Finite Group Databasebeta

← #21429000

Subgroups — #21429000

Order 7552.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#14273704C212yesmaximal, complemented
2C2×#14273692C211yesmaximal, characteristic, complemented
3C2×D4×Dic59C211yesmaximal, characteristic
4#16837334C211yesmaximal, characteristic, complemented
5#16837332C211yesmaximal, characteristic, complemented
6#16837316C211yesmaximal, characteristic
7#16837296C212yesmaximal, complemented
8#16837295C212yesmaximal, complemented
9#16837266C211yesmaximal, characteristic, complemented
10#16837260C212yesmaximal, complemented
11C59×#394C211yesmaximal, characteristic
12C22×Dic118C2211yescharacteristic
13C23×Dic59C2212yes—
14#14273704—28no—
15#14273692—24no—
16D4×Dic59—24no—
17C2×C4⋊Dic59C2212yes—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×C22⋊Dic59C2212yes—
24C2×C22⋊Dic59C2212yes—
25C2×C22⋊Dic59C2212yes—
26C2×C4×Dic59C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C59⋊#95C2211yescharacteristic
33C22×D4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2211yescharacteristic
35C2×C22⋊C4×C59C2212yes—
36C2×C22⋊C4×C59C2212yes—
37#95×C59C2211yescharacteristic
38C24×C59C2312yes—
39C2×D4×C59—24no—
40C2×D4×C59—22no—
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C22×Dic59—24no—
46C22×Dic59—24no—
47C22×Dic59—24no—
48C22×Dic59C2312yes—
49C22×Dic59C2311yescharacteristic
50C22×Dic59C2312yes—
51C22×Dic59C2311yescharacteristic
52C22×Dic59C2311yescharacteristic
53C22×Dic59C2311yescharacteristic
54C2×Dic118—22no—
55C2×Dic118—22no—
56C2×Dic118D414yescomplemented
57C4⋊C4×C59—22no—
58C22⋊C4×C59—24no—
59C22⋊C4×C59—24no—
60C22⋊Dic59—24no—
61C22⋊Dic59—24no—
62C22⋊Dic59—24no—
63C4⋊Dic59—22no—
64C4⋊Dic59—24no—
65Dic59⋊C4—22no—
66Dic59⋊C4—24no—
67Dic59⋊C4—22no—
68Dic59⋊C4—24no—
69C4×Dic59—22no—
70C4×Dic59—22no—
71C4×Dic59D414yes—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—22no—
75C23×C59—22no—
76C23×C59—22no—
77C23×C59—22no—
78C23×C59#4114yes—
79C23×C59C2411yescharacteristic
80D4×C59—28no—
81C2×C4×C59—21no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D412yes—
90C2×C4×C59C2×D412yes—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—22no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59—22no—
102C2×Dic59—48no—
103C2×Dic59C2×D412yes—
104C2×Dic59C2×D412yes—
105C2×Dic59C2×D412yes—
106C2×Dic59C2×D412yes—
107C2×Dic59#4112yes—
108Dic118—28no—
109C22×C59—24no—
110C22×C59—24no—
111C22×C59—24no—
112C22×C59—42no—
113C22×C59—42no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59C22×D411yescharacteristic
117C22×C59C22×D411yescharacteristic
118C22×C59C2×#4111yescharacteristic
119C22×C59C2×#4112yes—
120C22×C592−1+412yes—
121C4×C59—22no—
122C4×C59—22no—
123C4×C59—41no—
124C4×C59—42no—
125Dic59—22no—
126Dic59—22no—
127Dic59—42no—
128Dic59—41no—
129Dic59—42no—
130Dic59#12114yes—
131#2536—591nomaximal, Sylow
132C2×C59—44no—
133C2×C59C2×#12111yescharacteristic
134C2×C59#52511yescharacteristic
