Finite Group Databasebeta

← #21428569

Subgroups — #21428569

Order 7552.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14273705C211yesmaximal, characteristic
2C2×C4⋊C4×D59C211yesmaximal, characteristic
3#16837334C211yesmaximal, characteristic, complemented
4#16837333C211yesmaximal, characteristic, complemented
5#16837332C211yesmaximal, characteristic, complemented
6#16837306C212yesmaximal, complemented
7#16837276C212yesmaximal
8#16837273C212yesmaximal
9#16837271C212yesmaximal, complemented
10#16837249C211yesmaximal, characteristic
11C59×#398C211yesmaximal, characteristic, complemented
12C22×Dic118C2211yescharacteristic
13C22×C4×D59C2211yescharacteristic
14C22×C4×D59C2212yes—
15#14273705—24no—
16C2×C4⋊Dic59C2211yescharacteristic
17C2×C4⋊Dic59C2212yes—
18C2×Dic59⋊C4C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2212yes—
21C2×Dic59⋊C4C2212yes—
22C2×Dic59⋊C4C2212yes—
23C4⋊C4×D59—24no—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2211yescharacteristic
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2212yes—
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34C2×C4⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C22×C4×C59C2311yescharacteristic
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×Dic59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2312yes—
47C22×Dic59C2311yescharacteristic
48C2×C4×D59—24no—
49C2×C4×D59—24no—
50C2×C4×D59—42no—
51C2×C4×D59—42no—
52C2×C4×D59D414yes—
53C2×Dic118—22no—
54C2×Dic118—24no—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—22no—
57C4⋊C4×C59—42no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4Q818yescomplemented
61C4⋊Dic59—22no—
62C4⋊Dic59—42no—
63Dic59⋊C4—22no—
64Dic59⋊C4—24no—
65Dic59⋊C4—22no—
66Dic59⋊C4—42no—
67Dic59⋊C4—42no—
68C4×Dic59—24no—
69C23×C59C2411yescharacteristic
70C22×D59—22no—
71C22×D59—21no—
72C22×D59—21no—
73C22×D59C2×D412yes—
74C22×D59C2×Q814yes—
75C2×C4×C59—22no—
76C2×C4×C59—22no—
77C2×C4×C59—22no—
78C2×C4×C59—21no—
79C2×C4×C59—22no—
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—21no—
85C2×C4×C59—22no—
86C2×C4×C59C2×D412yes—
87C2×C4×C59C2×Q814yes—
88C2×Dic59—22no—
89C2×Dic59—22no—
90C2×Dic59—21no—
91C2×Dic59—22no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59—21no—
95C2×Dic59—22no—
96C2×Dic59—21no—
97C2×Dic59—22no—
98C2×Dic59C2×D412yes—
99C2×Dic59C2×Q814yes—
100C2×Dic59#4114yes—
101C4×D59—28no—
102C4×D59—48no—
103Dic118—44no—
104C22×C59C22×D411yescharacteristic
105C22×C59C22×Q812yes—
106C22×C59C2×#4112yes—
107C22×C59H(5,𝔽2)11yescharacteristic
108C22×C59H(5,𝔽2)11yescharacteristic
109C2×D59—22no—
110C2×D59—22no—
111C2×D59—24no—
112C2×D59—24no—
113C2×D59C4⋊Q814yes—
114C4×C59—22no—
115C4×C59—24no—
116C4×C59—41no—
117C4×C59—42no—
118C4×C59—41no—
119Dic59—24no—
120Dic59—41no—
121Dic59—42no—
122Dic59—41no—
123Dic59#12314yes—
124#2502—591nomaximal, Sylow
