Finite Group Databasebeta

← #21429962

Subgroups — #21429962

Order 7552.

500 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14273716C211yesmaximal, characteristic
2C2×#14273692C211yesmaximal, characteristic, complemented
3#16837337C212yesmaximal, complemented
4#16837321C211yesmaximal, characteristic, complemented
5#16837320C211yesmaximal, characteristic
6#16837319C211yesmaximal, characteristic
7#16837315C212yesmaximal, complemented
8#16837292C212yesmaximal, complemented
9#16837291C212yesmaximal, complemented
10#16837269C211yesmaximal, characteristic, complemented
11C59×#395C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×D236C2211yescharacteristic
14#14273716—24no—
15#14273692—24no—
16C2×Dic59⋊C4C2211yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×Dic59⋊C4C2212yes—
19C2×(C2×D59)⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2212yes—
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2212yes—
25C2×C4×Dic59C2211yescharacteristic
26C2×C4×Dic59C2211yescharacteristic
27C2×C4×Dic59C2211yescharacteristic
28C59⋊#95C2212yes—
29C59⋊#95C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C22×Q8×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2312yes—
38C2×Q8×C59—22no—
39C2×Q8×C59—42no—
40C22×C4×C59C2312yes—
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×C4×C59C2311yescharacteristic
45C22×Dic59C2312yes—
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C22×Dic59C2311yescharacteristic
49C22×Dic59C2311yescharacteristic
50C2×D236—22no—
51C2×D236—42no—
52C2×Dic118—22no—
53C2×Dic118—22no—
54C2×Dic118—22no—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—42no—
57(C2×D59)⋊C4—24no—
58(C2×D59)⋊C4—24no—
59(C2×D59)⋊C4—24no—
60(C2×D59)⋊C4—24no—
61(C2×D59)⋊C4—42no—
62(C2×D59)⋊C4—42no—
63Dic59⋊C4—22no—
64Dic59⋊C4—22no—
65Dic59⋊C4—42no—
66C4×Dic59—22no—
67C4×Dic59—22no—
68C4×Dic59D414yes—
69C23×C59C2411yescharacteristic
70C22×D59—22no—
71C22×D59—22no—
72C22×D59—22no—
73C22×D59—22no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—22no—
77Q8×C59—44no—
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—22no—
81C2×C4×C59—21no—
82C2×C4×C59—22no—
83C2×C4×C59—22no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—22no—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59C2×D412yes—
90C2×C4×C59#4112yes—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—21no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59—22no—
99C2×Dic59—22no—
100C2×Dic59—22no—
101C2×Dic59C2×D412yes—
102C2×Dic59C2×D412yes—
103C2×Dic59#4112yes—
104D236—44no—
105Dic118—28no—
106C22×C59C22×D411yescharacteristic
107C22×C59C2×#4111yescharacteristic
108C22×C59C2×#4111yescharacteristic
109C22×C59H(5,𝔽2)12yes—
110C22×C592−1+412yes—
111C2×D59—42no—
112C2×D59—42no—
113C2×D59—42no—
114C2×D59—42no—
115C2×D59—42no—
116C2×D59—42no—
117C2×D59—42no—
118C4×C59—22no—
119C4×C59—22no—
120C4×C59—41no—
121C4×C59—42no—
122C4×C59—42no—
123Dic59—22no—
124Dic59—22no—
125Dic59—22no—
126Dic59—41no—
127Dic59—42no—
128#2632—591nomaximal, Sylow
129C2×C59#52511yescharacteristic
130C2×C59#53511yescharacteristic
131C2×C59#53611yescharacteristic
132C2×C59#54212yes—
133C2×C59#54212yes—
134D59—82no—
135C2×#124—591no—
136C2×C4×Q8—591no—
137#399—592no—
138#395—591no—
139#395D5911yescharacteristic, complemented
140#394—591no—
141#394—591no—
142#393—592no—
143#388—592no—
144#388—592no—
145#383—591no—
146C59#263211yescharacteristic, complemented, Sylow
147C22×Q8—591no—
148C22×Q8C2×D5911yescharacteristic
149C22×D4—591no—
150#124—1184no—
151C4×Q8—1184no—
152C2×C4⋊C4—591no—
153C2×C4⋊C4—591no—
154C2×C4⋊C4—592no—
155C2×C4⋊C4C2×D5911yescharacteristic
156C2×C4⋊C4C2×D5912yes—
157C2×C22⋊C4—592no—
158C2×C22⋊C4—592no—
159C2×C22⋊C4—592no—
160C2×C22⋊C4—592no—
161C2×C22⋊C4—592no—
162C2×C22⋊C4—592no—
163C2×C42—591no—
164C2×C42—591no—
165C2×C42—591no—
166#95—592no—
167#95—592no—
168#95—591no—
169#95—592no—
170#95C2×D5911yescharacteristic
171#95C2×D5912yes—
172C24—592no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—1182no—
176C2×Q8—1182no—
177C2×Q8—1182no—
178C2×D4—1182no—
179C2×D4—2362no—
180C22×C4—591no—
181C22×C4—591no—
182C22×C4—591no—
183C22×C4—592no—
184C22×C4—591no—
185C22×C4C22×D5912yes—
186C22×C4C22×D5912yes—
187C22×C4C22×D5911yescharacteristic
188C22×C4C22×D5911yescharacteristic
189C22×C4C22×D5911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—1182no—
193C4⋊C4—1182no—
194C4⋊C4—2362no—
195C22⋊C4—1184no—
196C22⋊C4—1184no—
197C22⋊C4—1184no—
198C22⋊C4—1184no—
199C22⋊C4—2362no—
200C22⋊C4—2362no—
201C42—594no—
202C42—1182no—
203C42—1182no—
204C23—1182no—
205C23—1182no—
206C23—1182no—
207C23—1182no—
208C23—1182no—
209C23—1182no—
210C23—1182no—
211C23C23×D5911yescharacteristic
212Q8—44no—
213Q8—1188no—
214D4—2364no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—592no—
227C2×C4—592no—
228C2×C4—592no—
229C2×C4—1181no—
230C2×C4—1181no—
231C2×C4—1181no—
232C2×C4—1181no—
233C2×C4—1182no—
234C2×C4—1181no—
235C2×C4—1182no—
236C2×C4—1182no—
237C2×C4—1182no—
238C2×C4—1182no—
239C2×C4D4×D5912yes—
240C2×C4#1174568912yes—
241C22—2362no—
242C22—2362no—
243C22—2362no—
244C22—2362no—
245C22—2362no—
246C22—2362no—
247C22—2362no—
248C22C2×D4×D5911yescharacteristic
249C22#41×D5911yescharacteristic
250C22C2×#1174568911yescharacteristic
251C22#1427377212yes—
252C22#1427377512yes—
253C4—22no—
254C4—22no—
255C4—42no—
256C4—41no—
257C4—42no—
258C4—1182no—
259C4—1182no—
260C4—1182no—
261C4—2361no—
262C4—2362no—
263C2—4722no—
264C2#1683791511yescharacteristic
265C2#1683796711yescharacteristic
266C2#1683797711yescharacteristic
267C2#1683802212yes—
268C2#1683802612yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#395C2
hypercenter#395D59
hypocenterC59#2632
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#14273692C2semidirect
3. #16837337C2semidirect
4. #16837321C2semidirect
7. #16837315C2semidirect
8. #16837292C2semidirect
9. #16837291C2semidirect
10. #16837269C2semidirect
11. C59×#395C2semidirect
139. #395D59semidirect
146. C59#2632semidirect