Finite Group Databasebeta

← #21424323

Subgroups — #21424323

Order 7552.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#16837882C211yesmaximal, characteristic
2#16837445C211yesmaximal, characteristic, complemented
3C2×#14273655C211yesmaximal, characteristic
4#16837404C211yesmaximal, characteristic
5#16837272C211yesmaximal, characteristic, complemented
6#16837170C211yesmaximal, characteristic, complemented
7C59×#339C211yesmaximal, characteristic, complemented
8C2×#11745685C2211yescharacteristic
9C2×#11745664C2211yescharacteristic
10C4×Dic118—21no—
11C4×D236—21no—
12(C22⋊D59)⋊C4—22no—
13#14273685—21no—
14C2×C4⋊Dic59—22no—
15C2×C4⋊Dic59C2211yescharacteristic
16C2×C4⋊Dic59C2211yescharacteristic
17C4⋊C4×D59—21no—
18#14273660—21no—
19#14273658—21no—
20#14273655C414yescomplemented
21#14273652—21no—
22#14273649—21no—
23C2×M16×C59C2211yescharacteristic
24#117×C59C2211yescharacteristic
25C2×C42×C59C2211yescharacteristic
26C22×C4×C59—21no—
27C22×C4×C59C2311yescharacteristic
28C2×C22⋊D59—21no—
29C22×Dic59—21no—
30C22×Dic59D412yes—
31#11745685—21no—
32#11745685—21no—
33#11745685C2×C412yes—
34#11745685Q812yes—
35C2×D236D411yescharacteristic
36C2×C4×D59—21no—
37C2×C4×D59—22no—
38C2×Dic118D411yescharacteristic
39M16×C59—21no—
40M16×C59—21no—
41C2×C8×C59—21no—
42C4⋊C4×C59D411yescharacteristic
43C4⋊C4×C59D411yescharacteristic
44C22⋊C4×C59—21no—
45C42×C59—21no—
46C42×C59—21no—
47C42×C59C2×C412yescomplemented
48(C2×D59)⋊C4—22no—
49C4⋊Dic59—21no—
50C4⋊Dic59—21no—
51C4⋊Dic59—21no—
52C4⋊Dic59—21no—
53C4⋊Dic59—44no—
54Dic59⋊C4—22no—
55C4×Dic59—22no—
56#11745664—21no—
57#11745664C2×C412yescomplemented
58C2×C59⋊C8—21no—
59C23×C59C2×D411yescharacteristic
60C22×D59—21no—
61C2×C4×C59—22no—
62C2×C4×C59—22no—
63C2×C4×C59—22no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59C22×C411yescharacteristic
67C2×C4×C59C2×D411yescharacteristic
68C2×C4×C59C2×D411yescharacteristic
69C2×C4×C59C2×Q811yescharacteristic
70C2×C4×C59#4111yescharacteristic
71C2×C4×C59#4111yescharacteristic
72C22⋊D59—22no—
73C22⋊D59—22no—
74C2×Dic59—21no—
75C2×Dic59—22no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78C2×Dic59—41no—
79D236—21no—
80D236C4⋊C412yescomplemented
81C4×D59—22no—
82C4×D59—22no—
83C4×D59—82no—
84Dic118—21no—
85Dic118C4⋊C412yescomplemented
86C8×C59—41no—
87C59⋊C8—22no—
88C22×C59—21no—
89C22×C59—21no—
90C22×C59C4×D411yescharacteristic
91C22×C59#12011yescharacteristic
92C22×C59C22⋊Q811yescharacteristic
93C2×D59—22no—
94C2×D59—41no—
95C2×D59—41no—
96C4×C59—24no—
97C4×C59—41no—
98C4×C59—41no—
99C4×C59C2×C4⋊C411yescharacteristic
100C4×C59C4×D411yescharacteristic
101C4×C59C22⋊Q811yescharacteristic
102C4×C59#12311yescharacteristic
103Dic59—22no—
104Dic59—42no—
105Dic59—81no—
106#1859—591nomaximal, Sylow
107C2×C59—21no—
108C2×C59—21no—
109C2×C59#38511yescharacteristic
