Finite Group Databasebeta

← #21428583

Subgroups — #21428583

Order 7552.

596 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4⋊C4×D59C211yesmaximal, characteristic, complemented
3#16837329C211yesmaximal, characteristic, complemented
4#16837328C211yesmaximal, characteristic, complemented
5#16837327C211yesmaximal, characteristic, complemented
6#16837302C212yesmaximal, complemented
7#16837280C212yesmaximal, complemented
8#16837278C212yesmaximal, complemented
9#16837266C212yesmaximal, complemented
10#16837249C211yesmaximal, characteristic, complemented
11C59×#397C211yesmaximal, characteristic, complemented
12C22×D236C2211yescharacteristic
13C22×C22⋊D59C2211yescharacteristic
14C22×C22⋊D59C2211yescharacteristic
15C22×C4×D59C2211yescharacteristic
16C22×C4×D59C2212yes—
17#14273700—24no—
18C2×C4⋊Dic59C2211yescharacteristic
19C2×Dic59⋊C4C2211yescharacteristic
20C2×Dic59⋊C4C2212yes—
21C4⋊C4×D59—24no—
22C2×C22⋊Dic59C2212yes—
23C2×(C2×D59)⋊C4C2211yescharacteristic
24C2×(C2×D59)⋊C4C2212yes—
25C2×(C2×D59)⋊C4C2212yes—
26C2×(C2×D59)⋊C4C2212yes—
27C2×C4×Dic59C2212yes—
28C59⋊#95C2211yescharacteristic
29C59⋊#95C2212yes—
30C59⋊#95C2212yes—
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×C59C2311yescharacteristic
41C22×C4×C59C2312yes—
42C22×C4×C59C2312yes—
43C22×C4×C59C2311yescharacteristic
44C2×C22⋊D59—22no—
45C2×C22⋊D59—24no—
46C2×C22⋊D59—22no—
47C2×C22⋊D59—24no—
48C22×Dic59C2311yescharacteristic
49C22×Dic59C2312yes—
50C22×Dic59C2312yes—
51C22×Dic59C2311yescharacteristic
52C2×D236—22no—
53C2×D236—24no—
54C2×C4×D59—24no—
55C2×C4×D59—24no—
56C2×C4×D59—42no—
57C2×C4×D59—42no—
58C2×C4×D59D414yes—
59C4⋊C4×C59—22no—
60C22⋊C4×C59—22no—
61C22⋊C4×C59—42no—
62C22⋊Dic59—42no—
63(C2×D59)⋊C4—24no—
64(C2×D59)⋊C4—22no—
65(C2×D59)⋊C4—42no—
66(C2×D59)⋊C4—42no—
67C4⋊Dic59—22no—
68Dic59⋊C4—24no—
69Dic59⋊C4—22no—
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—21no—
80C22×D59—21no—
81C22×D59—22no—
82C22×D59—22no—
83C22×D59—21no—
84C22×D59—21no—
85C22×D59C2×D412yes—
86C22×D59#4114yes—
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—
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—
111C4×D59—48no—
112C22×C59—41no—
113C22×C59—41no—
114C22×C59—41no—
115C22×C59—42no—
116C22×C59—42no—
117C22×C59C22×D411yescharacteristic
118C22×C59C2×#4112yes—
119C22×C59C2×#4112yes—
120C22×C59H(5,𝔽2)11yescharacteristic
121C22×C59H(5,𝔽2)11yescharacteristic
122C2×D59—22no—
123C2×D59—22no—
124C2×D59—24no—
125C2×D59—24no—
126C2×D59—41no—
127C2×D59—41no—
128C2×D59—41no—
129C2×D59—42no—
130C2×D59—42no—
131C2×D59#12414yes—
132C4×C59—22no—
133C4×C59—41no—
134C4×C59—42no—
135C4×C59—42no—
136Dic59—41no—
137Dic59—42no—
138Dic59—42no—
139Dic59#12314yes—
140#2504—591nomaximal, Sylow
141C2×C59—81no—
142C2×C59C2×#12311yescharacteristic
143C2×C59C2×#12411yescharacteristic
144C2×C59#53511yescharacteristic
145C2×C59#55312yes—
146C2×C59#55312yes—
147D59—24no—
148D59—81no—
149C2×#121—591no—
150C22×C4⋊C4—591no—
151#397—591no—
