Finite Group Databasebeta

← #21435964

Subgroups — #21435964

Order 7552.

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

normal subgroups only

This group has 420 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#16838067C211yesmaximal, characteristic, complemented
2#16838057C211yesmaximal, characteristic
3#16837752C211yesmaximal, characteristic, complemented
4#16837731C212yesmaximal, complemented
5#16837688C211yesmaximal, characteristic, complemented
6#16837628C212yesmaximal, complemented
7#16837539C212yesmaximal, complemented
8C4×#11745670C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic, complemented
10#103×D59C212yesmaximal, complemented
11C59×#461C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×Q8×D59C2212yes—
14C2×#11745670C2211yescharacteristic
15C2×C8×D59C2212yes—
16#14273727C2211yescharacteristic
17#14273726—21no—
18#14273709—22no—
19#14273706—21no—
20#14273705—22no—
21#14273703C2212yes—
22#14273698C2212yes—
23C4×Dic118C2211yescharacteristic
24C4×D236C2211yescharacteristic
25#14273689—21no—
26C4⋊C4×D59C2212yes—
27#14273659C2212yes—
28#14273658C2211yescharacteristic
29#14273652C2212yes—
30#14273651C2212yes—
31#14273651C2212yes—
32#14273650C2211yescharacteristic
33#14273648C2211yescharacteristic
34(C2×D59)⋊C8C2212yes—
35C4×C59⋊C8C2211yescharacteristic
36C2×SD16×C59C2212yes—
37C4⋊Q8×C59C2211yescharacteristic
38C4×D4×C59C2211yescharacteristic
39C4⋊C8×C59C2211yescharacteristic
40#103×C59C2212yes—
41C2×Q8×C59C2312yes—
42C2×D4×C59C2311yescharacteristic
43C22×C4×C59—21no—
44C2×C22⋊D59—22no—
45Q8×D59—24no—
46Q8×D59—42no—
47#11745685—44no—
48C2×D236D411yescharacteristic
49C2×C4×D59—22no—
50C2×C4×D59—22no—
51C2×C4×D59C2312yes—
52C2×Dic118—21no—
53C2×Dic118—22no—
54C2×Dic118C2311yescharacteristic
55SD16×C59—42no—
56C2×C8×C59C2312yes—
57C4⋊C4×C59—21no—
58C4⋊C4×C59—21no—
59C4⋊C4×C59C2311yescharacteristic
60C22⋊C4×C59—21no—
61C42×C59C2311yescharacteristic
62C22⋊Dic59—22no—
63#11745670—22no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4D412yes—
66C4⋊Dic59—21no—
67C4⋊Dic59D411yescharacteristic
68C4⋊Dic59C2311yescharacteristic
69C4⋊Dic59C2312yes—
70Dic59⋊C4—21no—
71Dic59⋊C4—22no—
72Dic59⋊C4—22no—
73C4×Dic59—21no—
74C2×C59⋊C8C2311yescharacteristic
75C2×C59⋊C8C2311yescharacteristic
76C8×D59—42no—
77C23×C59—21no—
78C22×D59C2×D412yes—
79Q8×C59—22no—
80Q8×C59—22no—
81D4×C59—21no—
82D4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—42no—
86C2×C4×C59C2×D411yescharacteristic
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2411yescharacteristic
89C22⋊D59—44no—
90C2×Dic59—21no—
91C2×Dic59—21no—
92C2×Dic59—22no—
93C2×Dic59C2×D412yes—
94D236SD1614yescomplemented
95C4×D59—22no—
96C4×D59—22no—
97C4×D59—44no—
98C4×D59—44no—
99Dic118—21no—
100Dic118—44no—
101Dic118—42no—
102Dic118#4112yescomplemented
103C8×C59—22no—
104C59⋊C8—21no—
105C59⋊C8—21no—
106C22×C59—41no—
107C22×C59—41no—
108C22×C59—41no—
109C22×C59C22×D411yescharacteristic
110C2×D59—22no—
111C2×D59—22no—
112C2×D59C2×SD1614yes—
113C4×C59—21no—
114C4×C59—42no—
115C4×C59—41no—
116C4×C59C2×SD1612yes—
117C4×C59C2×#4111yescharacteristic
