Finite Group Databasebeta

← #21436034

Subgroups — #21436034

Order 7552.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#16838126C211yesmaximal, characteristic, complemented
2#16838072C211yesmaximal, characteristic
3#16837724C212yesmaximal, complemented
4#16837684C211yesmaximal, characteristic, complemented
5#16837630C212yesmaximal, complemented
6#16837599C211yesmaximal, characteristic, complemented
7#16837565C212yesmaximal, complemented
8C4×Dic236C211yesmaximal, characteristic, complemented
9C8×D236C211yesmaximal, characteristic, complemented
10#16837395C212yesmaximal, complemented
11C59×#486C211yesmaximal, characteristic, complemented
12C2×#11745687C2212yes—
13C2×Dic236C2211yescharacteristic
14C2×#11745670C2212yes—
15C2×C8×D59C2212yes—
16#14273723—21no—
17#14273722—22no—
18#14273716—21no—
19#14273707C2212yes—
20#14273699—22no—
21#14273698C2212yes—
22Q8×Dic59—21no—
23C4×Dic118C2211yescharacteristic
24C4×Dic118C2211yescharacteristic
25C4×D236C2211yescharacteristic
26D4×Dic59—21no—
27#14273685C2212yes—
28#14273661C2211yescharacteristic
29#14273658C2212yes—
30C4⋊(C59⋊C8)C2211yescharacteristic
31#14273652C2211yescharacteristic
32#14273652C2211yescharacteristic
33#14273650C2212yes—
34#14273648C2212yes—
35(C2×D59)⋊C8C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37#127×C59C2211yescharacteristic
38#102×C59C2212yes—
39#102×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C2×C22⋊D59—22no—
46C2×C22⋊D59—22no—
47C22×Dic59—22no—
48#11745687—24no—
49#11745687—42no—
50C2×D236D411yescharacteristic
51C2×C4×D59C2312yes—
52C2×Dic118C2311yescharacteristic
53C2×Dic118C2311yescharacteristic
54C2×C8×C59C2311yescharacteristic
55C2×C8×C59C2311yescharacteristic
56C4⋊C4×C59—21no—
57C4⋊C4×C59C2312yes—
58C42×C59C2311yescharacteristic
59C22⋊Dic59—22no—
60#11745670—42no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4D412yes—
64C4⋊Dic59—22no—
65C4⋊Dic59D411yescharacteristic
66C4⋊Dic59C2311yescharacteristic
67C4⋊Dic59C2311yescharacteristic
68Dic59⋊C4—21no—
69Dic59⋊C4—21no—
70C4×Dic59—21no—
71C4×Dic59—21no—
72C4×Dic59—22no—
73C2×C59⋊C8C2312yes—
74Dic236—22no—
75C8×D59—42no—
76C23×C59—22no—
77C22×D59C2×D412yes—
78Q8×C59—42no—
79D4×C59—22no—
80D4×C59—22no—
81D4×C59—42no—
82D4×C59—81no—
83C2×C4×C59—22no—
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2×D411yescharacteristic
86C2×C4×C59C2411yescharacteristic
87C22⋊D59—44no—
88C22⋊D59—82no—
89C2×Dic59—21no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—44no—
94C2×Dic59C2×D412yes—
95D236—22no—
96C4×D59—22no—
97C4×D59—22no—
98Dic118—21no—
99Dic118—21no—
100Dic118—21no—
101Dic118#4112yes—
102C8×C59—21no—
103C8×C59—21no—
104C59⋊C8—22no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59C22×D411yescharacteristic
109C2×D59—22no—
110C2×D59—22no—
111C2×D59—22no—
112C4×C59—21no—
113C4×C59—42no—
114C4×C59#13512yes—
115C4×C59C2×#4111yescharacteristic
116C4×C59H(5,𝔽2)11yescharacteristic
117Dic59—22no—
118Dic59—22no—
119Dic59—41no—
