Finite Group Databasebeta

← #21436728

Subgroups — #21436728

Order 7552.

426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 123 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#16838072C211yesmaximal, characteristic, complemented
2#16838067C211yesmaximal, characteristic, complemented
3#16837747C212yesmaximal, complemented
4#16837680C212yesmaximal, complemented
5#16837679C211yesmaximal, characteristic, complemented
6#16837596C212yesmaximal, complemented
7#16837594C211yesmaximal, characteristic, complemented
8C8×Dic118C211yesmaximal, characteristic, complemented
9C4×D472C211yesmaximal, characteristic, complemented
10#16837482C212yesmaximal, complemented
11C59×#486C211yesmaximal, characteristic, complemented
12C2×#11745687—21no—
13C2×Q8×D59—21no—
14C2×D472C2211yescharacteristic
15C2×#11745669C2212yes—
16#14273726C2212yes—
17#14273723C2212yes—
18#14273705—22no—
19#14273703—21no—
20#14273699—22no—
21#14273698—21no—
22C4×Dic118C2211yescharacteristic
23C4×D236C2211yescharacteristic
24C4×D236C2211yescharacteristic
25D4×Dic59C2212yes—
26#14273689C2212yes—
27#14273661C2211yescharacteristic
28#14273660C2212yes—
29C4⋊(C59⋊C8)C2211yescharacteristic
30Dic59⋊C8C2212yes—
31#14273649C2211yescharacteristic
32#14273649C2211yescharacteristic
33#14273648C2212yes—
34#14273647C2212yes—
35C8×Dic59C2212yes—
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—
48Q8×D59—44no—
49#11745687—44no—
50C2×D236C2311yescharacteristic
51C2×D236C2311yescharacteristic
52C2×C4×D59—21no—
53C2×C4×D59—21no—
54C2×C4×D59—22no—
55C2×Dic118—22no—
56C2×Dic118D411yescharacteristic
57C2×C8×C59C2311yescharacteristic
58C2×C8×C59C2311yescharacteristic
59C4⋊C4×C59—21no—
60C4⋊C4×C59C2312yes—
61C42×C59C2311yescharacteristic
62C22⋊Dic59—22no—
63#11745669—24no—
64(C2×D59)⋊C4—21no—
65(C2×D59)⋊C4—21no—
66(C2×D59)⋊C4—22no—
67C4⋊Dic59D411yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—22no—
71Dic59⋊C4D412yes—
72C4×Dic59C2312yes—
73C2×C59⋊C8C2312yes—
74D472—22no—
75C23×C59—22no—
76C22×D59—21no—
77C22×D59—21no—
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—44no—
92C2×Dic59C2×D412yes—
93C2×Dic59C2×D412yes—
94D236—21no—
95D236—21no—
96D236—21no—
97D236#4112yescomplemented
98C4×D59—42no—
99C4×D59—42no—
100C4×D59—44no—
101Dic118—44no—
102Dic118D814yescomplemented
103C8×C59—21no—
104C8×C59—21no—
105C59⋊C8—22no—
106C22×C59—42no—
107C22×C59—42no—
108C22×C59—42no—
109C22×C59C22×D411yescharacteristic
110C2×D59—22no—
111C2×D59—41no—
112C2×D59—41no—
113C2×D59—41no—
114C2×D59—41no—
115C2×D59—41no—
116C4×C59—21no—
117C4×C59—42no—
118C4×C59C2×D812yes—
119C4×C59C2×#4111yescharacteristic
120C4×C592−1+411yescharacteristic
121Dic59—22no—
122Dic59—41no—
123Dic59—41no—
124Dic59C2×D814yes—
125#3358—591nomaximal, Sylow
126C2×C59—82no—
127C2×C59#54811yescharacteristic
128C2×C59C22×D811yescharacteristic
129C2×C59#57711yescharacteristic
130D59—42no—
131D59—81no—
132#550—591no—
133D4×Q8—591no—
