Finite Group Databasebeta

← #21422458

Subgroups — #21422458

Order 7552.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C2×#14273705C211yesmaximal, characteristic
2#16837364C211yesmaximal, characteristic
3C22⋊C8×D59C211yesmaximal, characteristic
4#16837128C211yesmaximal, characteristic, complemented
5#16837127C211yesmaximal, characteristic, complemented
6#16837127C211yesmaximal, characteristic, complemented
7C59×#324C211yesmaximal, characteristic, complemented
8C22×Dic118C411yescharacteristic
9C22×C4×D59C2211yescharacteristic
10C2×#11745659—21no—
11C2×C8×D59—21no—
12#14273705—21no—
13#14273705—21no—
14#14273705—21no—
15#14273705—21no—
16C2×Dic59⋊C4C411yescharacteristic
17C2×Dic59⋊C4C2211yescharacteristic
18C2×(C2×D59)⋊C4C411yescharacteristic
19C2×(C2×D59)⋊C4C411yescharacteristic
20C22⋊(C59⋊C8)C2211yescharacteristic
21C22⋊(C59⋊C8)C2211yescharacteristic
22(C2×D59)⋊C8—21no—
23(C2×D59)⋊C8—21no—
24C2×C4⋊C4×C59C2211yescharacteristic
25C22⋊C8×C59C2211yescharacteristic
26C22⋊C8×C59C2211yescharacteristic
27C23×D59C2×C411yescharacteristic
28C22×C4×C59C2×C411yescharacteristic
29C22×C4×C59C2×C411yescharacteristic
30C22×C4×C59C2311yescharacteristic
31C22×Dic59C2×C411yescharacteristic
32C22×Dic59C2×C411yescharacteristic
33C22×Dic59C2×C411yescharacteristic
34C2×C4×D59—42no—
35C2×C4×D59D411yescharacteristic
36C2×C4×D59D411yescharacteristic
37C2×C4×D59D411yescharacteristic
38C2×C4×D59D411yescharacteristic
39C2×Dic118—21no—
40C2×Dic118—21no—
41C2×Dic118—42no—
42C2×C8×C59—21no—
43C2×C8×C59—21no—
44C4⋊C4×C59—21no—
45C4⋊C4×C59—21no—
46(C2×D59)⋊C4—21no—
47(C2×D59)⋊C4—21no—
48(C2×D59)⋊C4—21no—
49(C2×D59)⋊C4—21no—
50Dic59⋊C4—21no—
51Dic59⋊C4—21no—
52Dic59⋊C4—21no—
53Dic59⋊C4—21no—
54C2×C59⋊C8—21no—
55C2×C59⋊C8—21no—
56#11745659—42no—
57C8×D59—42no—
58C23×C59C22×C411yescharacteristic
59C22×D59—21no—
60C22×D59—21no—
61C22×D59—22no—
62C22×D59—41no—
63C22×D59C22⋊C411yescharacteristic
64C22×D59C22⋊C411yescharacteristic
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—41no—
70C2×C4×C59—41no—
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C2×Dic59—22no—
74C2×Dic59—21no—
75C2×Dic59—21no—
76C2×Dic59—21no—
77C2×Dic59—21no—
78C2×Dic59—41no—
79C2×Dic59C22⋊C411yescharacteristic
80C2×Dic59C22⋊C411yescharacteristic
81C4×D59—22no—
82C4×D59—22no—
83C4×D59—41no—
84C4×D59—41no—
85Dic118—42no—
86Dic118—42no—
87C8×C59—41no—
88C8×C59—41no—
89C59⋊C8—41no—
90C59⋊C8—41no—
91C22×C59—21no—
92C22×C59—21no—
93C22×C59C2×C22⋊C411yescharacteristic
94C22×C59#13111yescharacteristic
95C22×C59#13111yescharacteristic
96C2×D59—21no—
97C2×D59—21no—
98C2×D59—21no—
99C2×D59—21no—
100C2×D59—21no—
101C2×D59—42no—
102C2×D59—42no—
103C2×D59#10112yes—
104C4×C59—21no—
105C4×C59—21no—
106C4×C59—41no—
107C4×C59—41no—
108Dic59—21no—
109Dic59—41no—
110Dic59—41no—
