Finite Group Databasebeta

← #21436413

Subgroups — #21436413

Order 7552.

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

normal subgroups only

This group has 388 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#16838109C211yesmaximal, characteristic, complemented
2#16838057C211yesmaximal, characteristic
3#16837753C211yesmaximal, characteristic, complemented
4#16837733C212yesmaximal, complemented
5#16837693C211yesmaximal, characteristic, complemented
6#16837660C212yesmaximal, complemented
7#16837613C211yesmaximal, characteristic, complemented
8#16837566C212yesmaximal, complemented
9C4×#11745660C211yesmaximal, characteristic, complemented
10#16837404C212yesmaximal, complemented
11C59×#436C211yesmaximal, characteristic, complemented
12C2×#11745685C2212yes—
13C2×Dic236C2212yes—
14C2×#11745660C2211yescharacteristic
15#14273727C2211yescharacteristic
16#14273727C2211yescharacteristic
17#14273718—21no—
18#14273709—22no—
19#14273706C2212yes—
20#14273706C2212yes—
21#14273704—22no—
22#14273698—21no—
23C4×Dic118C2211yescharacteristic
24C4×D236C2211yescharacteristic
25D4×Dic59—21no—
26C2×C4⋊Dic59C2212yes—
27C4⋊C4×D59—21no—
28#14273659C2212yes—
29#14273659C2211yescharacteristic
30#14273652C2212yes—
31#14273652C2212yes—
32#14273652C2211yescharacteristic
33#14273652C2212yes—
34#14273649C2211yescharacteristic
35#14273649C2212yes—
36C2×M16×C59C2212yes—
37C4×D4×C59C2211yescharacteristic
38C4⋊C8×C59C2211yescharacteristic
39C22⋊C8×C59C2212yes—
40C4×C8×C59C2211yescharacteristic
41C2×D4×C59D411yescharacteristic
42C22×C4×C59C2312yes—
43C2×C22⋊D59—22no—
44C22×Dic59—22no—
45#11745685—24no—
46#11745685—42no—
47C2×D236C2311yescharacteristic
48C2×C4×D59—21no—
49C2×C4×D59—22no—
50C2×Dic118—21no—
51C2×Dic118C2312yes—
52C2×Dic118C2311yescharacteristic
53M16×C59—42no—
54C2×C8×C59C2311yescharacteristic
55C2×C8×C59C2311yescharacteristic
56C2×C8×C59C2312yes—
57C4⋊C4×C59D411yescharacteristic
58C22⋊C4×C59D412yes—
59C42×C59C2311yescharacteristic
60C22⋊Dic59—22no—
61C22⋊Dic59—22no—
62(C2×D59)⋊C4—21no—
63C4⋊Dic59—21no—
64C4⋊Dic59—22no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59C2311yescharacteristic
68C4⋊Dic59C2312yes—
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—22no—
71Dic59⋊C4—21no—
72Dic59⋊C4—22no—
73C4×Dic59—21no—
74Dic236—42no—
75#11745660—22no—
76C23×C59C2×D412yes—
77C22×D59—21no—
78D4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59—22no—
81C2×C4×C59C2×D412yes—
82C2×C4×C59C2×D411yescharacteristic
83C2×C4×C59C2×D411yescharacteristic
84C2×C4×C59C2411yescharacteristic
85C22⋊D59—44no—
86C2×Dic59—21no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90C2×Dic59—22no—
91C2×Dic59—82no—
92D236—21no—
93D236#4112yes—
94C4×D59—44no—
95C4×D59—42no—
96Dic118—21no—
97Dic118—22no—
98Dic118—21no—
99Dic118—22no—
100Dic118—81no—
101C8×C59—21no—
102C8×C59—22no—
103C8×C59—21no—
104C22×C59—22no—
105C22×C59—22no—
106C22×C59—22no—
107C22×C59C22×D411yescharacteristic
108C2×D59—22no—
109C2×D59—41no—
110C2×D59—41no—
111C4×C59—22no—
112C4×C59—21no—
113C4×C59#13712yes—
114C4×C59C2×#4111yescharacteristic
