Finite Group Databasebeta

← #21435301

Subgroups — #21435301

Order 7552.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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#16837954C211yesmaximal, characteristic
2C2×#14273718C211yesmaximal, characteristic
3#16837810C212yesmaximal, complemented
4#16837769C212yesmaximal, complemented
5#16837737C211yesmaximal, characteristic
6#16837733C211yesmaximal, characteristic
7#16837730C211yesmaximal, characteristic
8#16837708C212yesmaximal, complemented
9#16837707C212yesmaximal, complemented
10#16837456C211yesmaximal, characteristic
11C59×#484C211yesmaximal, characteristic
12#14273726C2211yescharacteristic
13#14273725C2211yescharacteristic
14#14273718—21no—
15#14273718—21no—
16#14273718C2212yes—
17#14273718C2212yes—
18#14273717—21no—
19#14273706C2211yescharacteristic
20#14273704—21no—
21Q8×Dic59C2211yescharacteristic
22#14273692—21no—
23#14273692C2211yescharacteristic
24#14273683—21no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2211yescharacteristic
27C2×Dic59⋊C4—21no—
28C2×C4×Dic59C2211yescharacteristic
29#14273660C2212yes—
30#14273659C2212yes—
31#14273658C2212yes—
32Dic59⋊C8C2212yes—
33#14273652C2212yes—
34#14273651C2212yes—
35#14273650C2212yes—
36C22⋊(C59⋊C8)C2211yescharacteristic
37#14273637C2212yes—
38C22⋊Q8×C59C2211yescharacteristic
39C2×C4⋊C4×C59C2211yescharacteristic
40#107×C59C2212yes—
41#103×C59C2212yes—
42C22⋊C8×C59C2211yescharacteristic
43C2×Q8×C59C2311yescharacteristic
44C22×C4×C59—21no—
45C22×C4×C59C2311yescharacteristic
46C22×Dic59—21no—
47C22×Dic59D411yescharacteristic
48C22×Dic59D411yescharacteristic
49C2×Dic118—21no—
50C2×Dic118C2311yescharacteristic
51C2×C8×C59C2312yes—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2312yes—
55C4⋊C4×C59C2311yescharacteristic
56C22⋊C4×C59—21no—
57C22⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59—22no—
60C4⋊Dic59—22no—
61C4⋊Dic59—21no—
62C4⋊Dic59C2312yes—
63C4⋊Dic59C2311yescharacteristic
64Dic59⋊C4—21no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4—21no—
68Dic59⋊C4—21no—
69Dic59⋊C4—21no—
70Dic59⋊C4—21no—
71C4×Dic59—21no—
72C4×Dic59—21no—
73C4×Dic59D411yescharacteristic
74C4×Dic59D411yescharacteristic
75C4×Dic59C2311yescharacteristic
76C4×Dic59C2311yescharacteristic
77C2×C59⋊C8C2312yes—
78C23×C59C2×D411yescharacteristic
79Q8×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—42no—
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C2×Dic59—22no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—22no—
91C2×Dic59—41no—
92C2×Dic59—42no—
93C2×Dic59C2×D411yescharacteristic
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97Dic118—22no—
98Dic118—42no—
99C8×C59—22no—
100C59⋊C8—22no—
101C22×C59—21no—
102C22×C59—21no—
103C22×C59#13712yes—
104C22×C59C22×D411yescharacteristic
105C4×C59—21no—
106C4×C59—41no—
107C4×C59—41no—
108C4×C59—42no—
109C4×C592−1+412yes—
110Dic59—21no—
111Dic59—21no—
112Dic59—21no—
113Dic59—21no—
114Dic59—41no—
115Dic59—42no—
116Dic59—41no—
117#3236—591nomaximal, Sylow
118C2×C59—22no—
119C2×C59#53611yescharacteristic
120C2×C59C2×#13711yescharacteristic
121C2×C59#57511yescharacteristic
122#533—591no—
123C2×#125—591no—
124#501—592no—
125#491—592no—
126#484—591no—
127#484D5911yescharacteristic
128#483—591no—
129#483—591no—
130#479—592no—
131#479—592no—
132#432—591no—
133C59#323611yescharacteristic, complemented, Sylow
134C4⋊Q8—591no—
135C4⋊Q8—591no—
136#125—592no—
137#125—592no—
138#125—1181no—
139#125—1181no—
140#125—1181no—
141C22⋊Q8—591no—
142C22⋊Q8—1181no—
143C22⋊Q8C2×D5911yescharacteristic
144C4×Q8—591no—
145C4×Q8—591no—
146C4×Q8—1181no—
147#117—1181no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4—1181no—
150C2×C4⋊C4—1181no—
151C2×C4⋊C4C2×D5911yescharacteristic
152C2×C42—591no—
153#107—592no—
154#107C2×D5912yes—
155#106—592no—
156#106—592no—
157C4⋊C8—592no—
158#103—592no—
159#103—592no—
160#103—592no—
161#103C2×D5912yes—
162C22⋊C8—591no—
163C22⋊C8C2×D5911yescharacteristic
164#97—592no—
165C2×Q8—591no—
166C2×Q8—1181no—
167C2×Q8C22×D5911yescharacteristic
168C22×C4—21no—
169C22×C4—591no—
170C22×C4—591no—
171C22×C4—1181no—
172C22×C4C22×D5911yescharacteristic
173C2×C8—592no—
174C2×C8C22×D5912yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—592no—
178C4⋊C4—591no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4—1181no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4—1181no—
187C4⋊C4—1181no—
188C4⋊C4—1181no—
189C4⋊C4—1181no—
190C4⋊C4C22×D5912yes—
191C4⋊C4C22×D5911yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—1181no—
194C42—591no—
195C42—591no—
196C42—591no—
197C42—591no—
198C42—1181no—
199C42—1181no—
200C23D4×D5911yescharacteristic
201Q8—22no—
202Q8—1182no—
203Q8—2362no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—591no—
210C2×C4—591no—
211C2×C4—591no—
212C2×C4—591no—
213C2×C4—1182no—
214C2×C4—1181no—
215C2×C4—1181no—
216C2×C4—1182no—
217C2×C4—2361no—
218C2×C4—2362no—
219C2×C4D4×D5911yescharacteristic
220C2×C4C23×D5911yescharacteristic
221C8—22no—
222C8—1182no—
223C22—21no—
224C22—21no—
225C22#1427375912yes—
226C22C2×D4×D5911yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—1181no—
232C4—1181no—
233C4—1181no—
234C4—1181no—
235C4—2362no—
236C4—2361no—
237C4—2361no—
238C4#1427377412yes—
239C2—22no—
240C2#1683797411yescharacteristic
241C2C2×#1427375911yescharacteristic
242C2#1683819811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#484C2
socleC22×C59C22×D4
hypercenter#484D59
hypocenterC59#3236
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #16837810C2semidirect
4. #16837769C2semidirect
8. #16837708C2semidirect
9. #16837707C2semidirect
133. C59#3236semidirect