Finite Group Databasebeta

← #21434827

Subgroups — #21434827

Order 7552.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#16837937C212yesmaximal, complemented
2#16837786C211yesmaximal, characteristic, complemented
3#16837759C212yesmaximal, complemented
4#16837661C211yesmaximal, characteristic, complemented
5#16837656C211yesmaximal, characteristic
6#16837649C212yesmaximal, complemented
7#16837513C211yesmaximal, characteristic, complemented
8#16837508C211yesmaximal, characteristic, complemented
9#16837501C212yesmaximal, complemented
10C4×#11745659C211yesmaximal, characteristic, complemented
11C59×#499C211yesmaximal, characteristic, complemented
12C2×Dic236C2211yescharacteristic
13C2×#11745660C2212yes—
14C2×D472C2211yescharacteristic
15C2×#11745659C2211yescharacteristic
16C2×#11745659C2211yescharacteristic
17#14273722—22no—
18#14273715C2212yes—
19#14273712—22no—
20#14273707C2212yes—
21#14273702C2212yes—
22#14273692C2212yes—
23#14273689—22no—
24#14273689C2212yes—
25#14273685—22no—
26C42×D59C2211yescharacteristic
27#14273650C2212yes—
28#14273650C2212yes—
29#14273647C2212yes—
30#14273647C2212yes—
31#14273637C2211yescharacteristic
32#14273637C2211yescharacteristic
33C4×C59⋊C8C2211yescharacteristic
34#125×C59C2212yes—
35#107×C59C2212yes—
36#106×C59C2211yescharacteristic
37#106×C59C2211yescharacteristic
38C4×C8×C59C2211yescharacteristic
39C2×D236—22no—
40C2×D236C2312yes—
41C2×C4×D59—22no—
42C2×C4×D59D412yes—
43C2×C4×D59C2311yescharacteristic
44C2×Dic118C2312yes—
45C2×C8×C59C2311yescharacteristic
46C2×C8×C59C2311yescharacteristic
47C4⋊C4×C59—22no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59C2312yes—
50C4⋊C4×C59C2312yes—
51C42×C59C2311yescharacteristic
52(C2×D59)⋊C4—22no—
53(C2×D59)⋊C4—22no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4—22no—
57C4⋊Dic59—22no—
58Dic59⋊C4—22no—
59C4×Dic59—22no—
60C4×Dic59D412yes—
61C4×Dic59C2311yescharacteristic
62C2×C59⋊C8C2311yescharacteristic
63C2×C59⋊C8C2311yescharacteristic
64Dic236—22no—
65D472—22no—
66#11745660—24no—
67#11745659—22no—
68#11745659—22no—
69C22×D59—22no—
70C22×D59C2×D411yescharacteristic
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59C2×D412yes—
74C2×C4×C59C2411yescharacteristic
75C2×Dic59—22no—
76C2×Dic59C2×D412yes—
77C2×Dic59C2×D411yescharacteristic
78D236—22no—
79D236—22no—
80D236—44no—
81C4×D59—21no—
82C4×D59—21no—
83C4×D59—42no—
84C4×D59—44no—
85Dic118—22no—
86Dic118—22no—
87C8×C59#4112yes—
88C8×C59#4112yes—
89C59⋊C8—21no—
90C59⋊C8—21no—
91C22×C59C22×D411yescharacteristic
92C2×D59—21no—
93C2×D59—22no—
94C2×D59—42no—
95C2×D59—42no—
96C2×D59—42no—
97C4×C59—22no—
98C4×C59—42no—
99C4×C59—42no—
100C4×C59C2×#4111yescharacteristic
101C4×C59C2×#4111yescharacteristic
102Dic59—21no—
103Dic59—22no—
104Dic59—42no—
105#3183—591nomaximal, Sylow
106C2×C59#53211yescharacteristic
107C2×C59#57512yes—
108D59—41no—
109D59—82no—
110#529—592no—
111#499D5911yescharacteristic, complemented
112#495—591no—
113#488—592no—
114#470—591no—
115#469—591no—
116#468—592no—
117#442—591no—
118#441—591no—
119#440—592no—
120C4×M16—591no—
121C59#318311yescharacteristic, complemented, Sylow
122C2×Q16—591no—
123C2×SD16—592no—
124C2×D8—591no—
125C2×M16—591no—
126C2×M16—591no—
127#126—1182no—
128#125C2×D5912yes—
129#124—592no—
130#123—1182no—
131C22⋊Q8—592no—
132#121—592no—
133C4×Q8—592no—
134C4×D4—592no—
135C4×D4—1182no—
136#117—1182no—
137C2×C42—591no—
138#107C2×D5912yes—
139#106C2×D5911yescharacteristic
140#106C2×D5911yescharacteristic
141#103—592no—
142#103—592no—
143#102—592no—
144#102—592no—
145#97—591no—
146#97—591no—
147C4×C8—591no—
148C4×C8C2×D5911yescharacteristic
149C2×Q8—592no—
150C2×D4—592no—
151C2×D4—1182no—
152C22×C4—591no—
153C22×C4—592no—
154C22×C4—1182no—
155Q16—1182no—
156SD16—1184no—
157D8—1182no—
158M16—1182no—
159M16—1182no—
160C2×C8—591no—
161C2×C8—591no—
162C2×C8C22×D5911yescharacteristic
163C2×C8C22×D5911yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4C22×D5912yes—
169C4⋊C4C22×D5912yes—
170C22⋊C4—1182no—
171C22⋊C4—1182no—
172C22⋊C4—1182no—
173C22⋊C4—1182no—
174C22⋊C4—1182no—
175C42—592no—
176C42—591no—
177C42—1182no—
178C42C22×D5911yescharacteristic
179C23—591no—
180C23—1182no—
181Q8—1182no—
182Q8—1182no—
183D4—1182no—
184D4—1182no—
185D4—2364no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—592no—
189C2×C4—591no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1182no—
193C2×C4—2362no—
194C2×C4—2364no—
195C2×C4D4×D5912yes—
196C2×C4C23×D5911yescharacteristic
197C8—1181no—
198C8—1181no—
199C8#1174568912yes—
200C8#1174568912yes—
201C22—1182no—
202C22—1181no—
203C22—2362no—
204C22—2362no—
205C22—2362no—
206C22C2×D4×D5911yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—1182no—
211C4—1181no—
212C4—2362no—
213C4C2×#1174568911yescharacteristic
214C4C2×#1174568911yescharacteristic
215C2—4722no—
216C2—2361no—
217C2#1683795311yescharacteristic
218C2#1683819912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#499C2
socleC22×C59C22×D4
hypercenter#499D59
hypocenterC59#3183
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #16837937C2semidirect
2. #16837786C2semidirect
3. #16837759C2semidirect
4. #16837661C2semidirect
6. #16837649C2semidirect
7. #16837513C2semidirect
8. #16837508C2semidirect
9. #16837501C2semidirect
10. C4×#11745659C2semidirect
11. C59×#499C2semidirect
111. #499D59semidirect
121. C59#3183semidirect