Finite Group Databasebeta

← #21435232

Subgroups — #21435232

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#16837952C211yesmaximal, characteristic
2#16837805C211yesmaximal, characteristic, complemented
3#16837798C211yesmaximal, characteristic, complemented
4#16837750C211yesmaximal, characteristic, complemented
5#16837750C211yesmaximal, characteristic, complemented
6#16837726C214yesmaximal, complemented
7#16837699C214yesmaximal, complemented
8#16837455C211yesmaximal, characteristic, complemented
9C59×#533C211yesmaximal, characteristic, complemented
10C2×#11745685—21no—
11#14273727C2211yescharacteristic
12#14273724C2211yescharacteristic
13#14273715—21no—
14#14273701—21no—
15#14273701C2212yes—
16C4×D236—21no—
17C4×D236C2212yes—
18#14273660C2214yes—
19#14273658C2214yes—
20C4⋊(C59⋊C8)C2212yes—
21#14273647C2214yes—
22#14273647C2214yes—
23C22⋊(C59⋊C8)C2212yes—
24C4×C59⋊C8C2211yescharacteristic
25C4×C59⋊C8C2211yescharacteristic
26C4⋊Q8×C59C2211yescharacteristic
27C4⋊Q8×C59C2211yescharacteristic
28#125×C59C2212yes—
29C22⋊Q8×C59—21no—
30C22⋊Q8×C59—21no—
31C4×Q8×C59—21no—
32C4×Q8×C59—21no—
33#117×C59C2212yes—
34C2×C42×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59—21no—
37C22×C4×C59D411yescharacteristic
38C22×C4×C59D411yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—22no—
41#11745685—44no—
42C2×D236—21no—
43C2×D236—21no—
44C2×D236C2312yes—
45C2×C4×D59—22no—
46C2×Dic118—21no—
47C4⋊C4×C59—22no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59—21no—
51C4⋊C4×C59C2312yes—
52C4⋊C4×C59C2312yes—
53C22⋊C4×C59—22no—
54C42×C59—22no—
55C42×C59D411yescharacteristic
56C42×C59D411yescharacteristic
57C42×C59C2311yescharacteristic
58C42×C59C2311yescharacteristic
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61C4⋊Dic59—21no—
62C4⋊Dic59C2312yes—
63C2×C59⋊C8C2312yes—
64C2×C59⋊C8C2312yes—
65C23×C59C2×D411yescharacteristic
66C22×D59—22no—
67Q8×C59—42no—
68Q8×C59—42no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2411yescharacteristic
80C22⋊D59—44no—
81C2×Dic59—22no—
82D236—24no—
83D236—42no—
84D236—42no—
85C4×D59—44no—
86Dic118—42no—
87C59⋊C8—22no—
88C59⋊C8—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—42no—
100C4×C59—42no—
101C4×C59#13512yes—
102C4×C59AGL(1,ℤ/8)12yes—
103C4×C592−1+412yes—
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#533D5911yescharacteristic, complemented
112#532—591no—
113#500—591no—
114#498—591no—
115#486—591no—
116#486—591no—
117#482—594no—
118#478—594no—
119#431—591no—
120C59#322811yescharacteristic, complemented, Sylow
121C2×#41—1181no—
122C4⋊Q8—591no—
123C4⋊Q8C2×D5911yescharacteristic
124C4⋊Q8C2×D5911yescharacteristic
125#127—591no—
126#125C2×D5912yes—
127#124—1181no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130#121—592no—
131#121—1181no—
132C4×Q8—21no—
133C4×Q8—21no—
134C4×D4—592no—
135C4×D4—1181no—
136#117C2×D5912yes—
137C2×C42C2×D5911yescharacteristic
138#107—594no—
139#106—594no—
140C4⋊C8—592no—
141#102—594no—
142#102—594no—
143C22⋊C8—592no—
144C4×C8—591no—
145C4×C8—591no—
146#41—2364no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—1181no—
150C2×D4—592no—
151C2×D4—1182no—
152C2×D4—1181no—
153C2×D4—1181no—
154C22×C4—1182no—
155C22×C4C22⋊D5911yescharacteristic
156C22×C4C22⋊D5911yescharacteristic
157C22×C4C22×D5911yescharacteristic
158C2×C8—592no—
159C2×C8—592no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—592no—
165C4⋊C4—1181no—
166C4⋊C4C22×D5912yes—
167C4⋊C4C22×D5912yes—
168C22⋊C4—22no—
169C22⋊C4—1182no—
170C22⋊C4—1182no—
171C42—22no—
172C42C22⋊D5911yescharacteristic
173C42C22⋊D5911yescharacteristic
174C42C22×D5911yescharacteristic
175C42C22×D5911yescharacteristic
176C23—1182no—
177C23C2×C22⋊D5911yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—2362no—
181D4—1184no—
182D4—2364no—
183D4—2362no—
184D4—2362no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1182no—
191C2×C4—2364no—
192C2×C4C2×C22⋊D5911yescharacteristic
193C2×C4C2×C22⋊D5911yescharacteristic
194C2×C4C2×C22⋊D5911yescharacteristic
195C2×C4C2×C22⋊D5911yescharacteristic
196C2×C4C2×C22⋊D5911yescharacteristic
197C2×C4C23×D5911yescharacteristic
198C8—1182no—
199C8—1182no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22C22×C22⋊D5911yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—2362no—
213C4#1427374712yes—
214C4#1427375212yes—
215C4#1427377512yes—
216C2—41no—
217C2—4722no—
218C2#1683797611yescharacteristic
219C2C2×#1427374711yescharacteristic
220C2C2×#1427375211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#533C2
socleC22×C59C22×D4
hypercenter#533D59
hypocenterC59#3228
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16837805C2semidirect
3. #16837798C2semidirect
4. #16837750C2semidirect
5. #16837750C2semidirect
6. #16837726C2semidirect
7. #16837699C2semidirect
8. #16837455C2semidirect
9. C59×#533C2semidirect
111. #533D59semidirect
120. C59#3228semidirect