Finite Group Databasebeta

← #21429665

Subgroups — #21429665

Order 7552.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14273689C211yesmaximal, characteristic, complemented
2C2×#14273685C211yesmaximal, characteristic, complemented
3#16837337C211yesmaximal, characteristic, complemented
4#16837319C211yesmaximal, characteristic, complemented
5#16837312C211yesmaximal, characteristic
6#16837291C212yesmaximal, complemented
7#16837280C212yesmaximal, complemented
8#16837280C212yesmaximal, complemented
9#16837276C212yesmaximal, complemented
10#16837269C211yesmaximal, characteristic, complemented
11C59×#400C211yesmaximal, characteristic, complemented
12C22×D236C2211yescharacteristic
13C22×D236C2212yes—
14C22×C4×D59C2211yescharacteristic
15C22×C4×D59C2212yes—
16#14273689—24no—
17#14273685—24no—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2212yes—
20C2×(C2×D59)⋊C4C2212yes—
21C2×(C2×D59)⋊C4C2211yescharacteristic
22C2×(C2×D59)⋊C4C2212yes—
23C2×(C2×D59)⋊C4C2212yes—
24C2×(C2×D59)⋊C4C2211yescharacteristic
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2211yescharacteristic
28C2×C4×Dic59C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
31C59⋊#95C2211yescharacteristic
32C2×C4⋊C4×C59C2211yescharacteristic
33C2×C4⋊C4×C59C2211yescharacteristic
34#95×C59C2211yescharacteristic
35#95×C59C2212yes—
36#95×C59C2212yes—
37C23×D59C2311yescharacteristic
38C23×D59C2312yes—
39C22×C4×C59C2312yes—
40C22×C4×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2311yescharacteristic
43C22×C4×C59C2311yescharacteristic
44C22×Dic59C2312yes—
45C22×Dic59C2311yescharacteristic
46C22×Dic59C2311yescharacteristic
47C22×Dic59C2311yescharacteristic
48C2×D236—24no—
49C2×D236—22no—
50C2×D236—24no—
51C2×D236—24no—
52C2×D236—42no—
53C2×C4×D59—22no—
54C2×C4×D59—22no—
55C2×C4×D59—22no—
56C2×C4×D59—24no—
57C2×C4×D59—42no—
58C2×C4×D59—42no—
59C4⋊C4×C59—22no—
60C4⋊C4×C59—22no—
61(C2×D59)⋊C4—24no—
62(C2×D59)⋊C4—22no—
63(C2×D59)⋊C4—24no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4—24no—
66(C2×D59)⋊C4—42no—
67(C2×D59)⋊C4—42no—
68C4⋊Dic59—22no—
69Dic59⋊C4—42no—
70C4×Dic59—22no—
71C4×Dic59D414yescomplemented
72C23×C59C2411yescharacteristic
73C22×D59—21no—
74C22×D59—22no—
75C22×D59—22no—
76C22×D59—21no—
77C22×D59—22no—
78C22×D59—22no—
79C22×D59—22no—
80C22×D59—22no—
81C22×D59—22no—
82C22×D59—22no—
83C22×D59#4114yes—
84C22×D59#4112yes—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—22no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
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—
97C2×C4×C59#4112yes—
98C2×Dic59—21no—
99C2×Dic59—21no—
100C2×Dic59—22no—
101C2×Dic59—21no—
102C2×Dic59—22no—
103C2×Dic59—22no—
104C2×Dic59—22no—
105C2×Dic59—22no—
106C2×Dic59C2×D412yes—
107C2×Dic59C2×D412yes—
108D236—28no—
109D236—48no—
110C4×D59—28no—
111C4×D59—48no—
112C22×C59C22×D411yescharacteristic
113C22×C59C2×#4111yescharacteristic
114C22×C59C2×#4112yes—
115C22×C59C2×#4111yescharacteristic
116C22×C59H(5,𝔽2)12yes—
117C2×D59—22no—
118C2×D59—24no—
119C2×D59—24no—
120C2×D59—24no—
121C2×D59—24no—
122C2×D59—41no—
123C2×D59—42no—
124C2×D59—42no—
125C2×D59—41no—
126C2×D59—42no—
127C2×D59—42no—
128C2×D59—42no—
129C4×C59—22no—
130C4×C59—22no—
131C4×C59—41no—
132C4×C59—42no—
133C4×C59—42no—
134Dic59—22no—
135Dic59—22no—
