Finite Group Databasebeta

← #21424478

Subgroups — #21424478

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#16838168C211yesmaximal, characteristic, complemented
2#16837952C211yesmaximal, characteristic
3#16837420C211yesmaximal, characteristic, complemented
4#16837418C211yesmaximal, characteristic, complemented
5#16837375C211yesmaximal, characteristic, complemented
6#16837162C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745685C2211yescharacteristic
10#14273735—22no—
11#14273733—22no—
12C2×#11745664C2211yescharacteristic
13M16×D59—22no—
14#14273727C411yescharacteristic, complemented
15#14273724C411yescharacteristic, complemented
16#14273715C411yescharacteristic, complemented
17#14273715C411yescharacteristic, complemented
18#14273701—22no—
19C4×D236—22no—
20#14273686C2211yescharacteristic
21#14273655—22no—
22#14273653—22no—
23#14273641—22no—
24C2×M16×C59C2211yescharacteristic
25#117×C59C2211yescharacteristic
26C2×C42×C59C2211yescharacteristic
27C22×C4×C59—21no—
28C22×C4×C59C2311yescharacteristic
29C2×C22⋊D59—21no—
30C2×C22⋊D59D412yes—
31#11745685—21no—
32#11745685—21no—
33#11745685—21no—
34#11745685—21no—
35#11745685—21no—
36#11745685—21no—
37#11745685—21no—
38#11745685—21no—
39C2×D236—22no—
40C2×D236C2×C411yescharacteristic
41C2×D236C2×C411yescharacteristic
42C2×C4×D59—21no—
43C2×C4×D59D412yes—
44C2×Dic118C2×C411yescharacteristic
45C2×Dic118C2×C411yescharacteristic
46M16×C59—21no—
47M16×C59D412yescomplemented
48C2×C8×C59—21no—
49C4⋊C4×C59—21no—
50C22⋊C4×C59—21no—
51C42×C59—21no—
52C42×C59—21no—
53C42×C59C2×C411yescharacteristic
54C42×C59C2×C411yescharacteristic
55C22⋊Dic59—21no—
56(C2×D59)⋊C4—22no—
57(C2×D59)⋊C4—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—21no—
60C4×Dic59—21no—
61#11745664—21no—
62#11745664D412yescomplemented
63C2×C59⋊C8—21no—
64#11745659—24no—
65C8×D59—24no—
66C23×C59C2×D411yescharacteristic
67C22×D59—21no—
68C22×D59C22⋊C412yes—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—42no—
72C2×C4×C59—41no—
73C2×C4×C59C22×C411yescharacteristic
74C2×C4×C59C2×D411yescharacteristic
75C2×C4×C59C2×D411yescharacteristic
76C2×C4×C59C2×D411yescharacteristic
77C2×C4×C59#4111yescharacteristic
78C2×C4×C59#4111yescharacteristic
79C22⋊D59—22no—
80C22⋊D59—22no—
81C22⋊D59—41no—
82C22⋊D59—41no—
83C2×Dic59—21no—
84C2×Dic59—41no—
85C2×Dic59C22⋊C412yes—
86D236—21no—
87D236—21no—
88D236—21no—
89D236—21no—
90D236—44no—
91C4×D59—22no—
92C4×D59—22no—
93C4×D59—41no—
94C4×D59—41no—
95Dic118—21no—
96Dic118—21no—
97Dic118—21no—
98Dic118—21no—
99C8×C59—22no—
100C59⋊C8—22no—
101C22×C59—41no—
102C22×C59C2×C22⋊C411yescharacteristic
103C22×C59#12111yescharacteristic
104C22×C59#12111yescharacteristic
105C2×D59—22no—
106C2×D59—42no—
107C2×D59—42no—
108C2×D59—41no—
109C4×C59—22no—
110C4×C59—41no—
111C4×C59—81no—
112C4×C59C4×D411yescharacteristic
113C4×C59C4×D411yescharacteristic
114C4×C59#12011yescharacteristic
115C4×C59#12311yescharacteristic
116Dic59—22no—
117Dic59—41no—
118Dic59—81no—
119#1884—591nomaximal, Sylow
120C2×C59—21no—
