Finite Group Databasebeta

← #21425038

Subgroups — #21425038

Order 7552.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#16837955C211yesmaximal, characteristic
2M16×Dic59C211yesmaximal, characteristic
3C4×Dic59⋊C4C211yesmaximal, characteristic
4#16837163C211yesmaximal, characteristic
5#16837162C211yesmaximal, characteristic
6#16837161C211yesmaximal, characteristic
7C59×#339C211yesmaximal, characteristic
8C2×#11745664C2211yescharacteristic
9#14273726C411yescharacteristic, complemented
10#14273726C411yescharacteristic, complemented
11#14273718C411yescharacteristic, complemented
12#14273718C411yescharacteristic, complemented
13#14273704—21no—
14#14273704—21no—
15C4×Dic118—21no—
16C4×Dic118—21no—
17#14273686C2211yescharacteristic
18C2×Dic59⋊C4—21no—
19C2×C4×Dic59C2211yescharacteristic
20C2×C4×Dic59C2211yescharacteristic
21#14273637—21no—
22C8×Dic59—21no—
23C59⋊#95—21no—
24C2×M16×C59C2211yescharacteristic
25#117×C59C2211yescharacteristic
26C2×C42×C59C2211yescharacteristic
27C22×C4×C59—21no—
28C22×C4×C59C2311yescharacteristic
29C22×Dic59—21no—
30C22×Dic59D411yescharacteristic
31C22×Dic59D411yescharacteristic
32C2×Dic118—21no—
33C2×Dic118—21no—
34M16×C59—21no—
35M16×C59Q812yescomplemented
36C2×C8×C59—21no—
37C4⋊C4×C59C2×C411yescharacteristic
38C4⋊C4×C59C2×C411yescharacteristic
39C22⋊C4×C59—21no—
40C42×C59—21no—
41C42×C59—21no—
42C42×C59—21no—
43C22⋊Dic59—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59C2×C411yescharacteristic
47C4⋊Dic59C2×C411yescharacteristic
48Dic59⋊C4—24no—
49Dic59⋊C4—21no—
50Dic59⋊C4—21no—
51Dic59⋊C4—21no—
52Dic59⋊C4—21no—
53C4×Dic59—21no—
54C4×Dic59—21no—
55C4×Dic59—21no—
56C4×Dic59C2×C411yescharacteristic
57C4×Dic59C2×C411yescharacteristic
58C4×Dic59D411yescharacteristic
59C4×Dic59D411yescharacteristic
60#11745664—21no—
61#11745664Q812yescomplemented
62C2×C59⋊C8—21no—
63C23×C59C2×D411yescharacteristic
64C2×C4×C59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—41no—
68C2×C4×C59—41no—
69C2×C4×C59C22×C411yescharacteristic
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×Q811yescharacteristic
72C2×C4×C59C2×Q811yescharacteristic
73C2×C4×C59#4111yescharacteristic
74C2×C4×C59#4111yescharacteristic
75C2×Dic59—22no—
76C2×Dic59—22no—
77C2×Dic59—21no—
78C2×Dic59—21no—
79C2×Dic59—41no—
80C2×Dic59—41no—
81C2×Dic59—41no—
82C2×Dic59C22⋊C411yescharacteristic
83C2×Dic59C22⋊C411yescharacteristic
84C2×Dic59C22⋊C411yescharacteristic
85C2×Dic59C22⋊C411yescharacteristic
86Dic118—42no—
87Dic118—42no—
88C8×C59—22no—
89C59⋊C8—22no—
90C22×C59—21no—
91C22×C59—21no—
92C22×C59C2×C22⋊C411yescharacteristic
93C22×C59#12411yescharacteristic
94C22×C59C4⋊Q811yescharacteristic
95C4×C59—42no—
96C4×C59—41no—
97C4×C59—41no—
98C4×C59C4×Q811yescharacteristic
99C4×C59C4×Q811yescharacteristic
100C4×C59C22⋊Q811yescharacteristic
101C4×C59C22⋊Q811yescharacteristic
102Dic59—21no—
103Dic59—21no—
