Finite Group Databasebeta

← #21435325

Subgroups — #21435325

Order 7552.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C4⋊Q8×D59C211yesmaximal, characteristic, complemented
2#16837934C211yesmaximal, characteristic
3#16837810C212yesmaximal, complemented
4#16837760C212yesmaximal, complemented
5#16837739C212yesmaximal, complemented
6#16837719C212yesmaximal
7#16837688C211yesmaximal, characteristic, complemented
8#16837684C211yesmaximal, characteristic, complemented
9#16837682C211yesmaximal, characteristic, complemented
10#16837458C211yesmaximal, characteristic, complemented
11C59×#474C211yesmaximal, characteristic, complemented
12C2×Q8×D59—21no—
13#14273727C2211yescharacteristic
14#14273726—21no—
15#14273726C2212yes—
16#14273725—21no—
17#14273720—21no—
18#14273718C2211yescharacteristic
19#14273714C2211yescharacteristic
20#14273709—21no—
21#14273707C2211yescharacteristic
22#14273698C2211yescharacteristic
23C4×Dic118C2211yescharacteristic
24C4×C22⋊D59—21no—
25#14273686—21no—
26C4⋊C4×D59—21no—
27C4⋊C4×D59C2212yes—
28C42×D59C2211yescharacteristic
29#14273660C2212yes—
30#14273659C2212yes—
31#14273658C2212yes—
32C4⋊(C59⋊C8)C2211yescharacteristic
33#14273652C2212yes—
34#14273650C2212yes—
35#14273648C2212yes—
36(C2×D59)⋊C8C2212yes—
37#14273637C2212yes—
38C4⋊Q8×C59C2211yescharacteristic
39C4×D4×C59C2211yescharacteristic
40#107×C59C2212yes—
41C4⋊C8×C59C2211yescharacteristic
42#102×C59C2212yes—
43C2×Q8×C59—21no—
44C2×D4×C59C2311yescharacteristic
45C22×C4×C59—21no—
46C2×C22⋊D59—21no—
47Q8×D59—44no—
48C2×C4×D59—22no—
49C2×C4×D59D411yescharacteristic
50C2×C4×D59D411yescharacteristic
51C2×C4×D59C2311yescharacteristic
52C2×Dic118—21no—
53C2×Dic118—22no—
54C2×Dic118C2311yescharacteristic
55C2×C8×C59C2312yes—
56C4⋊C4×C59—21no—
57C4⋊C4×C59C2312yes—
58C4⋊C4×C59C2311yescharacteristic
59C22⋊C4×C59—21no—
60C42×C59C2311yescharacteristic
61C22⋊Dic59—21no—
62C22⋊Dic59—21no—
63C22⋊Dic59—21no—
64(C2×D59)⋊C4—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68C4⋊Dic59C2312yes—
69C4⋊Dic59C2311yescharacteristic
70Dic59⋊C4—21no—
71Dic59⋊C4—22no—
72Dic59⋊C4—22no—
73Dic59⋊C4—21no—
74C4×Dic59—21no—
75C4×Dic59D411yescharacteristic
76C4×Dic59D411yescharacteristic
77C4×Dic59C2311yescharacteristic
78C2×C59⋊C8C2312yes—
79C23×C59—21no—
80C22×D59C2×D411yescharacteristic
81Q8×C59—42no—
82D4×C59—21no—
83D4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—21no—
86C2×C4×C59—42no—
87C2×C4×C59C2×D411yescharacteristic
88C2×C4×C59C2×D411yescharacteristic
89C2×C4×C59C2411yescharacteristic
90C22⋊D59—42no—
91C2×Dic59—21no—
92C2×Dic59—21no—
93C2×Dic59—22no—
94C2×Dic59C2×D411yescharacteristic
95C2×Dic59C2×D411yescharacteristic
96C2×Dic59C2×D411yescharacteristic
97C4×D59—22no—
98C4×D59—22no—
99C4×D59—21no—
100C4×D59—21no—
101C4×D59—44no—
102Dic118—21no—
103Dic118—21no—
104Dic118—44no—
105Dic118—42no—
106C8×C59—22no—
107C59⋊C8—22no—
108C22×C59—41no—
109C22×C59—41no—
110C22×C59—41no—
111C22×C59C22×D411yescharacteristic
112C2×D59—21no—
113C2×D59—21no—
114C2×D59#13712yes—
115C4×C59—21no—
116C4×C59—42no—
117C4×C59—41no—
118C4×C59AGL(1,ℤ/8)12yes—
119C4×C592−1+411yescharacteristic
120C4×C592−1+411yescharacteristic