121C2×C59—21no—
122C2×C59—21no—
123C2×C59#38611yescharacteristic
124D59—42no—
125D59—81no—
126#568—591no—
127#532—591no—
128#421—591no—
129#421—591no—
130#410—591no—
131#339—591no—
132#339D5911yescharacteristic, complemented
133C59#188411yescharacteristic, complemented, Sylow
134C2×#41—591no—
135C2×#41—591no—
136#131—1182no—
137#131—1182no—
138C2×M16—591no—
139C2×M16—1182no—
140C2×M16C2×D5911yescharacteristic
141C4⋊Q8—591no—
142#127—591no—
143#124—591no—
144#124—591no—
145#121—1182no—
146C4×D4—1182no—
147#117—591no—
148#117C2×D5911yescharacteristic
149C2×C42C2×D5911yescharacteristic
150#104—1182no—
151#104—1182no—
152#99—1182no—
153#41—1181no—
154#41—1181no—
155#41—1181no—
156#41—1181no—
157#41—1181no—
158#41—1181no—
159#41—1181no—
160#41—1181no—
161C2×Q8—591no—
162C2×Q8—591no—
163C2×D4—592no—
164C2×D4—591no—
165C2×D4—591no—
166C2×D4—1182no—
167C2×D4—1181no—
168C22×C4—21no—
169C22×C4—592no—
170C22×C4—1181no—
171C22×C4C22×D5911yescharacteristic
172M16—21no—
173M16—592no—
174M16—1184no—
175M16—1181no—
176M16D23612yescomplemented
177C2×C8—21no—
178C2×C8—1184no—
179C2×C8—1181no—
180C4⋊C4—21no—
181C4⋊C4—1182no—
182C4⋊C4—1181no—
183C22⋊C4—21no—
184C22⋊C4—1182no—
185C22⋊C4—1182no—
186C22⋊C4—1181no—
187C42—21no—
188C42—21no—
189C42—1181no—
190C42C4×D5911yescharacteristic
191C42C4×D5911yescharacteristic
192C23—592no—
193C23—1181no—
194C23D4×D5911yescharacteristic
195Q8—1181no—
196Q8—1181no—
197Q8—1181no—
198Q8—1181no—
199D4—1182no—
200D4—1182no—
201D4—1181no—
202D4—1181no—
203D4—1181no—
204D4—1181no—
205D4—2364no—
206D4—2361no—
207D4—2361no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—592no—
213C2×C4—1182no—
214C2×C4—1182no—
215C2×C4—1181no—
216C2×C4—2361no—
217C2×C4—2361no—
218C2×C4—2361no—
219C2×C4C2×C4×D5911yescharacteristic
220C2×C4C2×D23611yescharacteristic
221C2×C4#1174568511yescharacteristic
222C2×C4D4×D5911yescharacteristic
223C2×C4D4×D5911yescharacteristic
224C2×C4#1174568911yescharacteristic
225C8—22no—
226C8—1182no—
227C22—41no—
228C22—1182no—
229C22—2362no—
230C22—2362no—
231C22—2361no—
232C22C22⋊C4×D5911yescharacteristic
233C22#1427370011yescharacteristic
234C22#1427370211yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—1182no—
239C4—4721no—
240C4—2361no—
241C4#1427368911yescharacteristic
242C4C4×D23611yescharacteristic
243C4#1427369711yescharacteristic
244C4#1427371211yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—4721no—
249C2—2362no—
250C2#1683728011yescharacteristic
subgroupG/H
centerC4#14273697
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC2×C59#386
hypercenter#339D59
hypocenterC59#1884
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
1. #16838168C2semidirect
3. #16837420C2semidirect
4. #16837418C2semidirect
5. #16837375C2semidirect
6. #16837162C2semidirect
7. C59×#339C2semidirect
14. #14273727C4semidirect
15. #14273724C4semidirect
16. #14273715C4semidirect
17. #14273715C4semidirect
47. M16×C59D4semidirect
62. #11745664D4semidirect
132. #339D59semidirect
133. C59#1884semidirect
176. M16D236semidirect