118C4×C59H(5,𝔽2)11yescharacteristic
119Dic59—22no—
120Dic59—22no—
121Dic59—42no—
122Dic59—41no—
123#3298—591nomaximal, Sylow
124C2×C59—81no—
125C2×C59#54611yescharacteristic
126C2×C59C22×SD1611yescharacteristic
127C2×C59#57811yescharacteristic
128D59—24no—
129D4×Q8—591no—
130#547—591no—
131#487—591no—
132#483—592no—
133#475—591no—
134#465—592no—
135#461D5911yescharacteristic, complemented
136#448—592no—
137C4×SD16—591no—
138C8×D4—591no—
139C2×#103—592no—
140C59#329811yescharacteristic, complemented, Sylow
141C2×#41—1181no—
142C22×Q8—592no—
143C2×SD16—591no—
144C2×SD16C2×D5912yes—
145C22×C8—592no—
146C4⋊Q8—591no—
147C4⋊Q8—1181no—
148C4⋊Q8C2×D5911yescharacteristic
149#123—1182no—
150C22⋊Q8—592no—
151C22⋊Q8—1182no—
152C22⋊Q8—1181no—
153#121—592no—
154C4×Q8—591no—
155C4×D4—591no—
156C4×D4—1181no—
157C4×D4C2×D5911yescharacteristic
158C2×C4⋊C4—592no—
159#106—592no—
160#106—591no—
161C4⋊C8C2×D5911yescharacteristic
162#103—592no—
163#103—592no—
164#103—592no—
165#103—591no—
166#103C2×D5912yes—
167#102—591no—
168C22⋊C8—592no—
169C4×C8—591no—
170#41—2364no—
171C2×Q8—591no—
172C2×Q8—1182no—
173C2×Q8—1181no—
174C2×Q8—1184no—
175C2×Q8—2362no—
176C2×Q8C22×D5912yes—
177C2×D4—591no—
178C2×D4—1182no—
179C2×D4C22×D5911yescharacteristic
180C22×C4—21no—
181C22×C4—592no—
182C22×C4—1182no—
183C22×C4—1182no—
184SD16—42no—
185SD16—1182no—
186C2×C8—591no—
187C2×C8—591no—
188C2×C8—2362no—
189C2×C8C22×D5912yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—591no—
193C4⋊C4—591no—
194C4⋊C4—592no—
195C4⋊C4—1182no—
196C4⋊C4—1182no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4C22×D5911yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—592no—
202C22⋊C4—1182no—
203C22⋊C4—1182no—
204C42—1181no—
205C42C22×D5911yescharacteristic
206C23—21no—
207C23—592no—
208Q8—22no—
209Q8—22no—
210Q8—592no—
211Q8—1181no—
212Q8—2364no—
213Q8—2362no—
214D4—21no—
215D4—21no—
216D4—594no—
217D4—2364no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—592no—
222C2×C4—1181no—
223C2×C4—1182no—
224C2×C4—1182no—
225C2×C4—1181no—
226C2×C4—1182no—
227C2×C4—2364no—
228C2×C4—2364no—
229C2×C4D4×D5911yescharacteristic
230C2×C4D4×D5911yescharacteristic
231C2×C4C23×D5911yescharacteristic
232C8—22no—
233C8—1181no—
234C8—1181no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—594no—
239C22—1182no—
240C22—1182no—
241C22C2×D4×D5911yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—1182no—
246C4—1182no—
247C4—2362no—
248C4—2361no—
249C4SD16×D5912yes—
250C4#41×D5911yescharacteristic
251C4#1427377211yescharacteristic
252C2—81no—
253C2—1184no—
254C2#1683804911yescharacteristic
255C2C2×SD16×D5911yescharacteristic
256C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3298
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. #16838067C2semidirect
3. #16837752C2semidirect
4. #16837731C2semidirect
5. #16837688C2semidirect
6. #16837628C2semidirect
7. #16837539C2semidirect
8. C4×#11745670C2semidirect
9. #16837467C2semidirect
10. #103×D59C2semidirect
11. C59×#461C2semidirect
94. D236SD16semidirect
102. Dic118#41semidirect
135. #461D59semidirect
140. C59#3298semidirect