121Dic59—21no—
122Dic59—21no—
123Dic59—21no—
124Dic59—41no—
125Dic59—42no—
126Dic59—41no—
127#3239—591nomaximal, Sylow
128C2×C59—81no—
129C2×C59#53611yescharacteristic
130C2×C59C2×AGL(1,ℤ/8)11yescharacteristic
131C2×C59C2×#13711yescharacteristic
132D59—22no—
133C2×C4⋊Q8—591no—
134#529—591no—
135#501—592no—
136#489—592no—
137#484—592no—
138#481—592no—
139#475—591no—
140#475—591no—
141#474—591no—
142#474D5911yescharacteristic, complemented
143#432—591no—
144C59#323911yescharacteristic, complemented, Sylow
145C22×Q8—1181no—
146C4⋊Q8—592no—
147C4⋊Q8—591no—
148C4⋊Q8—1181no—
149C4⋊Q8—1181no—
150C4⋊Q8C2×D5911yescharacteristic
151#126—1181no—
152#125—591no—
153#124—591no—
154#123—1181no—
155C22⋊Q8—591no—
156#121—591no—
157C4×Q8—591no—
158C4×D4—1181no—
159C4×D4C2×D5911yescharacteristic
160#117—1181no—
161C2×C4⋊C4—592no—
162C2×C4⋊C4—1181no—
163C2×C42—591no—
164#107—592no—
165#107C2×D5912yes—
166#106—592no—
167#106—592no—
168C4⋊C8—591no—
169C4⋊C8C2×D5911yescharacteristic
170#103—592no—
171#103—592no—
172#102—592no—
173#102C2×D5912yes—
174C22⋊C8—592no—
175#97—592no—
176C2×Q8—21no—
177C2×Q8—591no—
178C2×Q8—1182no—
179C2×Q8—1181no—
180C2×Q8—2364no—
181C2×D4—1181no—
182C2×D4C22×D5911yescharacteristic
183C22×C4—21no—
184C22×C4—591no—
185C22×C4—591no—
186C22×C4—591no—
187C22×C4—1182no—
188C2×C8—592no—
189C2×C8C22×D5912yes—
190C4⋊C4—21no—
191C4⋊C4—592no—
192C4⋊C4—591no—
193C4⋊C4—1182no—
194C4⋊C4—1182no—
195C4⋊C4—1181no—
196C4⋊C4—1181no—
197C4⋊C4—1181no—
198C4⋊C4—1181no—
199C4⋊C4—1181no—
200C4⋊C4C22×D5912yes—
201C4⋊C4C22×D5911yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—1181no—
204C22⋊C4—1181no—
205C22⋊C4—1181no—
206C22⋊C4—1181no—
207C42—591no—
208C42—591no—
209C42—591no—
210C42—1181no—
211C42C22×D5911yescharacteristic
212C23—21no—
213C23—591no—
214Q8—42no—
215Q8—1181no—
216Q8—1181no—
217Q8—2364no—
218Q8—2362no—
219D4—21no—
220D4—21no—
221D4—2362no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—591no—
226C2×C4—591no—
227C2×C4—591no—
228C2×C4—1182no—
229C2×C4—1182no—
230C2×C4—1181no—
231C2×C4—1181no—
232C2×C4—1181no—
233C2×C4—1181no—
234C2×C4—1182no—
235C2×C4—2364no—
236C2×C4D4×D5911yescharacteristic
237C2×C4D4×D5911yescharacteristic
238C2×C4C23×D5911yescharacteristic
239C8—22no—
240C8—1182no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—592no—
245C22—1181no—
246C22—1181no—
247C22C2×D4×D5911yescharacteristic
248C4—21no—
249C4—41no—
250C4—42no—
251C4—1181no—
252C4—1181no—
253C4—1181no—
254C4—2362no—
255C4—2361no—
256C4—2361no—
257C4#1427375112yes—
258C4#1427377411yescharacteristic
259C4#1427377511yescharacteristic
260C2—81no—
261C2—1182no—
262C2#1683797511yescharacteristic
263C2C2×#1427375111yescharacteristic
264C2#137×D5911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#474C2
socleC22×C59C22×D4
hypercenter#474D59
hypocenterC59#3239
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D59C2semidirect
3. #16837810C2semidirect
4. #16837760C2semidirect
5. #16837739C2semidirect
7. #16837688C2semidirect
8. #16837684C2semidirect
9. #16837682C2semidirect
10. #16837458C2semidirect
11. C59×#474C2semidirect
142. #474D59semidirect
144. C59#3239semidirect