136Dic59—41no—
137Dic59—42no—
138#2598—591nomaximal, Sylow
139C2×C59#52511yescharacteristic
140C2×C59#52511yescharacteristic
141C2×C59#53511yescharacteristic
142C2×C59#55112yes—
143C2×C59#55312yes—
144D59—42no—
145D59—44no—
146C2×C4×D4—591no—
147C2×#117—591no—
148#400D5911yescharacteristic, complemented
149#399—591no—
150#394—591no—
151#392—591no—
152#388—592no—
153#386—592no—
154#386—592no—
155#385—592no—
156#383—591no—
157C59#259811yescharacteristic, complemented, Sylow
158C22×D4—591no—
159C22×D4—592no—
160C23×C4—591no—
161C23×C4—592no—
162C4×D4—1184no—
163#117—1184no—
164C2×C4⋊C4—591no—
165C2×C4⋊C4—592no—
166C2×C4⋊C4C2×D5911yescharacteristic
167C2×C4⋊C4C2×D5911yescharacteristic
168C2×C22⋊C4—591no—
169C2×C22⋊C4—591no—
170C2×C22⋊C4—592no—
171C2×C22⋊C4—592no—
172C2×C22⋊C4—592no—
173C2×C22⋊C4—592no—
174C2×C22⋊C4—592no—
175C2×C42—591no—
176C2×C42—591no—
177#95—592no—
178#95—592no—
179#95—591no—
180#95C2×D5911yescharacteristic
181#95C2×D5912yes—
182#95C2×D5912yes—
183C24—592no—
184C24—591no—
185C2×D4—1184no—
186C2×D4—1184no—
187C2×D4—1184no—
188C2×D4—1182no—
189C2×D4—2362no—
190C22×C4—591no—
191C22×C4—591no—
192C22×C4—592no—
193C22×C4—591no—
194C22×C4—1182no—
195C22×C4—1184no—
196C22×C4—1182no—
197C22×C4—1182no—
198C22×C4—2362no—
199C22×C4—2362no—
200C22×C4C22×D5912yes—
201C22×C4C22×D5911yescharacteristic
202C22×C4C22×D5912yes—
203C22×C4C22×D5911yescharacteristic
204C22×C4C22×D5911yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—1182no—
208C4⋊C4—2362no—
209C22⋊C4—1182no—
210C22⋊C4—1184no—
211C22⋊C4—1184no—
212C22⋊C4—1182no—
213C22⋊C4—1184no—
214C22⋊C4—2362no—
215C22⋊C4—2362no—
216C42—594no—
217C42—1182no—
218C23—594no—
219C23—592no—
220C23—1181no—
221C23—1182no—
222C23—1182no—
223C23—1182no—
224C23—1182no—
225C23—1182no—
226C23—1181no—
227C23—1182no—
228C23—1182no—
229C23—1182no—
230C23C23×D5911yescharacteristic
231D4—1188no—
232D4—2368no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—592no—
245C2×C4—592no—
246C2×C4—1188no—
247C2×C4—1181no—
248C2×C4—1181no—
249C2×C4—1182no—
250C2×C4—1181no—
251C2×C4—1182no—
252C2×C4—1182no—
253C2×C4—1182no—
254C2×C4—1182no—
255C2×C4—2368no—
256C2×C4D4×D5912yes—
257C2×C4#1174568912yes—
258C22—1184no—
259C22—1182no—
260C22—1184no—
261C22—1184no—
262C22—1184no—
263C22—2361no—
264C22—2362no—
265C22—2362no—
266C22—2361no—
267C22—2362no—
268C22—2362no—
269C22—2362no—
270C22C2×D4×D5911yescharacteristic
271C22#41×D5912yes—
272C22#41×D5911yescharacteristic
273C22C2×#1174568911yescharacteristic
274C22#1427377312yes—
275C4—22no—
276C4—22no—
277C4—41no—
278C4—42no—
279C4—42no—
280C4—1182no—
281C4—1182no—
282C4—2361no—
283C4—2362no—
284C2—2364no—
285C2—2362no—
286C2#1683791011yescharacteristic
287C2#1683791511yescharacteristic
288C2#1683797011yescharacteristic
289C2#1683807712yes—
290C2#1683810512yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#400C2
hypercenter#400D59
hypocenterC59#2598
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14273689C2semidirect
2. C2×#14273685C2semidirect
3. #16837337C2semidirect
4. #16837319C2semidirect
6. #16837291C2semidirect
7. #16837280C2semidirect
8. #16837280C2semidirect
9. #16837276C2semidirect
10. #16837269C2semidirect
11. C59×#400C2semidirect
71. C4×Dic59D4semidirect
148. #400D59semidirect
157. C59#2598semidirect