Finite Group Databasebeta

← #21436411

Subgroups — #21436411

Order 7552.

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

normal subgroups only

This group has 388 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#16838113C211yesmaximal, characteristic, complemented
2#16838055C211yesmaximal, characteristic
3#16837731C212yesmaximal, complemented
4#16837689C211yesmaximal, characteristic, complemented
5#16837659C212yesmaximal, complemented
6#16837609C211yesmaximal, characteristic, complemented
7#16837567C212yesmaximal, complemented
8C4×#11745660C211yesmaximal, characteristic, complemented
9#16837481C211yesmaximal, characteristic, complemented
10#16837402C212yesmaximal, complemented
11C59×#487C211yesmaximal, characteristic, complemented
12C2×#11745689C2212yes—
13C2×#11745672C2212yes—
14C2×#11745660C2211yescharacteristic
15C2×#11745659C2212yes—
16#14273718—21no—
17#14273712—22no—
18#14273707C2212yes—
19#14273703—22no—
20#14273703C2212yes—
21#14273702—21no—
22C4×Dic118C2211yescharacteristic
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273689—21no—
26C4⋊C4×D59—21no—
27C4⋊C4×D59C2212yes—
28#14273659C2211yescharacteristic
29#14273658C2212yes—
30C4⋊(C59⋊C8)C2211yescharacteristic
31#14273652C2211yescharacteristic
32#14273651C2212yes—
33#14273649C2211yescharacteristic
34#14273647C2212yes—
35(C2×D59)⋊C8C2212yes—
36C4⋊Q8×C59C2211yescharacteristic
37C4⋊Q8×C59C2211yescharacteristic
38#103×C59C2212yes—
39#103×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×Q8×C59—21no—
42C2×Q8×C59C2312yes—
43#11745689—24no—
44#11745689—42no—
45C2×D236—22no—
46C2×D236D411yescharacteristic
47C2×D236C2311yescharacteristic
48C2×C4×D59—21no—
49C2×C4×D59—22no—
50C2×C4×D59—22no—
51C2×C4×D59C2312yes—
52C2×Dic118C2311yescharacteristic
53C2×C8×C59C2311yescharacteristic
54C2×C8×C59C2311yescharacteristic
55C4⋊C4×C59—21no—
56C4⋊C4×C59—21no—
57C4⋊C4×C59—21no—
58C4⋊C4×C59C2312yes—
59C42×C59C2311yescharacteristic
60#11745672—42no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4D412yes—
65C4⋊Dic59—22no—
66C4⋊Dic59D411yescharacteristic
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—21no—
70Dic59⋊C4—22no—
71Dic59⋊C4—22no—
72C4×Dic59—21no—
73C2×C59⋊C8C2312yes—
74#11745660—22no—
75#11745659—42no—
76C22×D59—21no—
77C22×D59C2×D412yes—
78Q8×C59—22no—
79Q8×C59—22no—
80Q8×C59—81no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59C2×D412yes—
90D236—22no—
91D236—21no—
92D236—44no—
93D236#4112yes—
94C4×D59—22no—
95C4×D59—22no—
96C4×D59—44no—
97C4×D59—42no—
98C4×D59—82no—
99Dic118—21no—
100Dic118—21no—
101C8×C59—21no—
102C8×C59—21no—
103C59⋊C8—22no—
104C22×C59C22×D411yescharacteristic
105C2×D59—22no—
106C2×D59—22no—
107C2×D59—22no—
108C2×D59—22no—
109C2×D59—41no—
110C2×D59—41no—
111C4×C59—21no—
112C4×C59—42no—
113C4×C59—42no—
114C4×C59#13712yes—
115C4×C59C2×#4111yescharacteristic
116C4×C59H(5,𝔽2)11yescharacteristic
117Dic59—22no—
118Dic59—41no—
