Finite Group Databasebeta

← #21429891

Subgroups — #21429891

Order 7552.

548 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14273700C211yesmaximal, characteristic
2C2×#14273685C211yesmaximal, characteristic, complemented
3#16837339C211yesmaximal, characteristic, complemented
4#16837338C211yesmaximal, characteristic, complemented
5#16837328C211yesmaximal, characteristic, complemented
6#16837320C212yesmaximal, complemented
7#16837318C212yesmaximal, complemented
8#16837302C212yesmaximal, complemented
9#16837299C212yesmaximal, complemented
10#16837261C211yesmaximal, characteristic, complemented
11C59×#397C211yesmaximal, characteristic, complemented
12C22×D236C2211yescharacteristic
13C22×C22⋊D59C2211yescharacteristic
14C22×C22⋊D59C2211yescharacteristic
15C22×C4×D59C2211yescharacteristic
16#14273700—24no—
17#14273685—24no—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×C4⋊Dic59C2212yes—
20C2×Dic59⋊C4C2211yescharacteristic
21C2×Dic59⋊C4C2212yes—
22C2×Dic59⋊C4C2212yes—
23C2×C22⋊Dic59C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×(C2×D59)⋊C4C2212yes—
28C2×(C2×D59)⋊C4C2212yes—
29C2×C4×Dic59C2212yes—
30C59⋊#95C2211yescharacteristic
31C59⋊#95C2212yes—
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C22⋊C4×C59C2211yescharacteristic
34C2×C22⋊C4×C59C2212yes—
35#95×C59C2211yescharacteristic
36#95×C59C2212yes—
37C24×C59C2311yescharacteristic
38C23×D59C2311yescharacteristic
39C23×D59C2311yescharacteristic
40C22×C4×C59C2312yes—
41C22×C4×C59C2311yescharacteristic
42C22×C4×C59C2312yes—
43C22×C4×C59C2311yescharacteristic
44C2×C22⋊D59—22no—
45C2×C22⋊D59—22no—
46C2×C22⋊D59—24no—
47C2×C22⋊D59—42no—
48C22×Dic59C2312yes—
49C22×Dic59C2311yescharacteristic
50C22×Dic59C2312yes—
51C22×Dic59C2311yescharacteristic
52C2×D236—22no—
53C2×D236—42no—
54C2×C4×D59—24no—
55C2×C4×D59D414yes—
56C4⋊C4×C59—22no—
57C22⋊C4×C59—22no—
58C22⋊C4×C59—42no—
59C22⋊Dic59—42no—
60(C2×D59)⋊C4—24no—
61(C2×D59)⋊C4—22no—
62(C2×D59)⋊C4—42no—
63(C2×D59)⋊C4—42no—
64(C2×D59)⋊C4—42no—
65C4⋊Dic59—22no—
66C4⋊Dic59—42no—
67Dic59⋊C4—22no—
68Dic59⋊C4—24no—
69Dic59⋊C4—42no—
70C4×Dic59—24no—
71C23×C59—21no—
72C23×C59—22no—
73C23×C59—22no—
74C23×C59—21no—
75C23×C59—21no—
76C23×C59C2411yescharacteristic
77C22×D59—22no—
78C22×D59—21no—
79C22×D59—22no—
80C22×D59—21no—
81C22×D59—21no—
82C22×D59—22no—
83C22×D59—21no—
84C22×D59—22no—
85C22×D59—21no—
86C22×D59C2×D412yes—
87C2×C4×C59—22no—
88C2×C4×C59—22no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—22no—
94C2×C4×C59—22no—
95C2×C4×C59—22no—
96C2×C4×C59C2×D412yes—
97C22⋊D59—44no—
98C22⋊D59—44no—
99C2×Dic59—22no—
100C2×Dic59—21no—
101C2×Dic59—22no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59—22no—
107C2×Dic59C2×D412yes—
108C2×Dic59#4114yes—
109D236—44no—
110C4×D59—28no—
111C22×C59—41no—
112C22×C59—41no—
113C22×C59—41no—
114C22×C59—42no—
115C22×C59—42no—
116C22×C59C22×D411yescharacteristic
117C22×C59C2×#4112yes—
118C22×C59H(5,𝔽2)11yescharacteristic
119C22×C59H(5,𝔽2)12yes—
120C22×C592−1+411yescharacteristic
121C2×D59—22no—
122C2×D59—22no—
123C2×D59—22no—
124C2×D59—42no—
125C2×D59—42no—
126C2×D59—41no—
127C2×D59—41no—
128C2×D59—41no—
129C2×D59—42no—
130C2×D59—42no—
131C4×C59—22no—
132C4×C59—41no—
133C4×C59—42no—
134C4×C59—42no—
135Dic59—42no—
136Dic59—41no—
