteristic
54SD16×C59—42no—
55D8×C59—42no—
56C2×C8×C59C2312yes—
57C22⋊C4×C59—22no—
58C42×C59C2311yescharacteristic
59C22⋊Dic59—22no—
60C22⋊Dic59—22no—
61C22⋊Dic59—22no—
62#11745670—42no—
63#11745670—42no—
64(C2×D59)⋊C4D412yes—
65C4⋊Dic59—22no—
66C4⋊Dic59C2312yes—
67Dic59⋊C4—22no—
68Dic59⋊C4—22no—
69Dic59⋊C4D412yes—
70C4×Dic59C2311yescharacteristic
71C2×C59⋊C8C2312yes—
72C23×C59—21no—
73C23×C59—22no—
74C22×D59C2×D411yescharacteristic
75Q8×C59—22no—
76D4×C59—22no—
77D4×C59—22no—
78D4×C59—22no—
79D4×C59—82no—
80C2×C4×C59—21no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2411yescharacteristic
83C22⋊D59—42no—
84C22⋊D59—82no—
85C2×Dic59—21no—
86C2×Dic59—22no—
87C2×Dic59—21no—
88C2×Dic59—42no—
89C2×Dic59—82no—
90C2×Dic59C2×D412yes—
91C2×Dic59C2×D411yescharacteristic
92C4×D59—22no—
93C4×D59—42no—
94Dic118—22no—
95Dic118—22no—
96Dic118—42no—
97C8×C59—22no—
98C59⋊C8—22no—
99C22×C59—41no—
100C22×C59—42no—
101C22×C59—42no—
102C22×C59—42no—
103C22×C59—42no—
104C22×C59C22×D411yescharacteristic
105C2×D59—21no—
106C2×D59—22no—
107C4×C59—22no—
108C4×C59—41no—
109C4×C59H(5,𝔽2)12yes—
110Dic59—21no—
111Dic59—22no—
112Dic59—41no—
113Dic59—41no—
114Dic59—42no—
115#3221—591nomaximal, Sylow
116C2×C59—81no—
117C2×C59—82no—
118C2×C59#53511yescharacteristic
119C2×C59#57712yes—
120D59—41no—
121#540—591no—
122#536—591no—
123#496D5911yescharacteristic, complemented
124#492—591no—
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×SD16—592no—
137C2×SD16C2×D5912yes—
138C2×D8C2×D5912yes—
139C4⋊Q8—591no—
140C4⋊Q8—591no—
141#127C2×D5911yescharacteristic
142#125—591no—
143#124—591no—
144#124C2×D5911yescharacteristic
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#97C2×D5911yescharacteristic
159C4×C8—591no—
160#41—2362no—
161C2×Q8—591no—
162C2×Q8—591no—
163C2×Q8—1181no—
164C2×Q8—2362no—
165C2×Q8C22×D5911yescharacteristic
166C2×D4—22no—
167C2×D4—1182no—
168C2×D4—1181no—
169C2×D4C22×D5911yescharacteristic
170C2×D4C22×D5912yes—
171C22×C4—591no—
172C22×C4—1181no—
173C22×C4—1182no—
174C22×C4—1181no—
175SD16—42no—
176SD16—2362no—
177SD16—2362no—
178D8—42no—
179C2×C8—592no—
180C2×C8C22×D5912yes—
181C4⋊C4—592no—
182C4⋊C4—592no—
183C4⋊C4—1182no—
184C4⋊C4—1182no—
185C4⋊C4—1182no—
186C22⋊C4—22no—
187C22⋊C4—592no—
188C22⋊C4—1182no—
189C22⋊C4—1182no—
190C22⋊C4—1182no—
191C42—591no—
192C42C22×D5911yescharacteristic
193C23—21no—
194C23—22no—
195C23—591no—
196Q8—22no—
197Q8—1182no—
198Q8—1182no—
199Q8—2362no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—4722no—
205D4—2362no—
206C2×C4—21no—
207C2×C4—592no—
208C2×C4—591no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—1181no—
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—41no—
224C22—42no—
225C22—1182no—
226C22—1181no—
227C22C2×D4×D5911yescharacteristic
228C4—22no—
229C4—41no—
230C4—1182no—
231C4—1181no—
232C4—2362no—
233C4—2361no—
234C4—2361no—
235C4#1427377212yes—
236C2—82no—
237C2—81no—
238C2—2361no—
239C2#1683796511yescharacteristic
240C2#1683821212yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#496C2
socleC22×C59C22×D4
hypercenter#496D59
hypocenterC59#3221
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16838006C2semidirect
2. #16837972C2semidirect
3. #16837774C2semidirect
4. #16837771C2semidirect
5. #16837756C2semidirect
6. #16837615C2semidirect
7. #16837605C2semidirect
8. #16837544C2semidirect
9. #16837539C2semidirect
10. #16837464C2semidirect
11. C59×#496C2semidirect
123. #496D59semidirect
132. C59#3221semidirect