104Dic59—21no—
105Dic59—42no—
106Dic59—41no—
107Dic59—41no—
108Dic59#10412yes—
109#1986—591nomaximal, Sylow
110C2×C59—21no—
111C2×C59—21no—
112C2×C59#39111yescharacteristic
113C2×C59C2×#10411yescharacteristic
114C2×C59#42111yescharacteristic
115#533—591no—
116C4×M16—591no—
117C4×C4⋊C4—591no—
118#339—591no—
119#339—591no—
120#339—591no—
121#339D5911yescharacteristic
122C59#198611yescharacteristic, complemented, Sylow
123C2×M16—591no—
124C2×M16C2×D5911yescharacteristic
125C4⋊Q8—591no—
126C4⋊Q8—591no—
127#125—591no—
128#125—591no—
129C22⋊Q8—1181no—
130C22⋊Q8—1181no—
131C4×Q8—1181no—
132C4×Q8—1181no—
133#117—591no—
134#117C2×D5911yescharacteristic
135C2×C4⋊C4—1181no—
136C2×C42—591no—
137C2×C42—591no—
138C2×C42C2×D5911yescharacteristic
139#97—1181no—
140C4×C8—1181no—
141#95—1181no—
142C2×Q8—1181no—
143C2×Q8—1181no—
144C22×C4—21no—
145C22×C4—591no—
146C22×C4—591no—
147C22×C4—1181no—
148C22×C4C22×D5911yescharacteristic
149M16—21no—
150M16—592no—
151M16—1181no—
152M16Dic11812yescomplemented
153C2×C8—21no—
154C2×C8—1181no—
155C4⋊C4—591no—
156C4⋊C4—591no—
157C4⋊C4—1181no—
158C4⋊C4—1181no—
159C4⋊C4—1181no—
160C4⋊C4—1181no—
161C4⋊C4—1181no—
162C4⋊C4—1181no—
163C4⋊C4—1184no—
164C4⋊C4C4×D5911yescharacteristic
165C4⋊C4C4×D5911yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1181no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—591no—
172C42—591no—
173C42—591no—
174C42—591no—
175C42—1181no—
176C42—1181no—
177C42—1181no—
178C23D4×D5911yescharacteristic
179Q8—2362no—
180Q8—2362no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—591no—
187C2×C4—591no—
188C2×C4—591no—
189C2×C4—591no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—1181no—
193C2×C4—1181no—
194C2×C4—2361no—
195C2×C4—2361no—
196C2×C4—2361no—
197C2×C4C2×Dic11811yescharacteristic
198C2×C4C2×C4×D5911yescharacteristic
199C2×C4#1174568511yescharacteristic
200C2×C4D4×D5911yescharacteristic
201C2×C4#1174568711yescharacteristic
202C2×C4Q8×D5911yescharacteristic
203C8—22no—
204C8—1182no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D5911yescharacteristic
208C22#1427371311yescharacteristic
209C22#1427372611yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—592no—
214C4—1181no—
215C4—1181no—
216C4—1181no—
217C4—2362no—
218C4—2361no—
219C4—2361no—
220C4#1427369211yescharacteristic
221C4C4×Dic11811yescharacteristic
222C4#1427370411yescharacteristic
223C4#1427370511yescharacteristic
224C2—21no—
225C2—21no—
226C2#1683730611yescharacteristic
227C2#104×D5911yescharacteristic
228C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#339C2
socleC22×C59C2×C22⋊C4
hypercenter#339D59
hypocenterC59#1986
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14273726C4semidirect
10. #14273726C4semidirect
11. #14273718C4semidirect
12. #14273718C4semidirect
35. M16×C59Q8semidirect
61. #11745664Q8semidirect
122. C59#1986semidirect
152. M16Dic118semidirect