Finite Group Databasebeta

← #21424596

Subgroups — #21424596

Order 7552.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#16838202C211yesmaximal, characteristic
2C4×#11745685C211yesmaximal, characteristic, complemented
3#16837420C211yesmaximal, characteristic, complemented
4C2×#14273655C211yesmaximal, characteristic, complemented
5#16837375C211yesmaximal, characteristic, complemented
6#16837174C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745685C2211yescharacteristic
10#14273760—21no—
11#14273760C412yescomplemented
12#14273755—21no—
13#14273755C412yescomplemented
14#14273749—22no—
15C2×#11745664C2211yescharacteristic
16C4×Dic118—21no—
17C4×D236—21no—
18C4×C22⋊D59—22no—
19#14273686C2211yescharacteristic
20#14273684—21no—
21C42×D59—21no—
22#14273655—22no—
23#14273655—21no—
24#14273655—21no—
25#14273641—22no—
26C2×M16×C59C2211yescharacteristic
27#117×C59C2211yescharacteristic
28C2×C42×C59C2211yescharacteristic
29C22×C4×C59—21no—
30C22×C4×C59C2311yescharacteristic
31C2×C22⋊D59—21no—
32C2×C22⋊D59—21no—
33#11745685—21no—
34#11745685—21no—
35#11745685—21no—
36#11745685—21no—
37#11745685—21no—
38#11745685—21no—
39#11745685C2×C412yes—
40#11745685D412yes—
41C2×D236C2×C411yescharacteristic, complemented
42C2×D236D411yescharacteristic
43C2×C4×D59—21no—
44C2×C4×D59—22no—
45C2×C4×D59—21no—
46C2×Dic118C2×C411yescharacteristic, complemented
47C2×Dic118D411yescharacteristic
48M16×C59—21no—
49M16×C59C2×C412yescomplemented
50C2×C8×C59—21no—
51C4⋊C4×C59—21no—
52C22⋊C4×C59—21no—
53C42×C59—21no—
54C42×C59—21no—
55C42×C59D411yescharacteristic
56C42×C59D411yescharacteristic
57C22⋊Dic59D412yes—
58(C2×D59)⋊C4—22no—
59C4⋊Dic59—21no—
60Dic59⋊C4—22no—
61C4×Dic59—22no—
62C4×Dic59—21no—
63#11745664—21no—
64#11745664—21no—
65C2×C59⋊C8—21no—
66Dic236—22no—
67D472—22no—
68#11745660—22no—
69#11745660—22no—
70C23×C59C2×D411yescharacteristic
71C22×D59—21no—
72C22×D59—21no—
73C2×C4×C59—21no—
74C2×C4×C59—21no—
75C2×C4×C59—42no—
76C2×C4×C59—41no—
77C2×C4×C59C22×C411yescharacteristic
78C2×C4×C59C2×D411yescharacteristic
79C2×C4×C59C2×D411yescharacteristic
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59#4111yescharacteristic
82C2×C4×C59#4111yescharacteristic
83C22⋊D59—22no—
84C22⋊D59—22no—
85C22⋊D59—41no—
86C22⋊D59—41no—
87C2×Dic59—21no—
88C2×Dic59—21no—
89C2×Dic59—22no—
90D236—21no—
91D236—21no—
92D236—21no—
93D236C22⋊C412yes—
94C4×D59—22no—
95C4×D59—22no—
96C4×D59—44no—
97C4×D59—41no—
98C4×D59—41no—
99Dic118—21no—
100Dic118—21no—
101Dic118—21no—
102Dic118C22⋊C412yes—
103C8×C59—22no—
104C59⋊C8—41no—
105C22×C59—41no—
106C22×C59C4×D411yescharacteristic
107C22×C59#12011yescharacteristic
108C22×C59#12111yescharacteristic
109C2×D59—22no—
110C2×D59—42no—
111C2×D59—41no—
112C2×D59—81no—
113C4×C59—22no—
114C4×C59—41no—
115C4×C59—81no—
116C4×C59C2×C22⋊C411yescharacteristic
117C4×C59C4×D411yescharacteristic
118C4×C59#12111yescharacteristic
119C4×C59#12311yescharacteristic
120Dic59—22no—
121Dic59—42no—
122Dic59—41no—
123#1906—591nomaximal, Sylow
124C2×C59—21no—
125C2×C59—21no—
126C2×C59—21no—