137Dic59—42no—
138Dic59#12314yes—
139#2624—591nomaximal, Sylow
140C2×C59—81no—
141C2×C59C2×#12311yescharacteristic
142C2×C59#53511yescharacteristic
143C2×C59#53711yescharacteristic
144C2×C59#54012yes—
145C2×C59#54212yes—
146D59—42no—
147D59—81no—
148C2×#121—591no—
149C2×#117—591no—
150#399—591no—
151#399—591no—
152#397—591no—
153#397D5911yescharacteristic, complemented
154#394—592no—
155#394—592no—
156#390—592no—
157#389—592no—
158#380—591no—
159C59#262411yescharacteristic, complemented, Sylow
160C22×D4—591no—
161C22×D4—591no—
162C22×D4—591no—
163C23×C4—591no—
164#121—1184no—
165#117—1184no—
166C2×C4⋊C4—591no—
167C2×C4⋊C4—591no—
168C2×C4⋊C4—592no—
169C2×C4⋊C4—592no—
170C2×C4⋊C4—592no—
171C2×C4⋊C4C2×D5911yescharacteristic
172C2×C22⋊C4—592no—
173C2×C22⋊C4—591no—
174C2×C22⋊C4—592no—
175C2×C22⋊C4—592no—
176C2×C22⋊C4—592no—
177C2×C22⋊C4—592no—
178C2×C22⋊C4C2×D5911yescharacteristic
179C2×C22⋊C4C2×D5912yes—
180C2×C42—592no—
181#95—591no—
182#95—592no—
183#95C2×D5911yescharacteristic
184#95C2×D5912yes—
185C24—591no—
186C24—591no—
187C24C22×D5911yescharacteristic
188C2×D4—1182no—
189C2×D4—1182no—
190C2×D4—1184no—
191C2×D4—1182no—
192C2×D4—2362no—
193C2×D4—2362no—
194C22×C4—591no—
195C22×C4—594no—
196C22×C4—592no—
197C22×C4—591no—
198C22×C4—592no—
199C22×C4—1184no—
200C22×C4C22×D5912yes—
201C22×C4C22×D5912yes—
202C22×C4C22×D5911yescharacteristic
203C22×C4C22×D5911yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—1182no—
206C4⋊C4—1184no—
207C4⋊C4—1182no—
208C4⋊C4—2362no—
209C4⋊C4—2362no—
210C22⋊C4—22no—
211C22⋊C4—42no—
212C22⋊C4—1184no—
213C22⋊C4—1182no—
214C22⋊C4—2362no—
215C22⋊C4—2362no—
216C22⋊C4—2362no—
217C22⋊C4—2362no—
218C42—1184no—
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—592no—
225C23—1182no—
226C23—1181no—
227C23—1182no—
228C23—1181no—
229C23—1181no—
230C23—1182no—
231C23—1181no—
232C23—1182no—
233C23—1181no—
234C23C23×D5911yescharacteristic
235D4—2364no—
236D4—2364no—
237D4—2364no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—592no—
248C2×C4—594no—
249C2×C4—1188no—
250C2×C4—1182no—
251C2×C4—1181no—
252C2×C4—1182no—
253C2×C4—1182no—
254C2×C4—1182no—
255C2×C4—1182no—
256C2×C4—1182no—
257C2×C4—1182no—
258C2×C4D4×D5912yes—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—42no—
264C22—1182no—
265C22—1182no—
266C22—1182no—
267C22—2361no—
268C22—2361no—
269C22—2361no—
270C22—2362no—
271C22—2362no—
272C22—2362no—
273C22—2362no—
274C22C2×D4×D5911yescharacteristic
275C22#41×D5912yes—
276C22#1427377211yescharacteristic
277C22#1427377312yes—
278C22#1427377411yescharacteristic
279C4—22no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—594no—
284C4—2361no—
285C4—2362no—
286C4—2362no—
287C2—81no—
288C2—4721no—
289C2—2362no—
290C2#123×D5911yescharacteristic
291C2#1683797011yescharacteristic
292C2#1683798111yescharacteristic
293C2#1683800412yes—
294C2#1683801812yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2624
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14273685C2semidirect
3. #16837339C2semidirect
4. #16837338C2semidirect
5. #16837328C2semidirect
6. #16837320C2semidirect
7. #16837318C2semidirect
8. #16837302C2semidirect
9. #16837299C2semidirect
10. #16837261C2semidirect
11. C59×#397C2semidirect
153. #397D59semidirect
159. C59#2624semidirect