110C2×C59#45311yescharacteristic
111C2×C59#45611yescharacteristic
112D59—42no—
113#520—591no—
114#428—591no—
115C2×#104—591no—
116#417—591no—
117#384—591no—
118#343—591no—
119#339D5911yescharacteristic, complemented
120C59#185911yescharacteristic, complemented, Sylow
121C2×#41—591no—
122C2×M16—591no—
123C2×M16C2×D5911yescharacteristic
124C4×Q8—1181no—
125C4×D4—1181no—
126C4×D4—1182no—
127#117—1181no—
128#117C2×D5911yescharacteristic
129C2×C4⋊C4—591no—
130C2×C4⋊C4—591no—
131C2×C4⋊C4—1181no—
132C2×C4⋊C4—1182no—
133C2×C42C2×D5911yescharacteristic
134#107—1181no—
135#106—1181no—
136#104—594no—
137#103—1181no—
138#102—1181no—
139#41—592no—
140#41—592no—
141#41—1181no—
142#41—1181no—
143C2×Q8—591no—
144C2×D4—591no—
145C2×D4—1181no—
146C22×C4—21no—
147C22×C4—592no—
148C22×C4—1182no—
149C22×C4—1181no—
150C22×C4—1181no—
151C22×C4C22×D5911yescharacteristic
152M16—21no—
153M16—21no—
154M16—592no—
155M16—1181no—
156C2×C8—21no—
157C2×C8—1181no—
158C4⋊C4—1182no—
159C4⋊C4—1181no—
160C4⋊C4—1181no—
161C4⋊C4—1181no—
162C4⋊C4—1181no—
163C4⋊C4—2364no—
164C4⋊C4D23611yescharacteristic
165C4⋊C4D23611yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1182no—
168C42—21no—
169C42—21no—
170C42—1182no—
171C42C4×D5912yescomplemented
172C23—1181no—
173C23D4×D5911yescharacteristic
174Q8—592no—
175Q8—1181no—
176D4—592no—
177D4—1182no—
178D4—1182no—
179D4—1181no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—1181no—
186C2×C4—1182no—
187C2×C4—1182no—
188C2×C4—1182no—
189C2×C4—4722no—
190C2×C4—2362no—
191C2×C4—2361no—
192C2×C4—2362no—
193C2×C4C2×C4×D5911yescharacteristic
194C2×C4C2×D23611yescharacteristic
195C2×C4#1174568511yescharacteristic
196C2×C4D4×D5911yescharacteristic
197C2×C4#1174568711yescharacteristic
198C2×C4Q8×D5911yescharacteristic
199C8—41no—
200C8—1182no—
201C22—21no—
202C22—21no—
203C22—1182no—
204C22—2361no—
205C22—2361no—
206C22(C22⋊D59)⋊C411yescharacteristic
207C22#1427369711yescharacteristic
208C22#1427370511yescharacteristic
209C4—24no—
210C4—41no—
211C4—41no—
212C4—1182no—
213C4—4721no—
214C4—2362no—
215C4C4⋊C4×D5911yescharacteristic
216C4C4×D23611yescharacteristic
217C4#1427370711yescharacteristic
218C4#1427370911yescharacteristic
219C2—21no—
220C2—21no—
221C2—2362no—
222C2#1683727611yescharacteristic
223C2#1683757111yescharacteristic
224C2#1683758611yescharacteristic
subgroupG/H
centerC22#14273697
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59#120
hypercenter#339D59
hypocenterC59#1859
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16837445C2semidirect
5. #16837272C2semidirect
6. #16837170C2semidirect
7. C59×#339C2semidirect
20. #14273655C4semidirect
47. C42×C59C2×C4semidirect
57. #11745664C2×C4semidirect
80. D236C4⋊C4semidirect
85. Dic118C4⋊C4semidirect
119. #339D59semidirect
120. C59#1859semidirect
171. C42C4×D59semidirect