127C2×C59#38611yescharacteristic
128D59—42no—
129D59—81no—
130#575—591no—
131C4×#41—591no—
132#421—591no—
133C2×#104—591no—
134#410—591no—
135#344—591no—
136#339D5911yescharacteristic, complemented
137C59#190611yescharacteristic, complemented, Sylow
138C2×#41—591no—
139C2×#41—591no—
140#137—592no—
141#137—1181no—
142AGL(1,ℤ/8)—592no—
143AGL(1,ℤ/8)—1181no—
144#135—1182no—
145C2×M16—591no—
146C2×M16C2×D5911yescharacteristic
147C4×Q8—1181no—
148C4×D4—1181no—
149C4×D4—1182no—
150#117—591no—
151#117—1181no—
152#117C2×D5911yescharacteristic
153C2×C42—1181no—
154C2×C42C2×D5911yescharacteristic
155#104—1182no—
156#104—1181no—
157#104—1181no—
158#99—1182no—
159#41—592no—
160#41—592no—
161#41—1181no—
162#41—1181no—
163#41—1181no—
164#41—1181no—
165#41—1181no—
166#41—1181no—
167C2×Q8—591no—
168C2×Q8—591no—
169C2×D4—591no—
170C2×D4—591no—
171C2×D4—1181no—
172C2×D4—1181no—
173C22×C4—21no—
174C22×C4—1182no—
175C22×C4—1181no—
176C22×C4—1181no—
177C22×C4C22×D5911yescharacteristic
178Q16—1182no—
179SD16—1182no—
180SD16—1182no—
181D8—1182no—
182M16—21no—
183M16—1181no—
184M16—1181no—
185M16C4×D5912yescomplemented
186C2×C8—21no—
187C2×C8—1181no—
188C4⋊C4—21no—
189C4⋊C4—1182no—
190C4⋊C4—1181no—
191C22⋊C4—21no—
192C22⋊C4—592no—
193C22⋊C4—1182no—
194C42—21no—
195C42—21no—
196C42—1182no—
197C42—1181no—
198C42D23611yescharacteristic
199C42D23611yescharacteristic
200C23—1181no—
201C23—1181no—
202C23D4×D5911yescharacteristic
203Q8—592no—
204Q8—1181no—
205Q8—1181no—
206Q8—1181no—
207D4—592no—
208D4—1182no—
209D4—1182no—
210D4—1181no—
211D4—1181no—
212D4—1181no—
213D4—2361no—
214D4—2361no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—1181no—
220C2×C4—1182no—
221C2×C4—1182no—
222C2×C4—1181no—
223C2×C4—1182no—
224C2×C4—2364no—
225C2×C4—2361no—
226C2×C4—2361no—
227C2×C4C2×C4×D5911yescharacteristic
228C2×C4C2×D23611yescharacteristic
229C2×C4#1174568511yescharacteristic
230C2×C4D4×D5911yescharacteristic
231C2×C4D4×D5911yescharacteristic
232C2×C4#1174568911yescharacteristic
233C8—22no—
234C8—2361no—
235C22—41no—
236C22—1182no—
237C22—4721no—
238C22—2362no—
239C22—2361no—
240C22#1427368911yescharacteristic
241C22#1427369711yescharacteristic
242C22#1427370011yescharacteristic
243C4—22no—
244C4—41no—
245C4—81no—
246C4—1182no—
247C4—2362no—
248C4—2361no—
249C4C22⋊C4×D5911yescharacteristic
250C4C4×D23611yescharacteristic
251C4#1427370211yescharacteristic
252C4#1427371211yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—4721no—
257C2—2362no—
258C2#1683728011yescharacteristic
subgroupG/H
centerC4#14273702
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC2×C59#386
hypercenter#339D59
hypocenterC59#1906
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C4×#11745685C2semidirect
3. #16837420C2semidirect
4. C2×#14273655C2semidirect
5. #16837375C2semidirect
6. #16837174C2semidirect
7. C59×#339C2semidirect
11. #14273760C4semidirect
13. #14273755C4semidirect
41. C2×D236C2×C4semidirect
46. C2×Dic118C2×C4semidirect
49. M16×C59C2×C4semidirect
136. #339D59semidirect
137. C59#1906semidirect
185. M16C4×D59semidirect