120Dic59—41no—
121Dic59—41no—
122#3304—591nomaximal, Sylow
123C2×C59—82no—
124C2×C59#54611yescharacteristic
125C2×C59C2×#13511yescharacteristic
126C2×C59#57711yescharacteristic
127D59—42no—
128#556—591no—
129#550—591no—
130#486D5911yescharacteristic, complemented
131#482—592no—
132#475—591no—
133#465—592no—
134#460—591no—
135#452—592no—
136C4×Q16—591no—
137C8×D4—591no—
138#416—592no—
139C59#330411yescharacteristic, complemented, Sylow
140C2×#41—592no—
141C2×Q16—591no—
142C2×SD16—592no—
143C22×C8—592no—
144C4⋊Q8C2×D5911yescharacteristic
145#127—1181no—
146#127C2×D5911yescharacteristic
147#126—1182no—
148#124—1181no—
149C22⋊Q8—592no—
150#121—592no—
151#121—1182no—
152C4×Q8—591no—
153C4×Q8—591no—
154C4×Q8—1181no—
155C4×D4—591no—
156C4×D4—1181no—
157#117—592no—
158#107—591no—
159#106—592no—
160C4⋊C8—591no—
161#103—591no—
162#103—591no—
163#103—592no—
164#102—592no—
165#102C2×D5912yes—
166#102C2×D5912yes—
167C22⋊C8—592no—
168C4×C8C2×D5911yescharacteristic
169#41—1184no—
170#41—2362no—
171C2×Q8—21no—
172C2×Q8—591no—
173C2×Q8—591no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—591no—
177C2×D4—1182no—
178C2×D4—1182no—
179C2×D4C22×D5912yes—
180C22×C4—592no—
181C22×C4—1182no—
182Q16—1182no—
183SD16—2362no—
184C2×C8—592no—
185C2×C8—2362no—
186C2×C8C22×D5911yescharacteristic
187C2×C8C22×D5911yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—591no—
190C4⋊C4—591no—
191C4⋊C4—591no—
192C4⋊C4—1182no—
193C4⋊C4—1181no—
194C4⋊C4—1181no—
195C4⋊C4C22×D5912yes—
196C22⋊C4—592no—
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C22⋊C4—1182no—
200C42—1182no—
201C42—1181no—
202C42—1181no—
203C42C22×D5911yescharacteristic
204C23—22no—
205C23—592no—
206Q8—42no—
207Q8—592no—
208Q8—1181no—
209Q8—1181no—
210Q8—1181no—
211D4—22no—
212D4—22no—
213D4—42no—
214D4—81no—
215D4—1182no—
216D4—4722no—
217D4—2364no—
218C2×C4—22no—
219C2×C4—592no—
220C2×C4—1181no—
221C2×C4—1182no—
222C2×C4—1182no—
223C2×C4—1181no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—2364no—
227C2×C4D4×D5911yescharacteristic
228C2×C4D4×D5911yescharacteristic
229C2×C4C23×D5911yescharacteristic
230C8—21no—
231C8—21no—
232C8—1182no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—1182no—
237C22—1182no—
238C22—1182no—
239C22C2×D4×D5911yescharacteristic
240C4—21no—
241C4—42no—
242C4—1182no—
243C4—1182no—
244C4—2361no—
245C4—2361no—
246C4—2361no—
247C4#1427374612yes—
248C4#41×D5911yescharacteristic
249C4#1427377311yescharacteristic
250C2—82no—
251C2—2362no—
252C2#1683804511yescharacteristic
253C2C2×#1427374611yescharacteristic
254C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3304
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16838126C2semidirect
3. #16837724C2semidirect
4. #16837684C2semidirect
5. #16837630C2semidirect
6. #16837599C2semidirect
7. #16837565C2semidirect
8. C4×Dic236C2semidirect
9. C8×D236C2semidirect
10. #16837395C2semidirect
11. C59×#486C2semidirect
130. #486D59semidirect
139. C59#3304semidirect