Finite Group Databasebeta

← #21434817

Subgroups — #21434817

Order 7552.

402 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837957C211yesmaximal, characteristic, complemented
2#16837953C211yesmaximal, characteristic
3#16837805C211yesmaximal, characteristic, complemented
4#16837776C211yesmaximal, characteristic, complemented
5#16837749C211yesmaximal, characteristic, complemented
6#16837651C214yesmaximal, complemented
7#16837505C214yesmaximal, complemented
8C4×#11745659C211yesmaximal, characteristic, complemented
9C59×#487C211yesmaximal, characteristic, complemented
10C2×#11745689—21no—
11C2×#11745671C2214yes—
12C2×#11745659C2212yes—
13#14273727C2211yescharacteristic
14#14273724C2211yescharacteristic
15#14273718—21no—
16#14273716—21no—
17#14273707—21no—
18#14273703C2212yes—
19#14273702—21no—
20#14273702C2212yes—
21Q8×Dic59C2212yes—
22#14273692—21no—
23#14273689—21no—
24#14273689C2212yes—
25#14273685—21no—
26C42×D59C2211yescharacteristic
27#14273660C2214yes—
28#14273649C2214yes—
29#14273637C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37#11745689—44no—
38C2×D236—22no—
39C2×D236—21no—
40C2×D236—21no—
41C2×D236C2312yes—
42C2×C4×D59—22no—
43C2×C4×D59D411yescharacteristic
44C2×C4×D59D411yescharacteristic
45C2×C4×D59C2311yescharacteristic
46C2×Dic118—21no—
47C2×C8×C59C2312yes—
48C4⋊C4×C59—21no—
49C4⋊C4×C59—21no—
50C4⋊C4×C59—21no—
51C4⋊C4×C59C2312yes—
52C42×C59C2311yescharacteristic
53#11745671—28no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57C4⋊Dic59—21no—
58C4⋊Dic59—22no—
59C4⋊Dic59C2312yes—
60Dic59⋊C4—22no—
61C4×Dic59—22no—
62C4×Dic59D411yescharacteristic
63C4×Dic59D411yescharacteristic
64C4×Dic59C2311yescharacteristic
65C2×C59⋊C8C2312yes—
66#11745659—24no—
67C22×D59—22no—
68C22×D59C2×D411yescharacteristic
69Q8×C59—24no—
70Q8×C59—42no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59C2×D411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2411yescharacteristic
76C2×Dic59—22no—
77C2×Dic59C2×D411yescharacteristic
78C2×Dic59C2×D411yescharacteristic
79C2×Dic59C2×D411yescharacteristic
80D236—24no—
81D236—44no—
82D236—42no—
83D236—42no—
84C4×D59—22no—
85C4×D59—22no—
86C4×D59—22no—
87C4×D59—44no—
88Dic118—42no—
89C8×C59—22no—
90C59⋊C8#4114yescomplemented
91C22×C59C22×D411yescharacteristic
92C2×D59—21no—
93C2×D59—21no—
94C2×D59—21no—
95C2×D59—42no—
96C2×D59—42no—
97C2×D59—42no—
98C4×C59—42no—
99C4×C59—42no—
100C4×C59AGL(1,ℤ/8)12yes—
101C4×C59#13712yes—
102C4×C59C2×#4112yes—
103Dic59—21no—
104Dic59—21no—
105Dic59—21no—
106Dic59—42no—
107#3182—591nomaximal, Sylow
108C2×C59#53211yescharacteristic
109C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C59C2×#13711yescharacteristic
111D59—41no—
112D59—82no—
113#533—591no—
114#532—591no—
115#500—591no—
116#492—591no—
117#487D5911yescharacteristic, complemented
118#486—591no—
119#468—594no—
120#440—594no—
121C4×M16—591no—
122C59#318211yescharacteristic, complemented, Sylow
123C2×#41—1181no—
124C2×SD16—594no—
125C2×M16—592no—
126C4⋊Q8—591no—
127C4⋊Q8C2×D5911yescharacteristic
128C4⋊Q8C2×D5911yescharacteristic
129#127—591no—
130#125—1181no—
131#124—1181no—
132C22⋊Q8—592no—
133C22⋊Q8—1181no—
134#121—592no—
135#121—1181no—
136C4×Q8—592no—
137C4×Q8—1181no—
138C4×D4—592no—
139C4×D4—1181no—
140#117—1181no—
141C2×C42—591no—
142#107—594no—
143#103C2×D5914yes—
144#102—594no—
145#97—592no—
146C4×C8—591no—
147C4×C8C2×D5911yescharacteristic
148#41—2364no—
149C2×Q8—21no—
150C2×Q8—1181no—
151C2×Q8C22×D5912yes—
152C2×D4—592no—
153C2×D4—1182no—
154C2×D4—1181no—
155C2×D4—1181no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—591no—
159C22×C4—1182no—
160SD16—1188no—
161M16—1184no—
162C2×C8—592no—
163C2×C8C22×D5912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—592no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C4⋊C4—1181no—
171C4⋊C4C22×D5912yes—
172C22⋊C4—1182no—
173C22⋊C4—1182no—
174C22⋊C4—1182no—
175C42—591no—
176C42—591no—
177C42—591no—
178C42—1182no—
179C42C22×D5911yescharacteristic
180C23—591no—
181C23—1182no—
182Q8—24no—
183Q8—42no—
184Q8—2362no—
185D4—1184no—
186D4—2364no—
187D4—2362no—
188D4—2362no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—591no—
192C2×C4—591no—
193C2×C4—591no—
194C2×C4—1182no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—2364no—
199C2×C4D4×D5911yescharacteristic
200C2×C4D4×D5911yescharacteristic
201C2×C4C23×D5911yescharacteristic
202C8—22no—
203C8—594no—
204C22—1181no—
205C22—1181no—
206C22—1181no—
207C22—2362no—
208C22—2362no—
209C22—2362no—
210C22C2×D4×D5911yescharacteristic
211C4—42no—
212C4—42no—
213C4—1181no—
214C4—1181no—
215C4—1181no—
216C4—2362no—
217C4#1427375412yes—
218C4#1427375912yes—
219C4#41×D5912yes—
220C2—4722no—
221C2—2361no—
222C2#1683795111yescharacteristic
223C2C2×#1427375411yescharacteristic
224C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3182
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837805C2semidirect
4. #16837776C2semidirect
5. #16837749C2semidirect
6. #16837651C2semidirect
7. #16837505C2semidirect
8. C4×#11745659C2semidirect
9. C59×#487C2semidirect
90. C59⋊C8#41semidirect
117. #487D59semidirect
122. C59#3182semidirect