Finite Group Databasebeta

← #21435234

Subgroups — #21435234

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#16837959C211yesmaximal, characteristic, complemented
2#16837952C211yesmaximal, characteristic
3#16837807C211yesmaximal, characteristic, complemented
4#16837800C211yesmaximal, characteristic, complemented
5#16837749C211yesmaximal, characteristic, complemented
6#16837749C211yesmaximal, characteristic, complemented
7#16837727C214yesmaximal, complemented
8#16837703C214yesmaximal, complemented
9C59×#431C211yesmaximal, characteristic, complemented
10C2×#11745685—21no—
11#14273727C2211yescharacteristic
12#14273727C2211yescharacteristic
13#14273727C2211yescharacteristic
14#14273724C2211yescharacteristic
15#14273719C2212yes—
16#14273715—21no—
17#14273706—21no—
18#14273706—21no—
19#14273701—21no—
20#14273701C2212yes—
21C4×Dic118—21no—
22C4×Dic118—21no—
23C4×D236—21no—
24C4×D236C2212yes—
25#14273686C2212yes—
26#14273661C2214yes—
27#14273659C2214yes—
28#14273649C2214yes—
29#14273649C2214yes—
30C2×C42×C59C2211yescharacteristic
31C4⋊C8×C59C2212yes—
32C22⋊C8×C59C2212yes—
33C4×C8×C59C2211yescharacteristic
34C4×C8×C59C2211yescharacteristic
35C22×C4×C59D411yescharacteristic
36C22×C4×C59D411yescharacteristic
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—22no—
39#11745685—44no—
40C2×D236—21no—
41C2×D236—21no—
42C2×D236C2312yes—
43C2×C4×D59—22no—
44C2×Dic118—21no—
45C2×Dic118—21no—
46C2×Dic118—21no—
47C2×C8×C59C2312yes—
48C2×C8×C59C2312yes—
49C42×C59D411yescharacteristic
50C42×C59D411yescharacteristic
51C42×C59C2311yescharacteristic
52C42×C59C2311yescharacteristic
53C22⋊Dic59—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56C4⋊Dic59—21no—
57C4⋊Dic59—21no—
58C4⋊Dic59—21no—
59C4⋊Dic59C2312yes—
60C4⋊Dic59C2312yes—
61C4⋊Dic59C2312yes—
62Dic59⋊C4—22no—
63Dic59⋊C4—22no—
64C4×Dic59—22no—
65C23×C59C2×D411yescharacteristic
66C22×D59—22no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2411yescharacteristic
76C22⋊D59—44no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—22no—
80D236—24no—
81D236—42no—
82D236—42no—
83C4×D59—44no—
84Dic118—42no—
85Dic118—42no—
86Dic118—42no—
87C8×C59—22no—
88C8×C59—22no—
89C22×C59—21no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59C22×D411yescharacteristic
93C2×D59—42no—
94C2×D59—42no—
95C2×D59—42no—
96C4×C59—21no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59#13512yes—
100C4×C59AGL(1,ℤ/8)12yes—
101C4×C592−1+412yes—
102Dic59—42no—
103Dic59—42no—
104Dic59—42no—
105#3228—591nomaximal, Sylow
106C2×C59—41no—
107C2×C59#53611yescharacteristic
108C2×C59C2×#13511yescharacteristic
109C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
110D59—82no—
111#533—591no—
112#532—591no—
113#500—591no—
114#498—591no—
115#486—591no—
116#486—591no—
117#482—594no—
118#478—594no—
119#431D5911yescharacteristic, complemented
120C59#322811yescharacteristic, complemented, Sylow
121C2×#41—1181no—
122C4⋊Q8—591no—
123C4⋊Q8—591no—
124C4⋊Q8—591no—
125#127—591no—
126#125—592no—
127#124—1181no—
128C22⋊Q8—1181no—
129C22⋊Q8—1181no—
130#121—592no—
131#121—1181no—
132C4×Q8—1181no—
133C4×Q8—1181no—
134C4×D4—592no—
135C4×D4—1181no—
136#117—592no—
137C2×C42C2×D5911yescharacteristic
138#107—594no—
139#106—594no—
140C4⋊C8C2×D5912yes—
141#102—594no—
142#102—594no—
143C22⋊C8C2×D5912yes—
144C4×C8C2×D5911yescharacteristic
145C4×C8C2×D5911yescharacteristic
146#41—2364no—
147C2×Q8—1181no—
148C2×Q8—1181no—
149C2×Q8—1181no—
150C2×D4—592no—
151C2×D4—1182no—
152C2×D4—1181no—
153C2×D4—1181no—
154C22×C4—1182no—
155C22×C4D23611yescharacteristic
156C22×C4D23611yescharacteristic
157C22×C4C22×D5911yescharacteristic
158C2×C8C22×D5912yes—
159C2×C8C22×D5912yes—
160C4⋊C4—592no—
161C4⋊C4—592no—
162C4⋊C4—592no—
163C4⋊C4—1181no—
164C4⋊C4—1182no—
165C4⋊C4—1182no—
166C4⋊C4—1181no—
167C4⋊C4—1181no—
168C22⋊C4—1182no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C42—1182no—
172C42D23611yescharacteristic
173C42D23611yescharacteristic
174C42C22×D5911yescharacteristic
175C42C22×D5911yescharacteristic
176C23—1182no—
177C23C2×D23611yescharacteristic
178Q8—2362no—
179Q8—2362no—
180Q8—2362no—
181D4—1184no—
182D4—2364no—
183D4—2362no—
184D4—2362no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—1182no—
189C2×C4—1182no—
190C2×C4—1182no—
191C2×C4—2364no—
192C2×C4C2×D23611yescharacteristic
193C2×C4C2×D23611yescharacteristic
194C2×C4C2×D23611yescharacteristic
195C2×C4C2×D23611yescharacteristic
196C2×C4C2×D23611yescharacteristic
197C2×C4C23×D5911yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22C22×D23611yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—2362no—
211C4—2362no—
212C4—2362no—
213C4#1427374912yes—
214C4#1427375512yes—
215C4#1427377412yes—
216C2—41no—
217C2—4722no—
218C2#1683797811yescharacteristic
219C2C2×#1427374911yescharacteristic
220C2C2×#1427375511yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#431C2
socleC22×C59C22×D4
hypercenter#431D59
hypocenterC59#3228
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16837959C2semidirect
3. #16837807C2semidirect
4. #16837800C2semidirect
5. #16837749C2semidirect
6. #16837749C2semidirect
7. #16837727C2semidirect
8. #16837703C2semidirect
9. C59×#431C2semidirect
119. #431D59semidirect
120. C59#3228semidirect