111Dic59#9912yes—
112#1472—591nomaximal, Sylow
113C2×C59—21no—
114C2×C59—21no—
115C2×C59#40811yescharacteristic
116C2×C59C2×#9911yescharacteristic
117C2×C59C2×#10111yescharacteristic
118D59—22no—
119D59—41no—
120C2×C22⋊Q8—591no—
121#407—591no—
122C2×C22⋊C8—591no—
123#324—591no—
124#324—591no—
125#324—591no—
126#324D5911yescharacteristic, complemented
127C59#147211yescharacteristic, complemented, Sylow
128C22×Q8—591no—
129C23×C4—591no—
130C2×M16—1181no—
131C22×C8—1181no—
132C22⋊Q8—1181no—
133C22⋊Q8—1181no—
134C22⋊Q8—1181no—
135C22⋊Q8—1181no—
136C2×C4⋊C4—591no—
137C2×C4⋊C4—591no—
138C2×C4⋊C4C2×D5911yescharacteristic
139C2×C22⋊C4—591no—
140C2×C22⋊C4—591no—
141C22⋊C8—591no—
142C22⋊C8—591no—
143C22⋊C8—1181no—
144C22⋊C8—1181no—
145C22⋊C8C2×D5911yescharacteristic
146C22⋊C8C2×D5911yescharacteristic
147C24—591no—
148C2×Q8—1181no—
149C2×Q8—1181no—
150C2×Q8—2362no—
151C22×C4—591no—
152C22×C4—591no—
153C22×C4—591no—
154C22×C4—591no—
155C22×C4—591no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—2362no—
159C22×C4C4×D5911yescharacteristic
160C22×C4C4×D5911yescharacteristic
161C22×C4C22×D5911yescharacteristic
162M16—2362no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—1181no—
166C2×C8—1181no—
167C2×C8—2362no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—1181no—
171C4⋊C4—1181no—
172C4⋊C4—1181no—
173C4⋊C4—1181no—
174C22⋊C4—1181no—
175C22⋊C4—1181no—
176C22⋊C4—1181no—
177C22⋊C4—1181no—
178C23—591no—
179C23—591no—
180C23—1182no—
181C23—1181no—
182C23—1181no—
183C23—2361no—
184C23C2×C4×D5911yescharacteristic
185Q8—2362no—
186Q8—2362no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—591no—
194C2×C4—591no—
195C2×C4—1182no—
196C2×C4—1182no—
197C2×C4—1182no—
198C2×C4—1181no—
199C2×C4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—2361no—
203C2×C4—2361no—
204C2×C4—2361no—
205C2×C4D4×D5911yescharacteristic
206C2×C4D4×D5911yescharacteristic
207C8—41no—
208C8—41no—
209C8—2361no—
210C8—2361no—
211C22—21no—
212C22—21no—
213C22—592no—
214C22—1181no—
215C22—1181no—
216C22—1181no—
217C22—1181no—
218C22—1181no—
219C22—2362no—
220C22—2362no—
221C22C22⋊C4×D5911yescharacteristic
222C22#1427373311yescharacteristic
223C22#1427373511yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—592no—
229C4—1181no—
230C4—2361no—
231C4—2361no—
232C2—21no—
233C2—21no—
234C2—1182no—
235C2—2361no—
236C2#1683736711yescharacteristic
237C2#99×D5911yescharacteristic
238C2#101×D5911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC23×C59C22×C4
FrattiniC22×C4C22×D59
FittingC59×#324C2
socleC22×C59C2×C22⋊C4
hypercenter#324D59
hypocenterC59#1472
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
4. #16837128C2semidirect
5. #16837127C2semidirect
6. #16837127C2semidirect
7. C59×#324C2semidirect
126. #324D59semidirect
127. C59#1472semidirect