Finite Group Databasebeta

← #21436808

Subgroups — #21436808

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#16838113C211yesmaximal, characteristic, complemented
2#16838072C211yesmaximal, characteristic, complemented
3#16837765C212yesmaximal, complemented
4#16837700C212yesmaximal, complemented
5#16837689C211yesmaximal, characteristic, complemented
6#16837596C212yesmaximal, complemented
7#16837594C211yesmaximal, characteristic, complemented
8#16837532C211yesmaximal, characteristic, complemented
9#16837511C212yesmaximal, complemented
10C4×D472C211yesmaximal, characteristic, complemented
11C59×#486C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×D472C2211yescharacteristic
14C2×#11745669C2212yes—
15#14273723C2212yes—
16#14273718C2212yes—
17#14273707—21no—
18#14273703—22no—
19#14273699—22no—
20#14273698—21no—
21C4×Dic118C2211yescharacteristic
22C4×D236C2211yescharacteristic
23C4×D236C2211yescharacteristic
24D4×Dic59C2212yes—
25#14273689C2212yes—
26C4⋊C4×D59—21no—
27#14273661C2211yescharacteristic
28#14273658C2212yes—
29C4⋊(C59⋊C8)C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273649C2211yescharacteristic
32#14273649C2211yescharacteristic
33#14273648C2212yes—
34#14273647C2212yes—
35#14273637C2212yes—
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—44no—
49C2×D236C2311yescharacteristic
50C2×D236C2311yescharacteristic
51C2×C4×D59—21no—
52C2×C4×D59—21no—
53C2×C4×D59—22no—
54C2×Dic118D411yescharacteristic
55C2×C8×C59C2311yescharacteristic
56C2×C8×C59C2311yescharacteristic
57C4⋊C4×C59—21no—
58C4⋊C4×C59C2312yes—
59C42×C59C2311yescharacteristic
60C22⋊Dic59—22no—
61#11745669—24no—
62(C2×D59)⋊C4—21no—
63(C2×D59)⋊C4—21no—
64(C2×D59)⋊C4—22no—
65C4⋊Dic59—22no—
66C4⋊Dic59D411yescharacteristic
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69Dic59⋊C4—22no—
70Dic59⋊C4D412yes—
71C4×Dic59C2312yes—
72C2×C59⋊C8C2312yes—
73D472—22no—
74C23×C59—22no—
75C22×D59—21no—
76C22×D59—21no—
77Q8×C59—81no—
78D4×C59—22no—
79D4×C59—22no—
80D4×C59—42no—
81D4×C59—81no—
82C2×C4×C59—22no—
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2×D411yescharacteristic
85C2×C4×C59C2411yescharacteristic
86C22⋊D59—44no—
87C22⋊D59—82no—
88C2×Dic59—21no—
89C2×Dic59—21no—
90C2×Dic59—44no—
91C2×Dic59C2×D412yes—
92C2×Dic59C2×D412yes—
93D236—21no—
94D236—21no—
95D236—21no—
96D236#4112yescomplemented
97C4×D59—42no—
98C4×D59—42no—
99C4×D59—82no—
100Dic118—22no—
101C8×C59—21no—
102C8×C59—21no—
103C59⋊C8—22no—
104C22×C59—42no—
105C22×C59—42no—
106C22×C59—42no—
107C22×C59C22×D411yescharacteristic
108C2×D59—22no—
109C2×D59—41no—
110C2×D59—41no—
111C2×D59—41no—
112C2×D59—41no—
113C2×D59—41no—
114C4×C59—21no—
115C4×C59—42no—
116C4×C59AGL(1,ℤ/8)12yes—
117C4×C59C2×#4111yescharacteristic
118C4×C592−1+411yescharacteristic
119Dic59—22no—
120Dic59—22no—
121Dic59—41no—
122Dic59—41no—
123#3366—591nomaximal, Sylow
124C2×C59—82no—
125C2×C59#54811yescharacteristic