134#486—592no—
135#486D5911yescharacteristic, complemented
136#474—591no—
137#474—592no—
138#459—591no—
139#459—592no—
140C8×Q8—591no—
141C4×D8—592no—
142C4×D8—591no—
143C59#335811yescharacteristic, complemented, Sylow
144C2×#41—1181no—
145C22×Q8—1181no—
146C2×D8—592no—
147C2×D8—591no—
148C4⋊Q8—592no—
149C4⋊Q8C2×D5911yescharacteristic
150#127—592no—
151#127C2×D5911yescharacteristic
152C22⋊Q8—1182no—
153C22⋊Q8—1181no—
154#121—1181no—
155#121—1182no—
156C4×Q8—591no—
157C4×D4—592no—
158C4×D4—592no—
159C4×D4—591no—
160C4×D4—591no—
161#107—591no—
162#107—592no—
163C4⋊C8—592no—
164C4⋊C8—591no—
165#102—592no—
166#102—591no—
167#102—591no—
168#102—592no—
169#102C2×D5912yes—
170#102C2×D5912yes—
171C4×C8—592no—
172C4×C8C2×D5911yescharacteristic
173#41—2364no—
174C2×Q8—21no—
175C2×Q8—591no—
176C2×Q8—1182no—
177C2×Q8—2364no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—591no—
181C2×D4—591no—
182C2×D4—1182no—
183C2×D4—1182no—
184C2×D4C22×D5912yes—
185C22×C4—1182no—
186C22×C4—1182no—
187C22×C4—1181no—
188C22×C4—1181no—
189D8—1182no—
190D8—1184no—
191C2×C8—592no—
192C2×C8C22×D5911yescharacteristic
193C2×C8C22×D5911yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—592no—
196C4⋊C4—591no—
197C4⋊C4—591no—
198C4⋊C4—591no—
199C4⋊C4—1182no—
200C4⋊C4C22×D5912yes—
201C22⋊C4—1182no—
202C22⋊C4—1182no—
203C22⋊C4—1181no—
204C22⋊C4—1181no—
205C42—592no—
206C42C22×D5911yescharacteristic
207C23—22no—
208C23—1181no—
209C23—1181no—
210Q8—42no—
211Q8—594no—
212Q8—2364no—
213D4—22no—
214D4—22no—
215D4—42no—
216D4—81no—
217D4—592no—
218D4—1181no—
219D4—1181no—
220D4—1181no—
221D4—4722no—
222D4—2364no—
223C2×C4—22no—
224C2×C4—592no—
225C2×C4—592no—
226C2×C4—1181no—
227C2×C4—1181no—
228C2×C4—2364no—
229C2×C4—2364no—
230C2×C4—2362no—
231C2×C4—2362no—
232C2×C4D4×D5911yescharacteristic
233C2×C4D4×D5911yescharacteristic
234C2×C4C23×D5911yescharacteristic
235C8—21no—
236C8—21no—
237C8—1182no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—1182no—
242C22—2361no—
243C22—2361no—
244C22—2361no—
245C22—2361no—
246C22—2361no—
247C22C2×D4×D5911yescharacteristic
248C4—21no—
249C4—42no—
250C4—594no—
251C4—1182no—
252C4—2361no—
253C4—2361no—
254C4D8×D5912yes—
255C4#41×D5911yescharacteristic
256C4#1427377411yescharacteristic
257C2—82no—
258C2—4721no—
259C2—2362no—
260C2#1683806011yescharacteristic
261C2C2×D8×D5911yescharacteristic
262C2#1683820811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#486C2
socleC22×C59C22×D4
hypercenter#486D59
hypocenterC59#3358
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. #16838072C2semidirect
2. #16838067C2semidirect
3. #16837747C2semidirect
4. #16837680C2semidirect
5. #16837679C2semidirect
6. #16837596C2semidirect
7. #16837594C2semidirect
8. C8×Dic118C2semidirect
9. C4×D472C2semidirect
10. #16837482C2semidirect
11. C59×#486C2semidirect
97. D236#41semidirect
102. Dic118D8semidirect
135. #486D59semidirect
143. C59#3358semidirect