115C4×C59H(5,𝔽2)11yescharacteristic
116Dic59—42no—
117Dic59—41no—
118Dic59—41no—
119Dic59—42no—
120Dic59—41no—
121#3331—591nomaximal, Sylow
122C2×C59—42no—
123C2×C59#54611yescharacteristic
124C2×C59C2×#13711yescharacteristic
125C2×C59#57711yescharacteristic
126D59—42no—
127#554—591no—
128#547—591no—
129#487—591no—
130#483—592no—
131#476—591no—
132#470—592no—
133#462—591no—
134#452—592no—
135C4×SD16—591no—
136#436D5911yescharacteristic, complemented
137#417—592no—
138C59#333111yescharacteristic, complemented, Sylow
139C2×#41—592no—
140C2×Q16—592no—
141C2×SD16—591no—
142C2×M16C2×D5912yes—
143C4⋊Q8—591no—
144C4⋊Q8—591no—
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—1181no—
154C4×D4C2×D5911yescharacteristic
155C2×C4⋊C4—592no—
156C2×C4⋊C4—1181no—
157#106—591no—
158#106—592no—
159C4⋊C8C2×D5911yescharacteristic
160#103—592no—
161#103—592no—
162#103—591no—
163#103—592no—
164#102—591no—
165#102—592no—
166C22⋊C8C2×D5912yes—
167C4×C8C2×D5911yescharacteristic
168#41—1184no—
169#41—2362no—
170C2×Q8—592no—
171C2×Q8—591no—
172C2×Q8—1181no—
173C2×D4—591no—
174C2×D4—1182no—
175C2×D4D23611yescharacteristic
176C22×C4—1182no—
177C22×C4—1181no—
178C22×C4—1182no—
179C22×C4C22×D5912yes—
180Q16—2362no—
181SD16—1182no—
182M16—42no—
183C2×C8C22×D5911yescharacteristic
184C2×C8C22×D5911yescharacteristic
185C2×C8C22×D5912yes—
186C4⋊C4—591no—
187C4⋊C4—592no—
188C4⋊C4—591no—
189C4⋊C4—1182no—
190C4⋊C4—1181no—
191C4⋊C4—1182no—
192C4⋊C4—1181no—
193C4⋊C4—1181no—
194C4⋊C4—1182no—
195C4⋊C4—1181no—
196C4⋊C4D23611yescharacteristic
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C22⋊C4—1181no—
200C22⋊C4D23612yes—
201C42—1181no—
202C42C22×D5911yescharacteristic
203C23—1181no—
204C23C2×D23612yes—
205Q8—1181no—
206Q8—1182no—
207Q8—1181no—
208Q8—1182no—
209Q8—4721no—
210D4—22no—
211D4—592no—
212D4—1181no—
213D4—2364no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—1181no—
217C2×C4—1181no—
218C2×C4—1181no—
219C2×C4—1182no—
220C2×C4—1182no—
221C2×C4—4722no—
222C2×C4—2364no—
223C2×C4—2362no—
224C2×C4C2×D23611yescharacteristic
225C2×C4C2×D23612yes—
226C2×C4C2×D23611yescharacteristic
227C2×C4C23×D5911yescharacteristic
228C8—21no—
229C8—21no—
230C8—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—1182no—
235C22—2361no—
236C22—2361no—
237C22C22×D23611yescharacteristic
238C4—21no—
239C4—22no—
240C4—2361no—
241C4—2361no—
242C4—2362no—
243C4—2362no—
244C4—2361no—
245C4#1427376012yes—
246C4#41×D5911yescharacteristic
247C4#1427377211yescharacteristic
248C2—42no—
249C2—2362no—
250C2#1683804711yescharacteristic
251C2C2×#1427376011yescharacteristic
252C2#1683821411yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#436C2
socleC22×C59C22×D4
hypercenter#436D59
hypocenterC59#3331
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16838109C2semidirect
3. #16837753C2semidirect
4. #16837733C2semidirect
5. #16837693C2semidirect
6. #16837660C2semidirect
7. #16837613C2semidirect
8. #16837566C2semidirect
9. C4×#11745660C2semidirect
10. #16837404C2semidirect
11. C59×#436C2semidirect
136. #436D59semidirect
138. C59#3331semidirect