135C2×C59#53611yescharacteristic
136C2×C59#54812yes—
137C2×C59#55212yes—
138C2×C22⋊Q8—592no—
139C2×C4×Q8—591no—
140C2×C4×D4—591no—
141#398—591no—
142#398—591no—
143#394—591no—
144#394D5911yescharacteristic
145#388—592no—
146#388—592no—
147#382—591no—
148#380—592no—
149C59#253611yescharacteristic, complemented, Sylow
150C22×Q8—591no—
151C22×D4C2×D5911yescharacteristic
152C23×C4—592no—
153C22⋊Q8—1188no—
154C4×Q8—1184no—
155C4×D4—1184no—
156C2×C4⋊C4—591no—
157C2×C4⋊C4—591no—
158C2×C4⋊C4—591no—
159C2×C4⋊C4—592no—
160C2×C4⋊C4—592no—
161C2×C4⋊C4—592no—
162C2×C4⋊C4C2×D5911yescharacteristic
163C2×C22⋊C4—592no—
164C2×C22⋊C4—592no—
165C2×C22⋊C4—592no—
166C2×C22⋊C4C2×D5912yes—
167C2×C22⋊C4C2×D5912yes—
168C2×C42—591no—
169C2×C42—591no—
170C2×C42—591no—
171#95—592no—
172#95—592no—
173#95—592no—
174#95—591no—
175#95C2×D5911yescharacteristic
176C24C22×D5912yes—
177C2×Q8—594no—
178C2×Q8—1182no—
179C2×Q8—1182no—
180C2×D4—24no—
181C2×D4—22no—
182C22×C4—591no—
183C22×C4—591no—
184C22×C4—591no—
185C22×C4—592no—
186C22×C4—591no—
187C22×C4—592no—
188C22×C4—1184no—
189C22×C4—1184no—
190C22×C4—1184no—
191C22×C4C22×D5912yes—
192C22×C4C22×D5911yescharacteristic
193C22×C4C22×D5911yescharacteristic
194C22×C4C22×D5911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—1182no—
197C4⋊C4—1184no—
198C4⋊C4—1184no—
199C4⋊C4—1182no—
200C4⋊C4—1182no—
201C4⋊C4—1184no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—1184no—
205C22⋊C4—1184no—
206C22⋊C4—1184no—
207C42—594no—
208C42—1182no—
209C42—1182no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#1174568714yes—
217C23C23×D5911yescharacteristic
218Q8—1188no—
219D4—28no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—592no—
229C2×C4—592no—
230C2×C4—592no—
231C2×C4—592no—
232C2×C4—592no—
233C2×C4—1181no—
234C2×C4—1181no—
235C2×C4—1182no—
236C2×C4—1181no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4—1182no—
240C2×C4—1182no—
241C2×C4—1182no—
242C2×C4—1182no—
243C2×C4—1182no—
244C2×C4—2368no—
245C2×C4D4×D5912yes—
246C2×C4D4×D5912yes—
247C22—24no—
248C22—24no—
249C22—24no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×D4×D5911yescharacteristic
255C22C2×D4×D5911yescharacteristic
256C22#41×D5911yescharacteristic
257C22C2×#1174568712yes—
258C22#1427377412yes—
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—594no—
264C4—1182no—
265C4—1182no—
266C4—2362no—
267C4—2361no—
268C4—2362no—
269C2—44no—
270C2#121×D5911yescharacteristic
271C2#1683790811yescharacteristic
272C2#1683797211yescharacteristic
273C2#1683805812yes—
274C2#1683808912yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#394C2
hypercenter#394D59
hypocenterC59#2536
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14273704C2semidirect
2. C2×#14273692C2semidirect
4. #16837334C2semidirect
5. #16837332C2semidirect
7. #16837296C2semidirect
8. #16837295C2semidirect
9. #16837266C2semidirect
10. #16837260C2semidirect
56. C2×Dic118D4semidirect
149. C59#2536semidirect