119Dic59—41no—
120Dic59—41no—
121#3331—591nomaximal, Sylow
122C2×C59#54611yescharacteristic
123C2×C59C2×#13711yescharacteristic
124C2×C59#57711yescharacteristic
125D59—42no—
126D59—42no—
127#554—591no—
128#547—591no—
129#487D5911yescharacteristic, complemented
130#483—592no—
131#476—591no—
132#470—592no—
133#462—591no—
134#452—592no—
135C4×SD16—591no—
136#436—591no—
137#417—592no—
138C59#333111yescharacteristic, complemented, Sylow
139C2×#41—592no—
140C2×Q16—592no—
141C2×SD16—591no—
142C2×M16—592no—
143C4⋊Q8C2×D5911yescharacteristic
144C4⋊Q8C2×D5911yescharacteristic
145#125—1181no—
146#123—1182no—
147C22⋊Q8—592no—
148C22⋊Q8—592no—
149C22⋊Q8—1182no—
150#121—1181no—
151C4×Q8—591no—
152C4×D4—591no—
153C4×D4—591no—
154C4×D4—1181no—
155C2×C4⋊C4—592no—
156C2×C4⋊C4—1181no—
157#106—591no—
158#106—592no—
159C4⋊C8—591no—
160#103—592no—
161#103—591no—
162#103C2×D5912yes—
163#103C2×D5912yes—
164#102—591no—
165#102—592no—
166C22⋊C8—592no—
167C4×C8C2×D5911yescharacteristic
168#41—1184no—
169#41—2362no—
170C2×Q8—21no—
171C2×Q8—591no—
172C2×Q8C22×D5912yes—
173C2×D4—591no—
174C2×D4—591no—
175C2×D4—1182no—
176C22×C4—592no—
177C22×C4—1182no—
178C22×C4—1182no—
179C22×C4—1181no—
180Q16—2362no—
181SD16—1182no—
182M16—2362no—
183C2×C8—592no—
184C2×C8C22×D5911yescharacteristic
185C2×C8C22×D5911yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—591no—
190C4⋊C4—591no—
191C4⋊C4—591no—
192C4⋊C4—1182no—
193C4⋊C4—1182no—
194C4⋊C4—1182no—
195C4⋊C4—1181no—
196C4⋊C4C22×D5912yes—
197C22⋊C4—592no—
198C22⋊C4—1182no—
199C22⋊C4—1182no—
200C22⋊C4—1181no—
201C42—1181no—
202C42C22×D5911yescharacteristic
203C23—592no—
204C23—1181no—
205Q8—22no—
206Q8—22no—
207Q8—81no—
208Q8—1181no—
209Q8—1181no—
210D4—592no—
211D4—1182no—
212D4—1181no—
213D4—2364no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—592no—
217C2×C4—1182no—
218C2×C4—1182no—
219C2×C4—1181no—
220C2×C4—1181no—
221C2×C4—1181no—
222C2×C4—4722no—
223C2×C4—2364no—
224C2×C4—2362no—
225C2×C4D4×D5911yescharacteristic
226C2×C4D4×D5911yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—21no—
229C8—21no—
230C8—1182no—
231C22—1182no—
232C22—1182no—
233C22—1182no—
234C22—1182no—
235C22—2361no—
236C22—2361no—
237C22C2×D4×D5911yescharacteristic
238C4—21no—
239C4—42no—
240C4—42no—
241C4—1182no—
242C4—2361no—
243C4—2361no—
244C4—2361no—
245C4#1427375912yes—
246C4#41×D5911yescharacteristic
247C4#1427377311yescharacteristic
248C2—2362no—
249C2—2362no—
250C2#1683804511yescharacteristic
251C2C2×#1427375911yescharacteristic
252C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3331
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. #16838113C2semidirect
3. #16837731C2semidirect
4. #16837689C2semidirect
5. #16837659C2semidirect
6. #16837609C2semidirect
7. #16837567C2semidirect
8. C4×#11745660C2semidirect
9. #16837481C2semidirect
10. #16837402C2semidirect
11. C59×#487C2semidirect
129. #487D59semidirect
138. C59#3331semidirect