Finite Group Databasebeta

← #21435429

Subgroups — #21435429

Order 7552.

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

normal subgroups only

This group has 354 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#16837957C211yesmaximal, characteristic, complemented
2#16837934C211yesmaximal, characteristic
3#16837707C212yesmaximal, complemented
4#16837688C211yesmaximal, characteristic, complemented
5#16837682C211yesmaximal, characteristic, complemented
6#16837642C212yesmaximal, complemented
7#16837628C212yesmaximal
8#16837622C212yesmaximal, complemented
9#16837609C211yesmaximal, characteristic, complemented
10C4⋊C8×D59C211yesmaximal, characteristic, complemented
11C59×#461C211yesmaximal, characteristic, complemented
12C2×#11745672C2212yes—
13C2×C8×D59C2212yes—
14#14273727C2211yescharacteristic
15#14273720—21no—
16#14273718—21no—
17#14273718C2211yescharacteristic
18#14273714C2211yescharacteristic
19#14273709—21no—
20#14273707—21no—
21#14273707C2211yescharacteristic
22#14273703C2212yes—
23#14273698C2211yescharacteristic
24Q8×Dic59C2212yes—
25C4×Dic118C2211yescharacteristic
26#14273692—21no—
27C4×C22⋊D59—21no—
28#14273686—21no—
29#14273685—21no—
30C42×D59C2211yescharacteristic
31#14273660C2212yes—
32#14273659C2212yes—
33C4⋊(C59⋊C8)C2211yescharacteristic
34Dic59⋊C8C2212yes—
35#14273652C2212yes—
36#14273651C2212yes—
37#14273648C2212yes—
38C2×SD16×C59C2212yes—
39C4⋊Q8×C59C2211yescharacteristic
40C4×D4×C59C2211yescharacteristic
41C4⋊C8×C59C2211yescharacteristic
42#103×C59C2212yes—
43C2×Q8×C59C2312yes—
44C2×D4×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C2×C22⋊D59—21no—
47C2×C4×D59D411yescharacteristic
48C2×C4×D59D411yescharacteristic
49C2×C4×D59C2311yescharacteristic
50C2×Dic118—21no—
51C2×Dic118C2311yescharacteristic
52SD16×C59—42no—
53C2×C8×C59C2312yes—
54C4⋊C4×C59—21no—
55C4⋊C4×C59—21no—
56C4⋊C4×C59C2311yescharacteristic
57C22⋊C4×C59—21no—
58C42×C59C2311yescharacteristic
59C22⋊Dic59—21no—
60C22⋊Dic59—21no—
61C22⋊Dic59—21no—
62#11745672—42no—
63(C2×D59)⋊C4—22no—
64(C2×D59)⋊C4—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59—22no—
69C4⋊Dic59C2312yes—
70C4⋊Dic59C2311yescharacteristic
71Dic59⋊C4—21no—
72Dic59⋊C4—21no—
73Dic59⋊C4—22no—
74C4×Dic59—21no—
75C4×Dic59—22no—
76C4×Dic59D411yescharacteristic
77C4×Dic59D411yescharacteristic
78C4×Dic59C2311yescharacteristic
79C2×C59⋊C8C2312yes—
80C8×D59—42no—
81C23×C59—21no—
82C22×D59C2×D411yescharacteristic
83Q8×C59—22no—
84Q8×C59—22no—
85D4×C59—21no—
86D4×C59—21no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—42no—
90C2×C4×C59C2×D411yescharacteristic
91C2×C4×C59C2×D411yescharacteristic
92C2×C4×C59C2411yescharacteristic
93C22⋊D59—42no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—21no—
97C2×Dic59C2×D411yescharacteristic
98C2×Dic59C2×D411yescharacteristic
99C2×Dic59C2×D411yescharacteristic
100C4×D59—22no—
101C4×D59—22no—
102C4×D59—21no—
103C4×D59—21no—
104Dic118—21no—
105Dic118—21no—
106Dic118—42no—
107C8×C59—22no—
108C59⋊C8—22no—
109C22×C59—41no—
110C22×C59—41no—
111C22×C59—41no—
112C22×C59C22×D411yescharacteristic
113C2×D59—21no—
114C2×D59—21no—
115C2×D59#13712yes—
116C4×C59—21no—
117C4×C59—42no—
118C4×C59—41no—
