Finite Group Databasebeta

← #21435181

Subgroups — #21435181

Order 7552.

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

normal subgroups only

This group has 364 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#16838014C211yesmaximal, characteristic, complemented
2#16837978C211yesmaximal, characteristic
3#16837796C211yesmaximal, characteristic, complemented
4#16837782C211yesmaximal, characteristic, complemented
5#16837771C211yesmaximal, characteristic, complemented
6#16837757C211yesmaximal, characteristic, complemented
7#16837625C212yesmaximal, complemented
8#16837613C212yesmaximal, complemented
9#16837566C212yesmaximal
10#16837560C212yesmaximal, complemented
11C59×#433C211yesmaximal, characteristic, complemented
12C2×#11745685C2211yescharacteristic
13C22×Dic118C2211yescharacteristic
14C2×Dic236C2212yes—
15C2×Dic236C2212yes—
16C2×Dic236C2212yes—
17C2×#11745660C2212yes—
18#14273727C2211yescharacteristic
19#14273727C2211yescharacteristic
20#14273727C2211yescharacteristic
21#14273720—22no—
22#14273719C2211yescharacteristic
23#14273717—22no—
24#14273715C2211yescharacteristic
25#14273715C2211yescharacteristic
26#14273711—22no—
27#14273707—22no—
28#14273706C2212yes—
29C4×Dic118C2212yes—
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—
41C22×Dic59—21no—
42#11745685—42no—
43C2×D236C2311yescharacteristic
44C2×C4×D59—21no—
45C2×Dic118—21no—
46C2×Dic118—42no—
47C2×Dic118C2311yescharacteristic
48C2×Dic118C2311yescharacteristic
49C2×Dic118C2311yescharacteristic
50C2×Dic118C2312yes—
51C2×C8×C59C2312yes—
52C2×C8×C59C2312yes—
53C4⋊C4×C59D412yes—
54C22⋊C4×C59D412yes—
55C42×C59C2311yescharacteristic
56C42×C59C2311yescharacteristic
57C22⋊Dic59—22no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60C4⋊Dic59—22no—
61C4⋊Dic59—22no—
62C4⋊Dic59—22no—
63C4⋊Dic59C2312yes—
64Dic59⋊C4—22no—
65Dic59⋊C4—22no—
66Dic59⋊C4—22no—
67C4×Dic59—22no—
68Dic236—42no—
69Dic236—42no—
70Dic236—42no—
71#11745660—42no—
72C23×C59C2×D411yescharacteristic
73C22×D59—21no—
74C2×C4×C59—22no—
75C2×C4×C59C2×D412yes—
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59C2×D412yes—
78C2×C4×C59C2411yescharacteristic
79C22⋊D59—42no—
80C2×Dic59—22no—
81C2×Dic59—22no—
82C2×Dic59—21no—
83C2×Dic59—21no—
84C2×Dic59—21no—
85C2×Dic59—42no—
86D236—22no—
87C4×D59—42no—
88Dic118—22no—
89Dic118—22no—
90Dic118—22no—
91Dic118—22no—
92Dic118—22no—
93Dic118—42no—
94C8×C59—22no—
95C8×C59—22no—
96C22×C59—21no—
97C22×C59—22no—
98C22×C59C22×D411yescharacteristic
99C2×D59—41no—
100C2×D59—42no—
101C4×C59—21no—
102C4×C59—22no—
103C4×C59—22no—
104C4×C59H(5,𝔽2)12yes—
105Dic59—41no—
106Dic59—41no—
107Dic59—41no—
108Dic59—42no—
109Dic59—42no—
110#3223—591nomaximal, Sylow
111C2×C59—41no—
112C2×C59#53511yescharacteristic
113C2×C59#57812yes—
114D59—81no—
115#541—591no—
116#536—591no—
117#497—591no—
118#494—591no—
119#491—591no—
120#488—591no—
121#464—592no—
122#462—592no—
123#452—592no—
124#451—592no—
125#433D5911yescharacteristic, complemented
126C59#322311yescharacteristic, complemented, Sylow
127C2×#41—591no—
128C22×Q8—591no—
129C2×Q16—592no—
130C2×Q16—592no—
131C2×Q16—592no—
132C2×SD16—592no—
133C4⋊Q8—591no—
134C4⋊Q8—591no—
135C4⋊Q8—591no—
136#126—1182no—
137#125—591no—
138#125—1182no—
139#124—591no—
140#124—591no—
141#123—1182no—
142C22⋊Q8—592no—
143C22⋊Q8—1182no—
144C4×Q8—592no—
145#117C2×D5911yescharacteristic
146C4⋊C8C2×D5912yes—
147#103—592no—
148#103—592no—
149#103—592no—
150#102—592no—
151C22⋊C8C2×D5912yes—
152#97C2×D5911yescharacteristic
153C4×C8C2×D5911yescharacteristic
154#41—2362no—
155C2×Q8—591no—
156C2×Q8—591no—
157C2×Q8—591no—
158C2×Q8—592no—
159C2×Q8—1181no—
160C2×Q8—2362no—
161C2×D4—591no—
162C2×D4—1181no—
163C22×C4—1181no—
164C22×C4—1181no—
165C22×C4C22×D5911yescharacteristic
166Q16—2362no—
167Q16—2362no—
168Q16—2362no—
169SD16—2362no—
170C2×C8C22×D5912yes—
171C2×C8C22×D5912yes—
172C4⋊C4—592no—
173C4⋊C4—1182no—
174C4⋊C4—1182no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4D23612yes—
180C22⋊C4—1182no—
181C22⋊C4—1182no—
182C22⋊C4—1182no—
183C22⋊C4D23612yes—
184C42—1182no—
185C42C22×D5911yescharacteristic
186C42C22×D5911yescharacteristic
187C23—1181no—
188C23C2×D23611yescharacteristic
189Q8—1182no—
190Q8—1182no—
191Q8—1182no—
192Q8—1182no—
193Q8—1182no—
194Q8—2362no—
195D4—1182no—
196D4—2362no—
197C2×C4—22no—
198C2×C4—1182no—
199C2×C4—1182no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1181no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4C2×D23612yes—
206C2×C4C2×D23612yes—
207C2×C4C2×D23611yescharacteristic
208C2×C4C23×D5911yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—2362no—
214C22—2361no—
215C22C22×D23611yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—2362no—
220C4—2361no—
221C4—2361no—
222C4—2361no—
223C4—2362no—
224C4#1427377312yes—
225C2—41no—
226C2—4721no—
227C2#1683797111yescharacteristic
228C2#1683821912yes—
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#433C2
socleC22×C59C22×D4
hypercenter#433D59
hypocenterC59#3223
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. #16838014C2semidirect
3. #16837796C2semidirect
4. #16837782C2semidirect
5. #16837771C2semidirect
6. #16837757C2semidirect
7. #16837625C2semidirect
8. #16837613C2semidirect
10. #16837560C2semidirect
11. C59×#433C2semidirect
125. #433D59semidirect
126. C59#3223semidirect