126C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C59#57611yescharacteristic
128D59—42no—
129D59—81no—
130#554—591no—
131#550—591no—
132#490—592no—
133#486D5911yescharacteristic, complemented
134#478—592no—
135#476—591no—
136#459—591no—
137#459—592no—
138#446—591no—
139#442—592no—
140C4×D8—591no—
141C59#336611yescharacteristic, complemented, Sylow
142C2×#41—1181no—
143C2×D8—592no—
144C2×D8—591no—
145C4⋊Q8C2×D5911yescharacteristic
146#127—592no—
147#127C2×D5911yescharacteristic
148#125—592no—
149C22⋊Q8—1181no—
150C22⋊Q8—1182no—
151#121—1181no—
152#121—1182no—
153C4×Q8—591no—
154C4×D4—592no—
155C4×D4—592no—
156C4×D4—591no—
157C4×D4—591no—
158C2×C4⋊C4—1181no—
159#107—591no—
160#106—592no—
161C4⋊C8—592no—
162C4⋊C8—591no—
163#102—592no—
164#102—591no—
165#102—591no—
166#102—592no—
167#102C2×D5912yes—
168#102C2×D5912yes—
169#97—592no—
170C4×C8C2×D5911yescharacteristic
171#41—2364no—
172C2×Q8—21no—
173C2×Q8—591no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—591no—
177C2×D4—591no—
178C2×D4—1182no—
179C2×D4—1182no—
180C2×D4C22×D5912yes—
181C22×C4—1182no—
182C22×C4—1182no—
183C22×C4—1181no—
184C22×C4—1181no—
185D8—1182no—
186D8—1184no—
187C2×C8—592no—
188C2×C8C22×D5911yescharacteristic
189C2×C8C22×D5911yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—591no—
192C4⋊C4—592no—
193C4⋊C4—591no—
194C4⋊C4—591no—
195C4⋊C4—1182no—
196C4⋊C4—1182no—
197C4⋊C4C22×D5912yes—
198C22⋊C4—1182no—
199C22⋊C4—1182no—
200C22⋊C4—1181no—
201C22⋊C4—1181no—
202C42—592no—
203C42C22×D5911yescharacteristic
204C23—22no—
205C23—1181no—
206C23—1181no—
207Q8—81no—
208Q8—1182no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—592no—
214D4—1181no—
215D4—1181no—
216D4—1181no—
217D4—4722no—
218D4—2364no—
219C2×C4—22no—
220C2×C4—592no—
221C2×C4—592no—
222C2×C4—1181no—
223C2×C4—1181no—
224C2×C4—4722no—
225C2×C4—2364no—
226C2×C4—2362no—
227C2×C4—2362no—
228C2×C4D4×D5911yescharacteristic
229C2×C4D4×D5911yescharacteristic
230C2×C4C23×D5911yescharacteristic
231C8—21no—
232C8—21no—
233C8—1182no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—1182no—
238C22—2361no—
239C22—2361no—
240C22—2361no—
241C22—2361no—
242C22—2361no—
243C22C2×D4×D5911yescharacteristic
244C4—21no—
245C4—42no—
246C4—1182no—
247C4—1182no—
248C4—2361no—
249C4—2361no—
250C4#1427375412yes—
251C4#41×D5911yescharacteristic
252C4#1427377411yescharacteristic
253C2—82no—
254C2—4721no—
255C2—2362no—
256C2#1683806011yescharacteristic
257C2C2×#1427375411yescharacteristic
258C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3366
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. #16838113C2semidirect
2. #16838072C2semidirect
3. #16837765C2semidirect
4. #16837700C2semidirect
5. #16837689C2semidirect
6. #16837596C2semidirect
7. #16837594C2semidirect
8. #16837532C2semidirect
9. #16837511C2semidirect
10. C4×D472C2semidirect
11. C59×#486C2semidirect
96. D236#41semidirect
133. #486D59semidirect
141. C59#3366semidirect