Finite Group Databasebeta

← #21435159

Subgroups — #21435159

Order 7552.

388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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#16838007C211yesmaximal, characteristic, complemented
2#16837978C211yesmaximal, characteristic, complemented
3#16837791C211yesmaximal, characteristic, complemented
4#16837775C211yesmaximal, characteristic, complemented
5#16837771C211yesmaximal, characteristic, complemented
6#16837757C211yesmaximal, characteristic, complemented
7#16837618C212yesmaximal, complemented
8#16837608C212yesmaximal, complemented
9#16837549C212yesmaximal, complemented
10#16837543C212yesmaximal, complemented
11C59×#433C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×Dic118C2211yescharacteristic
14C2×#11745660C2212yes—
15C2×#11745660C2212yes—
16C2×#11745660C2212yes—
17C2×D472C2212yes—
18#14273727C2211yescharacteristic
19#14273727C2211yescharacteristic
20#14273724C2211yescharacteristic
21#14273719C2211yescharacteristic
22#14273715C2211yescharacteristic
23#14273715C2211yescharacteristic
24#14273712—22no—
25#14273711—22no—
26#14273707—22no—
27#14273701C2212yes—
28#14273700—22no—
29C4×D236C2212yes—
30#14273652C2212yes—
31#14273652C2212yes—
32#14273652C2212yes—
33#14273649C2212yes—
34#117×C59C2211yescharacteristic
35C4⋊C8×C59C2212yes—
36C22⋊C8×C59C2212yes—
37#97×C59C2211yescharacteristic
38C4×C8×C59C2211yescharacteristic
39C22×C4×C59C2311yescharacteristic
40C2×C22⋊D59—21no—
41C2×C22⋊D59—22no—
42C22×Dic59—21no—
43#11745685—42no—
44C2×D236—22no—
45C2×D236C2311yescharacteristic
46C2×D236C2312yes—
47C2×C4×D59—21no—
48C2×C4×D59—22no—
49C2×Dic118—21no—
50C2×Dic118—42no—
51C2×Dic118C2311yescharacteristic
52C2×Dic118C2311yescharacteristic
53C2×Dic118C2311yescharacteristic
54C2×C8×C59C2312yes—
55C2×C8×C59C2312yes—
56C4⋊C4×C59D412yes—
57C22⋊C4×C59D412yes—
58C42×C59C2311yescharacteristic
59C42×C59C2311yescharacteristic
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—22no—
64C4⋊Dic59—22no—
65C4⋊Dic59—22no—
66C4⋊Dic59C2312yes—
67Dic59⋊C4—22no—
68D472—42no—
69#11745660—42no—
70#11745660—42no—
71#11745660—42no—
72C23×C59C2×D411yescharacteristic
73C22×D59—21no—
74C22×D59—22no—
75C2×C4×C59—22no—
76C2×C4×C59C2×D412yes—
77C2×C4×C59C2×D412yes—
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2411yescharacteristic
80C22⋊D59—42no—
81C22⋊D59—82no—
82C2×Dic59—22no—
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—21no—
86C2×Dic59—42no—
87D236—22no—
88D236—22no—
89D236—22no—
90D236—82no—
91C4×D59—42no—
92C4×D59—82no—
93Dic118—22no—
94Dic118—22no—
95Dic118—22no—
96Dic118—42no—
97C8×C59—22no—
98C8×C59—22no—
99C22×C59—21no—
100C22×C59—22no—
101C22×C59C22×D411yescharacteristic
102C2×D59—41no—
103C2×D59—42no—
104C2×D59—42no—
105C2×D59—42no—
106C2×D59—42no—
107C4×C59—21no—
108C4×C59—22no—
109C4×C59—22no—
110C4×C59H(5,𝔽2)12yes—
111Dic59—41no—
112Dic59—41no—
113Dic59—41no—
114Dic59—42no—
115#3221—591nomaximal, Sylow
116C2×C59—41no—
117C2×C59#53511yescharacteristic
118C2×C59#57712yes—
119D59—81no—
120D59—82no—
121#540—591no—
122#536—591no—
123#496—591no—
124#492—591no—
125#491—591no—
126#488—591no—
127#463—592no—
128#461—592no—
129#449—592no—
130#448—592no—
131#433D5911yescharacteristic, complemented
132C59#322111yescharacteristic, complemented, Sylow
133C2×#41—591no—
134C22×Q8—591no—
135C2×SD16—592no—
136C2×SD16—592no—
137C2×SD16—592no—
138C2×D8—592no—
139C4⋊Q8—591no—
140C4⋊Q8—591no—
141#127—591no—
142#125—591no—
143#124—591no—
144#124—591no—
145#123—1182no—
146#123—1182no—
147C22⋊Q8—1182no—
148#121—592no—
149#121—1182no—
150C4×D4—592no—
151#117C2×D5911yescharacteristic
152C4⋊C8C2×D5912yes—
153#103—592no—
154#103—592no—
155#103—592no—
156#102—592no—
157C22⋊C8C2×D5912yes—
158#97C2×D5911yescharacteristic
159C4×C8C2×D5911yescharacteristic
160#41—2362no—
161C2×Q8—591no—
162C2×Q8—591no—
163C2×Q8—591no—
164C2×Q8—1181no—
165C2×Q8—2362no—
166C2×D4—591no—
167C2×D4—592no—
168C2×D4—1182no—
169C2×D4—1181no—
170C2×D4—1182no—
171C22×C4—1181no—
172C22×C4—1182no—
173C22×C4—1181no—
174C22×C4C22×D5911yescharacteristic
175SD16—2362no—
176SD16—2362no—
177SD16—2362no—
178D8—2362no—
179C2×C8C22×D5912yes—
180C2×C8C22×D5912yes—
181C4⋊C4—592no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C4⋊C4—1182no—
185C4⋊C4D23612yes—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—1182no—
189C22⋊C4—1182no—
190C22⋊C4D23612yes—
191C42C22×D5911yescharacteristic
192C42C22×D5911yescharacteristic
193C23—1181no—
194C23—1182no—
195C23C2×D23611yescharacteristic
196Q8—1182no—
197Q8—1182no—
198Q8—1182no—
199Q8—2362no—
200D4—1182no—
201D4—1182no—
202D4—1182no—
203D4—4722no—
204D4—4722no—
205D4—2362no—
206C2×C4—22no—
207C2×C4—1182no—
208C2×C4—1181no—
209C2×C4—1181no—
210C2×C4—1181no—
211C2×C4—4722no—
212C2×C4—2362no—
213C2×C4—2362no—
214C2×C4C2×D23612yes—
215C2×C4C2×D23612yes—
216C2×C4C2×D23611yescharacteristic
217C2×C4C23×D5911yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—21no—
222C22—2362no—
223C22—2362no—
224C22—2362no—
225C22—2361no—
226C22—2362no—
227C22C22×D23611yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—2362no—
232C4—2361no—
233C4—2361no—
234C4—2361no—
235C4#1427377312yes—
236C2—41no—
237C2—4722no—
238C2—4721no—
239C2#1683797111yescharacteristic
240C2#1683821412yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3221
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16838007C2semidirect
2. #16837978C2semidirect
3. #16837791C2semidirect
4. #16837775C2semidirect
5. #16837771C2semidirect
6. #16837757C2semidirect
7. #16837618C2semidirect
8. #16837608C2semidirect
9. #16837549C2semidirect
10. #16837543C2semidirect
11. C59×#433C2semidirect
131. #433D59semidirect
132. C59#3221semidirect