Finite Group Databasebeta

← #21425748

Subgroups — #21425748

Order 7552.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#16837974C211yesmaximal, characteristic
2#16837383C211yesmaximal, characteristic
3#16837374C211yesmaximal, characteristic
4#16837193C211yesmaximal, characteristic, complemented
5#16837192C211yesmaximal, characteristic, complemented
6#16837191C211yesmaximal, characteristic, complemented
7C59×#352C211yesmaximal, characteristic, complemented
8C2×#11745687C2211yescharacteristic
9C22×Dic118C411yescharacteristic, complemented
10M16×D59—21no—
11#14273726—21no—
12#14273713—21no—
13#14273711C411yescharacteristic, complemented
14#14273710C411yescharacteristic, complemented
15#14273708C2211yescharacteristic
16#14273705—21no—
17#14273704—21no—
18#14273683—21no—
19#14273683C411yescharacteristic, complemented
20#14273645—21no—
21#14273644C2211yescharacteristic
22#14273642C2211yescharacteristic
23#14273641—21no—
24#123×C59C2211yescharacteristic
25#100×C59C2211yescharacteristic
26#99×C59C2211yescharacteristic
27C2×D4×C59C2311yescharacteristic
28C22×C4×C59C2×C411yescharacteristic
29C2×C22⋊D59C2×C411yescharacteristic
30C2×C22⋊D59D411yescharacteristic
31C22×Dic59C2×C411yescharacteristic
32C22×Dic59C2×C411yescharacteristic
33C22×Dic59D411yescharacteristic
34#11745687—41no—
35#11745687—41no—
36C2×C4×D59D411yescharacteristic
37C2×Dic118—21no—
38C2×Dic118—21no—
39C2×Dic118—41no—
40C2×Dic118—41no—
41C2×Dic118D411yescharacteristic
42M16×C59—21no—
43C4⋊C4×C59—21no—
44C22⋊C4×C59—21no—
45C22⋊C4×C59—21no—
46C22⋊C4×C59C2×C411yescharacteristic
47C22⋊Dic59—21no—
48C22⋊Dic59—21no—
49C22⋊Dic59C2×C411yescharacteristic
50(C2×D59)⋊C4—21no—
51(C2×D59)⋊C4—21no—
52C4⋊Dic59—21no—
53Dic59⋊C4—21no—
54Dic59⋊C4—21no—
55Dic59⋊C4—21no—
56Dic59⋊C4—41no—
57C4×Dic59—21no—
58C4×Dic59—41no—
59#11745664—21no—
60#11745659—41no—
61C8×D59—41no—
62C23×C59C22×C411yescharacteristic
63C23×C59C2×D411yescharacteristic
64C22×D59C22⋊C411yescharacteristic
65D4×C59—41no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59C2×D411yescharacteristic
71C22⋊D59—41no—
72C22⋊D59—41no—
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59C22⋊C411yescharacteristic
82C2×Dic59C22⋊C411yescharacteristic
83C2×Dic59C22⋊C411yescharacteristic
84C4×D59—21no—
85C4×D59—21no—
86Dic118—41no—
87Dic118—42no—
88Dic118—41no—
89Dic118—41no—
90C8×C59—41no—
91C59⋊C8—41no—
92C22×C59—21no—
93C22×C59—21no—
94C22×C59—41no—
95C22×C59—41no—
96C22×C59C2×C22⋊C411yescharacteristic
97C2×D59—21no—
98C2×D59—41no—
99C4×C59—21no—
100C4×C59—41no—
101C4×C59—41no—
102C4×C59—81no—
103Dic59—21no—
104Dic59—21no—
105Dic59—41no—
106Dic59—41no—
107Dic59—81no—
108Dic59#9911yescharacteristic
109Dic59#9911yescharacteristic
110#2123—591nomaximal, Sylow
111C2×C59—21no—
112C2×C59—41no—
113C2×C59—41no—
114C2×C59C2×#9911yescharacteristic
115D59—41no—
116#536—591no—
117#413—591no—
118#410—591no—
119#352—591no—
120#352—591no—
121#352—591no—
122#352D5911yescharacteristic, complemented
123C59#212311yescharacteristic, complemented, Sylow
124C2×#41—591no—
125C22×Q8—591no—
126C2×M16—1181no—
127C4⋊Q8—1181no—
128#124—1181no—
129#123—591no—
130#123—591no—
131#123—591no—
132#123C2×D5911yescharacteristic
133C22⋊Q8—1181no—
134C22⋊Q8—1181no—
135#117—591no—
136#117—1181no—
137#101—1181no—
138#100—591no—
139#100C2×D5911yescharacteristic
140#99—591no—
141#99—1181no—
142#99C2×D5911yescharacteristic
143#41—2361no—
144#41—2361no—
145C2×Q8—591no—
146C2×Q8—1181no—
147C2×Q8—1181no—
148C2×Q8—2361no—
149C2×Q8—2361no—
150C2×D4—591no—
151C2×D4—591no—
152C2×D4C22×D5911yescharacteristic
153C22×C4—591no—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4C4×D5911yescharacteristic
158M16—21no—
159M16—1181no—
160M16—2361no—
161C2×C8—2361no—
162C4⋊C4—21no—
163C4⋊C4—1181no—
164C4⋊C4—1181no—
165C4⋊C4—1181no—
166C4⋊C4—1181no—
167C4⋊C4—2361no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—591no—
171C22⋊C4—1181no—
172C22⋊C4—1181no—
173C22⋊C4—1181no—
174C22⋊C4—1181no—
175C22⋊C4C4×D5911yescharacteristic
176C42—1181no—
177C42—2361no—
178C23—591no—
179C23C2×C4×D5911yescharacteristic
180C23D4×D5911yescharacteristic
181Q8—2361no—
182Q8—2361no—
183Q8—2361no—
184Q8—2362no—
185D4—41no—
186D4—2361no—
187D4—2361no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—591no—
193C2×C4—591no—
194C2×C4—591no—
195C2×C4—1181no—
196C2×C4—1181no—
197C2×C4—1181no—
198C2×C4—1181no—
199C2×C4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1181no—
203C2×C4—2361no—
204C2×C4—2361no—
205C2×C4D4×D5911yescharacteristic
206C8—41no—
207C8—2361no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—1181no—
213C22—2361no—
214C22C22⋊C4×D5911yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—591no—
220C4—591no—
221C4—1181no—
222C4—1181no—
223C4—4721no—
224C4—2361no—
225C4—2361no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—2361no—
230C2#99×D5911yescharacteristic
subgroupG/H
centerC2#99×D59
commutatorC23×C59C22×C4
FrattiniC2×D4C22×D59
FittingC59×#352C2
socleC2×C59C2×#99
hypercenter#352D59
hypocenterC59#2123
LCSG ▷ C23×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #16837193C2semidirect
5. #16837192C2semidirect
6. #16837191C2semidirect
7. C59×#352C2semidirect
9. C22×Dic118C4semidirect
13. #14273711C4semidirect
14. #14273710C4semidirect
19. #14273683C4semidirect
122. #352D59semidirect
123. C59#2123semidirect