119C4×C59#13512yes—
120C4×C59H(5,𝔽2)11yescharacteristic
121C4×C592−1+411yescharacteristic
122Dic59—21no—
123Dic59—21no—
124Dic59—21no—
125Dic59—41no—
126Dic59—42no—
127Dic59—41no—
128#3248—591nomaximal, Sylow
129C2×C59—81no—
130C2×C59#53711yescharacteristic
131C2×C59C2×#13511yescharacteristic
132C2×C59C2×#13711yescharacteristic
133D59—22no—
134#533—591no—
135#529—591no—
136#479—592no—
137#475—591no—
138#474—591no—
139#467—592no—
140#465—592no—
141#464—592no—
142#462—591no—
143#461D5911yescharacteristic, complemented
144C2×C4⋊C8—591no—
145C59#324811yescharacteristic, complemented, Sylow
146C2×Q16—592no—
147C2×SD16C2×D5912yes—
148C22×C8—592no—
149C4⋊Q8—591no—
150C4⋊Q8C2×D5911yescharacteristic
151#126—1181no—
152#125—591no—
153#125—1181no—
154#124—591no—
155#123—1181no—
156C22⋊Q8—592no—
157C22⋊Q8—591no—
158C22⋊Q8—1181no—
159#121—591no—
160C4×Q8—592no—
161C4×Q8—591no—
162C4×Q8—1181no—
163C4×D4—1181no—
164C4×D4C2×D5911yescharacteristic
165#117—1181no—
166#117—1181no—
167C2×C42—591no—
168#107—592no—
169#106—592no—
170C4⋊C8—592no—
171C4⋊C8—591no—
172C4⋊C8C2×D5911yescharacteristic
173#103—592no—
174#103—592no—
175#103C2×D5912yes—
176#102—592no—
177C2×Q8—591no—
178C2×Q8—1181no—
179C2×Q8C22×D5912yes—
180C2×D4—1181no—
181C2×D4C22×D5911yescharacteristic
182C22×C4—21no—
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—591no—
186Q16—2362no—
187SD16—42no—
188C2×C8—592no—
189C2×C8—2362no—
190C2×C8C22×D5912yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—592no—
194C4⋊C4—591no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1182no—
199C4⋊C4—1182no—
200C4⋊C4—1181no—
201C4⋊C4—1181no—
202C4⋊C4C22×D5911yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—1182no—
205C22⋊C4—1181no—
206C22⋊C4—1181no—
207C22⋊C4—1181no—
208C22⋊C4—1181no—
209C42—591no—
210C42—591no—
211C42—591no—
212C42—1182no—
213C42—1181no—
214C42C22×D5911yescharacteristic
215C23—21no—
216C23—591no—
217Q8—22no—
218Q8—22no—
219Q8—1181no—
220Q8—1181no—
221Q8—2362no—
222D4—21no—
223D4—21no—
224D4—2362no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—42no—
228C2×C4—591no—
229C2×C4—591no—
230C2×C4—591no—
231C2×C4—1182no—
232C2×C4—1182no—
233C2×C4—1181no—
234C2×C4—1181no—
235C2×C4—1181no—
236C2×C4—1181no—
237C2×C4—1182no—
238C2×C4D4×D5911yescharacteristic
239C2×C4D4×D5911yescharacteristic
240C2×C4C23×D5911yescharacteristic
241C8—22no—
242C8—1182no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—592no—
247C22—1181no—
248C22—1181no—
249C22C2×D4×D5911yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—1181no—
254C4—1181no—
255C4—1181no—
256C4—2362no—
257C4—2361no—
258C4—2361no—
259C4#1427374812yes—
260C4#1427377211yescharacteristic
261C4#1427377411yescharacteristic
262C2—81no—
263C2—1182no—
264C2#1683798111yescharacteristic
265C2C2×#1427374811yescharacteristic
266C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3248
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16837957C2semidirect
3. #16837707C2semidirect
4. #16837688C2semidirect
5. #16837682C2semidirect
6. #16837642C2semidirect
8. #16837622C2semidirect
9. #16837609C2semidirect
10. C4⋊C8×D59C2semidirect
11. C59×#461C2semidirect
143. #461D59semidirect
145. C59#3248semidirect