125C2×C59C2×#12311yescharacteristic
126C2×C59C2×C4⋊Q811yescharacteristic
127C2×C59#53511yescharacteristic
128C2×C59#55412yes—
129C2×C59#55412yes—
130D59—24no—
131C2×C22⋊Q8—591no—
132C22×C4⋊C4—591no—
133#398—591no—
134#398—591no—
135#398—591no—
136#398D5911yescharacteristic, complemented
137#391—592no—
138#385—592no—
139#385—592no—
140#384—592no—
141C4×C22⋊C4—591no—
142C59#250211yescharacteristic, complemented, Sylow
143C22×Q8—591no—
144C23×C4—591no—
145C23×C4—592no—
146C22⋊Q8—1184no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—591no—
149C2×C4⋊C4—591no—
150C2×C4⋊C4—591no—
151C2×C4⋊C4—592no—
152C2×C4⋊C4—592no—
153C2×C4⋊C4—592no—
154C2×C4⋊C4—1184no—
155C2×C4⋊C4C2×D5911yescharacteristic
156C2×C4⋊C4C2×D5911yescharacteristic
157C2×C4⋊C4C2×D5912yes—
158C2×C22⋊C4—592no—
159C2×C22⋊C4—591no—
160C2×C22⋊C4—591no—
161C2×C42—592no—
162#95—591no—
163#95—592no—
164#95—592no—
165#95—592no—
166#95C2×D5911yescharacteristic
167#95C2×D5912yes—
168C24—591no—
169C2×Q8—1182no—
170C2×Q8—1184no—
171C22×C4—591no—
172C22×C4—592no—
173C22×C4—594no—
174C22×C4—591no—
175C22×C4—592no—
176C22×C4—591no—
177C22×C4—1184no—
178C22×C4—1184no—
179C22×C4—2362no—
180C22×C4—2362no—
181C22×C4C22×D5911yescharacteristic
182C22×C4C22×D5912yes—
183C22×C4C22×D5911yescharacteristic
184C22×C4C22×D5911yescharacteristic
185C22×C4C22×D5912yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—1184no—
190C4⋊C4—1182no—
191C4⋊C4—1182no—
192C4⋊C4—1182no—
193C4⋊C4—2362no—
194C4⋊C4—2362no—
195C4⋊C4—2362no—
196C22⋊C4—598no—
197C22⋊C4—1182no—
198C22⋊C4—1182no—
199C42—1184no—
200C23—592no—
201C23—594no—
202C23—1182no—
203C23—1181no—
204C23—1181no—
205C23C23×D5911yescharacteristic
206Q8—2364no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—592no—
219C2×C4—594no—
220C2×C4—594no—
221C2×C4—1188no—
222C2×C4—1182no—
223C2×C4—1182no—
224C2×C4—1181no—
225C2×C4—1181no—
226C2×C4—1182no—
227C2×C4—1182no—
228C2×C4—1181no—
229C2×C4—1182no—
230C2×C4—1181no—
231C2×C4—1182no—
232C2×C4—2368no—
233C2×C4D4×D5912yes—
234C2×C4Q8×D5914yes—
235C22—594no—
236C22—1182no—
237C22—1182no—
238C22—1184no—
239C22—1184no—
240C22C2×D4×D5911yescharacteristic
241C22C2×Q8×D5912yes—
242C22#41×D5912yes—
243C22#1427377211yescharacteristic
244C22#1427377311yescharacteristic
245C4—22no—
246C4—24no—
247C4—41no—
248C4—42no—
249C4—41no—
250C4—594no—
251C4—1184no—
252C4—2361no—
253C4—2362no—
254C4—2361no—
255C2—1184no—
256C2#123×D5911yescharacteristic
257C2C4⋊Q8×D5911yescharacteristic
258C2#1683796811yescharacteristic
259C2#1683810612yes—
260C2#1683810812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2502
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #16837334C2semidirect
4. #16837333C2semidirect
5. #16837332C2semidirect
6. #16837306C2semidirect
9. #16837271C2semidirect
11. C59×#398C2semidirect
60. (C2×D59)⋊C4Q8semidirect
136. #398D59semidirect
142. C59#2502semidirect