Finite Group Databasebeta

← #21436733

Subgroups — #21436733

Order 7552.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#16838127C211yesmaximal, characteristic, complemented
2D4×Dic118C211yesmaximal, characteristic
3#16837752C211yesmaximal, characteristic, complemented
4#16837751C212yesmaximal, complemented
5#16837688C211yesmaximal, characteristic, complemented
6#16837685C212yesmaximal, complemented
7#16837605C212yesmaximal
8#16837526C211yesmaximal, characteristic, complemented
9SD16×Dic59C212yesmaximal
10C4×#11745670C211yesmaximal, characteristic
11C59×#461C211yesmaximal, characteristic
12C22×Dic118—21no—
13C2×#11745670C2211yescharacteristic
14#14273727C2211yescharacteristic
15#14273726C2212yes—
16#14273725C2212yes—
17#14273718—21no—
18#14273717—22no—
19#14273706—21no—
20#14273704—22no—
21Q8×Dic59C2212yes—
22C4×Dic118C2211yescharacteristic
23C4×Dic118C2211yescharacteristic
24#14273692—21no—
25D4×Dic59C2212yes—
26#14273659C2212yes—
27#14273658C2211yescharacteristic
28Dic59⋊C8C2212yes—
29#14273652C2212yes—
30#14273651C2212yes—
31#14273651C2212yes—
32#14273650C2211yescharacteristic
33#14273648C2211yescharacteristic
34C4×C59⋊C8C2211yescharacteristic
35C8×Dic59C2212yes—
36C2×SD16×C59C2212yes—
37C4⋊Q8×C59C2211yescharacteristic
38C4×D4×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59C2312yes—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C22×Dic59—22no—
45C2×Dic118—21no—
46C2×Dic118—22no—
47C2×Dic118—44no—
48C2×Dic118D411yescharacteristic
49C2×Dic118C2311yescharacteristic
50SD16×C59—24no—
51C2×C8×C59C2312yes—
52C4⋊C4×C59—21no—
53C4⋊C4×C59—21no—
54C4⋊C4×C59C2311yescharacteristic
55C22⋊C4×C59—21no—
56C42×C59C2311yescharacteristic
57C22⋊Dic59—22no—
58#11745670—22no—
59C4⋊Dic59—21no—
60C4⋊Dic59—22no—
61C4⋊Dic59D411yescharacteristic
62C4⋊Dic59C2311yescharacteristic
63C4⋊Dic59C2312yes—
64Dic59⋊C4—21no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67Dic59⋊C4—22no—
68Dic59⋊C4D412yes—
69C4×Dic59—21no—
70C4×Dic59—22no—
71C4×Dic59C2312yes—
72C2×C59⋊C8C2311yescharacteristic
73C2×C59⋊C8C2311yescharacteristic
74C23×C59—21no—
75Q8×C59—22no—
76Q8×C59—22no—
77D4×C59—21no—
78D4×C59#4112yes—
79C2×C4×C59—22no—
80C2×C4×C59—21no—
81C2×C4×C59—42no—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C2×Dic59—21no—
86C2×Dic59—21no—
87C2×Dic59—22no—
88C2×Dic59—44no—
89C2×Dic59C2×D412yes—
90C2×Dic59C2×D412yes—
91Dic118—21no—
92Dic118—21no—
93Dic118—42no—
94Dic118—44no—
95Dic118SD1614yescomplemented
96C8×C59—22no—
97C59⋊C8—21no—
98C59⋊C8—21no—
99C22×C59—22no—
100C22×C59—41no—
101C22×C59—41no—
102C22×C59C22×D411yescharacteristic
103C4×C59—21no—
104C4×C59—42no—
105C4×C59—41no—
106C4×C59C2×SD1612yes—
107C4×C59C2×#4111yescharacteristic
108C4×C592−1+411yescharacteristic
109Dic59—22no—
110Dic59—41no—
111Dic59—42no—
112Dic59—41no—
113Dic59C2×SD1614yes—
114#3359—591nomaximal, Sylow
115C2×C59—42no—
116C2×C59#54811yescharacteristic
117C2×C59C22×SD1611yescharacteristic
118C2×C59#57811yescharacteristic
119#557—591no—
120D4×Q8—591no—
121#487—591no—
122#487—592no—
123#475—591no—
124#475—592no—
125#461—592no—
126#461D5911yescharacteristic
127C8×Q8—591no—
128C4×SD16—592no—
129C4×SD16—591no—
130C59#335911yescharacteristic, complemented, Sylow
131C22×Q8—1181no—
132C2×SD16—591no—
133C2×SD16C2×D5912yes—
134C4⋊Q8—592no—
135C4⋊Q8—592no—
136C4⋊Q8—591no—
137C4⋊Q8C2×D5911yescharacteristic
138#125—1182no—
139#125—1181no—
140C22⋊Q8—1182no—
141C22⋊Q8—1181no—
142C4×Q8—591no—
143C4×Q8—592no—
144C4×Q8—591no—
145C4×Q8—1181no—
146C4×D4—592no—
147C4×D4C2×D5911yescharacteristic
148#106—592no—
149#106—591no—
150C4⋊C8—592no—
151C4⋊C8C2×D5911yescharacteristic
152#103—592no—
153#103—592no—
154#103—592no—
155#103—591no—
156#103C2×D5912yes—
157#102—591no—
158C4×C8—592no—
159C4×C8—591no—
160C2×Q8—591no—
161C2×Q8—591no—
162C2×Q8—1182no—
163C2×Q8—1181no—
164C2×Q8—2364no—
165C2×Q8C22×D5912yes—
166C2×D4C22×D5911yescharacteristic
167C22×C4—21no—
168C22×C4—1182no—
169SD16—24no—
170SD16—1182no—
171C2×C8—591no—
172C2×C8—591no—
173C2×C8C22×D5912yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—592no—
177C4⋊C4—591no—
178C4⋊C4—591no—
179C4⋊C4—592no—
180C4⋊C4—1182no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C4⋊C4—1181no—
185C4⋊C4—1181no—
186C4⋊C4C22×D5911yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1182no—
189C42—592no—
190C42—1182no—
191C42—1181no—
192C42C22×D5911yescharacteristic
193C23—21no—
194Q8—22no—
195Q8—22no—
196Q8—594no—
197Q8—1181no—
198Q8—1181no—
199Q8—2364no—
200Q8—2362no—
201D4—21no—
202D4#1174568712yes—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—592no—
207C2×C4—592no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1182no—
211C2×C4—2364no—
212C2×C4D4×D5911yescharacteristic
213C2×C4D4×D5911yescharacteristic
214C2×C4C23×D5911yescharacteristic
215C8—22no—
216C8—1181no—
217C8—1181no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22C2×D4×D5911yescharacteristic
222C4—21no—
223C4—41no—
224C4—42no—
225C4—594no—
226C4—1182no—
227C4—2362no—
228C4—2361no—
229C4—2361no—
230C4SD16×D5912yes—
231C4C2×#1174568711yescharacteristic
232C4#1427377411yescharacteristic
233C2—42no—
234C2#1683805811yescharacteristic
235C2C2×SD16×D5911yescharacteristic
236C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3359
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16838127C2semidirect
3. #16837752C2semidirect
4. #16837751C2semidirect
5. #16837688C2semidirect
6. #16837685C2semidirect
8. #16837526C2semidirect
95. Dic118SD16semidirect
130. C59#3359semidirect