Finite Group Databasebeta

← #21434710

Subgroups — #21434710

Order 7552.

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

normal subgroups only

This group has 362 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#16838021C212yesmaximal, complemented
2#16837800C211yesmaximal, characteristic, complemented
3#16837761C212yesmaximal, complemented
4#16837657C211yesmaximal, characteristic, complemented
5#16837652C211yesmaximal, characteristic
6#16837628C212yesmaximal, complemented
7#16837514C211yesmaximal, characteristic, complemented
8#16837509C211yesmaximal, characteristic, complemented
9SD16×Dic59C212yesmaximal, complemented
10#16837356C211yesmaximal, characteristic, complemented
11C59×#495C211yesmaximal, characteristic, complemented
12C2×#11745659C2211yescharacteristic
13C2×C8×D59C2211yescharacteristic
14#14273727C2212yes—
15#14273720—22no—
16#14273713—22no—
17#14273711—22no—
18#14273704—22no—
19#14273703C2212yes—
20#14273698C2212yes—
21Q8×Dic59C2212yes—
22D4×Dic59C2212yes—
23#14273684C2211yescharacteristic
24#14273659C2211yescharacteristic
25#14273659C2211yescharacteristic
26#14273659C2212yes—
27#14273651C2212yes—
28#14273651C2212yes—
29#14273648C2212yes—
30#14273648C2212yes—
31#14273638C2211yescharacteristic
32#14273637C2211yescharacteristic
33C8×Dic59C2211yescharacteristic
34C2×Q16×C59C2211yescharacteristic
35C2×SD16×C59C2212yes—
36C2×D8×C59C2211yescharacteristic
37#124×C59C2212yes—
38C4×C8×C59C2211yescharacteristic
39C2×Q8×C59C2312yes—
40C2×D4×C59C2312yes—
41C2×C22⋊D59—22no—
42C22×Dic59—22no—
43C2×C4×D59C2311yescharacteristic
44C2×Dic118—22no—
45Q16×C59—22no—
46SD16×C59—24no—
47D8×C59—22no—
48C2×C8×C59C2311yescharacteristic
49C2×C8×C59C2311yescharacteristic
50C22⋊C4×C59—22no—
51C22⋊C4×C59—22no—
52C42×C59C2311yescharacteristic
53C22⋊Dic59—22no—
54C22⋊Dic59—22no—
55(C2×D59)⋊C4—22no—
56(C2×D59)⋊C4D412yes—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59C2312yes—
60C4⋊Dic59C2312yes—
61Dic59⋊C4—22no—
62Dic59⋊C4D412yes—
63C4×Dic59—22no—
64C4×Dic59C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66C2×C59⋊C8C2311yescharacteristic
67#11745659—22no—
68C8×D59—22no—
69C23×C59—22no—
70C22×D59C2×D411yescharacteristic
71Q8×C59—22no—
72Q8×C59—22no—
73D4×C59—22no—
74D4×C59—22no—
75C2×C4×C59—22no—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2411yescharacteristic
78C22⋊D59—82no—
79C2×Dic59—22no—
80C2×Dic59—22no—
81C2×Dic59—82no—
82C2×Dic59C2×D412yes—
83C2×Dic59C2×D411yescharacteristic
84C4×D59—21no—
85C4×D59—21no—
86Dic118—82no—
87C8×C59#4112yes—
88C8×C59#4112yes—
89C59⋊C8—21no—
90C59⋊C8—21no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59—42no—
94C22×C59C22×D411yescharacteristic
95C2×D59—21no—
96C2×D59—22no—
97C4×C59—22no—
98C4×C59—42no—
99C4×C59C2×#4111yescharacteristic
100C4×C59C2×#4111yescharacteristic
101Dic59—21no—
102Dic59—22no—
103Dic59—42no—
104Dic59—42no—
105#3173—591nomaximal, Sylow
106C2×C59—82no—
107C2×C59#53211yescharacteristic
108C2×C59#57712yes—
109D59—41no—
110#542—592no—
111#498—591no—
112#495D5911yescharacteristic, complemented
113#489—592no—
114#470—591no—
115#469—591no—
116#465—592no—
117#442—591no—
118#441—591no—
119C4×SD16—592no—
120#405—591no—
121C59#317311yescharacteristic, complemented, Sylow
122C2×Q16C2×D5911yescharacteristic
123C2×SD16C2×D5912yes—
124C2×D8C2×D5911yescharacteristic
125C2×M16—591no—
126C22×C8—591no—
127C4⋊Q8—592no—
128#126—1182no—
129#124—1182no—
130#124C2×D5912yes—
131#123—1182no—
132C22⋊Q8—592no—
133C22⋊Q8—1182no—
134#121—592no—
135C4×Q8—592no—
136C4×D4—592no—
137#117—591no—
138#106—592no—
139#106—591no—
140#106—591no—
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—1182no—
150C2×Q8C22×D5912yes—
151C2×D4—1182no—
152C2×D4C22×D5912yes—
153C22×C4—591no—
154C22×C4—1182no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—1182no—
159C2×C8—591no—
160C2×C8—591no—
161C2×C8—1182no—
162C2×C8C22×D5911yescharacteristic
163C2×C8C22×D5911yescharacteristic
164C4⋊C4—592no—
165C4⋊C4—592no—
166C4⋊C4—592no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—592no—
173C22⋊C4—1182no—
174C22⋊C4—1182no—
175C22⋊C4—1182no—
176C42—591no—
177C42—1182no—
178C42C22×D5911yescharacteristic
179C23—22no—
180C23—591no—
181Q8—22no—
182Q8—22no—
183Q8—4722no—
184D4—22no—
185D4—22no—
186D4—4722no—
187C2×C4—22no—
188C2×C4—592no—
189C2×C4—591no—
190C2×C4—1181no—
191C2×C4—1181no—
192C2×C4—1182no—
193C2×C4—1182no—
194C2×C4—4722no—
195C2×C4D4×D5912yes—
196C2×C4C23×D5911yescharacteristic
197C8—1181no—
198C8—1181no—
199C8#1174568712yes—
200C8#1174568712yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1181no—
205C22—1182no—
206C22C2×D4×D5911yescharacteristic
207C4—22no—
208C4—42no—
209C4—1181no—
210C4—1182no—
211C4—2362no—
212C4—2362no—
213C4C2×#1174568711yescharacteristic
214C4C2×#1174568711yescharacteristic
215C2—82no—
216C2—2361no—
217C2#1683795011yescharacteristic
218C2#1683820912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#495C2
socleC22×C59C22×D4
hypercenter#495D59
hypocenterC59#3173
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16838021C2semidirect
2. #16837800C2semidirect
3. #16837761C2semidirect
4. #16837657C2semidirect
6. #16837628C2semidirect
7. #16837514C2semidirect
8. #16837509C2semidirect
9. SD16×Dic59C2semidirect
10. #16837356C2semidirect
11. C59×#495C2semidirect
112. #495D59semidirect
121. C59#3173semidirect