152#397—591no—
153#397—591no—
154#397D5911yescharacteristic, complemented
155#390—592no—
156#386—592no—
157#386—592no—
158#382—592no—
159C4×C22⋊C4—591no—
160C59#250411yescharacteristic, complemented, Sylow
161C22×D4—591no—
162C22×D4—591no—
163C22×D4—591no—
164C23×C4—591no—
165C23×C4—592no—
166#121—1184no—
167C2×C4⋊C4—592no—
168C2×C4⋊C4—591no—
169C2×C4⋊C4—591no—
170C2×C4⋊C4—1184no—
171C2×C4⋊C4C2×D5911yescharacteristic
172C2×C22⋊C4—591no—
173C2×C22⋊C4—592no—
174C2×C22⋊C4—592no—
175C2×C22⋊C4—592no—
176C2×C22⋊C4—592no—
177C2×C22⋊C4C2×D5911yescharacteristic
178C2×C22⋊C4C2×D5912yes—
179C2×C42—592no—
180#95—591no—
181#95—592no—
182#95—592no—
183#95—592no—
184#95C2×D5911yescharacteristic
185#95C2×D5912yes—
186C24—591no—
187C24—591no—
188C24C22×D5911yescharacteristic
189C2×D4—1182no—
190C2×D4—1184no—
191C2×D4—1182no—
192C2×D4—1184no—
193C2×D4—1182no—
194C2×D4—1184no—
195C22×C4—591no—
196C22×C4—594no—
197C22×C4—591no—
198C22×C4—592no—
199C22×C4—592no—
200C22×C4—1184no—
201C22×C4—1184no—
202C22×C4—2362no—
203C22×C4—2362no—
204C22×C4C22×D5911yescharacteristic
205C22×C4C22×D5912yes—
206C22×C4C22×D5912yes—
207C22×C4C22×D5911yescharacteristic
208C4⋊C4—22no—
209C4⋊C4—1184no—
210C4⋊C4—1182no—
211C4⋊C4—1182no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—1184no—
215C22⋊C4—1182no—
216C22⋊C4—2362no—
217C22⋊C4—2362no—
218C22⋊C4—2362no—
219C42—1184no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—592no—
226C23—594no—
227C23—1182no—
228C23—1181no—
229C23—1181no—
230C23—1181no—
231C23—1182no—
232C23—1182no—
233C23—1181no—
234C23—1181no—
235C23C23×D5911yescharacteristic
236D4—2364no—
237D4—2364no—
238D4—2364no—
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—22no—
248C2×C4—592no—
249C2×C4—594no—
250C2×C4—1188no—
251C2×C4—1181no—
252C2×C4—1182no—
253C2×C4—1182no—
254C2×C4—1182no—
255C2×C4—1182no—
256C2×C4—1182no—
257C2×C4—1182no—
258C2×C4—1182no—
259C2×C4—2368no—
260C2×C4D4×D5912yes—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22—594no—
267C22—1182no—
268C22—1182no—
269C22—1184no—
270C22—1184no—
271C22—2361no—
272C22—2361no—
273C22—2361no—
274C22—2362no—
275C22—2362no—
276C22C2×D4×D5911yescharacteristic
277C22#41×D5912yes—
278C22#41×D5912yes—
279C22#1427377211yescharacteristic
280C22#1427377311yescharacteristic
281C4—22no—
282C4—41no—
283C4—42no—
284C4—42no—
285C4—594no—
286C4—2361no—
287C4—2362no—
288C4—2362no—
289C2—81no—
290C2—1184no—
291C2—4721no—
292C2#123×D5911yescharacteristic
293C2#124×D5911yescharacteristic
294C2#1683796811yescharacteristic
295C2#1683809712yes—
296C2#1683810312yes—
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2504
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D59C2semidirect
3. #16837329C2semidirect
4. #16837328C2semidirect
5. #16837327C2semidirect
6. #16837302C2semidirect
7. #16837280C2semidirect
8. #16837278C2semidirect
9. #16837266C2semidirect
10. #16837249C2semidirect
11. C59×#397C2semidirect
154. #397D59semidirect
160. C59#2504semidirect