Finite Group Databasebeta

← #21435236

Subgroups — #21435236

Order 7552.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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#16837957C211yesmaximal, characteristic
2C4⋊Q8×D59C211yesmaximal, characteristic
3#16837800C211yesmaximal, characteristic, complemented
4#16837798C211yesmaximal, characteristic, complemented
5#16837752C211yesmaximal, characteristic, complemented
6#16837731C214yesmaximal
7#16837685C214yesmaximal, complemented
8#16837453C211yesmaximal, characteristic
9C59×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D59—21no—
11#14273727C2211yescharacteristic
12#14273727C2211yescharacteristic
13#14273726—21no—
14#14273726C2212yes—
15#14273725—21no—
16#14273718—21no—
17#14273707—21no—
18#14273703C2212yes—
19Q8×Dic59C2212yes—
20#14273692—21no—
21#14273685—21no—
22C4⋊C4×D59—21no—
23C4⋊C4×D59C2212yes—
24C42×D59C2211yescharacteristic
25#14273659C2214yes—
26#14273658C2214yes—
27Dic59⋊C8C2212yes—
28#14273651C2214yes—
29(C2×D59)⋊C8C2212yes—
30C4×C59⋊C8C2211yescharacteristic
31C4⋊Q8×C59C2211yescharacteristic
32C4⋊Q8×C59C2211yescharacteristic
33#103×C59C2214yes—
34C4×C8×C59C2211yescharacteristic
35C2×Q8×C59—21no—
36C2×Q8×C59C2312yes—
37Q8×D59—44no—
38C2×C4×D59—22no—
39C2×C4×D59D411yescharacteristic
40C2×C4×D59D411yescharacteristic
41C2×C4×D59C2311yescharacteristic
42C2×Dic118—21no—
43C2×Dic118—21no—
44C2×Dic118—22no—
45C2×C8×C59C2312yes—
46C4⋊C4×C59—21no—
47C4⋊C4×C59—21no—
48C4⋊C4×C59—21no—
49C4⋊C4×C59C2312yes—
50C42×C59C2311yescharacteristic
51(C2×D59)⋊C4—22no—
52C4⋊Dic59—21no—
53C4⋊Dic59—21no—
54C4⋊Dic59—22no—
55C4⋊Dic59C2312yes—
56C4⋊Dic59C2312yes—
57Dic59⋊C4—22no—
58Dic59⋊C4—22no—
59Dic59⋊C4—22no—
60C4×Dic59—22no—
61C4×Dic59D411yescharacteristic
62C4×Dic59D411yescharacteristic
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2312yes—
65C22×D59C2×D411yescharacteristic
66Q8×C59—24no—
67Q8×C59—42no—
68C2×C4×C59—22no—
69C2×C4×C59—22no—
70C2×C4×C59C2×D411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2411yescharacteristic
73C2×Dic59—22no—
74C2×Dic59—22no—
75C2×Dic59C2×D411yescharacteristic
76C2×Dic59C2×D411yescharacteristic
77C2×Dic59C2×D411yescharacteristic
78C4×D59—22no—
79C4×D59—22no—
80C4×D59—44no—
81C4×D59SD1614yes—
82Dic118—42no—
83Dic118—42no—
84Dic118—44no—
85C8×C59—22no—
86C59⋊C8—22no—
87C22×C59C22×D411yescharacteristic
88C2×D59—21no—
89C2×D59—21no—
90C2×D59C2×SD1612yes—
91C4×C59—42no—
92C4×C59—42no—
93C4×C59C2×SD1612yes—
94C4×C59#13712yes—
95C4×C592−1+412yes—
96Dic59—21no—
97Dic59—21no—
98Dic59—42no—
99Dic59—42no—
100Dic59C2×SD1612yes—
101#3229—591nomaximal, Sylow
102C2×C59#53611yescharacteristic
103C2×C59C22×SD1611yescharacteristic
104C2×C59C2×#13711yescharacteristic
105D59—22no—
106#533—591no—
107C2×C4⋊Q8—591no—
108#498—591no—
109#498—591no—
110#487—591no—
111#487D5911yescharacteristic, complemented
112#483—594no—
113#475—594no—
114#431—591no—
115C59#322911yescharacteristic, complemented, Sylow
116C22×Q8—1181no—
117C4⋊Q8—592no—
118C4⋊Q8—591no—
119C4⋊Q8—591no—
120C4⋊Q8—1181no—
121C4⋊Q8—1181no—
122C4⋊Q8C2×D5911yescharacteristic
123C4⋊Q8C2×D5911yescharacteristic
124#125—1181no—
125C22⋊Q8—592no—
126C22⋊Q8—1181no—
127C4×Q8—592no—
128C4×Q8—1181no—
129#117—1181no—
130C2×C4⋊C4—592no—
131C2×C4⋊C4—1181no—
132C2×C42—591no—
133#106—594no—
134#106—594no—
135C4⋊C8—592no—
136#103—594no—
137#103C2×D5914yes—
138C22⋊C8—592no—
139C4×C8—591no—
140C4×C8C2×D5911yescharacteristic
141C2×Q8—21no—
142C2×Q8—1182no—
143C2×Q8—1181no—
144C2×Q8—1181no—
145C2×Q8—2364no—
146C2×Q8C22×D5912yes—
147C22×C4—591no—
148C22×C4—591no—
149C22×C4—591no—
150C22×C4—1182no—
151C2×C8—592no—
152C2×C8C22×D5912yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—592no—
157C4⋊C4—592no—
158C4⋊C4—1182no—
159C4⋊C4—1182no—
160C4⋊C4—1182no—
161C4⋊C4—1182no—
162C4⋊C4—1181no—
163C4⋊C4—1181no—
164C4⋊C4C22×D5912yes—
165C22⋊C4—1182no—
166C42—591no—
167C42—591no—
168C42—591no—
169C42—1182no—
170C42C22×D5911yescharacteristic
171C23—591no—
172Q8—24no—
173Q8—42no—
174Q8—2364no—
175Q8—2362no—
176Q8—2362no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—591no—
180C2×C4—594no—
181C2×C4—591no—
182C2×C4—591no—
183C2×C4—1182no—
184C2×C4—1182no—
185C2×C4—1182no—
186C2×C4—1182no—
187C2×C4—2364no—
188C2×C4D4×D5911yescharacteristic
189C2×C4D4×D5911yescharacteristic
190C2×C4C23×D5911yescharacteristic
191C8—22no—
192C8—1182no—
193C22—592no—
194C22—1181no—
195C22—1181no—
196C22C2×D4×D5911yescharacteristic
197C4—42no—
198C4—42no—
199C4—592no—
200C4—1181no—
201C4—1181no—
202C4—2362no—
203C4—2362no—
204C4SD16×D5912yes—
205C4#1427375912yes—
206C4#1427377412yes—
207C2—1182no—
208C2#1683797211yescharacteristic
209C2C2×SD16×D5911yescharacteristic
210C2C2×#1427375911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#487C2
socleC22×C59C22×D4
hypercenter#487D59
hypocenterC59#3229
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #16837800C2semidirect
4. #16837798C2semidirect
5. #16837752C2semidirect
7. #16837685C2semidirect
9. C59×#487C2semidirect
111. #487D59semidirect
115. C59#3229semidirect